a) The power series representation of f(x) = 1/5 + x f(x) centered at x = 0 is f(x) = sigma^infinity_n = 0 ((x/5)^n)
b) The interval of convergence is (-5, 5)
To find the power series representation of f(x), we can use the formula for the geometric series
1 / (1 - r) = sigma^infinity_n = 0 (r^n)
where r is a constant.
In this case, we have
f(x) = 1/5 + x f(x)
We can solve for f(x) to get
f(x) = 1/5 / (1 - x)
Using the formula for the geometric series with r = x/5, we have
f(x) = sigma^infinity_n = 0 ((x/5)^n)
Multiplying both sides by 5, we get
5f(x) = sigma^infinity_n = 0 (x^n
So the power series representation of f(x) centered at x = 0 is
f(x) = sigma^infinity_n = 0 ((x/5)^n)
To determine the interval of convergence, we can use the ratio test
| (x/5)^(n+1) | / | (x/5)^n | = |x/5|
The series converges if the limit of |x/5| as n approaches infinity is less than 1. This is true when |x| < 5, so the interval of convergence is (-5, 5).
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Write the equation of the circle with its center at (8, 2)
that passes through (17, 14)
in standard form
The equation of the circle with center at (8, 2) that passes through (17, 14) in standard form is (x - 8)² + (y - 2)² = 225
In your problem, we are given that the center of the circle is located at (8, 2) and that the circle passes through the point (17, 14). To find the equation of this circle, we need to use the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius of the circle.
To find the radius of the circle, we can use the distance formula between the center of the circle and the point on the circle that is given to us. The distance formula is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) is the center of the circle and (x₂, y₂) is the point on the circle that is given to us.
Plugging in the values we have, we get:
d = √((17 - 8)² + (14 - 2)²) = √(81 + 144) = √(225) = 15
So the radius of the circle is 15.
Now we can plug in the values we have into the standard form of the equation of a circle:
(x - 8)² + (y - 2)² = 15²
which simplifies to:
(x - 8)² + (y - 2)² = 225
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suppose that a 17 ft ladder is sliding down a wall at a rate of 6 ft/sec. at what rate is the bottom of the ladder moving when the top is 8 ft from the ground?
The bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground
The bottom of the ladder is moving at a rate of 6 ft/sec when the top is 8 ft from the ground. This can be found by using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet (from the top of the ladder to the ground) and the time is 1/6 seconds (since the ladder is sliding down at a rate of 6 ft/sec). Therefore, the velocity of the bottom of the ladder when the top is 8 ft from the ground is 8/1/6 = 8/6 = 4/3 = 1.333 ft/sec.
To understand this concept more clearly, imagine a ball rolling along the ground. Its velocity is constant until it hits a slope and begins to move down the slope. At this point, its velocity increases as it moves further down the slope, and its velocity is higher when it is further down the slope.
This is the same concept as the ladder sliding down the wall; the bottom of the ladder is moving faster than the top, so the velocity of the bottom of the ladder increases as the top of the ladder gets closer to the ground.
In conclusion, the bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground. This can be found using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet and the time is 1/6 seconds since the ladder is sliding down at a rate of 6 ft/sec.
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you roll two 6-sided dice. what is the probability of either die rolling the value 3 or both dice rolling even values?
The probability of either die rolling the value 3 or both dice rolling even values is 5/9.
The probability of rolling a 3 on a single die is 1/6, so the probability of either die rolling a 3 is 2/6 or 1/3 (since there are two dice).
The probability of rolling an even number on a single die is 1/2 (since there are three even numbers and three odd numbers on a 6-sided die). The probability of rolling even values on both dice is the product of the probability of each die rolling an even value, which is (1/2) x (1/2) = 1/4.
To find the probability of either die rolling a 3 or both dice rolling even values, we need to subtract the probability of rolling both a 3 and an even value (since we would be double-counting this case). The only way to roll both a 3 and an even value is to roll two 6's, so the probability of this happening is 1/36.
Therefore, the probability of either die rolling 3 or both dice rolling even values is:
P(either die rolling 3 or both dice rolling even) = P(die 1 = 3 or die 2 = 3 or both dice even) - P(both dice = 6)
= (1/3 + 1/3) + (1/4 - 1/36)
= 5/9
Hence, the probability is 5/9.
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What are the steps to express 0.15 as a fraction in simplest form ? Order the following from 1-5
Answer:
0.15 expressed as a fraction in its simplest form is 3/20.
Step-by-step explanation:
To express a terminating decimal as a fraction:
Step 1Write the decimal as a fraction by dividing it by 1:
[tex]\boxed{\dfrac{0.15}{1}}[/tex]
Step 2Multiply the numerator and denominator by 10 for every number after the decimal point.
As there are two numbers after the decimal point, multiply the numerator and denominator by 100:
[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]
Step 3Find the highest common factor (HCF) of the numerator and denominator.
Factors of 15: 1, 3, 5 and 15.Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.Therefore, the HCF of 15 and 100 is 5.
Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:
[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]
Conclusion0.15 expressed as a fraction in its simplest form is 3/20.
Answer:
See below, please.
Step-by-step explanation:
Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.So the order would be:Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.if ratios x:y=3:4 and y:z=1:4
find x:y:z
Using the idea of comparable ratio, we may determine x:y:z to be 3:16:1, given as x:y=3:4 and y:z=1:4.
A ratio is what?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation wherein two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
Given that y is present in both ratios, we may begin by determining its value:
y = (4/1) * (y/z), multiplied by 4, which is the reciprocal of 1/4.
y = 4(y/z)
y/z = 1/4
z/y = 4/1
We can now find x by using the value of y:
x/y = 3/4 (given)
x = (3/4) * y x = (3/4) * 4(z/y) (simultaneously inserting y/z)
x = 3z
As a result, x:y:z = 3z: 4 is the ratio of x:y:z.
y : z\s= 3 : 4(4) : 1\s= 3 : 16 : 1
So, x:y:z = 3:16:1 is the solution.
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Solve for z.
d³ = −27
ANSWER FAST PLEASE
Answer:
d=-3
Step-by-step explanation:
d^3=-27
d=[tex]\sqrt[3]{-27} \\[/tex]
d=-3
Answer:
d=-3
Step-by-step explanation:
You must that 3rd root of -27, which is -3
SOMEONE PLS HELP MY LITTLE SISTER ON THIS QUESTION
Answer: 56448² ft
Step-by-step explanation:
7 x 4 x 18 x 4 x 7 x 4 = 56448 and square it to get 56448² and then add the unit to get 56448 ft² :)
The circumference of circle A is 21.99 cm. The circumference of circle B is 51.52 cm. What is the difference between the lengths of the radii to the nearest hundredth? Show all your work and circle your answer.
The difference between the lengths of the radii is approximately 4.70 cm.
What is circle ?
A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are at a given distance (called the radius) from a given point (called the center). It can also be defined as the locus of all points that are equidistant from a given point. A circle is a closed curve and its circumference is the distance around the circle.
We know that the formula for the circumference of a circle is:
C = 2πr
Where C is the circumference and r is the radius.
For circle A, we have:
21.99 = 2πr
Dividing both sides by 2π, we get:
r = 3.5
For circle B, we have:
51.52 = 2πr
Dividing both sides by 2π, we get:
r = 8.2
The difference between the radii is:
8.2 - 3.5 = 4.7
Rounding to the nearest hundredth, we get:
4.7 ≈ 4.70
Therefore, the difference between the lengths of the radii is approximately 4.70 cm.
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what happens to the variability of the sampling distribution of the mean as the number of observations units increases?
Larger sample sizes typically result in more precise population mean estimates with lower sampling variability. Thus, when calculating population metrics like the mean, it is frequently preferable to utilize larger sample numbers.
The variability of the sampling distribution of the mean reduces with an increase in the number of observation units. The central limit theorem refers to this.
According to the central limit theorem, the sampling distribution of the mean gets more normal as the sample size grows, and its standard deviation (i.e., the standard error of the mean) drops. Particularly, the square root of the sample size has an inverse relationship with the standard error of the mean.
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A farmer is selling watermelons. She has 43 watermelons and plans to sell them for $3 each. The farmer’s total sales, in dollars, is a function of the number of watermelons she sells. Select all the statements that correctly describe the domain or range of this function.
Responses
The domain is the set of all integers from 0 to 43.
The domain is the set of all real numbers from 0 to 43.
The range is the set of all integers between 0 and 129.
The range is the set of all multiples of 3 from 0 to 129.
all that apply
The range is the set of all multiples of 43 from 43 to 129.
Answer:
In summary, the correct statements are:
The domain is the set of all integers from 0 to 43.
The range is the set of all multiples of 3 from 0 to 129.
this is the best i could do, make what you want of it, good luck
Step-by-step explanation:
he domain of this function is the set of all possible inputs, which in this case is the number of watermelons the farmer can sell. Since the farmer has 43 watermelons and cannot sell a fraction of a watermelon, the domain is the set of all integers from 0 to 43. So, the first statement is correct.
The second statement is incorrect because the farmer cannot sell a fraction of a watermelon, so the domain cannot include all real numbers from 0 to 43.
The range of this function is the set of all possible outputs, which in this case is the total sales in dollars. Since the farmer sells each watermelon for $3, her total sales will be a multiple of 3. The minimum sales value is $0 (if she sells no watermelons) and the maximum sales value is $129 (if she sells all 43 watermelons). So, the range is the set of all multiples of 3 from 0 to 129. Therefore, the fourth statement is correct.
The third statement is incorrect because not all integers between 0 and 129 are possible values for the farmer’s total sales. For example, she cannot make $2 in sales because her sales will always be a multiple of 3.
The fifth statement is incorrect because it implies that the farmer can only make sales in multiples of 43, which is not true since she sells each watermelon for $3.
In summary, the correct statements are:
The domain is the set of all integers from 0 to 43.
The range is the set of all multiples of 3 from 0 to 129.
A truck whose bad is 2.5 m long 1.5 m wide and 1 m high is delivering sand for a sand sculpture competition about how many trips must the truck make to deliver 7 m3 of the sand
The truck must make 2 trips tο deIiver 7 m³ οf sand.
What is VοIume?VοIume is the amοunt οf space οccupied by an οbject οr substance. It is typicaIIy measured in cubic units such as cubic meters, cubic centimetres, οr cubic feet.
Tο caIcuIate the number οf trips the truck must make tο deIiver 7 m³ οf sand, we need tο determine hοw much sand the truck can carry per trip.
The vοIume οf the truck bed can be caIcuIated as fοIIοws:
VοIume οf the truck bed = Iength x width x height
= 2.5 m x 1.5 m x 1 m
= 3.75 m3
Therefοre, the truck can carry 3.75 m³ οf sand per trip.
Tο deIiver 7 m³ οf sand, we divide the tοtaI amοunt οf sand by the amοunt οf sand the truck can carry per trip:
Number οf trips = tοtaI amοunt οf sand / amοunt οf sand per trip
= 7 m³ / 3.75 m³ per trip
= 1.87
Since we cannοt make a partiaI trip, we must rοund up tο the nearest whοIe number.
Therefοre, the truck must make 2 trips tο deIiver 7 m³ οf sand.
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You have$ 11.50 and you need ti make copies of a flyer at a store that changes $0.30 per copy
Answer:
56
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
the answer is 56
please i need help, i’ve wasted like six papers trying to get this one right
Answer:5
Step-by-step explanation:
angle h and k are equal (because alternate exterior angles are equal)
2x+7=5x-8
8+7=5x-2x
15=3x
15/3=x
5=x
h=2x+7=2*5+7=17degrees
which shape has at least one circular face and no vertices
Answer:
cylinder
Step-by-step explanation:
A cylinder has 2 circular faces and no vertices.
how many ways can a person toss a coin 15 15 times so that the number of tails is between 4 4 and 11 11 inclusive?
The number of ways a person can toss a coin 15 times so that the number of tails is between 4 and 11 inclusive is the product of the total number of ways and the sum of probabilities for k=4 to k=11 inclusive.
Binomial distribution refers to the issue of tossing a coin 15 times and getting a specific amount of tails. The following gives the binomial distribution formula:
[tex]P(X=k) = C(n,k) (n,k) * p^k * (1-p)^(n-k) (n-k)[/tex]
Where P(X=k) denotes the likelihood that there will be k tails in n tosses, p is the likelihood that there will be one tail in a single toss, and C(n,k) denotes the number of combinations of n objects that will be picked up k at a time.
The total of probability for k=4 to k=11 inclusive must be calculated in order to find the solution. This is,
P (4), P (5), P (6), P (7), P (8), P (9), P (10) and P (11)
We can figure out and add up each of these probability using the technique above. As an alternative, we can compute the probabilities using a statistical software programme or a binomial probability table.
A person can flip a coin 15 times in a total of 32,768 different ways. By calculating the total number of ways by the sum of probabilities for k=4 to k=11 inclusive, one may get the number of ways that the number of tails is between 4 and 11 inclusive.
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answer question please but DO NOT ROUND IT . 1 / 3*5 + 2
[tex]=\frac{1}{15} +2\\[/tex]
⇒We can only add the numbers if they have the same denominator, to do so we can first convert 2 into a fraction
[tex]=\frac{1}{15} +\frac{2(15)}{1(15)} \\=\frac{1}{15} +\frac{30}{15} \\=\frac{31}{15} \\[/tex]
GUYS PLEASE HELP
* I’LL GIVE YOU BRAINLIEST
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
what is polynomial ?When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.
given
A = πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):
A₁ = π(4a-6)²
If we condense this phrase, we get:
A₁ = π(16a² - 48a + 36)
A₂ = π(4a-6)²
A₂ = π(16a² - 48a + 36)
A₃ = π(4a-6)²
A₃ = π(16a² - 48a + 36)
A₄ = π(4a-6)²
A₄ = π(16a² - 48a + 36)
We can add up the areas of each of the four circles to determine their combined area:
A1 + A2 + A3 + A4 Equals A total
A total is equal to π (16a2 - 48a + 36) + π(16a2 - 48a + 36) + π(16a2 - 48a + 36).
π(64a2 - 192a + 144) = A total
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
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five girls and five boys randomly sit in ten seats that are equally spaced around a circle. the probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is , where and are relatively prime positive integers. find .
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.
There are
[tex]{10\choose5}[/tex] =252
ways to seat the five girls and five boys.
There are 5 ways to choose a diameter of the circle.
Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).
There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.
Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.
Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.
Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]
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Two important properties of eigenvalues Recall that trace of a square matrix is the sum of the entries in main diagonal Let [ 1 -1 1] C = [-1 2 0] [ 0 -1 2] and [ 1 2 1] A = [ 6 -1 0]
[-1 -2 -1] Enter A and C in MATLAB Find trace of C and A by typing : trace(A) and trace(C) Find eigenvalues of A and C Explain Do you any relation between eigenvalues and trace of of a see matrix? Find det (A) and det(C) Explain Do you see any relation between eigenvalues and determinant of a matrix?
The product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.
To enter matrices A and C in MATLAB, we can use the following commands:
A = [6, -1, 0; -1, -2, -1; 0, -1, 2];
C = [1, -1, 1; -1, 2, 0; 0, -1, 2];
To find the trace of A and C, we can use the following commands:
trace_A = trace(A);
trace_C = trace(C);
The trace of matrix A is 6 - 2 + 2 = 6, and the trace of matrix C is 1 + 2 + 2 = 5.
To find the eigenvalues of A and C, we can use the eig() function in MATLAB:
[eig_vec_A, eig_val_A] = eig(A);
[eig_vec_C, eig_val_C] = eig(C);
The eigenvalues of matrix A are -1, 1, and 6, and the eigenvalues of matrix C are 1, 1, and 2.
There is a relationship between the trace of a square matrix and its eigenvalues. Specifically, the sum of the eigenvalues is equal to the trace of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then trace(A) = λ1 + λ2 + ... + λn. This relationship holds true for both matrices A and C.
To find the determinant of A and C, we can use the following commands:
det_A = det(A);
det_C = det(C);
The determinant of matrix A is 12, and the determinant of matrix C is 5.
There is also a relationship between the eigenvalues and the determinant of a square matrix. Specifically, the product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.
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the dimensions of the hole are 4-1/4 inches in diameter and at least 4-1/2 inches deep. group of answer choices true false
Answer:
True
Step-by-step explanation:
I did it
Triangle ABC is graphed.
Answer: 2+2
Step-by-step explanation: easy thanks :)
What is the solution to the equation 2y+4=12?
Answer:
y=4
Step-by-step explanation:
2y+4=12
2y=8
y=4
answer: y=4
Answer:
y=4
Step-by-step explanation:
2y+4=12
2y=8
y=4
how many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die.
The number of distinct sequences of letters is 8 × 26⁷.
How many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die?
We have to find the number of distinct sequences of letters that can be made. Here, the word 'die' can occur in any position of the ten-letter sequence. Therefore, we have to find the number of distinct sequences of seven letters that can be formed, which are not related to the word 'die'. The number of distinct sequences of seven letters that can be formed with no restrictions is:
26 × 26 × 26 × 26 × 26 × 26 × 26 = 26⁷
The word 'die' has three letters, and it can be placed in any of the eight positions of the seven-letter sequence (that is not related to the word 'die'). We have a total of 8 possibilities to choose where to put the word 'die'.Thus, the number of distinct sequences of letters is:
8 × 26⁷ (or) 703, 483, 260, 800.
The number of distinct sequences of letters is 8 × 26⁷.
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Yeidalis needs three pieces of wood as shown to create a new work of art. The pieces of wood she is going to use are sold in 15-inch-wide boards. What is the minimum length board that Yeidalis must buy in order to have enough to complete her artwork?
The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length
How to determine the minimum length board that Yeidalis must buy in order to have enough to complete her artworkBased on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.
The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.
Using the Pythagorean theorem, we can calculate the length of this diagonal as:
sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches
So Yeidalis needs a board that is at least 15 inches long to create her artwork.
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a random variable x is uniformly distributed between 45 and 150. what is the probability of xbegin mathsize 12px style less or equal than end style60?
The probability of x being exactly 48 when it is uniformly distributed between 45 and 150 is 1/105
Since x is uniformly distributed between 45 and 150, the probability of x taking any particular value in this range is the same. Let this probability be denoted by P(x).
To find P(x = 48), we need to first check if 48 lies within the range of values that x can take. In this case, 48 lies within the range of 45 and 150, so it is a possible value for x.
Since the distribution is uniform, the probability of x taking any particular value between 45 and 150 is given by
P(x) = 1 / (150 - 45) = 1 / 105
Therefore, the probability of x being exactly 48 is
P(x = 48) = 1 / 105
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The given question is incomplete, the complete question is:
A random variable x is uniformly distributed between 45 and 150. what is the probability of x = 48?
The volume of a cube is V = s³, where s is the length of one edge of the cube.
What is the edge length s for each cube?
Drag the answer into the box to match each description.
Answer: s = ∛125 in^3
Step-by-step explanation:
To find the edge length "s" of a cube with volume "V", we use the formula:
s = ∛V
For a cube with a volume of 125 cubic inches, we can find the edge length as:
s = ∛125
s = 5
So the edge length of a cube with a volume of 125 cubic inches is 5 inches.
Can you answer this please with workings out
Answer:
a) 640 ml
b) 40 ml
Step-by-step explanation:
The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be
[tex]\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}[/tex]
[tex]\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}[/tex]
Part a)
For all 400 ml of lime juice we would need
[tex]\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml[/tex]
Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade
= 400 + 240
= 640 ml
This is the answer to Part a)
Part b)
If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml
That means the amount of lemonade left over = 280 - 240 = 40 ml
Simplify. 2x + 6x^2 - 10 + 4x^2 - 3X + (-6) =
Answer:
[tex]\boxed{\mathtt{10x^{2}-x-16}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to simplify the given expression.}[/tex]
[tex]\textsf{Consider noting that this expression has like terms, meaning we can combine them.}[/tex]
[tex]\large\underline{\textsf{What are Like Terms?}}[/tex]
[tex]\textsf{Like terms are 2 or more terms that share similarity. They aren't different in a major way.}[/tex]
[tex]\textsf{Like terms are terms with the same type of number, variable, and or exponent.}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]
[tex]\mathtt{2x+6x^{2}-10+4x^{2}-3x-6}[/tex]
[tex]\boxed{\mathtt{10x^{2}-x-16}}[/tex]
tara plans to rent a car for the weekend. the cost to rent the car is $45 plus $0.15 for each mile she drives. write a function for the total cost of the rental. how much is the rental if she travels 500 miles?
The function for the total cost of renting a car for a weekend with a base cost of $45 and a mileage charge of $0.15 per mile can be written as:
Total Cost = 45 + 0.15 * miles driven
where "miles driven" is the number of miles the car is driven over the rental period.
To find out how much it would cost Tara to rent the car if she travels 500 miles, we can substitute "500" for "miles driven" in the function:
Total Cost = 45 + 0.15 * 500
Total Cost = 45 + 75
Total Cost = $120
Therefore, if Tara drives 500 miles over the rental period, the total cost of renting the car for the weekend would be $120.
Hence, the total cost of renting a car for a weekend with a base cost of $45 and a mileage charge of $0.15 per mile can be calculated using the function Total Cost = 45 + 0.15 * miles driven. To find the total cost for a specific number of miles driven, we can substitute that number for "miles driven" in the function.
In this case, if Tara drives 500 miles, the total cost of renting the car would be $120.
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Sarah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $54 for parts. The total was $585.25. Write and solve an equation which can be used to determine
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x, the cost of the labor per hour.
Sarah was charged $54 for parts after the store's technician worked on the computer for 4.25 hours. The cost came to $585.25. The value of x is $125.
Let's use the variable x to represent the cost of the labor per hour.
The technician worked on the computer for 4.25 hours, so the cost of the labor would be:
4.25x
The technician also charged Sarah $54 for parts. So the total cost of the repair is:
4.25x + 54
We know that the total cost of the repair was $585.25. Therefore, we can write the following equation:
4.25x + 54 = 585.25
To solve for x, we need to isolate the variable on one side of the equation. First, we can subtract 54 from both sides:
4.25x = 531.25
Next, we can divide both sides by 4.25:
x = 125
Therefore, the cost of the labor per hour is $125.
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