Answer:
Half of 40 is 20(new radius)
20^2 = 400
400 x 3.14 = 1256 meters^2
Formula of area of a circle:
πr2
pi(3.14 or 22/7 whatever they tell you to use for pi) x radius(half of your diameter or your given radius) being squared(^2 to the power of 2)
What is the relation between direction cosines of a vector?
The direction cosines of a vector are the cosines of the angles between the vector and the three mutually perpendicular axes of a coordinate system.
The direction cosines of a vector [tex]$\mathbf{a}$[/tex] are denoted by l, m and n. Mathematically, the relation between these direction cosines is given by:
[tex]$$\mathbf{a}=l\mathbf{\hat{i}}+m\mathbf{\hat{j}}+n\mathbf{\hat{k}}$$[/tex]
where i,j and k are unit vectors along the three axes of the coordinate system.
To calculate the direction cosines of a given vector [tex]$\mathbf{a}$[/tex] with components [tex]$a_x$, $a_y$ and $a_z$[/tex], we can use the following formula:
[tex]$$l = \frac{a_x}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
[tex]$$m = \frac{a_y}{\sqrt{a_x^2+a_y^2+a_z^2}}$$ \\ $$n = \frac{a_z}{\sqrt{a_x^2+a_y^2+a_z^2}}$$[/tex]
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6. Which inequality is shown in the graph? Why? Show or explain.
A. Y S x + 2
B. ys x+1
C. y > 2x + 1
D. y < 2x + 1
What is the nature of the roots of the quadratic equation 5x^2 4x 1?
The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
5x² = 4x - 1
transform it into the standard form:
5x² - 4x + 1 = 0
Calculate the discriminant:
D = (-4)² - 4 (5)(1)
= 16 - 20 = -4
Since D < 0, the roots are imaginary.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation 5x² = 4x - 1?
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There are 3 people in Lee's family
The range of their shoe sizes is 3
2 people in the family wear shoe size 6
Lee's shoe size is not 6 and it is not 3
What is Lee's shoe size
Answer:
9
Step-by-step explanation:
the range is the difference between the lowest and the highest number on the series
here the range is 3 two members have size 6 different from 6 and 3 which range its 3
You accumulated a balance of $2,300 on your credit card that carries an interest rate of 17%. You can't afford to pay the $2,300 all at once, but you can pay the minimum payment, which is 2% per month or $25, whichever is greater. What is the balance on your card after 5 years?
Answer:
$1,591.67
Step-by-step explanation:
The computation of the balance after 5 years is shown below:
Given that
Accumulated Balance on Credit Card = P = $2,300
r = Monthly interest amount = 17% ÷ 12 = 1.41666667%
M = Minimum payment = 2%
Now
Balance on Credit Card after t year = P × (1+r) ×(1-M)
= $2,300 × (1+1.41666667%)^t × (1 - 2%)^t
= $2,300 × (0.993883337)^t
SO,
Balance on Credit Card after 5 years is
= $2,300 × (0.993883337)^60
= $2,300 × 0.692029437
= $1,591.66771
= $1,591.67
Find the horizontal distance x the escalator covers to the nearest tenth of a foot.
Given:
Length of escalator = 26 ft
Angle of depression = 41 degrees
To find:
The horizontal distance x the escalator covers to the nearest tenth of a foot.
Solution:
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
Using this formula for the given triangle, we get
[tex]\cos 41^\circ=\dfrac{x}{26}[/tex]
[tex]26\cos 41^\circ=x[/tex]
[tex]26(0.7547)=x[/tex]
[tex]19.6222=x[/tex]
Round the value to the nearest tenth.
[tex]x\approx 19.6[/tex]
Therefore, the escalator covers 19.6 ft horizontally.
A small business makes bottles of
temonade. Today, they have 528 ounces
of lemonade to bottle. Each bottle holds
24 ounces of lemonade. They sell each
bottle for $2.
Write two equations with variables that
can be used to find how many dollars
the business will receive by selling all of
the bottles.
The amount of money that the business will receipt is $44.
given:
Small business makes bottles of lemonade today they have 528 oz of lemonade to the bottle each bottle holds 24 oz of lemonade they sell each bottle for $2 how much money will the business receipt
From the above question:
24oz of Lemonade = 1 bottle
528 oz of Lemonade = x
Cross Multiply
24 × x = 528
x = 528/24
x = 22 bottles
We are told that: they sell each bottle for $2
Hence:
1 bottle = $2
22 bottles = y
Cross Multiply
y = 22 × $2
y = $44
Therefore, the amount of money that the business will receipt = $44
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I need help on this question: Triangle ABC is similar to triangle XYZ. What is the length of AC in inches?
Answer: 3√13
Step-by-step explanation:
To find the length of AC we need to use the Pythagorean theorem.
Which is AC^2 = BC^2 + AB^2
AC^2 = 6^2 + 9^2
AC^2 = 36 + 81
AC^2 = 117
AC = √117
To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\overline{AB}$ . What is the area of the circular base of the fountain
The area of the circular base of the fountain is 179 square feet.
What is the area of the circular base ?A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.
A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.
Combined area of the walkway and fountain: (3.14)112=379.94 ft2.
Fountain area: (3.14)8*2=200.96 feet
Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.
The area of the circular base of the fountain is 179 square feet.
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The cost of a class field trip is $15 per person, plus $50 for a bus ride. Which function can be used to find the total cost C(x) of a field trip for x students
Select the theorem that can be used to prove that RST = VUT
The table shows the shoe sizes of women of different ages. A 2-column table with 4 rows. The first column is labeled age with entries 18, 30, 52, 64. The second column is labeled shoe size with entries 7, 10, 6, 9. Which best describes the strength of the model? a weak positive correlation a strong positive correlation a weak negative correlation a strong negative correlation
Answer:
A.) weak positive correlation
The person above just wanted to steal points.
Step-by-step explanation:
Answer:
The correct answer is a weak positive correlation
or
A
Step-by-step explanation:
The mighty oak tree outside of Matt's house had to be cut down. He missed the beautiful tree and the shade it provided and wanted to replace it with an oak tree that would grow quickly. The Nuttall Oak (Quercus nuttalli), the fastest-growing oak tree, grows 7 to 8feet per year (we'll assume it grows at a constant rate). At maturity, it can be up to 50 feet tall.
Which of the following equations, where t represents time in years and h represents the height in feet, describe growth that is slower than the Nuttall Oak growth rate?
CHOICES:
A: h=5t
B: h=8.5t
C: h=10t
D: h=50t
Growth that is slower than the Nuttall Oak growth rate is h=5t.
What is equation?An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.
This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.
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Please graph the question in the image.
Answer:
I used desmos to make the graph
Step-by-step explanation:
Hopefully this helps!
Mr. Mutler posts his students' artwork on a bulletin board.
The width and length of the bulletin board are whole
numbers. What could be the dimensions of the bulletin board
Mr. Butler uses?
Area - 15 square feet
The dimensions of the bulletin board could be as follows:
length = 5 ft.
width = 3 ft.
What is the are of rectangle?[tex]A = l\times w[/tex]
where, 'l' represents the length of the rectangle
and 'w' represents the width of the rectangle
What are factors?"If multiplying two whole numbers gives us a number, then the numbers we are multiplying are the factors of the product number."
For given example,
An area of the rectangular bulletin board is 15 sq. ft.
⇒ A = 15 sq. ft.
⇒ l × w = 15
Given that, the width and length of the bulletin board are whole
numbers.
Factors of 15 are,
15 = 5 × 3
15 = 15 × 1
From given figure we can say that he could use the dimension 5 ft. × 3 ft. for the bulletin board.
This means, the length of the bulletin board could be 5 ft. and the width could be 3 ft.
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Which graph represents the following system of inequalities? y>(1)/(2)x-1 y<=-x+1 y>-2x-1
Answer:
? We don't see any graphs to choose from
Step-by-step explanation:
[tex]y>\frac{1}{2}x-1[/tex] Graph a dotted line (to show it's not included) with y-intercept 1 and slope 1/2. Test the origin (0, 0) in the inequality:
[tex]0 > \frac{1}{2}0 - 1 = -1[/tex] This is true, so shade the side of the line that the origin is on (above the line).
Next inequality...
[tex]y \le x+1[/tex] Graph a solid line with y=intercept 1 and slope 1. Test the origin.
[tex]0 \le 0+1=1[/tex] True! Shade the side of the line the origin is on (below the line). See image2, attached.
[tex]y>-2x-1[/tex] Graph a dotted line with y-intercept -1 and slope -2. Test the origin (0, 0).
[tex]0>-2(0)-1=-1[/tex] True, so shade the side the origin is on (above the line).
The solutions are located where all the shadings intersect. See image3. The solutions are above the red line, above the green line and below the blue line.
A. X=9
B. X=14
C. X=16
D. X=12
E. X=10
Answer:
Angle K is 1/2 the measure of arc JL, so JL = 228. Add arc KL to arc JL to get 268 and subtract from 360. 360 - 268 = 92. 8x - 36 = 92. X = 16.
Step-by-step explanation:
HELP ASAP
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes. What does the number 3 represent in this equation?
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.
Given,
A snail is moving away from a rock.
The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.
The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.
Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.
For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.
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Angel missies 4% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 55
Answer:
Step-by-step explanation:
55 times 25, making Angel attempt 1375 free throws
Answer:
Step-by-step explanation:
Its 700% because 7x3 = 11
What is the volume of the composite shape to the nearest whole number? (Pls answer, due today!)
A. 1,178 in^3
B. 1,035 in^3
C. 960 in^3
D. 2,138 in^3
Answer:
2,138 in^3
Step-by-step explanation:
I know this is old but other people can find this helpful
Select the correct answer. Which logarithmic equation is equivalent to this exponential equation? 2,400=7,500 (10) ^ -x
The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C
How to solve for the equationfrom the question we have:
2400 = 7500(10)⁻ˣ
we would have to transform the equation that we have here into the logarithm form.
This is written as:
[tex]\frac{2400}{7500}=10^-^x[/tex]
from here we are to reduce the division
hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]
-x = log₁₀8/25
then
[tex]x = -log_{10} \frac{8}{25}[/tex]
option c is correct
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Which area model represents the factorization x2+3x+2=(x+2)(x+1)?
The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.
The standard form of a quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Given the polynomial:
x² + 3x + 2
Factorizing the polynomial:
x² + 2x + x + 2
= x(x + 2) + 1(x + 2)
= (x + 1)(x + 2)
The factorization gives (x + 1)(x + 2)
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Please answer these questions with steps explaining how to solve them. Also please go step by step explaining what you did.
x/3 - 3 = x/9 + 3
Answer:
what does x mean, like what number does it represent in this situation
Answer:
x = 27
Step-by-step explanation:
I made '3' into 9/3
x/3 - 9/3 = x/9 + 9/3
convert terms to fractions with a denominator of 9
x/3 = 3x/9
9/3 = 27/9
3x/9 - 27/9 = x/9 + 27/9
(3x-27)/9 = (x+27)/9
since each denominator equals 9 we can set the numerators equal to each other:
3x - 27 = x + 27
3x = x + 54
2x = 54
x = 27
A plane flying with an air speed of 300 mph at 50 degrees and it crosses the jet stream, which is blowing at 200 mph at an angle of 160 degrees. The plane's actual velocity with respect to the ground is the vector sum of these two velocities. Find the actual velocity to the nearest whole mph and degree (add the sum of the vectors).
Answer:
298.24 mph at an angle of 89 degrees
Step-by-step explanation:
[tex]v_p[/tex] = Velocity of plane = 300 mph at 50 degrees
[tex]v_j[/tex] = Velocity of jet stream = 200 mph at 160 degrees
The velocity of the plane in component form is
[tex]v_p=300\cos50^{\circ}\hat{i}+300\sin50^{\circ}\hat{j}[/tex]
The velocity of the jet stream in component form is
[tex]v_j=200\cos160^{\circ}\hat{i}+200\sin160^{\circ}\hat{j}[/tex]
Resultant velocity is given by
[tex]v=(300\cos50^{\circ}+200\cos160^{\circ})\hat{i}+(300\sin50^{\circ}+200\sin160^{\circ})\hat{j}\\\Rightarrow v=4.9\hat{i}+298.2\hat{j}[/tex]
Magnitude is given by
[tex]|v|=\sqrt{4.9^2+298.2^2}\\\Rightarrow |v|=298.24\ \text{mph}[/tex]
Angle is given by
[tex]\theta=\tan^{-1}\dfrac{298.2}{4.9}=89^{\circ}[/tex]
The velocity of the plane is 298.24 mph at an angle of 89 degrees.
please help me with these 4 questions will mark branliest whoever gets all of it right
Answer:
1. The answer is 40 degrees
2. Adjacent angles are sometimes congruent.
3. UPR is vertical to TPQ
4. The answer is 132 Degrees
What is the AAA equation?
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
Consider two triangles ABC and XYZ, if ∠ A = ∠X and ∠C = ∠Z then
ΔABC ~ΔXYZ.
If, two triangles ΔABC and ΔXYZ are similar only if,
i)∠A =∠X, ∠B =∠Y and ∠C=∠Z
ii)AB/XY=BC/YZ=AC/XZ
"AAA" means "Angle, Angle, Angle" when we know all three angles of a triangle, but no sides.
If two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
An AAA triangle is a triangle where only the three angles are defined:
α + β + γ = 180°
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Find the perimeter of the parallelogram using the Pythagorean Theorem
Answer:
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Step-by-step explanation:
We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.
First, we calculate the length of the oblique line, that is:
[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]
[tex]l_{O} = \sqrt{34}[/tex]
Second, we determine the length of the vertical line by direct observation, that is:
[tex]l_{V} = 12[/tex]
Lastly, the perimeter is determined by the following formula:
[tex]p = 2\cdot (l_{O}+l_{V})[/tex]
[tex]p = 24+2\sqrt{34}[/tex]
The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.
Answer: 35.7
(This is the answer squared by the way)
Step-by-step explanation:
In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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Gianna has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $356.46.
She buys 2 bicycle reflectors for $10.01 each and a pair of bike gloves for $20.72.
She plans to spend some or all of the money she has left to buy new biking outfits for $45.35 each.
Write and solve an inequality which can be used to determine
o
o, the number of outfits Gianna can purchase while staying within her budget.
Answer:
Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.
The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.
Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.
She wants to buy biking outfits that cost $45.35 each.
We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:
45.35o <= 372.81
This inequality can be solved by dividing both sides by 45.35:
o <= 8.24
Therefore, Gianna can purchase 8 biking outfits while staying within her budget.
Step-by-step explanation:
HELP THIS IS EASY I JUST DONT UNDER STAND MATH ITS ON PERCETEGES
Answer:
H 40%
Step-by-step explanation:
29+27+24=80
32/80=0.4
Answer:
Step-by-step explanation:
32/80 x 100 = 40%