Answer:
D. (f + g)(x) = -2x² - 2x + 8
Step-by-step explanation:
Given:
f(x) = 3x + 5g(x) = -2x² - 5x + 3Find (f + g)(x):
⇒ [tex]f(x) + f(g)[/tex]
⇒ [tex]3x + 5 + ( -2x^{2} - 5x + 3 )[/tex]
⇒ [tex]3x + 5 - 2x^{2} - 5x + 3[/tex]
Combine like terms:
⇒ [tex]-2x^{2} + 3x - 5x + 5 + 3[/tex]
⇒ [tex]-2x^{2} - 2x + 8[/tex]
Answer: D. (f + g)(x) = -2x² - 2x + 8
What are the solutions to log subscript 6 baseline (x squared 8) = 1 log subscript 6 baseline (x)
The antilog provides the solution to the logarithmic equation. Then x has values of 2 and 4.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The logarithmic equation is given below.
[tex]\log _6(x^{2} +8)= 1+ \log _6x\\\\\log _6(x^{2} +8)= \log_66+ \log _6x\\\\\log _6(x^{2} +8)= \log _66x\\[/tex]
Take antilog, then we have
[tex]\begin{aligned} x^{2} +8 &= 6x\\\\x^2 -6x + 8 &= 0\\\\x^2 -4x - 2x +8 &=0\\\\(x-4)(x-2) &= 0\\\\x&= 2, 4\end{aligned}[/tex]
Then the value of the x is 2 and 4.
More about the factorization link is given below.
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In one year a dog’s weight increased from 64 to 80. By what percentage did the dogs weight increase?
18. 54 grams of a certain brand of breakfast cereal contain 190 calories. Let g
represent grams of cereal and c represent calories. Identify the type of variation,
find the constant, and write an equation to represent the relationship between
grams and calories.
Answer:
The relation is c = 3.519g.
Step-by-step explanation:
This is direct variation.
c = kg where k is the constant of variation.
Substituting the given values:
190 = k * 54
so the constant of variation is:
k = 190/54 = 3.519 to nearest thousandth,
and the equation is:
c = 3.519g.
:)
25 point math problem
Answer:
B
Step-by-step explanation:
Inverse is opposite. So, domain becomes range and range becomes domain
x<2 of domain becomes y<2 for range
y>0 of range becomes x>0 of domain
Find the area of the figure.
A: 114 cm2
B: 350 cm2
C: 418 cm2
D: 447 cm2
Answer:
The answer is C. 418cm2
Step-by-step explanation:
Please help, will give brainest
Consider the trinomial 9x2 21x 10. what value is placed on top of the x? what value is placed on the bottom of the x? what is the factored form of 9x2 21x 10?
The factored form of the given quadratic equation is (3x+5)(3x+2).
The given quadratic equation is:
[tex]9x^{2} +21x+10[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
Splitting the middle term of the given quadratic equation:
[tex]9x^{2} +15x+6x+10[/tex]
[tex]3x(3x+5)+2(3x+5)[/tex]
[tex](3x+5)(3x+2)[/tex]
So this is the factored form of the given quadratic equation.
Hence, the factored form of the given quadratic equation is (3x+5)(3x+2).
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Answer:
picture of answer.
Step-by-step explanation:
Which expression is equivalent to startfraction c squared minus 4 over c 3 endfraction divided by startfraction c 2 over 3 (c squared minus 9) endfraction? startfraction c 3 over c squared minus 4 endfraction times startfraction c 2 over 3 (c squared minus 9) endfraction startfraction c squared minus 4 over c 3 endfraction divided by startfraction 3 (c squared minus 9) over c 2 endfraction startfraction c squared minus 4 over c 3 endfraction times startfraction 3 (c squared minus 9) over c 2 endfraction startfraction c squared minus 4 over c 3 endfraction times startfraction c 2 over 3 (c squared minus 9) endfraction
The options have not been given but three correct alternatives have been presented as the solution.
We have given,
[tex]\frac{c^2-4}{c+3} /\frac{c+2}{3(c^2-9)}[/tex]
Applying the rule a^2-b^2 to the numerator of the first term and the denominator of the second term,
What is the rule of a^2-b^2?[tex](a^2-b^2)=(a-b)(a+b)[/tex]
By applying the above formula we have:
[tex]=\frac{c^2-2^2}{c+3} /\frac{c+2}{3((c+3)(c-3)}[/tex]
[tex]=\frac{(c-2)(c+2)}{c+3} /\frac{c+2}{3((c+3)(c-3)}[/tex]
Therefore the solution is,
[tex]=(c-2) \times 3(c-3)\\\\=3(c^2-5c+6)\\\\=3c^2-15c+18[/tex]
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Answer:
C.) StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction 3 (c squared minus 9) Over c + 2 EndFraction"/>
Step-by-step explanation:
Which expression is equivalent to StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction c + 2 Over 3 (c squared minus 9) EndFraction?
StartFraction c + 3 Over c squared minus 4 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction 3 (c squared minus 9) Over c + 2 EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction 3 (c squared minus 9) Over c + 2 EndFraction
StartFraction c squared minus 4 Over c + 3 EndFraction times StartFraction c + 2 Over 3 (c squared minus 9) EndFraction
In a computer game whenever you shoot a dragon you get 12 points, but when you miss then you lose 4 points. After 100 shots you have 224 points. How many times have you hit a dragon
Answer:
39
Step-by-step explanation:
Let h: hit
Let n: not hit
1) We can create two equations and solve them simultaneously using the substitution method or elimination.
h + n = 100
12h - 4n = 224
2) Solve them. I will demonstrate using the substitution method.
n = 100 - h
-----------------------
12h - 4(100 - h) = 224
12h - 400 + 4h = 224
16h = 224 + 400
16h = 624
h = 624/16
h = 39
3) Substitute the result into one of the equations above.
n = 100 - 39
n = 61
Since the question wants you to write the number of times the dragon was hit, the answer is 39.
its 8th grade math i did not pay attention
Answer:
a = 11
Step-by-step explanation:
Using the Pythagorean Theorem:
[tex] {a}^{2} + {26.4}^{2} = {28.6}^{2} [/tex]
[tex] {a}^{2} + 696.96 = 817.96[/tex]
[tex] {a}^{2} = 121[/tex]
[tex]a = 11[/tex]
The difference between three times an angle's measure and its complement is 46. Find the measure of the angle
Answer:
Step-by-step explanation:
Equation
Let the angles measure = x
Let the complimentary angle = 90 - x
3x - (90 - x) = 46 Remove the brackets
Solution
3x - 90 + x = 56 Combine like terms on the left
4x - 90 = 56 Add 90 to both sides
4x - 90 +90 = 56 + 90 Combine
4x = 146 Divide by 4
4x/4 = 146/4
x = 36.5
Answer
The given angle is 36.5
I really hate maths :(
The equation p(h)=5,000 • 2^h represents a bacteria population as a function of time in hours.
Check the picture below.
[tex]p(h)=5000(2)^h\implies \stackrel{p(h)}{100000}~~ = ~~5000(2)^h\implies \cfrac{100000}{5000}=2^h \\\\\\ 20=2^h\implies \log(20)=\log(2^h)\implies \log(20)=h\log(2) \\\\\\ \stackrel{\textit{using the \underline{change of base rule}}}{\cfrac{\log(20)}{\log(2)}=h\implies \log_2(20)=h}\implies 4.3219\approx h[/tex]
Which expression is equivalent to 3(2x+4y)-y? Show your work
A. 17xy
B. 6x+12
C. 3(6xy)-y
D. 6(x+2y)-y
Answer:
D. 6(x+2y)-y
Step-by-step explanation:
Both expressions can be simplified into 6x + 11y
3(2x+4y)-y
6x + 12y - y
6x + 11y
6(x+2y)-y
6x + 12y - y
6x + 11y
Answer:
D. 6(x+2y)-y
Step-by-step explanation:
To solve for the equivilent expression, begin by simplifying the given expression. (1) To simplify 3(2x+4y)-y, you can first multiply 3 into the parentheses then combine like terms; (6x+12y)-y or 6x + 12y - y --> 6x + 11y. (2) Solve to find which expression listed will yield the same product, 6x + 11y, when simplified as well. This is quiet straightfoward to see and you wont be needing to solve each individual problem. 6(x+2y)-y will simplify to 6x + 12y - y which is then equal to --> 6x + 11y. Meaning, D. 6(x+2y)-y is equvillent to 3(2x+4y)-y.
PLEASEEEE HELPPPPP A flying disk is thrown into the air from a height of 25 feet at time t=0. The function that models this situation is h(t) = -16t2 + 75t + 25, where t is measured in seconds and h is the height in feet. Which values best describe the domain of the function in the context of the problem?
A. 0 ≤ t ≤ 5
B. 0 ≤ t ≤ 25
C. All real numbers
D. All positive integers
Answer:
A)
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+75t+25[/tex]
The domain (input values) will be the x-intercepts, so the values of t when h(t) = 0.
The quickest way to find these is to use the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-75 \pm \sqrt{75^2-4(-16)(25)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{-75 \pm \sqrt{7225}}{-32}[/tex]
[tex]\implies t=\dfrac{75 \pm 85}{32}[/tex]
[tex]\implies t=5, t=-\dfrac{5}{16}[/tex]
Time cannot be negative.
When h(t) = 0, the disk will hit the floor.
Therefore, the domain is restricted to 0 ≤ t ≤ 5
Please hurry!!!
A total surface area of all land on Earth is approximately 6.0x10^7 square miles. Land covers approximately 0.3 of the entire surface of Earth. Which number is closest to the approximate total surface area, in square miles, of Earth?
Answer: 1.8 X 10^8
Step-by-step explanation: 6.0 X 10^7 times .3 = 1.8 X 10^8
Find the area
15 in
10 in
Answer:
The area of the figure is 385.5 in²
Step-by-step explanation:
The area of the figure = area of hemisphere + area of rectangle
Radius of hemisphere = 10/2 = 5 in
=> 3πr² + length × breadth
=> { 3×(3.14) × 5 × 5} + { 15 × 10 }
=> { 9.42 × 25 } + { 150 }
=> 235.5 + 150
=> 385.5 in²
Which dog pens have the same perimeter?
Answer:
Problem 4: Dog pens 2 and 3
Problem 5: Dog Pens 1 and 2
Problem 6: 6cm and 6cm
problem 7: A
Step-by-step explanation:
im trying to get htis one right i dont get it
Answer:
I'd love to help, but I need the full question first!!!
I need to know what it is
Answer:
1. C 3 1/8
2. A 3
Step-by-step explanation:
The hands of clock form a 120° angle. What time is it? A. 2:00 B. 4:00 C. 6:00 D. 9:00
Answer:
4
Step-by-step explanation:
360 degrees in a circle /12 numbers on clock= 30 degrees for each number 120/30=4
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x 1 centimeters, 2x centimeters, and x 6 centimeters. the equation 2 x cubed 14 x squared 12 x = 400 can be used to find x. what is the length of the longest side? use a graphing calculator and a system of equations to find the answer. 4 centimeters 5 centimeters 8 centimeters 10 centimeters
A rectangular prism with a volume of 400 cubic centimeters has dimensions of 5 cm, 8 cm, and 10 cm with the value of x being 4.
What is the volume of the rectangular prism?The volume of the rectangular prism is the product of the length, breadth, and height of the given prism.
Volume of rectangular prism = (length x width x height)
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeter, 2x centimeters, and x + 6 centimeters.
Volume of rectangular prism = (length x width x height)
400 cm³ =( x + 1 )(2x)(x + 6 )
400 cm³ =( x + 1 )(2x)(x + 6 )
Substitute 4cm as the value of x.
x + 1 centimeters = 4 cm + 1 cm = 5 cm
2x centimeters = 2 ( 4cm) = 8 cm
x + 6 centimeters = 4 cm + 6 cm = 10 cm
Volume of rectangular prism = 10 cm × 5 cm × 8 cm
= 400 cm³
Thus, the given rectangular prism of 400 cubic centimeters has dimensions of 5 cm, 8 cm, and 10 cm.
Learn more about rectangular prism;
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Answer:
Step-by-step explanation:
its 10
The parallel sides of a Trapezium are 77 and 60 and its non parallel sides are 26 and 25 m find the area of trapezium
PLEASE GIVE FULL METHOD
Answer:
Area of Trapezium=1/2h(L1+L2)
I think it will help you
Please Help! Locks in an hour! Will give brainlest!
Answer:
1/4
Step-by-step explanation:
Amplitude is equal the A part of the function which is 1/4.
Brian is participating in a hotdog eating contest. There are 145 hotdogs on his plate and he will have 8 minutes to eat as many as he can. If he eats 12 hotdogs per minute, how many hotdogs will he have left over?
Answer:
49
Step-by-step explanation:
12 hotdogs per min × 8 minutes = 96
145-96= 49
So he will have 49 hotdogs left.
solve for the missing side round to the nearest 10th (look at image)
Answer:
14.3
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
14^2 + 3^2 = c^2
196 + 9 = c^2
205 = c^2
Take the square root of each side
sqrt(205) = sqrt(c^2)
14.31782106 = c
Rounding to the nearest tenth
14.3 = c
Answer :
14.3 yd⠀
Explanation :
This is Right Angled Triangle.⠀
Solution :
We'll solve this using the Pythagorean Theorem.where,
XY (3 yd) is the perpendicularYZ (14 yd) is the Base.XZ is the Hypotenuse.We know that,
[tex]{\longrightarrow \pmb{\mathbb {\qquad (XZ) {}^{2} = (XY) {}^{2} +( YZ) {}^{2} }}} \\ \\ [/tex]
Now, we will substitute the given values in the formula :
[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = (3) {}^{2} +( 14) {}^{2} }}} \\ \\ [/tex]
We know that, (3)² = 9 and (14)² = 196. So,
[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 9 +196 }}} \\ \\ [/tex]
Now, adding 9 and 196 we get :
[tex]{\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 205 }}} \\ \\ [/tex]
Now, we'll take the square root of both sides to remove the square from XZ :
[tex]{\longrightarrow \sf{\pmb {\qquad \sqrt{(XZ) {}^{2}} = \sqrt{205 }}}} \\ \\ [/tex]
When we take the square root of (XZ)² , it becomes XZ,
[tex]{\longrightarrow \sf{\pmb {\qquad XZ = \sqrt{205 }}}} \\ \\ [/tex]
We know that, square root of 205 is 14.317 (approx) .
[tex]{\longrightarrow { \mathbb{\pmb {\qquad XZ }}}} \approx \pmb{\mathfrak{14.317 } }\\ \\ [/tex]
So,
The measure of the missing side (XZ) is 14.3 (Rounded to nearest tenth)whats the answer to
2.4=-t/45
How many classes are there in the frequency distribution table that has 50 raw data?
Answer:
A frequency distribution is a table that shows “classes” or “intervals” of data entries with a count of the number of entries in each class.
Step-by-step explanation:
hope this helps you a little!
Colorado is roughly shaped like a rectangle. The state is about 6.12 x 105 m long and 4.5 x 105 m wide. Wyoming has an area of about 2.6 x 1011 m2. What is the estimated difference of area between the two states? Write your answer using scientific notation. Show your work.
The estimated difference of the area of Colorado and Wyoming in scienfic notation is 2 x [tex]10^{-1}[/tex]m².
What is the difference in the area of the states?Scienfic notation is used in expressing large numbers in smaller numbers. In order to write a number in stscienfic notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
Area of Colorado = (6.12 x [tex]10^{5}[/tex]) x (4.5 x [tex]10^{5}[/tex]) = 27.54 x [tex]10^{10}[/tex]
= 2.8 x [tex]10^{11}[/tex]m²
Difference in the areas = 2.8 x [tex]10^{11}[/tex]m² - 2.6 x x [tex]10^{11}[/tex]m² = 0.2m²
= 2 x [tex]10^{-1}[/tex]m²
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A class of 30 students must elect a representative to go to a local
conference. They must also elect one alternate representative, in case the
first representative becomes ill or unable to go at the last minute.
How many different ways can the class elect a representative and
a
alternate?
Answer:
870.
Step-by-step explanation:
There are 30 choices of representatives. This leaves 29 choices for alternate representatives.
If one person gets elected for representative, there are 29 choices for an alternate representative.
This is the case if any of the 30 students get elected as representatives.
That means you can set it up as:
x*y where x is the choice of representatives and y is the choice of alternate representatives.
30 * 29, or 870.
Here is a visual example. Students a - dd are shown here.
a b c d e f g h i j k l m n o p q r s t u v w x y z aa bb cc dd
In this case, a has been chosen as class president. Any of the other 29 students could be a alternate, and then paired with a. This makes 29 total possible pairings. This is then repeated for the possibility of every student becoming a president, which creates 30*29.
Please tell me if this is wrong, I will try to make changes!