[tex]\sin^2 x=1-\cos^2 x \\ \\ \cos^2 x=1-\sin^2 x[/tex]
If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = [?]x² + [ ]
⇒g(f(x)) means that in the place of x in the function g you will plug in the function f.
⇒This means that [tex]2x^{2} -5[/tex] will be plugged in the place of x in 5x+7 and the simplify.
⇒[tex]=5(2x^{2} -5)+7\\\\=10x^{2} -25+7\\=10x^{2} -18[/tex]
⇒Now you have the unknowns The coefficient of the variable [tex]x^{2}[/tex] is 10 and the constant number is -18.
Find the value of x so that the line m is parallel to line n. Need answers
○ 35
○ 30
○ 40
○45
You are working on a food budget for your family for the week. You know that you typically spend $90 at the grocery store, and you spend about $40 each time you go out to eat as a family. The graph of the relationship between the number of times you go out to eat and the total weekly budget for food is below.
Given the following question:
The family spends 90 dollars at a grocery store each week
The family spends 40 dollars each time they go out to eat.
Part one:
[tex]40\times4=160+90=250[/tex]If the family goes out to eat four times they would have spent 250 dollars.
Part two:
The final point on the graph is (6, 330)
Which means if the family goes out six times, the budget is 330 dollars.
So, your answer is 6.
[tex]6\times40=240+90=330[/tex]We can think of 3÷1/4 as the answer to the question " How many groups of 1/4 are in 3?" The tape diagram represents this situation. What is the answer to the question.A:12B:6C:9D:3
The length of the tape is 3 and it is divided into equal parts or groups. The length of each group is 1/4. This means that the number of groups in 3(the tape) would be
3÷1/4
We can hold 3 and flip the fraction, 1/4. If we flip 1/4, it becomes 4/1 and the division sign becomes multiplication. The expression would be
3 x 4/1 = 12
The correct option is A
I need help with this!! every time i use the formula i’m always one off
By using the secant line formula, the average rate of change of function f(x) on the interval [3, 11] is equal to 4.
How to determine the average rate of change of a function
In accordance with the statement, we must determine the average rate of change for a given closed interval of the function f(x). Graphically speaking, the average rate of change for this interval is represented by the slope of the secant line passing through the two limits of the interval [a, b], which is found by secant line formula:
m = [f(b) - f(a)] / (b - a)
If we know that a = 3, f(a) = 19, b = 11 and f(b) = 51, then the average rate of change is:
m = (51 - 19) / (11 - 3)
m = 32 / 8
m = 4
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how to graph:-8x-y=8
In order to graph this equation, we first need to find two ordered pairs that are solution to this equation.
To do this, we can choose a value for x and calculate the corresponding value of y.
Choosing x = 0 and x = -1, we have:
[tex]\begin{gathered} x=0\colon \\ -8\cdot0-y=8 \\ 0-y=8 \\ y=-8 \\ \\ x=-1\colon \\ -8\cdot(-1)-y=8 \\ 8-y=8 \\ y=0 \end{gathered}[/tex]Now, graphing the points (0, -8) and (-1, 0) and the line that passes through them, we have:
So the blue line represents the graph of the equation given.
Benji has four -0.5 cards. what is his total score
Benji's total score is -2.
What is the total of negative numbers?If two numbers are negative, their sum will also be negative. When two negative numbers are added together, their value is further diminished, hence the sum of the two negative numbers is always negative.
Given:
Benji has four -0.5 cards.
According to the question, we have to determine his total score which will be equal to adding scores on all four cards.
As we are adding negative scores, upon adding them place a negative sign in front of the sum.
The total score of Benji = (-0.5) + (-0.5) + (-0.5) + (-0.5)
= -2
Therefore, his total score is -2.
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A window for a new house is shown. How many squares feet or glass does the window require? Enter your answer in the box
ANSWER
[tex]14.4ft^2[/tex]EXPLANATION
To find the number of square feet the window requires, we have to find the area of the shape.
The shape given is a kite, and the area of a kite is:
[tex]A=\frac{pq}{2}[/tex]where p and q are the diagonal lengths.
From the question given:
[tex]\begin{gathered} p=3.2+4 \\ p=7.2\text{ ft} \\ q=2+2 \\ q=4\text{ ft} \end{gathered}[/tex]Therefore, the area of the kite is:
[tex]\begin{gathered} A=\frac{7.2\cdot4}{2} \\ A=14.4ft^2 \end{gathered}[/tex]That is the number of square feet of glass that the window requires.
A basketball backboard said that sold for $79 is discounted 15% what is the sale price?
Answer: 67.15
Step-by-step explanation:
What rule represents the translation from the pre image ABCD to the image A’ B’ C’ D’
Answer:
The second one
Step-by-step explanation:
Root of the equation 3x-8=1 is
Answer:
x= 3
Step-by-step explanation:
Add
8
to both sides
3x-8=1
2
Simplify
Add the numbers
3x=9
3
Divide both sides by the same factor
3x=9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
Answer:
x = 3
You first add 8 to both sides:
3x - 8 + 8 = 1 + 8
Simplify:
3x = 9
The divide both side by the same factor:
3x/3 = 9/3
9 divided by 3 is 3 so the solution is:
x = 3
Step-by-step explanation:
Hope it helps! =D
How many days will it take the crew to lay all the track? L(d)=189-7d
Answer:
HIH
Step-by-step explanation:
HOW ARE
Answer:
d = 189/L+7unless you are looking for L, then it's
L = 189/d-7
What is the distance between a and b on the number line below?0.550.652.484.85
Raina runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
raina runs 6 miles in 55 minutes
so it speed is 6/55 miles per minute
that means in one minute he runs 6/55 miles
so in 44 minutes
[tex]\begin{gathered} =\frac{6}{55}\times44 \\ =\frac{6\times4}{5}=\frac{24}{5} \end{gathered}[/tex]in 44 minutes he will run 24/5 miles or 4.8 miles
Enter values to complete the table below.
For the given values of x and y, the value of y/x (that represents the slope of the equation) = 3/1, 3/1, 3
What does slope mean in math?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.
Given are the values of the x and y
y/x represents the slope of the equation,
for x = -1 and y = -3,
y/x = 3/1
for x = 1 and y = 3
y/x = 3/1
for x = 2 and y = 6
y/x = 6/2 = 3
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I need help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A freight train travels 210 miles in the same amount of time a car travels 330 miles. If the rate of the car is 20 mph more than the rate of the train, find the rate of each.
Answer: the train is 230 and the car is 350
Step-by-step explanation: I think so im like 75% sure but that is still a risk so be carful
what is the, in units, between (-5,8) and (4,-4) in the coordinate plane
A rectangle is graphed on a coordinate plane. For two of the vertices of the rectangle are (-5,8) and (-5,-6) what is the distance between the two vertices
A 2units
B 4 units
C 10 units or
D 14 units
Find out the distance between the given vertices
we have that
the two coordinates have the same x-coordinate
that means
the distance between the points is the difference of the y-coordinates
8-(-6)=8+6=14 units
the answer is option DProblem N 2
we have that
between -1 and -2 there are 5 spaces
the value of each space is 1/5=0.20
therefore
point A is -1.60
option C
-what is 1 3/5 X -5 1/2
Answer:
-44/5 (in decimal -8.8)
Brian cut 4 1/12 yards of fishing line from a new reel. How much is this in inches? Write your answer as a whole number or a mixed number in simplest form.Include the correct unit in your answer.
Given: Brian cut
[tex]4\frac{1}{12}\text{ yards}[/tex]of fishing line from a new reel.
Required: To find how much Brian cut in inches.
Explanation: Since 1 yard is equivalent to 36 inches. Hence we need to multiply by 36 to convert yards to inches.
Hence Brian cut-
[tex]\begin{gathered} 4\frac{1}{12}\times36=\frac{49}{12}\times36 \\ =147\text{ inches} \end{gathered}[/tex]Final Answer: Brian cut 147 inches of fishing line from a new reel.
what is the answer to this please help 9/5 + 2 + 15/3
What’s the correct number and label for the
denominator of the ratio.
Answer:
see explanation
Step-by-step explanation:
ratio required is houses : turbines
let x be the number of turbines required for 26 houses , then
[tex]\frac{6houses}{18turbines}[/tex] = [tex]\frac{26houses}{x}[/tex] ( cross- multiply )
6x = 26 × 18 = 468 ( divide both sides by 6 )
x = 78
78 turbines are required for 26 houses
A large tank of sterile water holds 200 gallons . It is leaking at an unknown rate. At 8:30 am the tank had 137 gallons and at 11:00 am the tank had 115 gallons. Assuming the tank was full when the leak began , write a function to estimate how much water is in the tank. now find the time at which the tank began leaking and the time at which the tank will be empty.
The time that the tank began leaking water is 12:40am
The time the tank will be empty is 11 : 23 pm.
What is the time the tank began leaking water?The function that would determine the amount of water in the tank is a linear function. A linear function is a function that has a single power that is raised to the power of one. When drawn on a graph, a linear function is a straight line.
The first step is to determine the rate of leakage of the tank.
Rate = (water in the tank at 11am - water in the tank at 8:30am) / change in time
(137 - 115) / (11 - 8:30)
22 / 2:30
22 ÷ 2 1/2 hours = 8.8 gallons per hour
Linear function would have this form:
Water in the tank = water in the tank when full - (rate of leakage x number of hours)
137 = 200 - (8.8xh)
137 = 200 - 8.8h
200 - 137 = 8.8h
63 = 8.8h
h = 63 / 8.8
h = 7.16 hours = 7 4/15 hours
8 - 7 4/15 hours = 12 10/15 hours = 12.40am
When the tank is empty:
0 = 200 - 8.8h
200 - 0 = 8.8h
200 / 8.8 = 22.72 = 22 hours 43 minutes
22 hours 43 minutes + 12 : 40M = 11 : 23 pm
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Helppp
Express 27^1/2 as a power of 3
Express root 2 as a power of 8
Express root 2/16 as a power of 2
FOR THE FURST QUESTION.
[tex] {27}^{ \frac{1}{2} } \\ = (3^{3} )^{ \frac{1}{2} } \\ = {3}^{3 \times \frac{1}{2} } \\ = 3^{ \frac{3}{2} } [/tex]
FOR THE SECOND QUESTION
[tex] \sqrt{2} \\ = ( \sqrt[3]{8} )^{ \frac{1}{2} } \\ = ( {8}^{ \frac{1}{3} } )^{ \frac{1}{2} } \\ = 8^{ \frac{1}{3} \times \frac{1}{2} } ) \\ = 8^{ \frac{1}{6} } [/tex]
FOR THE THIRD ONE
[tex] \frac{ \sqrt{2} }{16} \\ = \frac{ \sqrt{2} }{16} \\ = \frac{ {2}^{ \frac{1}{2} } }{ {2}^{4} } \\ = 2^{ \frac{1}{2} - 4 } \\ = 2^{ - \frac{7}{2} } [/tex]
ATTACHED IS THE SOLUTION
I really need help I hate Sparx maths
Answer:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
Step-by-step explanation:
Given equations:
[tex]\begin{cases}y=10x+4\\2y+5x=13\end{cases}[/tex]
To solve the given equations by substitution, substitute the first equation into the second equation and solve for x:
[tex]\begin{aligned}\textsf{Equation 2}: \quad 2y+5x&=13\\\\y=10x+4 \implies 2(10x+4)+5x&=13\\20x+8+5x&=13\\25x+8&=13\\25x+8-8&=13-8\\25x&=5\\\dfrac{25x}{25}&=\dfrac{5}{25}\\x&=\dfrac{1}{5}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}\textsf{Equation 1}: \quad y &=10x+4\\\\x=\dfrac{1}{5} \implies y&=10\left(\dfrac{1}{5}\right)+4\\y&=\dfrac{10}{5}+4\\y&=2+4\\y&=6\end{aligned}[/tex]
Therefore, the solution to the equations is:
[tex]x=\dfrac{1}{5}, \quad y=6[/tex]
2x + 3y = 7
-2x + 5y = 9
Discuss the transformation of g(x)=2 (x−3)2 + 4 compared to the original function f(x)=x2. Select all that apply.
Group of answer choices
The graph is shifted right 4 units.
The graph has a horizontal stretch by a factor of 2.
The graph is shifted right 3 units.
The graph has a vertical stretch by a factor of 2.
The graph is shifted left 3 units.
The graph is shifted up 4 units.
The graph is shifted down 3 units.
The graph is shifted down 4 units.
The graph has a horizontal compression by a factor of 1/2.
The graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The function is:
f(x) = x²
First transformation:
x → (x- 3)
The graph is shifted right to 3 units.
F(x) = (x- 3)²
Second transformation:
F(x) → 2F(x)
The graph has a horizontal stretch by a factor of 2.
h(x) = 2(x- 3)²
Third transformation:
h(x) → h(x) + 4
The graph is shifted up 4 units.
g(x) = 2(x- 3)² + 4
Thus, the graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.
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hello i need help on this
A rational number is a number that can be expressed as a ratio of two integers. Integers can be positive or negative. Rational numbers are simply fractions. For example;
-5/2, -1/5, 3/1, 4/5 etc are all rational numbers because we can write them as a ratio of two integers.
Since some of this fractions can lead to both negativa and positive integers, hence rational number is a positive or negative whole number including 0.
Hence all the options are correct since rational numbers are are also repeating decimals
Find the derivative, ′, of = secx/e^x.Your final answer must be fully simplified
Simplify (9-2/square root of 9)^-2 +(1-6)^2
The simplification of the number (9-2/square root of 9)⁻² +(1-6)² is found as 25.18.
What is defined as the simplification?Simplify simply signifies to make something easier to understand. Simply or simplification in mathematics refers to reducing an expression /fraction /problem to a simpler form. It simplifies the problem by calculating and solving it.
We can —
Simplify fractions by removing all common factors from the numerator and denominator and composing the fraction through its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.For the given question;
The expression is given as;
(9-2/square root of 9)⁻² +(1-6)²
This can be written as;
= [(9-2)/√9]⁻² + (1-6)²
Do the prime factorization of √9 = √3×3
= [(9-2)/√3×3]⁻² + (1-6)²
On solving;
= [7/3]⁻² + (-5)²
Taking the reciprocal of first term
= (3/7)² + (-5)²
= (0.42)² + (-5)²
Squaring the values;
= 0.18 + 25
= 25.18
Thus, the result after the simplification becomes 25.18.
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