Answer:
y=4/3x-18
Step-by-step explanation:
4x-2=3y
y=4/3x-2/3
to parallel slope has to be the same
-6=9*(4/3)+b
b=-18
y=4/3x-18
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 65%pure antifreeze. The company wants to obtain 260 gallons of a mixture that contains 45% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be
Answer:
80 gallons of water
180 gallons of premium antifreeze solution.
Explanation:
Let's call X the number of gallons of water and Y the number of gallons of the premium antifreeze solution.
The company wants to obtain 260 gallons of the mixture, so our first equation is:
X + Y = 260
Additionally, the mixture should contain 45% of pure antifreeze and the premium antifreeze solution contains 65% pure antifreeze. So, our second equation is:
0.45(X + Y) = 0.65Y
Now, we need to solve the equations for X and Y. So, we can solve the second equation for X as:
[tex]\begin{gathered} 0.45(X+Y)=0.65Y \\ 0.45X+0.45Y=0.65Y \\ 0.45X=0.65Y-0.45Y \\ 0.45X=0.2Y \\ X=\frac{0.2Y}{0.45} \\ X=\frac{4}{9}Y \end{gathered}[/tex]Then, we can replace X by 4/9Y on the first equation and solve for Y as:
[tex]\begin{gathered} \frac{4}{9}Y+Y=260 \\ \frac{13Y}{9}=260 \\ 13Y=260\cdot9 \\ 13Y=2340 \\ Y=\frac{2340}{13} \\ Y=180 \end{gathered}[/tex]Finally, replacing Y by 180, we get that X is equal to:
[tex]\begin{gathered} X=\frac{4}{9}Y \\ X=\frac{4}{9}\cdot180 \\ X=80 \end{gathered}[/tex]Therefore, the solution should have 80 gallons of water and 180 gallons of premium antifreeze solution.
POSSIBLE POINTS: 1One-half of a number increased by 16 is 4 less than two-thirds of the number. What is the number?
Let the number be x.
[tex]\begin{gathered} \frac{1}{2}x+16=\frac{2}{3}x-4 \\ \\ \frac{2}{3}x-\frac{1}{2}x=20 \\ \frac{4-3}{6}x=20 \\ \frac{1}{6}x=20 \\ x=120 \end{gathered}[/tex]The number is 120
The surface area of a cell phone screen is 4900 mm². Use the fact that 10 mm = 1 cm to convert this area to cm². Round your answer to the nearest whole number. Do not type the units in the space below.
Answer:
49 cm²
Step-by-step explanation:
10 mm = 1 cm
1 mm = 1/10 cm
4900 mm² = 4900 × mm × mm
4900 mm² = 4900 × 1/10 cm × 1/10 cm = 49 cm²
What are the coordinates of point B (3,-2) after a 90° clockwise rotation about the origin?
I need help with this practice problem solving. It is trigonometry It asks to graph the function, if you can.. use Desmos to do so..
Notice that f(x) is
[tex]h(x)=\cos (x)[/tex]translated π/6 to the left.
Now, recall that the period of the cotangent is
[tex]\pi\text{.}[/tex]Since f(x) is just a translation, both functions have the same period.
Answer:
I am creating a study guide and need step by step explanation for this question please
After other workers taken 1 banana, 2 oranges and 1 pear then total fruits left in the basket
[tex]11[/tex]Now the number of oranges left is 4.
So the probability of picking an orange from the basket is
[tex]\frac{4}{11}[/tex]After she took 1st orange then the number of oranges left 3
So the probability of picking an orange for the 2nd time is
[tex]\frac{3}{10}[/tex]Now the number of oranges left is 2, and the total number of fruits is 9. So the probability of picking third fruit also orange is
[tex]\frac{2}{9}[/tex]LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
The function gives the cost to manufacture x items. C(x) = 15,000 + 8x - x2 -; X = 20,000 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated a smaller values of h to check your estimates. Round your answers to five decimal places.) h 10 1 Cave 5.99950 5.9995 x Estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. c' (20,000) = 6 $/item A Need Help? Read It Watch It
We can replace x=20000 in the function so:
[tex]c(20000)=15000+8(20000)-\frac{20000^2^{}}{20000}[/tex]and we simplify:
[tex]c(20000)=15500[/tex]now h=1 is the cost of one more item so we evaluate for 20001
[tex]\begin{gathered} c(20001)=15000+8(20001)-\frac{20001^2}{20000} \\ c(20001)=195010 \end{gathered}[/tex]So for h=1 will be :
[tex]C=0.599950[/tex]how would I solve and what would the answer be?
Given that:
f(x) = |x| and g(x) = x + 6
[tex](f\circ g)(x)=|x+6|[/tex]and
[tex](g\circ f)(x)=|x|+6[/tex]A number divisible by 2, 5 and 10 if the last digit is _______.
A. An even number
B. O
C. 0 or 5
D. An odd number
Answer :- B) 0
Only a number ending with the digit 0 is divisible by 2,5 and 10
Example :-
20 ÷ 2 = 10
20 ÷ 5 = 4
20 ÷ 10 = 2
Here, 20 is the number that ends with 0.
Steel bars shrink 8% when cooled from furnace temperature to room temperature. If a cooled steel bar is 46 in. long, how long was it when it was formed?The steel bar was __ in. long when it was formed.(Round to the nearest whole number as needed.)
Answer:
50 inches
Explanation:
Let the length of the steel bar when it was formed = y
Steel bars shrink 8% when cooled from furnace temperature to room temperature.
[tex]\begin{gathered} \text{Room Temperature Length}=(100-8)\%\text{ of y} \\ =92\%y \\ =0.92y \end{gathered}[/tex]Given that a cooled steel bar is 46 in. long, then:
[tex]0.92y=46[/tex]Divide both sides by 0.92.
[tex]\begin{gathered} \frac{0.92y}{0.92}=\frac{46}{0.92} \\ y=50\;in. \end{gathered}[/tex]The steel bar was 50 in. long when it was formed.
Find g(x), where g(x) is the translation 4 units left of f(x)=|x|.
The equation for the translated function is:
g(x) = |x + 4|
How to find g(x)?
For a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left.if N < 0, the translation is to the right.Here we have:
f(x) = |x|
And the translation is of 4 units to the left, so the translated function is:
g(x) = f(x + 4) = |x + 4|
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Ex) The function f(x) is shown on the graph. Plot two points on this grid to create the graph of the line that would represent f(x) - 2.
ANSWER and EXPLANATION
We have the graph of the function f(x) given.
We want to find 2 points that will represent f(x) - 2.
This (f(x) - 2) is a transformation of the function f(x).
It is called a vertical translation. It means that the function moves on the y axis.
It is generally represented as:
f(x) + b
Comparing the required translation with the general form, we can conclude that there is a -2 shift on the y axis.
Therefore, to find two points for the new function, we have to simply pick two points from the given graph and subtract 2 from their y coordinates.
Let the two points be:
(0, 1) and (-4, 4)
Therefore, the two points will be:
(0, 1) => (0, 1 - 2) = (0, -1)
(-4, 4) => (-4, 4 - 2) = (-4, 2)
Plotting them:
The green line is the line of the new function.
help me pleaseeeeeeeee
Answer:
x = -2
Step-by-step explanation:
f(x) = y
f(x) represents the y-axis
f(x) = -3 or y = -3 or y = (0, -3)
When y = -3, x = -2
x = -2
I hope this helps!
What is the area of the figure? Please if you don’t understand ask me to move onto the next tutor as many people have gotten these questions wrong thank you and please double check and take your time!
Determine the area of the figure.
[tex]\begin{gathered} A=3\cdot8+12\cdot9+\frac{1}{2}\cdot4\cdot6 \\ =24+108+12 \\ =144 \end{gathered}[/tex]So answer is 144 yards square.
You borrow 200 from a friend you repay the loan in two weeks and agreed to pay eight dollars for interest what is the annual percentage rate? Round your answer to the nearest 10th of a percent
11. (04.02 LC) Saving all the money in a safe at home most likely means (5 points) being stingy being dishonest being untrusting O being thrifty
Saving all the money in a safe at home most likely means D. being thrifty
What is money?Money is any commodity or verifiable record that is widely accepted in a given country or socioeconomic environment as payment for products and services and repayment of debts, such as taxes.
Money enables us to meet our most basic requirements, such as purchasing food and shelter and paying for healthcare. Meeting these demands is critical, and if we don't have enough money to do so, our personal well-being and the community's overall well-being suffer considerably.
In this case, saving the money means that the person is careful with spending and doesn't want to waste the money. This implies thrifty.
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Answer:
Being thrifty
what is its base of the parallelogram is72 meters²
The area of a parallelogram is computed using the formula base x height.
Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.
[tex]\begin{gathered} A=bh \\ 72=b(9) \\ \\ \frac{72}{9}=\frac{b(9)}{9} \\ \\ 8=b \end{gathered}[/tex]The base is 8 meters long.
Help math help math
What is the answer
The ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
What is ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. Ratio are represented in the following way - a : b, c : d etc
Given is 25 to 15.
We can express this ratio as a fraction in the simplest form as -
25 : 15 = 25/15
Now, we have to ensure that only whole numbers are their in the numerator and denominator. So in simplest form, we can write -
25 : 15 = 25/15 = (5 x 5)/(5 x 3) = 5/3
Simplest form in fraction will be 5/3
Therefore, the ratio 25 : 15 as a fraction in the simplest form can be written as 5/3.
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Enrique takes out a student loan to pay for his college tuition this year. Find the interest on the loan if he borrowed $2500 at an annual interest rate of 6% for 3 years.Simple interest
Answer:
$450
Explanation:
The interest of the loan can be calculated using the following equation:
[tex]I=P\cdot r\cdot t[/tex]Where P is the amount that he borrowed, r is the interest rate and t is the number of years.
So, replacing P by 2500, r by 0.06, and t by 3 years, we get:
[tex]\begin{gathered} I=2500^{}\cdot0.06\cdot3 \\ I=450 \end{gathered}[/tex]Then, the interest of the loan is $450.
A convention center is in the shape of the rectangular pyramid with a height of 444 yd. Its base measures 348 yd by 418 yd. Find the volume of the convention center. If necessary, round your answer to the nearest tenth.
Given:
Length of the base = 418 yd
Width of the base = 348 yd
Height of the pyramid = 444 yd
Find: Volume of the rectangular pyramid
Solution:
The formula to get the volume of the rectangular pyramid is:
[tex]V=\frac{1}{3}\text{Area of the base}\times height[/tex]Since the base is rectangular, we can replace the "area of the base" into "length x width" since that is the formula for the area of a rectangle.
[tex]V=\frac{1}{3}l\times w\times h[/tex]Let's plug in the given data to the formula above.
[tex]V=\frac{1}{3}418yd\times348yd\times444yd[/tex]Then, solve for V or volume.
[tex]\begin{gathered} V=\frac{1}{3}\times64,586,016yd^3 \\ V=21,528,672yd^3 \end{gathered}[/tex]Answer: The volume of the convention is 21, 528, 672 yd³.
Rhombus EfGH is shown in the diagram the measure of angle HEF =64 degrees. What is the measure of angle EJF.
Diagonals of a rhombus bisect each other at right angles, This means that
[tex]m\measuredangle EJF=90\text{ degre}es[/tex]9. In 1621, the remaining settlers from the Mayflower and Native Americans gathered for a
harvest feast. There were 140 people at the feast and 40 more Native Americans than settlers.
How many people were from each group?
In order to solve this, we have to formulate some equations describing the number of people. The total number of people can be calculated by adding the number of natives to the number of settlers, like this:
Total = N + S
Where N is the number of natives and S is the number of settlers. We already know that there were 140 people in total, then we can rewrite the above expression to get:
140 = N + S
We are also told that there were 40 more native Americans than settlers, then the number of natives can be calculated by adding 40 to the number of settlers like this:
N = S + 40
By replacing S + 40 for N into 140 = N + S, we get:
140 = N + S
140 = (S + 40) + S
140 = S + 40 + S
140 = S + S + 40
140 = 2S + 40
140 - 40 = 2S + 40 - 40
100 = 2S
100/2 = 2S/2
50 = S
S = 50
By replacing 50 for S into N = S + 40, we get:
N = S + 40
N = 50 + 40 = 90
N = 90
Then, there were a total of 90 natives and 50 settlers
7x - 15 < 48. Elrich planted seeds from each of x different seed packets in his garden. To plant these seeds, he had to remove plants that were already in the garden. Taking into account the plants he removed and the seeds he planted, he expected to have (select) plants in the garden. From how many different seed packets did Elrich recently plant seeds?
Elrich planted 7 seeds from each of x different seed packets in his garden. To plant these seeds, he had to remove 15 plants. that were already in the garden. Taking into account the plants he removed and the seeds he planted, he expected to have less than equal to 48 plants in the garden.
The inequality :
[tex]7x-15\leq48[/tex]Simplify for x:
[tex]7x-15\leq48[/tex]
in which quadrant is the given point located (2,-4)
Answer: 4th Quadrant
Step-by-step explanation:
When plotted, the point (2, -4) lies in the 4th quadrant.
What is the constant of proportionality of x 0 4 8 12 y 0 3 6 9
Answer:
3/4
Step-by-step explanation:
As y is changing by 3, x is changing by 4
help meeeeeeeeee pleaseee !!!!!
The composite functions are evaluated and simplified as:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3x² + 15
How to Evaluate a Composite Function?To evaluate a composite function, the inner function is evaluated first using the given input. After then, the output of the inner function is used as the input to evaluate the outer function.
Given the following:
f(x) = x² + 5g(x) = 3xTherefore:
a. (f o g)(x) = f(g(x))
Substitute g(x) for x into f(x) = x² + 5
f(g(x)) = (3x)² + 5
Simplify the function
f(g(x)) = 9x² + 5
b. (g o f)(x) = g(f(x))
Substitute f(x) for x into g(x) = 3x:
g(f(x)) = 3(x² + 5)
Simplify the function
g(f(x)) = 3x² + 15
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For each equation, choose the statement that describes its solution. If applicable, give the solution.
w=2
All real numbers are solutions
1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.
2) Let's begin with the first one, top to bottom
[tex]\begin{gathered} 2(w-1)+4w=3(w-1)+7 \\ 2w-2+4w=3w-3+7 \\ 6w-2=3w+4 \\ 6w-3w=4+2 \\ 3w=6 \\ \frac{3w}{3}=\frac{6}{3} \\ w=2 \end{gathered}[/tex]Note that we distributed the factors outside the parenthesis over the terms inside.
So for the first one, we can check w=2
3) Moving on to the 2nd equation, we can state:
[tex]\begin{gathered} 6(y+1)-10=4(y-1)+2y \\ 6y+6-10=4y-4+2y \\ 6y-4y-2y=4-4 \\ 6y-6y=0 \\ 0y=0 \end{gathered}[/tex]So, there are infinite solutions for this equation, or All real numbers are solutions
From the origin of the coordinate plane, how many units does one travel along the y-axis to find the point with the coordinates (1,8)?
Solution:
Let's recall that in a coordinate plane, we consider (0, 0) as the origin because this is the point where the x and y-axes intersect.
Therefore, the unit you travel along the y-axis from the origin is:
8 - 0 = 8 (Value of y given - Value of y at the origin)
The answer is 8 units
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Polly surveyed 850 teenagers to find out their favorite type of music she found that 32% of teenagers to Vader like hard rock how many Teenage evade light Hard Rock
The survryed was on 850 teenagers
Number of teenage that evade light hard rock = 32% of 850
=32/100 x850
=272