Answer:
6480
Step-by-step explanation:
6^4x5
Answer:
3750
Step-by-step explanation:
Hey there!
To solve this we must first make this into an equation
[tex]6x^4\\x=5\\6(5)^4\\6(625)\\3750[/tex]
171 is 0.9% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 171, slightly less than 171, slightly greater than 171, or a lot greater than 171? Explain. 171 is 0.9% of?
171 is 0.9% of 19000
Explanation:let the unknown number be = y
0.9% * y = 171
0.9% = 0.009
0.009 × y = 171
0.009y = 171
DIvide both sides by 0.009:
0.009y/0.009 = 171/0.009
y = 19,000
Hence, 171 is 0.9% of 19000
We would expect the answer to be a lot greater than 171 because the percentage is quite small (less than 1%). Divindg a number by a very small decimal makes the result large.
Hence, the number would be large.
Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.
Explanation:
The given information is
m∠4 = m∠2
m∠5 = m∠3
m∠DBE = 180
The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation
m∠4 + m∠1 + m∠5 = m∠DBE
But, we know that m∠DBE = 180, so by transitivity, we get:
m∠4 + m∠1 + m∠5 = 180
Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get
m∠2 + m∠1 + m∠3 = 180
Therefore, we can change the order by the commutative property to get
m∠1 + m∠2 + m∠3 = 180
Answer:
So, the answer is
If a full air container has a volume of 2.3 m3, and 78.1 % of that air is nitrogen, what is the volume of nitrogen in the container. Quote your answer to an appropriate number of significant figures.
The amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
From the data given:
The total volume of the air container = 2.3 cubic meters
78.1 % is nitrogen.
The amount of nitrogen = 78.1 % of 2.3
= (78.1/100)x2.3
= 1.7963 cubic meters
The number 1.7963 to three Significant Figures is 1.80
The amount of nitrogen = 1.80 cubic meters
Thus, the amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
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If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 32 when x = 20
The constant of variation is 1.6, and then the direct variation equation is:
y = 1.6*x
How to find the constant of variation?A direct variation between two variables can be written as:
y = k*x
Where k is called the constant of variation.
Here we know that when x = 20, the value of y is 32, replacing that in the above equation we get:
32 = k*20
Solving this for k we get:
32/20 = k = 1.6
Then the equation is:
y = 1.6*x
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Jake drew a rectangle ABCD. He will transform the rectangle by using the translation (x,y) -> (x+5, y-1).What would be the coordinate of A after the translation?
c) (1,0)
1) In order to perform this translation firstly, locate point A in the graph. A is at (-4, 1).
2) Secondly, apply the given rule for this translation for this point.
Pre-image rule Image
(-4,1) (x+5, y-1) (-4+5, 1-1)= (1, 0)
Since the question just asks us A' then We can stop it here and say A' will be at (1,0)
3) So A', is going to be located at point ( 1,0)
I am trying to simplify a composition of functions.(f o g) (7.5)f(x) = -x + 7f(g) = -4x -2
There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have
[tex]\begin{gathered} (f\circ g)(x)=-(-4x-2)+7 \\ (f\circ g)(x)=4x+2+7 \\ (f\circ g)(x)=4x+9 \end{gathered}[/tex]We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get
[tex]\begin{gathered} (f\circ g)(7.5)=4(7.5)+9 \\ (f\circ g)(7.5)=39 \end{gathered}[/tex]The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got
[tex]\begin{gathered} g(7.5)=-4(7.5)-2 \\ g(7.5)=-32 \\ \Rightarrow\Rightarrow f(-32)=-(-32)+7=39 \end{gathered}[/tex]This question is stunning me. It wasn’t taught to me in math class.
The next three terms of the following sequences are:
7. The next three terms are 2, 2, and 3.
8. The next three terms of the sequence are 4, 8, and 16.
9. The next three terms of the sequence are 3, 6, and 9.
10. The next three terms of the sequence are 1, 2, and 3.
7.
Consider the recursive formula,
f( 0 ) = 3, f( n ) = f( n - 1 ) + ( n - 2 )
The next three terms of the sequence will be n = 1, 2, and 3.
Then,
f( 1 ) = f( 1 - 1 ) + ( 1 - 2 )
f( 1 ) = f(0) - 1 = 3 - 1 = 2
The second term of the sequence,
f( 2 ) = f( 2 - 1 ) + ( 2 - 2 )
f( 2 ) = f( 1 ) + 0
f( 2 ) = 2
The third term,
f( 3 ) = f( 3 - 1 ) + ( 3 - 2 )
f( 3 ) = f( 2 ) + 1
f( 3 ) = 2 + 1 = 3
8.
Consider the recursive formula,
f( 1 ) = 2, f(n ) = 2f( n - 1 )
The next three terms of the sequence will be n = 2, 3, 4.
Therefore,
f( 2 ) = 2f( 2 - 1 )
f( 2 ) = 2( f (1) )
f( 2 ) = 4
f( 3 ) = 2f( 3 - 1 )
f( 3 ) = 2f( 2 )
f( 3 ) = 8
f( 4 ) = 2f( 4 - 1 )
f( 4 ) = 2f( 3 )
f( 4 ) = 16
Hence, the next three-term are 4, 8, and 16.
9.
Consider the recursive formula,
f( 0 ) = 0, f( n ) = f( n - 1 ) + 3
The next three terms of the sequence will be n = 1, 2, 3.
Then,
f( 1 ) = f( 1 - 1 ) + 3
f( 1 ) = 0 + 3 = 3
f( 2 ) = f( 2 - 1 ) + 3
f( 2 ) = 3 + 3 = 6
f( 3 ) = f( 3 - 1 ) + 3
f( 3 ) = f( 2 ) + 3
f( 3 ) = 6 + 3 = 9
10.
Consider the recursive formula,
f( 0 ) = 1, f( 1 ) = 1, f( n ) = f( n - 1) + f( n - 2 ), for n > 1
Then, the next three terms will be n = 2, 3, 4
f( 2 ) = f( 2 - 1 ) + f( 2 - 2 )
f( 2 ) = f( 1 ) + f( 0 )
f( 2 ) = 1 + 0 = 1
f( 3 ) = f( 3 - 1 ) + f( 3 - 2 )
f( 3 ) = f( 2 ) + f( 1 )
f( 3 ) = 1 + 1 = 2
f( 4 ) = f( 4 - 1 ) + f( 4 - 2)
f( 4 ) = f( 3 ) + f( 2 )
f( 4 ) = 2 + 1
f( 4 ) = 3
The next three terms of the sequence are 1, 2, and 3.
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The website for Company A receives 8 * 10 ^ 6 visitors per year. The website for Company B receives 4 * 10 ^ 3 visitors per year. Determine how many times more visitors per year the website for Company A receives than the website for Company B.
1) Let's find out how many times there are more visitors by dividing the number of visitors from A by B's visitors:
Dividing firstly 8 by 4, and then using the exponents pro
[tex]undefined[/tex]Which statement about this equatiin is true? 3+x=2-3x
1. The equation has no solution
2. The equation has one solution
3. The equation has infinitely many solutions
The equation has only one solution.
What is solution of equation?Equation solutions are numerical numbers that meet the requirements of the equation. When our answers are used to replace the variables in the equations, true assertions are obtained.
A mathematical equation proves the equality of two expressions. There is a mathematical formula: 4 + 4 = 8. A mathematical formula that has one or more variables is called an algebraic equation. Therefore, (2x + 5 = 35) is a linear equation with one variable. Its graph is a straight line, and its first-degree variable is (x).
Given
3+x = 2-3x
3-2 = -3x - x
1 = -4x
x = -1/4
Hence, x has only one value.
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How many times can 2/7 be subtracted from 6/7
Answer:
Exactly three times.
Step-by-step explanation:
(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3
Ximena needs to order some new supplies for the restaurant where she works. The restaurant needs at least 333 spoons. There are currently 255 spoons. If each set on sale contains 6 spoons, which inequality can be used to determine
s
s, the minimum number of sets of spoons Ximena should buy?
In linear equation, Joshua should buy is 255 + 6s ≥ 333.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let the sets of spoons be represented by s
The restaurant needs at least 333 spoons.
Each set on sale contains 8 spoons
There are currently 333 spoons.
At least as an inequality is ≥
Hence:
255 + 6 × s ≥ 333
255 + 6s ≥ 333
Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is
255 + 6s ≥ 333
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Maureen measured a house and its lot and made a scale drawing. The scale she used was
1 inch 8 feet. If the actual length of the house's driveway is 24 feet, how long is the
driveway in the drawing?
The most appropriate choice for unitary method will be given by-
Length of driveway in the drawing is 3 inch
What is unitary method?
Unitary method is the method in which value of a single unit can be calculated from the value of a multiple unit and value of a multiple unit can be calculated from the value of a single unit.
Sometimes value of single unit is less than value of multiple unit
For example - cost of food and quantity of food
Sometimes value of single unit is more than value of multiple unit
For example- Number of men and time taken by those men to do a work
Here,
Scale used by Maureen is 1 inch = 8ft
Actual length of house's driveway = 24 feet
8 ft of room is equal to 1 inch on scale
1 ft of room is equal to [tex]\frac{1}{8}[/tex] inch on scale
24 feet of room is equal to [tex]\frac{1}{8} \times 24[/tex] inch on scale
24 feet of room is equal to 3 inch on scale
Length of driveway in the drawing is 3 inch
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The graph of a function is shown below.Find one value of x for which f(x) = -3 and And /(o).
The graph of a function is given.
When the function of x is -3, that is
[tex]f(x)=-3[/tex]That means the input value which is x, gives us negative 3.
Looking at negative 3 from the graph, the value of x where the graph equals negative 3 (on the vertical axis, or y-axis) is either negative 2 or 1. That is
Also, when the input of the function is zero, then you'll have the output as
[tex]f(0)=1[/tex]This means when the value of x is zero, then the output as shown on the graph is 1 (that is the graph touches the y-axis at 1)
Therefore;
(a) One value of x for which f(x) = -3 is -2 (OR 1)
(b) f(0) = 1
Which statement about the following equation is true?
2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.
Answer:
The discriminant is greater than 0, so there are two real roots.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.2 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\If $b^2-4ac > 0 \implies$ two real roots\\If $b^2-4ac=0 \implies$ one real root\\If $b^2-4ac < 0 \implies$ no real roots\\\end{minipage}}[/tex]
Given equation:
[tex]2x^2-9x+2=-1[/tex]
Add 1 to both sides of the equation so that the equation equals zero:
[tex]\implies 2x^2-9x+2+1=-1+1[/tex]
[tex]\implies 2x^2-9x+3=0[/tex]
Compare the equation with ax²+bx+c=0:
a = 2b = -9c = 3Substitute the values of a, b and c into the discriminant formula and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(-9)^2-4(2)(3)\\&=81-4(2)(3)\\&=81-8(3)\\&=81-24\\&=57\end{aligned}[/tex]
As 57 > 0, the discriminant is greater than zero, so there are two real roots.
Answer:
B on Edge 23
Step-by-step explanation:
trust me bro
greatest to least -4.081, -4.018, -5.3, -5.043
Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter
Explanation:
Taking into account the law of cosines, we can write the following equation:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Then, replacing the values for a, b, and c, we get:
[tex]\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}[/tex]Solving for cos A, we get:
[tex]\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ \frac{-15}{-24}=\frac{-24\cos A}{-24} \\ 0.625=\cos A \end{gathered}[/tex]Therefore, the value of angle A is:
[tex]\begin{gathered} \cos ^{-1}(0.625)=A \\ 51.3=A \end{gathered}[/tex]Now, we can use the law of sines, we can write the following equation:
[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]So, replacing the values and solving for B, we get:
[tex]\begin{gathered} \frac{\sin B}{2}=\frac{\sin 51.3}{5} \\ \sin B=\frac{\sin 51.3}{5}\times2 \\ \sin B=0.3121 \\ B=\sin ^{-1}(0.3121) \\ B=18.2 \end{gathered}[/tex]In the same way, Angle C is equal to:
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \frac{\sin C}{6}=\frac{\sin 51.3}{5} \\ \sin C=\frac{\sin51.3}{5}\times6 \\ \sin C=0.9365 \\ C=\sin ^{-1}(0.9365) \\ C=69.5 \end{gathered}[/tex]So, the answers are:
A = 51.3°
B = 18.2°
C = 69.5°
please answer this question
It's important to know that similar figures have equal angles, for example, if two triangles are similar, then their corresponding angles are congruent.
Having said that, D is true because all rectangles have equal angles.
Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $118,500 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions.
What is Richard’s net pay for the week if he earns $2,200?
Richard’s net pay for the week if he earns $2,200 is equal to $1,797.65.
How to calculate net pay?Mathematically, net pay can be calculated by using this formula:
Net pay = Gross pay - Deductions.
First of all, we would determine Richard's Medicare tax and Social Security tax on $1,000 as follows:
Medicare tax = $2,200 × 1.45/100
Medicare tax = $31.9
Social Security tax = $1,000 × 6.2/100
Social Security tax = $62
Since Richard claims 2 exemptions and paid weekly, we would calculate the withholdings from his weekly pay by using the information provided in Table 1 (see attachment):
Two (2) exemptions = $76.9 × 2 = $153.8
Withholdings = $2,200 - $153.8
Withholdings = $2046.2
Since Richard claims to be married, we would calculate his federal tax withholdings by using the information provided in Table 1 (see attachment):
Over $1,606 = $198.40 plus 25%
= $2046.2 - $1,606 = $440.2
Federal tax withholdings = $198.40 + (25/100 × $440.2)
Federal tax withholdings = $198.40 + $110.05
Federal tax withholdings = $308.45
Now, we can calculate Richard's net pay as follows:
Richard's net pay = Gross pay - Medicare tax - Social Security tax - Federal tax withholdings
Richard's net pay = $2,200 - $31.9 - $62 - $308.45
Richard's net pay = $1,797.65
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In 2000, the profit of Company A was $9,875,000. Each year after 2000, the profits fell by $29,532 on average. Construct a linear model for this scenario and use it to solve for profits in the year 2030.
Given:
In 2000, the profit of Company A was $9,875,000.
Each year after 2000, the profits fell by $29,532 on average.
So, the losses of the profit per year = $29,532
We will construct a linear model for this scenario
Let the number of years after 2000 = x
And the profit after the year 2000 = y
the linear model will be: y = mx + b
Where m is the slope which represents the losses per year and the b is the initial profit of the year 2000
So, the linear model will be:
[tex]y=-29,532x+9,875,000[/tex]now, we will use the equation to find the profit in the year 2030
so, x = 2030 - 2000 = 30
substitute x = 30 into the equation:
[tex]y=-29,532(30)+9,875,000=8,989,040[/tex]So, the answer will be:
The equation of the model: y = -29532x + 9875000
The profit in the year 2030 = 8989040
Find the coordinate point for that would make ABCD a rhombus. Answer Choices: (3,5), (5,1), (1,1), (3,4)
A rhomus has te following shape:
therefore, the top part is missing, if we analyze, it should be 5 on the y axis and 3 on the x axis.
Answer: (3,5)
Patsy’s pizza sells one 20-inch cheese pizza or two 12-inch cheese pizzas for 11.99. Determine which size gives more pizza (A= 3.14r^2)
Since 20-inch pizza, means it is a circle with a diameter of 20 inches
Since the diameter is twice the radius, then
The raduis = 20/2 = 10 inches
Then the area of it is
[tex]\begin{gathered} A_1=\pi(r)^2 \\ A_1=3.14(10)^2 \\ A_1=3.14(100) \\ A_1=314 \end{gathered}[/tex]The area of the first pizza is 314 square inches
Since the diameter of the other area is 12 inches, then
The radius = 12/2 = 6 inches
Then the area of it is
[tex]\begin{gathered} A_2=3.14(6)^2 \\ A_2=3.14(36) \\ A_2=113.04 \end{gathered}[/tex]Then the area of the second pizza is 113.04 x 2 = 226.08 square inches
Since the area of the first offer is greater than the area of the second offer, then
The first size gives more pizza
Which numbers are irrational numbers?
Select each correct answer.
Responses
110−−√
square root of fraction 1 over 10 end fraction
116−−√
square root of fraction 1 over 16 end fraction
14√
square root of fraction 1 over 4 end fraction
12√
square root of fraction 1 over 2 end fraction
18√
square root of fraction 1 over 8 end fraction
Answer:Here I hope this helps
1/10=irrational
1/16=rational
1/4=rational
1/2=irrational
1/8=irrational
Step-by-step explanation: you can go into desmos graphing calculator and plug in each number into the square root and it will tell you if its irrational or not.
Brad stands 30 feet from a tree. He estimates the angle of elevation from a point onthe ground 30 feet from the tree to the top of the tree to be 60° as shown below.60°30 feetWhich of the following is closest to the height of the tree?
To determine the height of tree using trigonometric ratio,
2ax-b=cx+d solve for x
We have to solve the following equation for the variable x:
[tex]2ax-b=cx+d[/tex]For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.
[tex]\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}[/tex]Now, we will factor the variable x, as we want to have just one expression with x, thus:
[tex](2a-c)x=d+b[/tex]And lastly, we will divide both sides by 2a-c, and we obtain:
[tex]x=\frac{d+b}{2a-c}[/tex]Which is the asked expression for x.
1.Emily needs to make party hats in the shape of a cone. Shewants the hat to have a radius of 6 inches and a height of15 inches. What is the volume of the party hat?a) 565.2b) 94.2c) 2260.8d) 188.4
Emily needs to make party hats in the shape of a cone. She
wants the hat to have a radius of 6 inches and a height of
15 inches. What is the volume of the party hat?
a) 565.2
b) 94.2
c) 2260.8
d) 188.4
the volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
pi=3.14
r=6 in
h=15 in
substitute
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot6^2\cdot15 \\ V=565.2\text{ in3} \end{gathered}[/tex]answer is option A
If h(x) = 2x and k(x) =2x -k, what is h(k(x))?
If h(x) = 2x and k(x) =2x -k, then h(k(x)) would be:
h(k(x))= 2*(2x-k)
h(k(x))= 4x - 2k Using distributive property
Final answer is: h(k(x))= 4x - 2k
please help me I’m really not understanding this my answer was completely wrong
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the table, we can see that:
Gross profit for Q 1 = 85 x 1000= 85,000
Gross profit for Q 2= 94 x 1000 = 94, 000
Hence the increase in Gross profit = 94,000 - 85,000 = 9000
Then,
[tex]\begin{gathered} \text{Percentage change = }\frac{9000}{85000}\text{ x 100} \\ =\frac{900000}{85000} \\ =\text{ 10}.58823529 \\ \approx\text{ 10. 6 \% ( to the nearest tenth )} \end{gathered}[/tex]CONCLUSION:
The percent change = 10. 6 % ( to the nearest tenth)
help meee
solve for system of equations with steps shown please
1.
x+4y=0
3x+2y= 20
2.
6x+3y=54
2x+y=18
3.
x-3y=-2
10x+8y=-20
4.
3x-y=-8
5x+2y=5
The solutions to the equations are :
1. x= 8 ; y = -2
2.infinitely many solutions.
3. x= - 2 ; y = 0
4. x= -1 ; y = 5
How are the equations solved?
1. x+4y=0 --(1)
3x+2y= 20 ---(2)
(1)*3
3x+ 12y =0 ---(3)
(3) - (2)
(3x+ 12y) -(3x+2y -20)
10y +20= 0
10 y = -20
y = - 2
Substituting y in equation(1)
x+ 4 (-2) = 0
x = 8
The solutions to the equations are x= 8 and y = -2
2. 6x+3y=54 --(1)
2x+y=18 ----(2)
(2)*3
6x+3y=54 --(3)
(3) = (1)
0 = 0
The equations have infinitely many solutions.
3. x -3y= -2 --(1)
10x+8y=-20 ---(2)
(1)*10
10x - 30y +20 = 0--(3)
(3) - (2)
(10x - 30y +20 )- (10x+8y +20)
-38y = 0
y = 0
Substituting y in equation(1)
x - 0 = -2
x = -2
The solutions to the equations are x= - 2 and y = 0
4.
3x-y=-8 ---(1)
5x+2y=5 ---(2)
(1)*2
6x -2y+16 =0---(3)
(3) +(2)
(6x -2y+16) +(5x+2y-5)
11x +11 = 0
11x = -11
x = -1
Substituting x in equation(1)
3(-1) -y = -8
-3- y = - 8
- y = -8+3
-y = -5
y = 5
The solutions to the equations are x= -1 and y = 5
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the trapezoids shown below are similar. find Y
Since it is given that trapezoids are similar so,
[tex]\begin{gathered} \frac{y}{25}=\frac{12}{15} \\ y=\frac{4}{5}\times25 \\ y=20 \end{gathered}[/tex]So value of y is 20.
3 cookies and 5 brownies cost $19; 2 cookies and 10 brownies cost $26. How much do 13 cookies and 6 brownies cost?
ANSWER
$51
EXPLANATION
Let the cost of one cookie be c.
Let the cost of one brownie be b.
3 cookies and 5 brownies cost $19. This means that:
3 * c + 5 * b = 19
3c + 5b = 19 ___(1)
2 cookies and 10 brownies cost $26. This means that
2 * c + 10 * b = 26
2c + 10b = 26 ____(2)
We have two simultaneous equations:
3c + 5b = 19 ___(1)
2c + 10b = 26 ____(2)
From (2):
2c = 26 - 10b
Divide through by 2:
c = 13 - 5b
Put this in (1):
3(13 - 5b) + 5b = 19
=> 39 - 15b + 5b = 19
Collect like terms:
-15b + 5b = 19 - 39
-10b = -20
Divide through by -10:
b = -20 / -10
b = $2
Remember that:
c = 13 - 5b
=> c = 13 - 5(2)
c = 13 - 10
c = $3
Therefore, one cookie costs $3 and one brownie costs $2.
Therefore, the cost of 13 cookies and 6 brownies is:
13 * 3 + 6 * 2
=> 39 + 12
=> $51
13 cookies and 6 brownies cost $51
