Betty has a sister named Anne. Betty's sister, Anne, is 3 years younger than twice Betty's age.

Write an equation to represent the relationship between Anne's age and Betty's age. Let a represent Anne's age and b represent Betty's age.

Answer:

Step-by-step explanation:

[tex]-17(y-2)=-17y+64\qquad\text{use the distributive property}\\\\(-17)(y)+(-17)(-2)=-17y+64\\\\-17y+34=-17y+64\qquad\text{add}\ 17y\ \text{to both sides}\\\\-17y+17y+34=-17y+17y+64\\\\34=64\qquad\bold{FALSE}\\\\\bold{CONCLUSION:}\ \large\boxed{\text{no solution}}[/tex]

The equation -17(y-2)=-17y+64 have no solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

-17(y-2)=-17y+64

Now solving for y

-17y + 34= -17y + 64

0 = 30

As, there no variable left for which we have to find the value.

Hence, the equation have no solution.

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Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = 25

Then you square root 25 and that is 5

Answer:

[tex]\displaystyle \frac{5x}{8y^{4}}\sqrt{x}[/tex]

Step-by-step explanation:

Simplfy in Algebra

We have the following expression

[tex]\displaystyle E=\sqrt{\frac{25x^9y^3}{64x^6y^{11}}}[/tex]

Simplifying like factors in the denominator and numerator

[tex]\displaystyle E=\sqrt{\frac{25x^3}{64y^{8}}}[/tex]

All the factors are perfect squares except [tex]x^3[/tex], thus we rewrite:

[tex]\displaystyle E=\sqrt{\frac{25xx^2}{64y^{8}}}[/tex]

Taking the square root of all the perfect square factors:

[tex]\boxed{\displaystyle E=\frac{5x}{8y^{4}}\sqrt{x}}[/tex]

Answer:

D On edge.

Step-by-step explanation:

Its Very Simple i Took it just now :D

Answer:

6:5

Step-by-step explanation:

because 30 and 36 can both be divided by 6;

36/6= 6

30/6= 5

so the ratio is 6 to 5

The ratio of 36 nickels to 30 dimes, reduced to its lowest terms, is 6:5.

To write the comparison of 36 nickels to 30 dimes as a ratio reduced to its lowest terms, we need to find the greatest common divisor (GCD) of 36 and 30 and then divide both numbers by the GCD.

Step 1: Find the GCD of 36 and 30:

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.

The common factors are 1, 2, 3, and 6. The greatest common divisor (GCD) is 6.

Step 2: Divide both numbers by the GCD (which is 6):

36 ÷ 6 = 6

30 ÷ 6 = 5

The reduced ratio is 6:5.

So, the ratio of 36 nickels to 30 dimes, reduced to its lowest terms, is 6:5.

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Answer:

28 degrees

Step-by-step explanation:

step 1

Find the measure of angle 1

[tex]m\angle 1+65^o=180^o[/tex] ----> by supplementary angles

[tex]m\angle 1=180^o-65^o=115^o[/tex]

step 2

Find the value of x

[tex](10x+5)^o=m\angle 1[/tex] ----> by corresponding angles

substitute

[tex](10x+5)^o=115^o[/tex]

[tex]10x=110\\x=11[/tex]

step 3

Find the measure of angle 2

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

[tex]m\angle 1+m\angle 2+(4x-7)^o=180^o[/tex]

substitute

[tex]115^o+m\angle 2+(4(11)-7)^o=180^o[/tex]

[tex]m\angle 2=180^o-152^o=28^o[/tex]

Answer:

C

Step-by-step explanation:

f(x) = 3x + 5

Let y = 3x + 5

3x = y - 5

x = y/3 -5/3

The inverse of the function is

g(x) = x/3 - 5/3

Answer:

see explanation

Step-by-step explanation:

Using the sine ratio in right Δ ACD and the exact value

sin30° = [tex]\frac{1}{2}[/tex]

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AD}{AC}[/tex] = [tex]\frac{y}{150}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 150 ( divide both sides by 2 )

y = 75

----------------------------------------------------------------------

Using the tangent ration in right Δ ABD and the exact value

tan60° = [tex]\sqrt{3}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{BD}[/tex] = [tex]\frac{y}{z}[/tex] = [tex]\frac{75}{z}[/tex] = [tex]\sqrt{3}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] z = 75 ( divide both sides by [tex]\sqrt{3}[/tex] )

z = [tex]\frac{75}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{75\sqrt{3} }{3}[/tex] = 25[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Unit rate means one, if you buy 1 donuts you pay $0.60 for it, if you buy 12 you pay 5.88÷12=$0.49 per donut. The difference between them is 0.60-0.49=$0.11

Answer:

Step-by-step explanation:

The total surface area is 125 square yards.

The base area is 37.5 square yards.

Hence, the area of the curved surface is 125 - 37.5 = 87.5 square yards.

According, to the formula, the area of the curved surface is [tex]\frac{5}{2} \times bs[/tex], where b is the base length and s = slant height.

Here, it is given that b = 5 yards.

Thus, [tex]\frac{5\times5\times s}{2} = 87.5\\s = 7[/tex].

Answer:

Sample Response: First, draw and label a net of the pyramid. The triangular faces have a base of 5 yards and a height of 12 yards. Find the area of each of the faces. The square base has an area of 25 yd2. Each of the triangular faces has an area of 30 yd2. Add the areas together to find the surface area: 25 + 30 + 30 + 30 + 30 = 145 yd2.

Step-by-step explanation:

(❁´◡`❁):-P(✿◡‿◡)

Answer:

x=6

Step-by-step explanation:

The equation is 2/3x=4. So to get x alone we divide 2/3x by 2/3 and we divide 4/(2/3) because we have to do the same to both sides. So we end out with x=6. To check our work, we can do 2/3 * 6 and we get 4

Answer:

It means that it divides into two equal parts

Answer:x•0.70=y

Step-by-step explanation:

Answer:

0.30x

Step-by-step explanation:

Answer:

Let j =1

Step-by-step explanation:

9j+21+3j= 3(3j+j+7)

9j+21+3j=9j+3j+21

Since j=1,

9+21+3=9+3+21

Therefore both equations are equivalent

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Answer:

the gradient of the line is 4

Answer:

25 boys.

Step-by-step explanation:

To solve this problem, first add the two parts of the ratio. 9 + 5 = 14. Then divide 70 by 14 to get 5. Since the total is 5 times the ratio total, multiply both sides of the ratio by 5. The result is 45 : 25. If you add them together, you get a total of 70. Therefore, there are 25 boys in the class.

Answer:

There are 25 boys in the class.

Step-by-step explanation:

9-5

9-5=18-10

9-5=27-15

9-5=36-20

9-5=45-25

45+25=70

Answer:$58.50

Step-by-step explanation:

The price was 130

With 40% off

Which reads out in this format

40/100*130= 52 dollars off the real price

130-52=78 dollars

Then later reduce by 25 percent

Now the price is 78 dollars

25/100*78= 19.5 dollar off the new price

So the real price will be

78-19.5=$58.5

Solving [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex] we get [tex]x=\frac{77}{52}[/tex]

Step-by-step explanation:

We need to solve the problem: [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex]

Solving:

[tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)\\\frac{9}{4}(4x-1)=\frac{8}{5}(1+4x)\\9x-\frac{9}{4}=\frac{8}{5}+\frac{32x}{5}[/tex]

Add 9/4 on both sides:

[tex]9x-\frac{9}{4}+\frac{9}{4}=\frac{8}{5}+\frac{32x}{5}+\frac{9}{4}[/tex]

[tex]9x=\frac{8}{5}+\frac{9}{4}+\frac{32x}{5}\\9x-\frac{32x}{5}=\frac{8}{5}+\frac{9}{4}\\\frac{9x*5-32x}{5}=\frac{8*4+9*5}{20}\\\frac{45x-32x}{5}=\frac{32+45}{20}\\\frac{13x}{5}=\frac{77}{20}\\x=\frac{77}{20}\times \frac{5}{13}\\x=\frac{77}{4*13}\\x=\frac{77}{52}[/tex]

So, Solving [tex]2\frac{1}{4}(4x-1)=1\frac{3}{5}(1+4x)[/tex] we get [tex]x=\frac{77}{52}[/tex]

Keywords: Solving Fractions

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Answer:

238 is the answer

Step-by-step explanation:

68 percent of 350 is 238

                                         -DH

The number preferred to vacation in Florida is 238.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that, of the 350 people surveyed recently in New York, 68% said they prefer to vacation in Florida.

The number of people will be calculated as,

N = 68% of 350

N = ( 68 x 350 ) /100

N = 238

Therefore, the number preferred to vacation in Florida is 238.

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Answer:

therefore for direct variation that will include the point (4, 16) is  y = 4x

Step-by-step explanation:

i) for direct variation we can say that y = k [tex]\times[/tex] x

ii) substituting the given values of x and y into the equation in i) we get

16 = k [tex]\times[/tex] 4

Therefore  k  = [tex]\frac{16}{4}[/tex] = 4

iii) therefore for direct variation that will include the point (4, 16) is  y = 4x

Answer:

1. 6x + 2y = 25.92

4x + 3y = 33.93

2 the site charges $0.99 for a song and $9.99 for an album.

Step-by-step explanation:please see attachment for explanation

Answer:

Two

Step-by-step explanation:

If you have one and added one you have two

Answer:

4 Because that’s what you get when you add them together

Answer:

2130 feet per hour

Step-by-step explanation:

462*60; because your trying to find out how many feet per hour so you have to multiply 462 inches by 60 minutes because 60 minutes= 1 hour.

462*60= 27720

27720/12; because you want to find out how many feet and not inches, so you have to divide 27720 by 12 because there is 12 inches in one foot.

27720/12= 2130

so your answer is 2130 feet per hour. Hope this helps :D

Answer:

No solution.

Step-by-step explanation:

4x + 16y = -19

-2x – 8y = 10         Multiply this equation by 2:

-4x - 16y = 20      Add this equation to the first equation:

0  +    0   = 1

0 = 1

This is absurd so there are no solutions.

Answer:

The first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

Step-by-step explanation:

A dilation is said to be a transformation which generates an image that is the same shape as the original object, but has a different size.

If the scale factor is greater than 1, then the image will be enlarged. In other words,

If the scale factor is greater than 0 but less than 1, then the image will be reduced. In other words,

Considering the quadrilateral with the vertices (-6, 0), (0, 6), (6, 0) and (0, -6).

According to dilation rule, when a figure is dilated by a scale of factor of 1/3, the the coordinates of that point are multiplied by 1/3. So,

(x, y) → (1/3x, 1/3y)

So, lets apply this on the quadrilateral with the vertices  (-6, 0), (0, 6), (6, 0) and (0, -6).

For (-6, 0)

(x, y) → (1/3x, 1/3y) = (-6, 0) → (-2, 0)

For (0, 6)

(x, y) → (1/3x, 1/3y) = (0, 6) → (0, 2)

For (6, 0)

(x, y) → (1/3x, 1/3y) = (6, 0) → (2, 0)

For (0, -6)

(x, y) → (1/3x, 1/3y) = (0, -6) → (0, -2)

So, the image rectangle will have the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

Therefore, the first picture corresponds the correct dilation by a scale of factor of 1/3 as the image rectangle is reduced and has the coordinates (-2, 0), (0, 2), (2, 0), and  (0, -2) after a rectangle is dilated by a scale of factor of 1/3.

So, correct picture is also attached below.

Keywords: dilation, transformation, quadrilateral

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Answer:

(x - 3)² = - (y - 14)

The maxima of the function is (3,14).

Step-by-step explanation:

The formula of a quadratic function is given by y = - x² + 6x + 5

We have to write this in the vertex form.

Now, y = - x² + 6x + 5

⇒ y = - (x² - 6x + 9) + 9 + 5

⇒ y - 14 = - (x - 3)²

⇒ (x - 3)² = - (y - 14)  

This is the equation of the parabola in vertex form.

This parabola has the vertex at (3,14) and the axis of the parabola is parallel to the negative y-axis.

Therefore, the maxima of the function is at (3,14). (Answer)

Answer:

2x + y - 6 = 0

OR 2x + y = 6

Step-by-step explanation:

First write the equation given in the problem:

y = -2x + 6        This is in slope-intercept form (y = mx + b).

Standard form is written Ax + By + C = 0. When C is a negative number, you might also see it as Ax + By = -C.

The main difference between the two forms in that slope-intercept form isolates the 'y' whereas standard form equates to 0. Don't confuse the 'b' in standard from with the 'B' in slope-intercept form.

To convert from slope-intercept form to standard form, move everything over to the side with 'y'. When you move something, you do its reverse operation to the whole equation. (The reverse of addition is subtraction, the reverse of multiplication is division.)

y = -2x + 6         Do the reverse operations for -2x and +6

y + 2x - 6 = -2x + 2x + 6 - 6      Add 2x and subtract 6 on both sides

y + 2x - 6 = 0            Right side cancels out to be '0'.

2x + y - 6 = 0       Rewrite with the 'x' in front of the 'y'

Here you can see the new equation and what each variable in Ax + By + C = 0 is.

A = 2

B = 1              When a number is not written with the variable, it is 1.

C = -6

Some teachers ask it to be rewritten as Ax + By = -C when 'C' is a negative number.

2x + y = 6

The word problem 'A number x multiplied by 25 is 320' translates into the equation 25x = 320. Solving for 'x' by dividing both sides by 25 yields x = 12.8.

The question asks to write the word sentence as an equation, and then solve it. The word problem 'A number x multiplied by 25 is 320' can be written as the equation 25x = 320. To solve for 'x', we need to isolate 'x' by dividing both sides of the equation by 25. Thus, x equals 320 divided by 25, giving us x = 12.8 as the solution.

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Final answer:

The word sentence 'A number x multiplied by 25 is 320' can be translated into the equation 25x = 320. By dividing both sides by 25, we solve for x, which results in x = 12.8.

Explanation:

To translate the word sentence 'A number x multiplied by 25 is 320' into an equation, we use the symbol '*' for multiplication and '=' to denote equality, resulting in the equation 25x = 320. To solve for x, we divide both sides of the equation by 25:

x = 320 / 25

This gives us:

x = 12.8

Therefore, the number x is 12.8.

Answer: y - 4x + 11 = 0

Step-by-step explanation:

Formula

             y₂ - y₁

y -  y₁ =  ---------     ₓ  ( x - x₁ )

             x₂ - x₁

y - y₁ = 4( x - x₁ )

substitute for the coordinate of x and y

y - (-3) = 4( x - 2 )

y + 3 = 4x - 8

      y = 4x - 8 - 3

     y = 4x - 11

The equation now becomes

   y - 4x + 11 = 0

Answer:103/6

Step-by-step explanation:

All numerators above least common denominators 6

108-3-2/6

Calculate difference

103/6