Mackenzie wrote the following paragraph proof for the Vertical Angles Theorem:The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 _________________. Angle 1 is equal to angle 3 by the subtraction property of equality. Which phrase completes the proof?

Answer:

-29, -30, -31, -32, -33

Step-by-step explanation:

add them together

The perimeter of the rectangle:

[tex]P_R=2(4x+2+2x)=2(6x+2)=(2)(6x)+(2)(2)=12x+4[/tex]

The perimeter of the square:

[tex]P_S=2(5x-3+3x+1)=2(8x-2)=(2)(8x)+(2)(-2)=16x-4[/tex]

The perimeter of the rectangle is equal to the perimeter of the square. We have the equation:

[tex]12x+4=16x-4\qquad|\text{subtract 4 from both sides}\\\\12x=16x-8\qquad|\text{subtract 16x from both sides}\\\\-4x=-8\qquad|\text{divide both sides by (-4)}\\\\x=2[/tex]

The side lengths of the square:

[tex]5x-3\to5(2)-3=10-3=7[/tex]

The side lenghts of the rectangle:

[tex]4x+2\to4(2)+2=8+2=10\\2x\to2(2)=4[/tex]

Other method.

If the first figure is a square, then the length of the sides are equal.

Therefore

[tex]5x-3=3x+1\qquad|\text{add 3 to both sides}\\\\5x=3x+4\qquad|\text{subtract 3x from both sides}\\\\2x=4\qquad|\text{divide both sides by 2}\\\\x=2[/tex]

Further part of the solution as above.

The answer is  Credit Report

Answer:

Credit Report fellas!

Step-by-step explanation:

D

the volume (V ) of a cube = s³ ( where s is the length of the side )

here s = 20, hence

V = 20³ = 8000 cm³

Here you go the answers below

A ratio is used to describe how two or more quantities are related. For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:8. This means that for every 2 scoops sugar crystals, there will need to be 8 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 800 ounces of water.

Sure, we'll start off by simplifying the ratio 2:8. Simplifying it gives us 1:4.

Our aim is to find a number, let's denote it by x, such that the ratio 2:x will be the same as 1:4.

To find such an x, we need to set up an equation using the principle of equivalence of ratios. This gives us 2/x = 1/4.

Now we proceed to solve this equation for x. We do this by cross-multiplying the fractions in the equation.

Cross-multiplication gives us 2*4 = x*1. Simplifying this yields 8 = x.

Hence, we can conclude that the number x that makes the ratio 2:x equivalent to 2:8 is 8.

These are the polygons

The transformation of Polygon A to Polygon B could involve translation, rotation, or reflection. Observe differences in position and orientation between the two polygons to identify the type of transformation.

The transformation of a polygon to another can involve a series of moves such as translation (sliding), rotation (turning around a point), or reflection (flipping over a line). By closely comparing the two polyhgons A and B, you can determine which type of transformation has taken place.

For instance, if every point on polygon A has moved in the same direction and distance to form polygon B, a translation has taken place. If polygon B can be obtained by turning polygon A around a point, then a rotation has occurred. If polygon B is a mirror image of polygon A, then it has been reflected.

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By substituting x=1 into the function f(x)=3x5^x, we find that the point (1,15) is on the graph.

To find a point that lies on this graph, we can select a value for x, substitute it into the function, and calculate the corresponding y value. Let's try x=1:

f(1) = 3(1)51 = 3(5) = 15.

Therefore, the point (1,15) is on the graph of f(x)=3x5^x.

what do you mean ¨ what is the distance between¨ what is the rest of the question?

Simplifying

15 + -5(4x + -7) = 50

Reorder the terms:

15 + -5(-7 + 4x) = 50

15 + (-7 * -5 + 4x * -5) = 50

15 + (35 + -20x) = 50

Combine like terms: 15 + 35 = 50

50 + -20x = 50

Add '-50' to each side of the equation.

50 + -50 + -20x = 50 + -50

Combine like terms: 50 + -50 = 0

0 + -20x = 50 + -50

-20x = 50 + -50

Combine like terms: 50 + -50 = 0

-20x = 0

Solving

-20x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '-20'.

x = 0.0

Simplifying

x = 0.0

Answer:

a) 87 double scoops and 113 single scoops.

b) 287 scoops of ice cream.

Step-by-step explanation:

1. You need to make a system of equations, where double scoops are represented by [tex]x[/tex] and the single scoops are represented by [tex]y[/tex]:

[tex]\left \{ {{x+y=200} \atop {1.25x+y=221.75}} \right.[/tex]

2. You can apply the Elimination Method:

- Multiply the first equation by -1 to cancel the variable [tex]y[/tex] from the system. Add both equations:

[tex]0.25x=21.75[/tex]

- Solve for [tex]x[/tex]:

[tex]x=\frac{21.75}{0.25}\\x=87[/tex]

- Substitute the value of [tex]x[/tex] into one of the original equations and solve for [tex]y[/tex]:

[tex]87+y=200\\y=113[/tex]

3. You can calculate the total number of scoops of ice cream that where sold as below:

[tex]2x+y[/tex]

4. Substitute values:

[tex]2(87)+113=287[/tex] scoops of ice cream

Answer:  The number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.

Step-by-step explanation:  Given that at a a summertime poolside snack bar, 200 ice cream scoops were sold in one day.

Double scoops were sold for $1.25 each and single scoops were sold for $1 each. The proceeds from the sale of the cones were $221.75.

We are to find the number of single scoop cones, double scoop cones and the number of scoops of ice cream that sold.

We Let x and y represents the number of cones of single scoop and double scoop ice cream that sold.

Then, according to the given information, we have

[tex]x+y=200\\\\\Rightarrow x=200-2y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]1\times x+1.25y=221.75\\\\\Rightarrow x=221.75-1.25y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Comparing equations (i) and (ii), we get

[tex]200-y=221.75-1.25y\\\\\Rightarrow 1.25y-y=221.75-200\\\\\Rightarrow 0.25y=21.75\\\\\Rightarrow y=\dfrac{21.75}{0.25}\\\\\Rightarrow y=87.[/tex]

From equation (i), we get

[tex]x=200-87=113.[/tex]

Therefore, total number of scoops that were sold is

[tex]113+2\times87=113+174=287.[/tex]

Thus, the number of single scoop cones sold is 113, number of double scoop cones is 87 and the total number of cones sold is 287.

5-(-8) = 5 + 8 =13

As multiplication of two negatives is positive

[tex]\displaystyle\\4^2+7^2+\ldots+(3n+1)^2=\\\\\sum_{k=1}^n(3k+1)^2=\\\\\sum_{k=1}^n(9k^2+6k+1)=\\\\\sum_{k=1}^n9k^2+\sum_{k=1}^n 6k+\sum_{k=1}^n1=\\\\9\sum_{k=1}^nk^2+6\sum_{k=1}^n k+n=\\\\9\left(\dfrac{n(n+1)(2n+1)}{6}\right)+6\left(\dfrac{n(n+1)}{2}\right)+n=\\\\\dfrac{3n(n+1)(2n+1)}{2}+3n(n+1)+n=\\\\\dfrac{3n(2n^2+n+2n+1)}{2}+3n^2+3n+n=\\\\\dfrac{3n(2n^2+3n+1)}{2}+3n^2+4n=\\\\\dfrac{6n^3+9n^2+3n}{2}+\dfrac{6n^2+8n}{2}=\\\\\dfrac{6n^3+15n^2+11n}{2}[/tex]

The mean could increase from 25 to 27.

The mean number of books in each box is 25. If Javier fills two more boxes, one with 26 comic books and one with 30 comic books, the mean could increase or stay the same. Let's calculate the mean with and without the additional boxes:

Mean without additional boxes: (4 boxes * 25 books per box) / 4 = 25

Mean with additional boxes: (6 boxes * 25 books per box + 26 books + 30 books) / 8 = (150 + 26 + 30) / 8 = 27

Therefore, the mean could increase from 25 to 27 if Javier fills two more boxes with 26 and 30 comic books.

3a + 4bc - d = 5a - 8j

Add d to both sides.

3a + 4bc = 5a - 8j + d

Subtract 4bc from each side.

3a = 5a - 8j + d - 4bc

Subtract 5a from both sides.

-2a = -8j + d - 4bc

Divide both sides by -2

a = [tex]\frac{(-8j -4bc + d)}{-2}[/tex]

A=2bc+-1/2d+4j would be your answer

The answer is the speed is less than or equal to 55 mph.

S≤55

Answer:

1. The fixed costs is $40 and the cost per mile is [tex]\$\frac{3}{2}[/tex].

2.Therefore, the coffees did they sell is, 85 coffees

Step-by-step explanation:

1. To find the fixed cost and Cost per mile.

Since, a shipping company charges a fixed amount for their services and a certain amount per mile , they must travel.

Let the number of fixed amount be x and the certain amount per mile be y

then, the general linear equation for this we have:

[tex]x+y=C[/tex] where C is the charges cost by the shipping company.

It is given that for a 50 mile trip company costs $115 and an 80 mile trip costs $157.

we have an equation in linear form from the above data:

[tex]x+50y=\$115[/tex]            .....(1)

[tex]x+80y=\$157[/tex]           ....(2)

Now, solving these equation simultaneously we get,

[tex]y=\frac{3}{2}[/tex]

Substitute the value of y in equation (1),

[tex]x+50\times\frac{3}{2}=\$115[/tex]

[tex]x+75=\$ 115[/tex]

⇒[tex]x=\$40[/tex]

Therefore, the fixed costs is $40 and the cost per mile is [tex]\$\frac{3}{2}[/tex].

2.

Let the hot chocolate sells be x and that of coffee be y.

At one game they sold, $200 worth of drinks and used 295 cups. if hot chocolate sells for $0.75 and coffee sell for $0.50.

An equation from the given condition are given by:

[tex]x+y=295[/tex]

[tex]0.75x+0.50y=200[/tex]

Solving these equation simultaneously we get the value of y=85

Therefore, the coffees did they sell is, 85 coffees

Answer:

x=1.3288 or -1.1288

Step-by-step explanation:

Given [tex]20x^{2}-30=4x[/tex]

    Subtract 4x from both sides

         [tex]20x^{2}-4x-30=0[/tex]

Since we can factor out 2 from whole equation, let's factor out 2.

         [tex]2(10x^{2}-2x-15)=0[/tex]

Divide with 2 on both sides

         [tex]10x^{2}-2x-15=0[/tex]

We got the quadratic equation, we can solve for x using quadratic formula.

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac} } {2a}[/tex]

[tex]x=\frac{2\pm\sqrt{2^{2}-4X10X(-15)} } {2X10}[/tex]

[tex]x=\frac{2\pm\sqrt{604} }{20}[/tex]

[tex]x=\frac{2\pm2\sqrt{151}}{20}[/tex]

[tex]x=1.3288or-1.1288[/tex]

Use the distance formula to find the distance between points C (5,6) and D (2,2).

d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

Plug the corresponding values in to the equation.

d=[tex]\sqrt{(2-5)^2+(2-6)^2}[/tex]

Then simplify the rest of the equation.

d=[tex]\sqrt{(-3)^2+(-4)^2}[/tex]

d=[tex]\sqrt{9+16}[/tex]

d=[tex]\sqrt{25}[/tex]

d=[tex]5[/tex]

The distance of the two points CD is 5.

To find the distance between point C=(5,6) and point D=(2,2), we use the distance formula which results in d=5.0 units rounded to the nearest tenth.

To calculate the distance between point C and point D, we use the distance formula derived from the Pythagorean theorem. The coordinates given are C=(5,6) and D=(2,2). The distance formula is:

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

Substituting the coordinates of points C and D into the formula gives us:

d = √{(2 - 5)² + (2 - 6)²}

This simplifies to:

d = √{(-3)² + (-4)²}

Further simplifying:

d = √{9 + 16}

d = √{25}

Finally, taking the square root of 25:

d = 5

Therefore, the distance between point C and point D, rounded to the nearest tenth, is 5.0 units.

Answer is 71.1 because 0.9 x 079 in a calculator is 71.1

Given function : [tex]y=1.05(1.46)^x[/tex]

We need to identify a " initial amount", b "growth factor", r " rate of growth".

We know, exponential growth formula

[tex]y=a(b)^x[/tex], where a is initial amount, b is growth factor. On comparing with given function let us find values of a and b.

[tex]y=1.05(1.46)^x[/tex] ⇔ [tex]y=a(b)^x[/tex].

We can see a= 1.05 and b = 1.46.

Now, b=1+r.

Therefore, 1+r =1.46.

Subtracting 1 from both sides, we get

1+r-1 =1.46-1

r = 0.46.

On converting 0.46 into percentage, we get

0.46 × 100 = 46.

Therefore, intial amount a = a= 1.05 , growth factor b = 1.46, and the rate of growth r= 46%.

Final answer:

The initial amount, a, is 1.05, and the growth factor, b, is 1.46 in the exponential function y=1.05(1.46)ˣ. The growth rate, r, when expressed as (1+r), is 46%.

Explanation:

To identify the initial amount a and the growth factor b in the exponential function y=1.05(1.46)ˣ, we look at the standard form of an exponential function, which is y=a×bˣ. Comparing this with the given function, we can see that the initial amount a is 1.05 and the growth factor b is 1.46.

To express the growth factor in the form of (1+r), where r is the rate of growth, we can set b = 1 + r. This means that r would be b - 1, which is 1.46 - 1 = 0.46. To express r as a percentage, we multiply by 100, resulting in a growth rate of 46%.

B.) Any temperature change is the original temperature plus the numerical value of the change. (temp + change) If it is an increase, the number will be positive. If it is a decrease, the number will be negative. 

Since there is a decrease of 11, c would be replaced with -11. When you plug this into your expression (85 + c: 85 + -11), the answer to this would be 74.

                                                 hope it helps

Final answer:

Explaining how to define a variable, write an expression, and evaluate the temperature after a decrease in Fahrenheit degrees.

Explanation:

Variable: Let c represent the temperature change.

Expression: To find the new temperature after a decrease of 11°F, the expression is 85 - c.

Evaluation: By substituting c with -11 (decrease of 11°F), 85 - (-11) equals 96°F.

It must be 1.

Factors of prime numbers are 1 or themselves, the only factor common to all prime numbers is 1.

Echy~

The Greatest Common Factor (GCF) of two prime numbers is always 1.

The Greatest Common Factor (GCF) of two prime numbers is always 1 because prime numbers are numbers with only two factors: 1 and themselves.

For example, the GCF of 3 and 5, both prime numbers, is 1 because they do not have any common factors other than 1.

Therefore, when dealing with two prime numbers, the GCF will always be 1.

Zoe will have 210 beads left after making all six of the friendship bracelets.

Zoe has 1500 beads and wants to make 6 friendship bracelets, with 215 beads needed for each bracelet. To find the total number of beads needed for all the bracelets, multiply the beads required for one bracelet (215) by the number of bracelets (6). This equals 1290 beads. To find the number of beads Zoe will have left after making all the bracelets, subtract the total number of beads needed (1290) from the initial number of beads (1500). Therefore, Zoe will have 210 beads left.

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helppppppp with???????

Log explanation below; answer is at bottom.

If the length, l, is 12 units longer than the width, w, then w = l - 12. If the perimeter, p,

p = 2l +2w,

is 7 x w, then

w = p/7

When two things are set equal to the same variable, they are equal to each other, so,

l - 12 = p/7

Now you need to get rid of the p so you are only working with one variable. To do this you plug in whatever p is equal to for p, so,

l - 12 = (2l + 2w)/7 now to get rid of the w do the same thing we did with p just for w. So,

l - 12 = (2l + 2(l - 12))/7

To solve this you want to multiply both sides by 7 first to get rid of the fraction.

7l - 84 = 2l + 2(l - 12)

Next you want to distribute the 2 over the l and the 12.

7l - 84 = 2l + 2l - 24

Next you want to combine like terms on each side.

7l - 84 = 4l - 24

Next add 84 and subtract 4l from sides to isolate the variable.

3l = 60

Now divide each side by 11 to get your answer.

l = 20.

To find the width,

w = l - 12  

Just plug in and solve.

w = 20 - 12

w = 8

So your length and width are 20 and 8.

l = 20

w = 8

The width of the given rectangle is 8 units and the length is 20 units.

To find the length and the width of a rectangle when given that the length is 12 units longer than the width and the perimeter is 7 times the width, we can set up two equations. Let's denote the width as w and the length as l. According to the problem, l = w + 12 and the perimeter P = 2l + 2w is equal to 7w.

Set up the equations

l = w + 12

P = 2l + 2w

P = 7w

Substitute the value of l into the perimeter equation

7w = 2(w + 12) + 2w

Solve for w

7w = 2w + 24 + 2w

7w = 4w + 24

3w = 24

w = 8

Find the length using the width

l = w + 12

l = 8 + 12

l = 20