In triangle DEF, DK is the angle bisector of angle EDF. If EK=2, FK=5, and DF=10, what is the length of DE?

Answer: D. 2500

Step-by-step explanation:

If total expense is $5000 and the spend 20% on food

30% on housing

Which make is 50% on both hosing and food leaving 50% on other expenses

Which makes half of the total budget

50/100* $5000 =$2500

Answer:

D

Step-by-step explanation:

Answer:

If one ounce of toppings cost $0.50, then you would need to take $0.50*11

.5*11= 5.5

11 ounces would be $5.50

hope this helps ;)

Final answer:

The rectangle's width is found to be 7.3 cm, and the length is approximately 10.47 cm, both measured to three significant figures. This was determined by setting up equations based on the given perimeter and the relationship between the rectangle's length and width.

Explanation:

To find the dimensions of the rectangle, we need to set up an equation based on the given perimeter and the relationship between length and width.

Let's denote the width of the rectangle as w centimeters. According to the problem, the length l is 3 1/6 cm longer than the width, so l = w + 3 1/6 cm. The perimeter P of a rectangle is given by the formula P = 2l + 2w. Substituting the given perimeter 15 1/3 cm and the expression for l into the formula, we get:

15 1/3 = 2(w + 3 1/6) + 2w

To solve, first convert the mixed numbers to improper fractions:

46/3 = 2((6w + 19)/6) + 2w

Multiply through by 6 to clear the fractions, resulting in:

92 = 4w + 19 + 6w

Combine like terms and solve for w:

92 = 10w + 19

73 = 10w

w = 7.3 cm

Now that we have the width, calculate the length:

l = w + 3 1/6

l = 7.3 + 3 1/6

l = 7.3 + 19/6

l = 7.3 + 3.1667

l = 10.4667 cm

So the width of the rectangle is 7.3 cm, and the length is approximately 10.47 cm, to three significant figures.

Answer:

8(2x+7y)

Step-by-step explanation:

Answer:

x = 45/7

Step-by-step explanation:

Write as an algebraic equation.

Look at each part in the word question : 0.7 of what number is 4 1/2

"0.7 of what number" can be written as 0.7x

The word "is" means equals.

0.7x = 4 1/2     <= The equation, using 'x' to represent the number.

To find the number, isolate 'x'.

0.7x = [tex]4\frac{1}{2}[/tex]    Convert mixed fraction to improper fraction

0.7x = [tex]\frac{(4*2)+1}{2}[/tex]     Multiply the whole number by the denominator and add it to the numerator

0.7x = [tex]\frac{9}{2}[/tex]     Now isolate 'x'

0.7x/0.7 = [tex]\frac{9}{2}/0.7[/tex]     Divide both sides by 0.7

x = [tex]\frac{9}{2}/0.7[/tex]     Simplify right side

x = [tex]\frac{9}{2}/\frac{7}{10}[/tex]     Rewrite 0.7 as a fraction

x = [tex]\frac{9}{2}*\frac{10}{7}[/tex]     To divide, you multiply a flipped fraction

x = [tex]\frac{9*10}{2*7}[/tex]     Multiply across the top and across the bottom

x = 90/14      Reduce to lowest terms. Top and bottom are divisible by 2

x = 45/7        Answer

The drama club receives $7 for each ticket that they sell.

Step-by-step explanation:

Given,

Amount received by school = x dollars

Amount received by school for 96 tickets = 96x

Amount received by drama club = remaining amount after school

Total amount of 96 tickets = 96x+672

Here,

96x is the share of school

672 is the share of drama club for 96 tickets.

Therefore;

96 tickets = dollars

1 ticket = [tex]\frac{672}{96}[/tex]

1 ticket = 7 dollars

The drama club receives $7 for each ticket that they sell.

Keywords: division, addition

Learn more about division at:

#LearnwithBrainly

Answer:

6.219*10^3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

∠ FDG = ∠ CDB = 50° ( vertical angles are congruent ), thus

∠EDG = 90° - ∠ FDG = 90° - 50° = 40° → B

To find the total amount of water needed to water all the plants in the house, the amount of water for a part of the plants is used to set up a proportion. After cross-multiplying and calculating, it is determined that 10/3 liters or approximately 3.33 liters of water is required.

If 4/3 liters of water is enough for 2/5 of the plants, then the amount of water required for all the plants can be found by setting up a proportion. We use cross-multiplication to solve for the unknown amount of water needed to water all the plants.

First, we express the given information as a fraction:

(4/3) liters

(2/5) plants

Next, we solve for the total water required (let's call it x):

(4/3) / (2/5) = x / 1

We cross-multiply to solve for x:

4/3 * 1 = x * (2/5)

Multiplying both sides by the reciprocal of (2/5), which is (5/2), to isolate x, we get:

(4/3) * (5/2) = x

Now we calculate:

x = (4 * 5) / (3 * 2) = 20/6 = 10/3 liters

Therefore, 10/3 liters of water, or approximately 3.33 liters, is necessary to water all the plants in the house.

The volume of white color used by Maria is 20 liter

Solution:

Maria, a color specialist, mixes 2 parts of white and 13 parts of red to develop a particular shade

She creates 150 liters of the shade

Given ratio is:

2 parts of white and 13 parts of red

white : red = 2 : 13

Let the white mixed be 2x

Let the red mixed be 13x

Total shade = 150 liters

Therefore,

2x + 13x = 150

15x = 150

x = 10

Therefore, volume of white color used = 2x = 2(10) = 20

Thus, volume of white color used by Maria is 20 liter

Answer:

2.15

Step-by-step explanation:

The easiest way to convert a percentage to a decimal is to simply add a decimal on the number (If the number does not already have one), then move that decimal two places to the left.

We can do that like so:

1: Remove the percentage sign: 215% -> 215

2: Add a decimal at the end of the number: 215.

3: Move the decimal two places to the left: 2.15

So 215% converted to a decimal would be 2.15

Answer: [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Step-by-step explanation:

Since the zeros of the polynomials are -3 , 4 and 1 , then the equation will be in the form:

(x+3)(x-4)(x-1) = 0

Expanding (x+3)(x-4) , we have

[tex]x^{2}[/tex] - 4x + 3x - 12

⇒[tex]x^{2}[/tex] -x - 12

combining with (x-1) , we have

([tex]x^{2}[/tex] -x - 12) ( x -1 ) = 0

expanding , we have :

[tex]x^{3}[/tex] - [tex]x^{2}[/tex]-[tex]x^{2}[/tex] + x - 12x + 12 = 0

⇒[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0

Answer:

Step-by-step explanation:

Final answer:

The original dimensions of the cardboard sheet are 12 inches by 12 inches, which is calculated by setting up an equation using the provided volume of the open-top box and the size of the squares cut from each corner.

Explanation:

Solving for the Original Dimensions of the Cardboard Sheet

To solve this problem, we need to find the original dimensions of the square sheet of cardboard that will create an open-top box with a volume of 128 cubic inches after 2-inch squares are cut from each corner and the sides are folded up. Since the volume of the box (V) is given by the formula V = length x width x height, we first denote the original side length of the cardboard as x inches. After cutting out 2-inch squares from each corner, we will fold up the sides, which means the new length and width of the box will be (x - 4) inches (since we lose 2 inches on each side). The height of the box will be 2 inches, which is the size of the square cut out from each corner. Therefore, the volume of the box can be expressed as 2(x - 4)^2.

To find the value of x, we solve the equation 2(x - 4)^2 = 128. Simplifying, we get (x - 4)^2 = 64. Taking the square root of both sides, we have x - 4 = 8. Adding 4 to both sides gives us x = 12. So, the original dimension of the cardboard is 12 inches by 12 inches.

Answer:

[tex]\dfrac{1}{6}[/tex] hour or [tex]10[/tex] minutes

Step-by-step explanation:

Lisa:

Rate = 10 mph

Time = t hours

Distance = x miles

[tex]x=10\cdot t[/tex]

Jen:

Rate = 4 mph

Time = t hours

Distance = x - 1 miles

[tex]x-1=4\cdot t[/tex]

Hence,

[tex]10t-1=4t\\ \\10t-4t=1\\ \\6t=1\\ \\t=\dfrac{1}{6}\ hour[/tex]

Answer:

Step-by-step explanation: the sender below is not correct

Answer:

6-k

Step-by-step explanation:

Difference means subtraction.

Answer:

76

Step-by-step explanation:

456 divided by 6 equals 76. Hope that helps.

Answer

Emma made 456 cookies and she wanted to divid them to 6 friends. how manny cookies will each friend get?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets get started.

QM is the diameter given.

NL is the tangent given.

The tangent makes 90 degree angle with diameter.

hence the angle QML will be : 90°   ...............   Answer

Similarly, QMN will also be 90°

The angle PMQ is given as 27°

Hence the angle PMN will be = [tex]90-27[/tex]

Hence the angle PMN will be = [tex]63[/tex]°   .....................   Answer

Hope it will help :)

Answer:

slope = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Answer:

$39.50

Step-by-step explanation:

Multiply 7.9 by 5 to get 39.5

Answer:

if 10 of them costs $7.90 then 50 would cost $39.50.

there are two different ways of doing this:

1. you could divide $7.90 by 10 which would get you $0.79 (the price of one frozen juice bar) then multiply $0.79 by 50 to get $39.50 (the price of 50 frozen juice bars)

or

2. you could just take $7.90 and multipy it by 5 (b/c 10 x 5 is 50)

Answer:

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 , 5)

[tex]Slope = m =\dfrac{1}{3}[/tex]  

To Find:  

Equation of Line Passing through A with slope 1/3 =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e Equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 5) we get

[tex](y-5)=\dfrac{1}{3}(x-3)\\\\3y-15=x-3\\x-3y=-15+3=-12[/tex]

Therefore , Equation of Line Passing through A with slope 1/3 is

[tex]x-3y=-12[/tex]

Answer:

no bro

Step-by-step explanation:

because copy has same shape

Final answer:

A photocopy is not a dilation; dilations change size while maintaining shape, while photocopies replicate the original image at the same scale.

Explanation:

When you make a photocopy of an image, it is not considered a dilation. A dilation involves resizing an image while maintaining its shape, whereas a photocopy reproduces the original image at the same scale.

A dilation in physics refers to a transformation that changes the size of an object, typically without altering its shape. Examples of dilations can be seen in various optical processes such as lens systems and camera projections.

Photocopying is a replication process that duplicates an image onto another surface with the same proportions and characteristics as the original, making it distinct from a dilation.

Answer:

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\frac{1}{2x+6}[/tex]

To find the domain of the function in set notation.

Solution:

For the function [tex]f(x)[/tex] to exist the denominator must be ≠ 0

We have the denominator [tex](2x+6)[/tex] which  cannot be = 0.

Thus, we can find the domain of the function using the above relation.

The function [tex]f(x)[/tex] will not exist when:

[tex]2x+6=0[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by 6.

[tex]2x+6-6=0-6[/tex]

[tex]2x=-6[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}=\frac{-6}{2}[/tex]

∴ [tex]x=-3[/tex]

Thus, the function will not exist at [tex]x=-3[/tex]. This means it has all real number solutions except -3.

The solution set can be given as:

[tex]\{x|x\ \epsilon\ R,x\neq -3\}[/tex]

Answer:

0.5

Step-by-step explanation:

2 times 1/4 equals 0.5 or 1/2.

we can solve this equation by turning 2 into 2/1.

2/1 x 1/4 equals 1/2 or 0.5

Answer:

0

Step-by-step explanation:

It is counting by -2

Answer:

D negative four

Step-by-step explanation:

Answer:

d) y= -4

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Part one is always the ones 'in these: ( )'. 12/3=4 4*2=8. So now it is 8^2+8-7. 8^2 is 8*8=64. 64+8-7=64+1=65

Start by working inside the parentheses which are these things ( )

The things inside the ( ) is "12 divided by 3 times 2"

Division comes first so 12 divided by 3 = 4.

4 times 2 = 8

So now we have 8^2 + 8 - 7

In PEMDAS, Exponents come before addition and subtraction, so 8^2 is 64.

64 + 8 = 72

Lastly is subtraction

72 - 7 = 65

65 is your answer.

Answer:

10cm

Step-by-step explanation:

find the diameter of the circumference of 5cm:

d= c÷3.14

=5cm÷3.14

=1.6cm

Double 1.6cm:

1.6×2= 3.2

Find the new cicumference:

c= 3.14×d

= 3.14×3.2

= 10cm

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have

[tex](-6,\ 3)\to x_1=-6,\ y_1=3,\ m=\dfrac{5}{2}[/tex]

Substitute:

[tex]y-3=\dfrac{5}{2}(x-(-6))\\\\y-3=\dfrac{5}{2}(x+6)[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y-3=\dfrac{5}{2}(x+6)[/tex]         use the distributive property

[tex]y-3=\dfrac{5}{2}x+\dfrac{5}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3[/tex]

[tex]y-3=\dfrac{5}{2}x+15[/tex]           add 3 to both sides

[tex]y=\dfrac{5}{2}x+18[/tex]

Convert to the standard form:

[tex]Ax+By=C[/tex]

[tex]y=\dfrac{5}{2}x+18[/tex]              multiply both sides by 2

[tex]2y=5x+36[/tex]              subtract 5x from both sides

[tex]-5x+2y=36[/tex]          change the signs

[tex]5x-2y=-36[/tex]