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First image is for question 1, and second image is for question 2


1. Remember what we know about vertical angles and solve for x.








2. Use the figure to answer the questions.


(a) What additional information is needed to prove the triangles are congruent by SAS Postulate? Explain.

(b) What additional information is needed to prove the triangles are congruent by the HL Theorem? Explain.

Step-by-step explanation:

[tex] \because \sin \theta = \cos \theta \\ \\ \therefore \: \sin \theta = \sin(90 \degree - \theta) \\ \\ \therefore \: \theta = 90 \degree - \theta \\ \\ \therefore \: \theta + \theta= 90 \degree \\ \\ \therefore \: 2\theta = 90 \degree \\ \\\therefore \: \theta = \frac{90 \degree }{2} \\ \\ \huge \orange{\boxed{\therefore \: \theta = 45 \degree}}\\ \\[/tex]

Answer:

An expression to represent the number of butterflies he has is  y = 12 + 2x

Step-by-step explanation:

Let the number of butterflies in Eduardo’s collection be  y

Then according to the question

The number of moths = x

The number of butterflies y = 12 + twice the number of moths---------(1)

Twice the number of moths = [tex]2 \times \text{number of moths}[/tex]

Twice the number of moths = 2x -----------------------(2)

Substituting equation (2) in (1)

The number of butterflies y = 12 + 2x

Answer: 5 brownies

Step-by-step explanation:

cookies = 5 x $0.50 = $2.5

$15 - $2.5 = $12.5

$12.5 divided by $2.25 = $5.555

so at the most ella can buy 5 brownies if she buys 5 cookies

Answer:

If each cookie is .50 and she wants to buy 5 cookies @ .50= $2.50

Than subtract $2,50 from $15.00 (which she has to spend you have $12.50

Then divide 2.25 into $12.5 and you get an answer of 5 brownies with a $1.30 extra to spend

Step-by-step explanation:

Answer:

7.43

Step-by-step explanation:

52/7 = 7.4285714...

that can be shortened to 7.43

7.43

Step-by-step explanation:

52/7 = 7.428

Option C:

[tex]$\frac{\text{kg}}{\text{m}^3}}[/tex]

Solution:

Given data:

[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]

where "d" represents density

"m" represents mass

"V" represents volume

The unit of mass is kilogram (kg).

The unit of volume is cubic metres [tex](\text{m}^3)[/tex].

To find an appropriate measurement unit for density:

[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]

Substitute kg and [tex](\text{m}^3)[/tex] in mass and volume respectively.

[tex]$\text{d}=\frac{\text{kg}}{\text{m}^3}}[/tex]

Option C is the correct answer.

An appropriate measurement unit for density is [tex]$\frac{\text{kg}}{\text{m}^3}}.[/tex]

Answer:

option b Kg/m3

Step-by-step explanation:

same as other answer

Answer:

The total cost of the car including the down payment  = $12,500

Step-by-step explanation:

The Original price of the car  = $9800

The amount paid for down payment  = $500

Also, the monthly payment  amount  = $250

Now, the number of months, the amount is paid  = 48 months

So, the TOTAL amount paid in 48  months

= 48 x ( Amount paid each month)   = 48 x ( $250)

= $12,000

So, the TOTAL PRICE of CAR paid  = Total amount paid in 48 months  + The amount paid for down payment

= $12,000 +  $500

= $12,500

Hence, the total cost of the car including the down payment  = $12,500

Step-by-step explanation:

Reflection through y-axis.

Answer:wait

Step-by-step explanation:

Answer:

?

Step-by-step explanation:

Answer:

$425

Step-by-step explanation:

Answer:

the answer is c, $425

Step-by-step explanation:

just did the quiz

Answer:

40

Step-by-step explanation:

6 of 30 is the ratio 6 to 30 or 6/30.

6/30 reduces to 1/5

The survey shows that 1/5 of the students attend summer camp.

1/5 of 200 = 1/5 * 200 = 40

The x intercept is [tex](\frac{-2}{5}, 0)[/tex]

The y intercept is [tex](0, \frac{-2}{3})[/tex]

Solution:

Given equation is:

10x + 6y = -4

The x intercept is the point where the line crosses the x axis

The y intercept is the point where the line crosses the y axis

Find x intercept:

Substitute y = 0 in given equation

10x + 6(0) = -4

10x = -4

[tex]x = \frac{-4}{10}\\\\x = \frac{-2}{5}[/tex]

Thus the x intercept is [tex](\frac{-2}{5}, 0)[/tex]

Find y intercept:

Substitute x = 0 in given equation

10(0) + 6y = -4

[tex]6y = -4\\\\y = \frac{-4}{6}\\\\y = \frac{-2}{3}[/tex]

Thus the y intercept is [tex](0, \frac{-2}{3})[/tex]

Answer:

1. Yes

2. Yes

Step-by-step explanation:

Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1.

1. Can their sum equal 1?

Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{1}{7}.[/tex] Both these fractions have the same denominators and are less than 1. Find their sum:

[tex]\dfrac{6}{7}+\dfrac{1}{7}=\dfrac{7}{7}=1[/tex]

2. Can their sum be greater than 1?

Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{5}{7}[/tex]. Both these fractions have the same denominators and are less than 1. Find their sum:

[tex]\dfrac{6}{7}+\dfrac{5}{7}=\dfrac{11}{7}=1\dfrac{4}{7}>1[/tex]

Two fractions with the same denominator can sum to 1 if their numerators add up to the denominator, or they can sum to more than 1 if their numerators together exceed the denominator. This is based on the concept of adding fractions where only the numerators are summed.

Leah wrote two different fractions with the same denominator, and both were less than 1. Can their sum equal 1? Can their sum be greater than 1? The answer to both questions depends on the value of the numerators. Fractions represent parts of a whole. For two fractions with the same denominator to have a sum of 1, the numerators must add up to the denominator. If their sum is greater than the denominator, then the total sum would be greater than 1.

For example, if we have fractions ½ and ¾, their sum is ½ + ¾ = ¾ which is less than 1. However, if we have ¾ and ¾, the sum equals 6/4, which reduces to 1½, a sum greater than 1.

In conclusion, two fractions with the same denominator and each less than 1 can sum to 1 if the numerators total the denominator, or can sum to greater than 1 if the numerators together exceed the denominator. An important aspect of adding fractions is that we only add the numerators and never the denominators.

Answer:

12 : 3

Step-by-step explanation:

You put the depth of the deep before the depth of the shallowness to get the ratio.  The ratio could be written like,

12 : 3

12 / 3

12 to 3

Answer:

the answer to the question is 12:3

Answer:

Roxy has 7 necklaces.

Step-by-step explanation:

35 = n + 4n

35 = 5n

5  =   5

n = 7

The problem is a simple algebra problem related to ratios. By setting up an equation according to the given information, we find that Roxy has 7 necklaces.

This is a math problem concerning ratios and simple algebra. Let's denote the number of necklaces that Roxy has as R. Then, Kelly has 4 times more rings, which is 4R. Together they have 35. So, the equation can be set up as:

R + 4R = 35

Combine like terms, you get:

5R = 35

Then, you can solve for R by dividing both sides by 5:

R = 35/5 = 7

So, Roxy has 7 necklaces.

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Answer: C A L C U L A T O R probably on calculator soup

Step-by-step explanation:

Answer:

look at the picture shown

Answer:

n + (n+1) = 3n -1

n = 2

the integers are 2 and 3

Step-by-step explanation:

Answer: y = 64

Step-by-step explanation:

y <> x² ----------------------- 1

y = kx² ----------------------- 2

36 = 3²k

36 = 9k

K = 36/9

= 4.

To find y when x = 4, we substitute for x in equation 2

y = kx²

y = 4²k

y = 16 x 4

y = 64

The value of y, which varies directly as the square of x, is determined by first identifying the constant of variation from the given values, in this case, y = 36 when x = 3. The constant is found to be 4. Using this constant (k), when x is 4, y will be 64.

The value of y varies directly as the square of x, which is represented mathematically as y = kx², where k is the constant of variation. Using the given that y = 36 when x = 3, we can determine k by substituting these values into the equation. Thus, k = y/x² = 36/9 = 4. Now, having the value for k, we can find y when x = 4 by substituting these values into the equation: y = kx² = 4×16 = 64. Therefore, y equals 64 when x equals 4 in the given relation.

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Answer:

3 inches

It will fit in the paper.

Step-by-step explanation:

In the scale drawing the 2 feet original length is converted to 1 inch drawing length as Kelly constructs a scale model of the rock garden using the scale 1 inch  : 2 feet.

Now the proportion is 1 inch : (2 × 12) inches = 1 : 24 {Since 1 foot is equivalent to 12 inches}

Now, maintaining that scale ratio the 6 feet original length of the garden will be converted to [tex]\frac{1}{24} \times (6 \times 12) = 3[/tex] inches in the drawing.

It is also given that the width of the garden in the scale model is 5 inches and the scale is still 1 inch : 2 feet.

Therefore, the dimensions of the garden in the model is 3 inches by 5 inches and this will fit on a piece of paper that is 8.5 inches by 7 inches. (Answer)

The missing values are 11, 8, 5 and 2 respectively.

The picture of the question in the attached figure

we have

y=-3x+5

Substitute the different values of x in the linear equation, to obtain the

different values of y in the table

For x-2-> y=-3(-2)+5=11

For x=-1-> y=-3(-1)+5=8

For x-0->9=-3(0)+5=5

For x-1->y=-3(1)+5=2

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A. A 90° counterclockwise rotation of trapezoid JKLM about the origin will move angle L onto angle R.

Step-by-step explanation:

Since both the trapezoids, trapezoid JKLM and PQRS are congruent, we can do any transformation, may be rotation, reflection and translation.

A 90° counterclockwise rotation of trapezoid JKLM about the origin will move angle L onto angle R is the true statement others are incorrect statements.

When the Preimage is rotated 90° counterclockwise rotation, then its coordinates (x,y) changed into (-y,x)  

Answer:

387/4

Step-by-step explanation:

121+8=129

3/4(129)=387/4

Answer:

2 x 2 x 2 x 2 x 2 x 5 x 13

Step-by-step explanation:

The Prime Factorization is:

2 x 2 x 2 x 2 x 2 x 5 x 13

In Exponential Form:

25 x 51 x 131

CSV Format:

2, 2, 2, 2, 2, 5, 13

The prime factors of 2080 are 2, 2, 2, 2, 5, and 13.

Divide 2080 by the smallest prime number, which is 2:

2080 ÷ 2 = 1040

Continue dividing by 2:

1040 ÷ 2 = 520

Continue dividing by 2:

520 ÷ 2 = 260

Continue dividing by 2:

260 ÷ 2 = 130

Continue dividing by 2:

130 ÷ 2 = 65

Now, 65 is not divisible by 2.

Move to the next prime number, which is 5:

65 ÷ 5 = 13

13 is a prime number.

So, the prime factors of  2080 are 2, 2, 2, 2, 5, and 13. In exponential form, this can be written as 24 * 5 *13.

The length of the rectange is 20ft and width of the 5ft.

Step-by-step explanation:

Let us consider a rectangle and its area is known to be 100 sq ft.

We are given the information that the length of the rectangle is 10ft longer than twice its width.

⇒Length l = 2w+10.

Where w is the width of the rectangle.

The formula for area of the rectangle A = length × width.

A= (2w+10)×w.

100 = [tex]2w^2+10w[/tex].

0=[tex]2w^2+10w-100[/tex].

Thus it forms an quadratic equation we have to solve for the solution.

0=(2w-10)(w+10).

2w-10=0.    w+10=0.

2w=10.        w=-10. (negative value cannot be choosed.)

w=[tex](\frac{10}{2} )[/tex].        

w=5ft.

Thus width is is 5 ft.

Length = 2(5)+10.

=10+10.

=20ft.

Thus the length is 20ft.

Answer:

25.5

Step-by-step explanation:

Final answer:

there were 127 children and 264 adults.

Explanation:

To solve this problem, we use a system of equations. Let's denote the number of children as C and the number of adults as A. We know two facts: the total number of people is 391, and the total amount of money collected is $752.75. Therefore, we have the equations:

To solve this system, we first multiply the first equation by 1.25 to align the coefficient of C with the second equation:

Next, we subtract this result from the second equation to eliminate C, leaving an equation in terms of A only:

2.25A - 1.25A = 752.75 - 488.75

A = (264) / 1 = 264

Substituting the value of A into the first equation, we find the value of C:

C + 264 = 391

C = 127

Therefore, there were 127 children and 264 adults who swam at the public pool that day.

Answer: 1/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

-8 -(-1)-5

Opening bracket

= -8 + 1 - 5

= -12

The student's expression -8 -(-1)-5 simplifies to -8 + 1 - 5, which is equal to -12 after performing the addition and subtraction sequentially.

The expression in question is -8 -(-1)-5. To solve this, we need to recognize that subtracting a negative number is the same as adding its positive equivalent. So, the expression simplifies to -8 + 1 - 5.

Now, we perform the addition and subtraction in the order they appear:

Therefore, the expression -8 -(-1)-5 is equivalent to -12.