The lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel. If $\angle BAE=54^{\circ}$ and $\angle DCE=25^{\circ}$, what is the measure of $\angle AEC$?

Use an asymptote convertor if needed:

[asy]
size( 200 ) ;

pair A = (0,0) ;
pair B = (0,2) ;
pair C = (3,0.5) ;
pair D = (3,2.5) ;
pair ptE = extension( A , A+dir(90-54) , C , C+dir(90+25) ) ;

draw( (0,-0.5)--(0,3) , linewidth(1.3) ) ;
draw( (3,-0.5)--(3,3) , linewidth(1.3) ) ;
draw( A--ptE--C ) ;
dot(Label( "$A$" , A , W )) ;
dot(Label( "$B$" , B , W )) ;
dot(Label( "$C$" , C , E )) ;
dot(Label( "$D$" , D , E )) ;
dot(Label( "$E$" , ptE , N )) ;

label( "$54^{\circ}$" , A , 5dir(70) ) ;
label( "$25^{\circ}$" , C , 8dir(100) ) ;
[/asy]

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]

Step-by-step explanation:

Reflection through y-axis.

Answer:wait

Step-by-step explanation:

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:

?

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: 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:

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)

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:

25.5

Step-by-step explanation:

Answer:

13+11

Step-by-step explanation:

13-11=2 and 13+11=24

Answer:a

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

It is given that Marta sold [tex]$ x $[/tex] oranges on Thursday.

She has sold twice as many as on Friday. Therefore, she must have sold [tex]$ 2x$[/tex] oranges on Friday.

And the total amounts to 108.

That is, [tex]$ x + 2x = 108 $[/tex]

Hence, the table which has the total on the top and the entities on the bottom line would be the answer which is Option A.

Answer:

A

Step-by-step explanation:

Thursday is x because she sold x oranges. Friday is 2x because she sold double the amount she sold on Thursday. Then we add them together to make 108.

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

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:

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.

Answer: 1/9

Step-by-step explanation:

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

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:

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:

[tex]\sqrt{1.8}<1.8[/tex]

[tex]\sqrt{1.8}>1[/tex]

[tex]\sqrt{1.8}<\sqrt{1.9}[/tex]

[tex]1.3<\sqrt{1.8}<1.4[/tex]

[tex]\sqrt{1.8}+\sqrt{1.9}[/tex]

Step-by-step explanation:

[tex]\sqrt{1.8} = 1.34[/tex]     [tex]\sqrt{1.9} = 1.38[/tex]       [tex]\sqrt{1.8}+\sqrt{1.9}=1.34+1.38=2.72[/tex]

[tex]\sqrt{1.9}-\sqrt{1.8}=1.38-1.34=0.04[/tex]

1.

[tex]\sqrt{1.8}<1.8[/tex]

It is true. since 1.34<1.8

2.

[tex]\sqrt{1.8}>1[/tex]

It is true. Since 1.34>1

3.

[tex]\sqrt{1.8}<\sqrt{1.9}[/tex]

It is true. since 1.34<1.38

4.

[tex]1.3<\sqrt{1.8}<1.4[/tex]

It is true. Since 1.3<1.34<1.4

5.

[tex]\sqrt{1.8}+\sqrt{1.9}[/tex]>2

It is true. Since 2.72>2

6.

[tex]\sqrt{1.8}-\sqrt{1.9}>0.1[/tex]

It is false. Since 0.04<0.1

Answer:

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

n = 2

the integers are 2 and 3

Step-by-step explanation:

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:

387/4

Step-by-step explanation:

121+8=129

3/4(129)=387/4

Answer:

Discrete data means that it is not continuous and is graphed as a line with dashes.Continuous data goes on forever and is usually linear. It is graphed as a straight line all the way through.

Step-by-step explanation:

Hope that helps.

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:

Step-by-step explanation:

x-117+120

x+3