Solve the system of equations by the substitution method.
5x+4y=38 x=5y−4

The condition of two congruent angles in each triangle, can be used to

show that the two triangles are similar.

Response:

Part 1:

A two column proof is presented as follows;

Statement [tex]{}[/tex]                                    Reason

1. ∠D ≅ ∠A [tex]{}[/tex]                                   1. Given

2. ∠DCE ≅ ∠ACB [tex]{}[/tex]                        2. Vertical angle theorem

3. ΔCDE ~ ΔCAB [tex]{}[/tex]                         3. AA similarity postulate

Angle-Angle, AA, similarity postulate states that if two angles in one

triangle are congruent to two angles in a second triangles, then the two

triangles are similar.

Part 2:

From part 1, we have;

ΔCDE is similar to ΔCAB (ΔCDE ~ ΔCAB)

The ratio of corresponding sides of similar triangles are equal, which

gives;

[tex]\dfrac{\overline{CD}}{\overline{AC}} = \mathbf{\dfrac{\overline{CE}}{\overline{CB}}}[/tex]

Which gives;

[tex]\dfrac{12}{\overline{AC}} = \mathbf{\dfrac{8}{15}}[/tex]

[tex]\overline{AC}} = \dfrac{15}{8} \times 12 = \mathbf{22.5}[/tex]

Similarly, we have;

[tex]\dfrac{\overline{DE}}{\overline{AB}} = \mathbf{\dfrac{\overline{CE}}{\overline{CB}}}[/tex]

Which gives;

[tex]\dfrac{16}{\overline{AB}} = \dfrac{8}{15}[/tex]

[tex]{\overline{AB}} = \dfrac{15}{8} \times 16 = \mathbf{30}[/tex]

Learn more about AA similarity postulate here:

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Answer:

14

Step-by-step explanation:

65^2=25^2 + h^2 =52

Then, 65^2 =(25 + x) ^2 +52^2=>x=14

Answer:

2x^2+3x-13x-1

Step-by-step explanation:

Quadratic expressions are polynomial expressions in which the highest power of the variable is 2.

Looking at option A, the highest power of the variable in the polynomial is 4. Therefore, it is not a quadratic expression.

Looking at option B, the highest power of the variable in the polynomial is 3. Therefore, it is not a quadratic expression.

Looking at option C, the highest power of the variable in the polynomial is 2. Therefore, it is a quadratic expression.

Looking at option D, the highest power of the variable in the polynomial is 1. Therefore, it is not a quadratic expression.

Answer:

c

Step-by-step explanation:

its c bc i got it right on test

Answer:

Use a factor tree. For example, 625 = 5 x 125 = 5 x 5 x 25 = 5 x 5 x 5 x 5. Because there are 4 fives, and we are looking for the square root, (5 x 5) (5 x 5) = 625. Therefore the square root of 625 is 25.

Answer:

Np buddy its B. Hope u get a good grade

Answer:

y = -33x + 11.

Step-by-step explanation:

Answer:

The answer is 4:1

Step-by-step explanation:

Hope this helps!

By putting x = y-4 in the equation 2x-y = 5, we get;

=) 2(y-4) -y = 5

=) 2y - 8 - y = 5

=) 2y - y = 5 + 8

=) y = 13

Now, we got the value y = 13, so by putting it in the equation x = y-4, we get;

=) x = 13 - 4

=) x = 9

Therefore, x = 9 and y = 13

Answer:

the answer is (x,y) = (9,13)

Step-by-step explanation

Answer:

x = 2, y = 5

Step-by-step explanation:

Answer:

math equation

Step-by-step explanation:

ANSWER = s = -14

Proof -14+10=s

Answer:

  x = 53

Step-by-step explanation:

The sum of the exterior angles of a convex polygon is always 360°.

  x +x +59 +48 +50 +39 +58 = 360

  2x +254 = 360 . . . . simplify

  x +127 = 180 . . . . . . divide by 2

  x = 53 . . . . . . . . . . . subtract 127

Answer:

Step-by-step explanation:

Multiply 20 by 12:

Multiply 240 by 5:

Multiply the lengths:

Answer:

The missing side is 5 cm

Step-by-step explanation:

Step 1:  Determine the missing side

[tex]V=l*w*h[/tex]

[tex]1200\ cm^3 = 20\ cm * w * 12\ cm[/tex]

[tex]\frac{1200\ cm^3}{20\ cm * 12\ cm} = w[/tex]

[tex]\frac{1200\ cm^3}{240\ cm^2} = w[/tex]

[tex]5\ cm = w[/tex]

Answer: The missing side is 5 cm

1)a parallelogram is a quadrilateral with opposite sides being parallel so the lines AB must equal CD or otherwise it wouldn't be a parallelogram

2)for a quadrilateral to be proven to be a parallelogram the consecutive angles has to be supplementary which means they add up to 180 or for example you could slice the parallelogram in half down the middle you could piece the two consecutive angles together to make 180 degrees

Answer:

A quadrilateral is a polygon with four sides. A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. A rhombus is a parallelogram with four congruent sides. A trapezoid is a quadrilateral with exactly one pair of parallel sides. A kite is a quadrilateral with exactly two pairs of adjacent congruent sides. And A scalene quadrilateral is a four-sided polygon that has no congruent sides. Three examples are shown below.

Step-by-step explanation:

I hope this helps, I also couldn't find a answer :D

[tex] \rm \: p = \frac{favourable \: outcome}{total \: outcome} [/tex]

[tex] \rm \: p = \frac{12}{30} [/tex]

[tex] \rm \: p = \frac{2}{5} [/tex]

[tex] \rm \: p = 0.4[/tex]

[tex] \tt \: p = \frac{0.4}{100} [/tex]

[tex] \tt \: p = 40\%[/tex]

Expression giving the result of the perimeter of rectangle A and demonstrating  the closure property is given by: Option A: [tex]10x + 4[/tex] ; the answer is a polynomial

Closure property keeps the result in the same set.

If two polynomials [tex]f(x)[/tex] and [tex]g(x)[/tex] are there.

Then, [tex]f(x) + g(x) = h(x)[/tex]

where [tex]h(x)[/tex] is also a polynomial.

The result of the addition of two polynomials is also a polynomial. This property of polynomial for addition operation is called closure property of a polynomial for addition operation

For the given case, we have:

Perimeter of a rectangle with width W and length L = 2(L + W)

And using that formula, the perimeter of the considered rectangle is evaluated as:

[tex]P = 2(3x + 5 + 2x - 3)\\P = 2((3+2)x + 2) = 2(5x + 2)\\\\P = 10x + 4[/tex]

Thus, expression giving the result of the perimeter of rectangle A and demonstrating  the closure property is given by: Option A: [tex]10x + 4[/tex] ; the answer is a polynomial

Learn more about addition of polynomials here:

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Answer:

D) 1

Step-by-step explanation:

Given f(x) = 4x² - 3x - 6

f(-1)=4(-1)² -3 (-1) -6

f(-1)= 4+3-6

f(-1)= 1

Hope it helps! :)

Range is one of the important description of a data set. The range of the given data sets is given as:

Range = Maximum value of the data set - Minimum value of the data set.

For the given sets, we get their range as:

Maximum value = 48, minimum value = 11

Range of the data set = Maximum value - minimum value = 48-11 = 37

Maximum value = 49, minimum value = 40

Range of the data set = Maximum value - minimum value = 49 - 40 = 9

Maximum value = 96, minimum value = 31

Range of the data set = Maximum value - minimum value = 96-31=65

Maximum value = 175, minimum value = 112

Range of the data set = Maximum value - minimum value = 175-112 = 63

Thus, the range of the given data sets is given as:

Learn more about range here:

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Answer:  maybe about 45 or 75 i dont know

Step-by-step explanation:

Answer:

I think the answer is D

Step-by-step explanation:

The last figure is representing an undefined term "line".

A ray is a segment of a line where one point is fixed and the other has no defined end. It denotes that a ray has one terminating end and an indefinitely long other end.

The first illustration depicts a ray with an end point at X, which is a phrase that is described as "a ray is a line with one end point."

The second graphic depicts a line segment with endpoints at X and Y. This phrase is described as "A line segment is a line with 2 end points."

The joint of two rays in the third illustration creates an angle, which is once again a defined phrase.

The final illustration depicts a line that is not defined and has no endpoints.

Learn more about Ray here:

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#SPJ5

Answer:

53.6, 53.61, 53.77, 54

Step-by-step explanation:

That's the right order

Answer:

In order: -5, 3, 5

Step-by-step explanation:

-5g + 15h - 25

-5 ( g - 3h + 5 )

Hopefully this helps!

Brainliest please?

Step-by-step explanation:

Use the formula to find the answer:

1.

2.

Note. the numbers above are rounded

Answer: 40x

Step-by-step explanation:

Titiana read 40 pages of her book every night for x number of nights, which means she read 40 pages every day. So 40 times x is how many pages she read in all.

DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

Two shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.

Given that DE = AB and BC = EF.

In right triangle DEF, using Pythagoras:

DF² = DE² + EF²

Also, In right triangle ABC, using Pythagoras:

AC² = AB² + BC²

But DE = AB and EF = BC, hence:

AC² = DE² + EF²

AC² = DF²

Taking square root of both sides, hence:

AC = DF

Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.

Find out more on Congruent shape at: https://brainly.com/question/11329400

pythagorean theorem, division, substatution, SAS

Step-by-step explanation:

edmentum

Step-by-step explanation:

let x represent the no of pancakes,

she baked 1.5 times pancakes more than waffles,

so from this, no of pancakes = 1.5x,

then she baked more 45 waffles,

no of waffles = (x +45)

so you had 1.5x pancakes and the children ate 12 out of them. the no of pancakes has then been reduced by 12.

thus, no of pancakes = ( 1.5x -12 )

now they see that they have 17 more waffles that pancakes left. this means that :

no of waffles - no of pancakes = 17

(x+45) - (1.5x - 12) = 17

x - 1.5x + 45 + 12 = 17

x = -50 / -0.5

x = 100

hence, there were 100 waffles initially.

hope you understand this,

-s.