need proof that ABCD is a parallelogram

Answer:

x  , reciprocal= 1/x  

x+2(1/x)=27/5  

x+2/x=27/5  

x^2+2=27/5*x  

x^2-27/5*x+2=0  

(x-5)(x-2/5)=0  

x=5, 2/5

Answer:

The linear equation that represent this problem is [tex]y=50x-2,500[/tex]

Step-by-step explanation:

Let

x -----> the number of people

y ----> the profit in dollars

we have

For x=100, y=2,500

and

For x=80, y=1,500

Find the slope m

we have

(80,1,500) and (100,2,500)

The slope is equal to

[tex]m=(2,500-1,500)/(100-80)\\ \\m=50\frac{\$}{people}[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=50[/tex] and point (100,2,500)

substitute

[tex]y-2,500=50(x-100)[/tex] ----> equation in slope point form

Convert to slope intercept form

[tex]y=50x-5,000+2,500[/tex]

[tex]y=50x-2,500[/tex]

Answer:

6

Step-by-step explanation:

The interquartile range is a measure of the difference between the upper quartile and the lower quartile.

The first step is to organise the data in ascending order, that is

10, 12, 13, 15, 17, 18, 21

Next find the median which is the middle value of the data.

10, 12, 13, 15, 17, 18, 21

                 ↑ ← the median = 15

Now find the upper and lower quartiles which are the middle values of the data to the right and left of the median.

10, 12, 13, 15, 17, 18, 21

      ↑                    ↑

upper quartile = 18 and lower quartile = 12

interquartile range = 18 - 12 = 6

Interquartile range of the given data set is 6.

Interquartile is the difference between upper quartile and lower quartile

Lower quartile is the median of the lower half of the data set.

Upper quartile is the median of the upper half of the data set.

Given data set 13, 17, 18, 15, 12, 21, 10

Arranging the data set in ascending order we get 10, 12, 13, 15, 17, 18, 21

Number of values in the data set is n = 7

Lower quartile is given by [tex]Q_{1} =\frac{n+1}{4} =\frac{7+1}{4} =\frac{8}{2} =2^{nd} \ value[/tex]

Therefore, the lower quartile is [tex]Q_{1} =12[/tex]

Upper quartile is given by [tex]Q_{3}=\frac{3}{4} (n+1)=\frac{3}{4} (7+1)=\frac{3}{4}(8)=6^{th} \ value[/tex]

Therefore, the upper quartile is [tex]Q_{1} =18[/tex]

Therefore, the inter quartile is given by [tex]Q_{3}-Q_{1} =18-12=6[/tex]

Interquartile range of the given data set is 6.

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Answer:

224 square centimeters

Step-by-step explanation:

If you slice this rectangular prism parallel to the face BFCG, you will get another cross section that is a rectangle with base 32 cm and height 7 cm.

We know area of rectangle = base * height

Thus, the area of the cross section is 7 * 32 = 224 square centimeters.

Answer:

The answer for K12 is 216

NOT 224 i got it wrong on the test

Have a great day guys! You can do it!

Step-by-step explanation:

The answer is 6, reaosn is because 6/8 is not simplified, so if we divide both sides by 2 (the numerator and the denominator), we can get a simplified fraction, which is 3/4. Steps: 6/8, 6 divided by 2/8 divided by 2, 3/4.

Hope this helped!

Nate

A fraction is a way to describe a part of a whole. The missing number that will make this fraction equal is 6.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The missing number in the given fraction can be found as shown below,

3/4 = ?/8

? = 8 × (3/4)

? = 6

Hence, the missing number that will make this fraction equal is 6.

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Answer:

A 40, 80, 160

Step-by-step explanation:

Given:

2.5, 5, 10, 20, ...

geometric sequence has a constant ratio r and is given by

an=a1r(r)^(n-1)

where

an=nth term

r=common ratio

n=number of term

a1=first term

In given series:

a1=2.5

r= a(n+1)/an

r=5/2.5

r=2

Now computing next term a5

a5=a1(r)^(n-1)

   = 2.5(2)^(4)

   = 40

a6=a1(r)^(n-1)

   = 2.5(2)^(5)

   =80

a7=a1(r)^(n-1)

   = 2.5(2)^(6)

   =160

So the sequence now is 2.5, 5, 10, 20,40, 80, 160!

Answer:

5

Step-by-step explanation:

The radius is a distance on a circle from the center to a point on the circle.

We have both of these points describe here in this definition.  Using the distance formula will give us the radius.

[tex]\sqrt{(x \text{ difference })^2+(y \text{ difference})^2[/tex]

The difference between 1 and -3 is 1-(-3)=4.

The difference between 5 and 2 is 5-2=3.

[tex]\sqrt{4^2+3^2}[/tex]

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

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

[tex]5[/tex]

Answer:

Part 1) The greater unit rate of the two functions is the linear function of the table

Part 2) The greater y intercept of the two functions is the linear equation of the graph

Step-by-step explanation:

we know that

The rate of a linear function is equal to the slope

step 1

Find the slope of the linear equation in the table

we have

(0,5) and (5,15)

The slope is equal to

[tex]m=(15-5)/(5-0)=10/5[/tex]

To find the unit rate divide by 5 both numerator and denominator

[tex]m=2/1=2[/tex]

step 2

Find the slope of the linear equation of the graph

we have

(-4,0) and (0,6)

The slope is equal to

[tex]m=(6-0)/(0+4)=6/4=3/2[/tex]

To find the unit rate divide by 2 both numerator and denominator

[tex]m=1.5/1=1.5[/tex]

Compare the unit rate of the two linear equations

2 > 1.5

therefore

The greater unit rate of the two functions is the linear function of the table

step 3

Find the y-intercepts of the linear equations

Remember that the y-intercept is the value of y when the value of x is equal to zero

Linear equation of the table

Observing the table

For x=0, y=5

therefore

The y-intercept of the linear equation of the table is the point (0,5)

Linear equation of the graph

Observing the graph

For x=0, y=6

therefore

The y-intercept of the linear equation of the table is the point (0,6)

Compare the y-intercept both functions

6 > 5

therefore

The greater y intercept of the two functions is the linear equation of the graph

Answer:

the greater unit rate is 2 and the greater y intercept is 6

Step-by-step explanation:

Answer:

[tex]\large\boxed{C.\ y=\dfrac{1}{2}x-5}[/tex]

Step-by-step explanation:

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

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

m - slope

b - y-intercept

[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]

Parallel line have the same slope.

Therefore a line parallel to the line [tex]y=\dfrac{1}{2}x+1[/tex] has equation

[tex]y=\dfrac{1}{2}x+b[/tex]

Answer: Z=30.8 when X=14 and Z=16.7 when Y=7

Step-by-step explanation:

Z is directly proportional to X: Z=K*X, Where K is a constant

Z is inversely proportional to Y:[tex]Z=\frac{K_{1} }{Y}[/tex] where [tex]K_{1}[/tex] is another constant.

When Z=19.5 ,   X=9 , Using this condition we find K value  

19.5=K*9 so, K=[tex]K=\frac{19.5}{9}[/tex]=2,2

When Z=19.5 ,   Y=6 , Using this condition we find [tex]K_{1}[/tex] value  

19.5=[tex]\frac{K_{1} }{6}[/tex] so, [tex]K_{1}[/tex]=19.5*6=117

So, When X=14,  Z= 2.2*14=30.8

When Y=7  Z= [tex]\frac{117}{7}[/tex]=16.7

Answer:

It is F

Step-by-step explanation:

if you plug in the y and x values that should get you the answer

Answer:

F.

Step-by-step explanation:

Answer:

[tex](x-1)^2+(y-4)^2=4[/tex].

Step-by-step explanation:

So the standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center and r is the radius.

You are given (h,k)=(1,4) and r=2.

So we are going to plug in 1 for h, 4 for k, and 2 for r:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x-1)^2+(y-4)^2=2^2[/tex]

[tex](x-1)^2+(y-4)^2=4[/tex].

Answer:

(x-1)^2 + (y+4)^2 = 4

Step-by-step explanation:

APEXXXX

Answer:

[tex]\frac{1}{x+4}[/tex]

Step-by-step explanation:

because you want to do [tex]\frac{x}{x+4}[/tex] divided by 4 which would end up being [tex]\frac{x}{x(x+4)}[/tex] then you cancel out the x and you are left with [tex]\frac{1}{x+4}[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {\frac {x} {x + 4}} {x}[/tex]

Applying double C we have:

[tex]\frac {x} {x (x + 4)} =[/tex]

We simplify common terms of the numerator and denominator:

[tex]\frac {1} {x + 4}[/tex]

Finally we have:

[tex]\frac {1} {x + 4}[/tex]

Answer:

[tex]\frac {1} {x + 4}[/tex]

Answer:

15 cm, 15 cm, and 19 cm

Step-by-step explanation:

Isosceles Triangle is a type of triangle in which two of the three sides are equal in length. The perimeter is 49 cm. Therefore, in this question, since the sides are unknown, we can assume that:

Length of the longer side = x cm.

Length of the other sides = y cm.

The relationship between x and y is given by:

x = (2y - 11) cm (because it is mentioned that the longest side is 11 cm less than twice as long as the other sides).

Perimeter of a triangle = sum of all sides.

Since its an isosceles triangle, therefore:

Perimeter of the triangle = x + 2y.

Substituting the values in the perimeter formula gives:

Perimeter of the triangle = 2y - 11 + 2y.

49 = 4y - 11.

4y = 60.

y = 15 cm.

Substituting y = 15 in the equation x = 2y - 11 gives x = 2(15) - 11 = 19 cm.

So in the ascending order, the lengths are 15 cm, 15 cm, and 19 cm!!!

Final answer:

To solve for the lengths of the sides of the isosceles triangle, we create an equation based on the given perimeter and the relationship between the sides. After simplifying, we find that each of the equal sides is 15 cm and the longest side is 19 cm. Thus, the sides in ascending order are 15 cm, 15 cm, 19 cm.

Explanation:

The question involves finding the lengths of the sides of an isosceles triangle given the perimeter and a relationship between its sides. Let the length of the two equal sides be x cm. According to the problem, the longest side would be 2x - 11 cm. The perimeter of the triangle is the sum of the lengths of all sides, which is given as 49 cm.

Now we set up the equation:

x + x + (2x - 11) = 49

Combining like terms, we get:

4x - 11 = 49

Adding 11 to both sides of the equation, we get:

4x = 60

Dividing both sides by 4, we find:

x = 15

The lengths of the two equal sides are each 15 cm, and the longest side is:

2(15) - 11 = 30 - 11 = 19 cm

So, the lengths of the sides in ascending order are: 15 cm, 15 cm, 19 cm

Answer:

y = - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, - 6) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3+6}{4-1}[/tex] = [tex]\frac{9}{3}[/tex] = 3

y = 3x + c ← is the partial equation

To find c substitute any of the 2 points into the partial equation

Using (4, 3), then

3 = 12 + c ⇒ c = 3 - 12 = - 9, hence

y- intercept c = - 9 ⇒ (0, - 9 )

Answer:

=-9 (the first choice)

Step-by-step explanation:

To find the y-intercept we must first find the equation of the line in the form y=mx + c where m is the gradient and c is the y- intercept.

m=Δy/Δx

=(3--6)/(4-1)

=9/3

=3

Let us write the equation using any of the given points, say (4,3)

(y-3)/(x-4)=3

y-3=3(x-4)

y-3=3x-12

y=3x-12+3

y=3x-9

Using the format y=mx+c, the y-intercept is -9

Answer: False

Step-by-step explanation:

Lets assume 15/33=22/46

15x46=22x33 (according to the cross multiply rule)

690=726

Here^^ clearly the answer is not equal thus, the answer is false, hope this was helpful :D

The given proportion is not correct.

We have to given that,

Expression for proportion is,

15/33 = 22/46

Now, WE can simplify each fraction as,

15/33 = 5/11

22/46 = 11/13

Clearly, 5/11 ≠ 11/13

Hence, The given proportion is not correct.

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Answer:

the only answers are 8 and 5

Answer:

9/10p

Step-by-step explanation:

1/2p+ 2/5 p

Get a common denominator of 10

1/2 p *5/5 = 5/10 p

2/5p *2/2 = 4/10 p

1/2p * 2/5 p

5/10p * 4/10 p

9/10p

Answer:

red, red, red, red, red, red, green, red, red, yellow

A. red, red, red, red, red, red, green, red, red, yellow

Frequency state to the number of times an event and the value occurs. A frequency table is a table that lists items or shows the number of times the items occur. We represent a frequency by the English alphabet ‘f’.

From the frequency table, there are 8 red lights, 1 green light and 1 yellow light for a total of 10 lights.

In option A, there are 8 red lights, 1 green light and 1 yellow light, with 10 total lights.  This is the correct option.

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Answer:

3/6=1/2 so one half

Step-by-step explanation:

3/6 × 10 =30/60=3/6=1/2

Answer:

Average number of even number outcomes =5

Step-by-step explanation:

Probability = number of possible outcome / sample space

A fair die has sides labeled 1,2,3,4,5,6.

Therefore sample space = 6

Odd numbers = 1,3,5

Possible outcome of odd numbers = 3

Even numbers = 2,4,6

Possible outcome of even numbers = 3

Probability of even numbers = possible outcome of even numbers / sample space

Probability of even numbers = 3/6 = 1/2.

If the die is rolled 10times

Total number of outcome = 10

Average number of even number outcomes = probability of even numbers * total number of outcome

= 1/2 x 10

= 5

Average number of even number outcomes =5

Answer:

a. A parallelogram

Step-by-step explanation:

A trapezoid is a four-sided flat shape with a pair of parallel sides.

A parallelogram has two pairs of parallel sides.

b. can apply to a trapezoid. A polygon has three or more sides.

c. can apply to a trapezoid. A quadrilateral has four sides.

d. can apply to a trapezoid. A shape with four angles is also a quadrilateral.

The term that does not describe a trapezoid is A. a parallelogram.

The term that does not describe a trapezoid is A. a parallelogram. A trapezoid is indeed a polygon, which by definition is a plane figure with at least three straight sides and angles. Also, a trapezoid is a type of quadrilateral or quadrangle, meaning it has four sides. However, unlike a parallelogram, a trapezoid only has one pair of parallel sides, while a parallelogram has two pairs of parallel sides. The distinct characteristic of a parallelogram is that its opposite sides are not only parallel but also equal in length, which does not apply to a trapezoid.

Answer:

3q = 36

q = 12

Step-by-step explanation:

Just work out the steps and compare to the choices

√(3q) = 6

[√(3q)]² = 6²

3q = 36  (Answer)

q = 36/3 = 12 (Answer)

A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B. This can be obtained by finding the remaining steps for finding q.

Given that √3q=6

              (√3q)²=6²

                   3q = 6×6 = 36 ⇒ A = 36 (squaring both sides)

                     q = 36/3 = 12 ⇒ B = 12 (divide both sides by 3)

Hence A=36 and B=12 is the required steps for the equation √3q=6 given that 3q=A and q=B.

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Answer:

A.

Step-by-step explanation:

NOTE: The "larger number" will be referred to as y, and the "smaller number" will be referred to as x.

"A number, y, is equal to twice the sum of a smaller number and 3."

This tells us that we must add our smaller number (x) to 3 within parantheses and then multiply the entire term (x+3) by 2.

[tex]y=2(x+3)[/tex]

"The larger number is also equal to 5 more than 3 times the smaller number."

This tells us that we must multiply 3 against our smaller number (x) and add 5 to it.

[tex]y=3x+5[/tex]

Now, to find your answer, we can put the equations in the same form as the answer choices so as to find an equivalent equation. Lets start with the first equation.

This form calls for us to have our x term first, then our y term, then our constant.

[tex]y=2(x+3)\\y=2x+6\\-2x+y=6[/tex]

Now that we've gotten the equation in that form, we can see that our answer choices hold that our leading co-efficient must be positive, which we can adjust for by dividing both sides by -1.

[tex]-2x+y=6\\2x-y=-6[/tex]

This makes the only possible answer choices (A) and (C).

Now, lets do our second equation. The recipe calls for the same form, again with a positive leading coefficient.

[tex]y=3x+5\\-3x+y=5\\3x-y=-5[/tex]

This is only represented by choices (A) and (B).

Therefore, answer choice (A) is the only one which represents both equations.

Answer:

Estimate

Step-by-step explanation:

Estimation is the process by which we deduce a close value to the required value through the method of approximation.

A graph is one of the tools used for finding the exact value of a limit. It can help us to approximate a limit by allowing us to estimate the finite value we're approaching as we get closer asymptotically to some independent variable values.

When working with graphs, the best we can do is estimate the value of limits in an appropriate step or procedure.

Therefore, the great fall back plan hen working with graph is to estimate.

Answer: Create a t-chart to graph the coordinates

[tex]

f(x)=-x^2+6x-1 \\

g(x)=3x^2-4x-1 \\

f(x)+g(x)=-x^2+6x-1+3x^2-4x-1=\boxed{2x^2+2x-2}

[/tex]

The answer is A.

Hope this helps.

r3t40

Multiply 8 and 75% together

75/100 divide by 5

15/20 divide by 5

15/20=3/4

8*3/4

Cross out 8 and 4 , divide by 4

2*3= 6

Answer is 6- C.

Answer:

C. 6.

Step-by-step explanation:

We multiply the number of solo acts by the percent that were singers

8 * 75%

8 * .75

6

Answer:

x = 44

Step-by-step explanation:

Adjacent angles in a parallelogram add up to 180 degrees.

180 = 3x + 6 + 42

132 = 3x

x = 44

Please mark for Brainliest!!  :D Thanks!

For any questions, please comment below and I'll respond ASAP! :)

Answer:

Step-by-step explanation:

In each parallelogram angles at one side add up to 180°.

Therefore we have the equation:

[tex](3x+6)+42=180[/tex]

[tex]3x+(6+42)=180[/tex]

[tex]3x+48=180[/tex]     subtract 48 from both sides

[tex]3x=132[/tex]          divide both sides by 3

[tex]x=44[/tex]

Answer:

Step-by-step explanation:

The formula of a volume of a square pyramid:

[tex]V=\dfrac{1}{3}s^2H[/tex]

s - base length

H - height

We have the volume V = 32 ft³ and the base length s = 4 ft.

Substitute and solve for H:

[tex]\dfrac{1}{3}(4^2)H=32\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}(16)H=(3)(32)\\\\16H=96\qquad\text{divdie both sides by 16}\\\\H=\dfrac{96}{16}\\\\H=8\ ft[/tex]

Answer:

The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd

Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ true

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ true

# m∠ 2 + m∠ 4 = m∠ 5

∵ In any Δ, the measure of the exterior angle at one vertex of the

  triangle equals the sum of the measures of the opposite interior

  angles of this vertex

∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6

∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ true

# m∠1 + m∠2 = 90°

∵ ∠ 1 and ∠ 2 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠1 + m∠2 = 90° ⇒ Not true

# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

∵ There is no given about their measures

∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is

  equal to the measure of ∠ 2

∴ m∠4 + m∠6 = m∠2 ⇒ Not true

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ Not true

Answer: A,B,C. OR 1,2,3

Step-by-step explanation: