what type of shape is this?

The measure of the missing length of the trapezoid is equal to 3√39 units.

Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:

D = d + 2 · c

Where c is the length of the horizontal leg of the right triangle in a trapezoid.

And the missing leg can be found by means of Pythagorean theorem:

x = √(r² - c²)

Where:

First, determine the length of shortest leg: (D = 40, d = 26)

40 = 26 + 2 · c

14 = 2 · c

c = 7

Second, find the longest leg by Pythagorean theorem:

x = √(20² - 7²)

x = 3√39

To learn more on trapezoids: https://brainly.com/question/12623349

#SPJ1

Answer:

70.95$

Step-by-step explanation:

P = $1000

R = 2.365%

T = 3 years

[tex]\frac{PRT}{100}[/tex] = [tex]\frac{1000*2.365 * 3}{100}[/tex] = [tex]\frac{7095}{100}[/tex] = 70.95$

Answer: 20$

5$ for each person attending. Hope it helps.

Answer:

$20

Step-by-step explanation:

the unit rate (cost per person) is

 $15

-------------- = $5/person

3 people

For four people the total cost would be (4 people) ($5/person) = $20

Answer:

Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Right triangle fulfill the pythagorean theorem:

[tex]a^2+ b^2 = c^2[/tex]

Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.

[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]

Answer:

look at the photo x is the red and y is the blue

Step-by-step explanation:

[tex]midpoint = ( \frac{(2 + 8)}{2} , \frac{(3 + 9)}{2} ) \\ = (5,6)[/tex]

Answer:

√(x2-x1)²+(y2-y1)²

√(8-2)²+(9-3)²

√6²+6²

√36+36

√72

8.48528137424≈8.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?

Answer:

V  =  38.47 in^3

Step-by-step explanation:

The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in.  The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:

V = (1/3)(3.14)(1.75 in)^2*(12 in), or

V  =  38.47 in^3

Answer:

115.40 in3

that is the correct answer to this question.

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],

where a and b are positive integers.

The value of a + b is 96.

Let mid-point of DC be E and mid-point of AB be F.

Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.

Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]

Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]

Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]

Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference

Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.

Using the above information and symmetry,

[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]

Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)

and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)

Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]

And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]

Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]

And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]

Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.

BF = DE = [tex]\frac{12}{2}[/tex] = 6

[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]

And  PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]

Now, Let x = AP

Using law of cosine on [tex]$\triangle[/tex]ABP, we have

[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]

[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]

[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]

Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]

Therefore a + b = 72 + 24 = 96

For more questions on square

https://brainly.com/question/21327969

#SPJ4

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.

There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.

Therefore, the correct answer is option b) Unimodal.

To learn more about Unimodal refer to:

https://brainly.com/question/30125628

#SPJ1

The required correct option for the given question is uni-modal.

The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).

Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.

There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.

Therefore, the correct answer is option b) Uni-modal.

To learn more about Uni-modal refer to:

brainly.com/question/30125628

#SPJ1

Answer:

387420489

Step-by-step explanation:

I hope this helps if not let me know in the comments

here is the qr code it will show you the steps on how to do it if you click on it

Answer:

a = 4√2, h = 2√3

Answer:

yes

Step-by-step explanation:

yes

yes

yes

yes

yeyed

yes

Answer:

A. 35 million

B. $1519 increase

$7719 year end

Step-by-step explanation:

Answer:

184ft^2

Step-by-step explanation:

W have to find the area of triangles and rectangles and add them together to get the total area of the figure:

Area of triangles = 1/2(b)(h)

Area of rectangles = l x w

6 x 10 = 60

1/2(6)(4) = 12 (We can make this 12 a 24 because there are two of these triangles)

5 x 10 = 50 (We can also make this 50 a 100 because there are two of these rectangles)

100 + 24 + 60 = 184ft^2

The 40 50 90 triangle can be solved using Pythagoras theorem.

A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given:

We have 40 50 90 triangles.

A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.

Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.

So, Such type of Triangles can be solved using Pythagoras theorem.

Learn more about 40 50 90 triangle here:

https://brainly.com/question/29005645

#SPJ1

Answer:

The vertex is (-4, -9)

Step-by-step explanation:

The two roots are located at x = -7 and x = -1, which come from (x + 7) and (x + 1).  The axis of symmetry is located halfway between these values, at x = -4.  This axis passes through the vertex.  The y-value at the vertex is (-4 + 7)(-4 + 1), or -9.  The graph is a parabola that opens up.  The vertex is (-4, -9).

Answer: x = 3

Step-by-step explanation:

-3 +9x = 24

9x= 24+3

9x=27

9x/9= 27/9

x=3

Answer:

x = 3

Step-by-step explanation:

-3 + 9x = 24

rearrange:

9x - 3 = 24

Add 3 to both sides of the equation:

9x - 3 + 3 = 24 + 3

9x = 27

Divide both sides by 9:

9x/9 = 27/9

x = 3

Have a nice day!

The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.

A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.

The denominator is

(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)

(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)

So by  partial fraction expansion

(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))

(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²

A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4

(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4

Thus from coefficients of x³, x², x and 1,

A + B + C = 1

2A + 4B + C + D = 0

-A + 5B - C + D = 0

-2A + 2B - C - 2D = 4

Solving

A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2

--The question is not clear, the question is given below--

"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of

[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex]  "

To know more on partial fractions expansion

https://brainly.com/question/30079928

#SPJ4

answer: 47.5 cups

Step-by-step explanation:

2.50 x 19 = answer

Answer:

80x

Step-by-step explanation:

There is no substitution for the variable so the expression is 80x

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, and it can be interpreted in different ways.

Is the question a true or false question?

If yes, then both statements are true

As a further explanation, we consider a roll of die.

The sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

Because 1 to 6 appear just once on the die, then each have a probability of 1/6

[tex]Pr = \frac{1}{6}[/tex] --- This is referred to as the theoretical probability

But if after rolling the die 6 times, the outcome is:

[tex]Outcome = \{1,1,4,5,1,2\}[/tex]

The experimental probability of (say 1) is, the number of times 1 appeared divided by the number of times the experiment is carried out.

i.e.

[tex]Pr(1) = \frac{3}{6}[/tex]

Answer:

yes

Step-by-step explanation:

according to pythagoras theorem = hypotenuse² = √ base²+perpendicular²

so 21² + 28² = 35²

On solving the provided question, we can say that - here in the percentage obtained = 40 => so, 40/100X100 = 40%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is = 100

obtained = 40

so, 40/100X100 = 40%

To know more about percentage visit:

https://brainly.com/question/29306119

#SPJ1

Answer:

Infinutely many solutions

Step-by-step explanation:

y = 10x + 2 --------- (1)

y = 8x +2x +2

=> y = 10x + 2---------- (2)

(1) -> 10x -y + 2 = 0

(2) -> 10x -y + 2 = 0

a1=10 ; b1=-1 ; c1 = 2

a2=10 ; b2=-1 ; c2= 2

a1/a2 = 10/10 = 1

b1/b2 = -1/-1 = 1

c1/c2 = 2/2 = 1

therefore, a1/a2 = b1/b2 = c1/c2

Therefore the line coincides and there are infinitely many solutions.

Answer:

300 words in 6 minutes

300/6 words in 1 minutes

50 words in 1 minutes

Therefore,Lee can type 50 words in 1 minute.

The percent discount on the new phone is 15%.

Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.

To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.

Discount = Original Price - Sale Price

Discount = $46 - $39.10

Discount = $6.90

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($6.90 / $46) x 100

Percent Discount = 15%

Therefore, the percent discount is 15%.

Learn more about discount here: https://brainly.com/question/3434137

#SPJ4