The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?

Answer:

hope this will help you

Step-by-step explanation:

69+420/3

first of all divide 420 by 3 which is 140

69+140

then add with 69

209

Answer:

The correct answer should be 209.

Step-by-step explanation:

Also here Is your art my good sir!

Answer:

People can not be in fractions

[tex]\large \boxed{ \ \sf \dfrac{13}{36} \ }[/tex]

[tex]\rightarrow \sf 10 \dfrac{1}{9} - 9\dfrac{3}{4}[/tex]

[Convert to improper Fractions]

[tex]\rightarrow \sf \dfrac{91}{9} - \dfrac{39}{4}[/tex]

[Make the denominator same]

[tex]\rightarrow \sf \dfrac{4(91)}{36} - \dfrac{9(39)}{36}[/tex]

[Multiply Integers]

[tex]\rightarrow \sf \dfrac{364}{36} - \dfrac{351}{36}[/tex]

[Join both fractions]

[tex]\rightarrow \sf \dfrac{364-351}{36}[/tex]

[Subtract Integers]

[tex]\rightarrow \sf \dfrac{13}{36}[/tex]

Answer:

13/36.

Step-by-step explanation:

First convert to improper fractions:

10 1/9 = (10*9 + 1)/9 = 91/9.

9 3/4 = (9*4 + 3)/4 = 39/4.

Next find the Lowest Common Denominator of 9 and 4.

This is 9*4 = 36.

Now convert both fractions to 36th:

For 91/9 we multiply by 4/4 and for 39/9 we multiply by 9/9

91*4 / 9*4 =  364/36 and 39*9 / 9*4 =  351/36, so we have:

364/36 - 351/36

=  13/36

Applying the Pythagorean theorem, the distance between the Earth's horizon and the satellite would be 5756.70 miles.

To calculate the distance from the satellite to the Earth's horizon, it is necessary to use the Pythagorean Theorem as follows:

We must identify the data we have:

To calculate the distance from the satellite to the Earth's horizon, we must first establish the distance from the center of the Earth to the satellite, for this we calculate the radius of the Earth and add the distance to the satellite:

With these data we can draw an imaginary triangle from the center of the Earth, one of its legs would be the distance between the center of the Earth and the satellite, the other leg would be the distance between the center of the Earth and the Earth's horizon (at 90° to the other leg).

Now, to identify the distance between the horizon and the satellite, we apply the Pythagorean Theorem:

According to the above, the distance between the satellite and the horizon would be 5756.70 miles.

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Answer:

54.59

Step-by-step explanation:

carry the 10 over and 1-.41 is .59

Step-by-step explanation:

1 min 4 cals

60 cals how many mins?

1min. 60cals

____. × _______ = 15 mins

4cals. ?mins

we simplify the matter by simplifying 60 with 4 and striking out cals... then we will have 15 on the top right and then we multiply 1 and 15 together at the end we add the mark of the answer which is (min).

Check the picture below.

now, we're making an assumption that, the two blue shaded region are equal in shape, and thus if that's so, that area above the 14 is 6 and below it is also 6, 14 + 6 + 6 = 26.

so hmm if we simply get the area of the trapezoid and subtract the area of the yellow triangle and the area of the cyan triangle, what's leftover is what we didn't subtract, namely the shaded region.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=14\\ b=26 \end{cases}\implies A=\cfrac{15(14+26)}{2}\implies A=300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{trapezoid}{300}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(26)(9)}~~ - ~~\stackrel{cyan~triangle}{\cfrac{1}{2}(15)(6)}} \\\\\\ 300~~ - ~~117~~ - ~~45\implies 138\qquad \textit{blue shaded area}[/tex]

The side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

The length of the side of the square and the height will be

6.98 cm and 13.96 cm.

Pyramid is a three dimensional Structure ,having square , rectangle , hexagonal base , the faces for a square pyramid and hexagonal pyramid are triangle meeting at one point .

It is given in the question that

A toy is being constructed in the shape of a pyramid.

the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters.

the height of the toy is double the side length

Let us assume the side length to be x

and therefore the height of the toy is 2x

The surface area of the toy is given = 250 sq.cm

First let us consider for a square base

The surface area of a square pyramid is given by

[tex]\rm A = a^2 + 2 a\sqrt {\dfrac{a^2}{4}+h^2}[/tex]

Here a is the side length which x for us and h = 2x

[tex]\rm 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+(2x)^2}\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+4x^2}\\\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{17 x^2}{4}}\\\\\\250 = x^2 + x^2 \sqrt{17}\\\\\\250 = 5.132 x^2\\\\\\48.71 = x^2\\\\\\x = 6.98 cm .[/tex]

Therefore the length of the side of the square and the height will be

6.98 cm and 13.96 cm.

For a hexagonal base

The total surface area is given by

[tex]A =6ah + 3 \sqrt{3}a^2\\\\\\A = 6 \times x \times 2x + 3\sqrt{3} (x)^2\\\\250= 12x^2 + 3\sqrt{3} x^2\\\\\\250 = 17.196 x^2\\\\\\14.54 = x^2\\\\x = 3.81 cm\\\\[/tex]

Therefore the side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.

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Answer:

1456ft²

Step-by-step explanation:

A = lw

A = 60(20)

A = 1200ft²

A = 16(16)

A = 256ft²

1200 + 256 =

1456ft²

Answer:

[tex]V=12\pi\:\text{units}^3[/tex]

Step-by-step explanation:

[tex]\displaystyle V=\frac{\pi r^2h}{3}\\ \\V=\frac{\pi (3)^2(4)}{3}\\\\V=\pi(3)(4)\\\\V=12\pi[/tex]

Answer:

29 feet

Step-by-step explanation:

20^2 + 21^2 = 841

841sqrt = 29 feet

The slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

The formula for the slant height of the cone is given as:

[tex]l^2=r^2+h^2[/tex]

Here we have

r=2 units

h=4 units

By putting the values we will get

[tex]l=\sqrt{4^2+2^2[/tex]

[tex]l=\sqrt{16+4[/tex]

[tex]l=\sqrt{20}[/tex]

[tex]l=2\sqrt{5}[/tex]

Hence the slant height of the right circular cone will be  [tex]l=2\sqrt5}[/tex]

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Answer:

Find the area of the triangle side, then multiply by the length of the prism.Area of triangle = 1/2 x height x baseArea  = 1/2 x 2 x 3 = 3 square cmVolume = 3 x 4 = 12 cubic cm.Answer is A)

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

A gas station offers a lucky draw to customers. Each time you spend more than $20 on gas, you can make a draw to win a prize. The probability of winning a prize is 1/12 suppose you buy gas 4 times.

To Find:

what is the probability of you winning a prize each time?

Solve:

Since, it given that you buy gas 4 times. Thus that means:

1/12 × 1/12 × 1/12 × 1/12 or  1/12⁴

Now solving it:

1/12 × 1/12 × 1/12 × 1/12 = 1/20736

Which also means (0.0048%) in decimal form since, 1 divide by 2076 equal to 0.0048%

Kavinsky

Answers:

=======================================================

Part (a)

Let's find the distance from point D to point E.

In other words, this will compute the length of segment DE.

[tex]D = (x_1,y_1) = (0,-6) \text{ and } E = (x_2, y_2) = (3,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (-6-1)^2}\\\\d = \sqrt{(-3)^2 + (-7)^2}\\\\d = \sqrt{9 + 49}\\\\d = \sqrt{58}\\\\d \approx 7.6158\\\\[/tex]

Segment DE is roughly 7.6158 units long.

Let's repeat these steps to find the length of segment EF.

[tex]E = (x_1,y_1) = (3,1) \text{ and } F = (x_2, y_2) = (-2,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-2))^2 + (1-1)^2}\\\\d = \sqrt{(3+2)^2 + (1-1)^2}\\\\d = \sqrt{(5)^2 + (0)^2}\\\\d = \sqrt{25 + 0}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment EF is exactly 5 units long.

Lastly, we'll compute the length of segment FD.

[tex](x_1,y_1) = (-2,1) \text{ and } (x_2, y_2) = (0,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-0)^2 + (1-(-6))^2}\\\\d = \sqrt{(-2-0)^2 + (1+6)^2}\\\\d = \sqrt{(-2)^2 + (7)^2}\\\\d = \sqrt{4 + 49}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]

Segment FD is about 7.2801 units long.

This is close to the length of DE, but not quite.

To recap, we found these segment lengths:

As you can see, all three sides are different lengths. Therefore, triangle DEF is scalene.

----------------------------------

For part (b), follow the same template as part (a).

I'll be skipping the steps.

This is what you should get for the lengths of triangle TRI

Segments TR and IT are the same length (both exactly [tex]\sqrt{37}[/tex] units long), which means triangle TRI is isosceles.

-----------------------------------

For part (c), I'll also be skipping steps.

Here are the lengths you should find

All three lengths are different, making this triangle scalene.

Answer:

▪︎ Domain: all real numbers (x can be any number)

▪︎ Range: y <= 0 (y can never become greater than 0 bc the vertex of this function (highest point) is (0,0))

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

[tex]\\ \rm\Rrightarrow \dfrac{AB}{AD}=\dfrac{BC}{CD}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{18}{x}=\dfrac{19}{11}[/tex]

[tex]\\ \rm\Rrightarrow 19x=198[/tex]

[tex]\\ \rm\Rrightarrow x=10.4[/tex]

Answer:

x = 10.4 (nearest tenth)

Step-by-step explanation:

Angle Bisector Theorem

The angle bisector of any angle in a triangle will divide the side opposite the bisected angle in the ratio of the sides containing the angle.

Therefore:

AD : DC = BA : BC

Given:

Substituting the given values into the ratio and solving for x:

[tex]\implies \sf x : 11 = 18 : 19[/tex]

[tex]\implies \sf \dfrac{x}{11}=\dfrac{18}{19}[/tex]

[tex]\implies \sf 19x=18 \cdot 11[/tex]

[tex]\implies \sf 19x=198[/tex]

[tex]\implies \sf x=\dfrac{198}{19}[/tex]

[tex]\implies \sf x=10.4 \: (nearest\:tenth)[/tex]

Answer:

[tex]r = 2km[/tex]

Step-by-step explanation:

Area =

[tex]area = \pi {r}^{2} [/tex]

[tex]12.56 = 3.14 \times {r}^{2} [/tex]

[tex] {r}^{2} = \frac{12.56}{3.14} [/tex]

[tex] {r}^{2} = 4[/tex]

[tex]r = \sqrt{4} [/tex]

[tex]r = 2km[/tex]

The radius of the cone is 7 feet

The given parameters are:

Surface Area, A = 216π

h = 8/3r

The surface area of a cone is:

[tex]A = \pi r(r + \sqrt{h^2 + r^2})[/tex]

So, we have:

[tex]216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})[/tex]

Factor out r

[tex]216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})[/tex]

Evaluate the exponent

[tex]216\pi = \pi r(r + r * 2.85)[/tex]

Evaluate the sum

[tex]216\pi = \pi r(3.85r)[/tex]

Divide both sides by pi

[tex]216 = 3.85r^2[/tex]

Divide both sides by 3.85

[tex]56.10 = r^2[/tex]

Take the square roots of both sides

r = 7 (approximately)

Hence, the radius of the cone is 7 feet

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Answer:

The radius is about 9 feet.

Hope this helps!

Step-by-step explanation:

The quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

The table of values is given as:

x: 0     1       2    3     4     5   6

y: 4.1 -0.9 -3.9 -5.1 -4.1 -4.1 -1.1

To determine the quadratic regression equation, we make use of a graphing calculator

From the graphing calculator, we have the following calculation summary:

a = 0.7, b = -5.04 and c = 3.76

A quadratic regression equation is represented as:

y = ax² + bx + c

Hence, the quadratic regression equation of the table of values is y = 0.71x² - 5.04x + 3.76

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Answer:

I think 24.

Step-by-step explanation:

Step-by-step explanation:

it depends if you use degrees or radians as angle measure.

let's assume degrees.

arcsine is the inverse function of sine.

so, when sin(x) = 1/2, arcsin(1/2) = x

when now x = 2×arcsin(1/2), we get

x = 2×30 = 60°

the mean numbers of point scored is greater than 12 points(C.)

Answer:

(0, 2)

Step-by-step explanation:

it right I got 100% on my quiz

And… here are others that are right in the quiz

Identify coordinate point B.

(1, 5)

Identify coordinate point D.

(7, 3)

Identify coordinate point C.

(6, 7)

Hope it helps! :)

Solution:

[tex]x > - 1[/tex]

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

Interval Notation:

x ∈ (-1,∞)

Answer:

So, 5, 20, 45, 80,...5N2

Step-by-step explanation:

Divide the sequence by 5 and the answer becomes very obvious:

EX: 1, 4, 9, 16,...N2

Answer:

RT = 26

Step-by-step explanation:

Based on the figure we can say :

Scale factor :

Hence, as the proportions are the same :

The triangle ABC and RST will be similar triangles. Then the length of RT will be 26 units.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

If the two triangles are similar, the ratio of the corresponding sides will be constant.

The triangle ABC and RST will be similar triangles.

RT / 13 = 24 / 12

      RT = 26

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Using the z-distribution, the confidence coefficient for the 90% confidence interval is of 1.645.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.95[/tex], and the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

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