the ratio of the measures of the sides of a triangle is 21:8:14 if the perimeter of the triangle is 215 feet find the length of each side​

Answer:

884.4

Step-by-step explanation:

Answer:

The original price is 895.12$

I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this

Step-by-step explanation:

Answer:

C = 2 x 4.5 x π

Step-by-step explanation:

The equation to find the circumference of the circle is

C = 2π · r

r = 4.5 in

Looking at the options, the answer is C = 2 x 4.5 x π

Answer:

Below

Step-by-step explanation:

radius = 4.5       diameter = 2 x 4.5  in

the circumference of a circle is given by the formula   p * d

  substitute in the underlined equation for 'diameter')

          circumference = 2 * 4.5 * pi    inches

Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Answer:

UT = TW + WU = 27 + 27 = 54

WT = 27

ST = UT = 54

arc(XT) =  angle XZT = 52 degrees

arc(ST) = angle SZT = 104

arc(US) = arc(ST) + arc(UT) = 104 + 104 = 208

I know it was super drawn out and there were probably quicker ways to do it, but I was justusing methods that came to mind rather than going for efficiency.  let me know if any part is confusing.  

Step-by-step explanation:

Let's start by just building on what we know

Since we know sv and vz can be made into the side of two triangles, SZV and TZV, we can use some similar triangle rules.

In SZV and TZV we know SZ = TZ since they are both radii, ZV = ZV because they are the same line and angle ZVS = angle ZVT since they are supplementary and one is 90 degrees.  This allows us to solve and see if they are congruent or not.  To do so we use the normal trig functions

sin(ZTV) = ZV/ZT = ZV/12

sin(ZSV) = ZV/SV = ZV/12

So the angles could be equal, but just to be sure lets look at all possible answers.  with sine an angle x gives the same result as 180-x.  Since both angles are acute thugh we know this can't be true so both angles are equal.    Now we can say both triangles are congruent by AAS.  Since they are congruent we can then confirm SV = VT.

In general you can say if a radii intersects a chord at a right angle then the intersection is a bisection.  So now we know VT = 27

We can use similar methods to show UW = WT and if you made two triangles ZWT and ZWU you will see they are congruent.  and since arc UT is 104 degrees that means angle UZT is 104 degrees.  Since ZW bisects UT and the two triangles are congruent ZW also bisects angle UZT so UZW = TZW = 52 degrees.

Now we have 4 triangles, SZV, TZV, ZWT and ZWU and we know SZV and TZV are congruent and ZWT and ZWU are congruent.  Now, if we can make one from each pair congruent we would knwo all four are congruent.  Since TZV and ZWT share a side  that's a good place to start.  Looking at these two  triangles we know those two sides are equal, and they both have a right angle.  Also we know VZ = ZW fromt he instructions, so this is again a chance to check with trig.

Let's look at angle ZTW and ZTV.

sin(ZTW) = ZW/ZT = 27/ZT

sin(ZTV) = VZ/ZT = 27/ZT

Using the same reasoning as before we can say that the two angles are equal, so the two triangles are congruent.  Now we can say a lot.

angle UZT = angle SZT = 104 degrees

angle SZV = angle VZT = angle TZW = angle WZU = 52

SV = VT = TW = WU = 27

Let's start solving.

UT = TW + WU = 27 + 27 = 54

WT = 27

ST = UT = 54

arc(XT) =  angle XZT = 52 degrees

arc(ST) = angle SZT = 104

arc(US) = arc(ST) + arc(UT) = 104 + 104 = 208

Answer:

A. (5, 2)

Step-by-step explanation:

Given

\(\begin{cases}x+y=7,\\2x+3y=16\end{cases}\),

Multiply the first equation by 2, then subtract both equations to get rid of any terms with \(x\):

\(\begin{cases}2(x+y)=2(7),\\2x+3y=16\end{cases}\\\implies 2x+2y=14,\\2x+3y=16,\\2x-2x+2y-3y=14-16,\\-y=-2,\\y=\boxed{2}\)

Substitute \(y=2\) into any equation to solve for \(x\):

\(x+y=7,\\x+2=7,\\x=7-2=\boxed{5}\)

Since coordinates are written as (x, y), the solution to this system of equations is (5, 2).

Answer:

A. ( 5 , 2 )

Step-by-step explanation:

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.

Simplify.

Subtract 2x+3y=16 from 2x+2y=14 by subtracting like terms on each side of the equal sign.

Add 2x to -2x. Terms 2x and -2x cancel out, leaving an equation with only one variable that can be solved.

Add 2y to -3y.

Add 14 to -16.

Divide both sides by -1.

Substitute 2 for y in 2x+3y=16. Because the resulting equation contains only one variable, you can solve for x directly.

Multiply 3 and 2

Subtract 6 from both sides of the equation.

Divide both sides by 2.

The system is now solved.

x = 5 and y = 2

Answer:

4 popped

Step-by-step explanation:

6+8=14

14-10=4

Answer:

f(11) = 87

Step-by-step explanation:

substitute n = 11 into f(n) , that is

f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87

Answer:

21 diamonds.

Step-by-step explanation:

1 bracelet = 7 diamonds

3 bracelet= ? diamonds

All we have to do is multiply 3 by 7 to get the number of diamonds Jen have with three bracelets.

3 x 7 = 21

Answer:

1 bracelet has 7 diamonds, therefore 2 has 14 and 3 has 21 diamonds

Step-by-step explanation:

Answer:

D)

Step-by-step explanation:

Choice A is vertical angle

Choice B is complementary

Choice C is corresponding angle

Answer:

The rise is 3.6 and the run is 1

Step-by-step explanation:

The rise is 3.6 and the run of the slope is 1

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

Given that the equation of a line is y=3.6x+2.

By comparing the equation of straight line y = mx + c

Therefore, m = 3.6

Thus, the slope of the line is 3.6

We can conclude that the rise is 3.6 and the run is 1.

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Answer:letra    b

Step-by-step explanation:

A function assigns the values. The decrease in selling price from 700 units sold to 900 units sold is 10. Thus, the correct option is B.

A function assigns the value of each element of one set to the other specific element of another set.

Price of the unit when 900 units were sold,

P=1200-20s

900 = 1200 - 20s

s = 15

Price of the unit when 700 units were sold,

P=1200-20s

700 = 1200 - 20s

s = 25

Now, the difference in the selling price of the units is,

Difference = 25 - 15 = 10

Hence, the decrease in selling price from 700 units sold to 900 units sold is 10. Thus, the correct option is B.

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Answer:

the answer is 2.78 percent

Answer:

11.886

Step-by-step explanation:

Given :

\(log 50^7\)

Applying formula

\(log a^m=m log a\)

So,

\(7 log 50\\=7(1.698)\\=11.886\)

Answer will be 11.886

The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = LWH

Where:

Part a.

Therefore, the manager can use the following formula;

Volume of container = LWH

Volume of container = 7/2 × 3/2 × 3/2

Volume of container = 63/8 cm³.

Part b.

For the number of bento boxes that can fill the container, we have:

Number of bento boxes = Volume of container/Volume of bento boxes

Number of bento boxes = 63/8/(1/2)³

Number of bento boxes = 63/8/1/8

Number of bento boxes = 63/8 × 8

Number of bento boxes = 63 bento boxes = 3 layers × 21.

Part d.

Volume of container = Volume of bento boxes

63/8 cm³ = 63 × 1/8 cm³

63/8 cm³ = 63/8 cm³ (equal).

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Answer:

5

Step-by-step explanation:

area of rectangle = l(ength)×w(idth)

perimeter = 2×l + 2×w

diagonal = sqrt(l² + w²) (Pythagoras)

l×w = 12. => l = 12/w

2×l + 2×w = 14

2×12/w + 2×w =14

12/w + w = 7

12 + w² = 7w

w² - 7w + 12 = 0

=> (after a little thinking and trying : what 2 numbers multiply to 12 and add to -7 ? -3 and -4

=> (w-3)×(w-4) = 0

so, we get 2 solutions for w : 3 and 4

that gives us 2 solutions for l : 4 and 3

so, one is 3 and the other 4. it does not matter which is which. length 4 and width 3 produce the same diagonal as length 3 and width 4.

diagonal = sqrt(l² + w²) = sqrt(16 +9) = sqrt(25) = 5

Answer:

To solve this inequality, we need to solve each inequality separately and then find the values of x that satisfy both inequalities.

First, let's solve the inequality (x+1 < 4):

x + 1 < 4

x < 4 - 1

x < 3

Next, let's solve the inequality (x-8 > -7):

x - 8 > -7

x > -7 + 8

x > 1

Now we need to find the values of x that satisfy both inequalities. Since x must be less than 3 and greater than 1, we can write:

1 < x < 3

Therefore, the solution to the inequality (x+1<4) (x-8>-7) is 1 < x < 3.

Step-by-step explanation:

The value of simplified form of fraction is,

⇒ 35 / 111

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 0.315315315315....

Now, Let us assume that,

x = 0.315315315315....  .. (i)

Multiply both side by 100;

1000x = 315.315315315....  .. (ii)

Subtract (i) from (ii), we get;

999x = 315

x = 315/999

x = 35/111

Thus, The value of simplified form of fraction is,

⇒ 35 / 111

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Answer:

89

Step-by-step explanation:

Answer: 89 metres squared

Step-by-step explanation:

large area = 13 x 8 = 104

small area = 5 x 3 = 15

104 - 15 = 89

Answer:

The trigonometric ratios associated with (-5, -4) are \(\sin t \approx -0.625\), \(\cos t \approx -0.781\) and \(\tan t = 0.8\).

Step-by-step explanation:

Let \(\vec u = (x,y)\). From Trigonometry, we remember the following definitions for the trigonometric ratios, dimensionless:

\(\sin t = \frac{y}{\sqrt{x^{2}+y^{2}}}\) (1)

\(\cos t = \frac{x}{\sqrt{x^{2}+y^{2}}}\) (2)

\(\tan t = \frac{y}{x}\) (3)

If we know that \(x = -5\) and \(y = -4\), then the trigonometric ratios are, respectively:

\(\sin t = \frac{-4}{\sqrt{(-5)^{2}+(-4)^{2}}}\)

\(\sin t \approx -0.625\)

\(\cos t = \frac{-5}{\sqrt{(-5)^{2}+(-4)^{2}}}\)

\(\cos t \approx -0.781\)

\(\tan t = \frac{-4}{-5}\)

\(\tan t = 0.8\)

The trigonometric ratios associated with (-5, -4) are \(\sin t \approx -0.625\), \(\cos t \approx -0.781\) and \(\tan t = 0.8\).

We are given:

a right angled triangle with the angle of elevation = 20 degrees

Hypotenuse of the Triangle = 500 m

Finding the change in Elevation:

We will use trigonometry in the given triangle to find the length of the perpendicular of the triangle

Using trigonometry, we found that the perpendicular = 500 * Sin 20 degrees

Perpendicular = 500 * 0.342           [sin(20 degrees) = 0.342]

Perpendicular = 171 m

The closest value to 171m in the given options is 170m

Therefore, 170m (option B) is correct

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

30 more feet will cost 6.30$

Step-by-step explanation:

please mark brainliest

Answer: $6.30

Step-by-step explanation:

First you divide 14.70 by 70 (14.70÷70= 0.21)

This means 0.21 is your unit price

Secondly you multiply 0.21 and 30 (0.21×30= 6.30)

Answer:

\(P_{B}\) = 80

Step-by-step explanation:

given 2 similar figures with ratio of sides = a : b

then ratio of perimeters is also a : b

here ratio of sides = 24 : 15 = 8 : 5

the ratio of perimeters is also 8 : 5

then by proportion

\(\frac{ratioA}{P_{A} }\) = \(\frac{ratioB}{P_{B} }\) , that is

\(\frac{8}{128}\) = \(\frac{5}{P_{B} }\) ( cross- multiply )

8 \(P_{B}\) = 5 × 128 = 640 ( divide both sides by 8 )

\(P_{B}\) = 80

Answer:

Step-by-step explanation:

From the summary of the given data;

After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.

Let consider \(p_1\) to be the probability of those that experience the drowsiness in group 1

\(p_1\) = \(\dfrac{137}{452}\)

\(p_1\) = 0.3031

After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.

Let consider \(p_2\) to be the probability of those that experience the drowsiness in group 1

\(p_2\) = \(\dfrac{31}{99}\)

\(p_2\) = 0.3131

The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.

In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.

So; the null and the  alternative hypothesis can be computed as:

\(H_o :p_1 =p_2\)

\(H_a= p_1<p_2\)

The test statistics is computed as follows:

\(Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }\)

\(Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }\)

\(Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }\)

\(Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }\)

\(Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }\)

\(Z = \dfrac{-0.01}{0.051378 }\)

Z = - 0.1946

At the level of significance ∝ = 0.05

From the standard normal table;

the critical value for Z(0.05) = -1.645

Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.

Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2

Area of one face of the pentagon = Length x Breadth

We have 5 rectangles, area of the 5 rectangles

Area of bottom base

Answer:

21 green cars

Step-by-step explanation:

Answer:

70 x 30/100 = 21

21 cars are green

Step-by-step explanation: