Find the missing the side length leave the answer as radical form. Question 3.

Find The Missing The Side Length Leave The Answer As Radical Form. Question 3.

Answers

Answer 1

In order to calculate the value of x, we can use the cosine relation of the angle 60°.

The cosine is equal to the length of the adjacent leg to the angle over the length of the hypotenuse.

So we have:

[tex]\begin{gathered} \cos(60°)=\frac{2}{x}\\ \\ \frac{1}{2}=\frac{2}{x}\\ \\ x=4 \end{gathered}[/tex]

Now, to calculate the value of y, we can use the tangent relation of the angle 60°.

The tangent is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.

So we have:

[tex]\begin{gathered} \tan(60°)=\frac{y}{2}\\ \\ \sqrt{3}=\frac{y}{2}\\ \\ y=2\sqrt{3} \end{gathered}[/tex]


Related Questions

Please please please help me

Answers

The lines l, m, and n are parallel to each other and the value of x is 8.34.

What are parallel lines?

Parallel lines are lines that are equidistant from each other and do not meet no matter how far they extend in either direction. Parallel lines form angles when crossed by a transversal and show some significant properties.

Angles that correspond are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that are opposite each other are equal.On the same side of the transversal, a pair of interior angles are supplementary.

For the given question, we can see that lines l ║m ║n.

Therefore, (6x - 2)° = 52° [Vertically opposite angles are equal]

6x = 52 - 2

6x = 50

x = 50/6

x = 8.34

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in the diagram ,EF and AB are parallel .Line CD is a transversal PartA:Describe the transformation that will take

Answers

The described transformation is a translation and a reflection that is dilation.

By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made.

The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation. A function can be moved in one direction or another by translation, rotated around a point by rotation, reflected in its mirror image by reflection, and scaled by dilation.

The dilation is the transformation that causes the 2-d shape to stretch or contract vertically or horizontally by a fixed amount. The equation y = a.f. yields the vertical stretch (x). The function stretches in relation to the y-axis if a > 1.

Hence we get the required answer.

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A given circle has an approximate area of 78.5 square units. How long is the circles diameter?

Answers

Remember that

The area of a circle is equal to

[tex]A=\pi\cdot r^2[/tex]

we have

A=78.5 unit2

I will assume pi=3.14

substitute in the formula

[tex]\begin{gathered} 78.5=3.14\cdot r^2 \\ r^2=\frac{78.5}{3.14} \\ r=5\text{ units} \end{gathered}[/tex]

the diameter is two times the radius

so

D=2(5)=10 units

therefore

The diameter is 10 units

What is the component form of resultant of 4b⃗ −2aa = (7 , -5)b = ( -4 , 4)

Answers

[tex]\langle-30,26\rangle[/tex]

1) Since we have this expression, let's do it in parts.

[tex]\begin{gathered} 4\langle-4,4\rangle-2\langle7,-5\rangle \\ x-component=4(-4)-2(7)=-16-14=-30 \\ y-component=4(4)-2(-5)=16+10=26 \\ \end{gathered}[/tex]

Note that since each vector has two components x, and y. The resultant will be the vector:

[tex]\langle-30,26\rangle[/tex]

the ordered pair (2,16) is a solution for which equation(s) check all that apply

Answers

We have the following:

We must evaluate each equation (x = 2), if the result is 16 it will be a solution

A.

[tex]y=(2\cdot2)^2=4^2=16[/tex]

B.

[tex]y=(2+2)^2=(4)^2=16[/tex]

C.

[tex]y=2\cdot2^2=2\cdot4=8[/tex]

D.

[tex]y=2\cdot2+2=4+2=6[/tex]

Therefore, the correct answer is A and B

What is a discrete set?Is option d and e and possibly c?

Answers

Discrete sets are sets which members are countable and distinct.

That is, they are separable and can only have a certain value.

For example, the number of players in a rugby team is discrete because they are countable.

Hence, options C, Dare applicable.

picture with question

Answers

In order to determine if the given triangles are similar, it is necessary to find the values of the missing angles.

Take into account that the sum of the interior angles of a triangle is equal to 180°, the for the missing angles you have:

180° - 90° - 46° = 44°

180° - 38° - 46° = 96°

AS YOU CAN NOTICE THE THREE ANGLES ARE NOT EQUAL.

Then, the triangles are NOT similar because it is necessary that the three angles are equal.

Suppose that y varies jointly with w and x and inversely with z and y = 24 when w = 8, X= 9 and z = 6. Write the equation that models the relationship. Then find y when w = 2, X= 20 and z = 8.

Answers

We would have the following:

[tex]24=\frac{8\cdot9}{6}\cdot2[/tex]

From this, we will have the following expression:

[tex]z=2\cdot\frac{w\cdot x}{y}[/tex]

Now, we determine the values after replacing the ones given:

[tex]8=2\cdot\frac{2\cdot20}{y}\Rightarrow y=\frac{4\cdot20}{8}\Rightarrow y=10[/tex]

The value of y is 10.

How do you write 1.9 x 102 in standard form?

Answers

We are given the following number in scientific notation.

[tex]1.9\times10^2[/tex]

We are asked to write this number in standard form.

Method 1:

Simply multiply 1.9 by 10²

[tex]1.9\times10^2=1.9\times(10\times10)=1.9\times100=190[/tex]

Method 2:

Simply move the decimal point to the right by 2 places (since the exponent is 2

Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.

Answers

Answer:

[tex]84.3\text{ cm}^2[/tex]

Explanation:

Here, we want to calculate the area of the regular heptagon

Mathematically, we use the formula below:

[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]

where:

a is the length of the apothem which is 5 cm

n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)

Substituting the values, we have it that:

[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]

collin noticed that various combinations of the nickels and dimes could add uo to $0.75 let x equal the numver of nickles let y equal the number of dimes what is the domain where y is a function of x and the total value is $0.75

Answers

Input data

nickles = 5 cents

dimes = 10 cents

x = number of nickles

y = number of dimes

SI unit conversion Could you please help me with exercise number 12 please and explain the process? I copied exercise 11 from the board and trued to solve #13 but not sure if it’s correct

Answers

Given:-

[tex]9468mg=\ldots kg[/tex]

To find the required solution.

So we use the formula,

[tex]1\operatorname{kg}=1000000mg[/tex]

So now we substitute,

[tex]\frac{9468}{1000000}=0.009468[/tex]

So the required solution is 0.009468 kg.

determine the degree of the polynomial[tex] - 65b + {53x}^{3}y[/tex]

Answers

Determine the degree of the polynomial



656+ 3x^3 y

Degree of the polynomial = 4 = (3 + 1)

3x^3 grade (3)

y grade (1)

________________

The degree of the polynomial is 4

Tina babysits and cuts lawns to earn money. For one week, she babysits for 5 hours. She earns $8.25 per hour babysitting If Tina earns $92 this week, how much does tina earn cutting lawns? 1) $10.152) $16.753) $41.254( $50.75

Answers

Answer:

[tex]\text{ \$50.75}[/tex]

Explanation:

Here, we want to calculate how much Tina earns cutting lawns

From the question, she earns $8.25 per hour for 5 hours cutting lawns

What she earned in totality that week would be:

[tex]\text{ 5 }\times\text{ \$8.25 = \$41.25}[/tex]

What she earned cutting lawns would be the total earned minus what she earned cutting lawns

Mathematically, we have that as:

[tex]\text{ \$92 - \$41.25 = \$50.75}[/tex]

Solve the following system of equation using substitution4x + 2y = 10?/1x - y = 13What is the solution for x?

Answers

ANSWER

x = 6

EXPLANATION

The substitution method consists on taking one equation to solve for one variable as a function of the other. Then substitute that variable with the expression we find in the other equation and then solve for that other variable.

In this case, we want to solve for x, so we'll take one of the equations and find y as a function of x. For the second equation:

[tex]\begin{gathered} x-y=13 \\ y=x-13 \end{gathered}[/tex]

Now we replace y by x - 13 in the first equation:

[tex]4x+2(x-13)=10[/tex]

And solve for x:

[tex]\begin{gathered} 4x+2x-2\cdot13=10 \\ 6x-26=10 \\ 6x=10+26 \\ 6x=36 \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]

Find the slope of the line shown on the graph to the right.What is the slope of the line? The slop of the line is ___

Answers

The formula for determining slope is expressed as

slope = (y2 - y1)/(x2 - x1)

where

y1 and y2 are the y coordinates of initial and final points on the line

x1 and x2 are the x coordinates of initial and final points on the line

From the graph,

when x1 = - 4, y1 = 0

when x2 = 2, y2 = 4

slope = (4 - 0)/(2 - - 4) = 4/(2 + 4) = 4/6

Simplifying 4/6 to its lowest term

slope = 2/3

What function best represents the perimeter of the orange boxes? *

Answers

The formula used to calculate the perimeter of a rectangle is given to be:

[tex]P=2l+2h[/tex]

FIRST BOX

For the first orange box, we have that:

[tex]\begin{gathered} l=x+x=2x \\ h=2 \end{gathered}[/tex]

Note that the box is divided into 2 parts.

Therefore, this perimeter is:

[tex]P_1=2(2x)+2(2)=2(2x)+4[/tex]

SECOND BOX

For the second orange box, we have that:

[tex]\begin{gathered} l=x+x+x=3x \\ h=2 \end{gathered}[/tex]

Note that the box is divided into 3 parts.

Therefore, the perimeter is:

[tex]P_2=2(3x)+2(2)=2(3x)+4[/tex]

Using the associative property of multiplication, we have that:

[tex]P_2=3(2x)+4[/tex]

Since x = 5, we have:

[tex]\begin{gathered} P_1=2(10)+4 \\ P_2=3(10)+4 \end{gathered}[/tex]

where 2 and 3 are the number of divisions of the boxes.

If we represent the number of divisions with x, we have the perimeter's function to be:

[tex]P=10x+4[/tex]

ANSWER

The correct option is the THIRD OPTION.

a smmall rectangular tray measures 16 cm by 18 cm determine the length of the diagonal . round you're answer to the nearest tenth.m

Answers

Given the dimension of the rectangle:

16 cm by 18 cm

We have the image of the rectangle below:

To find the length of the diagonal AC, use pythagorean theorem since ACD form a right triangle.

Thus, we have:

[tex]\begin{gathered} AC^2=AD^2+DC^2 \\ \\ AC=\sqrt[]{AD^2+DC^2} \end{gathered}[/tex]

Input values into the formula:

[tex]\begin{gathered} AC=\sqrt[]{18^2+16^2} \\ \\ AC=\sqrt[]{324+256} \\ \\ AC=\sqrt[]{580} \\ \\ AC=24.08\approx24.1\text{ cm} \end{gathered}[/tex]

Therefore, the length of the diagonal is 24.1 cm

ANSWER:

24.1 cm

A plane has a speed of 400mi/h. On a windy day, theplane could fly 75 mi with thewind in the same time it tookto fly 65mi against the samewind. What is the rate of thewind?

Answers

The plane has a top speed of 400 miles per hour. That means if it travelled at this same speed on a windy day, it would cover

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An investment of R2000 is made at 10 %per year simple interest for 3 years. The amount earned is there invested for 5 years at 16 %simple interest calculator the value of the investment at the end of 8 year

Answers

Explanation

We are asked to calculate the value of the investment at the end of 8 years

For the first part, we will find how much R2000 will yield after 3 years

[tex]\begin{gathered} A=P(1+rt) \\ P=2000 \\ r=10\text{ \% =0.1} \\ t=3 \\ \\ A=2000(1+0.1\times3) \\ A=2000(1+0.3) \\ A=2000(1.3) \\ \\ A=R2600 \end{gathered}[/tex]

For the second part, we will have to know how much R2600 will yield after 5 years

[tex]\begin{gathered} P=2600 \\ t=5\text{ years} \\ r=16\text{ \%=0.16} \\ \\ A=2600(1+0.16(5)) \\ A=2600(1+0.8) \\ A=R4680 \\ \end{gathered}[/tex]

At the end of the 8 years, the value of the investment will be R4680

Write an equivalent expression of 4(6x+12), and state the property you used to write it.

Answers

Solution

Using the distributive property

4(6x + 12)

[tex]4(6x+12)=4\times6x+4\times12=24x+48[/tex]

Find the radius of the circle with a circumference of 39 yards. Round your answer to the nearest hundredth of a yard.the radius of the circle is blank yards

Answers

Answer:

6.207

Explanation:

The circumference C of the circle is given by

[tex]C=2\pi r[/tex]

where r is the radius.

Now we are given that C = 39 yd; therefore,

[tex]39=2\pi r[/tex]

dividing both sides by 2pi gives

[tex]\frac{39}{2\pi}=\frac{2\pi r}{2\pi}[/tex][tex]r=\frac{39}{2\pi}[/tex][tex]r=6.207yd[/tex]

Hence, the radius of the circle is 6.207 yards.

y=-2xy=x-8how do you do this

Answers

Separate

y =- 2xy

-2xy = x - 8

Now solve first equation

and then second equation

PART2

y = -2x

y= -4x + 10

Is solved by , substracting both equations

Then

(y - y) = -2x - ( -4x + 10)

0 = -2x + 4x - 10

10 = 2x

10/2= xx

(5n+6)(5n-5) distribute property

Answers

We have the following:

[tex](5n+6)\cdot(5n-5)[/tex]

we apply distribute property:

[tex]25n^2-25n+30n-30=25n^2+5n-30[/tex]

Resultant of the distributive property is 25n² + 5n - 30 .

Given,

(5n+6)(5n-5)

Now,

Distributive property in multiplication  : a x (b x c) = (axb) x c

Thus apply the property in the given expression,

(5n+6)(5n-5)

= 25n² - 25n + 30n - 30

Solve the terms with variable n,

= 25n² + 5n - 30

Final expression : 25n² + 5n - 30

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What is the system of inequalities associated with the following graph?A) {y<−1x {+y>1 B) {y>−1 {x+y≥1 C) {y<−1 {x+y≥1 D) {y < -1 {x + y <1

Answers

SOLUTION:

Step 1:

In this question, we are given the following:

What is the system of inequalities associated with the following graph?

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

C) {y<−1

{x+y≥1

Wyatt's eraser box is shaped as a rectangular prism. His erasers are cubes with 1-centimeter sides. The
bottom of the box can hold 14 erasers, and the box is 6 centimeters tall. How many erasers can Wyatt fit
in his box?

Answers

Each eraser has the shape of a cube with a side length of 1 cm.

The eraser box is a rectangular prism (a rectangular box).

We know the bottom of the box can hold 14 erasers. If we lay 14 more erasers on top of it, we would have used 2 cm of the box's height.

We can do it a total of 6 times until we top up the box, thus the total number of erasers that fit the box is 6*14 = 84 erasers

how do i do this i need answers help please

Answers

SOLUTION:

Step 1:

In Question 8, we have that:

The three vertices of Triangle ABC are located in Quadrant III.

The image of Triangle ABC after a reflection in the x-axis in the x-axis is

[tex]\text{Triangle A}^IB^IC^I[/tex]

Then, the triangle

[tex]A^IB^IC^I[/tex]

is located in II -- OPTION B

-3x + 5y = -155x - 2y = -101. Find the solution2. Write an equation to replace the second equation so that the system will have infinitely many solutions.

Answers

Problem

-3x + 5y = -15

5x - 2y = -10

Solution

For this case we can solve x from the first equation and we got:

3x = 5y +15

x= (5y+15)/3

Now we can replace this value into the second equation and we got:

5((5y+15)/3) -2y = -10

25/3y +25 -2y= -10

And solving for y we got:

(25/3 -2)y =-10-25

19/3 y = -35

y= -105/19

And then we can solve for x and we got:

x= (5*(-105/19) +15)/3 = -80/19

which inequality best represents that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C

Answers

that ice cream at -3 degrees C is cooler than ice cream at 1 degrees C:

[tex]-3C^{\circ}<1C^{\circ}[/tex]

A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?

Answers

Answer:

The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.

Explanation:

The given functions are:

[tex]\begin{gathered} f(\theta)=2\cos \theta+\sqrt[]{3} \\ g(\theta)=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]

The springs from the original pogo stick and the toddler's pogo stick length are equal when both functions coincide

That is;

[tex]\begin{gathered} f(\theta)=g(\theta) \\ \Rightarrow2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \end{gathered}[/tex]

Solving the equation, we have:

[tex]\begin{gathered} 2\cos \theta+\sqrt[]{3}=1-\sin ^2\theta+\sqrt[]{3} \\ Subtract\sqrt[]{3}\text{ from both sides} \\ 2\cos \theta=1-\sin ^2\theta \end{gathered}[/tex]

Note the identity below:

[tex]\begin{gathered} \cos ^2\theta+\sin ^2\theta=1 \\ \cos ^2\theta=1-\sin ^2\theta \end{gathered}[/tex]

This means

[tex]\begin{gathered} 2\cos \theta=\cos ^2\theta \\ \cos ^2\theta-2\cos \theta=0 \\ \cos \theta(\cos \theta-2)=0 \\ \cos \theta=0 \\ \Rightarrow\theta=\cos ^{-1}(0)=1 \\ \\ OR \\ \cos \theta-2=0 \\ \cos \theta=2 \\ \theta=\cos ^{-1}(2)=0.9994 \end{gathered}[/tex]

The springs from the original pogo stick and the toddler's pogo stick length are equal after 1 second and 0.9994 second.

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