Find x and y. Please write your answer in simplified radical form.

Answer:

6

Step-by-step explanation:

cause we will add them together

5x -1 = 3x +11

2x=12

x=6

The value of x if ∠3 = 5x - 1, and ∠5 = 3x + 11, is 6.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given;

∠3 = 5x - 1, and ∠5 = 3x + 11,

Calculate the value of x as shown below,

∠3 = ∠5  (Alternate interior angles between parallel lines are equal)

5x - 1 = 3x + 11

5x - 3x = 11 + 1

2x = 12

x = 12 / 2

x = 6

Thus, the value of x is 6.

To know more about angle:

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Answer:

-6.912

Step-by-step explanation:

Answer: -6.912

Step-by-step explanation: -6.912 Would Be Your Answer. Have A Great Day!

Answer:

59,000 * .02= $1,180 commission plus $300 = $1480

Answer:0.15789474

Step-by-step explanation:

5/2=2.5s+ 3/4=0.75 = 9/4=2.25

add 5/2/2.5 to the other side{like terms because of the letter s} which would=4.75s

now divide that to other side of .75 divided by 4.75 which would equal= 0.15789474

(i think, sorry if its incorrect)

Answer:

The value of s is -0.33

Step-by-step explanation:

Given the equation

[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]

we have to solve the above equation

[tex]\frac{5}{2s}+\frac{3}{4}=\frac{9}{4s}[/tex]

[tex]\frac{5}{2s}-\frac{9}{4s}=-\frac{3}{4}[/tex]

[tex]\frac{10-9}{4s}=-\frac{3}{4}[/tex]

[tex]\frac{1}{4s}=-\frac{3}{4}[/tex]

[tex]s=-\frac{1}{3}=-0.33[/tex]

The value of s is -0.33

Answer:

7+24i

Step-by-step explanation:

A math conjugate is formed by changing the sign between two terms in a binomial. For instance, the conjugate of x + y is x - y. We can also say that x + y is a conjugate of x - y. In other words, the two binomials are conjugates of each other.

The conjugate of a complex number is obtained by negating its imaginary part while keeping the real part unchanged. So, for 7 - 24i, the conjugate is 7 + 24i. The real part remains 7, and the imaginary part changes from -24i to +24i.

In the field of mathematics, specifically complex numbers, the conjugate of a complex number is formed by changing the sign of its imaginary part. Given the complex number 7 - 24i, its conjugate is obtained by changing the sign of the imaginary part (-24i) to a positive. So, the conjugate of 7 - 24i is 7 + 24i.

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Answer:

-3

Step-by-step explanation:

f(-1) = 3(-1)

f(-1) = -3

Answer with explanation:

The given function is:

     ⇒ y =3 x

And it's inverse function can be Calculated by, replacing , x by y, and , y by x, in the above equation

⇒x=3 y, is the equation of inverse function.

Both the original function , and inverse function passes through origin, As well as Origin is the point of Intersection, which can be shown as follows:

3 x-y=0-----(1)

x-3 y=0

3 x - 9 y =0 ------(2)

EQ.(1) - Eq.(2)

3 x - y - (3 x- 9 y)=0

-y + 9 y=0

8 y=0

y=0

Putting the value of , y in equation (2)

x=3 × 0

x=0

⇒Point of intersection of ,f(x) and it's inverse =(0,0)

Answer:

You can find the point of intersection of the line with the y-axis and the  the point of intersection of the line with the x-axis. See the graph attached.

Step-by-step explanation:

Find the intersection with the y-axis. Substitute [tex]x=0[/tex] into the equation and solve for y:

[tex]y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}[/tex]

[tex]y[/tex]≈3.33

Find the intersection with the x-axis. Substitute [tex]y=0[/tex] into the equation and solve for x:

[tex]y-3=\frac{1}{3}(x+1)[/tex]

[tex]0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10[/tex]

Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)

Answer:

About 11.96

Step-by-step explanation:

The mean of a data set is basically the average.

To find the average, add up all of the data values and then divide by the amount of numbers there are.

First, add the numbers.

3 + 19 + 21 + 6.8 + 9.3 + 21.7 + 2.9 = 83.7

There are 7 numbers in this data set so divide 83.7 by 7

83.7/7 = 11.95714285714286

Round this number to the nearest hundreth, to get 11.96

So, the mean of this data set is 11.96

I hope this helps!

Since the perimeter of said hexagon is 120√3, we simply multiply this number by 10 and divide it by 2.

1200√3/2 = 600√3

Answer:

The explicit rule is:

Step-by-step explanation:

The explicit rule is given by:

[tex]a_n=a_1+d(n-1)[/tex]

The given sequence is 25,21,17,13

[tex]a_1=25[/tex]

d=21-25

d=-4

We plug in the values into the formula to get;

[tex]a_n=25+-4(n-1)[/tex]

[tex]a_n=25-4n+4[/tex]

[tex]a_n=29-4n[/tex]

Answer:

314 cm²

Step-by-step explanation:

It's not the point O, but the circle O, a point has no area.

The area of a circle is given by the formula A = π r²

We don't have r (radius), but we have the diameter, which is double the radius.  So, r = d / 2 = 20 cm / 2 = 10 cm

Now, we can plug r directly into the equation:

A = π r² = π 10² = 100π = 314 cm²

Answer:

Option a) [tex]h=28\ cm[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

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

we have

Note In this problem the volume is equal to [tex]847\pi\ ml[/tex] instead of [tex]847\ ml[/tex]

so

[tex]847\pi\ ml=847\pi\ cm^{3}[/tex]

[tex]r=5.5\ cm[/tex]

substitute in the formula and solve for h

[tex]847\pi=\pi(5.5)^{2}h[/tex]

simplify

[tex]847=(5.5)^{2}h[/tex]

[tex]h=847/(5.5)^{2}[/tex]

[tex]h=28\ cm[/tex]

Answer:

[tex]f(x)=|x+4|+2[/tex]

Step-by-step explanation:

The given absolute value function is

[tex]f(x)=|x|[/tex]

This is the base or the parent function.

The transformation [tex]f(x)=|x+b|+c[/tex] will shift the parent function b units to the left and c units up.

From the question, b=4 units and c=2 units.

The new equation is [tex]f(x)=|x+4|+2[/tex]

Answer:  The equation of the new function is [tex]f(x)=|x+4|+2.[/tex]

Step-by-step explanation:  We are given to find the equation of the new function if we apply the following changes to the absolute value parent function f(x)=lxl :

Shift 4 units left   and  Shift 2 units up.

We know that

if we shift the absolute value parent function f(x) = |x| to h units left and k units up, then the new equation will be

[tex]f(x)=|x+h|+k.[/tex]

Therefore, if the function is shifted 4 units left and 2 units up, then the equation of the new function will be

[tex]f(x)=|x+4|+2.[/tex]

Thus, the equation of the new function is [tex]f(x)=|x+4|+2.[/tex]

Answer:

Finance charge =  $2.32

new balance = $201.51

Step-by-step explanation:

Finance charge = Previous balance×Periodic percentage rate

The previous balance is 199.19

The annual percentage rate is 0.14. Therefore, the periodic percentage rate is; (0.14/12)

Finance charge = 199.19 * (0.14/12)

                           = 2.3239 = $2.32

new balance = previous balance + finance charge

                      = 199.19 + 2.32

                      = $201.51

Plot the points ( -4,2.5), (-3,3), (-2,1.5), (-1,2), (0,1), (1,2), (2,3.5), (3,0.5), (4,2.5) then connect them with a line

Answer:

120

Step-by-step explanation:

it is an obtuse angle

The answer is:

The missing angle "x" is equal to 130°.

We need to remember that the sum of all of the angles of any polygon will be all equal to 360°.

So, we are given the following exterior angles:

[tex]140\°\\34\°\\56\°\\[/tex]

Now, if the sum of all the exterior angles is equal to 360°, we can use it to calculate "x", so:

[tex]360\°=140\°+34\°+56\°+x\\\\x=360\°-(140\°+34\°+56\°)=360\°-230\°\\\\x=130\°[/tex]

Hence, the missing angle "x" is equal to 130°.

Have a nice day!

Answer:

Option 1 and 2 are correct.

Step-by-step explanation:

1. {x:x <-3 or >4}

Here the values of x can be less than -3 or the values of x can be greater than 4. Since 5 is greater than 4 so, 5 is included in the solution

2. {x:x ≥5}

Here the values of x can be greater than or equal to 5. So, 5 is included in the solution.

3. {x:x <5}

Here the values of x can be less than 5. So, 5 is not included in the solution

4. {x:0<x<4}

Here the value of x is greater than 0 but less than 4. So, 5 is not included in the solution

So, Option 1 and 2 are correct.

Answer:

True

Step-by-step explanation:

The number 18.34 has four significant figures. Yes it is true that it has four significant figures.

For significant figures, we start counting from the first non zero digit.

The first non zero digit in 18.34 is 1.

Count from this number to the last number, we have four numbers.

Therefore, it is true that the number 18.34 has four significant figures.

Answer:

The answer is C. 119cm³

Step-by-step explanation:

SA= [tex]\pi r^{2} +\pi rl[/tex]

    = 49[tex]\pi +\pi 7(10)[/tex]

    = 49[tex]\pi +20\pi[/tex]

SA= 119[tex]\pi[/tex]

Answer:

The correct answer is option C.   119π cm²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the base radius and l is the lateral edge

To find the surface area of given cone

Here r = 7 cm and l = 10 cm

Surface area =  πrl + π r² =( π * 7 * 10) + (π *7²)

  = 70 π + 49π

  = 119π cm²

Therefore correct answer is option C.    119π cm²

Answer:

dssdac

Step-by-step explanation:

Answer:

1.5*10^-2

Step-by-step explanation:

You mean 15/1000 written in scientific notation?

In this case, it would be- 1.5*10^-2.

Solution:

Let t = working together in terms of days

(1/4) + (1/12) = 1/t

Solve for t.

Multiply both sides by the LCD.

LCD = 12t

3t + t = 12

4t = 12

t = 12/4

t = 3

Together, they can do the job in 3 days.

Answer:

the allocation of overhead to department A is $8,000.00

Step-by-step explanation:

Given that Department A had sales of $200,000.00 and Department B had sales of $600,000.00, the ratio of department A's sales to that of department B is 200,000.00 / 600,000.00 = 1/3.

The total overhead expenses were $32,000.00, the allocation of overhead to department A is  32,000.00 / (3 + 1) = $32,000.00 / 4 = $8,000.00

Answer:

[tex]\cos^{-1}(\frac{6.3}{9.8})[/tex]

[tex]\sin^{-1}(\frac{7.5}{9.8})[/tex]

Step-by-step explanation:

Recall the mnemonics SOH-CAH-TOA

The sine ratio is the length of the opposite side expressed over the hypotenuse.

[tex]\sin m\angle ABC=\frac{7.5}{9.8}[/tex]

Take the sine inverse of both sides to get;

[tex]m\angle ABC=\sin^{-1}(\frac{7.5}{9.8})[/tex]

The cosine ratio is the length of the adjacent side expressed over the hypotenuse.

[tex]\cos m\angle ABC=\frac{6.3}{9.8}[/tex]

Take the cosine inverse of both sides to get;

[tex]m\angle ABC=\cos^{-1}(\frac{6.3}{9.8})[/tex]

Answer:

Second graph

Step-by-step explanation:

The second graph is the correct one.  Why?  because the y intercept is (0, 3), and also because the base, 1/5, is between 0 and 1, which leads to a decaying exponential graph.

Answer:

The average rate of change is:

[tex]\frac{13}{161}[/tex]

Step-by-step explanation:

The rational function given to us is;

[tex]f(x)=\frac{3x+4}{2x+7}[/tex]

[tex]f(0)=\frac{3(0)+4}{2(0)+7}[/tex]

[tex]f(0)=\frac{4}{7}[/tex]

[tex]f(8)=\frac{3(8)+4}{2(8)+7}[/tex]

[tex]f(0)=\frac{28}{23}=1[/tex]

The average rate of change of this function from x=0 to x=8  is the slope of the secant line connecting:

(0,f(0)) and (8,f(8))

Average rate of change =[tex]=\frac{f(8)-f(0)}{8-0}[/tex]

[tex]=\frac{\frac{28}{23}-\frac{4}{7} }{8}[/tex]

[tex]=\frac{13}{161}[/tex]

Answer:

Kyle purchased 12 pencils

Step-by-step explanation:

p= pencils

1.24p - 5.12 = 20

or, you can do this back wards like this....

20 - 5.12 = 14.88

14.88 / 1.24 = 12

p=12

(sorry for any confusion, this is just how my brain works...)

Kyle bought 12 pencils at $1.24 each. This determination is based on subtracting the amount of change he received from his $20 payment and dividing by the cost per pencil.

Kyle bought x pencils for $1.24 each, paid with a $20 bill, and received $5.12 in change. Therefore, the total amount he spent can be calculated by subtracting the change from the total payment ($20 - $5.12 = $14.88). As he spent this amount on pencils that cost $1.24 each, the number of pencils he bought can be determined by dividing the total spent by the cost per item ($14.88 / $1.24). Therefore, Kyle bought approximately 12 pencils (the exact result is 12.003, but as pencils cannot be fractional, we round down to the nearest whole number).

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Find the x intercepts by setting each x to equal 0:

(4-x)=0

4 -4 = 0

First x intercept = (4,0)

(x+2) = 0

-2 + 2 = 0

Second x intercept = (-2,0)

Now find the Y intercept by setting the x's to 0 and solve for y:

y = (4-0)(0+2)

y = 4*2

y = 8

The Y intercept is (0,8)

Now find the graph the the parabola crosses the x axis at -2 and 4 and also crosses the Y axis at 8.

Graph A is the correct one.

Answer:

d. 40 pounds

Step-by-step explanation:

We know both weights of the astronaut, and we know one of the weight of the rock... we need to find the other weight of the rock (on Earth).

The easiest way to deal with those problems is to use a cross-multiplication.

We'll place on top the weights on Earth and as denominators the weights on Mars:

[tex]\frac{x}{16} = \frac{180}{72}[/tex]

So we isolate x = (16 * 180) / 72 = 2,880 / 72 = 40 pounds.

The rock then weights 40 pounds on Earth.

Answer:

[tex]A=(2x^{2}+9x-18)\ m^{2}[/tex]

Step-by-step explanation:

Let

L-----> the length of the concert hall

W----> the width of the concert hall

we know that

The area of a rectangle ( concert hall) is equal to

[tex]A=LW[/tex]

we have

[tex]L=(x+6)\ m[/tex]

[tex]W=(2x-3)\ m[/tex]

substitute the values

[tex]A=(x+6)(2x-3)\\ \\A=2x^{2} -3x+12x-18\\ \\A=(2x^{2}+9x-18)\ m^{2}[/tex]

The area of the concert hall's floor, in square meters, is represented by the simplified algebraic expression 2x² + 9x - 18, which is derived by multiplying the hall's length (x + 6) by its width (2x - 3) then simplifying the resulting expression.

The area of a rectangle is calculated by multiplying the length by the width. In this case, the length of the concert hall is given as (x + 6) meters and the width as (2x - 3) meters. Therefore, the area of the concert hall's floor, expressed in square meters, is the product of these two expressions.

So, you multiply (x + 6) by (2x - 3) to get the area, which gives you the following expression: 2x² - 3x + 12x - 18. Now, simplify this expression by combining like terms.

The simplified expression for the area of the floor in square meters is then 2x² + 9x - 18.

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