Find the measure of the reference angle for an angle of 152º.

Answer:

x = (C-By)/A

Step-by-step explanation:

Ax+ By = C

We want to isolate x

Subtract By from both sides

Ax+ By-By = C-By

Ax = C - By

Now divide both sides by A

Ax/A = (C-By)/A

x = (C-By)/A

[tex]Ax+ By = C\\Ax=C-By\\x=\dfrac{C-By}{A}[/tex]

Answer:

x=0.76 or -5.26

Step-by-step explanation:

You can apply the completing square method to solve this ;

[tex]2x^2+9x=8\\\\[/tex]

Rewrite the equation with a zero like below

[tex]2x^2+9x-8=0[/tex]

This is by taking 8 to the left side of the equation

Divide the terms by 2 in x²

[tex]\frac{2x^2}{2} +\frac{9x}{2} -\frac{8}{2} =\frac{0}{2}[/tex]

[tex]=x^2+4.5x-4=0[/tex]

Move the number term to the right side of the equation

[tex]x^2+4.5x=4[/tex]

complete square on the lefts side of the equation, how?

[tex]=(\frac{b^}{2})^2 =(\frac{4.5}{2} )^2=5.0625[/tex]

balance the equation by adding this value to the right side , in this form

[tex]x^2+4.5x+5.0625=4+5.0625\\\\[/tex]

Factorize the left side

[tex](x+2.25)(x+2.25)=9.0625\\\\\\(x+2.25)^2=9.0625\\[/tex]

Eliminate the square on the left side

[tex]x+2.25=\sqrt{9.0625}[/tex]

x+2.25= ± 3.010

Solve for x

x=+3.010-2.25=0.76

or

x=-3.010-2.25=-5.26

Answer:

x = 0.76 or x= -5.26

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given a quadratic equation,

2x² + 9x = 8

⇒ 2x² + 9x - 8 = 0

To find the solution

Here a = 2, b = 9 and c = -8

x = [-b ± √(b² - 4ac)]/2a

 = [-9 ± √(9² - 4*2*(-8))]/2*2

 = [-9 ± √(81 +64)]/4

 =  [-9 ± √(145]/4

 =  [-9 ± 12.04]/4

x =  [-9 + 12.04]/4 or x =  [-9 - 12.04]/4

x = 0.76 or x= -5.26

No the negative slope means the line moves down from left to right.

Hope this helps.

r3t40

Answer:

It slopes upwards from right to left.

Step-by-step explanation:

A negative slope means that a line rises from right to left. Like a back slash \.

Answer:

9

Step-by-step explanation:

(9*3) = 27 which is 20 more than 7

Answer: 9

Step-by-step explanation:

Answer:

The answer is the first one.

Step-by-step explanation:

What helped me figure this out was going to desmos.com which is a great site for graphing. If you put in the equations this should help you find the answer. I hope this helps love! :)

Answer: A. [tex]\dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]

Step-by-step explanation:

The equation of ellipse centered at origin is when the horizontal major axis (2a) and verticel minor axis (2b) is the major axis  :-

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

From the given picture , [tex]a=10[/tex]

[tex]b=8[/tex]

Now, the equation of the given ellipse :-

[tex]\dfrac{x^2}{(10)^2}+\dfrac{y^2}{(8)^2}=1\\\\\Rightarrow\ \dfrac{x^2}{100}+\dfrac{y^2}{64}=1[/tex]

Answer:

1698

Step-by-step explanation:

Answer:

They would need 1698 dominoes to complete the chain.

Step-by-step explanation:

all you would do is subtract 2,505 by 807 and you would get the same answer.

Answer:

Part 1) The volume of pyramid A is two times the volume of pyramid B

Part 2) The new volume of pyramid B is equal to the volume of pyramid A

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of pyramid

h is the height of the pyramid

Part 1

The heights of the pyramids are the same

Find the volume of pyramid A

Find the area of the base B

[tex]B=10*20=200\ m^{2}[/tex]

substitute

[tex]VA=\frac{1}{3}(200)h[/tex]

[tex]VA=\frac{200}{3}h\ m^{3}[/tex]

Find the volume of pyramid B

Find the area of the base B

[tex]B=10^{2}=100\ m^{2}[/tex]

substitute

[tex]VB=\frac{1}{3}(100)h[/tex]

[tex]VB=\frac{100}{3}h\ m^{3}[/tex]

Compare the volumes

[tex]VA=2VB[/tex]

The volume of pyramid A is two times the volume of pyramid B

Part 2)

If the height of pyramid B increases to twice that of pyramid A

we have that

[tex]VA=\frac{200}{3}h\ m^{3}[/tex]

Find the new volume of pyramid B

we have

[tex]B=100\ m^{2}[/tex]

[tex]h=2h\ m[/tex]

substitute

[tex]VB=\frac{1}{3}(100)(2h)[/tex]

[tex]VB=\frac{200}{3}h\ m^{3}[/tex]

Compare the volumes

[tex]VA=VB[/tex]

The new volume of pyramid B is equal to the volume of pyramid A

Answer:

The volume of pyramid A is  twice the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is  equal to  the volume of pyramid A.

Step-by-step explanation:

Correct for plato :)

Answer:

 [tex]f(-\frac{1}{2}) = 1[/tex]

[tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]

Step-by-step explanation:

Given the function [tex]f(x) = 4x + 3[/tex] and the function [tex]g(x) = 3x[/tex], to evaluate for [tex]x=-\frac{1}{2}[/tex], you need to substitute it into each function.

Then, for the function f(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = 4(-\frac{1}{2}) + 3[/tex]

 [tex]f(-\frac{1}{2}) = -\frac{4}{2}+ 3[/tex]

 [tex]f(-\frac{1}{2}) = -2 + 3[/tex]

 [tex]f(-\frac{1}{2}) = 1[/tex]

For the function g(x), when  [tex]x=-\frac{1}{2}[/tex], you get:

[tex]g(-\frac{1}{2} ) = 3(-\frac{1}{2})[/tex]

 [tex]g(-\frac{1}{2} ) = -\frac{3}{2}[/tex]

Answer:

f(-1/2) = 1

g(-1/2) =-3/2

Step-by-step explanation:

f(x) = 4x+3

Let x = -1/2

f(-1/2) = 4(-1/2) +3

f(-1/2) = -2 +3

f(-1/2) =1

g(-1/2) = 3(-1/2)

          = -3/2  

Answer:

right 2, up 3

Step-by-step explanation:

The original function is:

[tex]f(x) = x^2[/tex]

Translated to:

[tex]g(x)=(x-2)^2+3[/tex]

Lets look at the constants that are added or subtracted to determine the transformation.

As -2 is is added to x (grouped with x), the transformation is a horizontal transformation. The shift is of two to the right.

As +3 is not grouped with x, the transformation is vertical. The shift is vertical shift of 3 to upward direction.

So the correct answer is:

right 2, up 3 ..

Answer:

The quotient is 3x-8

Step-by-step explanation:

(6x^2-x-40)÷ (5 + 2x)

The above equation can be written as

(6x^2-x-40)÷ (2x + 5)

The division is shown in the figure below.

The quotient is 3x-8

Answer:

(6x^2-x-40)÷ (5 + 2x)

The above equation can be written as

(6x^2-x-40)÷ (2x + 5)

The division is shown in the figure below.

The quotient is 3x-8

Step-by-step explanation:

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

we have

[tex]3x-\frac{1}{9}y=18[/tex]

Substitute the value of y=27 in the equation and find the value of x

so

[tex]3x-\frac{1}{9}(27)=18[/tex]

[tex]3x-3=18[/tex]

[tex]3x=18+3[/tex]

[tex]3x=21[/tex]

[tex]x=7[/tex]

The missing value in the table is 38, obtained by using the concept of average rate of change which is consistent across the given values, suggesting that the function is linear.

In this question, the student needs to find the unknown value denoted by the "?" in the table of a function f(x), whose x-values are -2, 2, 5, 9, and the corresponding f(x)-values are 5, 17, 26, and unknown (?) respectively.

To predict the next value, we can use the concept of the average rate of change which is defined as the difference in the y-values divided by the difference in the x-values over the interval. This rate of change is the same between every pair of successive x-values in this table which suggests that the function might be linear.

We can calculate this using the formula, Average Rate of Change = Δf(x) / Δx. To illustrate, the average rate of change from x = -2 to x = 2 is (17-5) / (2 - (-2)) = 12 / 4 = 3. Similarly, the change from x = 2 to x = 5 is (26 - 17) / (5 - 2) = 9 / 3 = 3. Thus, the average rate of change is constant and equals 3.

If we follow the same pattern, then the missing f(x) value when x = 9 should be 26 (the last provided y-value) plus 4 (which is the next x interval) times 3 (the average rate of change) = 26 + 4*3 = 38. Hence, the missing value denoted by "?" is 38.

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Answer:

Output

Step-by-step explanation:

A function takes values of x (the horizontal axis on a plane)and returns the corresponding values of y (the vertical axis on a plane).

Thus, the values we get for y depends on the value of x.

The x's values that we give in a function are called the domain, and the values that the function returns to us are called the range of the function (the y's).

So a word that describes the range of a function well is that the range is the output of the function. Because the range is the set of values that the function returns to us when we plug an x value.

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=-\cfrac{5}{4}(x-8)\implies y+8=-\cfrac{5}{4}(x-8)[/tex]

The equation in point-slope form for this line is 4y = -5x + 8.

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the point-slope form. Here both the slope (m) and y-intercept (c) have real values. It is known as point-slope form as it gives the definition of both the slope, y-intercept and the points mentioned in the line.

It is given that the line passes through the point (8.-8) and has a slope of -5/4.

The general representation for straight line is y = mx + c .

Here, m = -5/4 , x = 8 and y = -8 .

Thus we have ,

⇒ -8 = -5/4 * 8 + c

⇒  c = 10 - 8

∴   c = 2

The y-intercept is 2.

The equation of straight line becomes,

⇒ y = -(5/4)x + 2

∴  4y = -5x + 8

Therefore, the equation in point-slope form for this line is 4y = -5x + 8.

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Answer:

values of x,y and z are x = -2, y= -9 and z=5

Step-by-step explanation:

2x+4y+1z=−35    eq(1)

3x+7y+7z=−34    eq(2)

2x+10y+6z=−64  eq(3)

We can solve using elimination method

Subtracting eq (1) from eq(3)

2x + 10y +6z = -64

2x +4y +1z = -35

______________

6y + 5z = -29     eq(3)

Multiplying eq(2) with 2 and eq(3) with 3 and subtracting

6x + 14y +14z = -68

6x + 30y +18z = -192

-     -         -          +

_________________

-16y -4z = 124     eq(4)

Multiply eq(3) with 4 and eq(4) with 5 and add both equations

24y + 20z = -116

-80y - 20z = 620

______________

-56y = 504

y = -504/56

y= -9

Putting value of y in equation(3)

6y + 5z = -29

6(-9) + 5z = -29

-54 + 5z = -29

5z = -29+54

5z = 25

z = 25/5

z =5

Now, putting value of y and z in eq(1)

2x + 4y +1z = -35

2x + 4(-9) +1(5) = -35

2x -36+5 = -35

2x -31 = -35

2x = -35+31

2x = -4

x= -4/2

x=-2

So, values of x,y and z are x = -2, y= -9 and z=5

Answer:

6w + 7

Step-by-step explanation:

There is nothing to simplify. Just remove the parentheses.

the least possible quotient of the two numbers would be C.) 111

Answer:

A=280in^2

Step-by-step explanation:

3*3=9

A=2LW+2WH+2LH

A=2(8*4)+2(4*9)+2(8*9)

A=2(32)+2(36)+2(72)

A=64+72+144

A=280in^2

Final answer:

Yes, 4/2 and 14/7 form a proportion because both ratios simplify to 2/1, which indicates they are equal and therefore proportional.

Explanation:

To determine if two ratios, 4/2 and 14/7, form a proportion, we need to compare the simplified forms of each ratio and see if they are equivalent. A proportion exists when two ratios are equal to each other. Simplifying both ratios, we get 4/2 = 2/1 and 14/7 = 2/1. Since both simplified ratios are equal to 2/1, we can conclude that 4/2 and 14/7 indeed form a proportion.

Answer:

x = 20

Step-by-step explanation:

see attached

From Pythagoras, [tex]\(z^2 - y^2 = 369\)[/tex]. Solving, z - y = 19, z + y = 19, yielding z = 19. Substituting, x = 17.

Given that Triangle A and Triangle B are right angle triangles with similar heights 'x' and different perpendicular (say 'y' and 'z' respectively).

From the Pythagoras theorem, we know that:

[tex](Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2[/tex]

Substituting the given values, we get:

[tex]y^2 = 16^2 + x^2[/tex]

[tex]z^2 = 25^2 + x^2[/tex]

Subtracting the two equations, we get:

[tex]z^2 - y^2 = 25^2 - 16^2[/tex]

(z - y)(z + y) = 625 - 256 = 369

z - y = 19

z + y = 369 / 19 = 19

Adding the two equations, we get:

2z = 38

z = 19

Substituting the value of 'z' in the equation:

[tex]z^2 = 25^2 + x^2[/tex]

[tex]19^2 = 25^2 + x^2[/tex]

[tex]x^2 = 19^2 - 25^2 = 289[/tex]

[tex]x = sqrt(289)[/tex] = 17

Therefore, the value of 'x' is 17.

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For this case we have the following equation:

[tex]2x-1 = 3[/tex]

If we add 1 to both sides of the equation we have:

[tex]2x = 3 + 1\\2x = 4[/tex]

Dividing between 2 on both sides of the equation we have:

[tex]x = \frac {4} {2}\\x = 2[/tex]

The graph of the solution is shown in the attached figure.

Answer:

See attached image

Answer:

D

Step-by-step explanation:

It turns out from similar triangles, that 7/BD = BD / 18. Use triangles  ABD and BDC to show this relationship. Solving this equation will give you BD

BD^2 = 7*18

BD^2 = 126     Just leave it in this form. Do your rounding at the end.

Because triangle BDC is a right angle triangle, use the Pythagorean Theorem to solve for m

m^2 =  BD^2 + 7^2

m^2 = 126 + 49

m^2 = 175                         Take the square root of both sides.

sqrt(m^2) = sqrt(175)

m = 13.22

so the answer is D

Answer:

Similarity cannot be determined ⇒ answer D

Step-by-step explanation:

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle

- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and

 m∠C= m∠F then ΔABC ≈ ΔDEF by AAA

2) AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles

   are similar.

- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then

  ΔPQR ≈ ΔDEF by AA

3) SSS similarity : If the corresponding sides of two triangles are

   proportional, then the two triangles are similar.

- Example : In ΔXYZ and ΔLMN, if [tex]\frac{XY}{LM}=\frac{YZ}{MN}=\frac{XZ}{LN}[/tex]

  then the two triangles are similar by SSS

4) SAS similarity : In two triangles, if two sets of corresponding sides

   are proportional and the included angles are equal then the two

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and [tex]\frac{BA}{ED}=\frac{CA}{FD}[/tex]

  then the two triangles are similar by SAS

* Now lets solve the problem

- In the triangles ABC and DEF

∵ m∠B = m∠E = 105°

∵ AB/DE = 16/4 = 4

∵ AC/DF = 36/9 = 4

∴ AB/DE = AC/DF = 4

∴ The two pairs of sides are proportion

∵ ∠B and ∠E are not the including angles between the sides AB , AC

  and DE , DF

∵ We could not find the including angles from the information of the

  problem

∴ We cannot prove the similarity

* Similarity cannot be determined

Answer:

D- can't be determined

Step-by-step explanation:

a p e x work

Answer:

-4

Step-by-step explanation:

mark branliest :))

Hello There!

The quotient of 32 and -8 is -8.

When dividing a positive number by a negative number, your final result will always end up with a negative number so 32 divided by 8 is 4 but it will be -4 instead of 4

To rationalize the denominator and simplify the given expression, multiply both the numerator and denominator by the conjugate of the denominator. Simplify the resulting expression by applying the FOIL method and simplifying square roots. The final simplified expression is 72+24 √6+20 √12/84.

To rationalize the denominator and simplify √6+5 √2/4 √6-3 √2, we need to eliminate the square root from the denominator. To do this, we can multiply both the numerator and denominator by the conjugate of the denominator, which in this case is 4 √6+3 √2. The conjugate of a binomial in the form a+b is a-b. So, we will multiply the numerator and denominator by 4 √6+3 √2:

(3 √6+5 √2)(4 √6+3 √2)/[(4 √6-3 √2)(4 √6+3 √2)]

Next, we can apply the FOIL method in the numerator and the difference of squares in the denominator to expand the expression:

(3*4*6+3*4*2 + 5*4 √6 √2 + 3* √2 √6)/ (16*6 - 9*2)

Simplifying further, we get:

(72+24 √6+20 √12)/102 - 18

The final simplified expression is:

72+24 √6+20 √12/84

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The temperature started at -12 degrees then increases by 8 degrees. This means that you can make an expression to solve this like so...

-12 + 8

When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then take the sign of the largest number. In this case the largest number is 12 and its sign is negative. Your answer will  have a negative sign.

Act as if you are subtracting...

12 - 8 = 4

Take the sign of  the largest number (12)

-4 (third option)<<<This is the temperature now.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

-4F

Step-by-step explanation:

We start at -12

We rise 8

-12 +8

-4

We will then be at -4

Answer:

8.1 ft

Step-by-step explanation:

hyp² = side² + side²

hyp² = 7² + 4²

hyp² = 49 + 16

hyp² = 65

hyp = sqrt of 65

hyp = 8.1 ft

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Answer:

[tex]\large\boxed{\sqrt{65}\ ft}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=4ft,\ leg=7ft,\ hypotenuse=AB[/tex]

Substitute:

[tex]AB^2=4^2+7^2\\\\AB^2=16+49\\\\AB^2=65\to AB=\sqrt{65}[/tex]

Answer:

[tex]\large\boxed{(f+g)(x)=-8x-6}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-5x-4,\ g(x)=-3x-2\\\\\text{Substitute:}\\\\(f+g)(x)=(-5x-4)+(-3x-2)\\\\=-5x-4-3x-2\qquad\text{combine like terms}\\\\=(-5x-3x)+(-4-2)\\\\=-8x-6[/tex]

Answer:

[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]

Step-by-step explanation:

The first number in the sequence, [tex] a_1 [/tex], is -2.

Each number after that is the previous number multiplied by -2.

[tex] a_1 = -2 [/tex]

[tex] a_2 = a_1 \times (-2) = -2 \times (-2) = 4 [/tex]

[tex] a_3 = a_2 \times (-2) = 4 \times (-2) = -8 [/tex]

etc.

[tex] a_n = -2a_{n - 1} [/tex]

We start by stating that [tex] a_1 = -2 [/tex].

Now we need to show that for all n greater than or equal to 2, each number in the sequence is the previous number multiplied by -2.

[tex] a_n = -2a_{n - 1} [/tex]

Answer:

[tex] a_1 = -2;~a_n = -2a_{n - 1}, ~n \ge 2 [/tex]

A recursive formula represents the relationship between each term and the ones before it. In the given geometric sequence (-2, 4, -8, 16,...), each term is -2 times the preceding term, hence the recursive formula is [tex]a_{n} = -2a_{n-1}[/tex] for n>1.

The given sequence is -2, 4, -8, 16, ..., which is an example of a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'.

Looking at the pattern, we notice that each term is -2 multiplied by the prior term. Therefore, the recursive formula for this sequence is [tex]a_{n} = -2a_{n-1}[/tex] where 'an' represents the nth term and 'an-1' represents the previous term, and n > 1.

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