Write your own word problem and share it with the group. Then translate your problem into its resulting math equation. What steps would you then follow to solve for the variable?

The exact value of a and b is 5 and 5√3 respectively. Thus option D) is correct

From triangle ABC
We have AB = 10 ; And angle A = 30°

Trigonometry is the branch of mathematics that deal with study of triangles.

Now,
cos30= AC/AB
√3/2=b/10
b=5√3

Sin30 = BC/AB
1/2 = a/10
a = 5

Thus, the required value is a = 5, b = 5√3

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Answer:

its the last option

Step-by-step explanation:



Answer:

Step-by-step explanation:

This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:

-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us

-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us

| 2x + 2 | = -10.

Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative is distance, there is no solution to this equation.

Answer:

no solution

Step-by-step explanation:

This is our absolute function for which we are tasked with finding the values of x that make the whole thing equal 6:

-.5 | 2x + 2 | + 1 = 6. Subtracting 1 from both sides gives us

-.5 | 2x + 2 | = 5. Dividing both sides by -.5 gives us

| 2x + 2 | = -10.

Because absolute value is in fact a distance measure, and one of the 2 things in math that will NEVER be negative

Answer:

A =7  B=14

Step-by-step explanation:

AREA OF RING

PERIMETER OF RING

Answer:

1124.

Step-by-step explanation:

The common difference (d)   is -16 - (-28) = 12,  ( also -28 - (-40) = 12).

The nth term of an A.S.  is a1 + d(n - 1)  where a1 = first term, d=common difference.

so the 96th term of the given A.S. is:

-16 + 12(96 - 1)

= -16 + 12*95

= 1124.

-1156Answer:

Step-by-step explanation:

Answer:

A: 4

B: -2

Step-by-step explanation:

calculate dy/dx:

A: 1 to the right and 4 up: gradient is 4/1 = 4

B: 2 to the right and 4 down: gradient is 4/-2 = -2

Answer:

Graph A

Step-by-step explanation:

You can use symmetry to find the inverse of a function because you know that the inverse of a function will be that function reflected across the line y=x. This is a line that has a slope of 1 and runs through the origin. Taking a look at the graph choices given, the only one that appears to have been reflected across y=x is graph A, since all of the points of pre-image and the corresponding points on the image are equally distant from y=x. Hope this helps!

Answer:  A (the first graph)

Step-by-step explanation:

Inverse is when you swap the x's and y's

A = (x, y)  →   A⁻¹ = (y, x)

I took three points from the graph (labeled A, B, C) and found their inverse.

A = (-7, 0)  →   A⁻¹ = (0, -7)

B = (0, 7)   →   B⁻¹ = (7, 0)

C = (9, 9)  →   C⁻¹ = (9, 9)

see graph below

Step-by-step explanation:

[tex] f(x) = 6x -4 \\ f(8) \\ f(x) = 6(8) - -4 \\ f(x) = 48 - 4 \\ f(x) = 44

[/tex]

Answer:

C.44

Step-by-step explanation:

Basically, the question is asking for you to plug in 8 for x into the equation, since the function of x is represented by the equation. Therefore, plug in 8 into the equation like this: 6(8)-4

Multiply 6 and 8, then subtract 4 from the product to get your answer

Answer:

-4/7, -1/19, 7/4

Step-by-step explanation:

The fractions converted into decimals would be -0.05, 1.75, -0.57

Answer:

B

Step-by-step explanation:

∠ 2 + ∠ 3 = 90° ← True

∠ 5 = ∠ 3 ← False

∠ 2 = ∠ 5 ← True ( vertical angles )

∠ 4 = 90° ← True

Thus the statement that you cannot make is ∠ 5 = ∠ 3 → B

Answer:

2....6......10........14.......18

Step-by-step explanation:

Add 4 each time

Answer:

-2

Step-by-step explanation:

The y intercept is where the graph crosses the y axis. The graph crosses the y axis at (0, -2), so the y intercept is -2.

The y intercept is useful in slope intercept form, (y=mx+b), where b is the y intercept.

Answer: -2

Step-by-step explanation: The y-intercept of a graph is where the graph crosses or intersects the y-axis.

Notice that the graph shown here hits the y-axis at -2.

So the y-intercept of this graph is -2.

Answer:

B) 16

Step-by-step explanation:

Answer:

B. 16

Step-by-step explanation:

CAH = Adjacent/Hypotenuse

cos60=8/x

xcos60=8

x= 8/cos60

x=8/0.5

x= 16

Answer:

What am I supposed to do

Step-by-step explanation:

Answer:

b. is correct

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Answer:

Option A

Step-by-step explanation:

Let us first consider the equation at hand. We are given that this equation is as follows, five less than three times a number equals four more than eight times the numbers. Convert this into a numerical format;

[tex]3x - 5 = 4 + 8x[/tex]

where x = " the number "

[tex]3x - 5 = 4 + 8x,\\- 5 = 4 + 5x,\\- 9 = 5x,\\\\x = - 9 / 5 \\\\Solution - Option A[/tex]

If you wish, take a look at this verbal explanation. To solve the equation 3x - 5 = 4 + 8x, one would first subtract 3x on either side of the equation, resulting in the simplified equation - 5 = 4 + 5x. Subtracting - 4 from either side, - 5 - 4 = - 9, and so we receive - 9 = 5x. Dividing 5 on either side, x = - 9 / 5, Option A.

Answer:

Ab, De

Step-by-step explanation:

You need the base and the height in order to find out if the triangles are similar

Answer:

Inequality form

x </ 22

Interval Notation

(-∞,22]

Step-by-step explanation:

Solve for x by simplifying both sides of the inequality, then isolating the varible

Answer:

(B) A right triangle with side length of StartRoot 47 EndRoot and hypotenuse of 10

Step-by-step explanation:

I just took the quiz on edge

Answer:

B

Step-by-step explanation:

Answer:

4√5

Step-by-step explanation:

Distance formula: [tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

Coordinates given:

H(8, 1)

G(0, -3)

d = [tex]\sqrt{(8-0)^2 + (1+3)^2}[/tex] = 4√5

Answer:

StartRoot 80 EndRoot

80 square root is the answer

Step-by-step explanation:

|GH|² = (8 - 0)² + (1 - (-3))²

|GH|² = 64 + 16

|GH|² = 80

GH = sqrt(80)

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Answer:

[tex]y = 0[/tex]

Step-by-step explanation:

Given

Line segment JK

[tex]J = (1,-10)[/tex]

[tex]K = (7,2)[/tex]

Ratio; [tex]m:n= 5:1[/tex]

Required

Find the coordinates of y

From the question; the formula to use is

[tex]y = (\frac{m}{m+n})(y_2 - y_1) + y_1[/tex]

We have that; m = 5; n = 1

[tex]J =(x_1, y_1) = (1,-10)[/tex]

Hence, [tex]y_1 = -10[/tex]

[tex]K = (x_2,y_2)= (7,2)[/tex]

Hence, [tex]y_2 =2[/tex]

Substitute the above values in the given formula;

[tex]y = (\frac{m}{m+n})(y_2 - y_1) + y_1[/tex] becomes

[tex]y = (\frac{5}{5+1})(2 - (-10)) + (-10)[/tex]

Solve brackets

[tex]y = (\frac{5}{6})(2 +10)) - 10[/tex]

[tex]y = (\frac{5}{6})(12)) - 10[/tex]

Open bracket

[tex]y = \frac{5}{6} * 12 - 10[/tex]

[tex]y = \frac{5*12}{6}- 10[/tex]

[tex]y = \frac{60}{6}- 10[/tex]

[tex]y = 10 - 10[/tex]

[tex]y = 0[/tex]

Answer: 0

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

This statement demonstrates the commutative property (of addition). This is because even though the order is switched, the result will remain unchanged and they are equal to each other.

Answer:

Commutative Property of addition

Step-by-step explanation:

This statement demonstrates the commutative property (of addition). means that no. After the order of your calculation, the end result will always be the same.

This is only applicable to addition and multiplication.

Hope this helps

Answer:

[tex](9y^2-4x)\,(9y^2+4x)=81y^4-16x^2[/tex]

and it is the special factor product that leads to a difference of squares

Step-by-step explanation:

The product: [tex](9y^2-4x)\,(9y^2+4x)[/tex]

is a product of the form:

[tex](a-b)\,(a+b) = a^2-b^2[/tex]

which leads as shown to a difference of squares. So they binomials [tex](a-b)[/tex] and [tex](a+b)[/tex]  are the factors of the difference of squares [tex]a^2-b^2[/tex].

In our case, the product:

[tex](9y^2-4x)\,(9y^2+4x)= (9y^2)^2-(4x)^2=81y^4-16x^2[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Tricia is correct because the sides of the triangle are congruent since they are  equidistant from the center of the circle.

Step-by-step explanation:

Given that the sides of ΔABC inscribed in a circle are equidistant from the center. This implies the triangle is drawn within the circumference of the circle with a center.

Bisecting the three sides of the triangle shows that the three bisectors intersect at a point which is the center of the circle, and the lines are equidistant to this point. This proves that the length of the sides of the triangle are equal, so that the triangle is an equilateral triangle. Therefore, Tricia's statement is correct.

Answer:

60

Step-by-step explanation:

hexagon is 6 sided shape. 10 * 6=60

elimination means to get rid of one variable by altering the coefficients of variable (by multiplying and diving by some constant number)

in this case, if you just add the two equation, y gets cancelled you get 5x=20 or x=4

put it in any equation to get y (this works because both lines pass through the same point, so they must satisfy that point) to get y=2

Answer: (4,2)

Step-by-step explanation:

You can solve this systems of equation by substitution, graphing, and elimination

Solving by Elimination was found to be the easiest for me.

3x+2y=16

2x-2y=4

eliminate 2y because a positive and a negative will equal zero.

3x+2x=5x, 16+4=20

5x=20, divide 5 on both sides

x=4

Now we solve for y

You can plug in 4 for x in either equations

I did the first equation

3(4) +2y=16

3*4=12

12+2y=16

-12        -12

2y=4

divide 2 on both sides

y=2

Answer is (4,2)

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Answer:

x≤1/2

Step-by-step explanation:

4x+16 ≤18

Subtract 16 from each side

4x+16-16 ≤18-16

4x≤2

Divide by 4

4x/4 ≤2/4

x≤1/2

Answer:

D

Step-by-step explanation:

she made a sign error when multiplying and should have had 256 as an answer

Answer:

the answer is D

Step-by-step explanation:

I'm taking the test now

Answer:

Option (B)

Step-by-step explanation:

In the figure attached,

A straight line is passing through two points (0, 2) and (3, 1).

Slope of this line ([tex]m_1[/tex]) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                   = [tex]\frac{2-1}{0-3}[/tex]

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

Let the slope of a parallel to the line given in the graph = [tex]m_2[/tex]

By the property of parallel lines,

[tex]m_1=m_2[/tex]

[tex]m_2=-\frac{1}{3}[/tex]

Equation of a line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Therefore, equation of the parallel line which passes through (-3, 0) and having slope = [tex]-\frac{1}{3}[/tex] will be,

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

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

Option (B). will be the answer.

Answer:

Step-by-step explanation:

Negative Radicand

The roots of the equation are imaginary because of negative radicand.

An imaginary number is a number that, when squared, has a negative result. Essentially, an imaginary number is the square root of a negative number and does not have a tangible value.

According to the given question.

We have to take square root both sides of the equation.

Then we get imaginary roots only when there is some negative number under the radical symbol. That is when the radicand is negative.

Hence, the roots of the equation are imaginary because of negative radicand.

Thus, option 1 is correct.

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