What is the length of QR?

Answer:

They have different slopes and different y-intercepts, so they have no solution

Step-by-step explanation:

Answer:

Infinite solutions Answer explained below

Step-by-step explanation:

Let us see the various conditions for intersections of two lines in simplest way.

1. Same slope and same y intercept : Infinite solutions

2. Same slope and different y intercepts : No solution

3. Different slope and same y intercept : unique solution

4. Different slope and different y intercept : Unique solution

Here slope means the tangent of the angle line makes with the positive x axis and y intercept is the y coordinate at which the line intersect the y axis.

In our equations , we our slopes and y intercepts as

y=-3x+6

slope = -3 and y intercept = 6

y=6-3x

slope = -3 and y intercept = 6

Hence same slope and same y intercept , thus have infinite solutions

Answer:

The answer is the first one. Inside the absolute value symbols it is negative but absolute value answers are always positive. Instead of -30 the answer is 30.

Answer:

332 square inch

Step-by-step explanation:

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 * apothem*perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Solving for the area:

Area = 1/2*10*66.3

Area = 331.5 inches²

The answer is 332.

Answer:

Option C. 332 in²

Step-by-step explanation:

In the figure attached, a regular octagon has been drawn with all equal sides and apothem OP = 10 in.

Perimeter of the given octagon is given as 66.3 in

We have to calculate the area of the octagon.

As we can see in the figure an octagon is a combination of 8 triangles.

So we will find the area of one triangle first.

Area of ΔBOC = [tex]\frac{1}{2}(BC)(OP)[/tex]

Since perimeter of octagon = 8 × one side = 8×BC

66.3 = 8× BC

BC = [tex]\frac{66.3}{8}[/tex]

BC = 8.288 in

Therefore, area of ΔBOC = [tex]\frac{1}{2}(10)(8.288)[/tex]

= 5×8.288

= 41.44 in²

Now area of octagon ABCDEFGH = 8×41.44 = 331.5 ≈ 332 in²

Therefore, area of the regular octagon will be 332 in²

Option C. is the answer.

Answer:

x=7

Step-by-step explanation:

7x-7 = 4x + 14

3x-7=14

3x = 21

x=7

Answer: 7

Step-by-step explanation:

Answer:

The set of ordered pair are { (-12,-18),(-3,-3), (0,2),(3,7),(12,22)}

Step-by-step explanation:

we have

[tex]f(x)=\frac{5}{3}x+2[/tex]

Find the values of f(x) for the domain values

For x=-12

substitute

[tex]f(-12)=\frac{5}{3}(-12)+2=-18[/tex]

The ordered pair is (-12,-18)

For x=-3

substitute

[tex]f(-3)=\frac{5}{3}(-3)+2=-3[/tex]

The ordered pair is (-3,-3)

For x=0

substitute

[tex]f(0)=\frac{5}{3}(0)+2=2[/tex]

The ordered pair is (0,2)

For x=3

substitute

[tex]f(3)=\frac{5}{3}(3)+2=7[/tex]

The ordered pair is (3,7)

For x=12

substitute

[tex]f(12)=\frac{5}{3}(12)+2=22[/tex]

The ordered pair is (12,22)

Answer with explanation:

The given function is

   [tex]f(x)=\frac{5x}{3}+2\\\\x=-12,-3,0,3,12\\\\f(-12)=\frac{5\times -12}{3}+2\\\\f(-12)=-20+2\\\\f(-12)=-18\\\\f(-3)=\frac{5 \times -3}{3}+2\\\\f(-3)=-5+2\\\\f(-3)=-3\\\\f(0)=\frac{5\times 0}{3}+2\\\\f(0)=2\\\\f(3)=\frac{5\times 3}{3}+2\\\\f(3)=5+2\\\\f(3)=7\\\\f(12)=\frac{5\times 12}{3}+2\\\\f(12)=20+2\\\\f(12)=22[/tex]

So, the ordered pair will be

   (-12, -18),(-3,-3),(0,2),(3,7),(12,22)

Answer:

C. y = 3x - 2

Step-by-step explanation:

Since the y intercept is negative, it is seen in this equation that the b value (the y intercept) is also negative.  Since the slope is increasing upward, we know that the slope is greater than 1 and is going upward, and it matches with the equation since it matches with both of the requirements.

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Answer: c and d

Step-by-step explanation:

Answer: 401.33 inches

Answer:

1. .0008

2. 1/125

3. 0.8% of a mile is 1/125th of a mile

Answer:

Down.

Step-by-step explanation:

ƒ(x) = 3x³ - x² + 4x - 2

"They" are asking you to determine the end behaviour of the function, that is, what happens to the function as x ⟶ -∞.

The important point to remember is that, when x is large enough, the term of highest degree (the x³ term) will be so large that you can ignore all the other terms.

If x is large and negative,  

f(x) ≈ 3(-x)³ = 3(-1)³(x)³= -3x³

Thus, the graph is in the third quadrant and the graph points down.

The figure below shows the graph of your function. It points sharply down on the left-hand side.

Answer:

see explanation

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] h(x + y)

Multiply both sides by 2 to eliminate the fraction

2A = h(x + y) ( divide both sides by h )

[tex]\frac{2A}{h}[/tex] = x + y ( subtract x from both sides )

y = [tex]\frac{2A}{h}[/tex] - x

The solution to the equation A=1/2h(x+y) for y in terms of A, h, and x, is y = 2A/h - x, obtained by algebraic rearrangement.

To solve the given equation A=1/2h(x+y) for y in terms of A, h, and x, we first perform algebraic rearrangement. We want to get y in terms of A, h, and x. So, the first step is to eliminate the 1/2h from the right side of the equation. We can do this by multiplying both sides of the equation by 2/h, we get: 2A/h = x + y.

Now, to solve for y, we can simply subtract x from both sides: y = 2A/h - x. So now we have y expressed in terms of A, h, and x.

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Answer:

42

Step-by-step explanation:

Line m and l are parallel so C and where that intersection is on the inside have the parallel lines, the angle there is an same side interior angle with C. Those add up to 180 degrees. So 180-82 is 98. Use vertical angle to find the angle in the triangle (not  x  yet; the other one).  Vertical angles are congruent so that one is 98.  

Now angles in a triangle add up to 180 degrees.

So we have 40+98=138.

The difference between 180 and 138 is 180-138=42 (that is x)

Answer:

42

Step-by-step explanation:

The solution is in the image below.

98+82 = 180

Answer:

7 pence

Step-by-step explanation:

7.00 / 100 = 7 pence

Answer:

7 cents

Step-by-step explanation:

7.00/100

Answer:

Option D. [tex]y-8=-5(x-1)[/tex]

Step-by-step explanation:

we know that

The equation of a line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex](x1,y1)=(1,8)[/tex]

[tex]m=-5[/tex]

substitute

[tex]y-8=-5(x-1)[/tex]

The correct point-slope equation for a line passing through the point (1, 8) with a slope of -5 is y - 8 = -5(x - 1).

The point-slope form of an equation of a line is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Given the point (1, 8) and a slope of -5, the correct point-slope equation is d. y - 8 = -5(x - 1).

Therefore, the correct answer is d. y - 8 = -5(x - 1).

Answer:

segment bisector

Step-by-step explanation:

Too cut in half, think bisect.

So we are talking about a segment, so segment bisector

Answer:

32/7

Step-by-step explanation:

5 1/3=16/3

1 1/6=7/6

----------------

(16/3)/(7/6)

(16/3)(6/7)

(16/1)(2/7)

32/7

Answer:

1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6

Step-by-step explanation:

So we need to know the 7th line of pascals triangle so let us write it out

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1 <----- This one

Now we know we will need coefficients of x from 0 to 6, let us call this i, and for each of these the coefficient is

(-2)^i * (1)^(6-i) * number in pascals triangle

Hence

i = 0, 1 * 1 * 1 = 1

i = 1, -2 * 1 * 6 = -12

i = 2, 4 * 1 * 15 = 60

i = 3, -8 * 1 * 20 = -160

i = 4, 16 * 1 * 15 = 240

i = 5, -32 * 1 * 6 = -192

i = 6, 64 * 1 * 1 = 64

Hence (1-2x)^6 = 1 - 12x + 60x^2 - 160x^3 + 240x^4 - 192x^5 + 64x^6

Answer:

11/13

Step-by-step explanation:

198/234

(198/18)/(234/18)

11/13

Answer:

11/13

Step-by-step explanation:

198 cents to 234 cents using a fraction in simplest form is 11/13.

Hope this helps!

Feel free to ask if you have anymore questions!

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\frac{1}{2}(3)(4)\\ h=&10 \end{cases}\implies V=\cfrac{1}{3}\cdot \cfrac{1}{2}(3)(4)(10)\implies V=20[/tex]

The point where f(x)= g(x) is  x = -2; x = 2.

The correct option is (A)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, from the graph the line graph for f(x) and g(x) is coinciding at two points at 2 and -2.

At these two points the two function line overlap.

So, point where f(x)= g(x) is x=2 and x=-2.

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Answer:

5x^2 + 12x -3 =0 ---------> solve by quadratic formula

x^2 -4x = 8          ----------> solve by completing the square

4x^2 -25 = 0        ----------> solve by square root method

x^2-5x+ 6 = 0       -----------> solve by factoring

Step-by-step explanation:

1. 5x^2 + 12x -3 =0

The best way to solve this equation is quadratic formula as all the terms in the equation have coefficients it will be convenient to solve it through quadratic formula.

2. x^2 -4x = 8

The best way to solve this equation is by completing the square as the factors cannot be made directly.

3. 4x^2 -25 = 0

the best way to solve this equation is to solve by square root method as the 25 and 4 are perfect squares.

4. x^2-5x+ 6 = 0

The best way to solve this equation is to solve by factoring as it can clearly be seen that it is convenient to make factors ..

Answer:

42-24n

Step-by-step explanation:

(7 - 4n) . 6

= (7)(6) - (4n)(6) ...........using distributive property, multiply each term by (6)

= 42 -24n (answer)

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies -\cfrac{5}{2} \\\\\\ \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}{2}[x-(-4)] \\\\\\ y+8=-\cfrac{5}{2}(x+4)\implies y+8=-\cfrac{5}{2}x-10\implies y=-\cfrac{5}{2}x-18[/tex]

For this case we have to:

[tex]1 \frac {3} {8} = \frac {8 + 3} {8} = \frac {11} {8}[/tex]

We must divide:

[tex]\frac {\frac {11} {8}} {\frac {1} {6}} =[/tex]

Applying double C we have:

[tex]\frac {11 * 6} {8 * 1} = \frac {66} {8} = \frac {33} {4}[/tex]

Converting to a mixed number we have:

[tex]8 \frac {1} {4}[/tex]

Answer:

[tex]8 \frac {1} {4}[/tex]

Answer:

[tex]\large\boxed{(f+g)(x)=4x^2+\dfrac{3}{2}x-7}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=\dfrac{x}{2}-3=\dfrac{1}{2}x-3,\ g(x)=4x^2+x-4\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{2}x-3\right)+(4x^2+x-4)\\\\=\dfrac{1}{2}x-3+4x^2+x-4\qquad\text{combine like terms}\\\\=4x^2+\left(\dfrac{1}{2}x+x\right)+(-3-4)\\\\=4x^2+1\dfrac{1}{2}x-7\\\\=4x^2+\dfrac{3}{2}x-7[/tex]

Answer:

Step-by-step explanation:

this angle is related to the ramp surface length (hypotenuse) and the rise in the ramp by the tangent function:

sin Ф = opp / hyp = 3 ft  /   5 ft = 0.60

Use the inverse sine function to determine the angle Ф.

arcsin 0.60 = 36.9 degrees

Final answer:

The angle of elevation of the ramp is approximately 36.87 degrees, calculated using the tangent function in trigonometry and the given dimensions of the ramp's rise and length.

Explanation:

To find the angle of elevation of the ramp, we can use trigonometry, specifically the tangent function, which relates the angle of a right triangle to the ratio of the opposite side (rise) to the adjacent side (run). In this case, the ramp surface is the hypotenuse of the right triangle, the rise is the vertical change, and the run is the horizontal distance, which would be the horizontal projection of the ramp if it were flat. Since we know the rise is 3 feet and the ramp length (hypotenuse) is 5 feet, we can calculate the run using the Pythagorean theorem.

The angle of elevation of the ramp is approximately 36.87 degrees.

To find the number of 3-digit multiples of both 4 and 6, we find the least common multiple (LCM) of 4 and 6, which is 12. Then, we count the number of 3-digit multiples of 12.

To find the number of 3-digit multiples of both 4 and 6, we need to find the least common multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12. Since 12 is a multiple of both 4 and 6, any multiple of 12 will be a multiple of both 4 and 6.

Now, we need to find the number of 3-digit multiples of 12. The smallest 3-digit multiple of 12 is 108, and the largest is 996. So, we need to find how many numbers from 108 to 996 are divisible by 12.

We can divide 996 by 12 to find that the quotient is 83 and the remainder is 0. So, there are 83 3-digit multiples of 12. Therefore, there are 83 3-digit multiples of both 4 and 6.

The probability she will choose a pair of white socks is [tex]\frac{2}{5}[/tex]

Given that,

Total number of outcomes [tex]=4+3+1+2=10[/tex]

We have to find the probability she will choose a pair of white socks.

Number of favourable outcomes[tex]=4[/tex]

the probability she will choose a pair of white socks is,

                  [tex]P=\frac{4}{10} =\frac{2}{5}[/tex]

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We know that the whole angle of the triangle is 73. Since the known angle is 45 degrees, we need to find out what the other is.

Subtract 45 from 73 to find the angle of the unknown triangle.

73-45=28.

Now that we know the value of the unknown triangle, solve for x

Make an equation.

2x+5=28

Subtract 5 on both sides.

2x=23

Divide 23 by 2 to isolate x.

X=11.5

The answer is C. 11.5

Hope this helps!

Answer:

3/5

Step-by-step explanation:

5 / -1 = -5  

so  

-3 / -5 = 3/5

To find x when y=-1, substitute y=-1 into the equation y = -173.5 + 4.83x and solve for x.

To find x when y=-1, you can use the equation of the line where y = 5 when x = -3. Based on the given information, the line of best fit is y = -173.5 + 4.83x. By substituting y = -1 into the equation, we can solve for x:

-1 = -173.5 + 4.83x

Adding 173.5 to both sides of the equation:

172.5 = 4.83x

Dividing both sides by 4.83:

x = 35.69

Therefore, when y = -1, x is approximately 35.69.

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[tex]\bf \begin{cases} f(x)=(7x^3+18)^2\\ f(x) = (h\circ g)(x)\\ h(x)=x^2 \end{cases}~\hspace{5em}(h\circ g)(x) = \stackrel{f(x)}{(7x^3+18)^2} \\\\\\ h(x) = x^2\implies \stackrel{(h\circ g)(x)}{h(~~g(x)~~)}=[g(x)]^2\implies h(~~g(x)~~)=\stackrel{f(x)}{(7x^3+18)^2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill g(x)=7x^3+18~\hfill[/tex]