What is the equation of a line in slope-intercept for that passes through (4,8) and (-1,-12)

Answer:

equation: y = -2x + 7

Step-by-step explanation:

y = mx + b   M: slope     b: y intercept

m = -2

x = 3 and y = 1

b = y - mx = 1 - (- 2) x 3 = 7

equation: y = -2x + 7

check:     ( 3,1)     -2 x 3 + 7 = 1

Answer:

The equation of the required line is,

y = -2x + 7

Step-by-step explanation:

We know that equation of a line passing through the point (x₁, y₁) and having slope 'm' is given by

(y - y₁) = m(x - x₁)

Now, the required line passes through the point (3, 1) and has a slope of -2.

So, (x₁, y₁) = (3, 1) and m = -2

So, equation of the line passing through (3, 1) and having a slope of -2 is given by,

  y - 1 = -2(x - 3)

⇒y - 1 = -2x + 6

⇒y = -2x + 6 + 1

⇒y = -2x + 7

So, the required equation of line in point-slope form is,

y = -2x + 7

Answer:

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Step-by-step explanation:

The complete question is

The angle θ1 is located in Quadrant 1, and cos (θ1)=10/17.

What is the value of sin(θ1)?

we know that

[tex]sin^2(\theta_1)+cos^2(\theta_1)=1[/tex] ---> trigonometric identity

we have

[tex]cos(\theta_1)=\frac{10}{17}[/tex]

The angle [tex]\theta_1[/tex] is located in Quadrant I, that means the sine of angle [tex]\theta_1[/tex] is positive

substitute the given value in the trigonometric identity

[tex]sin^2(\theta_1)+(\frac{10}{17})^2=1[/tex]

[tex]sin^2(\theta_1)+\frac{100}{289}=1[/tex]

[tex]sin^2(\theta_1)=1-\frac{100}{289}[/tex]

[tex]sin^2(\theta_1)=\frac{189}{289}[/tex]

take square root both sides

[tex]sin(\theta_1)=\pm\frac{\sqrt{189}}{17}[/tex]

Remember that the sine is positive (Quadrant I)

so

[tex]sin(\theta_1)=\frac{\sqrt{189}}{17}[/tex]

Simplify

[tex]sin(\theta_1)=3\frac{\sqrt{21}}{17}[/tex]

Answer:

The total cost to make 3 widgets is $64.

Step-by-step explanation:

As cost is give by quadratic function such as [tex]c(x) = ax^2 + bx + d[/tex]

As it costs $29 to produce 2 widgets. So,

[tex]c(2) = a(2)^2 + b(2) + d[/tex]

[tex]29= 4a+2b+d ....[A][/tex]

As it costs $115 to produce 4 widgets. So,

[tex]c(4) = a(4)^2 + b(4) + d[/tex]

[tex]115= 16a+4b+d ....[B][/tex]

As it costs $757 to produce 10 widgets. So,

[tex]c(10) = a(10)^2 + b(10) + d[/tex]

[tex]757= 100a+10b+d ....[C][/tex]

In order to find the values of a, b, c and d, we have to equations [A], [B] and [C]

Subtracting Equation [A] from [B] and [B] from [C]

 12a + 2b = 86  ........[D]

 84a + 6b = 642  ........[E]

Multiplying Equation [D] by 3 and subtracting from [E]

84a + 6b + 3(12a + 2b) = 642 - 86

48a = 384

a = 8

Putting value of a = 8 in equation [D]

12(8) + 2b = 86

96 + 2b = 86

2b = -10

b = -5

Substituting the value of a = 8 and b = -5 in Equation [A].

29= 4a+2b+d

29 = 4(8) + 2(-5) + d

29 = 32 - 10 + d

d = 29 + 10 - 32

d = 7

The required form of equation can be obtained by substituting a = 8, b = -5 and d = 7 in the cost equation. So,

[tex]c(x) = 8x^2 - 5x + 7[/tex] is the required form of equation.

Therefore, the total cost to make 3 widgets will be:

Putting x = 3 in [tex]c(x) = 8x^2 - 5x + 7[/tex]

[tex]c(3) = 8(3)^2 - 5(3) + 7[/tex]

[tex]c(3) = 72 - 15 + 7[/tex]

[tex]c(3) = 64[/tex]

Hence, the total cost to make 3 widgets is $64.

Keywords: quadratic equation, cost

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The value of x when y = 9 is x = 2 or x = -2

Solution:

Given that value of y varies inversely as the square of x, and y=4, when x=3.

Therefore the initial statement is:

[tex]y \propto \frac{1}{x^{2}}[/tex]

To convert to an equation, multiply by k, the constant  of variation

[tex]y = k \times \frac{1}{x^2}[/tex]

[tex]y = \frac{k}{x^2}[/tex]  --- eqn 1

Given that,

y = 4 when x = 3

Now find value of k

[tex]4 = \frac{k}{3^2}\\\\4 \times 9 = k\\\\k = 36[/tex]

Find the value of x when y = 9

x = ?

y = 9

From eqn 1,

[tex]9 = \frac{k}{x^2}\\\\9 = \frac{36}{x^2}\\\\x^2 = 4\\\\x = \pm 2[/tex]

Thus value of x is found

Final answer:

To find the value of x when y=9 for a scenario where y varies inversely as the square of x, and given y=4 when x=3, we first determine the constant of variation and then solve for x, resulting in x=2.

Explanation:

The student's question concerns an inverse variation where the value of y varies inversely as the square of x, with an initial condition that when x=3, y=4. To find the value of x when y=9, we recall that an inverse variation can be expressed as y = k/x², where k is a constant. Using the given condition, we can solve for k: 4 = k/3², leading to k = 36. To find x when y=9, we set up the equation 9 = 36/x² and solve for x, yielding x = 2.

Problem 1

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

Work Shown:

For any convex polygon, the sum of the exterior angles is always 360 degrees

Add up all the angles shown, set the sum equal to 360, then solve for v.

9v+(19v-21)+45+(v+48)+7v = 360

36v+72 = 360

36v+72-72 = 360-72

36v = 288

36v/36 = 288/36

v = 8

===============================================

Problem 2

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

Explanation:

Segment WU is not an altitude because we have no angle markers to show if WU is perpendicular to VT.

Segment WU is not a median since we dont know if TU = UV or not.

Segment WU is not an angle bisector. If it were an angle bisector, then the two angles marked (33 and 40) should be equal angles. In other words, an angle bisector cuts an angle into two equal halves.

Answer:

5/12x

Step-by-step explanation:

Answer:

y = 5/12x - 2

Step-by-step explanation:

5x - 12y = 24

We get -12y = -5x + 24

Divide all of the equation by -12

You get y = 5/12x -2

Answer:

It's C.

Step-by-step explanation:

x + y + x + y + 3(y + 5)

= x + y + x + y + 3y + 15

= 2x + 5y + 15.

Answer:

2x + y + 30

C.

Answer:

hi there!

the equation for this dot plot will be: y=15x

Step-by-step explanation:

if you look at the dots on the graph (2, 30) and (4,60) they both satisfy the equation

Answer:

B. (-4,5)

Step-by-step explanation:

a function cannot have any repeating x values....it can have repeating y values, just not the x values

so..going by ur answer choices, u can remove (-4,5) and it would be a function. The reason is because u have two sets of points with the same x value...so it is not a function unless u take out either (-4,5) or (-4,3)...because they both have the same x value.

Answer:

4875

Step-by-step explanation:

100%-84%=16%

16%x=780

x=4875

Answer:

Julie made $3 /hour more than Loren

Step-by-step explanation:

Loren makes 18 /2 = 9 ($9 / hour constant ratio)

Julie: 36 /3 = 12 ($12 / hour)

Julie - Loren = 12 -9 = 3

? in Loren's : 126, 144

? in Julie's : 72, 252

Step-by-step explanation:

Wooden Cars = 2 × Wooden Trains

Ratio is

2 : 1

In total there are 3 parts

228 ÷ 3 = 76 (1 part)

Wooden Cars = 2 × 76 = 152

Wooden Trains = 1 × 76 = 76

To find the number of wooden trains made, we can set up an equation and solve for 'x'.

To solve this problem, let's represent the number of wooden trains as 'x'.

According to the given information, there are twice as many wooden cars as wooden trains. So, the number of wooden cars can be represented as '2x'.

We are also given that the total number of wooden vehicles made is 228.

Therefore, the equation that represents the given information is: x + 2x = 228

Simplifying the equation, we get: 3x = 228

Dividing both sides by 3, we find that x = 228/3 = 76

So, they made 76 wooden trains.

Answer:

x ÷ 15

Step-by-step explanation:

quotient is division

Answer:

4

Step-by-step explanation:

10 - 2 = 8

4 x 2 = 8

4 x 3 = 12

Final answer:

The answer explains how to find a number given that two-thirds of it increased by two equals ten, using clear step-by-step instructions.

Explanation:

The subject of the question is Mathematics.

The question states that two-thirds of a number increased by two is equal to ten. To solve this equation:

Let the number be represented by x.

Translate the given information into an equation: (2/3)x + 2 = 10.

Solve for x: (2/3)x = 8, x = 12. Therefore, the number is 12.

Answer:

Answer:

The height of the rocket after 3 seconds is 63 feet.

Step-by-step explanation:

The path of a model rocket is represented by:

[tex]h(t)=-t^2+20t+12[/tex]

where [tex]h(t)[/tex] represents the height in feet of rocket and [tex]t[/tex] represents time in seconds.

To find the height of the model rocket after 3 seconds from launch.

Solution:

In order to find the  height of the model rocket after 3 seconds from launch, we will plugin [tex]t=3[/tex] in the given function of path of rocket.

Thus, we have

[tex]h(3)=-(3)^2+20(3)+12[/tex]

[tex]h(3)=-9+60+12[/tex]

[tex]h(3)=63[/tex]

Thus, height of the rocket after 3 seconds is 63 feet.

Answers:

a) [tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) 0.299 s

Step-by-step explanation:

a) We are given the following equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

If we divide by 2 both the numerator and the denominator, we will have:

[tex]t=\sqrt{\frac{2d/2}{(9.8)/2}}[/tex]

[tex]t=\sqrt{\frac{d}{4.9}}[/tex]

b) From this equation:

[tex]t=\sqrt{\frac{2d}{9.8}}[/tex]

[tex]t[/tex] is the reaction time in seconds

[tex]d=44 cm \frac{1 m}{100 cm}=0.44 m[/tex] is the distance

[tex]9.8 m/s^{2}[/tex] is the acceleration due gravity

Solving:

[tex]t=\sqrt{\frac{2(0.44 m)}{9.8 m/s^{2}}}[/tex]

[tex]t=0.299 s[/tex] This is the reaction time

Answer:

38 [tex]ft^{2}[/tex]

Step-by-step explanation:

We can see this figure as

WHOLE RECTANGLE - PORTION OF RECTANGLE CUT OUT

We know area of a rectangle is length * width

If this was the WHOLE RECTANGLE, the area would have been:

5 * 10 = 50 sq. ft.

The portion cut out is also a rectangle with dimensions:

Length = 6

Width = 5 - 3 = 2

Thus,

Area = 6 * 2 = 12 sq. ft.

So, the area of the figure is 50 - 12 = 38 sq. ft.

Answer:

f(3)=3/7

Step-by-step explanation:

Answer:

it is 4,000

Step-by-step explanation:

since you are rounding it to the nearest thousand, you loo at the 4, and the 2, the 2 is blow five, so it doesn't change the thousands place, but everything else becomes a 0

Answer: 4,000

Explanation: To round 4,279 to the nearest thousand, we first locate the digit in the rounding place which in this case is the 4 in the thousands place.

Next, we look at the digit to the right of the 4 which is 2. The rules of rounding tell us that if the digit to the right of the rounding place is less than 5, we round down and if the digit to the right of the rounding place is greater than or equal to 5, we round up.

In this problem, the digit to the right of the rounding place is less than 5 so we round down. This means that the 4 in the rounding place stays the same and all digits to the right of the 4 become zero.

Therefore, 4,279 rounded to the nearest thousand is 4,000.

Answer:

[tex]8b^2+7b-1=(b+1)(8b-1)[/tex]

The missing factor is: [tex](8b-1)[/tex]

Step-by-step explanation:

Given expression:

[tex]8b^2+7b-1=(b+1)(_-)[/tex]

To find the missing factor of the given expression.

Solution:

In order to factor the given term, we will split the middle term into two terms such that the product of the two terms is equal to the product of the first and last term of the expression.

The product of first and last term for the expression is = [tex](8b^2)(-1)=-8b^2[/tex]

The middle term = [tex]7b[/tex] which can be split into  [tex](8b-b)[/tex] as their product = [tex]-8b^2[/tex]

Thus, the expression can be rewritten as:

⇒ [tex]8b^2+8b-b-1[/tex]

We will factor in pairs by taking GCF.

⇒ [tex]8b(b+1)-1(b+1)[/tex]

Factoring the whole expression by taking the common factor.

⇒ [tex](b+1)(8b-1)[/tex]

Thus, the missing factor is: [tex](8b-1)[/tex]

Answer:

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation: To obtain number 28, we will find the factors of this number.

Factors of this number are: 1, 2, 4, 7, 14, 28

From the given factors, we can find the combinations which will givs us the product as 28

We are asked to find the multiplication ( times) of two number that will yield a number 28. So, the combinations will be

1\times 28=28\\2\times 14=28\\4\times 7=28

Step-by-step explanation:

Final answer:

To find numbers that multiply to 3.75, we can identify factor pairs like 1.5 and 2.5, or 1 and 3.75. Multiplying these pairs will result in 3.75.

Explanation:

To find which numbers multiplied together equal 3.75, we can look for factor pairs of the number 3.75. A factor pair is a set of two numbers that, when multiplied together, result in the given number. Since 3.75 can also be expressed as the fraction ⅓75/100 (or 15/4 in simplest form), we can find factor pairs by considering both whole numbers and decimals that multiply to give us the fraction equivalent.

For example, one obvious pair is 1.5 and 2.5. If we multiply 1.5 by 2.5, we get 3.75:

1.5 × 2.5 = 3.75

Another pair could be 1 and 3.75 as any number multiplied by 1 equals the number itself.

1 × 3.75 = 3.75

These are just two examples of factor pairs for 3.75, but there can be other combinations as well, particularly if we consider fractions or more decimal places.

To find the missing number so that the equation has infinitely many solutions, subtract -2x from both sides to eliminate x and find that the missing number can be any real number.

To find the missing number so that the equation has infinitely many solutions, we need to look at the given equation: -2x - 10 = -2x + c. Since the variable x is present on both sides, we can subtract -2x from both sides to get rid of it. This leaves us with -10 = c. In order for this equation to have infinitely many solutions, the missing number c can be any real number.

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Answer:

There was a 15 among the 7 numbers. That is the number you removed.

Step-by-step explanation:

x/7 = 9                       (1)

(x -  y)/6 = 8               (2)

Multiply 1 by 7

x/7 * 7 = 9*7

x = 63

Put 63 for x into equation 2

(63 - y)/6 = 8         Multiply by 6

6*(63-y)/6 =8*6

63 - y = 48            Add y to both sides

63-y+y = 48+y

63 = 48 + y           Subtract 48 from both sides

63-48=48-48+y

y = 15

Final answer:

The number removed from the list to change the average from 9 to 8 is 15, calculated by finding the difference between the total sum of the original and remaining lists.

Explanation:

To find the number that was taken away from a list when the average changes, you can first calculate the total sum of the original list, then the sum of the list after the number is removed.

Initially, the average of the 7 numbers is 9. To find the total sum of all 7 numbers, you multiply the average by the number of values.

Total sum of original list = 7 (number of values) × 9 (original average) = 63

After removing one of the numbers, the average of the 6 remaining numbers is 8.

Total sum of the remaining list = 6 (remaining values) × 8 (new average) = 48

The number that was removed can be found by subtracting the sum of the remaining list from the sum of the original list.

Number removed = Total sum of original list - Total sum of the remaining list = 63 - 48 = 15

Therefore, the number that was taken away from the list is 15.

Answer:

0.072

Step-by-step explanation:

3/4 percent of the number 9.6 is 0.072.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, 3/4% of 9.6.

Now, 0.75% of 9.6

= 0.0075×9.6

= 0.072

Therefore, 3/4 percent of the number 9.6 is 0.072.

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Answer:[tex]30 i -473 j -3 k[/tex]

Step-by-step explanation:

We are given two velocity vectors with its three components in unit notation:

Airplane's velocity:

[tex]\vec{p}=30i-492j+42k[/tex]

Crosswind velocity:

[tex]\vec{t}=0i+19j-45k[/tex]

Now, if we want to know the velocity of the airplane when it is affected by the wind, we have to add these two velocity vectors:

[tex]\vec{p} + \vec{t}=(30i-492j+42k) + (0i+19j-45k)[/tex]

Adding both vectors:

[tex]\vec{p} + \vec{t}=30i-473j-3k[/tex]

Answer:

D edge

Step-by-step explanation:

Answer:

y-2=2(x-9)

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-2=2(x-9)

Answer:

[tex]r=0.05[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

A is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=3\ years\\ P=\$3,000\\I=\$450\\r=?[/tex]

substitute in the formula above

[tex]450=3,000(3r)[/tex]

solve for r

[tex]450=9,000(r)[/tex]

[tex]r=450/9,000[/tex]

[tex]r=0.05[/tex]

The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x, where x represents the number of songs purchased.

The equation that represents the relationship between the remaining balance on Renata's gift card and the number of songs purchased is y = 20 - 1.25x.

Here's how we get to this equation:

For example, if Renata purchased 16 songs, the equation becomes y = 20 - 1.25(16) = 20 - 20 = 0, which matches the given information that the gift card has a remaining balance of $0 after 16 songs are purchased.

Answer:

They can never be both either increasing or decreasing.

Step-by-step explanation:

If the rate of change i.e. the slope of one linear function is positive, that means the graph of the linear function makes angle which varies between 0° to 90° with respect to the positive direction of the x-axis.

Therefore, the function must be increasing.

Again, if the rate of change i.e. the slope of one linear function is negative, that means the graph of the linear function makes angle which varies between 90° to 180° with respect to the positive direction of the x-axis.

Therefore, the function must be decreasing.

Hence, if the rate of change of one linear function is positive and for another is negative, they can never be both either increasing or decreasing. (Answer)