Write the equation of the line with
slope -3 that goes through the point (-1,3).
Switch the equation to slope y intercept form.

Answer:

Let x be the larger angle and y be the smaller angle

Larger angle is 2 less than 3 times the smaller angle that is x = 3y - 2

As the angles are complementary, their sum equals 90°

or, x + y = 90°

or, 3y - 2 + y = 90°

or, 4y = 92°

or, y = 23°

So, x = 3 * 23 - 2 = 67°

Larger angle = x = 67°

Smaller angle = y = 23°

The value of x = 25

The measure of the angle ∠R = 101°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be TPRS

Now , the measure of ∠T = ( 4x + 1 )°

The measure of ∠S = ( 3x + 4 )°

Now , from the properties of a parallelogram ,

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

So ,

The value of ∠T = ∠R

And , value of ∠T + ∠S = 180°

Substituting the values in the equation , we get

∠T + ∠S = 180°

( 4x + 1 ) + ( 3x + 4 ) = 180

On simplifying the equation , we get

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides , we get

x = 25

So , the value of x = 25

Now , the measure of ∠T = ( 4x + 1 )° = ∠R

So , the measure of ∠R = ( 4 x 25 + 1 )°

The measure of ∠R = 101°

Hence , The value of x = 25

The measure of the angle ∠R = 101°

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The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x² + 14x − 24 = 4x

Simplify the equation, then we have

x² + 14x − 24 = 4x

x² + 10x − 24 = 0

Factorize the equation, then we have

x² + 10x − 24 = 0

x² + 12x − 2x − 24 = 0

x(x − 12) − 2(x − 12) = 0

(x − 2)(x − 12) = 0

x = 2, 12

The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

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Answer:

x = 6

Step-by-step explanation:

We have a 30°-60°-90° right triangle here, so the length of the hypotenuse (12) is twice the length of the shorter leg (6). So x = 6.

Answer:

12/3=4

Step-by-step explanation:

You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.

12 blocks in total/ 3 sections each = 4 blocks per section

Answer:1

Step-by-step explanation: 6x2= 12. 12/4=3. 3/3 is 1.

Answer:

1

Step-by-step explanation:

We can see only multiply and divide here so we go from left to right

6x2/4/3

= 12/4/3

= 3/3

= 1

Answer:

Step-by-step explanation:

210x550=115500

115,500 divide 10,000=11.55?

Answer:

y = 2x + 7.

Step-by-step explanation:

An equation that passes through the point (-4,-1) and is parallel to the line y = 2x + 14 is of the form y = 2x + b, where b is the y-intercept of the line. Since the line passes through the point (-4,-1), we can use this point to solve for b:

-1 = 2 * (-4) + b

-1 = -8 + b

b = 7

Therefore, an equation that passes through (-4,-1) and is parallel to y = 2x + 14 is y = 2x + 7.

Answer:

y = 2x + 7

Step-by-step explanation:

parallel = same slope

y-(-1) = 2(x-(-4)

y+1 = 2(x+4)

y+1 = 2x + 8

y = 2x + 8 - 1

y = 2x + 7

Answer:

Below

Step-by-step explanation:

27 = 3^3        and 9 = 3^2

3^3  * (3^2)^3x

3^3 * 3^6x

3^(3+6x)     so k = 3+6x

The number of coins which Craig collected as calculated from the given data is 49.

Given ,

percentage of foreign coin = 72%

Therefore the percentage of normal coins will be 28%.

Hence , the number of normal coins which he collected can be found out as ,

 28% of 175

= 28% × 175

= 28/100 × 175

= 0.28 × 175

= 49

When we divide a given number by 100 as a fraction , the result we get is known as percentage .

It is represented by the percentage sign which is "%".

The percentage is denoted by the letters "pct" or "pc," respectively. In other words, the percent or % is calculated at a value of around 100 and represents the proportion of one quantity made up of another.

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Answer:

7 hours

every hour she makes $21

Step-by-step explanation:

378÷18=21

147÷21=7

7 hours

378÷18=21$/h in ONE hour Salma makes 21$ so you have to do 147÷21=7h

The area of the rectangle shown on the coordinate plane is 12 square units.

What is the area of the rectangle shown on the coordinate plane?

To calculate the area of a rectangle, multiply the length by the width of the rectangle.

To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4, 1)

2 - (-1,-2)

3 - (-3,-4)

4 - (-6, -1)

Then, calculating the length of the sides,

Consider rectangle ABCD  with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is

A = length * Width

Find the length and the width:

AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18

BC = √(-3 - (-1))² + (-4 - (-2))²  = √4 + 4 = √8

Then the area of the rectangle ABCD is

A = √18 * √8

A = 12 unit²

Hence, the area of the rectangle shown on the coordinate plane is 12 square units.

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1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.

2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.

The future value is the compounded present value at an interest rate.

The future value can be derived from an online finance calculator as follows:

With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.

Initial investment = $5,000

Interest rate = 2.5% compounded annually

Investment period = 2 years

N (# of periods) = 2

I/Y (Interest per year) = 2.5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $5,253.13

Total Interest = $253.13

Principal = $5,253.13

Interest rate = 8% per annum

Future amount = $10,000

Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate

= ($10,000/$5,253.13 - 1) ÷ 0.08

= 11.3 years

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option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

First, let us study the definition of Atomic Mass,

Atomic mass -

So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom

Therefore, option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

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Answer:

03

Step-by-step explanation:

it is 03. in a polynomial the hightest power of varibale shows the degree of it.

The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Here, we note the following

Let the person walking away from the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X,  2 ft/sec × 15 s = 30 ft away from the elevator

For Y,  7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

d=√ 30² +105² = 11925 ft²

d = √11925 ft²  = 109.202 ft

The rate of change of the distance between the two people, X and Y is given as

[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]

                (or)

[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]

Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec

Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]

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When jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters , the collection of nickels and quarters totaled $2.60 then he find eight quarters.

Given that:

Let N be the number of nickels.

     Q be the number of quarters.

The value of one nickels N is 0.05N

The value of quarters Q = 0.25Q

Sum of total quarters is $ 2.60

  Total number of coins

N + Q = 20   , N = 20 - Q

0.05 N + 0.25 Q = 2.60

substitute n = 20 - Q , we get

0.05 (20 - Q) + 0.25 Q = 2.60

    1 - 0.05 Q + 0.25 Q = 2.60

                       1 + 0.2Q = 2.60

                           0.2 Q = 1.6

                                  Q = 1.6 / 0.2

                                  Q = 8

Therefore , Jim finds 8 quarters

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When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   [tex]\\26 \frac{2}{5}[/tex].

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

[tex]$$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$[/tex]

Follow the PEMDAS order of operations

Multiply and divide (left to right) [tex]$12 \times \frac{6}{5}: \frac{72}{5}$[/tex]

[tex]=\frac{72}{5}+12$$[/tex]

Add and subtract (left to right) [tex]$\frac{72}{5}+12: \frac{132}{5}$[/tex]

[tex]=\frac{132}{5}$$[/tex]

Convert improper fractions to mixed numbers: [tex]$\frac{132}{5}=26 \frac{2}{5}$[/tex]

[tex]=26 \frac{2}{5}$$[/tex]

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Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².

The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

Given A = 4πr²

So, we have:

dA/dt = d/dt (4πr²)

= 4π * d/dt * (r²)

= 4π * 2r * dr/dt

= 8πr * dr/dt

Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:

dA/dt = 8πr * dr/dt

= 8π * 8 * 2

= 128π

Since we are measuring area, our unit is cm²/min, not cm/min.

Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

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The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

z - 5 = z² - 25

z - 5 = z² - 5²

By property that A² - B² = (A + B)(A - B)

z - 5 = (z - 5)(z + 5)

z + 5 = 1    

z = - 1 / 5 = - 4

Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".

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Answer:

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

Given equation:

Solve it as follows:

A problem that could be solved by multiplying 4.63 x 9 is "the product of 4.63 and 9"

From the question, we have the following parameters that can be used in our computation:

4.63 x 9

In the above expression, we can see that

4.63 and 9 are multiplied

This means that the problem is a product expression

And a problem that can represent 4.63 x 9 is "the product of 4.63 and 9"

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The product of linear factors of the given polynomial are;

(x + 3 )*(x² + 2x + 50 + (−100/(x + 3)))

We are given the polynomial expression as;

g(x)= x³ + 5x² + 56x + 150

Now, we are told that  -3 is a zero. Thus, if -3 is a zero that means x = -1

and x + 3 is a factor.

Using online polynomial division calculator, the the polynomial is divided by (x + 3) to get;

(x³ + 5x² + 56x + 150)/(x + 3) = x² + 2x + 50 + (−100/(x + 3))

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The measure of one angle is 1.56° and another angle is 88.64°.

Complementary angles are two angles whose combined angle is 90 degrees.

Let's consider the smaller angle as A and the larger angle as B.

Given that the two angles are complementary, then their sum is A+B = 90°.

The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,

A+44A+20° = 90°

45A = 90°-20°

A = 70°/45

A = 1.56°

Substitute A = 1.56°in B = 44A+20°, we get,

B = 44(1.56°)+20°

B = 88.64°

The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.

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The equation with x about the number thought by Natasha is (x + 2.5) × 2 = 61

Let the number thought by Natasha be x. To formulate the equation, we will perform the same operations as done by Natasha. Forming the equation now -

(x + 2.5) × 2 = 61

Performing multiplication on Left Hand Side of the equation

2x + 5 = 61

Rewriting the equation

2x = 61 - 5

Performing subtraction on Right Hand Side of the equation

2x = 56

Rewriting the equation

x = 56/2

Performing division on Right Hand Side of the equation

x = 28

Thus, the equation is (x + 2.5) × 2 = 61 and the number thought by Natasha is 28.

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Answer:

C

Step-by-step explanation:

S = .6T + 331.4    

When S = 331.4:

331.4 = .6T + 331.4    <=====you should be able to see this is true when T= 0

Both conditions must be met in order to ride: being at least five years old and being at least 36 inches tall. expression evaluates to true if a person can ride - (Age >= 5) && (Height > 36)

In order for a person to ride, two conditions must be true: they must be at least 5 years old and taller than 36 inches. In order to evaluate whether a person can ride, we can use the expression (Age >= 5) && (Height > 36). This expression evaluates to true if both conditions are true; if either one is false, then the expression will evaluate to false. For example, if a person is 4 years old and 40 inches tall, then the expression will evaluate to false because the first condition is false. On the other hand, if a person is 5 years old and 40 inches tall, then the expression will evaluate to true because both conditions are true.

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Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

Answer:

D. 142 degree

Step-by-step explanation:

A triangle has 180 degree

77 + 65 = 142 degree

180 - 142 = 38 degree

38 degrees is the missing angle of the triangle. This angle must add with angle 1 outside equal to 180

180 - 38 = 142 degree

So, the answer is D