Tyler borrowed $600. After one year, he paid the whole loan back, with a total maturity value of $640. What was the interest rate of the loan?

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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Answer:

1 kg = 1000 grams

15,000 grams = 15kg

Answer:

x is greater then 12

Step-by-step explanation:

Answer:

X > 12

Step-by-step explanation:

4x > 40 + 8

4x > 48

Divide both sides by 4

X > 12

Pls be careful with this, I am not sure if the sign changes

The length of the image of the line, after being dilated by the scale factor, would be B. 12 units.

To find the length of the image of the line after dilation, we need to calculate the distance between the two points on the dilated line.

The dilated line's points will be (3, 4 x 3) and (3, 8 x 3), which simplify to (3, 12) and (3, 24).

Then find the distance using the distance formula :

= √((x2 - x1) ² + (y2 - y1) ²)

= √((3 - 3) ² + (24 - 12) ²)

= √ (0 + 144)

= √144

= 12

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The answer for number 1 is 1.72. The answer for number 2 is 4.83.

So for number one, the first thing you need to do is determine how many sides are on the first shape. Since it is a pentagon, and one pentagon has 5 sides, then you use the following formula to determine the volume of a\(V = \frac {1}{4} \times \sqrt{5 \times (5 +2 \times \sqrt {5})} \times (10)^{2} \times 10\) pentagon: \(\alpha = \frac{1}{4} \times \sqrt[]{5(5+2 \sqrt[]{5}) \alpha ^{2} }\) And in this case, the area would be 1.72, because if you insert the side lengths, the equation would look like this: \(V = \frac {1}{4} \times \sqrt{5 \times (5 +2 \times \sqrt {5})} \times (10)^{2} \times 10\) , which if you solve this equation, then you will end up with the answer of 1.72.

For number two, the first thing you need to do is determine how many sides are on the second shape. Since it is an octagon, and the prefix oct means 8, the number of sides on the shape is 8. If the perimeter is 64, and there are 8 sides, you can divide 64 by 8 to get 8. The equation to solve for the area should look like this: \(V = 2(1 + \sqrt{2}) \times s^{2} \times h\). Now all you need to do is insert the side lengths to the proper places. It should then look like this: \(V = 2(1 + \sqrt{2}) \times 8^{2} \times 8\), after you solve the equation, you should end up with 4.83.

Answer:

\(Pr = \frac{1}{3}\)

Step-by-step explanation:

Given

\(n = 9\) --- total outcomes

Required

The probability of same number in both spins

The list of same outcomes are:

\(L = \{(1,1),(2,2),(3,3)\}\)

\(n(L) = 3\) ----- The number of outcomes

So, the probability is:

\(Pr = \frac{n(L)}{n}\)

\(Pr = \frac{3}{9}\)

\(Pr = \frac{1}{3}\)

So, each farmer pays the following amounts: The first farmer pays 738.40 euros. The second farmer pays 443.04 euros. The third farmer pays 418.56 euros

Proportion refers to the equality of two ratios. In other words, when two ratios are set equal to each other, they form a proportion. A proportion is typically written in the form of two fractions separated by an equals sign, such as a/b = c/d. Proportions are commonly used in mathematics to solve problems involving ratios and proportions, such as finding missing values or scaling up or down a given quantity.

Here,

To find out how much each farmer pays, we need to determine the proportion of the total rent that each farmer owes based on the number of sheep they have. First, we need to find the total number of sheep:

120 + 72 + 68 = 260

The first farmer has 120 sheep, which is 46.15% of the total number of sheep (120/260). Therefore, the first farmer owes 46.15% of the rent:

0.4615 x 1600 = 738.40 euros

Similarly, the second farmer has 72 sheep, which is 27.69% of the total number of sheep (72/260). Therefore, the second farmer owes 27.69% of the rent:

0.2769 x 1600 = 443.04 euros

The third farmer has 68 sheep, which is 26.15% of the total number of sheep (68/260). Therefore, the third farmer owes 26.15% of the rent:

0.2615 x 1600 = 418.56 euros

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Complete question:

The rent of 1600 euros for a piece of land is divided among three farmers who graze their sheep there. As they do not have the same number of sheep, they decide to pay proportionally according to the number of sheep each has. If the first one has 120 sheep, the second 72, and the third 68. How much does each one pay?

Answer: -2

Step-by-step explanation:

The slope of the line perpendicular to another slope is the opposite sign and flipped(reciprocal)

The slope of the line = 1/2

So the perpendicular slope = -2

Answer:

-1 is not in the domain of (f o g)(x)

Step-by-step explanation:

f(x) = sqrt(x - 9)

g(x) = -6x - 3

(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)

(f o g)(x) = sqrt(-6x - 3 - 9)

(f o g)(x) = sqrt(-6x - 12)

Let x = -1:

(f o g)(-1) = sqrt(-6(-1) - 12)

(f o g)(-1) = sqrt(6 - 12)

(f o g)(-1) = sqrt(-6)

Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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here you go i think im right

Step-by-step explanation:

please attach a picture for us to see the choices

Answer:

\(\large\boxed{\sf x = \frac{8y+1}{7} }\)

\(\large\boxed{\sf x = \frac{7x-1}{8} }\)

Group the Variable's:

2 x - 5 + 7 y - 3 = 9 x - 1 - y -8

2x -9x + 7y +y = -1 -8 +5 + 3

-7x + 8y = -1

From this find x and y

For X

-7x + 8y = -1

-7x = -1 -8y

7x = 8y + 1

x = (8y +1)/7

For Y

-7x + 8y = -1

8y = -1 +7x

y = (7x -1)/8

Answer:

18x +27

Step-by-step explanation:

-9(-2x-3)

Distribute

-9 * -2x -9*(-3)

18x +27

The length of the diagonal of a square with an area of 144 in² is approximately 16.97 inches.

The diagonal of a square can be calculated using the Pythagorean theorem, which states that the square of the length of the diagonal (d) of a right triangle is equal to the sum of the squares of the lengths of its two other sides (a and b):

d² = a² + b²

In the case of a square, both of its sides have the same length (let's call it s), so we can rewrite the equation as:

d² = s² + s²

d² = 2s²

To find the length of the diagonal (d), we can take the square root of both sides:

d = √(2s²)

Now, we can use the area of the square to find the length of its side (s):

144 in² = s²

s = √144 in²

s = 12 in

Substituting s = 12 in into the equation for the diagonal, we get:

d = √(2s²) = √(2(12 in)²) = √(2 * 144 in²) = √288 in ≈ 16.97 in

Hence, the length of the diagonal is 16.97 inches.

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Answer:

18x^2-45x

Step-by-step explanation:

-9x(5-2x)

-9x*5=-45x

-9x*-2x=18x^2

18x^2-45x

Answer:

Answer: X

Step-by-step explanation:

Answer:

B. X

BTW Jimin is living mochi!

Step-by-step explanation:

Answer:

P=4a=4·64=256

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Answer:

A or C

Step-by-step explanation:

Expectation is linear, meaning

E(a X + b Y) = E(a X) + E(b Y)

= a E(X) + b E(Y)

If X = 1 and Y = 0, we see that the expectation of a constant, E(a), is equal to the constant, a.

Use this property to compute the expectations:

E(X + 10) = E(X) + E(10) = $110

E(5Y) = 5 E(Y) = $450

E(X + Y) = E(X) + E(Y) = $190

Variance has a similar property:

V(a X + b Y) = V(a X) + V(b Y) + Cov(X, Y)

= a^2 V(X) + b^2 V(Y) + Cov(X, Y)

where "Cov" denotes covariance, defined by

E[(X - E(X))(Y - E(Y))] = E(X Y) - E(X) E(Y)

Without knowing the expectation of X Y, we can't determine the covariance and thus variance of the expression a X + b Y.

However, if X and Y are independent, then E(X Y) = E(X) E(Y), which makes the covariance vanish, so that

V(a X + b Y) = a^2 V(X) + b^2 V(Y)

and this is the assumption we have to make to find the standard deviations (which is the square root of the variance).

Also, variance is defined as

V(X) = E[(X - E(X))^2] = E(X^2) - E(X)^2

and it follows from this that, if X is a constant, say a, then

V(a) = E(a^2) - E(a)^2 = a^2 - a^2 = 0

Use this property, and the assumption of independence, to compute the variances, and hence the standard deviations:

V(X + 10) = V(X)  ==>  SD(X + 10) = SD(X) = $90

V(5Y) = 5^2 V(Y) = 25 V(Y)  ==>  SD(5Y) = 5 SD(Y) = $40

V(X + Y) = V(X) + V(Y)  ==>  SD(X + Y) = √[SD(X)^2 + SD(Y)^2] = √8164 ≈ $90.35

30 + 110 + 30 + 110 = 280

360-280 = 80

2y = 80

y = 40 degrees

If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.

30 + 40 = 70

The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.

In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180

Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.

Angles in triangle add to 180.

180 - 110 - 30 = 40.

Thus, x = 40 degrees

There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)

Hope this helps!

Answer:

37

Step-by-step explanation:

The 35.75 bars are made from the 13 metre chocolate bar

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator

Given that:

Willy Wonka makes a 13 metre chocolate bar

The chocolate bar is then cut into 4/11 of a metre

Since she cut the chocolate bar into 4/11 of a metre and she makes 13 metre bar. The number of bars will be:

Number of bars = 13 / (4/11)

Number of bars = 35.75

Therefore, the 35.75 bars are made

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Answer:

12

Step-by-step explanation:

2²×3

I hope its correct

Answer:

4

\( {( - 2 + 1)}^{2} + 5(12 \div 3) - 9 \\ 2 + 1 + 5 \times 4 - 9 \\ 3 + 20 - 9 \\ 23 - 9 \\ 14\)

Answer:

C

Step-by-step explanation:

\(\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ \frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{2x+1}\)

The denominator cannot equal 0, so:

\(2x+1 \neq 0 \implies x \neq -\frac{1}{2}\)