In the diagram below, segment PB is a tangent. IF AC = 18 and PA = 6, find PB.

Quinn got paid $121,560 in his first career and on switching, he made 55% less, i.e. he made 45% of his previous career.

This is because, if in a previous career he made 100%, then a 55% reduction in salary annually would mean, he is left with only 45%.

Let us suppose, previous salary as x

then, x= $121,560

so, 45% of x= 45% of $121,560

i.e. 45% of x= 45/100 x 121560

therefore, 45% of x= $54,702

Quinn makes $54,702 now.

Therefore, a reduction in 55% of earlier salary would mean that Quinn's salary reduced from $121,560 to $54,702

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Answer:

A) y = 23°

B) ∠A = 67°, ∠C = 113°, ∠D = 113°

Step-by-step explanation:

Hello!

Angle A and B are vertical angles, meaning they are equal in measure. We can solve for y by setting the two equations equal to each other.

Vertical angles are the opposite angles formed by the intersection of 2 lines.

Supplementary angles are angles that add up to 180°.

The value of y is 23°.

Measure of Angle A is 67°, as Angle A and B are vertical and equal in measure

Measure of Angle C is 113°, because the sum of angles on a line are equal to 180°, and are supplementary.

Measure of Angle D is also 113°, because it is vertical to Angle C.

Answer:

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this is the correct solution.

72.1232 rounded to the nearest thousandth is 72.123.

The term "rounding to the nearest thousandth" refers to the practice of rounding any decimal number to the next thousandth value. Thousandth in the decimal system signifies (1/1000) or 0.001. 3.125, for example, is the number 3.1249 rounded to the closest thousandth.

To round it to the closest thousandth, we must focus on the number following this spot - tens of thousandths. This figure will determine whether we round up or round down. "Five and above go up like a bird," as the phrase goes. Therefore, this will give a value of 72.123.

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The value of x is 10

From the diagram shown, we can see that it takes the shape of a   parallelogram

The properties of a parallelogram includes;

We can see that the diagonal bisects the parallelogram into equal halves and then the parallel and opposite sides are equal.

If the opposite sides of x = 10

Then, x = 10

Hence, the value is 10

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The equation of the line that is perpendicular to y = x + 6 is expressed as: y = -x - 7

The equation of a line can be written as y = mx + 1. The value of m is the slope while the value of b is the y-intercept.

The slopes of two lines that are perpendicular to each other are negative reciprocals. This means, if we multiply their slope values together, we will get -1.

Given the line, y = x + 6, the slope of the line is 1. The slope of the line it is perpendicular to is -1, because -1 is the negative reciprocal of 1.

Substitute m = -1 and (x, y) = (2, -9) onto y = mx + b to find the value of b:

-9 = -1(2) + b

-9 = -2 + b

-9 + 2 = b

-7 = b

b = -7

To write the equation of the perpendicular line, substitute m = -1 and b = -7 into y = mx + b:

y = -x - 7

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The net amount due on the order after partial payment done is $8700

Given,

A retailer purchases some merchandise;

The invoice price for the merchandise = $19,500

Terms of sale for the merchandise = 5/15, n/45

On 15th day partial payment done = $10,800

We have to find the net amount due on the order after partial payment is done.

Here,

Net amount due = Invoice price - Partial payment

Net amount due = 19,500 - 10,800

Net amount due = 8700

That is,

The net amount due on the order after partial payment done is $8700

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The dimension are 75 * 50 i.e, Width = 50 cm , Length = 75 cm

Define Dimension

A measurable extent of a particular kind, such as length, breadth, depth, or height.

Let,

T = how taller the poster is

W = how wide the poster is

According to question given,

T = W + 25  ---eq(i)

The total height is calculated by multiplying the top border by 5 and the bottom border by 5. The entire height is then multiplied by the border's width, 5, times 2, so there are two tall sides. then multiplying by 5 times 2 widths.The equation looks like that,

5 * (2 (T + 10)) + 5 * (2 * W) = 1350

Now substitute the eq(i) value,

5 * (2 ((W + 25) + 10)) + 5 * (2 * W) = 1350

Now, solve for W,

5 * (2W +50 + 20) + 10W = 1350

10W + 5(70)+ 10W = 1350

20W + 350 = 1350

20W = 1350 - 350

20W = 1000

W = 1000/20

W = 50

Now, put the W value in eq(i)

T = 50 + 25

T = 75

Therefore, The dimension are 75 * 50  i.e, Width = 50 cm , Length = 75 cm

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The two triangles are not similar to each other.

The perimeter of the triangle is the sum of the lengths of all its sides.

The angle of triangle = 62

The two equal angles = [4(x +2)] and (5x - 7)

According to the question,

The Perimeter of triangle are;

[4(x +2)] + (5x - 7) + 62 = 180

4x + 8 + 5x - 7 + 62 = 180

9x + 63 = 180

9x = 117

x = 13

The other triangle is

6x + 62 + 6x + 6 = 180

12x + 68 = 180

12x = 112

x = 9.33

Hence, the two triangles are not similar to each other.

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I would use weight of the rice after it has been fully cooked as a response variable.

The response variable I would use would be weight of the rice after it has been fully cooked. Different studies have depicted that when different types of rice are cooked, they absorb the water and the ingredients in which they are being cooked, and they concluded having different weights after being fully cooked. So, the suitable response variable would be the final weight of the rice after they are fully cooked. This response can be measured by comparing it to the initial weight of rice before cooking.

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Answer:

6 or 5.7

Step-by-step explanation:

w² = 32

w = root 32

w = 5.656854249

w = 6 or 5. 7

In a case whereby I baked a cake for my siblings ad  My brother ate large fraction 1/8 of the cake and my sister ate \large frac 3/4 ,  the amount of cake is left for me is 1/8.

In this question , we are dealing with fraction, which implies that the number of the cake that i am having is 1.

And we are told that 1/8 of the cake is been eaten by my brother, where 3/4 of the cake is been eaten by my sister, then to know the amount of cake that was left for me, we will need to perform some simplification as:

1-(1/8) - (3/4) =1/8.

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If a cake is baked, In which her brother ate 1/8 and sister ate 3/4. Then 1/8 of cake is left me.

A fraction represents a part of a whole

Given that a cake was baked for her  siblings.

Her big brother ate large part of the cake that is 1/8.

Her sister ate 3/4 of the cake.

We need to find the left out cake for her.

To do that we have to remove 1/8 and 3/4 from 1.

1-(1/8)-(3/4)

(8-1-6)/8

1/8

Hence she has 1/8 of cake which is left.

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Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Answer:

y < 9

Step-by-step explanation:

Hello!

We can solve the inequality for y by dividing both sides by 7.

Remember, when dividing or multiplying both sides of an inequality with a negative number, make sure to flip the sign. Since 7 is positive, we don't have to flip the sign.

So the inequality is true for all y values less than 9.

Hey there!

63 > 7y

7y < 63

DIVIDE 7 to BOTH SIDES

7y/7 < 63/7

SIMPLIFY IT

y < 63/7

y < 9

You have an open circle starting at 9 and going down to left side of the number line.

Therefore, your answer should beD

y < 9

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

  (c)  see attached

Step-by-step explanation:

You want the number line that shows the solutions to |-2x| = 4.

The absolute value equation resolves to two equations:

The solution will be plotted on the number line as solid dots at -2 and 2, as shown in the attachment.

Answer:

C

Step-by-step explanation:

If there is a negative number in "I  I", then it becomes positive but if it is a positive number, then it remains positive

Answer:

n>-1/40

Step-by-step explanation:

Hope this helps!! (I promise...it's the right one)

Answer:

b) n > (-1/40)

Step-by-step explanation:

Given equation,

→ n - (3/8) > (-2/5)

Now the value of n will be,

→ n - (3/8) > (-2/5)

→ n > (-2/5) + (3/8)

→ n > (-16/40) + (15/40)

→ n > (-16 + 15)/40

→ [ n > (-1/40) ]

Hence, value of n is -1/40.

Area under the standard normal curve of z - score :

P(z < 0.54) = 0.7054

Given:

The area under the standard normal curve left is z = 0.54.

and, also sketch the area of normal curve and allocate the area left to the z - score .

What do z-scores mean?

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.

Now,

The area under the curve represents the probability, therefore, the total area under the curve is equal to 1.

The Area under the standard normal curve of z - score :

P(z < 0.54) = 0.7054

Here, The sketch the under the standard normal curve  over the indicated interval.

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Rule for a dilation with center (0,0)

k is the scale factor.

For point P (0,3):

Answer:

3500

Step-by-step explanation:

split 7000 in half for stocks and treasury= 3500 each.

7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.

Here, 144=12×12=12². Therefore, 144 is a perfect square.

The given numbers are 29, 78, 144 and -6.

A perfect square is a positive integer that is obtained by multiplying an integer by itself. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.

By perfect square definition

29=29×1

78=2×2×17

144=2×2×2×2×3×3=12×12

-6=-2×3

So, from the above factors it is clear that, 144 is a perfect square.

Here, 144=12×12=12². Therefore, 144 is a perfect square.

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Answer:

1. 8 softballs

2. 16 softballs

3. 24 softballs

4. 32 softballs

5. 40 softballs

6. 48 softballs

Step-by-step explanation:

The triangle QRS with points Q(8, -4), R(-1, 2), and S(3, 7). After the triangle is reflected across Y axis, then the coordinates of vertex Q are (-8, -4).

How to determine reflection coordinates?

These are the specified parameters:

Q(8, -4), R(-1, 2), and S(3, 7)

Determine the reflected of Q(8, -4) across Y-axis

A(a, b) ⇔ A' (-a, b)

Q(8, -4) ⇔ Q' (-8, -4)

Determine the reflected of R(-1, 2) across Y-axis

A(a, b) ⇔ A' (-a, b)

R(-1, 2) ⇔ R' (1, 2)

Determine the reflected of S(3, 7) across Y-axis

A(a, b) ⇔ A' (-a, b)

S(3, 7) ⇔ S' (-3, 7)

The coordinates of vertex Q after the triangle is reflected across the y-axi are (-8, -4).

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SOLUTION

First let us get the monthly rate

This can be gotten using the formula

Where P is principal,

r is the percent interet rate per year, so to get monthly interest is divide by 12

i is the monthly interet.

Using column 1 to determine the rate, we have

Now, the interest rate r = 6%

The starting principal becomes

Therfore, the answer is 150000 dollars

The graph of g and f have equal intercepts while the slope of the graph of f is 5 times larger than the slope of the graph of g

Given: f(x) = 2x-5 and g(x)=2(0.2x)-5

To compare the two graphs, we can make use of the equation of a line:

The general form of the equation of a line is y = mx + c

Where m is the slope and c is the intercept

So we will compare two the functions with the equation of a line:

Comparing f(x) = (2x-5) with y = mx + c

The slope(m) of the line = 2 and the intercept(c) = -5

Also, comparing g(x) = 2(0.2x)-5 with y = mx + c

The slope(m) of the line = 2(0.2) = 0.4 and the intercept(c) = -5

Since the slope of f(x) = 2 and the slope of g(x) = 0.4. Thus:

slope of f(x) / slope of g(x)  = 2/0.4 = 5

So we can say the slope of  f(x) is  5 times the slope of g(x)

Therefore, the graph of g and f have the same intercept. But the slope of f(x) is  5 times the slope of g(x)

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The most appropriate choice for Quadratic equation and discriminant will be given by -

Discriminant = -244

What is Quadratic equation and discriminant?

At first it is important to know about equation.

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

If [tex]ax^2 + bx + c = 0[/tex] ([tex]a\neq0[/tex]) is a quadratic equation, discriminant is given by

[tex]D = b^2-4ac[/tex].

Here,

The given equation is

[tex]7x^2+23x+168=6x^2+3x+7[/tex]

[tex]7x^2 - 6x^2 + 23x - 3x + 168 - 7 = 0 \\x^2 + 20x +161 = 0\\[/tex]

Discriminant = [tex]20^2 - 4 \times 1 \times 161[/tex]

                     = [tex]400 - 644[/tex]

                     = -244

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Answer:

1. 4:3

2. 5:7

3. 9:4

4. 3:5

5. 7:12

Step-by-step explanation:

I'm sure you don't care how to get the answers, you just want them :)

Answer:

Step-by-step explanation:
Slope is gradient which is, change in y
                                              change in x
so, on the graph, change in y = 10-2.5 = 7.5
                              change in x = 5-0 =5
so, gradient is, 7.5/5
                     = 3/2

The inequality used to represent Paisley budget and the number of gigabytes Paisley can use while staying within her budget is 5 gigabyte

Information gotten from the question include

Paisley pays a flat cost of $60 per month and $3 per gigabyte

bill under $75 per month

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables to suit the problem to be solved

y = Total cost

m = cost per gigabyte

x = number of gigabyte

c = flat cost

The inequality equation as described in the problem is represented using linear function as as follows

3x + 60 < 75

3x < 75 - 60

3x < 15

x < 5

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When the remainder is zero, the statement that isn't true is that C. The solution of the divisor is a zero.

A dividend simply means the value that is divided by another value in order to far the result. It is the base of the division problem.

For example, 12 divided by 6 is 2. In this case, 6 is the dividend. 6 is a factor of 12.

Therefore, the correct option is C

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The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9

From the question, the given parameters are:

Roots = (-1 - √2)/3 and (-1 + √2)/3

The quadratic equation is then calculated as

f(x) = The products of (x - roots)

Substitute the known values in the above equation

So, we have the following equation

[tex]f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})[/tex]

This gives

[tex]f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})[/tex]

Evaluate the products

[tex]f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})[/tex]

Evaluate the like terms

[tex]f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}[/tex]

So, we have

f(x) = x²+ 2/3x - 1/9

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