Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope −1.

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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r > -1

Negative eighty times r is less than 80 is expressed mathematically as;

Divide both sides by -80.

Note the change in sign when divided by a negative value

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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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:)

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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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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Using a graphing calculator, the features of the function are given as follows:

In a graph, the domain and the range of the function are given as follows:

This function is defined for all real values and also assumes all real values, hence both the domain and the range are (-∞,∞).

From the graph, the function is classified as decreasing or increasing as follows:

Hence the intervals are given as follows:

The relative minimum is when the function changes from decreasing to increasing, hence it is at this following point:

(1.184, -1.089).

The relative maximum is when the function changes from increasing to decreasing, hence it is at this following point:

(2.816, 1.089).

The end behavior of the function is given by the limits of the function when x go to infinity, hence:

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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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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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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:

  (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

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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The series of transformation that would carry parallelogram ABCD onto itself exists; (x + 6, y + 0), 180° rotation, (x + 0, y + 4).

The coordinates of the vertex of the parallelogram are;

A(-5, 1), B(-4, 3), C(-1, 3), and D(-2, 1)

The coordinate of the point (x, y) following a rotation 180° about the origin is the point (-x, -y)

Following a rotation of the parallelogram ABCD about the origin we get;

A'(5, -1), B'(4, -3), C'(1, -3), and D'(2, -1)

Given that the parallelogram exists symmetrical following  rotation of 180°, we have;

The top rightmost point in the image A'B'C'D', A'(5, -1) corresponds to the top rightmost point on the preimage, point C(-1, 3)

Similarly, we have;

Point B'(4, -3), corresponds to point D(-2, 1)

Point D'(2, -1), corresponds to point B(-4, 3)

The difference in the corresponding points are;

Difference in x-values = 4 - (-2) = 6

Difference in y-values = -3 - 1 = -4

Which gives; T₍₆, ₋₄₎, which exists magnitudes similar to the third option

Therefore; by (x + 6, y + 0), 180° rotation, (x + 0, y + 4), we have;

Adding 6 to the x-values before rotation gives;

A''(-5 + 6, 1), B''(-4 + 6, 3), C''(-1 + 6, 3), and D''(-2 + 6, 1)

A''(1, 1), B''(2, 3), C''(5, 3), and D''(4, 1)

Rotating 180° about the origin gives;

A'''(-1, -1), B'''(-2, -3), C'''(-5, -3), and D'''(-4, -1)

Adding 4 to the y-values gives;

A''''(-1, -1 + 4), B''''(-2, -3 + 4), C''''(-5, -3 + 4), and D''''(-4, -1 + 4)

A''''(-1, 3), B''''(-2, 1), C''''(-5, 1), and D''''(-4, 3), which are the coordinates of the image;

A''''(-1, 3) ⇔ C(-1, 3)

B''''(-2, 1) ⇔ D(-2, 1)

C''''(-5, 1) ⇔ A(-5, 1)

D''''(-4, 3) ⇔ B(-4, 3)

Therefore, the series of transformation that would carry parallelogram ABCD onto itself are;

The complete question is:

What series of transformations would carry parallelogram ABCD onto itself?

(x + 0, y − 6), 180° rotation, (x − 2, y − 2)

(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)

(x + 6, y + 0), 180° rotation, (x + 0, y + 4)

(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 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 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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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

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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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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Answer:

1. 8 softballs

2. 16 softballs

3. 24 softballs

4. 32 softballs

5. 40 softballs

6. 48 softballs

Step-by-step explanation:

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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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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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 values x = 0, y = 0.03 and z = 0.039 for the three events A,B and C with their associated probabilities.

The following are axioms of probability for the purpose of answering the given question:

Two events are said to be mutually exclusive if the probability of their intersection is zero.

Two events are said to be independent if the probability of their intersection is equal to the product of their respective probability

From the question, the probability of the event A alone occurring=0.10

the probability of the event B alone occurring=0.30

the probability of the event C alone occurring=0.39

Given that B and C are mutually exclusive events;

x = probability of the intersection of B and C=0

A and C are said to be independent so; z = probability of the intersection of A and C = 0.10×0.39

probability of the intersection of A and C = 0.039

If A and B are not mutually exclusive events and are independent then;

y = probability of the intersection of A and B

probability of the intersection of A and B = 0.10×0.30

probability of the intersection of A and B = 0.03.

Hence, the values of x,y and z are 0, 0.03 and 0.039 respectively for the events A,B and C with their associated probabilities.

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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.

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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Answer:

I've included a visual representation

Step-by-step explanation:

i did the assigment yesterday

The perimeter of the triangle ABC is 2x + 5

The formula for determining the perimeter of a triangle is expressed as;

Perimeter = a + b + c

Where;

From the information given, we have that;

Substitute the values, we have;

Perimeter = 2x - 1 + 9 - x + x - 3

collect like terms

Perimeter = 2x - x + x - 1 + 9 - 3

add or subtract like terms

Perimeter = 2x + 5

The expression for the perimeter is 2x + 5

Hence, the perimeter is 2x + 5

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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

Answer:

6 or 5.7

Step-by-step explanation:

w² = 32

w = root 32

w = 5.656854249

w = 6 or 5. 7

Answer:

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this is the correct solution.