2 What is the slope of the line in the picture below?

Answer:

Step-by-step explanation:

Factorize the polynomial using the given details.

Since one of the factors known, try to factor it out and futher:

Find its zero's:

Answer:

[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.

Given polynomial function:

[tex]f(x)=2x^3-9x^2+13x-6[/tex]

Sum the coefficients:

[tex]\implies 2-9+13-6=0[/tex]

As the sum of the coefficients is zero, (x - 1) is a factor.

Therefore:

[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]

Expand the brackets:

[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]

[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]

Compare the coefficients with the given polynomial.

As the coefficient of the leading term of the polynomial is 2:

[tex]\implies a=2[/tex]

As the coefficient of the term in x² is -9:

[tex]\implies b-a=-9[/tex]

[tex]\implies b-2=-9[/tex]

[tex]\implies b=-7[/tex]

As the constant of the given polynomial is -6:

[tex]\implies c=6[/tex]

Substitute the found values of a, b and c into the factored form of the polynomial:

[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]

Factor the quadratic:

[tex]\implies 2x^2-7x+6[/tex]

[tex]\implies 2x^2-4x-3x+6[/tex]

[tex]\implies 2x(x-2)-3(x-2)[/tex]

[tex]\implies (2x-3)(x-2)[/tex]

Therefore, the fully factored polynomial is:

[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]

To find the zeros, set the function to zero:

[tex]\implies f(x)=0[/tex]

[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]

Apply the zero-product property:

[tex]\implies x-1=0 \implies x=1[/tex]

[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.

Answer:

[tex] 7^2[/tex]

Step-by-step explanation:

Answer:

7²

Step-by-step explanation:

the product of a number and its multiplicative inverse is equal to 1 , that is

a ×[tex]\frac{1}{a}[/tex] = 1

given

[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and

[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1

The angle measures in this problem are given as follows:

1. Angle SVT: 79º.

2. Angle BEC: 65º.

Angles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:

8y - 33 = 5y + 9

3y = 42

y = 42/3

y = 14.

Hence the measure of the angle SVT is of:

m<SVT = 5y + 9 = 5(14) + 9 = 79º.

The two angles given in this problem are also vertical, meaning that we can solve for x as follows:

5x - 10 = 3x + 40

2x = 50

x = 50/2

x = 25º.

Then the bottom angle is:

3 x 25 + 40 = 115º.

The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:

115 + m<BEC = 180

m<BEC = 180 - 115

m<BEC = 65º.

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Rule for a dilation with center (0,0)

k is the scale factor.

For point P (0,3):

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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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:

don't forget to give me brainest

star, like.

this is the correct solution.

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:

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.

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 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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Answer:

B. Opposite angles in a parallelogram are congruent.

Explanation:

The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.

Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.

So, the answer is B. Opposite angles in a parallelogram are congruent.

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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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 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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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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Step-by-step explanation:

x + 3y = 1

x = 1 - 3y-(i)

7x + 8y = 11

x= 11-8y/7-(ii)

substituting eqn (i) in eqn (ii)

11-8y/7= 1-3y

11-8y=7-21y

13y=-4

y=-4/13

putting the value of y in eqn (i)

x=1-(-12/13)

x=25/13

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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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.

⇒Given that the general rule to find the nth term is

[tex]T_{n} =-2+6(n-1)[/tex]

⇒To find the 11th term this means that they need a term which is in the position 11

⇒To get the number we plug in the 11 which is the position in the place of n and simplify.

[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]

The 11th term is 58

Goodluck!!!

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 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 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 value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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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 given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.

Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.

Negative correlation is when two variables move in different directions.  When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative  correlation is always negative.

Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.

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Plotted Answers:

12.) See attached for my work

13.) See attached for my work

14.) See attached for my work

Simplified Answers:

12.) y > –24

13.) x ≥ –12

14.) x > –7

Hope that helps! Have an amazing rest of your day! Please consider giving me the Brainliest! :)

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 :)

The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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