A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

Answer:

Multiply the denominator and numerator with root 2 to get a fair denominator and simplify if needed. Hope it helps

Answer:

1 + √3 - √5

Step-by-step explanation:

The given √2/√2 equals 1, and so we now have 1 + √3 - √5, whose denominator is the integer 1.  There's nothing left to rationalize.

Answer:

5x + 15

Step-by-step explanation:

To expand the binomial, you need to multiply each term inside the parentheses by 5.

(x + 3)5

= (x * 5) + (3 * 5)

= 5x + 15

Part 1

Using the distance formula,

[tex]AB=\sqrt{(-2-1)^{2}+(2-7)^{2}}=\sqrt{34}\\\\BC=\sqrt{(-2-4)^{2}+(2-2)^{2}}=6\\\\AC=\sqrt{(1-4)^{2}+(7-2)^{2}}=\sqrt{34}[/tex]

So, the measure of the longest side is 6 units.

Part 2

Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).

We already know that [tex]AB=\sqrt{34}[/tex]

Using the distance formula,

[tex]AD=\sqrt{(1-1)^{2}+(7-2)^{2}}=5\\\\BD=\sqrt{(-2-1)^{2}+(2-2)^{2}}=3[/tex]

So, ABD is a scalene triangle.

Part 3

From part 2, we know that the length of side AD is 5 units.

Answer:

The answer:

A. [tex]x= \frac{-5+ \sqrt{-11} }{2}[/tex]

F.[tex]x= \frac{-5- \sqrt{-11} }{2}[/tex]

Step-by-step explanation:

Step 1: Solve with quadratic formula

Step 2: Simplify

Step 3: Separate the solution

Answer:

[tex]\large {\textsf{A and F}}\ \implies \bold{x_1}=\dfrac{-5-\sqrt{-11}}{2},\ \bold{x_2}=\dfrac{-5+\sqrt{-11}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0.

Given polynomial: x² + 5x + 9

⇒ a = 1, b = 5, c = 9

Step 1: Rewrite to Standard Form.

⇒ x² + 5x + 9 = 0

Step 2: Substitute the values of a, b, and c into the formula.

⇒ a = 1, b = 5, c = 9

[tex]x=\dfrac{-5\pm\sqrt{\bold{5^2}-4\bold{(1)(9)}}}{\bold{2(1)}}\\\\x=\dfrac{-5\pm\sqrt{25\bold{\ - \ 4(9)}}}{2}\\\\x=\dfrac{-5\pm\sqrt{\bold{25-36}}}{2}\\\\x=\dfrac{-5\pm\sqrt{-11}}{2}[/tex]

Step 3: Separate into two possible cases.

[tex]x_1=\dfrac{-5-\sqrt{-11}}{2}\\\\x_2=\dfrac{-5+\sqrt{-11}}{2}[/tex]

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Answer:

(x-9)(x+8)

Step-by-step explanation:

Use the AC method

Answer:

17 in.

Step-by-step explanation:

There are two same angles shown, so two sides are equal. We can form an equation x+4=4x+1. Solution is x=1, then both unknown sides are 5 in. long. Given all side lengths we add them 7+5+5+15 getting the perimeter.

Answer:

most likely b

Step-by-step explanation:

the more than symbol tells me that it is going to move past 10.

Answer: 41

Step-by-step explanation:

If each line costs 2, then for the four-line ad, the cost is the initial price plus 4(2), meaning the initial cost is 25-8=17.

Thus, the cost of a 12-line ad is 17+2(12)=41

The graph is shown below:

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Rearrange unknown terms to the left side of the equation:

|x|  > 7/2-1

Now,

|x|  > (7-2)/ 2

Calculate the sum or difference:

|x|  > 5/ 2

Convert the absolute inequality to standard inequality:

x> 5/2  or  x< -5/2

Solve the inequality:

x> 5/2

Solve the inequality:

x< -5/2

Graph on number line is attached

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Answer:

Un= 1 + (n-1)4

Step-by-step explanation:

a=1

d=5-1=9-5=4

using the formula Un=a+(n-1)d

A picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The complete question is;

"Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2) .

Use the polygon tool to graph the dilated figure."

The center of dilation and figure are first translated, making the origin the center of dilation.

We map every point because the point (2, 2), which is our center of dilatation, must be translated left 2 and down 2 to become the origin.

(x, y)→(x-2, y-2)

Each point will be multiplied by two when the scale factor is two, giving us the rule.

(x, y)→(2x-4, 2y-4)

In order to return the figure to its original location, we must translate it right 2 and up 2; this gives us the rule.

(x,y)→(2x-4+2, 2y-4+2) = (2x-2, 2y-2)

At the top of the original figure, the first point is (0, 6). When we use the transformation, we get

(0, 6)→(2*0-2, 2*6-2) = (0-2, 12-2) = (-2, 10)

The pre-rightmost image's point is (2, 4). The results of using the transformation rule are;

(2, 4)→(2*2-2, 2*4-2) = (4-2, 8-2) = (2, 6)

The pre-leftmost image's point is at (-3, 3). The transformation rule being applied, w

(-3, 3)→(-3*2-2, 3*2-2) = (-6-2, 6-2) = (-8, 4)

Hence,an picture of the dilated figure with its points at (-2, 10), (2, 6), and (-8, 4) is provided.

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Answer:

Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.

x + y = 152,

8.5x + 12y = 1,656

How many hats were sold?

hats

Step-by-step explanation:

a) 74.857% of adult men are shorter than Michael

b) 84.134% of adult men are taller than Jack

c) 58.991% of adult men are of height between Jack and Michael

Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.

Given:

µ = 70in,  σ = 3in.

We know Z = (x-µ)/σ

a) Actor Michael B. Jordan is 6’0” (72”) tall.

Z = (72-70)/3 = 0.67

So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%

b. Comedian Jack Black is 5’7’ (67”) tall.

Z = (67-70)/3 = -1

The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.

But  the percentage of those taller than jack is = 1 – .15866 = 0.84134

c) P(X < 72) – P(x < 67)

= 0.74857 – 0.15866

= 0.58991

= 58.991%

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The Question attached here is incomplete, the complete question is

a. Actor Michael B. Jordan is 6’0” (72”) tall.  What percentage of adult men are shorter than Michael?

b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?

c. What percentage of adult men are of height between Jack and Michael?

Answer:

B. took test

Step-by-step explanation:

Answer:

B. Jonathan is correct. Kevin made an error at step 3.

Step-by-step explanation:

The range of the function will be all values that are greater than 17 that is y > 17

The range of a function is the dependent variable of the function for which it exists,

Given the linear function

y = 8x + 1

If the value of x is 2, hence;

y = 8(2) + 1

y = 17

Hence the range of the function will be all values that are greater than 17 that is y > 17

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Step-by-step explanation:

-6<2x-4<4

-2<2x<8

-1<x<4

x = (-1,4)

Answer:

[tex]3[/tex] and perpendicular

Step-by-step explanation:

It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].

[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.

Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.

In the first question, we are given the equation [tex]2x+6y=12[/tex].

We rearrange to make [tex]y[/tex] the subject:

[tex]6y = 12-2x[/tex]

Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:

[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]

To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.

So here, the slope is [tex]-\frac{1}{3}[/tex].

So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].

So, the perpendicular slope is [tex]3[/tex].

In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].

[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]

Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.

This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.

Answer:

15 sqrt a ^4

Step-by-step explanation:

Using percentages, we have that Puja Limbu did 80% of the problems and Raju Lama did 73.3%, hence Puja Limbu had the better performance.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

The percentage for Puja Limbu is:

[tex]P = \frac{8}{10} \times 100\% = 80\%[/tex]

The percentage for Raju Lama is:

[tex]P = \frac{11}{15} \times 100\% = 73.3\%[/tex]

80% > 73.3%, hence Puja Limbu had the better performance.

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An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.

(3m+7)/27 < n

Hence, the given statement can be modeled as (3m+7)/27 < n.

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Answer:

1.   won 50 games and lost 32 games

2.  233 Democrats and 202 Republicans

3.  360 miles

4.  6 hours

5.  18 miles

Step-by-step explanation:

Question 1

From the given information:

Substitute Equation 2 into Equation 1 and solve for y:

⇒ y - 18 + y = 82

⇒ 2y - 18 = 82

⇒ 2y = 100

⇒ y = 50

Substitute found value of y into Equation 2 and solve for x:

⇒ x = 50 - 18

⇒ x = 32

Therefore, the team won 50 games and lost 32 games.

Question 2

From the given information:

Substitute Equation 2 into Equation 1 and solve for d:

⇒ r + 31 + r = 435

⇒ 2r + 31 = 435

⇒ 2r = 404

⇒ r = 202

⇒ d = 233

Substitute found value of d into Equation 2 and solve for r:

⇒ 233 = r + 31

⇒ r = 202

Therefore, there were 233 Democrats and 202 Republicans.

Question 3

Given:

Distance (d) = vt

⇒ d = 180 × 2

⇒ d = 360 miles

Question 4

Given:

Time (t) = d ÷ v

⇒ t = 420 ÷ 70

⇒ t = 6 hours

Question 5

If the velocity of the bus is 12 mph less than the car then:

⇒ c = b + 12

Given journey times:

Distance (d) = vt

Create two equations for distance:

Bus

⇒ d = b × 0.75 = 0.75b

⇒ d = 0.75b

Car

⇒ d = (b + 12) × 0.5

⇒ d = 0.5b + 6

Distance for both vehicles is the same. Equate the two equations for d and solve for b (velocity of bus):

⇒ d = d

⇒ 0.75b = 0.5b + 6

⇒ 0.25b = 6

⇒ b = 24 mph

Substitute the value of b into one of the distance formulas and solve for d:

⇒ d = 0.5(24) + 6

⇒ d = 18 miles

If ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

Linear pair of angles are angles formed when two lines intersect each other at a single point.

Now, the angles are also said to be linear if they are adjacent to each other after the intersection of the two lines and the sum of the linear pair of angles is always equal to 180°.

Looking at the definition above we can say that if ÐABC and ÐCBD are a linear pair, then it means that their sum is 180°.

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Answer:

3 decimal places; 189/750 = 0.252

Step-by-step explanation:

Answer:

3 decimal places.

189/750 = 0.252

Step-by-step explanation:

If you are allowed to use a calculator, you divide. 189/750 means 189 ÷ 750.

You will get 0.252, which is three decimal places. If you are not allowed to use a calculator, you must do long division. The 750 goes outside the dividing frame and the 189 goes inside. There is an unwritten decimal point after the 9 in 189. Since 750 does not go into 189, put 0. to begin and put zeros after the 189 to do the long division. See image. Hopefully you can just use a calculator.

Answer:

-4n+7

Step-by-step explanation:

because you take away 4 each time and the nber that would come before 3 is 7.

Answer:

The area is approximately 28.73ft²

Step-by-step explanation:

Given: Circumference = 19 ft

The necessary formula area,

Area: A = πr²

Circumference: C = 2πr

Combine:

A = [tex]\frac{C^{2} }{4\pi }[/tex]

A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]

A = 28.72747

Option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

We have two tables given in the question.

The conditional relative frequency tables show the results of a survey asking students whether they are taking a foreign language or not.

The condition is: "Assuming a student is taking a foreign language"

Table B can be used to answer the above statement.

Thus, option fourth ''Table B, because the given condition is that the student is taking a foreign language" is correct.

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Answer:

Option b: Table A, because the given condition is that the student is taking a foreign language.

Step-by-step explanation:

on ed

Answer:

Maybe the question could've been 2+2+1. I'd say read the question properly.

Step-by-step explanation:

In which case, 2+2+1= 5

Standard form of quadratic equation: ax² + bx + c

Here given equation: f(x) = -(x - 4)²  + 2

Simplify the equation:

⇒ f(x) = -(x - 4)² + 2

Use perfect square formula: (a + b)² = a² + 2ab + b²

⇒ f(x) = -(x² + 2(x)(-4) + (-4)²) + 2

⇒ f(x) = -(x² - 8x + 16) + 2

⇒ f(x) = -x² + 8x - 16 + 2

⇒ f(x) = -x² + 8x - 14

[tex]\hrulefill[/tex]

Here given equation: f(x) = (x - 4)²  + 2

Simplify the equation:

⇒ f(x) = (x - 4)² + 2​

⇒ f(x) = x² + 2(x)(-4) + (-4)² + 2

⇒ f(x) = x² - 8x + 16 + 2

⇒ f(x) = x² - 8x + 18

Answer:

f(x)=x²-8x+18

Step-by-step explanation:

f(x) = (x-4)² + 2​

To find the answer for the first part (x-4)², you need to use the formula.

This is the formula: (a-b)²=a²-2ab+b²

Plug in x for a and -4 for b.

(x-4)²=x²-8x+16

Now, put x²-8x+16 for (x-4)².

f(x)=x²-8x+16+2

Add like terms.

f(x)=x²-8x+18

Our answer is already in standard form because it is from greatest to least.

Hope this helps!

If not, I am sorry.

By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

Let be f and g functions, there is a composition of f with respect to g when the input of the former is substituted by the output of the latter. It is to notice that composition is a binary operation between functions.

If we know that f(x) = - (1/2) · x² + 5 · x, g(x) = x² + 2 and x = -2, then the composed function evaluated is:

f(g (x)) = - (1/2) · (x² + 2)² + 5 · (x² + 2)

f(g (- 2)) = - (1/2) · 6² + 5 · 6

f(g (- 2)) = 12

By applying a composition of f(x) = - (1/2) · x² + 5 · x with respect to g(x) = x² + 2 and evaluating the resulting expression at x = - 2, the value of f(g (-2)) is 12. (Correct choice: C)

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