What are the solutions of the equation 2x² = 18? Use a graph of the related function.

Answer:

The numbers are 44 and 46

Step-by-step explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

x+2=44+2=46

therefore

The numbers are 44 and 46

Answer:

18°

P.S. Put as brainiest!

Answer:

Undefined

Step-by-step explanation:

Same x coordinates with different y values is considered undefined

[tex]

s=\frac{-2-6}{-4-(-4)}=\frac{-8}{0}=\boxed{undefined}

[/tex]

Answer:

Step-by-step explanation:

[ (x + 7) / 6 ] − [ (x + 5) / (x + 3) ]

First, we must find the common denominator.  In this case, that's 6 (x+3).  Multiply the first fraction by (x+3)/(x+3) and the second fraction by 6/6.

[ (x + 7)(x + 3) / (6 (x + 3)) ] − [ 6 (x + 5) / (6 (x + 3)) ]

Now distribute the numerators:

[ (x² + 10x + 21) / (6 (x + 3)) ] − [ (6x + 30) / (6 (x + 3)) ]

Now we combine the fractions:

((x² + 10x + 21) − (6x + 30)) / (6 (x + 3))

(x² + 10x + 21 − 6x − 30) / (6 (x + 3))

(x² + 4x − 9) / (6 (x + 3))

So the simplified form is:

[tex]\frac{x^{2} + 4x - 9}{6 (x + 3)}[/tex]

Answer: -8n^4 + 3n^2

(The ^ is the exponent)

Answer:

24

Step-by-step explanation:

8*3= 24

if you use this ratio and simplify the new ratio (8:24), you get the original ratio of 1:3

Answer:

Step-by-step explanation:

[tex]\text{We have the ratio}\\\\roses\ to\ dailes=\dfrac{roses}{dailes}\to1:3=\dfrac{1}{3}\\\\\text{We have}\ 8\ roses.\ \text{Substitute:}\\\\\dfrac{8}{dailes}=\dfrac{1}{3}\qquad\text{cross multiply}\\\\dailes=(3)(8)\\\\dailes=24[/tex]

Answer:

Step-by-step explanation:

Put the coordinates of the points to the inequality and check:

y < -1/2x + 2

for (2, 3) → x = 2, y = 3

3 < -1/2(2) + 2

3 < -1 + 2

3 < 1     FALSE

============================

for (2, 1) → x = 2, y = 1

1 < -1/2(2) + 2

1 < -1 + 2

1 < 1    FALSE

============================

for (3, -2) → x = 3, y = -2

-2 < -1/2(3) + 2

-2 < -1.5 + 2

-2 < 0.5      TRUE

============================

for (-1, 3) → x = -1, y = 3

3 < -1/2(-1) + 2

3 < 1/2 + 2

3 < 2 1/2      FALSE

the constant of variation or namely its slope will be

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{30}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{30-18}{5-3}\implies \cfrac{12}{2}\implies 6[/tex]

The mode in a stem-and-leaf plot is determined by identifying which leaf (end digit of a data point) occurs most often for a particular stem (leading digit(s)). For example, in the data set 4, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10 the mode is 7 as it appears most frequently.

The stem-and-leaf plot is a type of graph that provides a visual representation of data. It is a way of organizing data in which we can easily discover the mode, mean, median, and even the shape of the distribution (such as skewness). The mode in a data set is the value that appears the most often. In the context of a stem-and-leaf plot, identifying the mode involves finding which 'leaf' or end digit of a data point (the last digit in a number) occurs most frequently on a particular 'stem' or leading digit (all but the last digit of a number).

For example, in the stem-and-leaf plot of the data set given : 4, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10 the mode is 7 as the number '7' shows up the most often, which is 6 times. For identifying the mode, we closely look at the list of leaf values for each stem value and determine which leaf occurs more frequently than any other. Therefore, to answer the student's question about finding the mode from a stem-and-leaf plot, they simply need to identify which leaf value occurs most frequently in the data set presented in the plot.

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The mode of the set of data in the stem and Leaf plot is 51

From the question, we have the following parameters that can be used in our computation:

The stem and leaf plot

By identifying the stem with the most leaves, we have identified the stem represents the mode of the data set.

Using the above as a guide, we have the following:

The stem is 5 and the leaf is 1

So, the mode is 51

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Answer:

y = x + 3 or y = x - 3

Step-by-step explanation:

Rise over run for slope (m) and then get the y-intercept (b) by continuing the pattern from right to left until you cross the y-axis.

Plug m and b into y = mx + b

side p and side r are both perpendicular to side s.

Side p:

y = x + 3

Side s:

y = x - 3

Answer:

Second Option

f(x) − 2

Step-by-step explanation:

The function [tex]y=3 (2) ^ x[/tex] passes through point (0, 3) because:

[tex]f (0) = 3 (2) ^ 0 = 3 (1) = 3[/tex]

Then, if the transformed function passes through the point (0, 1) then this means that the graph of [tex]y = 3 (2) ^ x[/tex] was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

[tex]y = f(x) + k[/tex]

Where k is a negative number. In this case [tex]k = -2[/tex]

Then the transformation is:

[tex]y = f(x) -2[/tex]

and the transformed function is:

[tex]y = 3(2) ^ x -2[/tex]

Answer:

f(x − 2)

Step-by-step explanation:

thats the right answer

We know that there are 30 hallways and we know that there are 2 hall monitors for every hallway. Knowing this, we see that there are 60 total hall monitors

We also know that there are 4 supervisors for every 20 hall monitors.

60 hall monitors can also be thought of as 20 hall monitors + 20 hall monitors + 20 hall monitors

We see that there are 3 groups of 20 hall monitors

Group 1 will have 4 supervisors

Group 2 will have 4 supervisors

Group 3 will have 4 supervisors

Answer: 12 supervisors

y = mx + b

m = slope

b = y-intercept

Since it is parallel to the equation y = 3x it means that the equation that goes through point (-1, 0) has the same slope (3x)

To find the b plug the x and y of point (-1, 0) into the equation: y = 3x + b then solve for b

0 = 3(-1) + b

0 = -3 + b

0 + 3 = (-3 + 3) + b

3 = b

so...

y = 3x + b

Hope this helped and made sense!

~Just a girl in love with Shawn Mendes

Answer:

y = 3x - 3

Step-by-step explanation:

Since our line is parallel to y = 3x, our slope should be 3. We also have the points (-1, 0).

From here, we can use the point-slope form (how convenient):

y - y₁ = m(x - x₁), where (x₁, y₁) is the given coordinate on the line, and m is the slope of the line

Plug in: y - 0 = 3(x - 1)

We could leave it here, but we should convert this line into the more commonly-seen slope-intercept form.

Distribute: y - 0 = 3x - 3

Identity: y = 3x - 3

k(x)=5x-6

k(4)=5(4)-6

(k+k)(4)=k(4)+k(4)

=5(4)-6+5(4)-6

I think.

Answer:

The length of the line segment is 13 units

Step-by-step explanation:

The line segment joining the two points is horizontal since the y co-ordinate is the same.

For a horizontal line, the length of the line segment is simply the difference between the x co-ordinate values.

In this case we have;

7 - (-6) = 7 + 6 = 13

Therefore, the length of the line segment is 13 units

Answer:

your answer is 13 units

Step-by-step explanation:

I do K12

Answer:

4,582,500

Step-by-step explanation:

(30,000*611)/4=4,582,500

Answer:

Quarterly budget of $4582500 must be allocated.

Step-by-step explanation:

A facility spends on its inmates of an average = $30000 annually

Number of inmates = 611

Total amount to be spent = $30000×611

= $18330000

Since there are 4 quarters in a year so quarterly budget allocated

= [tex]\frac{18330000}{4}[/tex]

= $4582500

Therefore, quarterly budget of $4582500 should be allocated.

Answer: 6 units

Step-by-step explanation:

Area = 1/2 (base1 + base2) X height <-------- Formula for a trapezoid

24 = 1/2 (2 + 6) X h <----- We know that the area of the trapezoid is 24 units

squared and that both of the bases are 2 units and 6 units.

24 = 1/2 (8) X h <------- Add 6 + 2

24 = 4 X h <-----  Half of 8 is 4

h = 6 <------  6 X 4 = 24 , therefore the height is 6 units.

Hope this helps!

Perimeter: 2(l+w)

2•l+2•w

l+w+l+w

Area: l•w

wl

Neither: l+w

Divide the total inches by the scale inches:

7.5 / 3 = 2.5

Multiply that by the scale feet:

2.5 x 2 = 5 feet.

Answer: 5

Step-by-step explanation:

Answer:$400

Step-by-step explanation:

Because, if she spent ONLY 1/5 of her money, and she has $80 left, wouldn't you basically have to multiply 5 with 80 to get the original amount of money?

Answer:

$100

Step-by-step explanation:

If Maryna had $80 after spending 1/5, we know she has 4/5 left. Then, we divide 80 by 4/5. To divide a fraction, we multiply the number by rhe reciprocal. So, we multiply 80/1 by 5/4. 80 multiplied by 5 is 400, and divided by 4 is 100. This is how we get an original amount of $100.

I believe that it has two solutions

Answer:

The given equation has just one solution

Step-by-step explanation:

To find the solution to the problem given, we will follow the steps below;

5x + 3x - 4 = 10

We will first start by simplifying

8x - 4 = 10

Add 4 to both-side of the equation

8x - 4 + 4 = 10 + 4

8x = 10

Divide both-side of the equation by 8

8x/8 = 10/8

At the left-hand side of the equation, 8 will cancel-out 8 leaving us with just x while at the right-hand side of the equation 10 will be divided by 8

x=1.25

Therefore the given equation has just one solution

The k-th root's inverse function is raising to the k-th power.

So, if we raise the k-th root of some number x to the k-th power, we have applied a function and its inverse to x, and we must get x itself as output:

[tex]f(f^{-1}(x))=f^{-1}(f(x))=x\quad\text{for every invertible function f}[/tex]

So, in our case, we have

[tex](\sqrt[k]{x})^k = \left(x^{\frac{1}{k}}\right)^k=x^{k\cdot \frac{1}{k}}=x^1=x[/tex]

The equation that Arlene claim should be [tex]x^{k.\frac{1}{k}} \ = x^1 = x[/tex]

The k-th root's inverse function should be raising with respect to the k-th power.

Thus, in the case if we raise the k-th root of some number x to the k-th power, so here we used the function and its inverse to x, and we must get x itself in an output:

So,

[tex](k \sqrt x)^k = (x\frac{1}{k})^k = x^{k.\frac{1}{k}} \ = x^1 = x[/tex]

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1 ) Watts =E * I = 110 * 5 = 550 watts =.55 KW  

2) I = Watts / e = 1100 / 110 = 10 amperes  

3) 1 horsepower = 33000 ft/lbs per minute  

HP = ( 2000 * 1000) / (33000 *4) = 15.1515 hp  

4) cost = (10 * 100 / 1000) *11 * $0.10 = $1.10  

5) This answer will be incorrect because you have not stated the power factor of the motor.  

va = I * E = 7.5 * 240 = 1800  

2 hp = 2 * 746 watts = 1492 watts  

If the motor had a 1.0 power factor (it doesn't) the efficiency would be  

efficiency = output / input = 1492 / 1800 = 82.888 %  

6) I = watts / E =1000 / 120 = 8.333 amps  

7) 1 = watts / E = 1000 / 240 = 4.1616  

8) Kw-hr = (2 * 24 * 365 ) / 1000 = 17.52  

cost = kw-hr * $0.03 = 17.52 * $0.03 = $0.5256  

9) efficiency = (115 * 240) / (2400 * 12) = 95.8333 %  

10) KW = (I^2 * R) / 1000 = (20^2 * 5) / 1000 = 2  

the current required is 10 amperes.

To calculate the current required for a device rated at 1,100 watts operating at 110 volts, we use the formula P = IV, where P is power in watts, I is current in amperes, and V is voltage in volts.

Rearranging the formula to solve for current, we get I = P / V. Plugging in the given values, we have:

I = 1,100 W / 110 V

Thus, the current required is 10 amperes.

Answer:

Step-by-step explanation:

If you flip coins, you can get,

HT TH HH TT

There are 4 possible outcomes.

Out of these 4, Matt has to do chores if two heads are flipped. It is 1/4 chance.

Out of these 4, Mark has to do chores if two tails are flipped. Again, 1/4 chance.

The method of decision is far since both guys have the same chance of being picked to do chores.

To flip again, they would have to get either HT or TH out of the 4 choices. So 2/4=1/2 is the likeihood they must flip again.

0=1/2(2x²+13x+20)

0=x²+6,5x+10

[tex]x = \frac{ - 6.5 + \sqrt{2.25} }{2} \\ x = - 2.5 \\ x = - 4[/tex]

Answer:

x = - 2.5, x = - 4

Step-by-step explanation:

To find the zeros, set y = 0, that is

[tex]\frac{1}{2}[/tex](2x + 5)(x + 4) = 0

Equate each of the factors to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - 2.5

x + 4 = 0 ⇒ x = - 4

Answer:

1. the cost of the computer (c)

2. > (greater than)

3. how much ($300)

4. c > 300

The variable in the inequality represents the cost of the computer.

The inequality symbol needed is > (greater than)

The constant is how much ($300)

The inequality that correctly represents the problem is cost of the computer  > 300

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:

-8

Step-by-step explanation:

Simply plug in 8, then evaluate to arrive at your answer.

Answer:

a and f

Step-by-step explanation:

Vertical angles are directly opposite each other, created by two lines intersecting.

∠A and ∠F are congruent to each other because they are vertically opposite angles. Then the correct option is D.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

∠A and ∠F, ∠B and ∠E, ∠C and ∠H, and ∠D and ∠G are congruent to each other because they are vertically opposite angles.

Then the correct option is D.

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Answer:

A

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent in the terms of the polynomial. The leading coefficient is the coefficient of the term with the largest exponent.

Given

f(x) = 2x³ + 2x² - [tex]\frac{1}{x}[/tex]

The term - [tex]\frac{1}{x}[/tex] means that f(x) is not a polynomial

Since terms with division by a variable are not allowed.