solve for x

3(x-2)-2x+3=-12

help plz

Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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Answer:

13R - (-14)

Step-by-step explanation:

I believe this is the right answer i really hope it is im sorry if its wrong

Have a good day!

Answer -36r^2 + 101r - 45

Step-by-step explanation:

We have proved that there exist constants A and B such that ∣f(x)∣≤A+B∣x∣ for all x∈R, when f is uniformly continuous on R.

to prove that there are constants A and B such that ∣f(x)∣≤A+B∣x∣ for all x∈R, where f is a uniformly continuous real-valued function on R, we can use the definition of uniform continuity.

Since f is uniformly continuous on R, for any ε>0, there exists a δ>0 such that |f(x) - f(y)| < ε for all x, y in R, whenever |x - y| < δ.

Let's choose ε = 1. Then, there exists a δ>0 such that |f(x) - f(y)| < 1 for all x, y in R, whenever |x - y| < δ.

Now, let's choose x = 0. Since |x - y| < δ, we have |y| < δ.

Using the triangle inequality, we have |f(y)| ≤ |f(0)| + |f(y) - f(0)|.

Since |f(x) - f(y)| < 1 for all x, y in R, whenever |x - y| < δ, we can say |f(y) - f(0)| < 1.

Therefore, we have |f(y)| ≤ |f(0)| + 1.

Let A = |f(0)| and B = 1, we have |f(y)| ≤ A + B|y| for all y in R.

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The simplification of √x / √6 y³ after rationalizing all denominators is

\(\sqrt{6x}\) \(y^{-3}\)/ 6

Given; \(\frac{\sqrt{x} }{\sqrt{6} y^{3} }\) , we are to simplify and also rationalize the denominators

\(\frac{\sqrt{x} }{\sqrt{6} y^{3} }\)  *  \(\frac{{\sqrt{6} y^{3} }}{{\sqrt{6} y^{3} }}\)

= \({\sqrt{6} y^{3} }\) * \(\sqrt{x}\) / \({\sqrt{6} y^{3} }\)*  \({\sqrt{6} y^{3} }\)

=\(\sqrt{6x}\) * \(y^{3}\) / \(\sqrt{36}\)* \(y^{6}\)

= \(\sqrt{6x}\) *  \(y^{3}\) / 6 * \(y^{6}\)

=\(\sqrt{6x}\) * \(y^{3-6}\)  / 6

= \(\sqrt{6x}\) \(y^{-3}\) /6

The final answer to this question, is, \(\sqrt{6x}\) \(y^{-3}\) /6

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Answer:

15

Step-by-step explanation:

The area is approximately -1372.4 square units.

Given function is: F(x) = 0.7x³ + 7x² - 0.7x - 7

The interval is [−9,−4]

We have to approximate the area under the graph of F(x) over the interval [−9,−4] using 5 subintervals and using the left endpoints to find the heights of the rectangles.

Area of one rectangle = f(x)Δx = f(x) (b - a)/n = f(x) (5)/5 = f(x)

We have to find the sum of area of 5 rectangles.Δx = (b - a)/n = (-4 - (-9))/5 = 5/5 = 1

For left endpoint use: xᵢ = a + (i - 1)Δx, where i = 1, 2, 3, ..., n. = -9 + (i - 1)

Δx, where i = 1, 2, 3, ..., n. = -9 + (i - 1)(-1) [as Δx = -1]= -9 - i + 1= -i - 8

Area = ∑f(x)Δx =  ∑(0.7x³ + 7x² - 0.7x - 7)

Δxwhere x = -9, -8, -7, -6, -5= 0.7(-9)³ + 7(-9)² - 0.7(-9) - 7 + 0.7(-8)³ + 7(-8)² - 0.7(-8) - 7 + 0.7(-7)³ + 7(-7)² - 0.7(-7) - 7 + 0.7(-6)³ + 7(-6)² - 0.7(-6) - 7 + 0.7(-5)³ + 7(-5)² - 0.7(-5) - 7= -1372.4

Using a calculator, we get=-1372.4

Therefore, the area is approximately -1372.4 square units.

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The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Answer:

3. 72= (x)+(x+1)+(x+2) where x= the smallest number

72=3x+3

-3        -3

69=3x

/3   /3

x=23

x+1=24

x+2=25

smallest is 23

4. 48= (x)+(x+2)+(x+4)

48= 3x+6

-6        -6

42=3x

/3    /3

x=14

x+2=16

x+4=18

smallest is 14

5. all erasers were the same cost

25= 4x+5 (x= cost of erasers)

-5         -5

20=4x

/4   /4

x=5

each cost  $5

6. b= boxes

22= b/2 +7

-7            -7

15=b/2

multiply both sides by 2 to cancel the denominator

30=b

30 boxes originally

7. 40= total

8= left

2= balls given to each

x=number of friends

40= 2x+8

-8         -8

32=2x

/2   /2

x=16

she has 16 friends

8.  12= left

a= total allowance

12= (a/2) +4

-4            -4

8= a/2

multiply both sides by 2 to cancel the denominator

a= $16

she had an allowance of $16

9.  4 (2) = amount that her four children recieved

10=amount she took for herself

x= original

x= 4(2) + 10

x= 8 +10

x=18

she started with 18 candies

10. a= age

244= 400 - 2a

-400 -400

-156= -2a

/-2     /-2

a= 78

they are 78 years old

11. c= comic books

36=  c/2 + 16

-16           -16

20=c/2

multiply both sides by 2 to cancel the denominator

c=40

she started with 40 comic books

12.  b= students in buses

472= 9b + 4

-4             -4

468=9b

/9     /9

b= 52

52 students went in each bus

13. h= hats

17= h/2 +5

-5          -5

12=h/2

multiply both sides by 2 to cancel the denominator

h=24

she had 24 hats on monday

14. p= pies the club made

60= (p+4)/5

multiply both sides by 5 to cancel the denominator

300=p+4

-4         -4

p= 296

the club made 296 pies

Step-by-step explanation:

The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

The point estimate of P, is defined as the proportion of successes in the sample.

P' = X/N ; where X = number of successes; N = total trials.

Here, N = 1000

According to the Child outlook file, number of "yes" = 240.

Hence, P' = 240/1000

P' = 0.24

Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.

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We have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`.

We need to find `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`.

Solution:

`f(x) = (x+7)/x`

At `x=a`, we have

`f(a) = (a+7)/a`.

At `x = a + h`,

we have `

f(a+h) = [(a+h)+7]/(a+h)`.

So,

`f(a+h) = (a+h+7)/(a+h)`.

Now,

`f(a+h)−f(a)` is `[(a+h)+7]/(a+h) − (a+7)/a`.

LCM of `(a+h)` and `a` is `a(a+h)`.

So, we get `f(a+h)−f(a)` as `(a+h)(a+7)−a(a+h+7)/a(a+h)`.

On simplification, we have `f(a+h)−f(a)` as `(ah+7h)/(a(a+h))`.

Now, `(f(a+h)−f(a))/h` is `(ah+7h)/(ah+h^2)`.

On simplification, we have `(f(a+h)−f(a))/h` as `(h(a+7))/(ah+h^2)`.

Hence, `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

Given a function `f(x)` is defined by `f(x) = (x+7)/x`. We have found `f(a)`, `f(a+h)`, and the difference quotient `(f(a+h)-f(a))/h` where `h≠0`. Thus, we have `f(a) = (a+7)/a`, `f(a+h) = (a+h+7)/(a+h)`, and the difference quotient is `(h(a+7))/(ah+h^2)`.

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a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

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Answer: 185.7 miles

Step-by-step explanation:

To find the total distance, add the smaller distances together.

47.8 + 72 + 65.9 = 185.7

Factor 12 × 2+ 4=28

Factor x2-7x+12=(x-3) (x-4)

Answer:

-1/2

Step-by-step explanation:

slope is rise over run so find the difference between the y values (-9-(-5)) and divide that by the difference between the x values (-1-(-9)).

Answer:

Hi there!

Your answer is:

Median: 23.5

Mean: 25

Step-by-step explanation:

The mean is the average of all the numbers in your dataset. You determine this by adding all the numbers together and dividing by the # of numbers in your set!

35+28+19+18 = 100.

100/4 = 25

The median is the middle number of your data set! This is determined by counting off the numbers from each side of the equation after setting them in order from least to greatest. If there are 2 remaining, you must find the average of those!

35 , 28, 19 , 18 from least to greatest is

18, 19, 28, 35

/. /

Now find the average of 19 and 28!

19+28 = 47

47/2 = 23.5

Answer:

Step-by-step explanation:

Find the median and mean of the data set below:29,39,28,5029,39,28,50

The area of the shaded sector of the circle is 3π ft².

A sector of a circle is simply a region bounded by two radii of the circle and an arc of the circle.

The area of a sector can be found using the formula:

A = (θ/360) × πr²

Where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is pi.

From the image:

Central angle θ =  360° - 90° = 270°

Radius r = 2ft

Plug the given values into the above formula and solve for area.

A = (θ/360) × πr²

A = (270/360) × π × (2ft)²

A = (270/360) × π × 4ft²

A = 3/4 × π × 4ft²

A = 3π ft²

Therefore, the area is 3π ft².

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Answer:

-45

Step-by-step explanation:

(4.5)*5*(-2) = 4.5* (5*(-2)

                  = 4.5 * (-10)

                   = -45.0

                    = -45

Answer:

-45

Step-by-step explanation:

In order to find the answer simply multiply the numbers from left to right and make sure to remember a positive times a negative is a negative.

(4.5)(5)(-2)

4.5 × 5 = 22.5

22.5(-2)

22.5 × -2 = -45

= -45

Therefore your answer is the fourth option.

Hope this helps.

Answer: -27/40

Step-by-step explanation:

Answer:

Step-by-step explanation:

To write a number in scientific notation or standard form we write the number and multiply it by 10 to the power of any number

  The proper format for scientific notation is a x 10^b  and it is read "a times 10 to the power of b"

Given the diameter of 2.5

in standard form or scientific notation is \(2.5*10^0\)

AB is parallel to CD, AD is parallel to CD then ΔABC approximately equals to triangle ΔCDA

From given AB∥CD

AD∥CD from given

∠ABC = ∠CDA because of corresponding angles

BAC = ∠ACD because of alternate interior angles

ΔABC ≅ ΔCDA by By angle-angle (AA)

we are given that AB is parallel to CD and AD is parallel to CD.

We need to prove that ΔABC is approximately equal to ΔCDA.

To do this, we use the angle-angle (AA) similarity theorem.

First, we can identify that ∠ABC and ∠CDA are corresponding angles, as they are on the same side of the transversal line AB and CD, respectively, and they are formed by parallel lines.

Therefore, ∠ABC ≅ ∠CDA.

Hence, AB is parallel to CD, AD is parallel to CD then ΔABC approximately equals to triangle ΔCDA

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the value of the test statistic is -12.5.

To calculate the test statistic, we need to perform a one-sample t-test using the formula:

t = (x(bar)- μ) / (s / √n)

where:

x(bar) = sample mean (265,000 AED)

μ = hypothesized population mean (300,000 AED)

s = sample standard deviation (14,000 AED)

n = sample size (25)

Plugging in the values, we get:

t = (265000 - 300000) / (14000 / √25)

t = -35000 / 2800

t = -12.5

what is standard deviation?

Standard deviation is a statistical measure that measures the amount of variability or dispersion of a set of data points from the mean or average value. It is calculated as the square root of the variance and is expressed in the same unit as the data. A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

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The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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6. They have the same slope, therefore, lines g and n are parallel.

7. Lines j and m are not parallel.

8. Lines n and k are not perpendicular.

9. Lines h and j are perpendicular.

Slope of a line (m) = change in y / change in x or rise/run.

If two lines are parallel to each other, the slope values that both lines will have would be the same.

If the slope values are negative reciprocals of each other, then both lines are perpendicular to each other.

6. Slope of line g = rise/run = -3/5

Slope of line n = -3/5

They have the same slope, therefore, lines g and n are parallel.

7. Slope of line j = rise/run = 1/4

Slope of line m = 1/5

The slopes are not the same, therefore, lines j and m are not parallel.

8. Slope of line n = rise/run = -3/5

Slope of line k = 3/2

The slopes are not negative reciprocals, therefore, lines n and k are not perpendicular.

9. Slope of line h = rise/run = -4/1 = -4

Slope of line j = 1/4

The slopes are negative reciprocals, therefore, lines h and j are perpendicular.

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Answer:

B. Zero

Step-by-step explanation:

The slope of the line is in the the first two quadrants and is horizontal, meaning it has zero slope.

Answer:

Zero slope :)

Step-by-step explanation:

A zero slope is a horizontal line. When there is a zero slope, y will be equal to a constant. :)

Have an amazing day!!

Please rate and mark brainliest!!

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The measure of TN from the given figure is 22 units

According to the given triangle:

Given the following:

MT = 6x - 56

TP = 3x - 17

Equate

6x - 56 = 3x - 17

6x - 3x = -17 + 56

3x = 56

x =39/3

x = 13

Get the measure of TN:

TN = MT

TN = 6(13) - 56

TN =  78 - 56

TN = 22

Hence the measure of TN is 22 units

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The total probability of a girl having a "K-name" is 3/8. The total probability of there being a girl in the club is 5/8.

Therefore, the conditional probability of having a girl with a "K-name" given that there is a girl in the club can be calculated as follows:

P (Girl | K-name) = P (K-name | Girl) × P (Girl) / P (K-name) = 2/5 * 5/8 / 3/8 = 2/3

Therefore, the probability of a girl with a K-name given that there is a girl in the club is 2/3.

In a club consisting of 5 girls (Kirsten, Sarah, Suzie, Monica, and Katie) and 3 boys (Kevin, Steve, and Samuel), we are asked to find P(Girl | K-name).

We can use Bayes' theorem to calculate the conditional probability of this event. This theorem states that the probability of an event given another event can be calculated as the product of the probability of the second event Therefore, the probability of a girl having a "K-name" given that there is a girl in the club is 2/3.

The conditional probability of there being a girl in the club given that a girl has a K-name is 2/3.

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The required area of the section Dr. Gordan will search is equal to 48,000ft².

As given in the question,

Scale used by Dr. Gordan

2 in = 100 ft

⇒1 in = 50 ft

Dr. Gordon marks a 6 in. by 3.2 in section

Length = 6 in

           = ( 6 × 50 )ft

           = 300ft

Width = 3.2in

         = ( 3.2 × 50 )

         = 160ft

Area of the section = length × width

                                = 300 × 160

                                = 48,000 ft²

Therefore, the required area of the section Dr. Gordan will search is equal to 48,000ft².

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