The lengths in the diagram are in centimetres. The square (2x,2x) and the rectangle (10, x+8) have perimeters of the same length.
a. Write an equation to show this.
b. Solve the equation.
c. Find the length of the rectangle.

Answer:

The number is -36 or x = -36

Step-by-step explanation:

2x + 16 = -56
       2x = -72
         x = -36

Answer:

Y = 2x+8

Step-by-step explanation:

Y=mx=b equations

The equation 2.5x + 2y = 225 represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.

Let the quantity of the dried fruit is x,

And the quantity of nuts is y,

As per the given question, the equation would be as:

2.5x + 2y = 225

The above equation represents the total cost and 2.5x  represents the cost of dried fruit when its quantity is x.

Thus, 2.5x  represents the cost of dried fruit when its quantity is x.

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The probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

A data set with a normal distribution has the majority of its values clustered in the middle of the distribution and the remaining values tapering off symmetrical toward either end.

For the given question;

z = (x - μ)/σ

In which,

x = sample mean

μ = mean  (48,000)

σ = standard deviation (1500)

x = 35,000 and x = 52,000

For x = 35,000.

z = (35,000 - 48,000)/1500

z = -8.66

Check the p value from table

p(z = -8.66) = 0

For x = 52,000

z = (52,000 - 48,000)/1500

z = 2.66

p(z = 2.66) = 0.99617

P(35,000 < x < 52,000) = 0.99617 - 0

P(35,000 < x < 52,000) = 0.99617

Thus, the probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

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After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.

What is proportion?

 Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.

Here 16 oz medium size has 260 calories.

Then

=> [tex]\frac{size of coffee}{ calories}[/tex]

=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]

=>x=[tex]\frac{20*260}{16}[/tex]

=> x = 325

Hence 325 calories will she get if she drinks the larger 20 oz. size.

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The Equation of line is y= -1/3x + 5/3

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

x-intercept = (3,0) and y-intercept =  (0,1).

slope, m= 0-1/ 3-0= -1/3

so, The slope-intercept form of the equation of a line is

y= mx + b

y= -1/3x +b

Now, the passes through (-1, 2) we get

2= -1/3(-1) + b

2- 1/3= b

b= 5/3

So, the Equation of line is y= -1/3x + 5/3

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The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A linear equation or function is given as ;

y = mx + c

Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).

The slope of the line passing through (-4, -6) and (2, 8) will be,

m = (8 + 6)/(2 + 4)

m = 14/6

So, y = (14/6)x + c

Substitute,  (2, 8)

8 =  (14/6)2 + c

c = 8 - 14/3 = 10/3

Therefore, y = (14/6)x + 10/3

Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".

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Answer: -2x+y=-12

Step-by-step explanation:

After what I did this is what i got. Can't really explain it

Hope this helps :)

ΔBGC is right because Line EG is perpendicular-to CC'.

A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.

Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.

Given:

On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.

A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.

Hence, BGC is right triangle.

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Answer: D

Step-by-step explanation: Trust

The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

The given algebraic expression is -4x²+12x.

The factors are the polynomials which are multiplied to produce the original polynomial.

The factorization of the given polynomial is

-4x²+12x

= 4x(-x+3)

The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.

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Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

In this question, Mr. Harrington wants to buy a new TV for $500

He has a 10% off coupon.

After applying this coupon, the cost of TV would be,

500 - (10 percent of $500)

= 500 -[ (10/100) * 500]

= 500 - 50

= 450

He knows the tax be 13.5%.

13.5 percent of 450 would be,

(13.5/100) * 450

= 60.75

So, the amount he will need to save to buy the TV,

$450 + $60.75 = $510.75

Therefore, Mr. Harrington will need $510.75  to buy the TV

The correct answer is an option (a)

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Answer:

[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]

hopefully this will u...^⁠_⁠^

The total time it took Jace to out home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

So, the total number of minutes Jace takes to get back home after going out:

Total minutes:

(Refer to the graph attached below)

Therefore, the total time it took Jace to out of home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

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The inequality of the change of state of the gas in the driver's truck indicates;

Part A: The inequality  that represents the temperature at which the gas in the truck will be in liquid form is; -40 ≤ T ≤ 140

Part B: The graph is a shaded region bounded by two solid vertical lines at t = -40 and t = 140

Part C: The gas will be frozen because the temperature is below the freezing point temperature of the gas.

An inequality indicates the relationship between two expressions that are not equal

The temperature at which the gas freezes = -40 °F

Temperature at which the gas evaporates = 140 °F

Part A: The inequality that represents the temperature at which the gas in the truck will remain in liquid form, t is; -40 ≤ t ≤ 140

Part B: The description of the graph of the inequality is a region on the coordinate plane bounded by two solid vertical lines at x = -40 and x = 140, the region between the two solid vertical lines is shaded/.

Part C: The temperature of -49 °F obtained in January 1989 in Nome, Alaska is not in the feasible region of the graph of the inequality, therefore, the gas in the driver's truck will not remain in liquid form, and would freeze, such that the driver would not drive on the specified date.

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One-sided confidence interval which have the smallest margin of error.

Given that;

Researchers want to decrease the margin of error by adjusting the confidence level.

You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.

one-sided confidence interval:

The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.

Hence, we use one-sided confidence interval which have the smallest margin of error.

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The sequence has the 10th term of 15625000

The sequence is given as:

8,40,200,...

The above sequence has the following parameters

First term, a = 8

Common ratio, r = 5 i.e. 40/8 = 5

Number of terms , n = 10

This means that the sequence is a geometric sequence

The nth term of an geometric sequence is calculated as

f(n) = ar^(n - 1)

Substitute the known values in the above equation

So, we have the following equation

f(10) = 8 * 5^(10 - 1)

Evaluate

f(10) = 15625000

Hence, the 10th term for the sequence is 15625000

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In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

As given in the question,

In the given triangle KLM,

Coordinates of the triangle KLM are given by :

K(0,2) ,L(2 ,9) ,M(4,2)

Dilation from the origin is represented by:

a. K'(0,2) , L'(8,9) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

b. K'(0,2) , L'(2,36) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

c. K'(0,8) , L'(8,36) , M'(16, 8)

Multiply by scale factor 4.

Dilation exist.

d. K'(4,6) , L'(6,13) , M'(8, 6)

Scale factor of addition of 4.

Dilation does not exist.

Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

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The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial f(x) = x³ + 8x² - 23x - 30.

If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).

∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.

f₁(x) = x² + 11x + 10.

Now, x² + 11x + 10 = 0.

x² + 10x + x + 10 = 0.

x(x +10) + 1(x + 10) = 0.

(x + 10)(x + 1) = 0.

x + 10 = 0 Or x = 1 = 0.

x = - 10 Or x = - 1.

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Completely random design is used in this experiment.

In the given question,

A business wants to investigate the efficacy of a novel painkiller.

100 participants who suffer from chronic discomfort are enlisted.

Each participant takes the brand-new painkiller for two weeks before switching to a placebo for an additional two weeks.

The order of the tablets is chosen at random for each participant, and the subjects are unaware of which pill contains the actual medication.

Each subject's variance in total pain will be measured by researchers.

We have to check what type of experiment design is this.

As we can see in the question that they recruit 100 volunteers with chronic pain and each subject they use new pain relief medicine for a 2-week period and a placebo for another 2-week period.

They assign each subject randomly.

As we know that in a completely random design, treatments are randomly assigned to sampling material. The usual method for doing this is to make a list of the treatments and give each one a random number.

So we can see that completely random design is used in this experiment.

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From the figure, the lines parallel to AE are DH, CG, and EF.

Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.

If two straight lines are in the same plane and never intersect, they are said to be parallel lines.

So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.

As equidistant lines, they are always the same distance apart.

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Answer:

The coefficient is 9 in 9b.

Step-by-step explanation:

A coefficient is a number before a variable.

Examples: 9 in 9b, 5 in 5y, 3 in 3x.

Practically anything before a variable is declared                                                          a coefficient.

Pls vote brainliest if this was helpful!

It helps a lot :)

Answer:

Step-by-step explanation:

a find the interpret the slope and the y-intercept of the graph

The diagrams are shown in the solution.

A rectangle is a quadrilateral with all four interior angles 90°.

(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.

The dimension can be written as:

1/2 : 5/6

Multiply the ratio by 6:

3 : 5

Hence, the rectangle of  1/2 × 5/6 is proportional to 3×5.

The diagram is shown.

Similarly, the diagrams of other rectangles are shown.

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Answer:

Step-by-step explanation:

You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.

All sides of the square are the same length. Equating two different y-expressions, we get ...

  y -4 = 2y -12

We can use the solution to that to find x:

  y -4 = 3x -8

Adding 12-y to the first of these equations gives us ...

  8 = y

Using this value in the second equation, we have ...

  8 -4 = 3x -8

  12 = 3x . . . . . . add 8

  4 = x . . . . . . . . divide by 3

The side length is ...

  y -4 = 8 -4 = 4

The values of the variables are x = 4, y = 8, and the side length of the square is 4.

The value of PC is 40 when C is the circumcenter of triangle PQR.

Given that,

Consider the complete question is

C is the circumcenter of triangle PQR.

PC=3x-7

RC=5x-15 &

QC= 51-x

We have find the side PC.

A triangle's vertices are equidistance spaced from its circumcenter.

PC=RC=QC

RC=QC

5x-15= 51-x

5x+x= 51+15

6x=66

x=11

The value of x is 11.

We must determine PC's worth.

Substitute x=11 in the above equation.

PC= 3x+7

PC= 3(11)+7

PC=33+7

PC= 40

Therefore, The value of PC is 40 when C is the circumcenter of triangle PQR.

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Answer:

  38 units

Step-by-step explanation:

You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).

The perimeter of a plane figure is the sum of the lengths of its sides.

By counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:

  AB = 12, BC = 3, EA = 3

The lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.

The Pythagorean theorem, or the distance formula, will tell you the same thing:

  c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c

  c = √(a² +b²)

  diagonal length = √(6² +8²) = √100 = 10

Then the remaining two sides are ...

  CD = 10, DE = 10

The perimeter is ...

  perimeter = AB +BC +CD +DE +EA

  = 12 +3 +10 +10 +3 = 38 . . . units

The perimeter of pentagon ABCDE is 38 units.

The probability is 0.1.

acc to our question-

Hence,The probability is 0.1.

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Answer:

chemistry books is 220 and number of biology books is 220

Step-by-step explanation:

let y be biology books

let x be the number of chemistry books

x-58=y

equation 1 ) x+y=382

sub in x-58 for y

2. x+(x-58)=382

3. 2x-58= 382

4. 2x=382-58

5. 2x = 324

6. x/2 =324/2

7. x = 162

for x=y+58

y=162

x 220

220+162=382

y+x=382

Answer:

m=2

Step-by-step explanation:

-16=m-18

-16+18=m

2=m

Answer:

D: 12

Step-by-step explanation:

multiples of 4: 4,8,12,16,20

12 is the only number that can be divided by 4 on the list

Hopes this helps please mark brainliest

Answer:

D. 12

Step-by-step explanation:

12 is a multiple of 4 because 4 goes into 12 (evenly, with no remainder).

That's what being a multiple means.

All the "answers" to 4 times table questions are multiples of 4. Here they are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...

Can't actually list them all because the list goes on forever.