5) Write the equation of the line to the right.

The scale factor going from the first to the second triangle according to the task content is; 2.

The length of the longest side of.the triangle as required in the task content is; 24.

According to the task content, it follows that the two triangles are similar.

Therefore, the corresponding sides of such triangles must be in proportion.

Therefore the scale factor from the first to the second triangle as required is;

Scale factor = 12/6; since the shortest sides are corresponding sides.

Scale factor = 2.

Hence, since the length of the longest side in the first triangle is 14, the length of the longest side in the second triangle is;

L = 2 × 14

L = 28

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Answer:

C(x) = (1/9)x + 242/9

Step-by-step explanation:

Let x = number of pages.

Let y = cost.

We are given two ordered pairs, (x, y):

(100, 38) and (208, 50)

We must find the equation of the line that passes through these two points.

y = mx + b

m = (y_2 - y_1)/(x_2 - x_1) = (50 - 38)/(208 - 100) = 12/108 = 1/9

y = (1/9)x + b

Use point (100, 38) as x and y to find b.

38 = (1/9)(100) + b

38 × 9 = 100 + 9b

9b + 100 = 342

9b = 242

b = 242/9

The equation is:

y = (1/9)x + 242/9

Answer: C(x) = (1/9)x + 242/9

Answer:

The slope is 4/5

y = 4/5x + 20

Step-by-step explanation:

Slope:

Change in y over the change in x

(4 - 8) / -20 - -15

-4 / -20 + 15

-4 /-5

4 / 5

Equation of the line:

You could use either point given.  I am going to use the point (-20,4)  I will use -20 for x and 4 for y.  I will use 4/5 as the slope.  I will need to solve for the y-intercept

y = mx + b

4 = (4/5)(-20) + b

4 = -16 + b  Add 16 to both sides

20 = b

The equation will be

y = 4/5x + 20

Answer: So that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2.

Step-by-step explanation:

The original price of the suit before markdowns will be $520.83.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Le's suppose the original price was x dollars.

Now, the first discount of 40%

40% of x = 0.40x

Retail price = x - 0.40x = 0.60x

The second discount is 60% on the first retail price

60% of 0.60x = 0.60×0.60x

⇒ 0.36x

Final retail price = 0.60x - 0.36x

0.24x = 125

x = 520.83

Hence "The original price of the suit before markdowns will be $520.83".

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Answer:

Step-by-step explanation:

Answers in bold:

Problem 4) Shift 6 units left, 1 unit down

Problem 5) Shift 3 units right. Vertically stretch by a factor of 2.

The graphs are below.

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

Explanation:

In problem 4, the parent function is y = x^2

Replace every x with (x+6) and it will shift the parabola 6 units left. Why left instead of right? It's because the xy axis is moving 6 units to the right. Each old input x is now 6 units larger to get x+6. The xy axis moving 6 units right gives the illusion the curve shifts 6 units left. It's a bit backwards I know.

Luckily the -1 at the end is straight forward and it shifts everything down by 1 unit. This is because we subtract 1 from the y coordinate.

So that's how we get the "6 units left, 1 unit down" translation. No horizontal nor vertical dilations occur.

I recommend using GeoGebra or Desmos or similar to graph out the two equations, to see the comparison.

---------------------------------

For problem 5, the parent function is y = |x|

Replacing every x with x-3 means that the xy grid moves 3 units left. That gives the illusion the V shaped curve is moving 3 units right.

The 2 out front will double each y coordinate. This visually stretches the graph by a factor of 2. It is now twice as tall as it was before. This is equivalent to doing a horizontal compression (since the graph is more skinny now).

Answer:

4.  Translated 6 units left and 1 unit down.

5.  Translated 3 units right and stretched vertically by a factor of 2.

Step-by-step explanation:

Transformations

[tex]\textsf{For $a > 0$}[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Parent function:

[tex]f(x)=x^2[/tex]

Translated 6 units left:

Add 6 to the x-variable of the function:

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

Translated 1 unit down:

Subtract 1 from the function:

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

Parent function:

[tex]f(x)=|x|[/tex]

Translated 3 units right:

Subtract 3 from the x-variable of the function:

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

Stretched vertically by a factor of 2:

Multiply the function by 2:

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

The Area of the triangle with base 6 and height 4 is 12 square units.

Area of triangle with base "b" , and height "h" can be calculated using the formula

Area = 1/2*b*h  .

From the figure

It is given that height of triangle = 4

base of the triangle = 6

By using the formula for Area of the triangle we get ,

Area = 1/2*b*h

Substituting the value of base and height from above we get ,

Area= 1/2*6*4

=(6*4)/2

=24/2

=12

Therefore ,  the Area of the triangle with base 6 and height 4 is 12 Square units .

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The quotient after the long division of 35/456 is 0.076.

So, after the long division:

Therefore, the quotient after the long division of 35/456 is 0.076.

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The value of the x in the linear equation of the midpoint is a 3.85.

According to the statement

We have to find that the value of the x.

So, For this purpose, we know that the

Midpoint is the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.

From the given information:

Given K is the midpoint of GH, GK = 5x - 3,and GH = 2x + 24

As the midpoint the both equation are equal to the each other.

Then

GK = GH

5x - 3 = 2x + 24

5x+2x = 24+3

7x = 27

x = 27/7

x = 3.85.

So, The value of the x in the linear equation of the midpoint is a 3.85.

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Answer:

Question have problem.

Answer: use the 'grouping method' to get your answer (answer choice 'B')

Step-by-step explanation:

Take your first two terms, 2x^3 and 4x^2 and find a GCF. In this case, 2x^2 can go into both terms. Your first side should look like this 2x^2(x+2).

Take your last two terms (6x+12) and find a GCF. In this case, your GCF is 6 because both terms can fit into 6. Your second side should look like this 6(x+2).

We know we did this problem correctly because we can see that both parenthesis state the same thing, which is (x+2).

Your equation after finding a GCF in both sets should look something like this; 2x^2(x+2)+6(x+2).

Now, combine the 2x^2 and 6 together to get (2x^2+6) in one parenthesis set. Your second should include ONLY ONE of the '(x+2)'s.

Your final answer should look like this; (2x^2+6)(x+2). Therefore, your answer choice is 'B'.

Hope this helps, dawg.

Answer:

1 TABLET

Step-by-step explanation:

1 tablet should be given. The aim is to ensure that the amount of medicine you give matches what was prescribed. In order to do that, we must change either the amount we ordered or the amount that is available so that they are both measured in the same unit.

To decide the number of tablets that ought to be given, we have to be change over the accessible sum from grams to milligrams.

Given:

Ordered: 100 mg

Available: 0.1 g

1 g = 1000 mg

Converting the available sum to milligrams:

0.1 g * 1000 mg/g = 100 mg

Since the available amount is equal to the ordered sum, you'd have to be give 1 tablet.

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It should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

It should be noted that it's important to understand ratio and use ratio language to describe the relationship between two quantities.

For example, it van be stated that the ratio of wings to beaks in the bird house at the zoo is 2:1, this implies that b for every 2 wings there is 1 beak.

Therefore, it should be noted a term is one of the two numbers that are in the ratio. An example is that in the "ratio of a to b" a is the first term and b is the second term.

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Answer: B.

Step-by-step explanation:

the goal of the question is to make <AZB ≈ (around) <AYB. Answer b is the only one that makes sense because in the first answer triangle AYB is obtuse and much wider than triangle AZB. While in answer c, triangle AYB is acute and way too small to be around triangle AZB. In answer b, the angles are around the same even though one triangle is slightly larger than the other.

The amount of fencing needed to enclose the secular pond is 72.22 feet

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the area

The given parameter is

Diameter, d = 23 feet

The radius is calculated as

r = d/2

So, we have

r = 23/2

This gives

r = 11.5 feet

The circumference of the circle is calculated as

C = 2pi r

So, we have

C = 2 * 3.14 * 11.5 feet

Evaluate the product

C = 72.22 feet

Hence, the amount of fencing needed to enclose the secular pond is 72.22 feet

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The number of bottles that would be left is 1

The given parameters are

Number of Bottles = 7

Number of Friends = 3

Assume that the bottles are to be shared among the friends only

The number of bottles that would be left is

Bottles left = Number of Bottles % Number of Friends

This gives

Bottles left = 7%3

Evaluate the modulo operation

Bottles left = 1

Hence, the number of bottles that would be left is 1

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About 25 percent of the data are greater than 20.(option a)

About 50 percent of the data are less than 15. (option b)

20 is wrongly interpreted as the median. 20 is the third quartile. The data between 11 and 20 is 50%.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

The box plot consists of two whiskers and a box. The first whisker represent the minimum value. The second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile. 75% of the scores represents the upper quartile.

20 is the third quartile. Score greater than 20 is 25% (100% - 75%)

15 is the median. Scores less than 15 is 50% (100 - 50%),

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The minute hand has moved 25 times out of a possible 60 from the top of the clock as of 4:25. 150 degrees is 25 multiplied by 6 degrees. Simply subtracting those degrees from the above calculation, the angle from the minute hand to the hour hand is equal to 360 degrees. 342.5 degrees is 360 minus 17.5.

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Using a protractor, angles are measured in degrees (°).

An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.

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[tex]3 \cdot 3^2 + 8 : 2 - (4+3) =[/tex]

[tex]3 \cdot 3^2 + 4 - 7=[/tex]

[tex]3 \cdot 9 +4 -7=[/tex]

[tex]27 + 4 - 7 = 24[/tex]

==axel134==

Answer:

Step-by-step explanation:

Answer:

I believe it's 15.21x

Step-by-step explanation:

10.79 - 26 * x

10.79 - 26x =

15.21x

A mathematical model that gives the demand y in terms of the price x in dollars.

y = 1400/ x

This is further explained below.

Generally, The following formula would apply in the situation when there is an inverse link between y and x:

y = k/x

where k is constant.

In a relationship with an inverse connection, one variable will tend to decrease as the other variable grows.

y denotes the amount of demand.

x is equivalent to the cost.

400 = k/3.5

k = 400 * 3.5

k = 1,400

The following is the formula for the mathematical model that calculates the demand y based on the price x in dollars:

y = 1400/ x

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Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Given : A scientist had [tex]\frac{3}{4}[/tex] of a bottle of a solution.

The part of the solution she used in the experiment :  [tex]\frac{1}{6}[/tex]

The part of bottle she used is given by :

[tex]\frac{1}{6} *\frac{3}{4}[/tex]

= [tex]\frac{1*3}{4*6}[/tex]

= [tex]\frac{3}{24}[/tex]

Simplify = [tex]\frac{1}{8}[/tex]

Hence, she used [tex]\frac{1}{8}[/tex] of the bottle .

The age of accountant is more variable than salary.

Standard deviation is the square of difference between the sets of data and mean.

Comparison for variation of data can be determined by coefficient of variation (C.V).

We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.

First we are determining C.V for ages.

Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.

∴ C.V for ages, where  [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is

C.V = [tex]\frac{4}{25}[/tex] × 100.

C.V = 16.

[tex]C.V_a_g_e[/tex] = 16%.

Now C.V for salary,

where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.

C.V = [tex]\frac{4500}{30500}[/tex] × 100.

C.V = [tex]\frac{4500}{305}[/tex].

[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.

So, the coefficient of variation of age is more than that of salary.

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Answer:

  (d)  9x² -12y² -11x

Step-by-step explanation:

The sum of polynomials (8x² -9y² -4x) and (x² -3y² -7x) is found by combining like terms.

When simplifying the sum of polynomials, the distributive property comes into play. It lets you add and remove parentheses, recognizing that factors outside parentheses multiply each term inside parentheses.

  (8x² -9y² -4x) + (x² -3y² -7x)

  = 8x² -9y² -4x + x² -3y² -7x . . . . . eliminate parentheses

  = (8 +1)x² +(-9 -3)y² +(-4 -7)x

  = 9x² -12y² -11x

Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.

[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]

[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]

Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].

[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]

Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.

[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]

a. The distance around the park is 180 yards

b. QM = 18 yards

c. It takes 49 minutes  to travel the entire distance

a. The distance around the yard is given as;

PQ + QR + PQ

Where;

Total = 40 + 70 + 70 = 180 yards

b. To determine QM, we use the Pythagorean theorem;

PQ² = QM² + 1/2 PR²

40² = QM² + (35. 5)²

1600 = QM² + 1260. 25

Make 'QM' the subject

QM² = 1600 - 1260. 25

QM = √339. 75

QM = 18 yards

c. Average speed = 150 yards/ per minute

Total distance = 180 yards

Time = Average speed/ distance

Time = 150/ 180

Time = 0. 8 3 × 60

Time = 49 minutes

Thus, the distance around the park is 180 yards

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Here are the values of the expressions :

a. 3(4) = 12

b.  4 + 11 + (-4)  = 11

c. 3.2(2)  = 6.4

d. | (-2) + (-2) + (-2) | = 6

e. |2 (-7.5) |  = 15

f. 10 1/5(-5) = -51

a. 9(410)  = 3690

b. 6(592) = 3552

Take not of the following rules:

When a term is in bracket, it means that the values should be multiplied : 2 (3) = 2 x 3 = 6

When numbers are between this sings | |, it means that the answer should be an absolute value. e.g. | - 5 - 5 | = 10

When a negative sign is multiplied by a positive sign, the result would be a negative sign. -1 x + 1 = -1

a. 3(4) = 3 x 4 = 12

b.  4 + 11 + (-4)

= 4 + 11 - 4 = 11

c. 3.2(2)  = 3.2 x 2 = 6.4

d. | (-2) + (-2) + (-2) |

|- 2 - 2 - 2| = 6

e. |2 (-7.5) |

|2 x -7.5| = 15

f. 10 1/5(-5)

10 1/5 x - 5

51/5 x - 5 = -51

a. 9(410)

= (9 x 400) + (10 x 9)

3600 + 90 = 3690

b. 6(592)

= (6 x 500) + (92 x 6)

3000 + 552

3552

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