If A Polygon Is Translated, Which Of The Following Characteristics Of The Polygon Are The Same? Select (2024)

ANSWER:

[tex]32076+3x>70000[/tex]

STEP-BY-STEP EXPLANATION:

We know that the average is the amount of in each day, divided by the number of days, in this case it would be 7 days. We know that the total number of steps would be 4 times the average of 4 days and 3 times x, where x is the number of steps in each day, therefore:

[tex]\begin{gathered} \text{ \#total steps= 4}\cdot8019+3x \\ \text{ \#total steps= }32076+3x \end{gathered}[/tex]

Therefore, the equation would be the following:

[tex]32076+3x>70000[/tex]

Guven the matrix:

[tex]\begin{bmatrix}{17.5} & {42} & {37.4} & {13} \\ {27} & {16} & {19.1} & {15} \\ {13} & {18.9} & {31} & {17.3} \\ {} & {} & {} & {}\end{bmatrix}[/tex]

Let's find the value of the matrix at a21.

We have:

[tex]a_{\text{row,column}}=a_{2,1}[/tex]

The value at a21 is the value in the second row and first column.

Now, apply the matrix form:

[tex]\begin{bmatrix}{a_{11}} & {a_{12}} & {a_{13}} & {a_{14}} \\ {a_{21}} & {a_{22}} & {a_{23}} & {a_{24}} \\ {a_{31}} & {a_{32}} & {a_{33}} & {a_{34}} \\ {} & {} & {} & {}\end{bmatrix}[/tex]

Therefore, the value of the matrix at a₂₁ is 27.

ANSWER:

27

In order to find the line tangent to f(x) and parallel to the given equation, first let's find the slope of the given line, putting it in the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

So we have:

[tex]\begin{gathered} 15x-3y=8 \\ -3y=8-15x \\ 3y=15x-8 \\ y=5x-\frac{8}{3} \end{gathered}[/tex]

So the slope is m = 5.

Since parallel lines have the same slope, the slope of the tangent line is equal to 5.

In order to find when the slope of the tangent line is equal to 5, let's calculate the derivative of f(x). This derivative will give the slope in function of x:

[tex]\begin{gathered} m=f^{\prime}(x) \\ m=3^x\cdot\ln 3 \\ m=1.1\cdot3^x \end{gathered}[/tex]

Equating the slope to 5, we have:

[tex]\begin{gathered} 1.1\cdot3^x=5^{} \\ 3^x=4.545^{} \\ \ln (3^x)=\ln (4.545) \\ x\cdot\ln (3)=\ln (4.545) \\ x=\frac{\ln (4.545)}{\ln (3)}=\frac{1.5141}{1.099}=1.378 \end{gathered}[/tex]

Calculating the value of y for x = 1.378, we have:

[tex]\begin{gathered} y=3^{1.378} \\ y=4.544 \end{gathered}[/tex]

So the tangent line passes through the point (1.378, 4.544).

Using this point, let's find the y-intercept of the tangent line:

[tex]\begin{gathered} y=mx+b \\ 4.544=5\cdot1.378+b \\ 4.544=6.89+b \\ b=4.544-6.89 \\ b=-2.346 \end{gathered}[/tex]

So the tangent line is y = 5x - 2.346.

ANSWER and EXPLANATION

We have to fill the table with the rule/function:

y = -10x + 3

To do this, we substitute each of the values of x in the function to find y.

Therefore, we have:

when x = -5:

y = -10(-5) + 3

y = 50 + 3

y = 53

when x = -1:

y = -10(-1) + 3

y = 10 + 3

y = 13

when x = 0:

y = -10(0) + 3

y = 0 + 3

y = 3

when x = 1:

y = -10(1) + 3

y = -10 + 3

y = -7

Those are the values of y that complete the table.

Answer:

270 men

180 women

Step-by-step explanation:

women : men : total

6 : 9 : 15

15 units= 450

men = 9 units

= 450 ÷ 15 × 9

= 270

women = 6 units

= 450 ÷ 15 × 6

= 180

[tex]y(he+b)=d+z[/tex]

solve for y by dividing both sides by (he+b)

[tex]\begin{gathered} y\frac{\mleft(he+b\mright)}{\mleft(he+b\mright)}=\frac{d+z}{\mleft(he+b\mright)} \\ y=\frac{d+z}{(he+b)} \end{gathered}[/tex]

to solve for e start by dividing by y on both sides

[tex]\begin{gathered} \frac{y(he+b)}{y}=\frac{d+z}{y} \\ he+b=\frac{d+z}{y} \end{gathered}[/tex]

continue by substracting b on both sides

[tex]\begin{gathered} he+b-b=\frac{d+z}{y}-b \\ he=\frac{d+z}{y}-b \end{gathered}[/tex]

divide by h on both sides to solve for e

[tex]\begin{gathered} \frac{he}{h}=\frac{1}{h}\cdot(\frac{d+z}{y}-b) \\ e=\frac{d+z}{hy}-\frac{b}{h} \end{gathered}[/tex]

ANSWER

[tex]y=\frac{d+z}{(he+b)}[/tex]

[tex]e=\frac{d+z}{hy}-\frac{b}{h}[/tex]

.

The function f is given by:

[tex]\begin{gathered} f(x)=3x^2+3x \\ f(x+h)=3(x+h)^2-3(x+h) \\ f(x+h)=3(x^2+2xh+h^2)-3(x+h) \\ f(x+h)=3x^2+6xh+3h^2-3x-3h \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{3x^2+6xh+3h^2+3x-3h-(3x^2+3x)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{6xh+3h^2+3h}{h}=6x+3+3h \end{gathered}[/tex]

Therefore, the correct answer is 6x + 3 + 3h

To factorize an expression, we just remove the common factor and multiply by the remaining terms.

[tex]ab+ac=a(b+c)[/tex]

To find the common factor, we just need to look for an equal factor in all terms of the expression. On our problem we have two terms, and both of them are multiplied by (2c + 13), therefore, the factorized version of our expression is

[tex]\begin{gathered} 5c(2c+13)-(2c+13)=5c\cdot(2c+13)-1\cdot(2c+13) \\ =(5c-1)(2c+13) \end{gathered}[/tex]

For the given situation, we will select the corresponding figure:

1) He used an electric pump to inflate the pool toy.

So, this will be a line starting from the point (0, 0) with a constant rate.

2) He played with the toy for a while until it developed a slow leak.

The volume will be constant then the volume will decrease.

3) Air leaked from the toy at a constant rate until Adam noticed the leak.

So, the volume decrease with a constant rate

4) Adam patched the leak and set the toy aside while the glue in the patch dried.

This will ba constant volume for a time until the glue dried

5) When the glue dried, Adam reinflated the toy at the same rate as before.

So, the volume will increase at the same rate as point (1)

so, we will notice two parallel lines

So, the answer will be option C

We must research some before making an estimate.

A penny weighs 2.5 grams. Your weight is 116 pounds. Converting to kilograms:

116 pounds = 52.6 kilograms = 52600 grams

So your weight is 52600 ÷ 2.5 = 21040 pennies, or $210.40

A quarter is 1.75 mm tall. Your height is 5 feet + 6 inches. Converting to meters:

5 feet = 1524 mm

6 inch = 152.4 mm

Total height = 1524 + 152.4 = 1676.4 mm

Your height is 1676.4 ÷ 1.75 = 958 quarters, or $239.5

The stack of quarters is $239.5 - $210.40 = $29.10 more valuable than the pile of pennies.

Answer: A stack of quarters is more valuable than a pile of pennies.

since the instruction indicates queen and diamond, there is only 1 card that meets those requirements.

and since, a deck consists of 52 cards, of which there is only 1 queen of diamonds, the probability is:

[tex]P=\frac{1}{52}[/tex]

Answer:

22.4 square meters

Explanation:

Given: A bathroom is 2.6 m long, 2m wide, and has four walls that are 1.5 m tall.

The bathroom is in the shape of a rectangular prism with the following dimensions:

• Length = 2.6m

,

• Width = 2m

,

• Height = 1.5m

First, we find the surface area of the bathroom.

[tex]\begin{gathered} \text{Surface Area of a rectangular prism=}2(LW+WH+LH) \\ \implies\text{Area of the bathroom}=2(2.6\times2+2\times1.5+2.6\times1.5) \\ =2(5.2+3+3.9) \\ =2\times12.1 \\ =24.2m^2 \end{gathered}[/tex]

Recall that we are to subtract 1.8 meter square for the door and window.

[tex]\text{Area of tiles}=24.2-1.8=22.4\; m^2[/tex]

22.4 square meters of tile need to be laid.

Congruent angles are those that correspond. All angles that are positioned in the same way with respect to the parallel and transversal lines are considered matching pairs.

Which triangle fits the pattern ABC?Triangle ABC is congruent to triangle DEF if in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D. In other words, if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.Two triangles are said to be congruent if their two sides and included angle are equal to each other's respective two sides and included angle.Triangles that are congruent share the same size and shape. Congruent triangles have equal equivalent sides and corresponding angles.Triangles are said to be congruent according to the SAS Postulate if any pair of corresponding sides and their included angle are also congruent. if a triangle's third side matches the third side of another triangle's third side, the triangles are said to be congruent.

To learn more about SAS postulate refer to:

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Given:

The equation of the given graph is :

[tex]y=\frac{3}{4}x+2[/tex]

To locte different points on the graph,

Given the expression;

[tex](n^{-7}p^7)^{-8}[/tex]

First, we expand the expression using the indices rule that;

[tex](ab)^c=a^cb^c[/tex]

So, the expression is;

[tex](n^{-7}p^7)^{-8}=(n^{-7})^{-8}\times(p^7)^{-8}[/tex]

So, we apply another rule;

[tex](a^b)=a^{b\times c}=a^{bc}[/tex]

Thus, we have;

[tex]\begin{gathered} (n^{-7})^{-8}\times(p^7)^{-8}=n^{56}\times p^{-56} \\ (n^{-7}p^7)^{-8}=n^{56}p^{-56} \end{gathered}[/tex]

Then, we have;

[tex]\begin{gathered} n^{56}p^{-56}=\frac{n^{56}}{p^{56}} \\ n^{56}p^{-56}=(\frac{n}{p})^{56} \end{gathered}[/tex]

Given,

The total number of student got C is 15.

The total number of students is 61.

Required

The probability of getting C.

The probability of getting C is,

[tex]\begin{gathered} Probability=\frac{total\text{ number of students with C}}{total\text{ students}} \\ =\frac{15}{61} \\ =0.246 \end{gathered}[/tex]

Hence, the probability of student getting C is 0.246.

Answer:

7234.6

Explanation:

Given:

To find:

The volume of the sphere

We can see from the given sphere that the radius(r) is 12 in and we're given pi as 3.14, let's go ahead and determine the volume(V) of the sphere using the below formula;

[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ =\frac{4}{3}*3.14*12^3 \\ =\frac{4}{3}*3.14*1728 \\ =7234.6 \end{gathered}[/tex]

So the volume of the sphere is 7234.6

EXPLANATION:

We are given a triangle with sides;

14 meters

14 meters

14 meters

Note that all three sides have equal measure. A triangle that has all three sides having equal measure is an EQUILATERAL triangle.

Therefore, the triangle given here is NOT scalene

ANSWER:

No

The equations for the transform are x = ucos∅, y = usin∅ and 1 ≤ u ≤ √7 and 0≤v ≤ π/2

Consider a region R lies in the plane xy between the circles x² + y² = 1 and x² + y² = 7

We need to find the equations for a transformation T

Now, considering the parametric form in the xy plane

x = rcos∅, y = rsin∅

x² + y² = r²

r ² = 7

r = √7

This implies, 1 ≤ r ≤ √7

As r lies in the first quadrant

0 ≤ ∅ ≤ π/2

Thus in uv plane

x = ucosv, y= u sinv

u² = x² + y²

Thus the equations for the transform are x = ucos∅, y = usin∅ and 1 ≤ u ≤ √7 and 0≤v ≤ π/2

To learn more about transform refer here

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The integers numbers are the numbers that can be written without a fractional component. It is a subset of the rational numbers.

A. 3/4: Is not an integer, as it needs a fractional component.

B. - 1.326482546731654...: This is an irrational number, as it not possible to express it even as a fraction.

C. 725: Is an integer.

D. 0: Is an integer.

Given the following question:

a = 50 degrees

b = 60 degrees

To find which quadrat a angle lies we use a graph

We know that the top of the graph is at max 90 degrees and that the angles are positive so 50 and 60 degrees would indeed be within the first quadrat.

Now at most a triangle will equal 180 degrees and since we already have two of the angles we can just...

[tex]\begin{gathered} 50+60=110 \\ 110+70=180 \end{gathered}[/tex]

c = 70 degrees

So knowing that the top of the graph is at max 90 degrees and that all the following angles are below 90 degrees and are positive (which means all three angles will go in the top right direction). We know that angles A, B, and C are all apart of the first quadrant.

Answer:

2 students

Explanation:

The number of students in the classroom = 34

The number of tables = 8

Since 4 students can sit at a table, the number of students that will sit is:

[tex]4\times8=32[/tex]

Therefore, the number of students that cannot sit down at tables:

[tex]\begin{gathered} =34-32 \\ =2 \end{gathered}[/tex]

Answer:

11.7ft

Step-by-step explanation:

length of the vegetable garden is 11.7 ft.

This is further explained below.

What is the length of the vegetable garden?

Generally,

The dimension of the garden is 3 sections long and 2 sections wide.

let

each section length = x

Therefore,

length of garden = 3x

width of garden = 2x

Area of the vegetable garden = 91.26 ft²

3x(2x) =121.5 ft²

6x² = 121.5

x² = 121.5/ 6

x² = 20.25

x = √15.21

x = 4.5

length of the vegetable garden

x= 3(4.5)

x= 11.7 ft

SOLUTION

Let the cars weigh 3. 6 tons each

Let the trucks weigh 7. 5 tons each

Let c be the number of cars

Let t be the number of trucks

3. 6 c + 7. 5 t = 21600

a) when t = 480

3. 6 c + 7. 5 ( 480 ) = 21600

3. 6 c + 3600 = 21600

3. 6 c = 21600 - 3600

3.6 c = 18000

Divide both sides by 3. 6, we have:

c = 18000 / 3. 6

c = 5000 cars

b ) when t = 1500

3. 6 c + 7. 5 ( 1500 ) = 21600

3. 6 c + 11250 = 21600

3. 6 c = 21600 - 11250

3. 6 c = 10350

Divide both sides by 3.6 , we have:

c = 2875 cars

c ) when t = 2736

3. 6 c + 7. 5 ( 2736 ) = 21600

3. 6 c + 20520 = 21600

3.6 c = 21600 - 20520

3.6 c = 1040

Divide both sides by 3. 6, we have :

c = 300 cars

d) when t = t trucks

3. 6 c + 7. 5 t = 21600

3. 6 c = 21600 - 7. 5 t

c = 1 / 3. 6 ( 21600 - 7.5 t )

In order to calculate the limit of the function for a specific value of x, you just need to apply this value of x in the equation.

If the limit says "x -> 1-", it means we are approaching the value of 1 by the left (that is, from 0 to 1 for example).

If the limit says "x -> 1+", it means we are approaching the value of 1 by the right (that is, from 2 to 1 for example).

a)

To calculate this limit, we use the first part of the piecewise function, as we are approaching by the left (values lesser than 1):

[tex]\begin{gathered} g(x)=2-x \\ \lim _{x\to1^-}g(x)=2-1=1 \end{gathered}[/tex]

b) To calculate this limit, we use the second part of the piecewise function, as we are approaching by the right (values greater than 1):

[tex]\begin{gathered} g(x)=\frac{x}{2}+1 \\ \lim _{x\to1^+}g(x)=\frac{1}{2}+1=\frac{3}{2} \end{gathered}[/tex]

c) As the limit at 1 from the left is diferent from the limit at 1 from the right, the limit at 1 does not exist (it's undefined).

d) For x = 1, we need to use the first part of the piecewise function (because x = 1 is inside the inverval x <= 1), so we have:

[tex]\begin{gathered} g(x)=2-x \\ g(1)=2-1=1 \end{gathered}[/tex]

The area of the red sector is given by:

[tex]\pi\cdot r^2\cdot\frac{(\angle AOB)}{360\degree}=\pi\cdot11^2\cdot\frac{29\degree}{360\degree}\approx30.6\text{ cm}^2[/tex]

ANSWER

Graph #4

EXPLANATION

To graph this inequality, we can solve it for y to obtain the equation of the line. First, subtract 3x from both sides of the inequality,

[tex]\begin{gathered} 3x-3x-4y\le-3x+24 \\ -4y\le-3x+24 \end{gathered}[/tex]

And divide both sides by -4. Remember that when we multiply or divide both sides of an inequality by a negative value, we have to flip the inequality sign,

[tex]\begin{gathered} \frac{-4y}{-4}\ge\frac{-3x+24}{-4} \\ y\ge\frac{3}{4}x-6 \end{gathered}[/tex]

Thus, the solution set of this inequality is the line y = 3/4x - 6 and all points above the line. Note that the line has a positive slope, so the graphs can only be the second or fourth, and only on the fourth graph, the shaded area is above the line.

Since the student worked 53 hours, and for the first 40 hours he gets paid normally, then we have that the difference between 53 and 40 is the hours that he worked overtime, then, 53 -40 = 13 hours he workd overtime. Thus, we can separate the total time like this:

[tex]\begin{gathered} 40\text{ hours of normal time} \\ 13\text{ hours of overtime} \end{gathered}[/tex]

then, for the first 40 hours the student earned the following:

[tex]40(5.30)=212[/tex]

then, for the overtime we have:

[tex]13(7.95)=103.35[/tex]

adding these two quantities we get:

[tex]212+103.35=315.35[/tex]

therefore, the student earned $315.35 during the week

According to the given statement, we can conclude that it is a contrapositive statement.

This is because the hypothesis and the conclusion are switched and the opposite of them are considered.

If you are wearing green is the hypothesis (p).

You are Irish is the conclusion (q).

Here we are considering the opposite of both (~p, ~q) but switched, that is why we say it is a contrapositive statement.

It will take 20 boxes until both companies charge the same amount of money

Here, we want to find the number of candy boxes that both companies will produce, such that the cost will be same.

Since we do not know the number of candies, we will need to represent it by a variable. Let the number of candies produced be x candies

Let us calculate the cost for Candy Crush company

For candy crush company, the cost is as follows;

$5.75 for 1 box, so for x boses, the cost will be x * 5.75 = $5.75x

Let us add the delivery fee to get the total cost.

That would be $5.75x + $30

Now; Let us calculate for Layla's Lollipops

Same x boxes

Cost of x boxes at $2.75 per box is 2.75 * x = $2.75

Adding the delivery cost, we have a total of

$2.75x + $90

So since the cost will be equal for x boxes, We equate the total costs for both companies;

Hence;

5.75x + 30 = 2.75x + 90

We proceed to collect like terms

5.75x - 2.75x = 90-30

3x = 60

divide both sides by 3;

x = 60/3

x = 20