Triangle J′K′L′ shown on the grid below is a dilation of triangle JKL using the origin as the center of dilation:



Which scale factor was used to create triangle J′K′L′?

4
2
one quarter
one half

Answer:

Hi

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Step-by-step explanation:

-3 1/4 ÷ 2 1/3

Change to improper fraction

-13/4 ÷ 7/3

-13/4 × 3/7

-39/28 or -1 11/28

Answer:

  (a)  Multiply (200.96)(22).

Step-by-step explanation:

You want the volume of the cylinder with base area 200.96 mm² and height 22 mm.

The volume is found using the formula ...

  V = Bh

where B is the base area, and h is the height.

For base area 200.96 mm² and height 22 mm, the volume is ...

  V = (200.96)(22) mm³

You find the volume by multiplying 200.96 and 22.

<95141404393>

The correct matches are:

-10u³ ⇒ -15u³ + 5u³

  5u³ ⇒ 10u³ + (-5u³)

 15u³ ⇒ 10u³ + 5u³

 -5u³ ⇒ 5u³ + (-10u³)

For the expressions:

Expression 1:

-15u³ + 5u³

To add these expression taking u³,

⇒ (-15 + 5)u³

⇒ -10u³

Expression 2:

⇒ 10u³ + (-5u³)

To add these expression taking u³

⇒ (10 - 5)u³

⇒ 5u³

Expression 3:

⇒ 10u³ + 5u³

To add these expression taking u³

⇒ 15u³

Expression 4:

⇒ 5u³ + (-10u³)

To add these expression taking u³

⇒ (5 - 10)u³

⇒ -5u³

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The complete question is attached below:

Answer:

The polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Step-by-step explanation:

To find the factors of the polynomial 2x^3 + x^2 - 2x - 1, we can use synthetic division or long division to divide the polynomial by the factor x + 1.

Using synthetic division:

-1 | 2 1 -2 -1

| -2 1 1

___________________

2 -1 -1 0

The result of the division is 2x^2 - x - 1.

So, the polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Answer:

Step-by-step explanation:

Solution

verified

Verified by Toppr

given, 2x

3

+x

2

−2x−1

=x

2

(2x+1)−1(2x+1)

=(x

2

−1)(2x+1)

=(x+1)(x−1)(2x+1)

The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.

Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.

The graph that represent this data using the points is added as an attachment

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

The x and y values

Where

x = stars

y = price

To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph

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The table is attached below.

The given equation is,

y = x² + 2x + 11

The given equation is a quadratic equation

Now to find X intercept put y = 0

⇒  x² + 2x + 11 = 0

Now the discriminant is,

⇒ 2² - 4x1x11 = -11 < 0

Hence there is no real solution,

Thus,

There is no x intercept.

To find Y axis is,

put x = 0

y = 11

Hence the y intercept is 11

Now plot the graph of the given equation to find the axis of symmetry.

Then we get line of symmetry is x = -1

Domain: real number

Range : [10 , ∞)

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The  best measure of center for the data shown is the median, and its value is 17.

The median is the best measure of center for the given data set. To find the median, we arrange the numbers in ascending order:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Since the data set has an odd number of values, the median is the middle value, which in this case is 17.

Therefore, the best measure of center for the data shown is the median, and its value is 17.

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The probability that all three coins will be displaying heads is 1/8 or 0.125.

When flipping a fair coin, there are two possible outcomes: heads (H) or tails (T).

Since each coin flip is independent, we can calculate the probability of all three coins displaying heads by multiplying the probabilities of each coin landing on heads.

The probability of one coin landing on heads is 1/2, or 0.5.

Since there are three coins flipped simultaneously, the probability of all three coins displaying heads is:

(1/2) × (1/2) × (1/2)

= 1/8

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Ricardo's annual interest rate is equal to 6%.

In Mathematics and Financial accounting, compound interest can be calculated by using the following mathematical equation (formula):

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

Where:

By substituting the given parameters into the formula for compound interest, we have the following;

[tex]2721.03 = 1500(1 + \frac{r}{4})^{4 \times 10}\\\\1.81402=(1 + \frac{r}{4})^{40}[/tex]

By taking 40th root of both sides of the equation, we have:

1.01500002226 = 1 + r/4

r/4 = 1.01500002226 - 1

r = 0.01500002226 × 4

Interest rate, r = 0.06 ×  100

Interest rate, r = 6%.

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By SSS postulate, triangle SQY is similar to triangle PTY.

From the given figure, consider ΔSQY and ΔPTY.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

Here, SQ/PT = SY/PY = YQ/YT

8/4 = 12/6 = 4/2

2 = 2 = 2

By SSS postulate, ΔSQY~ΔPTY.

Hence, by SSS postulate, triangle SQY is similar to triangle PTY.

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The first three pairs are of vertically opposite angles.

Given figure,

Vertical angles are the angles that are opposite to each other.

Hence the pairs of vertical angles will be opposite to each other as well as will be equal to each other.

So,

Vertical opposite angles are :

Option A

Option B

Option C

Thus 3 pairs will be considered for vertical angles .

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Step-by-step explanation:

This is of the form

(x-h)^2 + ( y-k)^2 = r^2        so r^2 = 16  means r = 4   units

The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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Answer(s):

Inequality Form:

-3.75 < x < -2.25

Interval Notation:  

x ∈ ( -3.75, -2.25)

Step-by-step explanation:

Equation:  |0.2x +0.6| <0.15

{0.2x + 0.6 > -0.15

{0.2x + 0.6 < 0.15

{(0.2x + 0.6) + (-0.6) > -0.15 + (-0.6)

{(0.2x + 0.6) + (-0.6) < 0.15 + (-0.6)

{0.2x + 0.6 - 0.6 > -0.15 - 0.6

{0.2x + 0.6 - 0.6 < 0.15 - 0.6

{0.2x > - 0.75

{0.2x < -0.45

{0.2x / 0.2 > - 0.75/0.2

{0.2x / 0.2 < - 0.45/0.2

{x > - 0.75/0.2

{x < - 0.45/0.2

{x > -3.75

{x < -2.25

-3.75 < x < -2.25

Answer: x ∈ ( -3.75, -2.25)

Hope this helps!

Simplification of the expression gives:

-3x² - 7x + 16

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

We have the expression:

(-8x+10) - (3x²-x+6)

We can simplify as follow:

(-8x+10) - (3x²-x+6) = -8x+10 -3x²+x+6    (remove parenthesis)

                               = -3x² - 8x + x + 10 + 6  (collect like terms)

                               = -3x² - 7x + 16  (add/subtract like terms)  

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Approximately 34.87% of the readers surveyed don't use e-readers.

To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):

Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed

Approximate sample proportion = 1954 / 3000 ≈ 0.6513

To express this as a percentage, we multiply the sample proportion by 100:

Approximate sample proportion as a percentage = 0.6513 × 100

= 65.13%

Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.

This means that approximately 65.13% of the readers surveyed use e-readers.

To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:

Percentage of readers who don't use e-readers = 100% - 65.13%

= 34.87%

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Answer:

A

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc

the sum of the arcs in a circle in a circle = 360°

since LK is a diameter the arc KL is equal to the measure of its central angle , that is

arc LK = 180° , then

LJ + JK + KL = 360°

LJ + 74° + 180° = 360°

LJ + 254° = 360° ( subtract 254° from both sides )

LJ = 106°

Then

∠ JKL = [tex]\frac{1}{2}[/tex] × 106° = 53°

The time period with the given principal, rate of interest and amount is 10 years.

Given that,

Principal = $1000, time period = 1 year and rate of interest =$40.

We know that, Simple interest = (Principal×Rate×Time)/100

48 = (1000×r×1)/100

4800=1000r

r=4800/1000

r=4.8%

Principal=$200, time period= 3 years and amount = $248

Simple interest = 248-200

= $48

48=(200×r×3)/100

4800=600r

r=4800/600

r=8%

Principal=$5000, rate of interest=2% and amount=$6000

Simple interest =6000-5000=$1000

Here, 1000=(5000×2×t)/100

1000=(100t)

t=10 years

Therefore, the time period with the given principal, rate of interest and amount is 10 years.

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The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}[/tex]

Therefore, the slope of the line is -4/7.

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He went to station Y, and the cost for 20 liters is 32 pounds.

Here we know taht Daniel went to a petrol store, and bought 15 L of petrol for 24 pounds.

So we need to use the graphs of the linear relations to see which store he went to.

We can see that in store X, for 15L the cost is 28 pounds, and for store Y the cost is 24 pounds.

So the correct option is Y.

Now, for 20 litres in that station, (using the same graph) we can see that the cost will be C=  32 pounds.

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The general journal entries Adriana Graphic Design should record the transaction  as;  Cash 1,650 Accounts Receivable 1,650.

When Adriana Graphic Design receives $1,650 from a client billed in a previous month for services provided, the firm is collecting an amount that was previously recognized as an account receivable.

In scenario provided, the firm will decrease its Accounts Receivable a debit entry, because Accounts Receivable is an asset account and assets decrease on the credit side and increase its - Cash account a credit entry, because Cash is also an asset account and assets increase on the debit side.

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Answer:

C and D

Step-by-step explanation:

[tex]\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}[/tex]

The inequality to solve for p is 6p > 600 and the solution is p > 100

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

Selling price = $6 per apple

So, we have

Total = 6p

Also, we have

Spendings = $600

To make profit, we have

6p > 600

Divide by 6

p > 100

Hence, the inequality to solve for p is 6p > 600 and the solution is p > 100

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Answer: The water that overflows from the rectangular tank is 4.25 liters or 4250 milliliters.

Step-by-step explanation: To calculate the volume of the rectangular tank, we need to multiply its length, width, and height. The measurements are given in centimeters, so we need to convert the result to liters.

Volume of the rectangular tank = length × width × height

= 55 cm × 35 cm × 30 cm

Converting the volume to liters:

1 liter = 1000 cubic centimeters (cm³)

Volume of the rectangular tank = (55 cm × 35 cm × 30 cm) / 1000

= 57750 cm³ / 1000

= 57.75 liters

Mr. Tay emptied 62 liters of water into the rectangular tank. Since the tank's volume is only 57.75 liters, the excess water will overflow.

Overflow = Volume of water emptied - Volume of the rectangular tank

= 62 liters - 57.75 liters

= 4.25 liters

To convert the overflow from liters to milliliters:

1 liter = 1000 milliliters (ml)

Overflow in milliliters = 4.25 liters × 1000

= 4250 milliliters

Answer:

The fourth vertex needed to create the rectangle is (-7,-25).

Step-by-step explanation:

As per the property of a rectangle, the lengths of the opposite sides of a rectangle are the same.

Let,

point A=(-4,-25)

point B=(-4,-12)

point C=(-7,-12)

Thus, point D or the fourth vertex is (-7,-25).

Refer to the image for a better understanding.

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The surface area of the triangular prism is 137ft².

To get the surface area of a triangular prism, we will calculate the area of each face and then sum them up.

Base area = (4 ft * 5 ft) / 2

Base area = 20ft/2

Base area = 10 ft²

Since triangular prism has two triangular bases, the total area of the triangular bases is:

= 2 * Base area

= 2 * 10 ft²

= 20 ft².

Perimeter of the triangular base:

= 4 ft + 5 ft + 4 ft

= 13 ft

Face area = Perimeter * Height

Face area = 13 ft * 3 ft

Face area = 39 ft²

The total area of the rectangular faces is:

= 3 * Face area

= 3 * 39 ft²

= 117 ft².

The Surface area of the triangular prism will be:

= Total area of triangular bases + Total area of rectangular faces

= 20 ft² + 117 ft²

= 137 ft².

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The capacity of the tin is  235.62 cm³ and the density of the polish is approximately 1.27 g/cm³.

The formula to calculate the volume of a cylinder is:

Volume = π r² h

where π is approximately 3.14159, r is the radius of the cylinder (half of the diameter), and h is the height of the cylinder.

Given:

Diameter = 10 cm

Radius (r) = Diameter/2 = 10 cm / 2 = 5 cm

Height (h) = 3-5 cm (range) = 3cm

Volume = 3.14159×25 cm² × 3 cm

Volume ≈ 235.62 cm³

Therefore, the capacity of the tin is approximately 235.62 cm³.

To calculate the density of the polish, we use the formula:

Density = Mass / Volume

Given:

Mass = 300 g (grams)

Volume = 235.62 cm³ (cubic centimeters)

Density = 300 g / 235.62 cm³

Density = 1.27 g/cm³

Therefore, the density of the polish is 1.27 g/cm³.

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The polar coordinates (r, θ) for the given rectangular coordinates are

(10, π/3)

To convert rectangular coordinates (5, 5√3) to polar coordinates (r, θ), we can use the following formulas:

r = √(x² + y²)

θ = arc tan (y/x)

Given the rectangular coordinates (5, 5√3), we have:

x = 5

y = 5√3

let's calculate the values

r = √(5² + (5√3)²

= √(25 + 75)

= √100

= 10

θ = arctan(5√3/5)

= arctan (√3)

= π/3 (since θ is in the interval [0,2π))

Therefore, the polar coordinates (r, θ) for the given rectangular coordinates are (10, π/3).

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Based on the information provided, the triangle ABC is an Isosceles triangle.

If triangle ABC is equal to triangle DEF and AB is equal to EF, it means that the corresponding sides and angles of the two triangles are congruent.

Based on the information given, we can conclude that triangle ABC is an isosceles triangle. An isosceles triangle is a triangle that has two sides of equal length. In this case, sides AB and EF are equal in length, making triangle ABC isosceles.

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