Question Number 7 of 10 - 8th Grade Math
Which graph shows only a translation?

The value of x that makes the rational expression undefined is x = -3.

The rational expression is undefined when the denominator is equal to zero, because division by zero is undefined.

In the given rational expression (x - 3) / (3 + x), we need to find the value of x that makes the denominator (3 + x) equal to zero.

To find this value, we set the denominator equal to zero and solve for x:

3 + x = 0

Subtracting 3 from both sides:

x = -3

Therefore, the value of x that makes the rational expression undefined is x = -3.

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The center of the circumscribed circle is (1, 5).

We calculate the midpoint and slope of the line segment AB:

Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)

Midpoint of AB = (1, 8)

Slope of AB = (y₂ - y₁) / (x₂ - x₁)

= (8 - 8) / (0 - 2)

Slope= 0

We can notice that the equation of the perpendicular bisector of AB is x = 1.

We also find midpoint and slope of the line segment  BC

Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

= ((0 + 2) / 2, (8 + 2) / 2)

= (1, 5)

Slope of BC = (y₂ - y₁) / (x₂ - x₁)

= (2 - 8) / (2 - 0)

= -3

y - 5 = -3(x - 1)

y - 5 = -3x + 3

3x + y = 8

we have the equations of two perpendicular bisectors which are

x = 1 and 3x + y = 8.

We Substitute x = 1 into 3x + y = 8:

3(1) + y = 8

3 + y = 8

y = 5

In conclusion, center of the circumscribed circle is (1, 5).

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Let's solve the inequality to determine the number of outfits Tariq can purchase while staying within his budget.

Given:

Amount Tariq has to spend: $640

Cost of a new bicycle: $291.24

Cost of 4 bicycle reflectors: $19.56 each

Cost of bike gloves: $16.52

Cost of each biking outfit: $50.80

Let's assume the number of outfits Tariq can purchase is represented by x.

The total cost of the items he has already purchased is:

Cost of bicycle = $291.24

Cost of 4 bicycle reflectors = $19.56 * 4 = $78.24

Cost of bike gloves = $16.52

The remaining amount Tariq has to spend can be calculated as:

Remaining amount = Total amount - (Cost of bicycle + Cost of reflectors + Cost of gloves)

Remaining amount = $640 - ($291.24 + $78.24 + $16.52)

Now, we need to determine the maximum number of outfits Tariq can purchase with the remaining amount. Each outfit costs $50.80.

Inequality: x * $50.80 ≤ Remaining amount

Substituting the values:

x * $50.80 ≤ $640 - ($291.24 + $78.24 + $16.52)

Simplifying further:

x * $50.80 ≤ $640 - $385

x * $50.80 ≤ $255

To solve for x, we divide both sides of the inequality by $50.80:

x ≤ $255 / $50.80

x ≤ 5

Therefore, the maximum number of outfits Tariq can purchase while staying within his budget is 5.

Beth and Kelly were on vacation for 6 days.

Let's assume that Beth and Kelly were on vacation for "x" days.

For Beth:

The cost per day for dog sitting at Rover Sleepover is $24.50.

Beth also paid a fee of $90.50 for food and cleaning.

So the total cost for Beth's dog sitting can be expressed as:

Total cost for Beth = (Cost per day × Number of days) + Cleaning fee

Total cost for Beth = ($24.50 × x) + $90.50

For Kelly:

The cost per day for dog sitting at Pet Palace is $32.

Kelly also paid a fee of $45.50 for cleaning.

So the total cost for Kelly's dog sitting can be expressed as:

Total cost for Kelly = (Cost per day × Number of days) + Cleaning fee

Total cost for Kelly = ($32 × x) + $45.50

Since both Beth and Kelly spent the same total amount of money, we can set up an equation:

($24.50 × x) + $90.50 = ($32 × x) + $45.50

Simplifying the equation, we get:

$24.50x + $90.50 = $32x + $45.50

Moving the variables to one side and constants to the other side:

$32x - $24.50x = $45.50 - $90.50

Combining like terms, we have:

$7.50x = $45

Dividing both sides of the equation by $7.50:

x = $45 / $7.50

x = 6

Therefore, Beth and Kelly were on vacation for 6 days.

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The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

Therefore, this can be expressed as:

[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]

Cross multiply:

[tex]360^{\circ} \cdot s=C \cdot A[/tex]

Now, divide both sides by A to isolate C:

[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]

Where the above is given, Area of Δ ACB ≈ 282.62

The area of a triangle is given as

Area = 1/2 Base x Height

In this case,

Base = AB

Height = CP

Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.

First we need to find the height and hypotenuse of the triangle.

that is CP and CB.

CB = a/Cos (63)

CB = 26.43227

CP = √(CB²-PB²)

CP = √(26.4322711750232² - 12²)

CP = 23.55133

Area of ΔPCB = (CP x PB)/2

(12 × 23.551326066062)/ 2

= 141.30796

Since ΔPCB = ΔPCA

and ΔACB = ΔPCB + ΔPCA

Thus,

Area of  ΔACB = 141.30796 + 141.30796 = 282.61592

≈ 282.62

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

The volume of the trapezoidal prism is 420 cm³

Volume is the amount of space that is occupied by a three dimensional shape or object.

The volume of a trapezoidal prism is the product of the base area and its height.

For the trapezoidal prism:

Area of base = (1/2)(15 + 5) * 7 = 70 cm²

Volume of Prism = Area of base * height = 70 cm² * 6 cm = 420 cm³

The volume of the figure is 420 cm³

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The complete sentence is shown below:

Reason: Given

Reason: Angles forming a linear pair sum to 180° (Given)

Reason: Substitution from Statement 1.

To complete the proof that HJ GI, we can use the given statements and reasons:

Statement 1: <HKI = <GKH

Reason: Given

Statement 2: m<GKH + m<HKI = 180°

Reason: Angles forming a linear pair sum to 180° (Given)

Statement 3: m,GKH + m<GKH = 180°

Reason: Substitution from Statement 1

Statement 4: m<GKH = 90°

Reason: From Statement 2 and Statement 3, we can subtract m<GKH from both sides, which results in m<GKH = 180° - m<GKH.

Since the angles forming a linear pair sum to 180°, m<GKH + m<GKH = 180° implies that m<GKH = 90°.

Therefore, based on the given statements and reasons, we can conclude that HJ and GI are congruent (m<GKH = 90°)

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The area of the kite is 38 mm squared.

A kite is a quadrilateral with two pairs of adjacent sides equal. The diagonals of a kite are perpendicular. The vertex angle are bisected by the diagonals.

It has two pairs of consecutive equal sides and perpendicular diagonals.

Therefore,

area of a kite = ab / 2

where

Therefore,

a = 9.5 mm

b = 4 mm

Therefore,

area of a kite = 9.5 × 4 / 2

area of a kite = 38 / 2

area of a kite = 19 mm²

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Answer:

The area of the kite would be 19 mm².

Step-by-step explanation:

A kite is a quadrilateral with two pairs of equal-length adjacent sides. The diagonals of a kite are perpendicular to each other and intersect at a right angle, dividing the kite into four right triangles. The area of a kite can be calculated by finding the product of the lengths of its diagonals and dividing it by 2.

If we assume that the height and width you provided are the lengths of the diagonals, we can calculate the area using the following formula:

Area = (height * width) / 2

Substituting the given values:

Area = (9.5 mm * 4 mm) / 2

= 38 mm² / 2

= 19 mm²

Therefore, if the height and width represent the lengths of the diagonals, the area of the kite would be 19 square millimeters.

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The measure of angle C is 13°.

To find the measure of angle C in the given circle, we need to use the properties of angles subtended by arcs in a circle.

Given information:

m∠J = 88° (angle J)

mArc DF = 62° (arc DF)

mArc BD = 136° (arc BD)

We can start by using the fact that the measure of an angle formed by a chord and an arc is equal to half the measure of the intercepted arc.

Since mArc DF = 62°, the measure of angle DJF (angle formed by chord DF and arc DF) is 62°/2 = 31°.

Next, we can use the fact that angles subtended by the same arc are equal.

Since mArc BD = 136°, angle BJD (angle formed by chord BD and arc BD) is also 136°.

Now, let's find angle BCD (angle formed by chord BD and chord CD). The sum of angles in a triangle is 180°, so angle BCD = 180° - angle DJF - angle BJD.

Angle BCD = 180° - 31° - 136°

Angle BCD = 180° - 167°

Angle BCD = 13°

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The surface area of this composite solid is 265.36 units².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[3 × 5 + (3× 10) + (5 × 10)]

Surface area of rectangular prism = 2[15 + 30 + 50]

Surface area of rectangular prism = 190 units².

Surface area (SA) of a cylinder = 2πrh + 2πr²

Surface area (SA) of a cylinder = 2 × 3.14 × 2 × 4 + 2 × 3.14 × 2²

Surface area (SA) of a cylinder = 50.24 + 25.12

Surface area (SA) of a cylinder = 75.36 units².

Therefore, we have:

Surface area of composite solid = 190 units² + 75.36 units².

Surface area of composite solid = 265.36 units²

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Answer:

Not a right triangle

Step-by-step explanation:

[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]

As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.

Step-by-step explanation:

prism

v=1/2 X 12cm X 8cm

V= 48

rectangular prism

v=80cm+48cm

v=128cm

Answer:

D = 90 FT

Step-by-step explanation:

40 / d = 20 / 45

cross multiply

45 × 40 = 20d

1800 = 20d

divide both sides by 20

1800 / 20 = 20d / 20

d = 90 ft

In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.

In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.

The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.

The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.

The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.

To summarize:

Initial amount (a) = -2

Growth/decay factor (b) = 0.5

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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The vertical asymptote of the function are x = ±1/2

Given that we need to determine what is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.

This is because division by zero is undefined, and the function may have vertical asymptotes at those points.

The denominator of the function is 4x² - 1.

To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:

4x² - 1 = 0

Adding 1 to both sides:

4x² = 1

Dividing both sides by 4:

x² = 1/4

Taking the square root of both sides:

x = ±√(1/4)

Simplifying further, we get:

x = ±1/2

Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.

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Translation =

What is value of the vertical asymptote of the function =

(2x + 1) / (4x²-1)

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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[tex] \begin{aligned}3 ^{3k} &= \frac{1}{81} \\3^{3k} &= \frac{1}{3^{4} } \\ 3^{ \blue{3k}} &= 3^{ - \blue{4}} \\ 3k&= - 4 \\ k&= \frac{ - 4}{3} \\ k&= \bold{ - \frac{4}{3} } \end{aligned}[/tex]

[tex]\rm{The\:value\:of\:\mathit{k}\:is\:\bold{ - \frac{4}{3}}} \\ \\ \small{ \blue{ \mathfrak{That's\:it\: :)}}}[/tex]

The calculated volume of the sphere is 44602.24 ft³

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

Radius = 22 ft

The volume of a sphere can be expressed as;

V = 4/3πr³

Where

r = 22

substitute the known values in the above equation, so, we have the following representation

V = 4/3π * 22³

Evaluate

V = 44602.24

Therefore the volume of the sphere is 44602.24 ft³

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Question

Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.

Radius = 22 ft

Answer:

45/49

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

9/14 * 10/7 = 90/98

divide the numerator and the denominator by 2.

90 * 2 = 45

98 * 2 = 49

45/49

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

[tex]a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c[/tex]

[tex]\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ[/tex]<-- You can also use other trig ratios

[tex]B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ[/tex]

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

The preparation of the income statement of Buildex Company's adjusted trial balance is as follows:

Buildex Company

Services revenue           $70,500

Interest revenue                 5,700

Total revenue                $76,200

Expenses:

Depreciation expense   $4,700

Wages expense            52,000

Insurance expense         4,400

Supplies expense           2,700

Utilities expense              1,700

Total expenses          $65,500

Net income                 $10,700

The income statement is a financial statement that shows the financial performance of a business over a period.

In the income statement, the total expenses are deducted from the total revenue to compute the profit or loss.

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Use the following selected accounts and amounts with normal balances from Buildex Company's adjusted trial balance to prepare its income statement for the year ending December 31. Hint: Not all accounts need to be used.

Cash                        $10,400           Depreciation expense $4,700

Building                   185,000           Wages expense          52,000

Accounts payable      9,400           Insurance expense        4,400

Services revenue    70,500           Supplies expense          2,700

Interest revenue        5,700           Utilities expense             1,700

Fred will pay $43.05 in sales tax if he buys the new refrigerator.

To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.

The cost of the new refrigerator is $615.

To calculate the sales tax, we multiply the cost by the tax rate of 7%:

So, Sales tax = 7% of $615

Sales tax = (7/100) x $615

Sales tax = $43.05

Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.

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The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

The roots of the quadratic equation are the values of x that make the equation equal to zero.

Therefore, if a quadratic equation has the roots 3 + i and 3 - i, it can be written in the factored form as (x - (3 + i))(x - (3 - i)) = 0. Expanding this product yields x² - (3 + i + 3 - i)x + (3 + i)(3 - i) = 0.

Simplifying this expression further results in the quadratic equation x² - 6x + 10 = 0.

The quadratic equation that has the roots 3 + i and 3 - i is x² - 6x + 10 = 0.

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Step-by-step explanation:

1 qt = 2 pts     multiply both sides by two

2 qt = 4 pints

The x-intercept in the graph represent the height where the football was when the ball was kicked.

The x-intercept is the point where the graph of the line crosses the x-axis.

Therefore, the x-intercept the value of x when y equals to zero.

Therefore, let's find what the x-intercept of the graph represent in terms of the football.

The graph shows the height of the ball in metres after t second.

The y axis represent the height while the x-axis represent the time.

Hence, he x-intercept represents the height where the football was when the ball was kicked.

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The curved surface area of the cylinder is 24 cm².

We have,

To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).

Given:

Circumference (C) = 4 cm

Height (h) = 6 cm

The formula to calculate the curved surface area of a cylinder is A =  Ch, where A is the curved surface area, C is the circumference, and h is the height.

Substituting the given values:

A = 4 cm x 6 cm

A = 24 cm²

Therefore,

The curved surface area of the cylinder is 24 cm².

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2.63 is the value or quotient of 616/265 using long division.

We have to find the value of 616/265

In the given division the numerator is a dividend and the number in the denominator is a divisor.

616 is the dividend and 265 is the divisor.

When we perform long division the quotient will be 2.63 which is the require value.

       2.63  

____________

265 | 616

-530

______

860

-795

______

650

-530

______

120

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The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.

Here we have the summatory:

[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]

So we just need to add the 5 terms (between n = 1 and n = 5)

So we will get the sum:

S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]

S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]

S = [0.5 + 1 + 2 + 4 +8]

S = 15.5

So the correct option is the second one.

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