Find the value of each of the following by using prime factorisation.
(b) 13824

Ivory's scaled counterpart has a 48-square-unit area.

Ivory's scale factor for producing their scaled replica is;

On the graph, one interval corresponds to four units of the rectangle. This ratio is 1:4.

We can see from the provided image that the rectangle's y-axis has three intervals and its x-axis has one interval.

Now, the picture informs us that the scaled copy's area is 48 square units.

This indicates that the triangle she is attempting to depict with that graph has an area of 48 square units.

Now, if one of the graph's intervals is in units of x, then it indicates;

Y-axis: length; 3x units

size; x-axis equals x units

A rectangle's area is

based on the formula Area = Length Width, 3x [tex]\times[/tex] x = 48.

1 interval on the graph corresponds to 4 units of the rectangle because 3x2 = 48 x2 = 48/3 x2 = 16 x = 16 x = 4.

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Answer:

Thus, the value of x in the given triangle is 55°

Step-by-step explanation:

Given - Dimensions of triangle and angles

of triangle

Find - Value of x

Solution - The value of x in the given triangle is 55°.

As per the given dimensions of the triangle, the triangle is isosceles. This states that the neighbouring angle will be x° as well.

Thus, the mathematical expression of all the angles of a given triangle will be -

x + x + 80 = 190

2x + 80 = 190

2x = 190 - 80

2x = 110

x = 110/2

x = 55°

.

The length and width of the given rectangle is 10.77 and 5.385 respectively.

According to the question statement, The length of a rectangle is twice the width and the area of the rectangle is 58 square units.

We are supposed to find the length and width of the rectangle.

Before solving this we need to know that the area of the rectangle is the product of its length and width,

Let's assume the length be "l" and width be "w"

Therefore Area = l*w

Now as length is twice the width so [tex]l=2w[/tex]

Area = [tex]58 square units[/tex]

Therefore [tex]l*w=58\\[/tex]

but [tex]l=2w[/tex]

[tex]2w*w = 58\\2w^{2}=58\\w^{2} = \frac{58}{2} \\w^{2}= 29[/tex]

[tex]w=\sqrt{29} \\w=5.385[/tex]

as [tex]l=2w[/tex]

[tex]l=2*5.385\\l=10.77[/tex]

Hence length l = 10.77 unit and width w = 5.385 unit

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The number of bills received by brady family are 781.

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved utilizing basic algebraic operations.

Let x equal the number of letters obtained,

(x - 3) equal the number of bills obtained,

(x + 5) equal the number of advertisements received, and also

the number of magazines did receive is also given (x - 3).

The following equation can be derived:

x + (x - 3) + (x + 5) + (x - 3) = 3131

4x - 1 = 3131

4x = 3132

x = 784

Thus, number of bills received are-

(x - 3) = 784 - 3

number of bills received = 781.

Therefore, the number of bills obtained by brady family are 781.

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Step-by-step explanation:

1

A: is a function since 2 different x values can have the same y value

B: not a function since the x value 0 gives different values which makes it not a function.

C: since 4 corresponds to 2 different y values it is not a function.

D and E are not function since there are different y values for the same x value.

2: all of the answers are determined by the vertical line test.

A NOT A FUNCTION

B NOT A FUNCTION

C A FUNCTION

D UNCLEAR

E NOT A FUNCTION

hope this helps and make sure to ask any qs if you doubt anything :)

Answer:58.8km/h

Step-by-step explanation: V= 1.67/1.7= 0.98 km/min

0.98*60min=58.8

Answer:

11/3 or 3 2/3

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

There are 46,656 cubic inches in a cubic yard.

Explanation:      

for an approximate result, multiply the volume value by 46660

Answer:

Starting from the left, the points plotted are:

-√9, -1.75, -3/2, -5/3, √4

The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is

What is a quadratic equation?

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.

a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .

formula: −b±√b2−4ac/2a

Given equation ,

2[tex]x^{2}[/tex] -12x-20=0

By comparing with the quadratic equation

Here, a=2, b= -12, c= -20.

X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a

X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)

X=12+-  [tex]\sqrt{144-160}[/tex]/4

X=12+- [tex]\sqrt{-16}[/tex]/4,

X=12+- (-4)/4

X=12+(-4)/4 and x=12-(-4)/4

X= 12-4/4 and x=12+4/4

X=8/4 and x= 16/4

X=2 and x= 4

Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.

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The largest size of identical felt squares that can be used to cover the top of rectangle is 5 squares of side 24cm.

The rectangle is a 2-dimensional figure with length and breadth which may or may not be same. A square is also a 2-dimensional figure with equal length of its sides.

When the dimensions of rectangle are given, it's are is given as the product of the sides of the rectangle which is given as:

Area of rectangle = Length × Breadth = 60 × 48 = 2880 cm square

The length of the square that entirely covers up the top side i.e., rectangular top can be determined by hit and trial mechanism starting from the lowest whole number in order to determine the length of largest squares of equal dimensions. Then comparing the area of the rectangular top and product of number of squares needed and area of each square, we can find the largest size of the square.

Area of square = length × length = l²

Since, Area of rectangular top = No. of squares × Area of 1 square

Therefore, 2880 = N (l²)

Putting N =1, 2, 3, 4, 5 and so on, we find that when N = 5, the value of square root of l is a perfect whole number.

Hence, 2880 = 5 × (l²)

l = √576 = 24

Thus, 5 squares of side 24cm will be used to cover the rectangular top entirely.

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Answer: u = 80° v = 25°

Step-by-step explanation:

(a) angles on a straight line = 180° - 130° = 50°

In isosceles triangle, both angles on each side is equal, so

180° - 50° - 50° = 80°

u = 80°

(b) u = (2v + 30°) because opposite angles of a parallelogram are equal.

u = 80°

80° = 2v + 30°

80 - 30 = 50

50° = 2v

25° = v

The angle measures, in order from least to greatest, of the dilated image  45°,55° and 80°.

A dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.

Euclidean space, In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.

Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still 45 °, 55 °, and 80 °.

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Answer:45,55,80

Step-by-step explanation:  dilations preserve angles measures regardless of the scale factor. Therefore the angle measures of the image will be the same of that of the pre-image ,so our answer is still 4545,5555,8080 .

Answer:

when the variable is on both sides of the equation first collect the same variable in one side end evaluate it,

Step-by-step explanation:

when solving the them, we collect like term and put the same term in one side to other

A ratio can be introduced as an ordered pair of numbers, and it can be represented as x:y.

A ratio can be introduced or described as an ordered pair of numbers.

For example, given two numbers x and y, where y is not equal to 0, the ratio can be represented as follows:

x:y

For example, let x represent the number of plates and equal to 2, and y represents the number of spoons and equal to 5, we will have the ratio as follows:

2:5

The ratio 2:5 implies that for every 2 plated there are 5 spoons.

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Step-by-step explanation:

Just do the calculations at last by using the value of x

The tanker has been filling the reservoir for 4 minutes given that it fills at a rate of 10 1/4 gallons per minute.

Rate refers to the relationship of two quantities of different units. Usually, it is a measure or quantity of something per unit time.

rate = amount / time

If a tank truck fills the gas station's reservoir at the rate of 10 1/4 gallons per minute, and if the reservoir is empty at the start and become 41 gallons full, we can determine how long the tanker has been filling the reservoir by dividing the final amount by the rate.

time = amount / rate

where amount = 41 gallons

rate = 10 1/4 gallons per minute

time = 41 gallons / 10 1/4 gallons per minute

time = 4 minutes

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Answer:

85%

Step-by-step explanation:

Total no. of matches played,

→ x = 20 matches

No. of matches they won,

→ y = 17 matches

Now the win percentage will be,

→ (y/x) × 100

→ (17/20) × 100

→ 0.85 × 100

→ 85%

Hence, the percentage is 85%.

The result are-

The values of x that correspond to the given quadratic equation ax² + bx + c = 0 are known as its roots.

For, the given expression;

x² + px + q = 0.      ....... (equation 1)

where p and q are constants, has roots -3 and 5.

Part 1: solve for p and q.

Put x = -3 in equation 1.

p(-3) = (-3)² + p(-3) + q = 0

9 - 3p + q = 0         .........(equation 2)

Now, put x = 5 in equation 1.

p(5) = (5)² + p(5) + q = 0

25 + 5p + q = 0     ..........(equation 2)

Solve equation 2 and 3 by elimination method.

p = -2 and q = -15.

Part 2: Estimate the constant r.

The equation is; x² + px + q + r = 0.

Substitute the values of p = -2 and q = -15.

x² + (-2)x + (-15) + r = 0.

As, the equation given real equal roots; then,

discriminant value: b² - 4ac = 0.

Substitute the values;

(-2)² - 4×1×(-15 + r) = 0

On simplification;

4 + 60 - r = 0

r = 64.

Therefore, the value of the constant r is estimated as 64.

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Ralph would most likely get more items correct than his Grandmother.

If both Ralph and his Grandmother took the Intelligence Quotient i.e., IQ test, then Ralph would most likely get more items correct than his Grandmother. This is due to Flynn Effect.

Flynn Effect refers to secular increase in population intelligence quotient observed throughout the 20th century. It demonstrates that the average of the IQ scores will change as varying generations have different thresholds for what intelligence is necessary.

Flynn Effect is documented by Flynn in a study on intelligence quotient. As Ralph's grandmother was born on 1925 and Ralph was born in 1990, so they have a generation gap of almost six decades. That is why Ralph will have a higher IQ than his grandmother.

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Answer:

36/5 as a decimal is 7.2

Step-by-step explanation:

In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".

When we calculated 36 divided by 5, we found that 36/5 in decimal form is:

36 ÷ 5 = 7.2

Therefore, the decimal form of 36/5 is 7.2

There is a lower limit but no upper limit for a random variable that follows the exponential probability distribution.

We know that, an exponential distribution is a type of continuous distributions.

This probability distribution times the occurrence of events.

In exponential probability distribution, events happen continuously and independently at a constant average rate.

The continuous random variable, say X is said to have an exponential distribution, if it has the following probability density function:

[tex]f_X(x)=\left \{ {{\lambda e^{-\lambda x~~~x > 0}} \atop {0~~~~~~~x\leq 0}} \right.[/tex]

The exponential distribution is memoryless.

We know that, for exponential the lower limit is 0, but the upper limit is infinity, meaning there is no upper limit.

Therefore, There is a lower limit but no upper limit for a random variable that follows the exponential probability distribution.

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Answer:

1/7

Step-by-step explanation:

You can just divide all the possible answers.

1/9 = 0.1111111 (1 repeating

1/7 = 0.142857142857

1/11 = 0.090909090909 (repeating)

1/14 = 0.0714285714286 (repeating)

The rectangle's width is 8m and the length is 4 times the width, so the length = 4 x 8 = 32m

To calculate the area of a rectangle, we take the width and multiply it with the length

A = 32 x 8 = 256m2

Answer:

1 kilometer is equal to 1000 meters

Step-by-step explanation: