A small square has an area of 40 inches squared. A large square has sides that are 8 times longer than the small square. What is the area of the large square?

Answer:

Step-by-step explanation:

looking at all the stress you're in I knew I had to help so all your lists are bunched up, so I went of the picture C is correct because B 4 and 7 aren't even a part of the question itself and A has 16 and 49 but it doesn't have sqrt so it's not = to the question and D is not correct either because it doesn't have one sqrt it has two on top of each other. HOPE THIS HELPED!

The equation of his allowance in slope-intercept form is y = 0.5x + 8

He received $18 in allowance the week he did 20 chores.

He received $12 in allowance the week he did 8 chores.

The ordered pairs will be (8,12) and (20,18)

The slope intercept form is

y = mx + b

Where m is the slope

b is the y intercept

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

m = (18-12)/(20-8)

m = 6/12

= $0.5 per chores

Now we have to find b,

Substitute the value of any ordered pair in the slope intercept form

12 = 0.5×8+b

12 = 4+b

b = 12-4

b = 8

Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8

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The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 2.5

μ = mean = 2.28

σ = standard deviation = 0.37

z-score = (2.5 - 2.28) / 0.37

z-score = 0.22 / 0.37

z-score = 0.5946

To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0.5946

By interpolating the values,

probability = 0.724

proportion = 0.724

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Answer:

1/5

Step-by-step explanation:

I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.

Answer:

3.525/0.25=14.1

Step-by-step explanation:

Answer: 14.1

Step-by-step explanation:

3.525/0.25 = 14.1

Since "quotient" just means the result of two numbers being divided together. Therefore we would divide the two numbers you just gave.

△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

So, to prove that △PQR ≅ △STU:

So, with these three conditions, △PQR ≅ △STU is under ASA condition.

Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

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Answer:

1/4

Step-by-step explanation:

The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,

[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]

Okay, here we have this:

Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:

So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:

p=4x/5+25

Replacing:

p=4(30)/5+25

p=120/5+25

p=24+25

p=49

So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.

Answer:

y > -1

Step-by-step explanation:

8y+9 > 1

   -9    -9

8y > -8

/8    /8

y > -1

Answer:

for the first one: d ≥ 1

for the second one: d > 5

Answer:

the length of AB is 9

Step-by-step explanation:

an isosceles triangle is a type of triangle i which two of its sides are equivalent(equal). let AB=AC=x

perimeter=22

                  perimeter=AB+AC+BC

                                22=x+x+4

                                 22-4=2x

                                      18/2=2x/2

                                           9=x

The system of equations has one solution, so it is consistent and independent, the correct option is C.

Here we have the system of equations:

x = 5

y = 6

-x - y + z = 0

By replacing the first and second equations into the third one, we get:

-5 - 6 + z = 0

-11 + z = 0

z = 11

So the solution is (5, 6, 11)

So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).

Then the correct option is C.

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Answer:

[tex]\frac{109}{20}[/tex]

Step-by-step explanation:

.45 mean [tex]\frac{45}{100}[/tex] so  5.45 means 5 [tex]\frac{45}{100}[/tex]  = [tex]\frac{9}{20}[/tex]  If I divide the top and bottom of [tex]\frac{45}{100}[/tex] by 9

5 [tex]\frac{9}{20}[/tex] is a mixed number.  I can make this an improper fraction by changing 5 to 1+1+1+1+1  Another name for 1 is any number over itself as a fraction.

I am going to write 1 as [tex]\frac{20}{20}[/tex]

5 can be written

[tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] = [tex]\frac{100}{20}[/tex]

5 [tex]\frac{9}{20}[/tex]  Can be written

[tex]\frac{100}{20}[/tex] + [tex]\frac{9}{20}[/tex] = [tex]\frac{109}{20}[/tex]

Answer:

(109/20) Is the answer.

The relation which represents a function is the mapping diagram.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).

In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.

Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.

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The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

Let the number be x,

Twice the difference of three times a number and five = 2(3x - 5)

The sum of four times a number and six is  (4x + 6)

2(3x - 5) ≤ (4x + 6)

6x - 10 ≤ 4x + 6

6x - 4x ≤ 6 + 10

2x ≤ 16

x ≤ 8

x can be any positive number less than or equal to 8.

Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]

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Answer:

x = 12

Step-by-step explanation:

since the triangles are congruent then corresponding angles are congruent, so

∠ CBD = ∠ ABD , that is

9x - 9 = 99 ( add 9 to both sides )

9x = 108 ( divide both sides by 9 )

x = 12

Answer: Uncle Luke is at 50 years old

Step-by-step explanation: I went through trial and error first with simple t-charts.  In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:

[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]

Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex]        |             [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex]  (remember there are 1 increments)

Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50

A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.

Using the Unitary Method:

∵ In '3' years, a forest decreased in size by '60' hectares

∴ In '1' year, a forest will be decreased in size by '20' hectares

Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.

The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.

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Answer:

Step-by-step explanation:

y=-3x+24

(0,24)

a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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We will have the following:

Inferring from the information presented in the diagram we can conclude that the measurements will be:

Base: 3ft * 12ft = 36f t^2

Side1: 3ft * 2ft = 6 ft^2

Side 2: 12ft * 2ft = 24 ft^2

So, the values that would represent the dimension will be:

Length: 12 ft.

Width: 3 ft.

Height: 2 ft.

Based on the center of the regular decagon, we can find that the perimeter of the decagon would be 98.9 units.

When given the midpoint of a decagon and the measurement of the radius, the perimeter can be found by the formula:

= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

Given a radius of 16 units, the perimeter of this decagon is:

= 10 x ( (2 x  16) / (1 + √5)))

= 10 x ( (32 / (1 + √5)))

= 98.9 units

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Perimeter of Decagon with radius and midpoint given is 100 units.

Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Given polygon is a decagon. A decagon is a polygon which have ten sides with same length with centre o.

The radius of the decagon is 16.

When radius and midpoint is given the perimeter can be given by formula

Perimeter= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

=10×((2×16) / (1 + √5)))

=10×((32) / (1 + √5)

=320/1+√5

=320/1+2.2

=320/3.2

=100 units.

Hence perimeter of Decagon with radius and midpoint given is 100 units.

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SOLUTION:

Case: Transformation:

To find the transformation, compare the equation to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Method:

1,

Transformation features:

Horizontal: None

Shift: None

Stretch/Compression: None

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5

2.

Transformation features:

Horizontal:

Shift: left by 9 units

Stretch/Compression: None

Vertical:

Shift: None

Stretch/Compression: Stretches by a factor of 7.

Final answer:

1.

Vertical:

Shift: Down by 3 units

Stretch/Compression: Stretch by a factor of 5.

2.

Horizontal:

Shift: left by 9 units

Vertical:

Stretch/Compression: Stretches by a factor of 7.

The width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200.

A rectangular garden has a length of 60 feet (ft)

a width of w ft

and a perimeter of 200 ft.

The formula of perimeter of a rectangle is 2(lenght + width)

The equation that represents the garden's perimeter is 2(60 + w) = 200

2(60 + w) = 200

120 + 2w = 200

2w = 200 - 120

2w = 80

w = 40

Therefore, width of the rectangular garden is 40feet. The equation that represents the garden's perimeter is 2(60 + w) = 200

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A perfect square is a number that is gotten by multiplying it by itself.

An example of a perfect square is 25 and one that is not is 7.

A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of another integer and itself. For instance, 9 is a square number since it equals 3² and may be expressed as 3 × 3.

A perfect square is a number that can be written as the product of two integers or as an integer's second exponent. 25 is a perfect square because it is the product of the integer 5 and itself, 5 × 5 = 25. A perfect square is a positive integer formed by multiplying an integer by itself.

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The equation of the line that passes through point (-5,3) and perpendicular to y=5x-3 is y = -(1/5)x + 2.

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

Given the data in the question;

First, determine the slope of the initial line using the slope intercept-form. y = mx + b

y = 5x - 3 compared with the slope intercept form,

Slope m = 5

Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.

Hence, slope of the perpendicular line is;

Slope m = -1/5

Next, find the equation of the perpendicular line, by using the point slope formula.

y - y₁ = m( x - x₁ )

Plug in the slope m ( -1/5 ) and point (-5,3).

y - y₁ = m( x - x₁ )

y - 3 = -1/5( x - (-5) )

y - 3 = -1/5( x + 5 )

y - 3 = -1/5(x) -5/5

y - 3 = -1/5(x) - 1

y = -1/5(x) - 1 + 3

y = -(1/5)x + 2

Therefore, the equation of the perpendicular line is y = -(1/5)x + 2.

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Answer:

28°

Step-by-step explanation:

AB and CD are straight lines, all angles in a straight line add up to 180

If two expressions have the same coefficients of the variable, then the variable can be any number

For the first choice

3(3r + 3) = 9r + 9 === 1st expression

6r + 6 ===== 2nd expression

If we equate them

9r + 9 = 6r + 6

If we solve the equation we will find just one value of r

9r + 9 - 6r = 6r - 6r + 6

3r + 9 = 6

3r + 9 - 9 = 6 - 9

3r = -3

r = -1

But in the other choices, the two expressions have the same coefficients of r

Then when we equate them they will cancel each other

Then r can be any value

Because it does not affect the equation

Answer: y=x/3 + 4

Step-by-step explanation: