Which of the following is the difference of two squares?
16a ˆ2-9bˆ6
25mˆ2+100nˆ2
2xˆ2-4yˆ2
4g-16h

Answer:

Fred would take 33 days to save $ 70.95.

Step-by-step explanation:

The number of days (\(t\)) is directly proportional to the quantity of money saved (\(c\)), in monetary units, then we can calculate the time taken to save $ 70.95 by simple rule of three:

\(t = 17\,d\,\times \frac{\$\,70.95}{\$\,36.55}\)

\(t = 33\,d\)

Fred would take 33 days to save $ 70.95.

Answer:

roughly 12.57

Step-by-step explanation:

pi times \(r^{2}\)

Answer:

4π

Step-by-step explanation:

Hello!

The area of a circle is calculated using the formula \(A = \pi r^2\).

To solve for the area, we plug in the value for the radius.

Usually we round Pi to 3.14 and multiply, but since it's asking for the exact value, we can just leave it as is.

The area in terms of Pi is 4π.

Answer:

The slope is 0, then the line is horizontal.

y = 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that the sides in a square are equal length. We also know that you have to multiply length by width to get area. So if we know that the length of one side is 16 feet then all we have to do if multiply 16 by 16. Hence why the answer is 256 square feet of carpet.

Answer:

The small balloon bouquet uses  7 balloons and the large one uses

18 balloons.

Step-by-step explanation:

Let's say that small balloon bouquets are S and large balloon bouquets are L. For the graduation party the employee assembled 6 small bouquets and 6 large bouquets, the total number of balloon used is 150. To put the sentence into an equation will be:

6S + 6L= 150

S+L= 25   ----> 1st equation

For Father's Day, the employee uses 6 small bouquet and 1 large bouquet, the total number of balloons used is 60. The equation will be:

6S + 1L= 60

1L= 60- 6S   ----> 2nd equation

We can solve the number of small balloon bouquet by substitute the 2nd equation into 1st. The calculation will be:

S+L = 25

S+ (60-6S)= 25

-5S= 25-60

-5S= -35

S= -35/-5

S=7

Then we can find L by substitute S value to 1st or 2nd equation.

S+L=25

7+L=25

L=18

Hope this helps ;)

Answer:

193 = 7s + 8l ( Grad Party Equation)

92 = 8s + 2l (Father's Day Equation)

The small balloon bouquet uses 7 balloons and the large one uses 18 balloons

Step-by-step explanation:

First we need to separate something, I chose l...

...and we can replace this for l in the other equation!

Now that we have found the number of balloons needed for a small bouquet we can place that in an equation to find out how many balloons it takes to make a large bouquet.

Now just to make sure we got that right. Just check them!

Grad Party Equation

We got one right and the other one...

Fathers Day Equation

We got both right yay!

Answer:

\({ \tt{(f + g)x = ( {x}^{3} - 2 {x}^{2} + 1) + (4 {x}^{3} - 5x + 7)}} \\ \\ { \tt{(f + g)x = ( {x}^{3} + 4 {x}^{3}) + ( - 2 {x}^{2} ) + ( - 5x) + (1 + 7) }} \\ \\ { \boxed{ \rm{(f + g)x = {5x}^{3} - 2 {x}^{2} - 5x + 8 }}}\)

Answer:

£80.62

Step-by-step explanation:

100+12%=112%

112/100= 1.12

1.12*£72 =£80.62

The scale factor from the smaller prism to the larger prism is 2. This means that the larger prism is twice as large as the smaller prism in all dimensions.

To find the scale factor of a prism to another prism, you need to compare the corresponding dimensions of the two prisms. For example, if you have a rectangular prism with dimensions of 4 cm x 3 cm x 5 cm and another rectangular prism with dimensions of 8 cm x 6 cm x 10 cm, you can compare the lengths, widths, and heights to find the scale factor.
To do this, you can divide the corresponding dimensions of the larger prism by the corresponding dimensions of the smaller prism. In this example, the scale factor would be:
Length: 8 cm ÷ 4 cm = 2
Width: 6 cm ÷ 3 cm = 2
Height: 10 cm ÷ 5 cm = 2
Therefore, the scale factor from the smaller prism to the larger prism is 2. This means that the larger prism is twice as large as the smaller prism in all dimensions.

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Answer:

1

Step-by-step explanation:

\(( { \sec}^{2} \theta - 1)( { \csc}^{2} \theta - 1) \\ \\ = { \tan}^{2} \theta. { \cot}^{2} \theta \\ \\ = 1\)

Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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The grams of cocoa does it contains is 36.57 grams

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

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

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

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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\(\huge\underline\red{Answer -}\)

\(\bold{8 \frac{2}{5} }\: \\\\ \implies \: \frac{5 × 8 + 2}{5} \: \\ \\ \implies \: \frac{ 40 + 2}{5} \\\\ \implies \frac{42}{5} \\\\ \rightarrow \:\boxed {reciprocal \: = \frac{5}{42} } \\ \\\)

hope helpful ~

\(\huge\text{Hey there!}\)

\(\mathsf{8 \dfrac{2}{5}}\\\\\mathsf{= \dfrac{8\times5+2}{5}}\\\\\mathsf{= \dfrac{40 + 2}{5}}\\\\\mathsf{= \dfrac{42}{5}}\\\\\mathsf{=\dfrac{5}{42}}\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{\dfrac{5}{42}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

3 ways

Step-by-step explanation

Say there was 4 winners that got the silver than the next 4 got the silver medal and then last of the next 4 got the bronze 4+4+4=12 then among each of the ones that went across the finish line first and then the next four and then the next they would be equal among each other.

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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Answer:

A parallel line has the same slope, but is translated away from the line it is parallel to. Let's create an equation using what we have:

−

1

=

−

3

(

−

2

)

+

b

−

1

=

6

+

b

−

7

=

b

y

=

−

3

x

−

7

Hope this helped!!

Answer:

Step-by-step explanation:

its none, if it was SAS then the 10 would be closer to the angle

The graph of the function is added as an attachment

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

f(x) = 4x

The above expression is a linear equation that implies that:

Slope = 4

y-intercept = 0

Next, we plot the graph using a graphing tool

One of the points on the line is (1, 4)

See attachment for the graph of the equation

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Answer:

100, 25, 50

Step-by-step explanation:

\(700: \frac{700}{700} \times 100=100 \\ \\ 175: \frac{175}{700} \times 100=25 \\ \\ 350: \frac{350}{700} \times 100=50\)

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

$45

Step-by-step explanation:

I = prt

I = interest earned

p = principal = amount invested

r = interest rate; 5.25% = 5.25/100 = 0.0525

t = time in years; 6 months = 0.5 years

$4,000.00 at 5.25% interest

I = 4000 × 0.0525 × 0.5 = 105

$105 interest in 6 months

$2,000.00 at 6.00% interest

I = 2000 × 0.06 × 0.5 = 60

$60 earned in 6 months

$105 - $60 = $45

The difference is $45.

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

There are 45 blue marbles

Step-by-step explanation:

Well if 4 times 9 is 36, then 5 times 9 is 45

= 36 : 45

Answer:

40x + 30y ≤ 6,550

Step-by-step explanation:

Given:

Cost of each apple bushels = $40

Cost of each corn bushels = $30

Total budget = $6,550

Find:

Inequality

Computation:

Assume;

Total number of apple bushels = x

Total number of corn bushels = y

So,

40x + 30y ≤ 6,550

Answer:

The population reached a total of 19880 people in 1967.

Step-by-step explanation:

The population in t years after 1951 is given by:

\(P(t) = 130t + 17800\)

Which year the population reached a population of 19880 people.

This is t years after 1951

t is found when \(P(t) = 19880\)

So

\(P(t) = 130t + 17800\)

\(19880 = 130t + 17800\)

\(130t = 2080\)

\(t = \frac{2080}{130}\)

\(t = 16\)

1951 + 16 = 1967

The population reached a total of 19880 people in 1967.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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Step-by-step explanation:

the volume of the cylinder is

pi×r²×height = base area × height = 42×13 = 546 in³

the volume of a cone is

pi×r²×height/3 = base area × height / 3

so, the volume of the cone with the same basic sizes as the cylinder is the volume of the cylinder / 3 =

= 546 / 3 = 182 in³

The value of one of the tangent ratios = 1 because tan(A) = tan(X)

If ΔABC ~ ΔXYZ, then the corresponding angles are congruent, which means that:

∠A ≅ ∠X

∠B ≅ ∠Y

∠C ≅ ∠Z

Therefore, we can write:

tan(A) = tan(X)

This is because tangent is a ratio of two sides, and corresponding sides of similar triangles are proportional.

So, the ratio of two tangent ratios:

tan(A) / tan(X) = 1

So, we know the value of one of the tangent ratios = 1 we can use the above relationships to find the other tangent ratios.

since tan(A) = tan(X), we can say that they are equal. This means that the two triangles have equal angles, and they are similar. It also means that the ratio of the corresponding sides of the two triangles is constant.

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The discriminant of the quadratic equation is zero, thus, we have a double root.

A general quadratic equation can be written as:

y = a*x^2 + b*x + c

The discriminant is defined as:

D = b^2 - 4ac

In this case, the quadratic equation is:

16x^2 + 8x + 1 = 0

So the discriminant is:

D = 8^2 - 4*16*1

D = 0

So we have a double root.

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