One number is 7 more than another number. The sum of these two numbers is 101. What are the numbers?

The equivalent expressions of 45 + 2i are (13 + 4i) + (32 - 6i) and  (9 + 4i) + 2(4 + 7i)(1 - 2i)

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

Complex number: 45 + 2i

Next, we test the options:

(13 + 4i) + (32 - 6i) = 13 + 4i + 32 - 6i

(13 + 4i) + (32 - 6i) = 45 - 2i --- true

(13 + 4i) + 2(7 + 2i)(2 -i) = (13 + 4i) + 2(14 - 7i + 4i - 2)

(13 + 4i) + 2(7 + 2i)(2 -i) = 13 + 4i + 28 - 14i + 8i - 4

(13 + 4i) + 2(7 + 2i)(2 -i) = 37 - 2i --- false

(2 + 8i) + (30 - 6i) = 2 + 8i + 30 - 6i

(2 + 8i) + (30 - 6i) = 32 + 2i--- false

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  (9 + 4i) + 2(4  - 8i + 7i + 14)

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  9 + 4i + 8  - 16i + 14i + 28

(9 + 4i) + 2(4 + 7i)(1 - 2i) =  45+ 2i --- true

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Answer:

(-10, 12).

Step-by-step explanation:

A dilation with a scale factor of 2 centered at the origin expands distances from the origin by a factor of 2. If a point in the plane is represented by the coordinates (x, y), then the point obtained by a dilation centered at the origin with scale factor k is represented by (kx, ky).

So, if the original point is (-5, 6), then after the dilation of 2 centered at the origin, the new point is represented by (2 * -5, 2 * 6) = (-10, 12).

So the coordinates of (-5, 6) after a dilation of 2 centered at the origin are (-10, 12).

Answer:

So Gary ran the longest

Step-by-step explanation:

Gary ran for 22 minutes + 7 minutes = 29 minutes.

Herbert ran for 29 minutes - 12 minutes = 17 minutes.

So Gary ran the longest, followed by Sandy and then Herbert.

If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would  save in finance charges Round to the nearest ten dollars is $80.

Finance charge if bought on the first day

Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 7400  ×  0.011

Finance charge= $81.40

Finance charge if bought on the last day

Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 238.709677 ×  0.011

Finance charge= $2.625

Finance charge = $2.63

Savings = $81.40 - $2.63

Savings = $78.77

Savings = $80 ( Approximately)

Therefore the savings is $80.

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The equation of line passing through the points (-2, 4) & (4, 2) is :

y = -1/3 x + 6

The value of b = 6

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where m is the slope of the line and (x₁, y₁) is any point on the line.

To find the slope of the line, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two given points.

Plugging in the values for the given points, we get:

m = (2 - 4) / (4 - (-2))

m = -2 / 6

m = -1/3

Next, we can use one of the given points to write the equation in point-slope form:

y - 4 = -1/3 (x - (-2))

y - 4 = -1/3 x + 2

y = -1/3 x + 6

This is the equation of the line passing through the two given points (-2, 4) and (4, 2).

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Answer:

Step-by-step explanation:

To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin, you would need to double the x and y-coordinates of each vertex of the square.

Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:

(2a, 2b)

(2a, 2b + 2)

(2a + 2, 2b + 2)

(2a + 2, 2b)

So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.

To graph the image, you would plot each of the new vertices and connect them to form the image square.

The solution is given below.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

To graph the image of square CDEF after a dilation with a scale factor of 2, centered at the origin,

we would need to double the x and y-coordinates of each vertex of the square.

Assuming square CDEF has vertices at (a, b), (a, b + 1), (a + 1, b + 1), and (a + 1, b), the image of the square after the dilation would have vertices at:

(2a, 2b)

(2a, 2b + 2)

(2a + 2, 2b + 2)

(2a + 2, 2b)

So, the side length of the image square would be double the side length of the original square, and its overall shape would be the same.

To graph the image, we would plot each of the new vertices and connect them to form the image square.

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The measure of angle ∠T found using the law of sines is about 72°

The law of sines states that the ratio of the of the sine of an angle in a triangle to the length of the opposite side, is the same for the three angles in a triangle.

Mathematically, where the side lengths of the triangle are; a, b, c, and the corresponding opposite angles are ∠A, ∠B, and ∠C, we get;

[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]

The parameters in the question are;

AT = 28

AD = 37

m∠D = 46°

DT = a

Therefore, according to the law of sines, we get;

37/(sin∠T) = 28/(sin(46°))

Inverting both sides, we get;

(sin∠T)/37 = (sin(46°))/28

(sin∠T) = 37 × (sin(46°))/28

∠T = arcsine(37 × (sin(46°))/28) ≈ 72°

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Two other points on this line are (1, 1.5) and (2, 3)

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

This means that the slope (m) of the line is

m = 6/4

Evaluate

m = 1.5

For the other points, we have

f(2) = 2 * 1.5 = 3

f(1) = 1 * 1.5 = 1.5

So, we have (1, 1.5) and (2, 3)

Hence, the points are (1, 1.5) and (2, 3)

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Answer:

Cost $50.63

Step-by-step explanation:

To calculate the cost, we need to find out how many gallons of gasoline the car will consume in 450 miles. We can use the formula:

Gallons = Total miles / Miles per gallon

Gallons = 450 miles / 24 miles per gallon

Gallons = 18.75

Next, we multiply the number of gallons by the cost per gallon to get the total cost:

Total cost = Gallons * Cost per gallon

Total cost = 18.75 gallons * $2.70 per gallon

Total cost = $50.63

So, it will cost $50.63 to drive 450 miles when gasoline costs $2.70 per gallon and your car gets 24 miles per gallon.

The probability that their average length is less than 10 inches is; 5.71%

The formula for z-score is;

z = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

x' = 10 inches

μ = 9.7 inches

σ = 1.2 inches

n = 40

Thus;

z = (10 - 9.7)/(1.2/√40)

z = 0.3/0.1897367

z = 1.58

From online p-value from z-score calculator, we have;

P(z < 1.58) = 0.0571 or 5.71%

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The ratio of stars to red stripes is 50 to 7

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

Number of stars = 50

Red stripes = 7

White stripes = 6

Using the above as a guide, we have the following:

Ratio = Stars : Red stripes

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

Stars : Red stripes = 50 : 7

Hence, the ratio is 50 : 7

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Answer:

oranges

Step-by-step explanation:

20% of 460 = 92

30% of 340 = 102

The length of the ladder needed to reach the window to the nearest tenth of a foot is option (a). 17.0 feet.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given,

Length of the moat = 8 feet

Height of the window from the ground = 15 feet

Using the concept of right triangle, from the figure, length of the moat is the base and height of the window is the altitude.

Length of the ladder is the hypotenuse.

By Pythagoras theorem,

Length of the ladder = [tex]\sqrt{8^{2}+15^2 }[/tex] = [tex]\sqrt{289}[/tex] = 17

Hence the length of the ladder is 17.0 feet to the nearest tenth of a foot.

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Answer: That’s easy… The answer is -13

Step-by-step explanation: -2 x 3 + -7 = ?

-2 x 3 = -6

-6 + -7 = -13

since we know the number is doubling, so if say it was "x" right now so 30 minutes later will be "x" + 100 of "x", namely 2x, so that simply means the rate of growth is 100%.

[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ t=minutes\\ c=period \dotfill &30 \end{cases} \\\\\\ A=P(1 + 1.00)^{\frac{t}{30}}\implies A=P(2)^{\frac{t}{30}}\hspace{5em}f(x)=P(2)^{\frac{x}{30}}[/tex]

The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).

Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza

The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.

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STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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Answer:

a) $4096 b) $1884,8 ■■ im not 100% sure

Step-by-step explanation:

a) 3200×0.064×2=$4096 in intrest

b) 12,400×0.076×2=$1884,8 in intrest

On solving the provided question, we cans ay that the equation is 4(8x + 2) = 4(7x + 2 + x); when we put x = , LHS = RHS

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation is

4(8x + 2) = 4(7x + 2 + x)

32x + 8 = 28x + 8 + 8x

36x - 32x = 0

4x = 0

x = 0

when we put x = , LHS = RHS

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Answer:

Step-by-step explanation:

Martina has been given 5 bands and asked to place a vote for her favorite and second favorite bands. The number of different votes possible can be calculated using combinations.

A combination is a way of selecting items from a set, where order does not matter and repetition is not allowed. To find the number of combinations, we can use the formula:

C(n, k) = n! / (k! * (n - k)!)

where:

n is the number of items

k is the number of items being selected

! denotes factorial, which is the product of all positive integers up to that number

Step-by-step, the calculation is as follows:

Determine the number of items and the number of items being selected:

n = 5 (the number of bands)

k = 2 (the number of bands Martina is voting for)

Calculate the number of combinations using the formula:

C(n, k) = n! / (k! * (n - k)!)

C(5, 2) = 5! / (2! * (5 - 2)!)

C(5, 2) = 120 / (2 * 3!)

C(5, 2) = 120 / (2 * 6)

C(5, 2) = 120 / 12

C(5, 2) = 10

So, there are 10 different votes possible for Martina's favorite and second favorite bands from the list of 5 bands.

Answer: The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).

In this case, the function s(x) = 6/25 - x^2 has no restrictions on the input values for x, so the domain of the function is all real numbers.

Therefore, the domain of the function s(x) = 6/25 - x^2 is:

(-∞, ∞)

This means that the function can be evaluated for any real value of x.

Step-by-step explanation:

The statement that is true about the graphs is Graph A is a linear function because it has a constant rate of change

A graph is a pictorial representation of a function.

Given the graphs A and B, to determine which statement is true, we need to find the characteristics of each graph.

Comparing all the statements with the given characteristics of both graphs, we see that the statement that is true is Graph A is a linear function because it has a constant rate of change

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The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:

[tex]log a^b = blog a[/tex]

Using this rule, we can write the expression as:

[tex]r log a + y log c = log a^r + log c^y[/tex]

Now we can use the rule that says:

log a + log b = log ab

to combine the two logarithms:

[tex]log a^r + log c^y = log (a^r c^y)[/tex]

Therefore, the expression r log a + y log c simplifies to:

[tex]r log a + y log c = log (a^r c^y)[/tex]

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If 60 dogs are registered in Castroville, we can find the number of Golden Retrievers and Boxers by using the given percentages.

Number of Golden Retrievers = 0.45 x 60 = 27

Number of Boxers = 0.55 x 60 = 33

To find how many more Boxers there are than Golden Retrievers, we can subtract the number of Golden Retrievers from the number of Boxers:

Boxers - Golden Retrievers = 33 - 27 = 6.

Therefore, there are 6 more Boxers than Golden Retrievers in the group of 60 registered dogs in Castroville.

The given information only provides the percentages of Golden Retrievers and Boxers among registered dogs in Castroville, so we don't have enough information to directly calculate the percentage of all other dog breeds. However, we know that the total percentage of all dog breeds must add up to 100%. Since Golden Retrievers and Boxers make up 45% and 55% of the registered dogs, respectively, the percentage of all other dog breeds must be 100% - 45% - 55% = 0%. This means that there are no other registered dog breeds in Castroville, and all registered dogs belong to either the Golden Retriever or Boxer breed.

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The value of the length of  hypotenuse when base length is  11cm and angle is 24°:  12.04 cm

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

The length of hypotenuse = x

The length of base =  11 cm

The angle = 24°

It is known that,

cosФ = base/hypotenuse

         = 11/x

cos24° = 11/x

x = 11/cos24°

  = 12.4

Therefore, the length of the hypotenuse is approximately 12.04cm.

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In the experiment in which researcher randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention, this type of experiment design is a randomized block design where the pet types (dogs and cats) are the blocks.

Randomized block design is a type of experimental design that is used to control for the effects of extraneous variables. It involves dividing the subjects or treatments into groups, or blocks, that are similar with respect to the extraneous variable.

These blocks are then randomly assigned to the treatments being tested. By controlling for the extraneous variable in this way, the randomized block design can reduce error and increase the accuracy of the results.

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Answer:

answer B (Khan)

Step-by-step explanation:

A randomized block design where the pet types (dogs and cats) are the blocks

The number of rotational symmetries that the figure has would be C. 1 at 360 degrees.

The number of times the geometric figure is similar to the original figure after undergoing a full revolution is known as the order of rotational symmetry. The order of rotational symmetry is determined by how many times the rotated figure perfectly fits within the original figure.

When the Figure F is rotated, the only times that it can be rotated to be able to give the same figure of F, is once, and that once has to be a full revolution of 360 degrees.

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The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.

We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.

Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.

In a week there are 20 hours

So, in 4 weeks, there will be 80 hours

Take - home pay before deductions = 80 * $11.66 = $932.8

Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94

This is equal to ¢ 68094.

Hence, the monthly take-home pay is ¢ 68094.

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Answer:

= 7022cm

Step-by-step explanation:

The Perimeter of a rectangle =

[tex] = 2(l) + 2(w)[/tex]

From the question

L= 15.47m

w= 19.64m

therefore perimeter of a rectangle

=

[tex] = 2(15.47) + 2(19.64) \\ = 30.94 + 39.28 \\ = 70.22 m[/tex]

Also since rectangle are in centimetres

than if. 1 m = 100cm

than 70.22m = ?

therefore 70.22/1 = 100cm

=7022cm

therefore the Perimeter of a rectangle = 7022