14) Determine the base and height of the given parallelogram, and then find the area

If jack has three packs of gum and sam has 4 packs of gum, then the total amount of gum they have together is 7 packs.

What is the addition?

The addition is putting numbers together to make a sum or total. The plus sign + tells you to add two numbers. = is an equals sign. It shows that things on either side of it are equal.

We have given,

Jack has 3 packs of gum and Sam has 4 packs of gum.

To find the total number of packs of gum they have together, we simply add their individual amounts:

3 packs (Jack) + 4 packs (Sam) = 7 packs

Therefore, the total amount of gum they have together is 7 packs.

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Answer:

Step-by-step explanation:

To find the value of "a" in the equation y = a(x + 3)(x - 5), we can use the fact that the function passes through the point (6, 45).

Step 1: Substitute the x and y values of the point into the equation:

45 = a(6 + 3)(6 - 5)

45 = a(9)(1)

Step 2: Solve for "a":

45 = 9a

a = 45/9

a = 5

The value of "a" in the equation y = a(x + 3)(x - 5) is 5.

Answer:

$150.35

Step-by-step explanation:

Total commission taken from sale = $155,000 * 5% = $7,750.

Broker = $7,750 * 2% = $155.

Office assistant = $7,750 * 1% = $77.5.

Debby's profit = $7,750 - $155 - $77.5 = $7,517.5 * 2% = $150.35.

Answer:

rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.

Step-by-step explanation:

hopefully this is the answer you are looking for.

Answer:

Step-by-step explanation:

Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on.

Is the population of bacteria a function of the number of days? If so, is it linear? The population of bacteria is a function. The relationship is linear.

Answer:

$55.44 is the price of the sunglasses

Step-by-step explanation:

Price Of Sunglasses = $56

10% Discount = $5.6

So, $56-$5.6 = $50.4 <------ Applying Discount

10% of $50.4 = $5.04 <------ Price of Processing Fee for Discounted Price

$50.4+$5.04 = $55.44 <------ Total Price

The discounted price is $50.4 and we take 10% of that [discounted price] and we add it to the discounted price. 10% of that is $5.04. = $55.44

Answer:

$55.44

Step-by-step explanation:

56 - 56(0.10) = 50.40  price with 10% off

50.40 + 50.40(0.10) = 55.44   10% processing fee added to discounted price

The two solutions of the quadratic equations are 8,-4 and the negative solution -4

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: when 32 subtracted from the square of a number and the result is 4 times the number.

Let x be the number then we have

x²-32=4x

x²-4x-32=0

x²-8x+4x-32=0

x(x-8)+4(x-8)=0

(x-8) (x+4) =0

Thus the two solutions of the quadratic equations are 8,-4

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Check the picture below.

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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Answer:

Step-by-step explanation:

[tex]x_{1}[/tex] = - 5 , f( [tex]x_{1}[/tex] ) = 0 ;

[tex]x_{2}[/tex] = - 2 , f( [tex]x_{2}[/tex] ) = 0 ;

[tex]x_{3}[/tex] = 4 , f( [tex]x_{3}[/tex] ) = 0 ;

Answer:

Below

Step-by-step explanation:

12 + 3s + 9s + 2 =

(3s+9s) + (12+2) =

12s + 14           ( or   2 (6s+7)   )

Answer:

Let's call the measure of the first angle "x". Then, the equation can be written as:

x = 3y - 8

Since the angles are supplementary, their measures add up to 180 degrees, so:

x + y = 180

We can substitute the first equation into the second equation to solve for y:

3y - 8 + y = 180

4y = 188

y = 47

Now that we know the measure of y, we can substitute it back into the first equation to find x:

x = 3(47) - 8 = 133

So the measure of the larger angle is 133 degrees.

Repeatedly  sample variance from a small population without replacement leads to the outcomes in our sample being non-independent, as the same individuals may be chosen multiple times.

Repeatedly  sample variance from a small population without replacement can lead to skewed results, as the same individuals may be chosen multiple times. This can be problematic when the sample size is small, as the same individuals may be overrepresented in the sample. This can lead to outcomes that are not representative of the population and can lead to inaccurate results. As the same individuals are chosen multiple times, the outcomes in the sample are not independent; the outcomes of one individual can influence the outcomes of other individuals in the sample. This can lead to bias in the results and should be avoided when possible. When sampling from a small population without replacement, it is important to ensure that the sample size is large enough that the same individuals are not chosen multiple times, otherwise the results may be skewed or biased.

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Sampling repeatedly from a small population without replacement leads the outcomes in our sample to be dependent.

In dependent samples, subjects in one group do provide information about subjects in other groups.

The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,

⇒ f (x) = x³ + 4x² - 7x - 10

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

For a polynomial,

A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Now, We know that;

The standard polynomial is given by:

⇒ f (x) = a (x - p) (x - q) ...

Where, 'a' is leading coefficient and p, q, .. are zeroes.

Here, A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Hence, The polynomial is,

⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)

⇒ f (x) = (x + 5) (x + 1) (x - 2)

⇒ f (x) = (x + 5) (x² - 2x + x - 2)

⇒ f (x) = (x + 5) (x² - x - 2)

⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10

⇒ f (x) = x³ + 4x² - 7x - 10

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Answer:

x = 0.4

Step-by-step explanation:

1.5 * x = 0.6

x = 0.6 / 1.5

x = 0.4

Answer:

0.4

Step-by-step explanation:

To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.

First, we can divide both sides of the equation by 1.5 to isolate the variable:

1.5 * ? / 1.5 = 0.6 / 1.5

Simplifying, we get:

? = 0.4

Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.

The simplified expression 2-6/-2-4-12/6x-3 is given as follows:

-2 - 2x.

The expression for this problem is defined as follows:

[tex]2 - \frac{6}{-2} - 4 - \frac{12x}{6} - 3[/tex]

The division operation has a higher precedence over the subtraction operations, hence:

Hence the expression can be written as follows:

2 - (-3) - 4 - 2x - 3 = 2 + 3 - 4 - 2x - 3.

Then combining the like terms, which are the constant, the simplified expression is given as follows:

-2 - 2x.

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Answer:

x = 2/3

y = 5

Step-by-step explanation:

6x + y = 9

3x -4y = -18

Times the second equation by -2

6x + y = 9

-6x + 8y = 36

9y = 45

y = 5

Now put 5 in for y and solve for x

6x + 5 = 9

6x = 4

x = 2/3

Let's check

6(2/3) + 5 = 9

4 + 5 = 9

9 = 9

So, x = 2/3 and y = 5 is the correct answer.

Answer:

x = 1.523

Step-by-step explanation:

Given
[tex]\quad\quad e^{x-1} = 3^{2-x}[/tex]

we are asked to solve for x

Take natural logs on both sides:
[tex]\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)[/tex]substitute on left side of original eqn

[tex]\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\[/tex]

Therefore we get
[tex]\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)[/tex]

But ln(e) = 1

So we get
[tex]x - 1 = (2-x)\;\ln(3)\\\\[/tex]

So the expression becomes

[tex]x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)[/tex]

Add [tex]x\ln(3)[/tex] on both sides:

x + x ln(3) - 1 = 2ln(3)

Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1

x(1 + ln(3)) = 2 ln3 + 1

ln(1 + \ln(3)) = 2.09861

2ln(3) + 1 =3.1972

So we get

x(2.0986) = 3.1972

x = 3.1972/2.0986 = 1.52349

Rounded to 3 decimal places, the answer is 1.523

Answer:

314 ft^3

Step-by-step explanation:

The equation that needs to be set up is 1/3 × pi × r^2 ×h which r is the radius and h is the height. If we substitute 1/3 × pi × 5 × 12= 100 × pi. Once you finish the equation out by multiplying 100 and pi (3.14) It can be rounded to 314 ft ^3

The slope-intercept form of the linear equation is:

y = 7 + (7/3)*x

A linear equation in the slope-intercept form is:

y = a*x + b

So, to write the given line in that form, we just need to isolate the variable x.

We have the equation:

-7x + 3y = 21

3y = 21 + 7x

y = (21 + 7x)/3

y = 7 + (7/3)*x

That is the equation in the slope-intercept form.

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Answer:

Step-by-step explanation:

Answer:

To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.

To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.

AB^2 = BO^2 + AO^2 = 9 + 36 = 45

AB = sqrt(45) = 3 sqrt(5)

Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)

Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:

240° / 360° = 2/3 of the circumference

Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)

Finally, we can find the surface area of one engine part:

Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))

To paint 20 engine parts, the cost would be:

20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p

Since 1 pound is equal to 100 pence, the cost in pounds would be:

720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264

So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.

In the morning, the train went 170 miles. in the afternoon the train went 50 more miles. The Train ended up going 220 miles in total.

In the morning, the train traveled 170 miles.

In the afternoon, it traveled an additional 50 miles.

To find the total distance traveled by the train, we need to add the distance traveled in the morning and the distance traveled in the afternoon:

Total distance = Distance traveled in the morning + Distance traveled in the afternoon

Total distance = 170 miles + 50 miles

Total distance = 220 miles

So, the train ended up traveling a total of 220 miles.

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Answer:

Subtracting an expression is similar to distributing a -1 because it cancels out the numbers in the expression.

Step-by-step explanation:

Answer: To find the mean hourly wage, you need to sum up the total wages of all employees and then divide by the number of employees. The total hourly wage for 25 phone operators is 25 * $22.85 = $571.25. The total hourly wage for 5 supervisors is 5 * $27.25 = $136.25. The combined total is $571.25 + $136.25 = $707.50. The mean hourly wage for the 30 employees is $707.50 / 30 = $23.58. So, the answer is approximately $23.58.

Step-by-step explanation:

Step-by-step explanation:

x+4y=0

2x−y=18

​To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

x+4y=0,2x−y=18

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.

x+4y=0

Subtract 4y from both sides of the equation.

x=−4y

Substitute −4y for x in the other equation, 2x−y=18.

2(−4)y−y=18

Multiply 2 times −4y.

−8y−y=18

Add −8y to −y.

−9y=18

Divide both sides by −9.

y=−2

Substitute −2 for y in x=−4y. Because the resulting equation contains only one variable, you can solve for x directly.

x=−4(−2)

Multiply −4 times −2.

x=8

The system is now solved.

x=8,y=−2

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The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,

known as roots.

A quadratic equation is an algebraic expression in the form of variables and constants.

itsA quadratic equation has two roots as it's degree is two.

We know, The general form of a quadratic equation is x² + bx + c.

Let, y = x² + bx + c.

At, (0, - 2).

- 2 = 0 + 0 + c.

c = - 2.

At, (4, 0).

0 = 4² + 4b - 2.

0 = 14 + 4b.

b = - 7/2.

So, It is x² - (7/2)x - 2 = 0.

2x² - 7x - 4 = 0.

2x² - 8x + x - 4 = 0.

2x(x - 4) - 1(x - 4) = 0.

(x - 4)(x - 1) = 0.

So, the zeroes of the function are 4 and 1.

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The column vectors of the given matrix is linearly dependent as determinant is equal to zero.

To find the column vectors of the matrix is linearly independent or linearly dependent.

Value of the determinant is equal to zero it implies linearly dependent.

And if determinant is not zero it is linearly independent.

Let 'A' be the given matrix is:

A = [tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

Determinant of A

= 1 ( 8 - (-12)) - 0( -16 -0 ) + 5 (-4 -0 )

= 1 (20 ) - 0  -20

= 20 -20

= 0

Here det(A) = 0

Therefore, the column vectors of the matrix is linearly dependent as det(A) = 0.

The above question is incomplete, the complete question is:

Are the column vectors of this matrix linearly independent or linearly dependent? show all explanations or computations.

[tex]\left[\begin{array}{ccc}1&0&5\\-2&1&-6\\0&2&8\end{array}\right][/tex]

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Answer:

Geometry in Mathematics is the study of shape and figures.

Answer:

Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.

There, ages are as follows:

Madhu's grandfather age = 72 years

Madhu father's age = 46 years

Madhu age = 17 years

Madhu's father is 26 years younger than Madhu's grandfather and 29 years older than Madhu.

The sum of the ages of all three is 135 years.  

Therefore, let's find their ages as follows:

Let

Madhu's grandfather age = x

Madhu father's age = x - 26

Madhu age = x - 26 - 29 = x - 55

Therefore,

x + x - 26 + x - 55 = 135

3x = 135 + 81

3x = 216

divide both sides by 3

x = 216 / 3

x = 72

Hence,

Madhu's grandfather age = 72 years

Madhu father's age = 72 - 26 = 46 years

Madhu age = x - 26 - 29 = 72 - 55 = 17 years

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