Find three consecutive even integers such that the sum of the first, twice the second, three times the third is -76. What is the number?
(the three numbers is the same number)

Answer:

x=4 and y=5

Step-by-step explanation:

The given system of equations are

[tex]2x+6y=38[/tex]

[tex]5x-y=15[/tex]

The matrix form is

[tex]\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]

Let as assume

[tex]A=\begin{bmatrix}2&6\\ \:5&-1\end{bmatrix}[/tex]

[tex]X=\begin{bmatrix}x\\ \:y\end{bmatrix}[/tex]

[tex]B=\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]

then,

[tex]AX=B[/tex]

[tex]X=A^{-1}B[/tex]

We know that,

[tex]\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}^{-1}=\frac{1}{\det \begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}}\begin{bmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{bmatrix}[/tex]

[tex]A^{-1}=\frac{1}{\det \begin{bmatrix}2&6\\ 5&-1\end{bmatrix}}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]

[tex]A^{-1}=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}[/tex]

[tex]X=\frac{1}{-32}\begin{bmatrix}-1&-6\\ -5&2\end{bmatrix}\begin{bmatrix}38\\ \:15\end{bmatrix}[/tex]

[tex]X=\frac{1}{-32}\begin{bmatrix}\left(-1\right)\cdot \:38+\left(-6\right)\cdot \:15\\ \left(-5\right)\cdot \:38+2\cdot \:15\end{bmatrix}[/tex]

[tex]X=\frac{1}{-32}\begin{bmatrix}-128\\ -160\end{bmatrix}[/tex]

[tex]\begin{bmatrix}x\\ \:y\end{bmatrix}=\begin{bmatrix}4\\ 5\end{bmatrix}[/tex]

Therefore, the value of x is 4 and value of y is 5.

Answer:

The ratio of their areas is 4:9

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ---> the scale factor

x ---> the area of the smaller polygon

y ---> the area of the larger polygon

[tex]z^2=\frac{x}{y}[/tex]

we have

[tex]z=\frac{2}{3}[/tex] ---> the scale factor is given

substitute

[tex](\frac{2}{3})^2=\frac{x}{y}[/tex]

[tex]\frac{4}{9}=\frac{x}{y}[/tex]

Rewrite

[tex]\frac{x}{y}=\frac{4}{9}[/tex]

therefore

The ratio of their areas is 4:9

Answer:

f(x) = (2x + 1)(2x − 1)

Explanation:

As we can see from the above function f(x) = 4[tex]x^{2}[/tex] − 1, we need to find x-intercept, i.e., the value of x where this function's value is zero.

So let us Equate the function with zero

4[tex]x^{2}[/tex] - 1 = 0 => 4[tex]x^{2}[/tex] = 1 => [tex]x^{2}[/tex] = 1/4 => x = [tex]\sqrt{1/4}[/tex]

Hence we get 2 values of x, i.e., +1/2, and -1/2.

So now we need to check out the functions which are zero at this values of x, so let us substitute values of x in each and every option and see the values of functions.

Option A - f(x) = (4x + 1)(4x − 1) = 3, -3

Option B - f(x) = (2x + 1)(2x − 1)  = 0

Option C - f(x) = 4(x2 + 1)  = 5

Option D - f(x) = 2(x2 − 1) = -3/2

Hence answer is Option B

Answer:

Okay, so the first one is" The point (0, 2.50) is on the graph" second one is "The graph has a y-intercept but no x-intercept" And the third one would be "The graph increases from left to right"

Good evening ,

Answer:

x²-9x+12 = (x - (9/2))²- (33/4)

Step-by-step explanation:

Look at the photo below for the details.

:)

In order to find the variables p and q in the equation x^2 - 9x + 12 = (x-p)^2 - q, we first complete the square on the left-hand side which leads us to determine that p=4.5 and q=32.25.

The original equation given is x^2 - 9x + 12 = (x-p)^2 - q. To find the values of p and q, we need to rewrite the left-hand side of the equation in the format of (x-p)^2. This can be done through a process known as completing the square. Looking at the equation x^2 - 9x + 12, we have a perfect square x^2 - 9x + (9/2)^2 = (x-4.5)^2. However, remember, we added (9/2)^2 to both sides, so we have (x-4.5)^2 = x^2 - 9x + 12 + 20.25. Simplifying, (x-4.5)^2 = x^2 - 9x + 32.25, which is our original equation format. Thus, p=4.5 and q=32.25.

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Answer:

Tom paid $51 renting the bike for 5 hours

Step-by-step explanation:

Given:

Oceanside bike rental charges $11 plus $8 per hour for renting.

Tom paid $51 to rent a bike.

To find the number of hours Tom rented the bike for.

Solution:

Let Tom rent the bike for =[tex]x[/tex] hours.

Hourly rate of renting = $8 per hour

Using unitary method find cost of renting for [tex]x[/tex] hours.

If renting for 1 hour costs = $8

Then for [tex]x[/tex] hours, the cost in dollars will be = [tex]8x[/tex]

Fixed charges = $11

∴ Total cost of renting a bike in dollars for [tex]x[/tex] hours will be given as:

[tex]8x+11[/tex]

Tom paid a total charge of = $51.

So, we have:

[tex]8x+11=51[/tex]

Subtracting both sides by 11.

[tex]8x+11-11=51-11[/tex]

[tex]8x=40[/tex]

Dividing both sides by 8.

[tex]\frac{8x}{8}=\frac{40}{8}[/tex]

∴ [tex]x=5[/tex]

Thus, Tom rents the bike for 5 hours.

Answer:

the square root of -1 is i

Step-by-step explanation:

Answer:

[tex]\large\boxed{\sqrt{-1}=i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\\i-\text{immaginary unit}\ \left(i^2=-1\right)\\\\\text{It's a complex number.}[/tex]

Answer:

A. 1.0797

Step-by-step explanation:

Given the equation,

3e^2x+2=28

To solve for x, first we move 2 to the other side of the equation.

3e^2x = 28-2

3e^2x = 26

Dividing both sides by 3

e^2x = 26/3

e^2x = 8.67

Taking the natural logarithm if both sides

ln(e^2x) = ln8.67

2x = ln8.667

2x = 2.1595

x = 2.1595/2

x = 1.0797

Answer:

There are three decimal places in the final answer.

Step-by-step explanation:

We have to calculate the expression 4.2 × 12.3 × 14.6, in which the floor dimensions are 12.3 ft by 14.6 ft. which I have to cover with tiles and each square foot of tile costs $4.20.

So, the area of the floor is (12.3 × 14.6) sq. ft. = 179.58 square feet.

Now, the cost of covering the floor with tiles will be = $(179.58 × 4.2) = $754.236.

Therefore, there are three decimal places in the final answer. (Answer)

Matched pairs before and after design?

The design of this experiment is a Within-Subjects Design, where each participant is exposed to both types of signs and their reaction times are compared.

The design of this experiment most closely resembles a Within-Subjects Design. In this design, each participant is exposed to both conditions, in this case, the No Left Turn and the Left Turn Only signs. The participants' reaction times to each sign are measured and compared within the same group of participants, allowing for a direct comparison between the two types of signs.

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Answer:

False

Step-by-step explanation:

The only vertical angles shown are 1 and 3. The other pair is 2 and 4

Answer:

Step-by-step explanation:

Intercept c = 21 and slope m = -5

y = mx + c

y = -5x + 21

Answer:

b

Step-by-step explanation:

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of bracelets sold = 5

The number of necklaces sold = 1

Cost of the necklace = $22.50

Cost of the bracelets = x

The amount left = $150

The total amount in the account after selling them = $235

Now,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

Thus,

The equation can be used to find the cost of the bracelets.

5x + 22.50 + 150 = 235

Learn more about expressions here:

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Answer:

1.25

Step-by-step explanation:

x+1/8=1.375

x=1.375-0.125

x=1.25

Answer: 1.25

Move all terms not containing  x  to the right side of the equation.

Exact Form:

x  =  54

Decimal Form:

x  =  1.25

Mixed Number Form:

x  =  1  1/4

Hope this helps

Answer:

12 degrees.

Step-by-step explanation:

8 - (-4) = 12. So, the temperature increased by 12 degrees.

The temperature increased by 12 degrees from -4 to 8.

The question is asking for the temperature change from -4 to 8 degrees. To find the increase in temperature, you subtract the initial temperature from the final temperature. In this case, 8 (final temperature) minus (-4) (initial temperature), equals 12°C. Hence, the temperature increased by 12 degrees.

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Answer: Function

Step-by-step explanation: A function is a special type of relation and for a relation to be a function, each x-term must correspond with exactly 1 y-term.

The easiest way to determine whether a relation is a function is to look at the x-coordinate of each ordered pair. If any of our ordered pairs have the same x-coordinate with a different y-coordinate, then our relation is no a function.

Since none of our x-terms repeat with different y-terms, this is a function.

Answer:

x=-11

Step-by-step explanation:

11-3x=44

3x=11-44

3x=-33

x=-33/3

x=-11

Answer:

2.480 is test statistic

Step-by-step explanation:

Given that the claim is most adults would ease all of their personal information online if they could.

[tex]H_0: p = 0.50\\H_a: p >0.50[/tex]

(right tailed test)

p difference = 0.05

Std error=

[tex]\sqrt{pq/n} =\sqrt{0.5*0.5/609}[/tex]

0.0202

p difference / std error

Test statistic = p difference / std error

= [tex]\frac{0.05}{0.0202} \\=2.480[/tex]

Answer:

2x^2-16x+34

Step-by-step explanation:

Since Y is equal to -5

And  you substitute -5 in the equation.

You now have -5=2x^2-16x+29

Add 5 to both sides

5-5=2x^-16x+29+5

The solution of the system of equations will be given as x = 4 ± i.

The solution of the equation means the value of the unknown or variable.

The equations are given below.

y = – 5                      ....1

y = 2x² – 16x + 29    ....2

From equation 1 and 2, we have

2x² – 16x + 29 = –5

2x² – 16x + 34 = 0

x² – 8x + 17 = 0

Then the value of x will be

[tex]\rm x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4 * 1 * 17}}{2*1}\\\\x = \dfrac{8\pm \sqrt{-4}}{2}\\\\x = \dfrac{8 \pm 2\iota}{2}\\\\x = 4 \pm \iota[/tex]

More about the solution of the equation link is given below.

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Answer:

yes

Step-by-step explanation:

it is possible that a body can be moving and at rest at the Same time. this is relative motion. an object that seem to be in motion for one subject can be stationary for another.

For example, A passenger in a bus. he/she is moving for a person walking on the pathway. but for the passenger next to him/her, they are at rest.

Answer:

Yes

Step-by-step explanation:

It is possible if you take into account different points of reference.

If you are in a car, sitting on a seat, while the car is moving, you are not moving with respect with the car. Since the car is moving with respect to the ground, you are moving with respect to the ground.

If you think bigger, you are always in motion. You may be standing in a position not moving at all with respect to the ground, but since the Earth is moving around the sun, you are moving with respect to the sun.

Answer:

Step-by-step explanation:

30 lbs in 3 hrs....

30/3 = 10 lbs per hr <==

Answer:

10 pounds

Step-by-step explanation:

if you divide 30 by 3 you will get 10 and becuase there are three hours you will have the answer as 10

30÷3=10

10×3=30

Answer :The value of x when log(x) = -5 is 0.00001.

Step-by-step explanation:

Answer: [tex]x=2[/tex]

Step-by-step explanation:

Given a System of linear equations, the solution of the system is the point [tex](x,y)[/tex] in which the lines intersect, where "x" is the x-coordinate and "y" is the y-coordinate.

Having the following System of equations:

[tex]\left \{ {{9x - 6y = 12} \atop {3x + 2y =8}} \right.[/tex]

You can use the Elimination method to find the value of "x":

-Multiply the second equation by 3.

- Add the equations.

- Solve for "x".

Then, you get:

[tex]\left \{ {{9x - 6y = 12} \atop {9x +6y =24}} \right.\\.......................\\18x=36\\\\x=\frac{36}{18}\\\\x=2[/tex]

Answer:

Step-by-step explanation:

10 5/6 km...in 5 days

(10 5/6) / 5 =

(65/6) / 5 =

65/6 * 1/5 =

65/30 =

2 1/6 kilometers per day <===

8 ÷ 3 = 2 2/3 miles

yeeeeeeeee

Answer:

2.66 miles every hour

Step-by-step explanation:

8/3

The taxable amount was $80.86

Step-by-step explanation:

Given,

Sales tax = .07

Total grossed = $1236.00

Let,

x be the price before sales tax, therefore,

Amount of sales tax = 0.07x

Price before sales tax + Sales tax = Total amount grossed

x+0.07x = 1236

1.07x=1236

Dividing both sides by 1.07

[tex]\frac{1.07x}{1.07}=\frac{1236}{1.07}\\x=1155.14[/tex]

Taxable amount = Total amount grossed - Price before tax

Taxable amount = 1236 - 1155.14 = $80.86

The taxable amount was $80.86

Keywords: subtraction, addition

Learn more about subtraction at:

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Answer:

$80.86 was taxed

Step-by-step explanation:

Answer:

The denominator of the fraction is 2x and the answer is a= -[tex]\frac{b}{2x}[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation of the form:

ax²+bx+c

The axis of symmetry of the parabola is given by:

[tex]x= \frac{-b}{2a}[/tex]

From here, we must clear the value of a.

For this, we follow the following steps:

1) Pass 2a multiplying to the other side of the equation:

2ax=-b

2) Clear the value of a by passing 2x to divide:

[tex]a= \frac{-b}{2x}[/tex]

Answer:

B.

a= -b/2x

Step-by-step explanation:

Answer:

The area of each slice of cake is [tex]\frac{25}{12}\pi\ in^2[/tex]

Step-by-step explanation:

step 1

Find the area of the complete cake

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=\pi (5)^{2}[/tex]

[tex]A=25\pi\ in^2[/tex]

step 2

Find the area of each slice of cake

Remember that the area of complete circle subtends a central angle of 360 degrees

If you cut the cake into 12 equal slices

then

the central angle of each slice is equal to [tex]\frac{360^o}{12}=30^o[/tex]

so

Using proportion

Find out the area of each slice for a central angle of 30 degrees

[tex]\frac{25\pi}{360^o}=\frac{x}{30^o} \\\\x= \frac{25\pi}{360^o}(30^o)\\\\x=\frac{25}{12}\pi\ in^2[/tex]

Note This problem could be solved by directly dividing the area of the circle by 12, however, proportions and concepts of central angle were applied for didactic purposes

Each slice of the 10-inch diameter cake, cut into 12 equal slices, has an area of approximately 6.54 square inches.

To find the area of each slice of the cake, we need to calculate the area of the entire cake first and then divide it by 12 since the cake is divided into 12 equal slices.

The formula for the area of a circle is: Area = πr².

Given the diameter of the cake is 10 inches, we first need to find the radius: radius = diameter / 2 = 10 / 2 = 5 inches.

Now, calculate the area of the entire cake:

Area of the full cake = π × (5 inches)² = 25π square inches.

Since the cake is cut into 12 equal slices, the area of each slice is:

Area of each slice = (25π) / 12 = 25π / 12 ≈ 6.54 square inches.

Therefore, each slice of cake has an area of approximately 6.54 square inches.