( Solving Linear Equations in One Variable )

What is the solution of the equation? Show your work.

1/4(2x + 1.2) = 3(0.7x + 3) - 5 1/2

Answer:

y=5x

Step-by-step explanation:

y=ax

use any value of x and y from the table

I chose (2,10)

10=2a

10/2=a

a=5

The outline that that illustrate how k values change so that the solutions are the ones in the question are as follows

(a) The number line solution contains zero

Using algebra, we have;

The given quadratic inequality is; -x² + 4 ≥ x + k

The number line solution is the expression of the solution on the number line.

We have;

-x² + 4 ≥ x + k

-x²  - x + 4 - k ≥ 0

Dividing by (-1), we get;

x² + x - 4 + k ≤ 0

When - 4 + k = -2

k = 2, we get;

x² + x - 4 + 2 ≤ 0

x² + x - 2 ≤ 0

(x - 1)·(x + 2) ≤ 0

Given that the result of the product is less than zero, we have;

((-3) - 1)·((-3) + 2) > 0

Therefore, the solution are;

x ≤ 1, or x ≥ -2

Which gives

-2 ≤ x ≤ 1

The solution of the above inequality includes 0 as shown in the attached number line

The graph of the inequality is plotted using MS Excel, showing the solution set, of -2 ≤ x ≤ 1

(b) There are no solution to the inequality

In the present case, we have;

((-1)² - 4×(-1) × (4 - k) <  0

17 - 4·k < 0

[tex]k > \dfrac{17}{4}[/tex]

Let k = 5, we have;

-x² + 4 ≥ x + k

-x² - x + 4 - 5 ≥ 0

-x² - x  -1 ≥ 0

The discriminant, is (1² - 4×(-1)×(-1)) = -3 < 0, therefore, there are no real

roots to inequality, and -x² - x  -1 is not equal to zero.

Please find attached the graph of the function, which does not intersect with the x-axis, and therefore, has no values at which y = 0

(c) The solution is a single number

-x² + 4 ≥ x + k

When k = x + 5, we have;

0 ≥ x² + 2·x + 1

0 ≥ (x + 1)²

Therefore;

The only solution is; x = -1

Using diagrams:

Please find attached the solution of the function on the number line

The graph of the function showing only one intercept is attached

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The Correct choice is ~

[tex]\boxed{y = \bigg({\dfrac{1}{2} \bigg) }^{x - 3} + 1}[/tex]

[tex]\\ \sf\longmapsto y=\left(\dfrac{1}{2}\right)^{x-3}+1[/tex]

Graph attached

Answer:

Option A

Step-by-step explanation:

Answer:

2x-7

Step-by-step explanation:

let the no be X

twice the no =2X

diminished by 7= 2X-7

Answer:

C)2x - 7..................

Answer:

P and R

Step-by-step explanation:

P and R are similar because R is the same thing as P but 2 times bigger.

Answer:

3

Step-by-step explanation:

To calculate the amount that Mary pays in state income tax, we need to find 8% of her annual salary.

Given that Mary's annual salary is $147,362, we can calculate the state income tax as follows:

State Income Tax = (8/100) * Annual Salary

State Income Tax = (8/100) * $147,362

State Income Tax = $11,788.96

Therefore, Mary pays $11,788.96 in state income tax.

The correct answer is C) $11,788.96.

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Answer:

45 miles per hour.  270 divided by 6 is 45 there.

Step-by-step explanation:

Answer:

#1

Slope: 1/2

Y Intercept: -3

#2

Slope: -3

Y Intercept: 2

Answer:

(0,0) (3,2) and (-2,-2) (4,2)

Step-by-step explanation:

To find the slope, you do [tex]\frac{y_{1}-y_{2} }{x_{1}-x_{2}}[/tex], which would work for both.

2-0/3-0=2/3

2-(-2)/4-(-2)=2+2/4+6=2/3

Answer:

I hope this helps.

Step-by-step explanation:

The quotient of 5 divided by q minus the product of 5 and q.

Answer: (5/q-5q)

The product of 5 and the difference of q minus 5.

Answer: (5(q-5)

The quotient of q divided by 5 plus the product of 5 and q.

Answer: (q/5+5q)

The sum of 5 and the product of 3 times q.

Answer: (5+3q)

The type of energy transfer that Leana is seeing as a result of steam rising is radiation.

Radiation is:

The steam rising from the tea is energy and it shows energy moving from the tea to the air. There is space between the tea and the air which means that it is radiation that the energy transfer is using as a conduit.

In conclusion, this statement describes radiation.

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Answer:

t is a right angle q is a vertex of a right angle

Answer:

He did not simplify correctly and forgot to place the decimal point correctly.

Step-by-step explanation:

To simplify the equation, one needs to divide both sides of the equal sign by 5.

i.e 5.25/5=5/5

Here we find 1.05=1

Note the placement of the decimal point.

Answer:

2

Step-by-step explanation:

Answer:

x = 1

y = -3

Step-by-step explanation:

There are 2 ways, in this case the best way is by substitution so:

y = x - 4

y = -3x

basically you replace one of the unknown numbers in one of the equations so the equation will have only one unknown number.

y = -3x

so that means that

-3x = x - 4

you solve the equation:

-3x - x = -4

-4x = -4

x = -4 : -4

x = 1

Now we know that x is 1 so now we find out what is y

y = 1 - 4

y = -3

The average rate of change of the function is -59.4

The formula for calculating the rate of change of the function is expressed as:

[tex]f'(x)=\frac{f(b)-f(a)}{b-a}[/tex]

Given the function

[tex]f(x)=120(0.1)^x\\f(0) = 120(0.1)^0\\f(0)=120\\[/tex]

Get the value of f(2)

[tex]f(2)=120(0.1)^2\\f(2) = 120(0.1)^2\\f(2)=1.2\\[/tex]

Substitute into the formula to have:

[tex]f'(x)=\frac{1.2-120}{2-0}\\f'(x)=\frac{118.8}{2} \\f'(x)= -59.4[/tex]

Hence the average rate of change of the function is -59.4

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$6.60 because 6.00 + 0.60 = 6.60

Answer:

See below.

Step-by-step explanation:

Hi there!

We want to find the equation of the line that has a slope (m) of 1 and that passes through the point (-10, -6)

There are 3 ways to write the equation of the line:

Since we are given both a point and a slope in this situation, it makes sense to write the equation in point-slope form.

Let's label the values of everything we were given to avoid confusion and mistakes:

m=1

[tex]x_1=-10\\y_1=-6[/tex]

Now substitute these values into the equation (note: we have NEGATIVE numbers, while the formula gives SUBTRACTION, which is why we're subtracting a negative)

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y--6=1(x--10)[/tex]

Simplify:

y+6=1(x+10)

The equation can be left as this, or it can be converted into slope-intercept form if you wish.

In that case, we would distribute 1 to each number on the right side.

y+6=x+10

Then, we'll isolate y on one side. Subtract 6 from both sides.

y=x+4

You can also convert it into standard form if you would prefer it that way. To do that, start with slope-intercept form, which we earlier found as y=x+4

In standard form, x and y are on the same side. So subtract x from both sides to move it

-x+y=4

Remember we don't want a (the coefficient in front of x) to be negative. In order to flip the sign, multiply both sides by -1

x-y=-4

Therefore, the answer can be written as y+6=1(x+10), y=x+4, or x-y=4.

Hope this helps!

Answer:

5 would be the answer.

Step-by-step explanation:

13 divided by 3(weeks) = 4.3

4.3 x 5 = 21.

= 5.

Answer:

6z-30 :D

Step-by-step explanation:

Step-by-step explanation:

The perimeter of a square is just all the sides added up together. To do this we can make an equation.

2(z-5) + 2(2z - 10)

This represents two sides with different lengths two times. To solve, you first use the distributive property to multiply z-5 by 2.

2z - 10 + 2(2z - 10)

We then use the distributive property by multiplying 2z - 10 by 2.

2z − 10 + 4z − 20

We then combine 2z and 4z to get 6z.

6z − 10 − 20

Subtract 20 from 10 to get -30.

6z-30.

Answer: 21120 feet.

Step-by-step explanation: We start with the fraction 1/180, found by putting 20 seconds over one hour. Then, we need to get the amount of miles the speed of sound travels in 20 seconds. We can use the fraction above as a ratio to get it. 720/1 x 1/180 = 4 miles. Then, we'll just do 4 times 5280, which is 21120.

The distance travelled by sound in 20 seconds is 21120 feet.

In unit time the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time.

Given that,

The speed of sound = 720 miles per hour.

According to given condition,

1 hour = 720 miles

Since, 1 hour = 60 minutes

60 minutes = 720 miles

1 minute = 12 miles.

1 minute = 60 seconds

60 second = 12 miles

1 second = 12 / 60  = 1/5 miles

20 second = 20 / 5 = 4 miles

According to given condition,

1 mile = 5280 feet

Therefore,

20 second = 5280 x 4 = 21120 feet

The distance travelled in 20 seconds is 21120 feet.

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No, an object can't be reflected over a line without changing its position.

A Reflection is a transformation representing a flip of a figure.

Given that an object can be Reflected over a line without moving its position,

There are certain rules for reflection of figures,

Using these rules, a point is reflected, so it's not possible for an object to be reflected without changing position.

Hence, an object can't be reflected over a line without changing its position.

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The number of rows that would be returned from the cross join of tables A and B is 144 rows.

The cross join of table A and table B is the cartesian product of A and B.

Since table A = 8 rows and table B = 18 rows, the cartesian product of the rows is 8 × 18 = 144 rows.

So, the number of rows that would be returned from the cross join of tables A and B is 144 rows.

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