Find the equation of the line specified.
The slope is -7, and it passes through ( 5, -3).

a.
y =  -7x - 3
c.
y =  -14x + 32
b.
y =  -7x + 32
d.
y =  -7x - 38




 

Please select the best answer from the choices provided

The scientific notation for 710,000 is [tex]7.1 \times 10^5[/tex].

Identify the significant digits:

In 710,000, the significant digits are “7.1”.

Determine the power of 10:

To convert 710,000 into a number between 1 and 10 times a power of 10, you notice that moving the decimal point 5 places to the left gives “7.1”.

This is because:

[tex]710,000 = 7.1 \times 100,000 = 7.1 \times 10^5[/tex]

Write the number in scientific notation:

Combine the significant digits with the power of 10.

[tex]7.1 \times 10^5[/tex].

Answer:

2400

Step-by-step explanation:

Given : The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each.

To Find: If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?

Solution:

No. of faces of first die = 6

No. of faces of second die = 4

No. of faces of third die = 10

No. of faces of fourth die = 10

Now we are supposed to find the the number of possible outcomes exist.

So, Number of possible outcomes if all the dice are thrown together :

= [tex]6 \times 4 \times 10 \times 10[/tex]

=[tex]2400[/tex]

Hence there are 2400 possible outcomes if all the dice are thrown together and their combination dictates a certain outcome of the game.

Answer:

Given the data, the pool has a diameter of 20 feet, so, R=10ft.

The pool cover expands 12 inches beyond the pool, so, 12in.= 1 foot

Therefore, the radius of the pool cover will then be: 10+1= 11ft.

ANSWER A (pool cover)) r² π = 11² π = 121 π ft²

A.)= 121 π ft²

ANSWER B (rope)) l = 2 r π = 2 · 11 π = 22 π ft.

B.)=  22 π ft

Step-by-step explanation:

I got a 100% on it on founders edtell

Answer:

D.

Step-by-step explanation:

:)

Answer:

Increase in price per mint is 2.5 cents .

Step-by-step explanation:

The price of mints is raised from 5 cents each to 15 cents for two.15 cents is the rice in price for two mints .Hence rise in price for each mint is 15÷2=7.2 cents.

Rise  in price for each mint = 7.2-5=2.5cents.

Percent increase = [tex]\frac{2.5}{5} (100)=50[/tex]

There is 50% increase in price per mint.

Answer:

False; only true for postulates!!!

Step-by-step explanation:

On BYU :)

To use the linear combination method and addition to eliminate the y-terms, the second equation should be multiplied by 4.

An equation is like a relationship between two or more variables. It is expressed in equal to form. Equation of two variables looks like: ax+ by=c.

It is solved to find the value of variables.

The given equations are 7x+16y= -2 and 9x-4y=22 and we have to solve using linear combination method.

First we have to change  -4y to -16y because after we have to do addition so we will multiply the second equation by 4 which makes the equation as under:

36x-16y=88

Adding equation 1 and 2

7x+16y+36x-16y=-2+22

42x=20

x=20/42

x=10/21

Put the value of x in 7x+16y=-2

7(10/21)+16y=-2

10/3+16y=-2

16y=-2-10/3

16y=-16/3

y=-1/3

Hence to solve the equations we need to first multiply second equation by 4 which is option D.

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We are given the two functions:

f(x) = 2x + 7

g(x) = 6x – 5

Part A. Find (f + g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 2 x + 7 + 6 x – 5

(f + g)(x) = 8 x + 2

Part B. Find (f ⋅ g)(x)

(f ⋅ g)(x) = f(x) ⋅ g(x)

(f ⋅ g)(x) = (2 x + 7) (6 x – 5)

(f ⋅ g)(x) = 12 x^2 – 10 x + 42 x – 35

(f ⋅ g)(x) = 12 x^2 + 32 x – 35

Part C. Find f[g(x)]

f[g(x)] = 2 (6 x – 5) + 7

f[g(x)] = 12 x – 10 + 7

f[g(x)] = 12 x - 3

In mathematics, an exclamation point represents a factorial, meaning the product of an integer and all the positive integers below it. For example, 5 factorial, or 5!, is 5 x 4 x 3 x 2 x 1 = 120. Unlike exponentials, factorials involve consecutive multiplication of integers.

In mathematics, the exclamation point is used to represent a factorial. Factorial indicates the product of an integer and all the positive integers below it. For instance, 5! would be 5 x 4 x 3 x 2 x 1 =  120. This calculation method is a significant concept especially in exponential arithmetic.

Contrary to exponential notation, factorials do not deal with the concept of powers or repeated multiplication of the same number. Instead, they focus on consecutive multiplication of descending positive integers. For example, 3! is evaluated as 3 x 2 x 1 = 6, instead of 3 x 3.

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Answer:

Option B is correct.

(1 , -5) lies on the graph.

Step-by-step explanation:

Given the points (4,1) and (-2 , -11)

First find the linear equation for the given points.

Equation of line for two points [tex](x_1, y_1)[/tex] and  [tex](x_2, y_2)[/tex]

is given by:   [tex]y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)[/tex]

Substitute the given points (4,1) and (-2 , -11)  in above equation to find the equation of line:

[tex]y-1=(\frac{-11-1}{-2-4})(x-4)[/tex]

or

[tex]y-1=(\frac{-12}{-6})(x-4)[/tex]

or

[tex]y-1=2(x-4)[/tex]

Using distributive property on RHS ( i.e,  [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex] )

we have;

y -1 = 2x-8

Add 1 to both sides of an equation;

y-1+1 = 2x-8+1

Simplify:

y = 2x -7

Therefore, the equation of line for the given point is: y =2x - 7     ....[1]

To find which points lies on the graph ( i.e, Line)

Substituting the given options in equation [1] we have;

A . (1,1)

Put x =1 and y =1

[tex]1 = 2\cdot 1 -7 = 2-7[/tex]

1 = -5 which is not true.

Similarly

B. for (1, -5)

[tex]-5= 2\cdot 1 -7 = 2-7[/tex]

-5 = -5 which is true.

C. for (1, 2)

[tex]2= 2\cdot 1 -7 = 2-7[/tex]

2 = -5 which is not true.

And

D.  For (1 , -7)

[tex]-7= 2\cdot 1 -7 = 2-7[/tex]

-7 = -5 which is also not true.

Therefore, the only point which lies on the  line graph [1] is; (1 ,-5)

The possible rational roots are given by the ratio of the constant term to the leading coefficient. That is [tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on and this can be determined by using the arithmetic operations.

Given :

Polynomial Equation -- [tex]2x^3+5x^2-8x-20=0[/tex]

The following steps can be used in order to determine the rational roots of the given polynomial equation:

Step 1 - Write the given polynomial equation.

[tex]2x^3+5x^2-8x-20=0[/tex]

Step 2 - The coefficient of [tex]x^3[/tex] is 2. So the factors of 2 are [tex]\pm[/tex]1, [tex]\pm[/tex]2.

Step 3 - The constant term of the given polynomial is -20 and the factors of the constant term are  [tex]\pm[/tex]1,  [tex]\pm[/tex]2,  [tex]\pm[/tex]5,  [tex]\pm[/tex]10,  [tex]\pm[/tex]20.

Step 4 - The rational roots are given by the ratio of the constant term to the leading coefficient. That is,

[tex]\pm[/tex]1/1, [tex]\pm[/tex]1/2,  [tex]\pm[/tex]1/5,  [tex]\pm[/tex]1/10,  [tex]\pm[/tex]1/20, and so on.

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Answer:

(D)[tex]96^{\circ}=(arc)BC[/tex]

Step-by-step explanation:

It is given from the figure that m∠BAC=48° and arcAC=110°.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Now, using the above property, we have

[tex]m{\angle}BAC={\frac{1}{2}}(arc)BC[/tex]

Substituting the given values, we get

[tex]48^{\circ}=\frac{1}{2}(arc)BC[/tex]

[tex]96^{\circ}=(arc)BC[/tex]

Thus, the measure of the arc BC is 96 degrees.

Hence, option D is correct.

Answer:

6^2 + x^2 = 9^2

36 + x^2 = 81

81-36= 45

square root of 45 is approximately 6.71 miles

Step-by-step explanation:

Using the theram theroy is very important to know the fulma and steps

Answer:

True

Step-by-step explanation:

Apex approved

Answer:

this answer is true

Step-by-step explanation:

i say this because 142.2 is an outlier.

Solution

The equation of two curves are

     [tex]y_{1}=y=2 \times (5 x+3)\\\\y_{2}=y=x^2-15[/tex]

Equating the two curves that is y values, to find their point of Intersection

→  2 × (5 x+3)=x²-15

→10 x +6=x²-15⇒⇒Used distributive property of multiplication with respect to addition

→x² -10 x -15 -6=0

→x² -10 x-21=0

For a Quadratic equation of the type

   [tex]\rightarrow ax^2+b x +c=0\\\\x=\frac{-b \pm \sqrt{D}}{2 a}\\\\D=b^2-4ac[/tex]  

Using discriminant method to solve the problem

   [tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4 \times 1 \times (-21)}}{2 \times 1}\\\\x=\frac{10 \pm \sqrt{100+84}}{2}\\\\x=\frac{10 \pm \sqrt{184}}{2}\\\\x=5 \pm \sqrt{46}\\\\x_{1}=5+6.78\\\\x_{1}=11.78\\\\x_{2}=5-6.78\\\\x_{2}=-1.78[/tex]

The x coordinate of point of intersection are, 11.78 and -1.78.

Answer:

The answers are:

345 dollars

34500 cents

Step-by-step explanation:

In order to determine the answers, we have to know about the percentage notation. For any "x" value that is expressed as x%, it is the same that:

x%=[tex]\frac{x}{100}[/tex]

So, first we determine the value in dollars and then we determine the value in cents, where:

1 dollar=100 cents

In dollars $:

=5.75%*$6000

=[tex]\frac{5.75}{100}[/tex]*$6000

=$345.00

In cents c:

=5.75%*6000*100

=[tex]\frac{5.75}{100}[/tex]*6000*100

=34500.00 cents

Based on the labor force participation rate, the number of unemployed people is 1.5 million people.

The unemployed rate is based on the labor force participation rate and not the adult population.

The labor force is 60% and in absolute value this is:

= 60% x 50 million people

= 30 million people

The unemployment rate is 5% of this:

= 5% x 30 million

= 1.5 million people

In conclusion, there are 1.5 million unemployed people

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