what operation helps calculate unit rates and unit prices

Answer

x = 2, and y = 3

Explanation:

given the following linear equation

7x - 6y = -4------------- equation 1

14x + 5y = 43 ---------- equation 2

This equation can be solve simultaneously by using elimination method

Step 1 : eliminate x

To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1

7x * 2 - 6y * 2 = -4 * 2

14x * 1 + 5y * 1 = 43 * 1

14x - 12y = -8 ----------------- equation 3

14x + 5y = 43------------------ equation 4

Substract equation 4 from3

(14x - 14x) - 12 - 5y = -8 - 43

0 - 17y = -51

-17y = -51

Divide both sides by -17

-17y/-17 = -51/-17

y = 51/17

y = 3

To find x, put the value of y into equation 1

7x - 6y = -4

7x - 6(3) = -4

7x - 18 = -4

Collect the like terms

7x = -4 + 18

7x = 14

Divide both sides by 7

7x/7 = 14/7

x = 2

Therefore, x = 2 and y = 3

Given:

Required:

To find the value of f(-8), f(0), f(4), and f(-100)+f(100).

Explanation:

f(-8) :

Clearly -8<0,

So

f(0) :

Clearly 0=0,

f(4) :

Clearly 4>0,

f(-100)+f(100) :

-100<0

100>0

Final Answer:

ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.

The sum of angles at a point is known to be 360 degrees.

Therfore,

Therefore, the measure of "a" is

Answer:

Compound interest with addition formula:

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

PMT = Regular contributions (additional money added to investment)

in this example

P = 2500

r = 8% = 0.08

n = 4

t = 5 years

PMT = 2500

solving for A:

Therefore, his investment after 5 years will be

$189,408.29

If f(x) is a linear function and gives f(3) = 3 and f(9) = -2

Part a

The slope of the line = -5/6

Part b

The y-intercept = 11/2

Part c

f(x) = (-5/6)x + 11/2

The values of

f(3) = 3

f(9) = -2

The points are (3,3) and (9,-2)

Part a

The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

= [tex]\frac{-2-3}{9-3}[/tex]

=-5/6

Part b

The slope intercept form of the line

y = mx+b

b is the y intercept

Substitute the values in the equation

3 = (-5/6)×3 + b

3= -5/2 + b

b = 11/2

Part c

Then the linear function f(x) = (-5/6)x + 11/2

Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2

Part a

The slope of the line = -5/6

Part b

The y-intercept = 11/2

Part c

f(x) = (-5/6)x + 11/2

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Step 1

Given;

Step 2

Answer;

Answer:

Step-by-step explanation:

18098

we have the following:

Therefore:

The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.

Answer: Options B and D.

Given:

Line equation, y=1+4x

The point, (1,2)

To find the slope intercept form:

The general slope intercept form is, y=mx+b.

First to find m:

From the line equation,

y=4x+1

We have, m=4

Next to find b:

Substitute m=4, and (1,2) in the general intercept form is,

Now, substitute m=4 and b=-2 in the slope intercept form

Thus, the slope intercept form is,

If a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.

Here a random number generator is used to select an integer from 1 to 100.

Therefore the range of the outcome = 1 to 100

Here we have to find the probability of selecting the integer 730

The probability = Number of favorable outcomes / Total number of outcomes.

Here a random number generator is used to select an integer from 1 to 100, but the given number is 730  which is out of range. Therefore the probability is zero

Hence, if a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.

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Answer:

b = -2

Step-by-step explanation:

y = mx + b;         (-2, 4)

y = -3x + b          (x₁, y₁)

m = -3

y - y₁ = m(x - x₁)

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

y - 4 = -3(x + 2)

y - 4 = -3x - 6

   +4           +4

------------------------

y = -3x - 2

I hope this helps!

The length of the line segment from a to b is 6.08 units or [tex]\sqrt{37}[/tex] units.

The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.

Relation between the coordinates and length:  [tex]\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }[/tex]

Now let point a be ([tex]x_{1},y_{1}[/tex]) and point b be ([tex]x_{2},y_{2}[/tex])

Thus putting values,

length = [tex]\sqrt{(3-(-3))^{2}+(4-3)^{2} }[/tex]

length = [tex]\sqrt{36+1}[/tex]    

length = [tex]\sqrt{37}[/tex]

Hence the length of ab is [tex]\sqrt{37}[/tex] or 6.08 units.

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7. The figure has line and rotational symmetries. There are 2 lines of symmetry. The angle of symmetry is 180°

8. The figure has no symmetry

ANSWER

Rational number and Real number

EXPLANATION

We want to identify what type of number -3.7 is.

A natural number is a number that is a positive integer, used in counting things. Examples are 4, 7 and 55.

A whole number is a number that is used in counting, including 0 i.e. natural numbers including 0.

An integer is a whole number but the difference is that an integer can be positive, negative or zero.

A rational number is a number that can be expressed as a fraction of two integers i.e. a/b while an irrational number is one that cannot be expressed as a fraction of two integers.

A real number is any number that can be found as a distance between two points on the number line.

From the definitions above, we see that we can classify -3.7 as a rational number and a real number.

It is not a natural number, whole number, irrational number or an integer.

The slope in the equations represent the change in temperature by the change in lattitude. This means that for each unit change in the latitude the temperature will decrease by an amount given by the slope.

to know y -intercept we only need to replace x by 0. And we get

so the y-intercept is 9

The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.

According to the question,

We have the following information:

f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]

Now, to find the value of f(0), we will put 0 in place of x.

f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]

f(0) = 0+7*0-0+12

(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)

f(0) = 0+0-0+12

f(0) = 12

Now, to find the value of f(2), we will put 1 in place of x:

f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]

f(2) = -8+7*4-4+12

f(2) = -8+28-4+12

f(2) = 40 -12

f(2) = 28

Now, to find the value of f(2), we will put -2 in place of x:

f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]

f(-2) = -(-8) + 7*4+4+12

f(-2) = 8+28+4+12

f(-2) = 52

Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.

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Adam had $200

He spent $75 on clothes and $55 on video game

The total money spent by Adam is

The amount left with Adam is

Then his mom gave him $20

The total amount of money Adam have now is

Hence, the answer is $90

I would loan my money to the one who pays the compound interest.

This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.

Okay, here we have this:

Considering the provided information we are going to calculate what is the probability that the two candies selected are taffy. So, for this, first we are going to calculate the probability that the first is taffy, and then the probability that the second is taffy. Finally we will multiply these two probabilities to find the total probability.

Remember that the simple probability of an event is equal to favorable events, over possible events.

First is taffy:

At the beginning there are 14 sweets, and 3 are taffy, so there are 3 favorable events and 14 possible, then:

First is taffy=3/14

Second is taffy:

Now, in the bag there are 13 sweets left, and of those 2 are taffy, so now there are 2 favorable events out of 13 possible:

Second is taffy=2/13

The first and second are taffy:

First is taffy*Second is taffy=3/14*2/13

First is taffy*Second is taffy=3/91

First is taffy*Second is taffy=0.033

First is taffy*Second is taffy=3.3%

Finally we obtain that the probability that the two candies selected are taffy is aproximately 0.033 or 3.3%.

8/12 -3/8=16/24-9/24=7/24

You should make like numbers then subtract

If you need to simplify at the end

Given,

We have,

when,

The zeros of the function are x=-3,-3,-3

Let us first understand what are discrete and continuous variables.

Discrete variable:

A discrete variable is countable in a finite amount of time.

For example:

The number of coins in your pocket

The number of trees in the garden

It is not possible to have 2.5 coins or 7.3 trees

Continuous variable:

A continuous variable can take any numeric value.

For example:

The height of the tree

The room temperature

These values can be in decimal like 7.3, 0.23 etc

Now let us come to the question, the distance a person has driven can take any value

for example, it can be 50 miles or 23.4 miles or 120.5 miles

So, decimal values are possible

This means that it must be a continuous graph

The distance a person has driven over time an example of a continuous graph.

Ready

Points A = (-5, -2) C = (7, 2) E = (1, 0)

1.- Find the slope

m = (y2 - y1) / (x2 - x1)

m = (2 + 2) / (7 + 5)

m = 4/ 12

m = 1/3

2.- Find the equation of the line

y - y1 = m(x - x1)

y + 2 = 1/3(x + 5)

y + 2 = 1/3x + 5/3

y = 1/3x + 5/3 - 2

y = 1/3 x + 5/3 - 6/3

This is the equation:

y = 1/3 x - 1/3

my pleausre

To calculate which value in Celsius the temperature of 5 Fº equates to, we first need to rewrite the expression isolating the "C" variable on the left side.

We now need to replace F by 5.

The temperature is -15 degrees in Celsius.

Tangent segment, of a circle

Apply formulas

20^2 - 15^ 2 = AB^2

Also

15^2 = 20•( 20 - AB)

225 = 400 - 20AB

Then

20AB = 400-225= 175

AB = √ 175= 13 + 6/25 =13.24

we have the equation

y=x^2-6x+2

this equation represents a vertical parabola open upward (because the leading coefficient is positive)

that means

the vertex is a minimum

Convert to vertex form

y=a(x-h)^2+k

where

(h,k) is the vertex

Complete the square

y=(x^2-6x+9)+2-9

y=(x-3)^2-7

therefore

the vertex is (3,-7)

The graph of the functions f and g are given.

It is required to complete the statement concerning how to produce g.

The graph of the parent function f is shown:

Reflect the graph of f across the x-axis:

Translate the function 5 units vertically upwards:

The given parent function is y=f(x).

Reflect the graph across in the x-axis to get the equation y=-f(x).

Translate the graph 5 units up to get y=-f(x)+5

Answers:

To produce g, the function f was reflected over the x-axis and shifted up 5 units.

Function g is defined as g(x)=-f(x)+5.

In the given figure we can observe a triangle with vertices located at:

(-3,-2)

(-5,-4)

(1,-5).

We need to draw it after a 90° clockwise rotation.

We can apply the rule for 90° clockwise rotation, which is:

Each point of the given figure has to be changed from (x, y) to (y, -x) and then we need to graph the new coordinates.

By applying the rule to the given coordinates we obtain:

Now we have to draw the new coordinates: