The perimeter of a rectangular picture frame can be represented by the expression 6x,where x is one of the side lengths. Rewrite the expression as the sum of the four side lengths.

Given the word problem:

The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.

The numerator will be the value on top in a fraction.

Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)

The denominator is the value below in a fraction.

Here, the denominator is the product of negative 8 and x ==> -8x

Therefore, the expression that fits this description is:

c-884= -853

solve for c​

that means Isolate the variable c

so

step 1

Adds 884 both sides

c-884+884=-853+884

simplify

Answer:

a=75

Step-by-step explanation:

76=4/5a+16

first get the a term by itself on one side

76-16=4/5a

simplify

60=4/5a

now divide both sides by 4/5 or multiply by 5/4(its the same thing)

60*5/4=4/5a*5/4

now simplify

75=a

Let:

x = The smaller number

y = The larger number

Replace (1) into (2):

Add like terms:

Solve for x:

Replace x into (1):

Answer:

The smaller number is 5

The larger number is 20

x - 4 = 4 - x

4 is subtracting on the left, then it will add on the right

x is subtracting on the right, then it will add on the left.

x + x = 4 + 4

2x = 8

2 is multiplying on the left, then it will divide on the right

x = 8/2

x = 4

So, there is only one solution

First we need to convert 1 ft to inches

1ft= 12 in

We will use the formula of surface area

where l is the length, w is the width and h is the height

In our case

l=12 in

w=8in

h=6 in

we substitute

we simplify

She needs 432 square inches

A) D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]

B) R =(-7,-5) U (-4,5] U [6, 7]

C)

i. f(0) = 1

ii. f(-2) = 1

iii. f(8) = 7

iv. f(3) = 4

D.

x= 1,

x= -2

x= -4

x = -7.7 (approximately)

A) Examining the graph, we can write the Domain (the set of entries) as:

D = [-8, 5) U [-4, -1) U (-1, 3] U (3, 5) U [6,8]

Note that as we're dealing with the Real Set there are infinite values within each interval. And the Domain is the union of all intervals.

B) Examining that, for the Range (Outputs) y-axis, we can write the following:

R =(-7,-5) U (-4,5] U [6, 7]

Note that as there are some discontinuities we can't write them as a unique interval.

C) For this item, let's find out each value by locating the y-coordinate on the graph when the value of x is within the parentheses:

i. f(0) = 1 When x = 0, y = 1

ii. f(-2) = 1

iii. f(8) = 7

iv. f(3) = 4

Note that for this value, we have an open dot for -5 so it does not include it

v. f(-1) = Undefined

Both open dots

D. When f(x) = 1, i.e. y= 1 we have the following x-coordinates:

x= 1,

x= -2

x= -4

x = -7.7 (approximately)

See graph below

We have two inequalities:

y < 6

y > x + 3

To plot the inequalities on a graph, we change the inequality sign to equal to in order to get points to plot the graph:

y = 6

This means at y = 6, there will be an horizontal line for all values of x. But due to the less than sign, it means the horizontal line will be shaded down.

y = x + 3

We assign values to x inorder to get y values:

let x = -2, 0, 2, 4

when x = -2

y = -2 + 3 = 1

when x = 0

y = 0 + 3 = 3

when x = 2

y = 2 +3 = 5

when x = 4

y = 4 + 3 = 7

When we plot this points, we get a straight line. SInce the sign is greater than, the line will be shaded towards the positive side

plotting the graph:

First inequality

Both inequalities:

Given,

The expression is,

Taking x =1,

Subsituting the value of x in the given function then,

Taking x =2,

Subsituting the value of x in the given function then,

Divide f(1) by f(2) then,

Hence, the simplified value is 1/3.

When converting a number from decimal to scientific notation,

The exponent is positive if the movement of the decimal point is to the left

The exponent is negative if the movement of the decimal point is to the right.

Examples :

The decimal point moves from the right of the last digit to the place between 1 and 2. It moves to the left so the exponent is positive.

The decimal point will move 3 places to the right, so the exponent will be negative.

Let x be the amount invested in the account paying 7% and y the amount invested in the account paying 8%, then we can set the following system of equations:

Solving the first equation for x and substituting it in the second equation we get:

Solving for y we get:

Substituting y=3000 in the first equation and solving for x we get:

Therefore, $2000 was invested in the account paying 7%, and $3000 was invested in the account paying 8%.

If a shop sells on average 250 can's of juice a day and  there are 25500 cans, these stocks last​ for 102 days

A shop sells on average 250 can's of juice a day, it has, it has 25500 cans in stock. We need to find the number of days these stocks will last.

The number of days can be found by using unitary method

1 can of juice is being sold in 1/250 day

25500 can of juice will be sold in 1/250 (25500)

25500 can of juice will be sold in 102 days

Therefore, if a shop sells on average 250 can's of juice a day and  there are 25500 cans, these stocks last​ for 102 days.

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ANSWER

c = 6.4

EXPLANATION

The intersecting chords theorem says that the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.

One secant segment is (9+19) and its external segment is 9. The other is (13+c) and its external segment is 13:

Solving for c:

Number of composition books: 27

Number of packs of map pencils: 9

The ratio of packs of maps pencils to composition books: 9 to 27

9/27 = 1/3

1:3

The coordinates of the vertex are:

"The square of x..." translates to x²

"...is greater than or equal to 10." translates to ≥ 10.

To determine if 3 is a solution, substitute 3 to the inequality.

The resulting number, 9 is not greater than 10. Therefore, 3 is not a solution.

Given a polygon ABCDE with the coordinates

The image of the polygon has vertices A'B'C'D'E' with coordinates

The transformation rule as observed from the image is

Hence, the polygon has been shifted to the right by 1 unit and down by 4 units

Option A is the right answer

We have an expression:

We have to evaluate it when a = 3 and x = -5. To do that we replace a and x by its values and calculate:

Answer: the expression value is -29

If an event has a probability P of happening, then there is a probability of (1-P) of the event not happening.

In this case the probability of the event is p=20/69.

Then, the probability of the event not happening is:

Answer: the probability of the event not happening is 49/69.

SOLUTION

To answer this question, let us first understand some rules that guide operations as this:

So going back to treat this question:

Re-writing this subtraction as an ADDITION of signed numbers, we will have:

Now to complete this problem the final solution will result in:

The final answer is -2

Here, we want to get the value of x

As we can see, we have the interior angle as 45;

The other is 90; and that means the last angle will be 45

This mean that we have an isosceles right-triangle

The sides that face the angles are equal

These sides are x and 12

That means x = 12

To get the value of y, we have to use the Pythagoras' theorem

The square of the hypotenuse (the longest side and the side that faces the right angle) is equal to the sum of the squares of the two other sides

The side facing the right angle is y

So, the sum of the squares of x and 12 will give the square of y

Mathematically, we have this as follows;

Answer:

Distribution property method

Applying the translation rule:

G(0, 4) → (0-5, 4+2) → G'(-5, 6)

Solution

First find the g(x)

g(-2)= 3(-2) +5

g(-2)= -6+5

g(-2)= -1

substitute for x in f(x) when x is -1

The correct option is the last option

Answer:

They can speak in 40, 320 different orders

Explanation:

Given that 8 people have to give a presentation in class.

They can speak in many different orders:

First could be second, second could be first, third could be eight, seventh could be fifth, and so on.

This number of ways result in factorial 8.

This is written as:

Which represents the multiplications of numbers on the number line from 8 down to 1.

That is:

The required perimeter of the scale drawing is given as 18 inches.

Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
According to the question,

L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing  = 2[l + w]
                                                       = 2 [5 + 4] = 18 inches

Thus, the required perimeter of the scale drawing is given as 18 inches.

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Answer:

=[tex] \sqrt{85} [/tex]

Step-by-step explanation:

let, (x1,y1) = (2,-5) & (x2,y2) = (-7,-7)

now, for distance between two points,

D = [tex]\sqrt[]{(x_{1}-x_{2} )^{2} +(y_{1}-y_{2} )^{2} }[/tex]

=[tex]\sqrt[]{(2-(-7))^{2}+(-5-(-7))^2 }[/tex]

[tex]=\sqrt{(2+7)^2+(-5+7)^2}[/tex]

[tex]=\sqrt{9^2+2^2}[/tex]

[tex]=\sqrt{81+4}[/tex]

[tex]=\sqrt{85}[/tex]

Answer:

[tex] \huge{ \boxed{ \sqrt{85} \: \text{or} \: 9.219 \: \text{units}}}[/tex]

Step-by-step explanation:

The distance between two points say [tex] A(x_1,y_1) [/tex] and B(x_2,y_2) can be found by using the formula;

[tex] \bold{d = \sqrt{{x_2-x_1}^{2}+{y_2-y_1}^{2}}} [/tex]

From the question the points are (2, – 5) and ( – 7, – 7)

[tex] x_1=2 \\ y_1=-5 \\ x_2=-7 \\ y_2=-7 [/tex]

Substituting the values into the formula that is;

[tex]d = \sqrt{ {( - 7 - 2)}^{2} + {( - 5 - - 7)}^{2} } \\ d = \sqrt{ {( - 9)}^{2} + {(2)}^{2} } \\ d = \sqrt{81 + 4} \\ d = \sqrt{85} = 9.219[/tex]

We have the final answer as

ANSWER:

(-1, 0) and (3, 0)

STEP-BY-STEP EXPLANATION:

The x-intercept is the points where the graph crosses the x-axis, we can calculate it graphically like this:

price: $40

Given that you get a 15% discount, you get a discount of $40*15% = $6.

Then, you have to pay $40 - $6 = $34