Select which of these transformations is hardest for you to write using algebraic notation.

Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.

To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.

Now, total distance in race

8/18 + 16/18

= (8+16)/18

= 24/18

= 4/3

= [tex]1\frac{1}{3}[/tex] kilometers

Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.

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The scale factor can be obtained by determining the ratio of the length of the sides of the old and new figures.

In other words, it can be obtained by stating that:

Specifically, we can say that:

Now, if each block (or cell) on the graph represents 1 units, we have that:

X'Y' = 10 units and XY = 5 units

Therefore:

The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]

The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:

V = 2x (x - 1) (x + 2) ≤ 280

Divide both sides by 2:

x (x - 1) (x + 2) ≤ 140

x³ + x² - 2x - 140 ≤ 0

(x - 5) (x² + 6x + 28) ≤ 0

Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:

x - 5  ≤ 0

or x  ≤ 5

Using the interval notation, x = (-∞, 5]

However, remember that the dimension is always a positive number.

Hence,

x - 1 ≥ 0

or x  ≥ 1

Therefore, the solution is [1, 5]

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The equivalent expression of  4(8g + 5) + 6 is 4(5 + 8g) + 6

Equivalent expressions are expressions that work the same even though they look different.

In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Therefore, let's find the equivalent expression of 4(8g + 5) + 6.

Hence,

4(8g + 5) + 6

32g + 20 + 6

32g + 26

Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6

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A few properties of a parallelogram.

1) Opposite sides are always equal.

2) Opposite angles are always equal.

3) The sum of all the angles is 360.

In part 2, we are given the angles. Therefore, we can apply the 2nd property.

11x = 55

5y = z (lets say the unknown is z).

Now, 11x = 55

x = 55/11

x = 5

Now, we have to angles of 55 degrees but we don't know about y and z. Therefore, we have to apply the third property.

55 + 55 + 5y + z = 360

110 + 5y + z = 360

5y + z = 360 -110

5y + z = 250. (i)

According to property 2, 5y = z. Hence, put the value of 5y in the equation (i), we get

5y + z = 250

z + z = 250

2z = 250

z = 250/2

z = 125

From the value of z, we can find the value of y using z = 5y

125 = 5y

5y = 125

y = 125/5

y = 25

Hence, x = 5 and y = 25

Answer:

-1/2; take both points which equals to -1/2

Step-by-step explanation:

A bearing is a measurement of direction that uses North as a point of reference. Your bearing is 00° if you are moving north.

The angle from north to this bearing, measured counterclockwise, is the actual bearing. Utilize the knowledge that west is 270° from the north, south is 180°, and east is 90°.

The number of degrees in the angle measured counterclockwise from the north line to the line connecting the center of the compass is the bearing of a point.

How do you determine bearing angle?

The bearing is the angle subtracted in a clockwise direction from north to west. The bearing is 270° - 17° = 253° since the angle from north to west is 270°.

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Answer:

I'll do #17 as an example of how to do the others. #15 doesn't make sense.  What is "= ≤⁄x?"

Step-by-step explanation:

17. (-3, 2); y=-4

y=4 is a horizontal line, where all values of y are 4, regardless of x.  A horizontal line has a slope of 0.  [Y does not depend on x].

That leaves us with y =0x + b

For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0].  Since y=0 regardless of x, b must be 2.

The parallel line that goes through (-3,2) is:

y = 0*x + 2, or

y = 2

Answer:

E

Step-by-step explanation:

[tex]\sqrt{144} = 12\\ \frac{234}{3}= 78\\[/tex]

12, 68.12, 78

Answer:

1/4

Step-by-step explanation:

The square root of 1/16 = 1/4

they probably

Only $28.25 are available. After Lena uses the card for 15 minutes of calls, there are still 28.25 credits left.

Given that,

Lena spent $30.50 on a prepaid phone card. With this card, calls cost 15 cents each minute. the amount of credit, c (in dollars), remaining on the card following x minutes of calls

It can be written as,

C(x) = 30.50 - 0.15x

C(x) = 30.50-(0.15 x 15)

after Lena uses it for 15 minutes,

C(x) = 30.50 – 2.25 = $28.25 in remaining credits.

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The simplified value of the expression given as -9 (-5 - 4c) is 45 + 36c

From the question, the expression is given as

-9 (-5 - 4c)

To simplify the expression, we start by opening the bracket

So, we have the following equation

-9 (-5 - 4c) = -9 (-5 - 4c)

Remove the brackets

So, we have

-9 (-5 - 4c) = -9 x -5 -9 x - 4c

Evaluate the products

So, we have

-9 (-5 - 4c) = 45 + 36c

Hence, the value of the expressions is  -9 (-5 - 4c) = 45 + 36c

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By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.

We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet

Notice that both of these are in scientific notation.

To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:

(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)

= 0.3251*(10^1) = 3.251

The atlantic ocean is 3.251 times deeper than the artic.

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The determinant of the given matrix is [tex]2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]

Determinant of the matrix:

Determinant of the matrix is defined as a scalar value which is associated with the square matrix.

Given,

Here we have the matrix show in the question.

Now, we need to find the determinant of the matrix.

To find the determinant of the matrix we have to do the following steps:

1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.

2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.

This process can be elaborated in the following steps:

[tex]=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)[/tex]

When we expand the equation then we get,

[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)[/tex]

Group the similar terms and arrange them in order,

[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)[/tex]

Again we have to expand it and then we get,

[tex]= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4[/tex]

After the simplification, the resulting determinant is

[tex]=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]

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The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.

The value of the basket in 2018 can be calculated by using multiplication and addition.

First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.

Lollipop: $0.80 × 15 = $12

Chocolate: $3.75 × 10 = $37.5

Peanut butter: $4.25 × 4 = $17

Ice-cream cake: $12.99 × 2 = $25.98

Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;

Value of basket = $12 + $37.5 + $17 + $25.98

Value of basket = $92.48

Hence the value of the basket in 2018 is $92.48

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The prices for jeans and shirts are $6 and $6

Given that:

3 pairs of jeans and 7 shirts for $60.

And 2 pairs of jeans and 3 shirts for $30.

Let jeans be x

Let shirts be y

3x + 7y = 60.... eq 1

2x + 3y = 30...... eq 2

Let us make x the subject formula from equation 2

2x = 30-3y

x= (30-3y)/2..... eq 3

Put the value of x into equation 1

3 * (30-3y)/2 + 7y = 60

(90- 9y)/2 + 7y = 60

45 - 4.5y + 7y = 60

2.5y =15

y = 6

Then, put the value of y into eq 3

x= (30-3(6))/2

x= 15 - 9

x= 6

Hence, we can see that the values of x and y are 6 apiece.

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Answer:

yeah it's correct , very much well

Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;

The red graph represents x + y =<20

The blue graph represents 5x +8y =>120

Observe that the region where the blue and red are "mixed" together represent the solution region.

Option A (4, 15)

Option B (5, 12) and

Option C (10, 9) are possible solutions

Answer:

plan b

Step-by-step explanation:

unless your making 120 calls or more plan B is better

24-18=6

6/0.05

=120

Answer:

x intercept is -3

Step-by-step explanation:

We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1)     = (2- -4)/(6- -3)     = (2+4)/(6+3)     =6/9     = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x  Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3  

Answer:

x = ?

Step-by-step explanation:

Since there are two congruent angles, their respective sides are also congruent (an angle's respective side is the side opposing it, the side that it does not touch). Meaning, the 3x-7 side is congruent to the 2x side.

So just set them equal to each other to find x.

3x - 7 = 2x

x = ? (You can do this. Solve for x algebraically.)

The 4x-10 doesn't really matter here since you just need to find x.

Given:

The length of the rectangular room is 6 more than the width.

The area of the room, A = 27 square units.

Required:

We need to find the dimensions of the given rectangular room.

Explanation:

Let w be the width of the rectangle.

6 more than means add 6.

The length of the rectangle, l= w+6.

Consider the area of the rectangle formula.

Substitute A = 27, and l=w+6 in the formula.

Subtract 27 from both sides of the equation.

Take out the common multiple.

The measure is always positive.

Substitute w =3 in the equation l =w+6.

We get l =9 units and w =3 units.

Final answer:

The dimensions of the room are 3 and 9.

The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700

The equation is

2x+5 = 1.99x+22

First we have to rearrange the given term and combine the like terms, then we have to find the value of x

Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation

2x+5 = 1.99x+22

2x-1.99x = 22-5

We have to do the subtraction in like  terms

(2-1.99)x = 22-5

0.01x = 17

Move the number 0.01 to the right hand side of the equation

x = 17/0.01

Division

x = 1700

Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.

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Step-by-step explanation:

there is one item and it cannot be split.

the winning bid was $8,000.

that means the fair share for each one of the 5 participants is

8000/5 = $1,600

the winner is getting one item with a value greater than his fair share.

so, he has to pay the difference into the kitty :

8000 - 1600 = $6,400

Answer: 14

Step-by-step explanation:

87.5% of 105 is 91.875 (91)

105-91=14

Answer:

60 yards

Step-by-step explanation:

100 feet + 20 feet + 60 feet = 180 feet

180 feet = 60 yards (there are 3 feet in 1 yard)

Answer: y = -4 + x/2

Step-by-step explanation:

Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.

Write the given lines in standard form

Line a -5x + y = -3

Line b x + 5y = 2

Line c -2x - 10y = 0

a1 = -5, b1 = 1, c1 = -3

a2 = 1, b2 = 5, c2 = 2

a3 = -2, b3 = -10, c3 = 0

a1/a2 = -5/1

b1/b2 = 1/5

c1/c2 = -3/2

As we see that

a1/a2 ≠ b1/b2

Hence, lines a and b are intersecting.

a1/a3 = -5/-2

b1/b3 = 1/-10

As we see that

a1/a3 ≠ b1/b3

Hence, lines a and c are intersecting.

a2/a3 = 1/-2

b2/b3 = 5/-10 = 1/-2

c2/c3 = 2/0

As we see that

a2/a3 = b2/b3 ≠ c2/c3

Hence, lines b and c are parallel.

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