Simplify the following expressions and then find the numerical values for x = -2.

There are 300 apples and peaches for sale at a farmers market. The ratio of the number of apples to the number of peaches is 7:8

Sidana [21]

Answer:

The ratio of the reaming apples to peaches is 3 : 4

Step-by-step explanation:

* Lets solve the problem

- There are 300 apples and peaches

- The ratio of the number of apples to the number of peaches is 7 : 8

- To find the the numbers of apples and peaches add the terms of the

ratio and then divide the total number of apples and peaches by this

sum and then multiply each terms of the ratio by this quotient

∵ The ratio of apples to peaches = 7 : 8

∴ apple : peach : sum

7 : 8 : 15

? : ? : 300

∴ The number of apples = (300 ÷ 15) × 7 = 20 × 7 = 140 apples

∴ The number of peaches = (300 ÷ 15) × 8 = 20 × 8 = 160 peaches

- 50 apples and 40 peaches are sold

∴ The remaining number of apples = 140 - 50 = 90 apples

∴ The remaining numbers of peaches = 160 - 40 = 120 peaches

- To find the ratio simplify the numbers to its simplest form

∵ There are 90 apples and 120 peaches

∴ apple : peach

90 : 120 ⇒ divided both by 10

∴ 9 : 12 ⇒ divide both by 3

∴ 3 : 4

∴ The ratio of the reaming apples to peaches is 3 : 4

4 0

3 years ago

TOPIC: simultaneous linear equations<br><br>p + 2q = 3, <br>p - 2q = 3

snow_tiger [21]

Answer:

p=3 q=0

Step-by-step explanation:

p+2q=3

p-2q=3

p+2q=3

p=3-2q---------eqn i

p-2q=3

3-2q-2q=3

3-4q=3

-4q=3-3

q=0÷-4

q=0

putting the value of q in equation i

p=3-2q

=3-2×0

=3

6 0

4 years ago

Read 2 more answers

HELP, WILL MARK BRAINLIEST+100 POINTS. PLEEEEES Square EFGH is drawn on a coordinate plane. Diagonal FH is on the line y − 3 = n

vova2212 [387]

1) Slope of diagonal GE: 3

2) Equation of the line: $x-y=P-Q$

3) Slope of the line: 1

4) y-intercept: 4

Step-by-step explanation:

1)

Here the diagonal FH is given by the line with equation

$y-3=-\frac{1}{3}(x+9)$

This line is written in the form

$y-y_0 = m(x-x_0)$

where m is the slope of the line and $(x_0,y_0)$ are the coordinates of a point on the line.

Therefore, for line FH we have:

$m=-\frac{1}{3}$ (slope)

$(x_0,y_0)=(-9,3)$

Diagonal GE is perpendicular to diagonal FH (the diagonals in a square are perpendicular): this means that its slope must be equal to the inverse reciprocal of the slope of FH. THerefore, the slope of diagonal GE is

$m_{GE}=-\frac{1}{m_{FH}}=-\frac{1}{-1/3}=3$

2)

Two lines are said to be parallel when they have same slope.

Here, we see that the line given in the plot passes through the points

$(x_1,y_1)=(0,5)\\(x_2,y_2)=(-3,2)$

Therefore the slope of the line shown is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{0-(-3)}=1$

This means that also the line that we want to find must have slope of 1:

$m=1$

Now we can use the following form to write the equation of this line:

$y-y_0 = m(x-x_0)$

where:

$m=1$

$(x_0, y_0)=(P,Q)$ is the point that must be on the line

Therefore,

$y-Q=1(x-P)\\y-Q=x-P\\x-y=P-Q$

3)

In order to solve this problem, we have to find the slope of the side WV.

The coordinates of the two points are:

$V(a+5,b-1)\\W(a+3,b-3)$

Therefore, the slope of side WV is given by:

$m=\frac{y_W-y_V}{x_W-x_V}=\frac{(b-3)-(b-1)}{(a+3)-(a+5)}=\frac{-2}{-2}=1$

And we said that two lines are parallel if they have same slope: therefore, the slope of the line parallel to the line that contains side VW is also 1.

4)

The line given in this problem has equation:

$y=\frac{4}{3}x+1$

where

$m=\frac{4}{3}$ is the slope of the line

$q=+1$ is the y-intercept of the line

Here we want to find the line perpendicular to the given line and passing through the point (4,1).

A line perpendicular to the given one must have a slope which is equal to the negative of the reciprocal of the original one, therefore:

$m'=-\frac{1}{m}=-\frac{1}{4/3}=-\frac{3}{4}$

Now we can use the form

$y-y_0 = m'(x-x_0)$

and the coordinates of the point are

$(x_0,y_0)=(4,1)$

Substituting,

$y-1=-\frac{3}{4}(x-4)\\y-1=-\frac{3}{4}x+3\\y=-\frac{3}{4}x+4$

We have written the line in the form $y=mx+q$ , with $q=4$ : so the y-intercept is 4.

Learn more about parallel and perpendicular lines:

brainly.com/question/3414323

brainly.com/question/3569195

#LearnwithBrainly

5 0

3 years ago

Read 2 more answers

8. Noah rides his motorcycle 90 miles in 2 hours 30 minutes. What is his average speed in

Nookie1986 [14]

Hey there! I'm happy to help!

We see that Noah rides his motorcycle 90 miles is 2 hours and 30 minutes, which is 150 minutes. We want to find his mph. To find this his mph, we want to find how far he has gone in one hour.

How much bigger is 150 than 60?

150/60=2.5

150 is 2.5 times bigger than 60. This means that we need to divide 90 by 2.5 to figure out how far Noah rode in 1 hour.

90/2.5=36

Therefore, Noah's average speed is 36 mph.

Have a wonderful day! :D

6 0

3 years ago

margarite owns a boutique. she sells her jewelry at a 30% markup. if she buys a bracelet for $22, what would she sell it for aft

skad [1K]

She would sell it for $26.60 after the markup.

7 0

3 years ago