What is the length of BC?

Answer:

The function of the equation is f(x) =  [tex]-\frac{1}{2}[/tex]  [tex]-\frac{3}{2}[/tex] x

Step-by-step explanation:

The function form of the linear equation is f(x) = m x + b, where

∵ The equation is 3x + 7 = 2(3 - y)

→ Simplify the right side by multiplying the bracket by 2

∵ 3x + 7 = 2(3) - 2(y)

∴ 3x + 7 = 6 - 2y

→ Add 2y for both sides

∵ 2y + 3x + 7 = 6 - 2y + 2y

∴ 2y + 3x + 7 = 6

→ Subtract 7 from both sides

∵ 2y + 3x + 7 - 7 = 6 - 7

∴ 2y + 3x = -1

→ Subtract 3x from both sides

∵ 2y + 3x - 3x = -1 - 3x

∴ 2y = -1 - 3x

→ Divide each term by 2

∴ y = [tex]-\frac{1}{2}[/tex] - [tex]\frac{3}{2}[/tex] x

→ Replace y by f(x)

∴ f(x) =  [tex]-\frac{1}{2}[/tex]  [tex]-\frac{3}{2}[/tex] x

∴ The function of the equation is f(x) =  [tex]-\frac{1}{2}[/tex]  [tex]-\frac{3}{2}[/tex] x

Step-by-step explanation:

x^2+9x<-20

x^2+9x+20<0

( x+5)(x+4)<0

x+5<0,x+4<0

x<-4 (because x<-5 is extraneous solution)

Answer:

y=12

x=30

Step-by-step explanation:

2x-3y=24 ... 1

x+6y=18 ... 2

2*2:

2x+12y=36...3

3-1:

y=12

x=30

When the following system of equations 2x - 3y = -24 and x + 6y = 18 are solved, the value of x and y is found to be -6 and -4 respectively.

Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.

Given the system of equations:

2x - 3y = -24 (equation1)

x + 6y = 18 (equation2)

From equation 2,

x = 18 - 6y

Now, substitute this expression for x in equation (1):

2(18 - 6y) - 3y = -24

36 - 12y - 3y = -24

36 - 15y = -24

-15y = -60

y = [tex]\frac{(-60)}{(-15)}[/tex]

y = 4.

Now substitute it back into equation (2) to solve for x:

x + 6(4) = 18

x + 24 = 18

x = 18 - 24

x = -6

Therefore, the solution to the system of equations is x = -6 and y = 4.

Learn more about equations here:

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Answer:

$0.50 per kilogram

Step-by-step explanation:

($300/trip)/(50 packs/trip) = $6/pack

($6/pack)/(12 kilograms/pack) = $0.50/kilogram

Answer:

60 degrees

Step-by-step explanation:

All the angles are the same so 180 divided by 3 is 60

Answer: 4.17%

Step-by-step explanation:

Formula for percentage error = [tex]\dfrac{|\text{Estimated weight - Actual weight}|}{\text{Actual weight}}\times100[/tex]

Given: Estimated weight = 2.5 oz

Actual weight = 2.4 oz

Percentage error = [tex]\dfrac{2.5-2.4}{2.4}\times100\%[/tex]

[tex]=\dfrac{0.1}{2.4}\times100\%\\\\=\dfrac{100}{24}\%=4.17\%[/tex]

Hence, the percent error = 4.17%

Answer:

301.44

Step-by-step explanation:

Answer:

Please check the number line attached below.

Step-by-step explanation:

Please check the attached graph below.

The line graph is representing that a number line:

From the graph, it is clear that the point 0 is taken as arbitrary. The left side number units from 0 represent the negative values and the right-sided number units from 0 represent the positive values.

When we move on the right side from the 0, the numbers increase and when you move on the right side from the 0, the number decreases.

Answer:

The number line shows -2 through 2, divided into fourths, with zero in the middle. The numbers increase as you move right and decrease as you move left.

Step-by-step explanation:purrr

Answer: it is

Step-by-step explanation: the next numbers are 1.5, 3, 4.5.

Answer:

y = 5x + 16

Step-by-step explanation:

5y + x = 20

5y = -x + 20

y = [tex]-\frac{1}{5}[/tex]x + 20

Points: (-2, 7)

Slope (m⊥): = 5

y = 5x + b

7 = 5 ( -2 ) + b

6 = -10 + b

b = 16

y = 5x + 16

Answer:

16 students are girls.

Step-by-step explanation:

5:4=36

5x+4x=36

9x=36

x=4.

So we can multiply the ratio by 4.

4(5+4)

20+16.

Since girls is 4, there are 16 girls.

Hope this helps plz hit the crown :D

Answer:

let ratio of boys and girl be 5x and 4x

now

5x+4x=36

9x=36

x=36÷9

x=4

now

number of boys in class is 5x=5*4=20

Number of girls in class is= 4x

=4*4

=16 ans

Answer:

The slope of the line that joins the points is negative.

i.e m = -6/5

Step-by-step explanation:

Taking two points from the graph to determine the slope

Finding the slope between (-3, 4),(2, -2)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]'

[tex]\left(x_1,\:y_1\right)=\left(-3,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:-2\right)[/tex]

[tex]m=\frac{-2-4}{2-\left(-3\right)}[/tex]

[tex]m=-\frac{6}{5}[/tex]

Therefore, the slope of the line that joins the points is negative.

i.e m = -6/5

Answer:

k=4

Step-by-step explanation:

cross multiply so it would be:

8k+24=56

subtract 24 from 56

8k+24-24=56-24

8k=32

divde

8k/8=32/8

k=4

Answer:

This is the answer. All the very best

Answer:

10

Step-by-step explanation:

i think

Answer:

1/512

Step-by-step explanation:

The probability is 2 out of 2^10 , because there are only two sequences when  same result (heads or tails) shows twice in a row exactly once in the ten tosses (HTHTHTHTHT and THTHTHTHTH) out of 2^10 possible sequences.

2/2^10 = 2/1024 =1/512

Answer:

-23, -15, -10, -7, -3, -2, -1, 0, 2, 2, 3, 5, 10, 15, 23  

Step-by-step explanation:

:)

Note: It seems you may have unintentionally missed writing the complete question. As total cost is missing.

So, I am assuming how many tickets Mr. XYZ can buy if he/she pays 170 dollars.

The solution would still clear your concept though.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

[tex]c(x) = 18x -10[/tex]

The slope-intercept form of the line equation

We know that the slope-intercept form of the line equation

y=mx+b

where m is the slope and b is the y-intercept

so

[tex]c(x) = 18x - 10[/tex]

comparing with the slope-intercept form of the line equation

here:

and

'x' represents the number of tickets

Assuming the total cost i.e. c(x) = $170

In order to determine the value of x, set c(x) = 170

i.e.

170 = 18x -10

switch sides

18x - 10 = 170

add 10 to both sides

18x - 10 + 10 = 170 + 10

18x = 180

Divide 18 to both sides

18x/18 = 180/18

x =  10

Therefore, if you can buy x = 10 tickets if you pay  170 dollars.

Answer:

$14

Step-by-step explanation:

ok so since he is delivering groceries he gets $4.

now when he delivers he get $2 more, so for each house he delivers to he adds $2 to that $4.

so the easiest was to do this is 5x2.

5x2 is 10.

now $10 is how much more he gets on top of the $4, so now we need to add the $4 to the $10.

your answer is $14  

plz mark brainliest!

Answer:

g(x) = 6x+4

Step-by-step explanation:

The given function f(x)=x

Let p(x) be an intermediate function after translation of f(x).

So, after the translation 4 unit down, the new function

p(x) = f(x) - 4

p(x) = x-4

Now, there is a horizontal shrink by a factor of 6, so the required function g(x) is

g(x) = p(6x) [here 6 is the horizontal shrink factor]

g(x) = 6x-4

Hence, the required function is g(x) = 6x+4

Answer:

C

Step-by-step explanation:

I got it right

Answer:

They are neither perpendicular nor parallel.

Step-by-step explanation:

Find the gradient of 2x + 6y = 42 by rearranging it in the form y = mx + c:

6y = -2x + 42

y = -(1/3)x + 7

The gradient is the co-efficient of x

Therefore the gradient is -(1/3)

The gradient of y = 2x - 1 is 2.

If they were parallel they would have the same gradient.

If they were perpendicular then the gradient of one would be the negative reciprocal of the other, e.g: if one was 2, the other would be -(1/2).

Neither of these are true, so they are neither perpendicular nor parallel.

The lines 3x+6y=42 and y=2x-1 are perpendicular

Two lines are parallel if they have equal slope

Two lines are perpendicular if the product of their slopes equals -1

The given lines are:

3x+6y=42 and y=2x-1

Rewrite each of the equations in the form y = mx + c

For line 3x + 6y = 42:

[tex]6y = -3x + 42\\\\y=\frac{-3}{6} x+\frac{42}{6}\\\\y=-0.5x+7[/tex]

The slope, m₁  =  -0.5

For line y = 2x - 1

The slope, m₂ = 2

Since m₁  ≠ m₂, lines 3x+6y=42 and y=2x-1 are not parallel

m₁ m₂  =  -0.5(2)

m₁ m₂  = -1

Since the product of the slopes equals -1, the lines 3x+6y=42 and y=2x-1 are perpendicular

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Answer:

5,548.9861375

Step-by-step explanation:

First year

4700/100×5.5=258.5

So his account will be 4700+285.5=4985.5

Second year

4985.5/100×5.5=274.2025

His account will be 4985.5+274.2025=5,259.7025

Third year

5,259.7025/100×5.5=289.2836375

The total in his account after three years equal to

289.2836375+5259.7025=5,548.9861375

Answer:

$0.18 sales tax will be added to the purchase price.

Step-by-step explanation:

Given that:

Cost of cupcake = $3

Sales tax applied = 6%

Amount of sales tax = 6% of cost of cupcake

Amount of sales tax = [tex]\frac{6}{100}*3[/tex]

Amount of sales tax = 0.06 * 3 = $0.18

Hence,

$0.18 sales tax will be added to the purchase price.