find the equation of a line that passes through (-2,4) and (1,-2)

A total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

Step-by-step explanation:

Step 1:

Assume the number of non-commercial vehicles to be x and the number of commercial vehicles to be y.

It is given that for every 14 non-commercial vehicles there will be 5 commercial vehicles. So a ratio can be formed as follows;

[tex]\frac{x}{14}[/tex] = [tex]\frac{y}{5}[/tex], cross multiplying, we get [tex]5 x=14 y[/tex], take this as equation 1.

Step 2:

It is also given that there were 108 more non-commercial vehicles than commercial vehicles. So

[tex]x=y+108[/tex], take this as equation 2.

If we solve equations 1 and 2, we will get the values of x and y.

Step 3;

Substitute equation 2 in equation 1.

[tex]5(y+108)=14 y[/tex],

[tex]5y+540 = 14y[/tex],

[tex]y = \frac{540}{9} = 60[/tex].

Substitute [tex]y = 60[/tex] in equation 2.

[tex]x=60+108 = 168[/tex].

So x = 168 and y = 60.

So a total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

The fish is 2.25 ft above the water surface.

Step-by-step explanation:

⇒ y = -16(0.375)² + 12 × 0.375 = -2.25 + 4.5 = 2.25 ft

Answer:

211

Step-by-step explanation:

952 + 1520 then divide by 12

The best prediction is that around 4 students (40% of 10 students) will receive historical fiction novels during Miss Nestor's class free reading time.

Miss Nestor is randomly passing out books to her students for free reading time. With a mix of 10 mysteries, 8 historical fiction novels, and 2 biographies in her basket, and 10 students in the class, we can make a prediction. Assuming each genre of book has an equal chance of being selected and each student gets one book, the probability of getting a historical fiction novel is the number of historical fiction novels divided by the total number of books. That's 8 historical fiction novels divided by (10 mysteries + 8 historical fiction novels + 2 biographies), which equals 8/20 or 40%. Therefore, if we predict using probability, around 40% of the students, which equals 4 students (40% of 10 students), will receive historical fiction novels for free reading time.

the best prediction of the number of students who will receive historical fiction novels for free reading time is 4.

To predict the number of students who will receive historical fiction novels, we can use the concept of probability.

First, let's find the probability that a student randomly selects a historical fiction novel from the basket.

The total number of books in the basket is 10 + 8 + 2 = 20

The probability of selecting a historical fiction novel is the ratio of the number of historical fiction novels to the total number of books:

[tex]\[ P(\text{historical fiction}) = \frac{8}{20} = \frac{2}{5} \][/tex]

Now, if there are 10 students in the class, the expected number of students who will receive historical fiction novels can be found by multiplying the probability by the total number of students:

Expected number of students receiving historical fiction = P(historical fiction) * Total number of students

[tex]\[ = \frac{2}{5} \times 10 \][/tex]

= 4

So, the best prediction of the number of students who will receive historical fiction novels for free reading time is 4.

Answer: Brownies that are $1.58 for a 6-pack

Step-by-step explanation:

Well, since 6 times 2 is 12, why don’t you just add $1.58 again, right? So if you do you get $3.16. So Brownies that are $1.58 for a 6-pack are better.

Answer:

Step-by-step explanation:

First you divide 1.58 and 6 to find how much one brownie is.

So that would be roughly $0.26.

Now you divide 3.99 and 12 which is roughly $0.33.

So you now have to see which one has a smaller cost. Which is $0.26. SO it would be the 6-pack.

Another way to figure is out to multiply 0.26 and 12, and 0.33 and 6.

0.33 x 6=1.98

0.26 x 12=3.12

So that makes it more clear that the 6 pack is a better buy!

Answer: is where that one dot is at home n the y-axis

Step-by-step explanation:

Step-by-step explanation:

Line is passing through the points (6, 2) & (0, 4)

Therefore slope

[tex]m = \frac{2 - 4}{6 - 0} = \frac{ - 2}{6} = - \frac{1}{3} \\ [/tex]

Answer: It's B

Step-by-step explanation: Got 100% on the quiz

Answer:

x= 45

y= 18.5 (3 s.f.)

Step-by-step explanation:

Since the quadrilateral has 4 equal sides, it is a square and hence the 4 angles are right angles.

I have drawn the 2 triangles of the square separately for better understanding.

Please see the attached pictures for full solution.

Step-by-step explanation:

x=y

y=1/z^3

Now,

for equation,

x=y=1/z^3

x is directly proportional to y and is inversely proportional to the cube of z.

Then, x = y = [tex]$\frac{1}{z}^{3[/tex].

If y exists directly proportional to x then,

y/x = k

⟹ y = kx

If y exists inversely proportional to x then,

yx = k

⟹ y = k/x

Let, x is directly proportional to y.

It suggests that when all other phrases which affect x exist kept constant, x changes at a rate that exists a constant multiple of the rate at which y changes.

Let, x ∝ y

⟹ x = ky, x ∝ y

⟹ x = ky

Where k is constant.

when you exist told that x exists directly proportional to y.

x = y

y = [tex]$\frac{1}{z}^{3[/tex]

From the given information, we get

x = y = [tex]$\frac{1}{z}^{3[/tex]

Here, x is directly proportional to y and is inversely proportional to the cube of z.

Therefore, x = y = [tex]$\frac{1}{z}^{3[/tex].

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Answer:

x = 2

Step-by-step explanation:

Step 1:  Convert words into an expression

What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?

13x - 2(8 + 5x) = 12 - 11x

Step 2:  Distribute

13x - 2(8 + 5x) = 12 - 11x

13x - 16 - 10x = 12 - 11x

Step 3:  Solve for x

13x - 16 - 10x + 11x + 16 = 12 - 11x + 11x + 16

14x / 14 = 28 / 14

x = 2

Answer:  x = 2

Answer:

x=2

Step-by-step explanation:

Just took the test

The options A, B and C are geometric sequences whereas option D is not.

Step-by-step explanation:

Step 1:

For a series to be a geometric sequence, the numbers in the series must be of a common multiplying ratio. So multiplying a constant value with any number will give the value of the next number.

The multiplying constant can be determined by;

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3^{rd} term}{2^{nd} term} = \frac{4^{th} term}{3^{rd} term} =[/tex]  The common multiplying ratio.

Step 2:

For option A, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{10}{5} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{20}{10} =2, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{40}{20} =2.[/tex]

Since there is a common multiplying ratio of 2, option A is a geometric series.

Step 3:

For option B, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{5}{10} =0.5,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{2.5}{5} =0.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{2.5}{1.25} =0.5.[/tex]

Since there is a common multiplying ratio of 0.5, option B is also a geometric series.

Step 4:

For option C, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3}{1} =3,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{3} =3, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{27}{9} =3.[/tex]

Since there is a common multiplying ratio of 3, option C is a geometric series.

Step 5:

For option D, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{6}{3} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{6} =1.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{12}{9} =1.33.[/tex]

Since there is no common multiplying ratio, option D is not a geometric series.

Answer: C & D

Step-by-step explanation:

Step-by-step explanation:

[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ [/tex]

[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ speed \: of \: car = 10(t + 3) \\ \hspace{60 pt} = 10(1.5 + 3) \\ \hspace{60 pt}= 10 \times 4.5 \\ \red{ \boxed{ \bold{ \therefore \: speed \: of \: car = 45 \:km/ h}}} \\ [/tex]

Answer:

(20+2) (20-2) = 20² - 2²

20² - 2² = 396

Step-by-step explanation:

from the rule of the difference of two square which states thate

       (a + b)(a − b) = a² − b²

therefore, 22 can also be written as (20 + 2),

while 18 can be written as (20 -2)

therefore by the rule of the difference of two square the product of both expression will give

      (20+2) (20-2) = 20² - 2² = 400 - 4 = 396

Step-by-step explanation:

= (20 + 2) × (20 - 2)

= 22 × 18

= a^2 - b^2 = 396

= (a + b) × (a - b) = 396

From the above, a = 20 and b = 2.

Therefore,

(20^2) - (2^2) = 396.

Solution:

The slope intercept form of equation is given as:

y = mx + c ------ eqn 1

Where,

m is the slope of line

c is the y intercept

From given,

slope = m = 3

y intercept = c = 5

Substitute m = 3 and c = 5 in eqn 1

y = 3x + 5

3x - y = -5

Thus the equation of line is found

Answer:

48.

Step-by-step explanation:

Perimeter is 2l+2w

current perimeter is 16

16x3=48

16x²-49=

(4x)²-7²=

(4x-7)(4x+7)

Here I have used the expression:

a²-b²=(a-b)(a+b)

Answer:

(4x-7)(4x+7)

Step-by-step explanation:

16x² - 49

realize that 16 = 4² and 49 = 7²

Substituting these values into the expression,

16x² - 49

= 4²x² - 7²

= (4x)² - 7²

recall the algebra property :  a² - b² = (a+b)(a-b)

Applying this to our expression:

(4x)² - 7²

= (4x-7)(4x+7)     Answer

Option B:

[tex]$x=\pm 2\frac{1}{2}[/tex]

Solution:

Given expression:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

To find the value of x:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

Convert mixed fraction into improper fraction.

[tex]$3 x^{2}= \frac{18\times 4+3}{4}[/tex]

[tex]$3 x^{2}= \frac{75}{4}[/tex]

Divide by 3 on both sides of the equation, we get

[tex]$x^{2}= \frac{25}{4}[/tex]

[tex]$ x^{2}= \frac{5^2}{2^2}[/tex]

Taking square root on both side of the equation.

[tex]$\sqrt{ x^{2}}= \sqrt{\frac{5^2}{2^2}}[/tex]

[tex]$ x=\pm \frac{5}{2}[/tex]

Convert improper fraction into mixed fraction.

[tex]$x=\pm 2\frac{1}{2}[/tex]

Hence option B is the correct answer.

He needs to drink 3 cups MORE to meet his daily requirement.

Step-by-step explanation:

Here, as given in the question:

The total need for water = half a gallon = 0.5 gallon

1 gallon  = 128 oz

So, 0.5 gallon = 128/2  = 64 oz

Now, the capacity of 1 cup = 3.5 oz

The number of cups already drank by the person = 15 cups

So, the total amount of water already taken by him

= 15 cups x Capacity of 1 cup

= 15 x (3.5 oz)  = 52.5 oz

So, the amount of water left to be drink by him

= Total Need - Already covered

= 64 oz - 52 . 5 oz  =  11.5 oz

Now, as 1 cup = 3.5 oz

So, 11.5 oz  has [tex]( \frac{11.5}{3.5} )[/tex]cups  = 3.28 cup≈ 3 cups

Hence, he needs to drink 3 cups MORE to meet his daily requirement.

Final answer:

Abby has already consumed 52.5 oz of water by drinking 15 small cups at 3.5 oz each. Since the recommended daily intake is 64 oz, she needs to drink an additional 11.5 oz to meet the daily hydration recommendation.

Explanation:

The question pertains to calculating the amount of water a person needs to drink to meet the recommended daily hydration level. In this case, the student needs to find out how much more water Abby should drink after having consumed 15 cups of 3.5 oz each.

First, we calculate the total amount of water Abby has already consumed -

Therefore, Abby needs to drink an additional 11.5 ounces of water to meet the daily recommendation of half a gallon.

Answer:

Step-by-step explanation:

0.103 <= You want to round the number to two decimal places, we will use the  3 to see if it should be rounded up, or stay the same

3 is less than or not equal to 5, so therefore it should be rounded down

0.10 <= Your answer should be like this, or 0.1 if you don't want to add the 0 (because they are the same thing)

I hope this helps! Make sure to give me the brainliest answer , because it is greatly appreciated. Thank You!

Answer: Alonso has $7 and Rico has $700

Step-by-step explanation:

Kendra= 70$

Alsonso= 70 * 0.1 = 7$

Rico= 70 *10 = 700$

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Answer:Alonso has $7 and Rico has $700

Step-by-step explanation:

Kendra= 70$

Alsonso= 70 * 0.1 = 7$

Rico= 70 *10 = 700$

please give brainliest!

Answer:

square area is 100 in

triangle area is 12

so your full area of the figure would be 112 i believe

Step-by-step explanation:

Hope this helps have a wonderful day

Answer:

the answer is 36xy squared

Answer:

15 hours

Step-by-step explanation:

To solve this you start by setting up the proportion: [tex]\frac{3}{x} \\\\[/tex] = [tex]\frac{20}{100}[/tex]. This is because we want to know if 3 hours is 20 percent, then how much is 100 percent.

Next we cross multiply to get 300 = 20x

Now we can divide both sides by 20 to get 15.

To check the work we can multiply 15 by .2 and we get 3, so we know it's correct.

Answer:

15 hours to do the entire project

Step-by-step explanation:

20% is the same as 1/5.

"percent" means "per 100", so 20% means 20/100 which reduces to 1/5.

20% of an art project took 3 hours. That means that 1/5 of the art project took 3 hours. The entire project then takes 5 times as much time.

5 * 3 hours = 15 hours

It takes 15 hours to do the entire project.

15 - 3 = 12

It takes 12 more hours after 20% was done.

The length of image of AB after the dilation is 18 cm

Solution:

Given data:

Length of AB = 9 cm

Scale factor (k) = 2

Length of image of AB = ?

By the definition of scale factor,

[tex]$k=\frac{\text { Length of Dilated image AB }}{\text { Length of original image } \mathrm{AB}}$[/tex]

[tex]$2=\frac{\text { Length of Dilated image AB }}{9}[/tex]

Do cross multiplication, we get

2 × 9 = Length of dilated image of AB

18 = Length of dilated image of AB

Hence the length of image of AB after the dilation is 18 cm.

Answer:

70

Step-by-step explanation:

Step 1:  Divide

420 / 670

70

Answer:  70

Answer:

b

Step-by-step explanation:

when you have the l-10l  it means the distance from 0  and the distance from 0 from -10 is 10

The cost of the phone, without tax is,

⇒ $150

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

Desmond paid 8.5% sales tax when he bought a new phone.

And, The sales tax was $12.75.

Now,

Let the cost of the phone, without tax = x

Hence, We can formulate;

⇒ 8.5% of x = 12.75

⇒ 8.5/100 × x = 12.75

Multiply by 100;

⇒ 8.5x = 12.75 × 100

⇒ 8.5x = 1275

Divide by 8.5 both side;

⇒ x = 1275/8.5

⇒ x = 150

Therefore, We get;

The cost of the phone, without tax is,

⇒ $150

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To find the cost of the phone without tax, convert the tax rate to a decimal and then divide the amount of sales tax paid by this decimal. The calculation shows that the phone cost $150.00 before tax.

Desmond paid an 8.5% sales tax on a new phone and the amount of tax was $12.75. To find the cost of the phone without tax, we can divide the amount of sales tax paid by the tax rate expressed as a decimal.

Let's do the calculation:

$12.75 \/ 0.085 = $150.00

Therefore, the cost of the phone before the addition of sales tax was $150.00.