Noa buys 6 items that each cost $4.25 and 3 items that each cost $6.75. How much does Noa spend in total?
A$20.25
B$25.50
C$38.25
D$45.75

Answer:

[tex]y = \frac{1}{3} x + 20[/tex]

Step-by-step explanation:

We know that the toll road is 3 times faster than the side streets.

If 'x' represents the number of minutes she usually spend taking the side streets. The [tex]\frac{1}{3} x[/tex]  represents the time she takes taking the toll road.

Also we need to create an equation to represent her total travel time, including wait time. Therefore, the equation is:

[tex]y = \frac{1}{3} x + 20[/tex]

Therefore, the equation is:  [tex]y = \frac{1}{3} x + 20[/tex]

Answer:

12 students from math club

Step-by-step explanation:

Number of vans = 2

Number of students in each van = 6

Number of students who went from math club to the soap box = ?

You can apply the following expression:

Total  number of students=Number of students per van * Number of vans

Total  number of students= 6 *2

= 12 students from math club....

Answer:

Step-by-step explanation:

Answer:

The correct answer is last option 362.9 ft

Step-by-step explanation:

Points to remember

Sin θ = Opposite side/Hypotenuse

To find the value of x

It is given that length of slope = 1500 ft

From the figure we can get,

Sin 14 =  Opposite side/Hypotenuse

 =  x/1500

x = 1500 * sin(14)

 = 1500 * 0.2419

 = 362.88 ft ≈ 362.9 ft

The correct answer is last option 362.9 ft

Answer:

2x^2 -8x

Step-by-step explanation:

2x(x-4)

Distribute the 2x

2x*x -2x*4

2x^2 -8x

For this case we must reduce the following fraction:

[tex]\frac {130xy} {50x}[/tex]

Canceling similar terms in the numerator and denominator:

[tex]\frac {130y} {50}[/tex]

Dividing by 10 the numerator and denominator we have:

[tex]\frac {13y} {5}[/tex]

Finally, the expression is reduced to:

[tex]\frac {13y} {5}[/tex]

Answer:

[tex]\frac {13y} {5}[/tex]

Answer:

t = 3.5c

Step-by-step explanation:

The correct table is attached in the image below. Since the papers are being folded at a constant rate, there is a linear relationship between c, the number of crane and t, the total time in minutes.

We can find the equation of this linear relation using any two pair of points from the table. Using the first two points: (5, 17.5) and (8, 28)

First we need to find the slope of the line which gives the relation between the two variables.

[tex]Slope=\frac{\text{Difference in y coordinates}}{\text{Difference in x coordinates}}[/tex]

y coordinates represents the dependent variable which is the time in this case and x coordinates represents the independent variable which is number of cranes in this case. Using the values from the two points we considered:

[tex]Slope=\frac{28-17.5}{8-5}=3.5[/tex]

Thus, the equation of the line will be of the form:

t = mc + b

m is the slope here. Using its values, we get:

t = 3.5c + b

b is known as y-intercept. We need the value of b to complete the equation. Substituting the value of t and c from any pair we can find the value of b.

Using the point (5, 17.5), we get:

17.5 = 3.5(5) + b

b = 0

This means, the equation of the line would be:

t = 3.5c

Answer:

t=3.5c

Step-by-step explanation:

38<4x+3+7-3x

38<x+10

28<x

Ans: x>28

For this case we must solve the following inequality:

[tex]38 <4x + 3 + 7-3x[/tex]

We add similar terms to the right side of inequality:

[tex]38 <4x-3x + 3 + 7\\38 <x + 10[/tex]

We subtract 10 from both sides of the inequality:

[tex]38-10 <x\\28 <x[/tex]

Thus, the solution will be given by all values of "x" greater strict to 28.

Answer:

[tex]x> 28[/tex]

Answer:

28

Step-by-step explanation:

8C2 = 28

Answer:

-1 and 3

Step-by-step explanation:

The x intercepts are where the graph crosses the x axis.

Looking at the graph it crosses at two points

x = -1 and x=3

Answer:

[tex]5x \log_{10}(x)-2 \log_{10}(x)[/tex]

(If that closed circle is an open circle, please let me know because that means something totally different)

Step-by-step explanation:

I think you are given:

[tex]f(x)=\log_{10}(x) \text{ and } g(x)=5x-2[/tex]

and that you are asked to find:

[tex]f(x) \cdot g(x)[/tex]

That operation means multiplication. (Let me know if is an open circle because that means something difference).

[tex]f(x) \cdot g(x)[/tex]

[tex](\log_{10}(x) \cdot (5x-2)[/tex]  

Distribute:

[tex]\log_{10}(x)(5x)-\log_{10}(x)(2)[/tex]

Reorder a little (commutative property):

[tex]5x \log_{10}(x)-2 \log_{10}(x)[/tex]

Answer:

f(x) ⋅ g(x) = log10x^(5x − 2)

Step-by-step explanation:

Answer:

[tex]y=7x+49[/tex]

Step-by-step explanation:

To find the slope of a line which is perpendicular to another line, you need to find the opposite reciprocal of the first line's slope.

To find the opposite, flip the slope's sign. Your original slope is [tex]-\frac{1}{7}[/tex], so your opposite slope is positive [tex]\frac{1}{7}[/tex].

To find the reciprocal, flip the fraction. This changes your slope from [tex]\frac{1}{7}[/tex] to [tex]\frac{7}{1}[/tex], which may be written as just 7.

Therefore, your slope is 7.

To find your b term (your y-intercept) given that your x-intercept is -7, you can make use of point-slope form.

[tex]y-y1=m(x-x1)[/tex]

(m=slope)

If your x-intercept is -7, then the point at which your line intersects the x-axis is (-7, 0).

[tex]y-0=7(x-(-7))\\y=7(x+7)\\y=7x+49[/tex]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y < -3x-2 -----> inequality A

The solution of the inequality A is the shaded area below the dashed line y=-3x-2

The slope of the dashed line is negative m=-3

The-y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (-0.67,0)

y > -3x+8 -----> inequality B

The solution of the inequality B is the shaded area above the dashed line y=-3x+8

The slope of the dashed line is negative m=-3

The-y-intercept of the dashed line is (0,8)

The x-intercept of the dashed line is (2.67,0)

using a graphing tool

The system of inequalities y < -3x-2 and y > -3x+8 has no solution (parallel lines)

see the attached figure

Answer:

m∠P = 70°, m∠T = 20°, m∠SKP = 40° , and m∠MKT = 70°

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ PST

∵ m∠S = 90°

∴ m∠T + m∠P = 90° ⇒ interior angles of a triangle

∵ m∠SPK/m∠KPT = 5/2

- The ratio between the two angles are 5 : 2 , multiply the parts of the

  ratio by x, where x is a real number

∴ m∠SPK = 5x

∴ m∠KPT = 2x

∵ m∠SPK + m∠KPT = m∠P

∴ m∠P = 5x + 2x = 7x

- In ΔPKT

∵ KM ⊥ PT

∵ MP = Mt

∴ KM is perpendicular bisector of PT

∴ ΔPKT is an isosceles triangle with KP = KT

∵ KP = KT

∴ m∠KPT = m∠T

∵ m∠KPT = 2x

∴ m∠T = 2x

∵ m∠T + m∠P = 90°

∵ m∠P = 7x

∵ m∠T = 2x

∴ 2x + 7x = 90 ⇒ solve for x

∴ 9x = 90 ⇒ divide both sides by 9

∴ x = 10

∵ m∠P = 7x

∴ m∠P = 7(10) = 70°

∴ m∠P = 70°

∵ m∠T = 2x

∴ m∠T = 2(10) = 20°

∴ m∠T = 20°

- In ΔSKP

∵ m∠S = 90°

∵ m∠SPK = 5x = 5(10) = 50°

∴ m∠SKP = 180° - (90° + 50°) = 180° - 140° = 40° ⇒ interior angles of a Δ

∴ m∠SKP = 40°

- In Δ KMT

∵ m∠KMT = 90°

∵ m∠T = 20°

∴ m∠MKT = 180° - (90° + 20°) = 180° - 110° = 70° ⇒ interior angles of a Δ

∴ m∠MKT = 70°

Answer:

Var(U)=50

Step-by-step explanation:

Given

Var(X) = 2

We have to find

Var(U) when U = 5x+2

So,

When a variable is multiplied with an integer, the variance of that variable is multiplied with the square of that number i.e. Var(aX) = a^2 Var(X) This the property of variance.

As here x is multiplied with 5,

Var(5x) = 5^2 var(X) = 25*2 = 50

If the same integer is added to all the data values, there is no change in variance that is why the +2 will not affect the variance of U ..

Answer:

The average weight of African elephant is about 2 .5 to 7 tons or we can say that 1800 kg to 6300 kg.

Weight of females are about 3 to 4 tons .On the other hand weight of males are about 2.5 to 7 tons.

African element can live up to 70 years but on the other hand the life of Asian

elephants up to 60 years.

The appropriate measurement for the weight of an African elephant is between 2,268 to 6,350 kg. Male elephants can grow significantly larger than the female elephants.

African elephants are the largest land animals in the world. They are larger than the Asian elephant. The average weight of the African elephants is between 2,268 to 6,350 kg, the trunk alone can weigh as much as 140 kg and they can grow between 2.5 to 4 m in height.

On the other hand, the Asian elephant's weight is between 2000 to 5000 kg. African elephants are famous for their large ears, that help them to stay cool in hot African weather. Both male and female African elephant has ivory tusks, but the male's tusk is longer and heavier than the female's.  

Elephants are herbivores. It means they only eat grasses, herbs, fruits, plants, and trees. African elephants can eat 150 kg of food a day. An elephant’s brain can weigh as much as 4-6 kg, they are famous as intelligent creatures. There are two kinds of African elephants which are the Savanna elephant and the Forest elephant. Savanna elephants are larger than forest elephants.

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Keywords: African elephant, Asian elephant, the average weight of an elephant

Answer:

the IQR is 41 because 62-21=41

Answer:

83

Step-by-step explanation:

12, 21, 43, 62, 71

Median: 43

Lower quartile: 16.5

Upper quartile: 66.5

Interquartile range: 66.5 - 16.5 = 83

Answer:

David might be 40

Step-by-step explanation:

Brianna = 20 + 20 = 40 = David

James = 10 x 2 = Brianna

David = 40 - 20 = Brianna

To find David's age, we can use the given information and algebraic equations. We can determine James' age, which is x, and use it to calculate David's age as 4x. Thus, David is 40 years old.

To find the age of David, we need to first determine the age of James. Let's assume James is x years old.

According to the given information, Brianna is twice as old as James, so Brianna's age would be 2x years.

Similarly, David is four times as old as James, so David's age would be 4x years.

Finally, we're told that Brianna is 20 years younger than David. So, the equation would be: 2x = 4x - 20.

To solve this equation, we can subtract 2x from both sides, which gives us: -2x = -20. Then, dividing both sides by -2, we get x = 10. Therefore, James is 10 years old and David is 4x = 4 * 10 = 40 years old.

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The surface area of a sphere that is 8 inches is 201.06in²

Answer:

64 π inches^2  or 201.06 inches^2  to the nearest hundredth.

Step-by-step explanation:

The radius = 1/2 * the diameter

= 1/2 * 8

= 4 inches.

The surface area = 4 π r^2

4 π 4^2

= 64 π inches^2

or  201.06 inches^2  to the nearest hundredth.

Answer:

y+4=-(2/5)(x-5) ----> equation of the line into point slope form

y=-(2/5)x-2 ----> equation of the line into slope intercept form

2x+5y=-10 ----> equation of the line in standard form

Step-by-step explanation:

step 1

Find the slope of the given line

we have

5x-2y=-6

isolate the variable y

2y=5x+6

y=2.5x+3

The slope m of the given line is m=2.5

step 2

Find the slope of the line perpendicular to the given line

We know that

If two lines are perpendicular, then their slopes are inverse reciprocal each other

so

m1=5/2

the inverse reciprocal is

m2=-2/5

step 3

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-2/5

point (5,-4)

substitute

y+4=-(2/5)(x-5) ----> equation of the line into point slope form

y=-(2/5)x+2-4

y=-(2/5)x-2 ----> equation of the line into slope intercept form

Multiply by 5 both sides

5y=-2x-10

2x+5y=-10 ----> equation of the line in standard form

The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) are as follows:

[tex]y+4=-\frac{2}{5}(x-5)[/tex]  

[tex]y=-\frac{2}{5}x-2[/tex]

2x + 5y = - 10

Perpendicular lines follows the mathematical principle below.

where

m₁ and m₂ are slopes.

Therefore, using slope intercept form,

y = mx + b

where

m = slope

b = y-intercept

Therefore,

5x - 2y = -6

-2y = -5x - 6

y =  5 / 2 x + 3

The slope is 5 / 2 x

Applying perpendicular rule,

5 / 2m₂ = - 1

m₂ = - 2 / 5

Passing through (5, -4)

-4 = -2/5 (5) + b

-4 + 2 = b

b = - 2

Therefore, the equation is [tex]y=-\frac{2}{5}x-2[/tex]. It can be simplified as follows

5y = -2x - 10

Therefore,

2x + 5y = - 10

using y - y₁ = m (x - x₁)  it will be as follows:

[tex]y+4=-\frac{2}{5}(x-5)[/tex]

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The completed table:

x y

2 2

4 6

6 10

7 12

For each value of x, we substitute it into the function rule y = 2x - 2 and evaluate to find the corresponding value of y.

Calculations:

When x = 2: y = 2(2) - 2 = 4 - 2 = 2

When x = 4: y = 2(4) - 2 = 8 - 2 = 6

When x = 6: y = 2(6) - 2 = 12 - 2 = 10

When x = 7: y = 2(7) - 2 = 14 - 2 = 12

After simplifying each proportion or using cross-multiplication, it is clear that option B.) 18/48 = 20/50 is the false proportion.

For A.) 24/30 = 20/25, we can simplify by dividing both sides by 5. Simplified, it becomes 4/5 = 4/5, which is true.

For B.) 18/48 = 20/50, simplifying both sides by 2 gives us 9/24 = 10/25, which is not equivalent since 9x25 is not equal to 24x10. Therefore, this proportion is false.

For C.) 25/45 = 75/135, simplifying by dividing both numbers by 15 gives us 5/9 = 5/9, which is true.

For D.) 10/25 = 40/100, simplifying by dividing both sides by 10 gives us 1/2.5 = 4/10. If we further simplify 4/10 by dividing both the numerator and denominator by 2, we get 1/2.5 = 2/5, which is true after rounding the decimal in the first ratio to 2.5.

Comparing these results, option B is the false proportion.

Answer:

9

Step-by-step explanation:

Each animal have 2 eyes so basically 18/2 = 9

That's the answer, hope this helps.

:)

Answer:

20 animals.

Step-by-step explanation:

Sparkles the unicorn is eating an apple, when a chango removes the apple from its mouth and bites it. We already have 2 animals in the forest: the unicorn and the monkey.

Then,  the unicorn realizes that 18 pairs of eyes are watching the monkey. That gives us another 18 animals (considering everyone has 2 eyes).

so, in total we have 20 animals:  (18 + unicorn + monkey) = 20 animals.

Answer:

[tex]\large\boxed{\$10,999}[/tex]

Step-by-step explanation:

In this question, we're trying to find the value of Tom's car after 3 years.

From the question, we know that:

With the information above, we can solve the question.

We can do the simplest way by multiplying 250 by 36, since there's 36 months in 3 years, and then we would subtract that from our starting value.

Solve:

[tex]250*36=9000\\\\\text{We would then subtract 9000 from 19,999}\\\\19,999=10,999\\\\\text{Cars value after 3 years is}\, \bf\$10,999[/tex]

When you're done solving, you should get 10,999.

This means that Tom's car worth in 3 years is $10,999.

Answer:

10,999

Step-by-step explanation:

250 x 36 = 9,000

9,000 is how much the car went down in value it went down 3,000 a year for three years

19,999 - 9,000 = 10,999

10,999 is how much the car is worth after 3 years

Answer:

x=200 Minutes

Step-by-step explanation:

Using the given information, we can set up slope equations for each set of numbers. Plan A has an equation of y=.05x+30. Plan B has an equation of y=.1x+20. These plans both equal y, so they can be made equal to each other. This looks like .05x+30=.1x+20. Subtract 20 from each side to aid in getting x by itself. This will look like .05x+10=.1x. Subtract .05x from each side to get all the x's to one side. This looks like .05x=10. Divide by .05 to get x. 10/.05=200. This shows how many minutes it takes for the plans to cost the same.

Answer:

(3x-2) (9x^2 + 6x +4)

Step-by-step explanation:

27x^3−8

This is the difference of cubes

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

a^3 =27x^3  so a = 3x

b^3 =8  so b=2

a^2 = (3x)^2 = 9x^2   ab = (3x)*2 = 6x   b^2 = 2^2 =4

27x^3 -8 = (3x-2) (9x^2 + 6x +4)

Answer:

its all of them except for A cuz i got it wrong with the other answer.

Step-by-step explanation:

A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.

A pentagon is a polygon that has five sides and five angles. A regular pentagon is a pentagon in which all the sides are equal. A line of symmetry is a line that cuts a shape exactly in half.

A regular pentagon is a polygon that has 5 equal sides as well as 5 lines of symmetry.

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Answer:

[tex]-\frac{1}{4} x=1[/tex]

Step-by-step explanation:

To isolate your terms, start by combining your x terms by adding 1/4x to both sides.

[tex]-\frac{1}{2} x+3=4-\frac{1}{4} x\\-\frac{1}{4} x+3=4[/tex]

Next, combine your constant terms by subtracting 3 from both sides.

[tex]-\frac{1}{4} x=1[/tex]

To isolate the variable terms on one side and the constant terms on the other side, follow these steps: subtract the variable terms and add the constant terms, then move the variable terms to one side and the constant terms to the other side.

To isolate the variable terms on one side and the constant terms on the other side for the equation -1/2x+3=4-1/4x, you can follow these steps:

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Answer:

The value of x is 7 ⇒ 1st answer

Step-by-step explanation:

* Lets revise a fact in the circle

- The two tangents drawn from a point out side the circle are equal

∵ RSTUV is circumscribed about a circle

∴ Each side of the pentagon is a tangent to the circle

- Look to the attached figure to know how we will solve the problem

- Each tangent divided into two parts

# RS = x + y

∵ RS = 8

∴ x + y = 8 ⇒ (1)

# RV = x + n

∵ RV = 12

∴ x + n = 12 ⇒ (2)

- Subtract (2) from (1)

∴ y - n = -4 ⇒ (3)

# ST = y + z

∵ ST = 12

∴ y + z = 12 ⇒ (4)

# TU = z + m

∵ TU = 15

∴ z + m = 15 ⇒ (5)

- Subtract (5) from (4)

∴ y - m = -3 ⇒ (6)

# UV = m + n

∵ UV = 9

∴ m + n = 9 ⇒ (7)

- Add (6) and (7)

∴ y + n = 6 ⇒ (8)

- Lets solve equation (3) and equation (8) to find y

∵ y - n = -4 ⇒ (3)

∵ y + n = 6 ⇒ (8)

- Add (3) and (8)

∴ 2y = 2 ⇒ divide two sises by 2

∴ y = 1

- Lets substitute the value of y in equation (1)

∵ x + y = 8 ⇒ (1)

∵ y = 1

∴ x + 1 = 8 ⇒ subtract (1) from both sides

∴ x = 7

* The value of x is 7

Answer:

x = 2, y = -6, and z = 9

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

Step 1: Convert the system into the augmented matrix form:

•  3  -4   1      |  39

•  -3   1  -2     |  -30

•  2  -2  3      |  43

Step 2: Add row 1 it into row 2:

•  3 -4   1 |  39

•  0  -3  -1 |   9

•  2 -2  3 |  43

Step 3: Multiply row 1 with -2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4   1   |  39

•  0  -3  -1   |   9

•  0  2    7  |  51

Step 4: Multiply row 2 with 2/3 and add it in row 3 and then multiply row 3 with 3:

•  3 -4     1       |  39

•  0 -3    -1       |   9

•  0 0   19/3     |  57

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• 3x - 4y + z = 39  

• -3y - z = 9

• (19/3)z = 57 (This implies that z = 9.)

Step 6: Since we have calculated z = 9, put this value in equation 2:

• -3y - 9 = 9

• -3y = 18

• y = -6.

Step 8: Put z = 9 and y = -6 in equation 1:

• 3x - 4(-6) + 9 = 39

• 3x + 24 + 9 = 39

• 3x = 6.

• x = 2.

So final answer is x = 2, y = -6, and z = 9!!!

Answer:

See below.

Step-by-step explanation:

[tex] f(x) = x^2 - 16 [/tex]

Replace f(x) with y.

[tex] y = x^2 - 16 [/tex]

Switch x and y.

[tex] x = y^2 - 16 [/tex]

Solve for y.

[tex] y^2 = x + 16 [/tex]

[tex] y = \pm\sqrt{x + 16} [/tex]

Replace y with f^(-1)(x).

[tex] f^{-1}(x) = \pm\sqrt{x + 16} [/tex]

The relation above is not a function, so the given function f(x) does not have an inverse unless the domain is restricted.

Answer:

F-1(x) =  √(x + 16).

Step-by-step explanation:

Let y = x^2 - 16

First make x the subject:

x^2  = y + 16

x = √(y + 16)

Now  replace x by the inverse  f-1(x) and replace y by x:

f-1(x) =  √(x + 16).

Note we only take the positive square root otherwise we would not have a function.