Barabas received a mark of 50% on a recent test. Barabas answered 13 of the first 20 questions correctly. Barabas also answered 25% of the remaining questions on the test correctly. If each question on the test was worth one mark, how many questions in total were on the test?

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The car can go 28.5 miles in 1 gallon of gas.

According to the question,

We have the following information:

Mamadou’s car used [tex]2\frac{2}{3}[/tex] gallons to travel 76 miles.

Now, we can easily find the distance covered by car in one gallon of gas but we will first convert the gas given from mixed fraction.

8/3 gallons of gas = 76 miles

Now, the distance covered in 1 gallon of gas can be found by dividing 76 by 8/3.

1 gallon of gas = 76/(8/3)

1 gallon of gas = 57/2 miles

1 gallon of gas = [tex]28\frac{1}{2}[/tex] miles or 28.5 miles

Hence, the car can go 28.5 miles in 1 gallon of gas.

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The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.

Given that,

The quadratic equation is x²-4x+2=0

We have to find the factor by using quadratic formula.

The word "quadratic," which meaning square, is derived from the word "quad." A quadratic equation is a "equation of degree 2," to put it another way.
A quadratic equation is a second-degree algebraic equation in x. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, x's coefficients are a and b, and c is just a constant.

x=[tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]

Take the equation,

x²-4x+2=0

Here,

a=1, b=-4 and c=2

Substitute the values in the formula.

x=[tex]\frac{-(-4)\pm\sqrt{(-4)^{2}-4(1)(2) } }{2(1)}[/tex]

x=[tex]\frac{4\pm\sqrt{16-8 } }{2}[/tex]

x=[tex]\frac{4\pm\sqrt{8 } }{2}[/tex]

x=[tex]\frac{4\pm\sqrt{4 \times 2 } }{2}[/tex]

x=[tex]\frac{4\pm2\sqrt{2 } }{2}[/tex]

x=2±√2

x=2+√2    or    x=2-√2

x=3.414     or     x=0.585

Therefore, The factors of the equation x²-4x+2=0 by using quadratic formula is x=3.414 and 0.585.

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Answer:

it will increase

Step-by-step explanation:

6 is bigger than 10

The side length of a single cube will be 6 centimeters.

The volume of the cube will be -

V = (a x a x a) cubic units

We have the volume of Prism as V[P] = 25920 cm³ which is made up of [n] = 120 cubes of the same volume.

The volume of a single cube will be -

V[c] = V[P]/n

V[c] =  25920/120

V[c] = 216 cm³

Volume of a cube = V[c] = (a x a x a)

Equating volume, we get -

a³ = 216

a = 6 cm

Therefore, the side length of a single cube will be 6 centimeters.

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The required height of the cliff is  5√3/(√3)-1.

The angle of depression is defined as the If a human looks down at an object, then the angle of depression of that human is the angle between the horizontal line of sight and the object.

we have, angle of depression to top of pole = 45°

that of to foot of pole = 60°

Height of pole is 5 meter.

Then distance between tower is = 5+x/√3        ∴  tan(theta)=P/B

and, tan(45) = x/5+x/√3 = √3x/5+x   =1               ∴  tan(45) =1

5+x =√3x

X = 5/(√3)-1

Now height of cliff = 5+5/(√3)-1 = 5√3/(√3)-1 meter

Thus, the height of cliff is  5√3/(√3)-1.

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Answer:

The answer is 12 hours

Step-by-step explanation:

Jenny would have to work 12 hours to make $156

234/18 = 13

156/13 = 12

If the counterpart likes to have a video call with him 5 pm on Friday London time, it will be 2 am on Saturday in Melbourne.

Given in ques,

When it is 5 pm in Melbourne, he found out that its 8 am in London.

The time difference is of 9 hours with Melbourne's time being ahead.

So, when its 5 pm on Friday in London, Melbourne's time will be ahead by 9 hours which would be 2 am on Saturday.

Hence, it would be 2 am in the morning on Saturday in Melbourne when its 5 pm in the evening on Friday in London.

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Answer:

v=-14

Step-by-step explanation:

Subtract 5 from both sides

5+v=-9

-5 -5

v=-14

Answer:

4 over 81

use a calculator then simplify

Answer:

14

Step-by-step explanation:

Correct me if I'm wrong

Answer:answer is 14

Step-by-step explanation:

hope this helps

Answer:

111

Step-by-step explanation:

1 is squared of the right one so ya

The linear function that represents the total cost per week is y = 4x + 250

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. The y-intercept and slope are represented by c and m respectively.

The equation can be represented in the form of y = mx + c

Data;

The equation to represent the amount spent weekly is y = 4x + 250

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With the help of probability we can conclude our answer.

acc to our question-

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The number of shelves is x/20.

From the question, we have

You collect miniature cars and display them on shelves that hold 20 cars each.

Number of shelves = x/20

Divide:

Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.

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The respective names of the point of concurrency is:

1. Circumcenter

2. Incenter.

3. Centroid

4. Orthocenter

Point of concurrency:

The point of concurrency is a point where three or more lines or rays intersect with each other.

Circumcenter:

The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.

Incenter:

The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.

Centroid:

The point where three medians of the triangle meet is known as the centroid.

Orthocenter:

The point where three altitudes of the triangle meet is known as the orthocenter.

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The rate of increase in the value of the baseball card per year is 0.42.

The value of a baseball card in dollars has been found to be 0.42y + 068, where y is the number of years since it was released. We need to find out by how much the value of the baseball card is increasing per year. Let the value of the baseball card be denoted by the variable "V".

V = 0.42y + 068

The value of the baseball card when it has been x years since it was released is : V1 = 0.42x + 068. The value of the baseball card when it has been (x + 1) years since it was released is : V2 = 0.42(x + 1) + 068.

The increase in the value of the baseball card per year is the difference in the values in any two consecutive years.

I = V2 - V1 = [0.42(x + 1) + 068] - [0.42x + 068] = 0.42

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6-3y=2x

-3y=2x-6

y=(2x-6)/-3

y=-(2/3)x+2


No me deja adjuntar la imagen de la gráfica, te recomiendo una página de internet llamada Desmos

X=0
y=-(2/3)(0)+2=2
(0,2)esmos


x=3
y=-(2/3)(3)+2=-2+2=0
(3,0)

x=-3
y=-(2/3)(-3)+2=2+2=4
(-3,4)

The meters of rope used for knot tying is 10 meters.

According to the question,

We have the following information:

A cout mater bough 45 meter of rope he used two-ninth of the rope for knot tying.

So, we have the following expression for the rope used for knot tying:

45 of 2/9

We know that the word of is replaced by multiplication.

45*2/9

Now, we will first multiply the numbers in the numerator and then we will divide the obtained result by denominator.

90/9

Dividing 90 by 9:

10 meters

Hence, the meters of rope used for knot tying is 10 meters.

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Answer:

She can rent the room for 6 hours.

Step-by-step explanation:

65 - 41 = 24

So she has left 24$ to use

24 divided by 4 = 6

She can rent the room for 6 hours.

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

A proportional relationship exists when each pair of data values is related in the same way, by multiplying by a factor. A proportional relationship can be identified by looking at data, an equation, or a graph. A proportional relationship with a constant of proportionality k between two quantities y and x is represented by the equation y = kx.

They pass through the source. They are linear (straight lines) and pass through the origin as well. The x to y ratio is a proportionality constant. For example, consider the following number pairs with a ratio of 2.5: 5 and 2; 10 and 4; 100 and 40; 2.5 and 1. These number pairs are all proportional to one another.

Note that an overview was his as the information is incomplete.

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The correct option is (a) i.e. the slope intercept form of the given line is y = 6x-14.

The slope of the line through two points (x₁ ,y₁) and (x₁ ,y₂) can be found by using the formula below.

  m = (y₂ - y₁) / (x₂ - x₁).

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.

Here we have a line that passes through two points (x₁ ,y₁) = (3 ,4) and  (x₁ ,y₂) =(5 ,16).

The slope of the line m = (y₂ - y₁) / (x₂ - x₁) = (16 -4) /(5 -3) = 12/2 = 6.

 ⇒ slope m = 6.

And we know the slope intercept form  is

  y = mx + b

⇒ 4 = 6*3 + b  {with points  (3 ,4)}

⇒ b =4 - 18 = -14 ⇒ b = -14.

So the slope intercept form is y = 6x-14.

The slope-intercept form of the equation with m =6 and y-intercept as -14 was found to be

  y = 6x -14.

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope intercept form equation of the line that passes through (3 ,4)and (5,16)?

(a) y = 6x − 14  

(b) y = −6x +14

(c) y = −6x − 14

(d) y = 6x + 14?

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=6.4 \end{cases}\implies 6.4=ab^2\implies \cfrac{6.4}{b^2}=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=5\\ y=409.6 \end{cases}\implies 409.6=ab^5\implies \stackrel{\textit{substituting from the 1st equation}}{409.6=\left( \cfrac{6.4}{b^2} \right)b^5} \\\\\\ 409.6=6.4b^3\implies \cfrac{409.6}{6.4}=b^3\implies 64=b^3\implies \sqrt[3]{64}=b\implies \boxed{4=b} \\\\\\ \cfrac{6.4}{b^2}=a\implies \cfrac{6.4}{4^2}=a\implies \boxed{0.4=a}~\hfill {\Large \begin{array}{llll} y=0.4(4)^x \end{array}}[/tex]

Answer:

Step-by-step explanation:

3x+4y=38

Answer:

y = - x - 13

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 4 ← is in slope- intercept form

with slope m = 1

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1 , then

y = - x + c ← is the partial equation of line q

to find c substitute (- 10, - 3 ) into the partial equation

- 3 = 10 + c ⇒ c = - 3 - 10 = - 13

y = - x - 13 ← equation of line q

Answer:

  8196.83

Step-by-step explanation:

You want the quantity after 6 weeks of a value initially 5500 and growing at a continuous rate of 0.95% per day.

Where r is the growth rate in some time period, the value after t periods is ...

  value = initial value × e^(rt)

Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.

That value is ...

  value = 5500·e^(0.0095·42) = 5500·e^0.399 ≈ 8196.83

After 6 weeks, the quantity is 8196.83.

The value of quantity grows to 8196.83 at exponential rate.

What is exponential rate?

Exponential growth may be a method that will increase amount over time. It happens once the instant rate of modification (that is, the derivative) of a amount with relevancy time is proportional to the amount itself.

Main body:

Continuous growth

Where r is the growth rate in some time period, the value after t periods is  value = initial value × [tex]e^{rt}[/tex]

Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.

That value is ...

 value = 5500·e^([tex]e^{0.0095*42}[/tex]) = 5500·[tex]e^{0.399}[/tex] ≈ 8196.83

After 6 weeks, the quantity is 8196.83.

Therefore the value of quantity grows to 8196.83

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The distance from the base to the summit of the mountain is 3600 meters

The speed when going from base to summit = 45 meter / minute

The time taken for going from base to summit  = x minutes

The speed when descents from top to bottom = 60 meter / minute

The time taken for descents from top to bottom = x - 20 minutes

The speed = Distance / Time

The Distance = Speed × Time

Here in both case the distance is same

Then

45x = 60(x-20)

Solve the equation

45x = 60x - 1200

60x - 45x = 1200

15x = 1200

x = 1200/15

x = 80 minutes

Then the distance = 45x

= 45×80

= 3600 meters

Hence, the distance from the base to the summit of the mountain is 3600 meters

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