Noah runs a farm stand that sells bananas and raspberries. Each pound of bananas
sells for $3 and each pound of raspberries sells for $2.25. Noah made $72 from
selling a total of 28 pounds of bananas and raspberries. Graphically solve a system of
equations in order to determine the number of pounds of bananas sold, a, and the
number of pounds of raspberries sold, y.

The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

According to the question,

We have the following expressions:

f(x) = -5x+9/2

Now, we will find the all the values of f(x) by replacing x with the given digits:

f(4) = -5*4+4.5

f(4) = -20+4.5

f(4) = -15.5

The value of f(1/4):

f(1/4) = -5/4+4.5

f(1/4) = -1.25+4.5

f(1/4) = 1.375

The value of x when f(x) = 2:

-5x+4.5 = 2

-5x = 2-4.5

-5x = -2.5

x = 2.5/5

x = 0.5

g(x) = 1.5[tex]x^{2}[/tex]-8

Now, we will find all the values of g(x) by replacing x with the given digits.

The value of g(-2):

g(-2) = 1.5(-2)(-2)-8

g(-2) = 6-8

g(-2) = -2

The value of g(2.5):

g(2.5) = 1.5*2.5*2.5-8

g(2.5) = 9.375-8

g(2.5) = 1.375

The value of x when g(x) = 16:

1.5[tex]x^{2}[/tex]-8 = 16

1.5[tex]x^{2}[/tex] = 16+8

1.5[tex]x^{2}[/tex] = 24

[tex]x^{2}[/tex] = 24/1.5

[tex]x^{2}[/tex] = 16

x = +4 and -4

Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

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The length of side GF from the similar triangles shown is GF = √10 units

A mathematical phrase known as an equation demonstrates the connection between two or more variables and numbers.

If a pair of triangles share the same shape, all of their angles are equal, and their ratio of comparable sides is proportionate, then they are said to be similar.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." Standard form, slope-intercept form, and point-slope form are the three primary types of linear equations.

In a similar triangle, DE = GF, Hence:

GF/DF = GH/DE

GF / 5 = 2 / GF

GF² = 10

GF = √10

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Answer:

70%

Step-by-step explanation:

Answer:

y=100t+1200, where t is years since 2013 and

Step-by-step explanation:

We only have two points from which to form an equation.  Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0).  Let's make the x axis the year and y the student population.

Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013.  "t is the number of years after 2013."  (0,1200) becomes is the data point for 2013.  The school's population will be the y-axis.

(0,1200)   [primary school had 1200 students enrolled in 2013], and

(3,1500)   [1500 students in 2016]

---

First calculate m, the slope.  Slope is the Rise/Run between the two points (the change in y over the change in x)

Going from (2013,1200) to (2016,1500) we find that:

  Rise  (in y) = (1500 - 1200) = 300 students

  Run  (on x) = (2016 - 2013) =     3 years

The Rise/Run, or slope, m, is 300/3 or 100:  m = 100

Lets put that into our equation format:

y = 100x + b

X will be the time, in years.  The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:

y = 100t +b, where t is years after 2013.

(The 100 tells us that the student population increases by 100 per year)

We now need b, the y-intercept.  One can either graph this and look for the value of y when x=0, of simply input either of the data points.  This looks easy enough to input a point and solve for b:

Remember that t is the (year - 2013)

y = 100t +b   Solve for (2013,1200)

 t = 2013 - 2013 = 0

1200 = 100*(0) + b

b = 1200

Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).

The equation becomes y = 100t + 1200

See the attached graph.

A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)

Given that,

Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.

Solution is as given below :

90% Confidence Interval for μ is

μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]

μ = 75  ± (1.75) * 3/[tex]\sqrt{16}[/tex]

μ = (73.69, 76.31)

Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)

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It takes almost 5.7 hours the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches.

First, we must determine how quickly the hose operates.

By dividing the volume of the first aquarium by the length of time it took to fill it, we may determine that.

The following formula can be used to determine the volume of the first aquarium: V =L*B*H

where the aquarium's length is L and its width is B

Its height is H.

Thus, the first aquarium's volume is:

V =L*B*H = 3*8*11 = 264 inches^3

We have the filling rate as:

264/3 inches ^3 per minute,

Let's now determine the second aquarium's volume.

The first formula is what we employ.

The volume is as follows:

V =L*B*H = 26*33*35 = 30030 inches ^3

Now, we divide the capacity of the second aquarium by the pace of the first aquarium to obtain the amount of time.

According to mathematics, that is:

30030 * 3/264 = 341.25 minutes = 5.7 hours approximately

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Answer: “y is a function of x.” The letter x represents the input value or independent variable. The letter y, or f(x), represents the output value, or dependent variable.

Step-by-step explanation:lol i have no idea

The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.

How to find the length of a line segment?

A line segment is defined as a line bounded by two  points on a line.

The line segment from negative 5 comma 5 to 3 comma negative 1

is found by using the formula

square root of (x2-x1)² +(y2-y1)²

[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]

[tex]\sqrt{8^{2}+6^{2} }[/tex]

[tex]\sqrt{100}[/tex]

=10 units

therefore the length of the line segment is 10 units

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Answer:

41.2

Step-by-step explanation:

1 is in the tenths place.  Because the number the next number is a five, we must round up and 0.20 is the nearest tenth to 0.153.

Answer:

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is your slope and b is your y-intercept.

To find your equation with what you are given, you have to plug in your values.

(-5, 6) = (x, y) so plug -5 in where there is x and 6 in where there is y

then your slope, m, is 2 so plug 2 in where there is m.

so it should look like

6=2(-5)+b, now you are solving for b.

  6    = -10+b

+10      +10

___________

16     =  b           Then take the values and plug back into the slope intercept formula, y=mx+b.

Plug 16 in for b and 2 in for m (m represents slope and they told us the slope =2)

*you no longer need the y and x values because you only use those to solve for m or b, in this case b, so leave y and x in your equations*

y=2x+16

Answer:

f(- 5) = 7

Step-by-step explanation:

f(- 5) means what is the value of y when x = - 5

locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7 ), then

f(- 5) = 7

The zero of the function f(x) = 2x² - 8 is ± 2.

Zeros of the function

Zero of the function means the values of x when f(x) is equal to 0. Which  means that when f(x) = 0, x is a zero of the function.

Given,

Here we have the function f(x) = 2x² - 8.

Here we need to find the zero of the function.

As per the definition of the zeros of the function,

We have to apply the value of f(x) = 0, then we get,

2x² - 8 = 0

Now, we need the value of x only, so we have to move the other numbers to the other side , then we get,

2x² = 8

Now, move the number 2 to the right hand side then it will be dividing the number 8,

x² = 8/2

x² = 4

x = √4

Therefore, the value of x is ± 2.

So, the zeros of the function is either +2 or -2.

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The values satisfies the linear equation y = −47x−2 is (0, -2).

For the given question.

The linear equation is given as;

y = −47x −2

Check the result by putting the values from option.

For : −7 −6

Put x = -7

y = −47(-7) −2

y = 799 -2

y = 498 (incorrect)

For: 0 −2

Put x = 0

y = −47x −2

y = −47(0) −2

y = -2 (correct)

Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).

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The number that should be on the bottom left stamp is 1. It was gotten by dividing 2 by 2.

From the first picture, we have 82 and the number below it is 4. This was gotten as:

= 8 ÷ 2

= 4

The second picture has 93 and the number below it is 3. This was calculated as:

= 9 ÷ 3

= 3

The third picture has 61 and the number below it is 6. This was calculated as:

= 6 ÷ 1

= 6

The fourth picture will be:

= 2 ÷ 2

= 1

Therefore the value is 1.

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The value of y which the slope formula  is 34.

Slope can be defined as the rate of change of a body.

To calculate the value of y, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1 and solve for y

Hence, the value of y is 34.

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Answer:

x < 10 - 2y

Step-by-step explanation:

The approximate percentage of sales tax is 1%

A gymnastics mat priced at $53.

A cost of mat after adding sales tax = $53.53

So, the tax amount would be,

53.53 - 53 = 0.53

We need to find the sales tax percentage.

Let x be the percentage of sales tax.

x = (0.53)/(53.53)  * 100

x = 0.0099 * 100

x = 0.99%

x ≈ 1%

Therefore, the approximate percentage of sales tax is 1%

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The slope and the intercepts of the graph are determined.

Given:

the equation is :

2x+3y=6

we first find the slope of the equation:

m = -a/b

m = -2/3

now solve the intercepts:

to find x intercept, substitute in 0 for y and solve for x.

⇒ 2x+3y=6

⇒ 2x+3(0)=6

⇒ 2x+0=6

⇒ 2x=6

⇒ x=6/2

⇒ x=3

hence we get (3,0)

now, to find y intercept, substitute in 0 for x and solve for y.

⇒ 2x+3y=6

⇒ 2(0)+3y=6

⇒ 0+3y=6

⇒ 3y=6

⇒ y=6/3

⇒ y=2

hence we get (0,2) as the intercepts.

Therefore we plot the required graph.

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The slope of the line from the given points will be equal to 3/2 in the simplest form.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given points in the question,

(1, -9) and (4, -7).

x1 = 1 and x2 = 4

y1 = -9 and y2= -7

Slope  = (x2- x1)/(y2- y1)

= (4 - 1)/(-7 - (-9))

Slope = 3/2

Therefore, the slope of the line will be 3/2.

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Answer:

Im gonna assume its counter clockwise (excuse the bad drawing)

Step-by-step explanation:

The vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

Given that, triangle FGH has vertices F(-3, 4), G(2, 0), and H(-1, -2).

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

So, (x, y) → (x+3, y+6)

F(-3, 4) → (-3+3, 4+6) → F'(0, 10)

G(2, 0) → (2+3, 0+6) → G'(5, 6)

H(-1, -2) → (-1+3, -2+6) → H'(2, 4)

Therefore, the vertices of triangle F'G'H' after a rotation of 180° about (-3, -6) are F'(0, 10), G'(5, 6) and H'(2, 4).

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Answer:

SAS

Step-by-step explanation:

By applying the Side Angle Side Postulate (SAS), you can be sure that your two triangles are congruent.

The vertices of a parallelogram are given, according to which the area of the parallelogram will be equal to 58 units.

The perimeter of a shape is its boundary's length, regarded as a whole. A form's circumference can be calculated by adding the lengths of all of its sides and edges. Utilizing linear length units like centimeters, millimeters, yards, and feet, it is determined.

The total of all a parallelogram's sides is its perimeter.

Firstly, solve for vertices AB:

AB = √(17- 1)² + (1 - 1)² = 16

Then,

BC = √(22 - 17)² + (13 - 1)² = 13

Then,

CD = √(6 - 22)² + (13 - 13)² = 16

Lastly,

AD = √(6 - 1)² + (13 - 1)² = 13

Add all the values,

P = 16 + 13 + 16 + 13

P = 58 units.

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The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

The slope of the line = -3/4

The slope of the line the change in y coordinate with respect to the change in x coordinate of the function

The line is passing through the point (0,10)

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-10 = -3/4(x-0)

y - 10 = -3/4x

y = -3/4x + 10

The equation of the line in slope intercept form is

y = -3/4x + 10

Plot the graph using the slope intercept form

Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

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Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.

Here,

There are 3 book,

3!=6

3 different mathematics books,

3!=6

4 different physics books,

4!=24

2 psychology books

2!=2

by fundamental counting principle,

6*6*24*2=1728

There are 1728 different ways to arrange the books because the mathematics and physics books must be together.

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There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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Answer:

13

Step-by-step explanation:

-3-10, or 10+3 is equal to 13

Answer:

13

Step-by-step explanation:

-3+13=10

angle bcd is 140. see explanation in image

The total cost of painting is $564.

What is surface area of cuboid ?

  A cuboid is a three-dimensional figure enclosed by six rectangular planes, each of which has a different size in terms of length, breadth, and height. Anything in the shape of a rectangle, such as a box, brick, or other object, may be a cuboid if you look about. When viewed from any of the ends, a cuboid (3-dimensional) can be seen to be made up of different-sized rectangles (2-dimensional). A cuboid's area is its surface because it is a solid with three dimensions. Since a cuboid's faces are rectangular, its area may be determined using the formula for the area of a rectangle.

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

We have been given that a community hall is in the shape of a cuboid. The hall is 40m long 15m high and 3m wide.

The paint will be required for 4 walls and ceiling.

Let us find area of walls and ceiling.

Area of walls and ceiling = 2( 40*15) + 2(3*15) + (40*3)

=> Area of walls and ceiling = 2(600)+2(45)+120

=> Area of walls and ceiling = 1200+90+120

=> Area of walls and ceiling = 1410 [tex]m^2[/tex]

Therefore, the area of walls and ceiling is 1410 square meters.

Here Cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter.

Then total cost of paint = 10*[tex]\frac{1410}{25}[/tex] = 10*56.4 = $564.

Hence cost of paint is $564.

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The required values are x=0 and x=2/3.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

f(x) = -3x² + 2x - 1

Substitute f(x) = -1

-1 = -3x² + 2x - 1

-3x² + 2x - 1+1=0

-3x² + 2x = 0

x( -3x+2)=0

=> x=0,

 -3x+2 = 0

-3x=-2

x=2/3

The required values are x=0 and x=2/3.

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