How do you sketch the graph of a function of two variables?.

Answer:

39 miles

Step-by-step explanation:

We can start by using algebra to represent the problem in equation form. Let j be the number of miles Jacob ran.

From the information given, we know that:
Adam ran 21.5 miles less than Jacob.
Adam ran 17.5 miles.

We can use these two pieces of information to set up the following equation:
j = 17.5 + 21.5

Now we can solve for j by adding 21.5 to both sides:
j = 39

So Jacob ran 39 miles.

Answer:

the b part

Step-by-step explanation:

Answer: The y-intercept of y=mx+b is B

Step-by-step explanation:

1. Y is the y-variable

2. Mx is the slope

3. B is the y-intercept.

Answer:

-26

Step-by-step explanation

1) substitute -2 for X

4(-2)(2)-3(-2)-16

2) solve

-8(2)+6-16

-16+6-16

-10-16

-26

The value of function at x= -2 is f(-2) is 54.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 4x² - 3x - 16.

Now, to find the value of f(-2) put the value of x= -2.

so, f(-2)= 4(-2)² - 3(-2) - 16

= 4(16) + 6 - 16

= 64 -10

= 54

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Step-by-step explanation:

x1, y1 = (-5,-2)

slope,m = -6/5

general equation, y= MX + C

(y-y1)/(x-x1)=m

(y+2)/(x+5)=-6/5

5y+10=-6x-30

5y=-6x-40

y=-(6x/5) - 8

The number of cans required for John to paint the wall is given by the equation A = 3.375 cans ≈ 4 cans

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the wall be A

Now , the area of wall A = area of rectangle + area of triangle

The side length of the rectangle = 3m

The width of the rectangle = 2 m

The height of the triangle = 1 m

The base of the triangle = 1.5 m

So , the area of the triangle = ( 1/2 ) x 1.5 x 1 = 0.75 m²

Now , the area of the rectangle = length x width

Area of the rectangle = 3 x 2 = 6 m²

So , the area of the figure = 6.75 m²

Now , 11 can of paint covers an area of 22 square meters

So , 1 square meters = 11/22 cans

1 square meters = 1/2 cans

And , the number of cans required for 6.75 m² of area = 6.75 ( 1/2 ) cans

The number of cans required for 6.75 m² of area = 3.375 cans

The number of cans required for 6.75 m² of area = 4 cans

Hence , the number of cans is 4 cans

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The volume and value of x is x>9.

Since x represents the width, it clearly must be greater than zero since a box must have each dimension be positive which makes the lower bound. The question is whether (17-2x) and (4-2x) represent the other 2 dimensions or not.

If so, then (4-2x) must also be greater than zero which makes the possible range of x as 0<x<1.5

If not, then in addition to the above range, values of x such that both 4-2x and 17-2 evaluate to negative still result in a positive volume.

Therefore, additional values of x are x>9.

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Adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

Let the fractions be 1/8 and 1/12

8 = 2 × 4

12 = 3 × 4

By using LCM, we get

[tex]$2 \times 3 \times 4=24 \quad\{L C M\}$[/tex]

= 1/8 + 1/12

simplifying the equation, we get

[tex]$=\frac{1 \times 3}{8 \times 3}+\frac{1 \times 2}{12 \times 2}$[/tex]

= 3/24 + 2/24

= 5/24

Therefore, adding the fractions 1/8 and 1/12 by using the LCM of 8 and 12 as the common denominator exists 5/24.

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Answer:

g = -19

Step-by-step explanation:

Given equation,

→ -3g = 57

Now the value of g will be,

→ -3g = 57

→ g = 57/-3

→ g = -(57/3)

→ [ g = -19 ]

Hence, the value of g is -19.

Answer:g=-19 I hope this helps

Step-by-step explanation:

-3g=57

Divide both sides of the equation by -3

-3g divide (-3)=57 divide (-3)

Any expression divided by itself equals 1

g=57 divide (-3) then you do

Dividing a positive and a negative equals a negative: (+) divide(-)=(-)

g=-57 divide 3

Next thing you do is

Calculate the quotient which something like this

g=-19

So you’re answer is g=-19

The required slope of the curve at the designated point P is 1/4.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the curve at point p is given as
= rise/run

From the graph,
rise = 2 and run = 8
slope of the curve at point P = 2 / 8 = 1/4

Thus, the required slope of the curve at the designated point P is 1/4.

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Answer:

$41.04

Step-by-step explanation:

set up a proportions equation:

[tex]\frac{18.20}{2\frac{1}{3}} =\frac{x}{5\frac{1}{4}}[/tex]

cross multiply and solve for x. this gives you:

x = 41.04

hope this helped, good luck!

The inverse of 8 is 1/8.

The multiplicative inverse of a number for any n is simply 1/n. It is denoted as:

1/x (or) x⁻¹

It is also called the reciprocal of a number and 1 is called the multiplicative identity.

The reciprocal of a number obtained is such that when it is multiplied by the original number, the value equals identity 1.

There are a few steps to find the inverse of a number:

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The set of potential output values of a function is often referenced by the range () function.

A built-in Python function called range() can be used to produce a series of numbers. The range() function's parameters can be supplied by the user if they want to generate a series of numbers given the starting and ending values.

It can be used to generate a list of numbers or to iterate over a series of numbers in for loops.

For example, range(5) will generate a sequence of numbers from 0 to 4, and range(2, 5) will generate a sequence of numbers from 2 to 4.

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Step-by-step explanation:

-8(-5/8x + y = -1/4)

5x - 8y = 2 is the standard form

Answer:  u = sr/qut

Step-by-step explanation:

Given the equation sr = qut, we can solve for u by isolating it on one side of the equation. To do this, we divide both sides by qut. This gives us sr/qut = u. This means that u can be represented in terms of q, r, s, and t as sr/qut. This is the final result.

.........

Given the equation sr = qut, we can solve for u in terms of q, r, s, and t by isolating u on one side of the equation.

To do this, we can divide both sides of the equation by (qut)

sr/qut = u

Then we have u = sr/qut

So, u is expressed in terms of q, r, s, and t as u = sr/qut

a)  Pam overtime wage for that week is 110.625

b) Pam works a basic week of 40 hours her basic wage is 150.

c)  Pam gross wage for that week during Christmas 114.375.

What is Basic wages?

An employee may not legally sell their labor for less than the minimum wage, which is the lowest compensation a business may pay their staff. By the turn of the 20th century, minimum wage laws were in place in the majority of nations.

What is Gross wages?

The total of the base salary, overtime compensation, commissions, bonuses, and other regular cash payments is referred to as the monthly gross wage. It does not include employer CPF contributions, bonuses, stock options, other lump sum payments, or payments-in-kind. It is prior to deducting employee CPF contributions and personal income tax.

Given that;

a)Calculation for  Pam overtime wage for that week ;

So, 25% of 3.75 = 0.9375

and add it to 3.75.

then 0.9375 + 3.75 = 4.6875

Since she worked 6 hours at that new wage,

then 6 x 4.6875 = 28.125

Now for 50% of 3.75 =1.875

and add it to 3.75

then  1.875 + 3.75 = 5.625

Since she worked 8 hours at that new wage,

then 8 x 5.625 = 45

She works double time, which means she receives two times her regular pay.

Since she worked five hours at the wage, double her basic wage by two and then by five.

then  2 x 3.75 x 5 = 37.5

So, Pam overtime wage for that week is ;

28.125 + 45 +  37.5 = 110.625

b) Pam works a basic week of 40 hours  her basic wage is ;

    40 x 3.75 = 150

c) Pam gross wage for that week during Christmas is ;

  total wages + overtime wages

⇒110.625 + 3.75 = 114.375

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Answer:

acute and scalene, remember:

Isoceles: An isosceles triangle is a triangle with two sides of equal length. The two equal sides are called legs and the third side is called the base.

Scalene: A scalene triangle is a triangle with all sides of different lengths. None of its angles are congruent.

Equilateral: An equilateral triangle is a triangle with all three sides of equal length. All three angles are congruent and measure 60 degrees.

The value of variable, x when f(x) = 4 according to the given function expression; f(x) = -x + 3 is; -1.

It follows from the task content that the value of x is to be determined according to the given function expression; f (x) = -x + 3.

Hence, when f (x) = 4, the resulting expression is;

4 = -x + 3

Hence, to determine the value of x, we must solve for x as follows;

4 - 3 = -x

1 = -x

x = -1.

Ultimately, the value of x for which the function instance f(x) = 4 is; x = -1.

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Step-by-step explanation:

for questions about % always find out first what 100% or what 1% are.

everything else can be calculated out of these 2 numbers.

in our case here

100% = 389 ml

1% = 100%/100 = 389/100 = 3.89 ml

18.6% = 18.6×1% = 18.6 × 3.89 = 72.354 ml

so, there are 72.354 ml of acid in the solution.

FYI

as you can see, we can combine both steps into one and do any of the following

18.6% = 18.6 × 100%/100 = 18.6 × 389/100 =

= (18.6/100) × 389 = 0.186 × 389

Answer: A. 9/19

Step-by-step explanation:

20 + 18(amount of cookies) = 38

there are 18 chocolate chip cookies, so it's an 18/38 chance it's a chocolate chip cookie that broke, but 18/38 can be simplified.

18 divided by 2 is 9 and 38 divided by 2 is 19

so 9/19

Answer:

An increase of 20

Step-by-step explanation:

-20 + 20 = 0

The change in temperature in degrees Fahrenheit required is A = 20°F

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The current temperature is -20°F, and we want to know how much it needs to increase to reach 0°F.

On simplifying the equation , we get

We can calculate this by finding the difference between the two temperatures:

0°F - (-20°F) = 0°F + 20°F = 20°F

Hence , the temperature needs to increase by 20°F to reach 0°F

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The value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

Since ZU and ZV is equal to 8, then QR is equal to ST and the radii ZY and ZW bisect ST and QR respectively.

we shall solve for x in the circle as follows:

QR = ST

4x - 5 = 7

4x = 7 + 5 {add 5 to both sides}

4x = 12

x = 12/4 {divide through by 4}

x = 3

The length VS = 7/2

VS = 3.5

Therefore, the value of x is equal to 3 and the length of VS is 3.5 for the circle Z.

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Answer: 7 seats in each row.

Step-by-step explanation:

14 / 2 = 7 seats in each row.

Answer:

25°

Step-by-step explanation:

Please see the attached document for how I set up this problem. I used the law/theorem of alternate interior angles to solve for the missing angle we're looking for, and knowing that a straight line will also have an angle measure of 180 degrees. We can also check the answer we arrive at by adding up all the angles that we have and seeing if they add up to 360 degrees, just as all the angles in a four-sided shape would.

The angle of KLM is 50 degrees. The opposite angle, MJK, is also 50 degrees. JKL and LMJ have the same angle of 130 degrees. When we add this together, we reach 360 degrees, letting us know our answer is correct.

The height of the rocket 45.161 km.

By adding a and b to h=-b2a, you may determine h, the x-coordinate of the vertex.

Determine k, the vertex's y-coordinate, by calculating k=f(h)=f(b2a).

According to the graph, the velocity first increases for 20 seconds before declining for 120 seconds before changing course.

Thus, it was at its highest peak at t=120 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular = 2 120 * 1000 * 60 km.

The rocket reaches a peak height of 112 feet at a time of 2.48 seconds. The rocket then falls and hits the ground 5.12 seconds after it was launched.

According to the graph, the velocity first increases for 20 seconds before declining for 112 seconds before changing course.

Thus, it was at its highest peak at t = 112  

2.48 seconds.

Therefore, all that is left to do is figure out the triangle OAB's area at its highest point. This is 2 base + perpendicular =  112 * 1000 /2.48 = 45.161 km.

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The measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

here, we have,

It is given that:

The diagram shows two parallel lines cut by a transversal.

As we know from the definition of the vertically opposite angles:

b = 54 degrees

a + c = 54 + b  (a = c)

2a = 54x2

a = 54 degrees

Since a and g are opposite interior angles, they are congruent, so you proceed with the process as you did for the first and check to see if the angles are acute or obtuse to ensure that the angle measurements are accurate.

Similarly:

b = 54

c = 126

d = 54

e = 126

f = 54

g = 126

Thus, the measure of the angles are a = 54, b = 54, c = 126, d = 54, e = 126, f = 54, and g = 126 degrees.

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We would expect about 80 seventh-graders to attend after-school programs.

To estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:

28 out of 140 respondents attend after-school programs, which is a proportion of

= 28 / 140

= 0.2.

We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:

400 * 0.2 = 80

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The original dimensions of the garden are 12 ft by 16 ft.

Width: x + 4 (not 2 because the width has two ends)

Length: x + 8 (same reason; this is x + 4 + 4)

The area of the garden and the border combined is 320 sq. ft.

The dimensions of the garden with the border around it are (x + 4) and (x + 8).

A (rectangle) = lw

A (garden with border) = lw

320 sq. ft. = (x + 4) (x + 8)

320 sq. ft. = x2 + 12x + 32

Transpose 320 to the right side of the equation.

0 = x2 + 12x + 32 - 320

0 = x2 + 12x - 288

Factor out.

0 = (x + 24) (x - 12)

One or both of the amounts are equal to zero when the product of two values is zero.

Equate the factors to 0.

x + 24 = 0 x - 12 = 0

x = - 24 x = 12

Since we cannit have a negative measure of distance, x = 12.

Find the original dimensions of the garden.

The original dimensions of the garden (without the border) are x and x + 4.

Width = x = 12

Length = x + 4 = 12 + 4 = 16

The original dimensions of the garden are 12 ft by 16 ft.

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Answer:

x = - [tex]\frac{6}{5}[/tex] , x = - 1

Step-by-step explanation:

(x + 1)(5x + 6) = 0 ← in standard form

equate each factor to zero and solve for x

5x + 6 = 0 ( subtract 6 from both sides )

5x = - 6 ( divide both sides by 5 )

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

or

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

Suppose vector "a" is given and we want to determine an expression to produce vector "b". To do this, we need to find two vectors, "c" and "d", such that:

a = c + d

where c and d are the vectors that when added together produce vector a. The expression to produce vector b can then be represented as:

b = d - c

The expression can be determined by first finding the components of vector a, and then using these components to determine the components of vectors c and d. For example, if vector a is represented as:

a = <a1, a2, a3>

We can set c and d equal to:

c = <a1/2, a2/2, a3/2>

d = <a1/2, a2/2, a3/2>

So, the expression to produce vector b can be represented as:

b = d - c = <a1/2, a2/2, a3/2> - <a1/2, a2/2, a3/2> = <0, 0, 0>

Expression to produce vector b: b = d - c, where d and c add to a. Find d and c using a's components, b is inverse of a.

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Let's say vector a is represented by the expression (a1, a2), and vector b is represented by the expression (b1, b2).

Then, the expression for the resultant vector (c1, c2) can be calculated as follows:

c1 = a1 + b1

c2 = a2 + b2

So the expression for the resultant vector is (a1 + b1, a2 + b2).

To determine an expression that produces vector b from vector a, you would need to know the relationship between the two vectors. If vector b is a scalar multiple of vector a, the expression for vector b can be represented as:

b = k * a

Where "k" is the scalar factor. If vector b is a vector that is in the opposite direction of vector a, the expression for vector b can be represented as:

b = -1 * a

In this case, the scalar factor is -1.

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