During breakfast, the school cafeteria sells half of the milk they have. they sell twice as much milk as orange juice. by the end of breakfast, they have sold 3 gallons of orange juice. write and explain how to find how much milk the cafeteria had at the beginning was f the day.

he started with 90 dollars and spent $3.50 each day

The value of x for log₉3=x is 1/2 or 0.5.

An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.

The equation given is -

log₉3=x

It can be expressed in the form -

3 = 9ˣ

3 = 3²ˣ

As base is same,

1 = 2x

x = 1/2 = 0.5

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The value of y is 1/ 2

The slope of a line can be defined as a number that describes;

Slope of a line is also called the gradient of a line.

It is also known as the ratio of the rise to the run, or the quotient of  the riser to the run.

The formula for slope is expressed as;

Slope = y2 - y1/ x2 - x1

Now, substitute the values

-2/ 7 = 4 - y/3 - 10

Find the ratio

-2/ 7 = 4 - y/-7

cross multiply

14 = 7(4 - y)

expand the bracket

14 = 28 - 7y

collect like terms

14 - 28 = -7y

-14 = -7y

Make 'y' the subject of formula

y = 1/2

Thus, the value of y is 1/ 2

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The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

the algebraic expression given in the question is a linear equation in three variables that are x , y and z and the simplification of this algebraic expression would also contain all the three variables

To solve this question we have to use the algebraic of  distributive property of addition over multiplication

so, using the above property and substituting the values given in the question we get

6x(3y +4z) = 6x(3y) + 6x(4z)

                  = 18 xy + 24 xz

Hence, The algebraic expression 6x(3y + 4z) can be simplified as 18xy + 24xz

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Step-by-step explanation:

It sounds like you need to find your slope. The equation is y2-y1/x2-x1

Say you have two points, and those two points make a line.

Say those points are (0,0), and (5,5).

To find the slope, we need which is equal to x2-x1/y2-y1 (the two coordinates for the points) which in this case, equals one. That means the constant rate of going up is, 1 each time it moves to the left once.

I hope this answers your problems. If you don't understand anything, I can try to help in the comments!

Answer:

-a^2*(a^2+21a+22)

best I can do

When y= 105 then x= 15.

A proportion is an equation in which two ratios are set equal to each other.

given:

At x=3, y=21

at y= 105 , x=?

So, creating proportionality

105/x= 21/3

105/x = 7

x= 105/7

x=15

Hence, when y= 105 then x= 15.

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The question attached here is incomplete.

The complete question is

The value of y varies directly with x. If x = 3, then y = 21. What is the value of x when y = 105?

Answer:

1 and 1.50 or 1 and 2, but most likely the first one.

Step-by-step explanation:

Answer:

the 1st value represents x, the independent value

the 2nd value represents y, the dependent value

I think that is what it is asking

It is a vague question

Answer:

Step-by-step explanation:

You want to know the meaning of the first and second values in the ordered pairs that represent the relation shown in the diagram.

The ordered pairs representing a relation are understood to be ...

  (first value, second value) = (input value, output value)

  = (value at arrow tail, value at arrow head)

The diagram labels the ends of the arrows as "Grade" and "Hours Studied." That tells you the values mean ...

 first value: Grade

  second value: Hours Studied

Answer:

-55

Step-by-step explanation:

The pattern here is subtracting by 2 higher than the previous term.

As you can see

1 -2 = -1

-1 - 4= -5

-5 - 6 = -11

etc.

Continuing until the eighth term gets you   - 41 - 14 = -55

The distance, in miles, from Pine Gap to Turkey Trot is 48 miles.

Here, we are given that on a road map, the distance from Pine Gap to Turkey Trot is 2 inches. The scale of the maps shows that 1 inch is equal to 24 miles.

This simply means that 1 inch on the map is equal to 24 miles in reality. Usually maps use a scale factor to compare the distances as the map is a condensed version of the actual geographical area. Here, the scale factor is 1 inch : 24 yards.

Thus, a distance of 2 inches on the map will be equal to 24 × 2 = 48 miles.

Therefore, the distance, in miles, from Pine Gap to Turkey Trot is 48 miles.

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Answer:

p = 8

Step-by-step explanation:

3 + 1 + p = 12

Rearrange the equation so that you have integers on one side and algebra on the other.

3 + 1 + p = 12

p = 12 - 3 - 1

p = 8

By evaluating the equation we found  3 pairs we can write the table:

x = -7, 0, 7

y = 2, -2, -6

Which represents our equation.

We want to get a table of the form:

x: x₁, x₂, x₃, ...

y: y₁, y₂, y₃, ...

To get that, we need to evaluate the given equation in some different values of x, so let's do that.

if we take x = 0, then we get:

y = -(4/7)*0 - 2 = -2

So we have the pair (0, -2)

If x = 7, then:

y = (-4/7)*7 - 2 = -4 - 2 = -6

So we have the pair (7, -6)

If x = -7 then:

y = (-4/7)*-7 - 2 = 4 - 2 = 2

So we have the pair (-7, 2)

So now that we have 3 pairs we can write the table:

x = -7, 0, 7

y = 2, -2, -6

Which represents our equation.

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The inverse of the function y= 10 - 2x² is y =√ (10 - x) / 2. .

Inverse Variation:

A connection between two variables is said to have inverse variation when one of the variables rises while the other falls.

When two variables, let's say X and Y, are coupled in such a way that raising X results in a drop in Y and vice versa, this is known as indirect or inverse variation.

All we have to do to find the inverse of a function is switch the variables x and y.

x = 10 - 2y²

Now, solve for y as follows:

2y² = 10 - x

y² = (10 - x)/2

y = √ (10 - x) / 2

Therefore,  the inverse of the function y=10 - 2x² is y = √ (10 - x) / 2.

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The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].

A function's inverse is a function that reverses the action of a function, say [tex]f[/tex]. If the inverse of f exists, it is denoted by f ⁻¹ and exists only if f is a bijective function.

The domain of a relation's inverse corresponds to the original relation's range. In other words, the inverse's x values are the relation's y values.

Consider the function,

f(x) = y = 2x² - 8

Swapping x and y, to find the inverse.

x = 2y² - 8

Adding 8 on both sides of the equation.

x + 8 = 2y² - 8 + 8

2y² = x + 8

Dividing each side of the equation by 2.

y² = ( x + 8 )/ 2

Taking the square root of the equation.

[tex]\sqrt{y^{2}}=\pm\sqrt{\frac{x+8}{2} }[/tex]

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

The inverse of the function f(x) = y = 2x² - 8 is [tex]y=\pm\sqrt{\frac{x+8}{2} }[/tex].

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Answer: The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.

The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.

Step-by-step explanation:

Given data,

PHYSIOLOGY If you know how tall you were at the age of 2, you can estimate your adult height (in inches).

Girls can use the expression 25+ 1.17h

where, h is the height (in inches) at the age of 2.

and, Boys can use the expression 22.7 + 1.37h.

So,

Let adult height of boys is represented by = y and

Let adult height of girls is represented by = x

From the equation,

adult height of girls expression is x = 25+ 1.17h

adult height of boys expression is y = 22.7 + 1.37h

First we can solve option a,

We have been asked to find the adult height of a girl who was 34 inches tall at age 2.

                         x = 25+ 1.17h

where, h = 34 inches

                          x = 25 + 1.17 (34)

                          x = 25 + 39.78

                          x = 64.98 inches

Therefore,

The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.

First we can solve option b,

We have been asked to find the adult height of a boy who was 33 inches tall at age 2.

                        y = 22.7 + 1.37h

where, h = 33 inches

                        y = 22.7 + 1.37(33)

                          y = 22.7 + 45.21

                          y = 67.91 inches

Therefore,

The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.

So,

The adult height of a girl who was 34 inches tall at age 2 is = 64.98 inches.

The adult height of a boy who was 33 inches tall at age 2 is = 67.91 inches.

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We conclude that the percent error in Terry's reading is 8.3 percent.

If you did a reading on a value V, and your reading is another value V', the percent error in your reading is given by the formula:

P = 100%*|V - V'|/V

In this case, Terry's reading of the volume of the liquid is V' = 33.0, while the actual value is V = 36.0

Replacing that in the formula for the percent error we get:

P = 100%*|36.0 - 33.0|/36.0 = (3.0/36.0)*100% = 8.3%

We conclude that the percent error in Terry's reading is 8.3 percent.

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x = -4 is the extraneous solution of the equation.

The equation is

(5 - x )^1/2 = x + 1

To find the extraneous solution first we need to find the value of x.

So we need to square on both sides of the equation

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

5 - x = [tex]x^{2}[/tex] +2x + 1

[tex]x^{2}[/tex] + 3x - 4= 0

[tex]x^{2}[/tex] + 4x - x - 4 = 0

x( x + 4 ) - 1 ( x + 4) = 0

( x + 4)( x - 1) =0

x = -4, 1

Now put both the value of x in the solution in the equation.

x = -4

[tex]\sqrt{5 - (-4)}[/tex] = -4 + 1

[tex]\sqrt{9}[/tex] = -3

3≠ -3

Now put

x = 1

[tex]\sqrt{5 -1}[/tex] = 1 +1

[tex]\sqrt{4}[/tex] = 2

2 = 2

Therefore we get that x = -4 is the extraneous solution of the equation and x = 1 is the solution of the equation.

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Answer:

SQUARE 1:

100% ; 75%

Step-by-step explanation:

I'm pretty sure this is right i hope this help

Answer:

Solution:

Total 94 vehicles

Washed on saturday:

34+27=61

94-61=33

So 33 vehicles are washed on Saturday.

The value of given expression for x=0 is 0, x=-2 is -1.25 and x=2 is -1.25.

Given the expression is -5x⁻².

Firstly, we will simplify the given expression -5x⁻² for x=0.

Substitute the value x=0 in given expression, we get

-5x⁻²=-5(0)⁻²

-5x⁻²=-5(0)

As we know that something multiply with 0 is zero.

So, we get

-5x⁻²=0

Now, we will simplify the given expression -5x⁻² for x=2.

Substitute the value x=2 in given expression, we get

-5x⁻²=-5(2)⁻²

Now, we will square the expression to simplify it, we get

-5x⁻²=-5(4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, we get

-5x⁻²=-5/4

-5x⁻²=-1.25

Furthermore, we will simplify the given expression for x=-2.

Substitute the value x=-2 in given expression, we get

-5x⁻²=-5(-2)⁻²

Now, we will square the given expression, we get

-5x⁻²=-5(4)⁻¹

Further, we will divide it above expression by 1 to remove negative sign, we get

-5x⁻²=-5/4

-5x⁻²=-1.25

Hence, the value of expression -5x⁻²  for x=0, 2 and -2 is 0, -1.25 and -1.25.

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Each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.

Given, a yearly subscription to a monthly magazine costs £42.00 i.e., 12 months to a monthly magazine costs £42.00.

one month will cost £42.00 divide by 12 and let it be x.

we simply calculate the value of x by dividing £42.00 by 12.

x = 42.00/12

x = 3.5

x = £3.5

Therefore, each issue will cost £3.5 if a yearly subscription to a monthly magazine costs £42.00.

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The  values of for which the rocket's height is 29 meters are 0.75 and -0.67.

The rocket's height h (in meters) after t seconds is given by the following.

h=57t-5t^2

Then the equation after the height is 29 meters was given will be

[tex]h=57t-5t^2[/tex]

29=57t-5t^2

then we will have  [tex]57t-5t^2-29=0[/tex]

Then this is a quadratic equation, which can be solved, to find t, then after using the quadratic formular the values of t are:

0.75 and -0.67

Then we can chose 0.75 seconds

Therefore, from the question, we can see that after the quadratic equation has been performed  0.75 and -0.67 serves as the values for the height of 29 metres.

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Answer:solve for x

x>3

Step-by-step explanation: 12x<9(2x−3)+9

Use the distributive property to multiply 9 by 2x−3.

12x<18x−27+9

Add −27 and 9 to get −18.

12x<18x−18

Subtract 18x from both sides.

12x−18x<−18

Combine 12x and −18x to get −6x.

−6x<−18

Divide both sides by −6. Since −6 is negative, the inequality direction is changed.

x>

−6

−18

​

Divide −18 by −6 to get 3.

x>3

The diagonal of the given brick using the Pythagorean Theorem is 5√2.

So, let the diagonal be 'x'.

Pythagorean formula: x² = b² + h²

Now,

Therefore, the diagonal of the given brick using the Pythagorean Theorem is 5√2.

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If the expression is log₃(2 x)², then the expansion of this looks like

2 (log 2+log x)/log 3.

Given that the expression is log₃(2 x)².

We are required to expand the expression by using the properties of logarithmic function.

The change of base formula is basically the formula that will give you the answer of a log with a different base by using only log calculations with a base of 10.

The expression is log₃(2 x)².

log₃(2 x)²=2 [tex]log_{3}[/tex] 2x

=2 (log 2+log x)/log 3

Hence if the expression is log₃(2 x)², then the expansion of this looks like 2 (log 2+log x)/log 3.

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The probability that the first student selected is a psychology major and the second student is an art major is 0.057.

Probability for psychology = 4/21

Probability for art major = 6/21

Therefore, the probability that the first student selected is a psychology major and the second student is an art major will be:

= P(Psychology) × P(art)

= 4/21 × 6/20

= 24/420

= 0.057

Therefore, the probability that the first student selected is a psychology major and the second student is an art major is 0.057.

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Answer:

40 cm^2

Step-by-step explanation:

Area of rectangle = length * width.
Area of square = length^2

To find the area of the given shape, we must subtract the area of the square from the area of the rectangle.

Area of the given rectangle = 8 * 7 = 56 cm^2
Area of the given square = 4^2 = 16 cm^2

56 - 16 = 40 cm^2