Evaluate the function.
ƒ(x) = −x² + x + 16
Find ƒ(−7)

Answer:

1.5x10^12

1500000000000

Step-by-step explanation:

Simplify the expression.

A new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 centimeters by 30 centimeters.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object

Sandy Island Beach is building a new Snack Shack based on a scale drawing that is 60 centimeters by 20 centimeters which are given in the question

Here the scale 1 cm : 1.5 m

As per the given scale, the dimensions would be as

60 centimeters :

⇒ 60 × 1.5 = 90

20 centimeters :

⇒ 20 × 1.5 = 30

Therefore, a new Snack Shack is being constructed at Sandy Island Beach which dimensions are 90 by 30 cm.

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The most appropriate choice for unitary method will be given by-

y =38x is the equation to represent the distance, y, in miles Sofia's

car can travel on x gallons of gas.

What is unitary method?

Unitary method is the method in which the value of single unit can be calculated from the value of multiple unit and value of multiple unit can be calculated from the value of single unit.

Sometimes value of single unit is more than value of multiple unit

For example - Relationship between price of a commodity and quantity of a commodity

Sometimes value of single unit is less than value of multiple unit

For example - Relationship between number of men and number of days taken by those men to do a work

Here,

Let y be the distance travelled by Sofia's car  in miles and let Sofia's

car can travel on x gallons of gas.

On 6 gallons of gas, Sofia's gas can travel 228 miles

On 1 gallon of gas, Sofia's car can travel [tex]\frac{228}{6}[/tex] miles

On 1 gallon of gas, Sofia's car can travel 38 miles

On x gallons of gas, Sofia's car can travel 38x miles

By the problem,

y = 38x

This is the equation  to represent the distance, y, in miles Sofia's

car can travel on x gallons of gas.

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A right triangle is a triangle with a right angle. The opposite side to the right angle is called the hypotenuse and the other sides are the legs. Given an angle in a right triangle, the ratio between the leg adjacent to the angle and the hypotenuse is equal to the cosine of the angle.

Using this relation in our problem, we have the following:

Solving this expression for q, we have:

And this is our answer.

We know that

< means smaller than

≤ means smaller or equal to

> means greater than

≥ means greater or equal to

We want to find a number (let's call it x), greater than -34

Since, > means greater than, we use this symbol:

y > -34

Hello!

What is the equation for the slope:

 [tex]\hookrightarrow \text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

    [tex]Slope =\dfrac{18-9}{-10-(-10)} =\dfrac{9}{0} \\[/tex]

Thus the slope is undefined:

Hope that helps!

Answer:[tex]b=4, c=-7[/tex]

Step-by-step explanation:

Parallel lines have the same slope.

The slopes of the lines are [tex]\frac{8-b}{c+1}[/tex] and [tex]-\frac{3}{2}[/tex].

Therefore, [tex]\frac{8+b}{c+1}=-\frac{3}{2}[/tex], and one possible pair is [tex]b=4, c=-7[/tex].

Answer:

Plane RAT

Step-by-step explanation:

:]

Answer:

Undefined slope

Step-by-step explanation:

Slope , m is equal to rise/run    Or   ( y1-y2) / ( x1 -x2)

              This line is a vertical line at x = -8    And thus has undefined slope

              (Because you cannot divide by zero)

Answer:

Undefined

Step-by-step explanation:

Hey! Let's help you with your question here! I am unsure if the points are correct cause you've written each one down twice. If it does change, I will change my answer accordingly.

We're looking for a slope of the line that passes through 2 points I see! Alright, so as you would recall, most equations of a linear line are described in the form of slope-intercept form. And that being this:

[tex]y=mx+b[/tex]

When we're finding for slope of the line, we're essentially just look for m. But how can we find m with only just 2 points? Well, we can! Using a formula that helps us find the slope using exactly 2 points! And that is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, all we have to do is plug in the values as such and solve:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-11-(-1)}{-8-(-8)}[/tex]

From here, we come to a problem. If we were to solve this equation to find the slope, we will get an undefined value mainly because the denominator will equal 0 and we can't have it equal 0. So therefore, it is undefined.

we have the following:

in this case we must find the largest divisor between the numbers 12 and 20, this number is 4:

Therefore 3 flyers for the science club and 5 flyers for the music club. And it would be 4 places

From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)

It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.

To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.

The slope is given by y = mx + c  where m is the slope.

Hence, the slope of the given equation 3x -y = 10 is  arrived at by re-writing the expression as follows:

Y = 3x -10 where

slope m₁ = 3

given Lets attempt to derive the slope of the options given:

1) y = 3x + 5

m₂ = 3
The product of the slopes are:
= m₁ x m₂

=  3 x 3

⇒ 9 ≠ -1

Therefore, this is not a perpendicular line.

2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1

Again, this is not the required line.

3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3

Compute for slope:

= 3 x - (1/3)
= -3/3
= -1

Hence,  x + 3y = 27 is the perpendicular line.

4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39

Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.

Thus, we have our final answer as option C.

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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.

The slope of the perpendicular lines is equal to the inverse and of the opposite sign.

Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,

Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,

Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.

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The expression which correctly represents the number of students studying German as required is; 3y + 2x -35.

It follows from the task content that the number of students studying German be determined from the given information.

Therefore since the total number of students is; 100.

35 students study Spanish of which y are boys, therefore, the number of girls studying Spanish is; (35 - y).

Also, since there are 3x girls in total and x of which study French, the remaining 2x study Spanish and German.

Hence, the number of girls who study German is; 2x - (35 - y).

Therefore, the total number of students (boys and girls) who study German is; 2y + 2x - (35 - y).

= 3y + 2x -35.

Ultimately, the total number of students who study German are; 3y + 2x -35.

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Standard form of equation is 3x + 5y = 2.

Ax+ By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful. A linear equation has the conventional form Ax+ By=C. A slope-intercept form equation (y=mx+ b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.

Slope = 2

Points = (3, 5 )

Standard form of equation,

Ax + By = C

Equating,

3x + 5y = 2

Standard form of equation is 3x + 5y = 2.

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Answer:

c) f = 28

Step-by-step explanation:

Given problem,

→ f³ = 21952

Now the value of f will be,

→ f³ = 21952

→ f = ³√21952

→ [ f = 28 ]

Let's check the following,

→ 28³

→ (28 × 28) × 28

→ 784 × 28 = 21952

Hence, option (c) is correct.

Answer:

price for one ribbon =19 cents

she got $20

20- 16.77 the rest from the money = 3.23

so she spends 3.23 from buying the ribbon

how much ribbon does she buy

3.23 ÷ 0.19= 17 ribbons

The number of game disks that must be produced for the average cost to be $4.70 is 2600.

Given:

The average cost of producing x game disks for a computer is given by the function C(x) = 2.6+5460/x

To determine the number of game disks that must be produced for the average cost to be $4.70.

Substitute the average cost in the equation and solve to find the value of x i.e. number of disks,

4.70 = 2.6 + 5460/x

4.70 - 2.6 = 5460/x

2.1x = 5460

x = 5460/2.1

x = 2600

Therefore, the number of game disks that must be produced for the average cost to be $4.70 is 2600.

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Answer:

y = 3 and x = - 6

Step-by-step explanation:

y + 4 = 0 ( subtract 4 from both sides )

y = - 4

this is the equation of a horizontal line, parallel to the x- axis.

a parallel line will also be horizontal with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 6, 3 ) with y- coordinate 3 , then

y = 3 ← equation of parallel line

a line perpendicular to the given line will be a vertical line with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (- 6, 3 ) with x- coordinate - 6 , then

x = - 6 ← equation of perpendicular line

The last month's payment for this family can be algebraically expressed this way: 2665 - d - 11m.

We can obtain an algebraic statement for the last month's payment when we assign alphabetic values to the variables provided.

First, the price is the primary figure that is = 2665

The down payment is represented with the alphabet d dollars.

The monthly payment is denoted by m dollars.

Since we are given a duration of one year or twelve months, we will have to subtract one month from 12 to give us, 11 months.

Given these substitutions, the algebraic statement can be represented thus:

2665 - d - 11m.

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The counter example to the statement  “Two angles that are supplementary are always different measures” is 90° and 90°.

Supplementary angles are those angles that sum up to 180 degrees

In other words, two Angles are Supplementary when they add up to 180 degrees.

For example 130 degrees and 50 degrees are supplementary angles.

The statement says "two angles that are supplementary are always

different measures".

Therefore, the counter example to this statement is 90 degrees and 90 degrees. This is because they are the same and it still sum to 180 degrees.

In other words, the angles are supplementary and the same which is counter example to the statement.

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The number of pounds of pork he bought in decimal is 12.21 lb

Decimal:

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

For example 12.34 is a decimal.

Given,

At a butcher​ shop, karl bought 2 7/20 lb of beef and some pork. he left with 14 14/25 lb of meat.

Here we need to find the number of pounds of pork he bought using a decimal.

First, we have to convert the given fractions into decimal then we get,

Amount of beef = 2 7/20

Which is equal to,

=> 2 + 7/20

=> 2 + 0.35 = 2.35 lb

Similarly,  total amount of meat = 14 14/25

=> 14 + 14/25

=> 14 + 0.56 = 14.56

Therefore, the amount of pork is,

=> total amount of meat - the amount of beef

=> 14.56 - 2.35

=> 12.21.

Therefore, the the number pounds of pork in decimal is 12.21 lb.

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PLUG IN

[tex] \frac{11}{10} [/tex]

in the place of x in the function and simplify.

[tex]f( \frac{11}{10} ) = 2( \frac{11}{10} ) - 7 \\ f( \frac{11}{10} ) = \frac{22}{10} - 7 \\ f( \frac{11}{10} ) = \frac{ - 48}{10} \\ f( \frac{11}{10} ) = \frac{ - 24}{5} [/tex]

ATTACHED IS THE SOLUTION

Hello!

To solve for f(11/10)

 ==> must simply plug '11/10' into x's position in the equation

    [tex]f(\dfrac{11}{10} )=2(\dfrac{11}{10} )-7=\dfrac{11}{5} -7=\dfrac{11}{5} -\dfrac{35}{5} =-\dfrac{24}{5}[/tex]

Hope that helps!

17j+7 is the algebraic expression for Seven more than the product of 17 and Julie's savings.

Expression is a combination of variables, operators and numbers.

The given phrase is

"Seven more than the product of 17 and Julie's savings"

and j is variable to represent Julie's savings.

In the phrase we have Seven more than, it means we are adding 7 to something.

According to problem we are adding 7 to "product of 17 and Julie's savings"

Product means multiplying a number with another factor. Here the factor is julies saving j.

17j+7 is the translated algebraic expression.

Hence 17j+7 is the translation of  Seven more than the product of 17 and Julie's savings.

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Answer:

a) do the first three terms

Answer: a) -4, -2, 0      b) 14

Step-by-step explanation:

To find any term, we plug the number into the equation for n.

a)

1st term => 2(1) - 6 = 2 - 6 = -4

2nd term => 2(2) - 6 = 4 - 6 = -2

3rd term => 2(3) - 6 = 6 - 6 = 0

b)

10th term => 2(10) - 6 = 20 - 6 = 14

Answer:

3ab

Step-by-step explanation:

i hope you don't want to know how i did this :)

If n is a real number, then its reciprocal will be 1/n.

1. If the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex] then the value of x = 12.

2. If the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex] then the value of x = -7.

The inverse of a value or a number is the definition of reciprocal in mathematics. If n is a real number, then its reciprocal will be 1/n. Reciprocals are used to convert division to multiplication when dividing fractions, which simplifies the division process.

1. Let the equations be [tex]$\left(\frac{3}{4}\right) x=9$$[/tex]

Multiply both sides by 4

[tex]$4 \cdot \frac{3}{4} x=9 \cdot 4$$[/tex]

Simplifying the above equation, we get

3x = 36

Divide both sides by 3

[tex]$\frac{3 x}{3}=\frac{36}{3}$$[/tex]

Simplify

Therefore, the value of x = 12.

2. Let the equations be [tex]$-4=\left(\frac{4}{7}\right) x$$[/tex]

Switch sides

[tex]$\left(\frac{4}{7}\right) x=-4$$[/tex]

Multiply both sides by 7

[tex]$7 \cdot \frac{4}{7} x=7(-4)$[/tex]

Simplifying the above equation, we get

4x = -28

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{-28}{4}$$[/tex]

Therefore, the value of x = -7.

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Answer:

Step by step solution of a set of 2, 3 or 4 Linear Equations using the Substitution Method x-y=7;2x-2y=14 Tiger Algebra Solver.

Step-by-step explanation:

The solution of the given linear equation is x = -9.53

Here we have the linear equation:

-0.24*x - 16.4 = 1.48*x

To solve this, first we need to move all the terms with x to the left and the terms without x to the right.

-0.24*x - 1.48*x = 16.4

(-0.24 - 1.48)*x = 16.4

-1.72*x = 16.4

Now we can divide both sides by -1.72 to get:

x = 16.4/-1.72 = -9.53

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Answer: c) (is it c?)

Step-by-step explanation: c) x= - 74.5

0.24x+16.4=-1.48 step 1- subtract: -1.48- 16.4

0.24x= -17.88    (divide)

x= −74.5

there

i hope this helps!!