2
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If the graph of f(x) = 4x is shifted 7 units to the left, then what would be the equation of the new grap
O A.
О в.
O C.
O D.
g(x) = 4(x-7)
g(x) = 4x + 7
g(x) = 4(x+7)
g(x) = 4x - 7
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Answer: only y=3x+4 is a function

Step-by-step explanation:

vertical line test. basically a function has to have one output (y) for every input (x)

The expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

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Answer:

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Step-by-step explanation:

Answer:

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

First lets find out the parentheses. ( The first thing we always do ):

89+9=98 ( Lets keep this aside )

Now lets find out what is : [tex]12^{2}[/tex] =

12 x 12 = 144.

Now lets add 144+98 = 242

Now subtract 78 from 242 =

164

Now lets add 398 =

562.

Now divide it by 12.

[tex]\frac{281}{6}[/tex] or 46 [tex]\frac{5}{6}[/tex]

The rations for sin M, cos M and tan M is  [tex]\sqrt{11}[/tex]/6, 5/6, [tex]\sqrt{11}[/tex]/5

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

Given;

Height=[tex]2\sqrt{11}[/tex]

Base= 10

Hypotenuse= 12

Now,

sin M= 2[tex]\sqrt{11}[/tex]/12

=[tex]\sqrt{11}[/tex]/6

cos M= 10/12

=5/6

tan M= 2[tex]\sqrt{11}[/tex]/10

=[tex]\sqrt{11}[/tex]/5

Therefore the trigonometric rations will be [tex]\sqrt{11}[/tex]/6, 5/6, [tex]\sqrt{11}[/tex]/5

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Answer:

A = 811.84 centimeters squared

Step-by-step explanation:

I cut the shape in half (two trapezoids)

I did the area for one trapezoid:

A = 22.3+46.5/2 (11.8)

A = 68.8/2 (11.8)

A = 34.4 (11.8)

A = 405.92 centimeters squared

Since this is only half of the shape, I multiplied the area by 2.

A = 405.92 (2)

A = 811.84 centimeters squared

Answer: 1.5 dollars

Step-by-step explanation: 24 times 1.5 is 36

Answer: 3/2 or 1.5 dollars per cupcake

Step-by-step explanation:

Use ratios:

$36 : 24 cupcakes

Divide by 24 on each side:

$36/24 : 1 cupcake

36/24 = 3/2 or 1.5 dollars per cupcake

Since it is stated that O is the centroid (also known as the point of intersection of the three medians), the segment JN, which traverses a triangle's vertex, would have to be a median to segment IK. IK = 24

As a segment is divided into two congruent pieces by medians, IN = NK = 12 since IN = 12.

IK is the sum of the measure of IN and NK, so in other words:

IK = IN + NK = 12 + 12 = 24

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In triangle IJK, O is the intersection of the three medians. If IN = 12 then the value of IK is 24.

A triangle's median is a line segment that connects a vertex to the middle of the side directly across from it.

Given that, O is the intersection of the three medians. Then, the segment JN which passes through a vertex of the triangle, would have to be a median to segment IK.

A median divides the segment into two equal parts. Thus, median JN divides the segment IK into two equal parts.

Thus, IN = NK

The value of IN = 12, hence NK = 12.

The value of IK is:

IK = IN + NK = 12 + 12 = 24

Hence, in triangle IJK , O is the intersection of the three medians . If IN = 12 then the value of IK is 24.

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Answer:

Essentially, in The Great Gatsby, Gatsby loses Daisy because he is trying to recapture something that never existed in the first place.

Answer:

$645

Step-by-step explanation:

300 + 4600(.075)

= 300 + 345  

= 645

The number of years after which the population of North Dakota equals the population of South Dakota is 150.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

North Dakota:

Population in 2012 = 0.3 million

Growth rate per year = 0.017 million

The population after x years.

= 0.3 + 0.017x

South Dakota:

Population in 2012 = 0.9 million

Growth rate per year = 0.013 million

The population after x years.

= 0.9 + 0.013x

Now,

The number of years after which the population is equal.

0.3 + 0.017x = 0.9 + 0.013x

Solve for x.

0.017x - 0.013x = 0.9 - 0.3

0.004x = 0.6

x = 0.6/0.004

x = 150

Thus,

After 150 years, the population will be the same.

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The histogram's graph of her number of handkerchiefs, y, in relation to the length of weeks since she last used one, x, is accurate.

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The ninth term of the geometric sequence is 2048.

Given is the geometric sequence as -

8, -16, 32, -64, .....

We can write the 9th term as -

a{9} = ar ⁹ ⁻ ¹

a{9} = ar⁸

a{9} = 8 (-2)⁸

a{9} = 8 x 16 x 16

a{9} = 2048

Therefore, the ninth term of the geometric sequence is 2048.

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The relative frequency for Point 3 will be 28.57 and cumulative frequency will be 28.

What is relative and cumulative frequencies?

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

To calculate the relative frequency two things must be known:

Number of total events/trials

Frequency count for a category/subgroup.

Relative frequency = subgroup frequency/ Total frequency

Cumulative frequency-

In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on. Frequencies that are obtained this way are known as cumulative frequency (c.f.).  

Now,

For Relative frequency

subgroup frequency for point 3=8

Total frequency = 28

Therefore,

Relative frequency=8/28

=2/7

=0.2857

Relative frequency=28.57 (upto two decimal points)

For cumulative frequency,

add all the subgroup frequency and that will be 28.

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On solving the provided question, we can say that form an equation = area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

to find the area

we have to form an equation =

area of the figure = x = 1/2*9*9 + 6*18 = 40.5 + 48 = 88.5

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Answer:

-56

Step-by-step explanation:

Substitute:

12*(-9)+52 =

-108+52 =

-56

Answer: -56

Step-by-step explanation:

if z is an exponent then the whole answer would be different but im guessing it is not ? I hope this helps.

Answer:

10 dollars for adult tickets and 6 dollars for student tickets

Step-by-step explanation:

a=adult tickets

s=student tickets

4a+2s=52              3a+5s=60

5(4a+2s=52)         2(3a+5s=60)

20a+10s=260        6a+10s=120

-6a+10s=120

14a=140

a=10

10 dollars per adult ticket

4(10)+2s=52

40+2s=52

2s=12

s=6

6 dollars per student ticket

The relationship between x and y in the equation y = x + 6. the relationship is Linear because the value of y is can be represented in a straight line

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Given the equation:

y = x + 6

This is a linear equation.

The slope (rate of change) is 1 and the initial value (y intercept) is 6

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Therefore, the answer to the given ratio problem comes out to be 300,000.

In mathematics, the term "portion" or "fraction" refers to the proportion of one number that is present in another. In a fruit platter with eight oranges and six lemons, for instance, the ratio of citrus to lemon is eight over six, meaning 8:6, which would be equivalent to the ratios of 4:3 or the decimals 1.333.

Here,

We must use our grasp of proportionality to establish the maximum amount of shares that can be owned in this exercise.

The 20 huge variations will allow Blackbird Oil to store a total of 300,000 gallons.

The details in the assertion can be summed up as follows:

20 brand-new, sizable oil storage tanks.

The ratio is 4:5 for 12,000 gallons.

Because of the proportional ratio of 4.05, the enormous receptacles are 1.25 times larger than the ordinary ones, giving us:

=> 1200 * 1.25 = 15000

=> 15000 * 20 = 300000

As a result, the supplied problem's answer equals 300,000.

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Answer:

The reflection of point S across the y-axis is point V

Point Q reflected across the x-axis - S (5, -5.5)

Point Q reflected across the y-axis - T (-5, 5.5)

The family buys around 19 cases of sparkling water in 30 days

lnequality is relationship between two expressions or values that are not equal to each other.

Let the total number of sparkling cans of water used in a day be =x

As mentioned, the family uses more than 15 cans each day so inequality becomes , ×> 15

As they buy cases of water with 24 cans in each case. So less than 1 case is used in a day.

Number of cans used in a day is more than 15, so approx number of cans used in 30 days will be = 30 x 50 =450

As each case contains 24 cans, so the number of cases that will contain 450 cans will be,  450÷24 =18.75 cases. Rounding this off to nearest whole number, we get 19 cases.

Hence, the family buys around 19 cases of sparkling water in 30 days

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The width of the room for the given condition is [tex]7\frac{3}{4}[/tex] feet.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

An operator is a symbol used to represent a mathematical operation. Examples include multiplication, division, addition, and subtraction.

Given the width of the nightstand [tex]3\frac{1}{4}[/tex] feet = 13/4 feet

and width of double-sized bed = 9/2 feet

width of room =  the nightstand and the bed arranged side by side

width of room = sum of width of nightstand and bed

width of room = 13/4 + 9/2

width of room = (13 + 9(2))/4

width of room = 31/4

width of room = [tex]7\frac{3}{4}[/tex] feet

Hence width of the room is [tex]7\frac{3}{4}[/tex] feet.

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The complete question is in image.

25 hours, 12 dollars an hour.

How can we set this up?

25 hours, 12 dollars per hour.  So 12 dollars per each hour, adding up to 25 hours in total.

12 (1 hour), 12 (1 hour), 12 (1 hour)..

Or you could do 12 x 25 to find it, just to make things a little more simple. 25 x 12 = 50
             250
= $300

The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

A polynomial with only one term is called a monomial. An algebraic expression known as a "monomial" has a single term but can also include several variables and a higher degree.

Given Monomial Rational expressions can be solved as follows

17.  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = \frac{4 \times x \times x \times y \times y \times}{x \times y\times y} = 4\times x[/tex]  

=>  [tex]\frac{4x^{2} y^{3} }{xy^{2} } = 4x[/tex]  

18.  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = \frac{2 x^{3} \times x\times y^{2} \times y }{2x^{3} y}[/tex]  

=>  [tex]\frac{2x^{4}y^{3} }{2x^{3} y } = x y^{2}[/tex]    

19.  [tex]\frac{8x^{2} y^{2} }{4xy} = \frac{2xy (4xy)}{4xy}[/tex]  

=>  [tex]\frac{8x^{2} y^{2} }{4xy} = 2xy[/tex]  

20.  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = \frac{3xy (2x^{2} y^{3} )}{2x^{2} y^{3} }[/tex]  

=>  [tex]\frac{6x^{3} y^{4} }{2x^{2} y^{3} } = 3xy[/tex]  

21.  [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = \frac{3x^{2} y^{6} (4x^{4} y^{2})} {4x^{4} y^{2} }[/tex]

=> [tex]\frac{12x^{6} y^{8} }{4x^{4} y^{2} } = 3x^{2} y^{6}[/tex]  

22. [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = \frac{13x^{6} y (2x^{3} y^{4})}{2x^{3} y^{4}}[/tex]  

=>  [tex]\frac{26x^{9} y^{5} }{2x^{3} y^{4} } = 13x^{6} y[/tex]  

23.  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = \frac{8x^{6}y^{2}(10 x^{6}y^{7})}{10 x^{6}y^{7} }[/tex]  

=>  [tex]\frac{80x^{12}y^{9} }{10 x^{6}y^{7} } = 8x^{6}y^{2}[/tex]  

24.  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = \frac{19x^{9}y^{5}(5x^{9}y^{2}) }{5x^{9}y^{2} }[/tex]  

=>  [tex]\frac{95x^{18}y^{7} }{5x^{9}y^{2} } = 19x^{9}y^{5}[/tex]    

25.  [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = \frac{5y (40x^{3}y^{7}) }{40x^{3}y^{7}}[/tex]  

=>   [tex]\frac{200x^{3}y^{8} }{40x^{3}y^{7} } = 5y[/tex]  

26.  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = \frac{-5x^{11}y^{4} (3x^{6} y^{9} )}{3x^{6} y^{9} }[/tex]  

=>  [tex]\frac{- 15x^{17} y^{13} }{3x^{6} y^{9} } = -5x^{11}y^{4}[/tex]  

27.  [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = \frac{ -8x^{5}y^{3} (8x^{3}y^{7} )}{8x^{3}y^{7} }[/tex]  

=> [tex]\frac{-64x^{8}y^{10} }{8x^{3}y^{7} } = -8x^{5}y^{3}[/tex]  

Therefore,

The simplest form of monomial rational expressions are

17. 4x,         18. xy²,        19. 2xy      

20. 3xy,      21. 3x²y⁶,    22. 13x⁶ y

23. 8x⁶y²,   24. 19x⁹y⁵,   25. 5y

26. -5x¹¹y⁴,  27. -8x⁵y³.

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x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

x + 3x - 4 = 10 - 3x

or, 4x - 4 = 10 - 3x

or, 4x + 3x = 10 + 4

or, 7x = 14

or, x = 14/7

or, x = 2

Thus, x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x

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The image of point Q under a translation by 4 units to the right and 1 unit up is Q'(5, 5).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, A point Q with coordinates (1, 4).

Now, The translation of point Q  4 units to the right and 1 unit up would be,

Q'(1 + 4, 4 + 1).

= Q'(5, 5).

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The value of the composite function h(1) is 24

From the question, we have the following parameters that can be used in our computation:

f(x) = -5x, g(x) = x + 3 and

h(x) = -2f (x + 2) - 2g(x - 1)

The above are individual functions

This means that

h(x) = -2(-5(x + 2)) - 2(x + 3 - 1)

For h(1), we have

h(x) = -2(-5(1 + 2)) - 2(1 + 3 - 1)

Evaluate

h(x) = 24

Hence, the value of the composite function is 24

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The new graph after the given transformations would have an equation; y = -f (x + 2).

It follows from the task content that the pre-image graph; y = f (x) is to be translated 2 units to the left and afterwards reflected across the X axis.

First, when a function, f (x) is translated k units to the left, the resulting function is; f (x + k).

Hence, when the graph is translated w units to the left, the resulting function is; y = f (x + 2).

Additionally, when a function, f (x) is reflected across the x-axis, the resulting function is; -f (x).

Ultimately, the resulting graph upon reflection over the x-axis is; y = -f (x + 2).

Complete question: The graph is reflected over the x-axis.

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Answer: 5

Step-by-step explanation:

-4 < 5+x < 0

The smallest x can be is -8

The largest x can be is -4

There are 5 whole numbers from -8 to -4