The function y=f(x)is graphed below. What is the average rate of change of the function f(x) on the interval 7≤x≤8?

Answer:

x = 20

y = 20

Step-by-step explanation:

In the given triangle, we can deduce that angle x is congruent to angle y using the Isosceles Triangle Theorem. Hence, we can construct the equation xº = yº.

We also know that the measures of the interior angles of a triangle add to 180º. Hence, we can construct the equation xº + yº + 140º = 180º.

We now have a system of equations, and since we already have an identity for xº (and also for yº), we can solve the system using the substitution method.

xº + yº + 140º = 180º

↓ substituting xº for yº

xº + xº + 140º = 180º

↓ subtraction 140º from both sides

2xº = 40º

↓ dividing both sides by 2

xº = 20º

↓ removing degree sign from both sides

x = 20

Now that we have solved for x, we have also essentially solved for y, as plugging this x-value into the equation xº = yº will just yield:

20 = y

y = 20

The linear equation that is represented in the table is:

y = 3*x + 2

A general linear equation can be written in the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

First, notice that on the table we can see the point (0, 2), then the y-intercept of the linaer function is b = 2

Then we can write:

y = m*x + 2

Now we can use any other point on the table to find the value of the slope m.

Using the second point (1, 5),replacing the values we will get:

5 = m*1 + 2

Solving for m, we will get:

5 = m + 2

5 - 2 = m

3 = m

Then the linear equation is:

y = 3*x + 2

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Answer:

Step-by-step explanation:

A = x 14%=.14x

B=8 (4%)=.04(8)

  =8x   12%= .12*8x

.14x+.04(8)=.12(8x)

.14x+.32=96x-.14x

.32=.82x/x

.32/.82=.39

The amount of 14 % of ethanol that needs to mixed is A = 36 gallons

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

14% ethanol fuel mixture should be mixed with 8 gal of 3% ethanol fuel mixture to get a mixture that is 12% ethanol

So , the equation is

A ( 14 % ) + ( 8 ) ( 3 % ) = ( A + 8 ) ( 12 % )

On simplifying , we get

14A + 24 = 12A + 96

Subtracting 12A on both sides , we get

2A + 24 = 96

Subtracting 24 on both sides , we get

2A = 72

Divide by 2 on both sides , we get

A = 36 gallons

Therefore , the value of A is 36 gallons

Hence , the equation is A = 36 gallons

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1000

Step-by-step explanation:

5000

Answer: y = 40deg, x = 80deg

Step-by-step explanation:

1. Because we see that there are parallel lines in the triangle to the left, we know that two of the angles of that triangle are 50deg

2. using the fact that triangles have a total of 180deg we get x = 80deg

To solve for y, we also know that there are two angles in that triangle which are the same, and one of them is y, therefore 2y + 100deg = 180deg, meaning 7 = 40deg

Answer:

80

Step-by-step explanation:

80,80,83,84,85,87,91,96,97

in this numbers there is one mode which is 80 . it is mono.

The corrective action that offices that consistently charged excessive fees would be subject to by JTFH is a. The office will immediately be terminated from the Program.

JTH Financial, LLC (JTHF)  is a company that was formed in 2010 in Virginia and their goal and mode of operation is to help customers with tax settlement products that can help them get the best amount to pay for taxes.

JTH Financial, LLC has affiliate offices that engage in tax preparation for clients around the United States but they monitor these offices to ensure that their tax preparation fee averages is not excessive. If an office consistently has excessive fees charged to its customers, then JTH Financial terminates them from the program to protect its customers.

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The shape that results from a plane passing through a cone that is perpendicular to the base is option B: Circle.

When a plane passes through a cone perpendicular to the base, it intersects the cone at a circle. This is because the plane is cutting the cone at a 90-degree angle to the base, and so it is cutting through the circular cross-section of the cone.

Therefore, If the plane were to be tilted or angled, the shape of the intersection would be an ellipse, which is a flattened circle. This is because an ellipse is the shape that results when a plane intersects a cone at an angle that is not perpendicular to the base.

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Carly can walk 1 mile in 264 seconds.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Unit rate of Carly is given.

Unit rate of an object in terms of distance covered and time taken is actually the speed of the object.

The formula for speed is,

Speed = Distance / Time

Speed = 20 feet per second

Distance = 1 mile = 5280 feet

Time taken be t.

20 = 5280 / t

t = 5280 / 20

t = 264 seconds

Hence it will take 264 seconds for Carly to walk a mile.

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Answer:

The unit of length that a microscope best helps to see is 1 millimeter.

Step-by-step explanation:

Microscopes are instruments used for viewing objects that cannot be seen with eyes. The unit length of an object that a microscope can view should be a length that is very small

Answer:

[tex]2 \, \dfrac{4}{25} \textrm{ ft}[/tex]

Step-by-step explanation:

First, solve for how many feet Jason has dug after 40 minutes:

[tex]\dfrac{\dfrac{3}{5} \textrm{ ft}}{10 \textrm{ min}} \times 40 \, \textrm{min} = 2 \dfrac{2}{5} \, \textrm{ft}[/tex]

So, the hole he has dug is 2 2/5 ft deep.

Next, we can solve for how deep the hole will be after placing a plant in by simply multiplying 9/10 by the depth of the hole dug.

[tex]2\, \dfrac{2}{5} \times \dfrac{9}{10} = \dfrac{12}{5} \times \dfrac{9}{10} = \dfrac{6 \times 9}{5 \times 5} = \dfrac{54}{25} = 2 \, \dfrac{4}{25} \textrm{ ft}[/tex]

Answer:

[tex]\textsf{1.\;\;Equation:\quad$A=720(1.048)^{t}$}[/tex]

    [tex]\textsf{Solution:\quad$\$1263.77$}[/tex]

[tex]\textsf{2.\;\;Equation:\quad$y=2^x$}[/tex]

    [tex]\textsf{Solution:\quad$8$}[/tex]

Step-by-step explanation:

Assuming the account earns annual compound interest.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values or P and r into the annual compound interest formula to create an equation for the amount of money in the account after t years:

[tex]\implies A=720(1+0.048)^{t}[/tex]

[tex]\implies A=720(1.048)^{t}[/tex]

To find the amount of money in the account after 12 years, substitute t = 12 into the equation:

[tex]\implies A=720(1.75523549...)[/tex]

[tex]\implies A=1263.76955...[/tex]

[tex]\implies A=1263.77[/tex]

---------------------------------------------------------------------------------

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given values:

Substitute the given values or a and b into the exponential function formula to create an equation for the number of bacteria after x days:

[tex]\implies y=1(2)^x[/tex]

[tex]\implies y=2^x[/tex]

To find the number of bacteria after 3 days, substitute x = 3 into the equation:

[tex]\implies y=2^3[/tex]

[tex]\implies y=8[/tex]

Answer: The greatest common factor for 15 and 64 is 1.

Answer:

35.26°

Step-by-step explanation:

You have to visualize this or draw a diagram

If a cube has side a, the face diagonal of the cube is √2a . The diagonal of the cube is √3a

One side of length a, another side of length √2a (face diagonal) and the third of √3a form a right triangle with the angle opposite √3a being the 90° angle

Therefore we can find the angle [tex]\theta[/tex]  which the cube diagonal makes with the face diagonal using the fact
[tex]\dfrac{a}{\sqrt{2}a} = \tan\theta[/tex]

[tex]\theta = tan^{-1}\left(\dfrac{1}{\sqrt{2}\right)} \\= 35.26^\circ[/tex]

Answer: After investing for 10 years at 8% interest

Step-by-step explanation: your $10,000 investment will have grown to $21,589 This calculator determines the future value of $10k invested for 10 years at a constant yield of 8.00% compounded annually

Answer:

21/8

Step-by-step explanation:

When you are dividing fractions, use Keep-Change-Flip. See image.

Keep-Change-Flip changes the problem to a multiplication.

To multiply fractions, multiply straight across:

top × top and bottom×bottom see image.

We get 21/8 is already in lowest terms.

The solution of the simultaneous equations using target matrix are; x = 51/37 and y = 33/37

The target variable is defined as the variable whose values are modeled and predicted by other variables.

We are given the simultaneous equations as;

5x - y = 6

2x + 7y = 9

In matrix form, it is expressed as;

5 -1 6

2 7 9

row 2 = row 2 + row 1 * 7

This gives us;

37   0   51

Thus;

x = 51/37

Plugging in 51/37 for x in eq 1 gives;

5(51/37) - y = 6

Multiply through by 37 to get;

5*51 - 37y = 37*6

255 - 37y = 222

-37y = 222 - 255

y = 33/37

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A frequency table is a list of objects with the frequency of each item given in the table. The frequency table is attached below.

The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.

The steps are lengthy to explain in words, but the process is fairly straightforward.  So Start with figure 1 in the diagram below. The letters A through O represent the steps you'll take to replace them. we'll replace A with 219 since that's the grand total.

Then B is replaced with 137 since we're given that 137 girls were surveyed. Then C gets replaced with 219-137 = 82, and so on.

Using arithmetic (adding and subtracting) to gradually replace each letter with the proper number as figure 2 shows.

The alphabetical order directly corresponds to the order in which the values are given by teacher.

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Citizens have the freedom and independence to choose their own career paths, as well as the ability to change jobs relatively easily if they desire.

The evaluation of the equation in the question for the number of solutions is as follows;

2) The values of S and T for which the equation Sx + 81 = -24x + T have infinitely many solutions is S = 24 and T = -81

c. S = 24 and T = -81

An equation is a statement of equivalence of two expressions.

The specified equation is presented as follows;

S·x + 81 = -24·x + T

The equation will have infinitely many solutions when both sides of the equation refer to the the sam line

The power of x on both sides of the equation is one, therefore, both expressions on the left and right side of the equation refer to linear relationships

The graph of two lines are the same if they have the same slope and the same y-intercept.

The slope of the expression on the left = S

The y-intercept of the expression on the left = 81

The slope of the expression on the right = -24

The y-intercept of the expression on the right = T

When both sides refer to the same line, we get;

S = -24, and T = 81

Therefore, both sides of the equation refers to the same line and therefore have infinitely many solutions when S = -24 and T = 81.

The correct option is option c

(c) S = -24 and T = 81

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The price of each bag of popcorn and the price of each drink is $7.5 and $4 respectively.

Let the drinks be represented as d.

Let the popcorn be represented as p.

From the information, Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:

6p + 4d = 65

Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:

9p + 8d = 107.50

Equating the equation

6p + 4d = 65 ..... i

9p + 8d = 107.50 ..... ii

Multiply equation i by 8

Multiply equation ii by 4

48p + 32d = 520

36p + 32d = 430

12p = 90

Divide

p = 90/12

= 7.5

6p + 4d = 65 .

6(7.5) + 4d = 65

4d = 65 - 45

4d = 20

d = 20/4

drink = 5

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The statement  means "whenever x is close to (but not equal to) a, then f(x) is a large positive number.

When x is close to (but not equal to) a, then f(x) is a large positive number, according to the expression limxaf(x)=. In other words, f(x) grows larger and larger without bound as x approaches a.

For a rational function, we divide the numerator and denominator by the highest power of x that appears in the denominator to get the limits at infinity. This establishes which term in the overall expression controls how the function behaves at high x values.

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Answer:

Step-by-step explanation: At the end of what? I need the rest of the question in order to help you.

Los números enteros están constituidos por todos los números que no tienen cifras decimales, por lo que sería verdadero afirmar que 5% es un numero entero.

¿Qué son los números enteros?

Los números enteros son un conjunto de números que se caracterizan por no tener cifras decimales. En general, los números enteros incluyen los positivos, negativos y el cero.

De acuerdo con lo anterior, podemos inferir que es verdadero afirmar que el 5% es un numero entero debido a que no tiene cifras decimales y es un número positivo. Por otra parte, si fuera 5.2% u otro valor con cifras decimales sería falsa la respuesta.

Nota: Esta pregunta está incompleta debido a que tiene información faltante. Aquí está la información faltante:

De acuerdo a reglas sobre los números, se puede concluir que 5 por ciento si es un número entero.

Opciones

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Answer:

A. The speed of the boat going against a current with a rate of x mph is (13 - x) mph.

B. The speed of the boat going with a current with a rate of x mph is (13 + x) mph.

Step-by-step explanation: