Evaluate each function.

k(a) = |-2a + 3| - 1; Find k(3).

g(x) = 4^2x-1 + 7; Find g(1).

f(x) = |8x^2 - 5x + 3|; Find f(-2).

h(x) = -3x + 9; Find h(-1 + x).

f(n) = 5n - 1, Find f(- 3n).

He should have 27.5 left I'm 100% sure

I think it a but I sorry if it wrong

Answer:

Part 1) The measure of angle C is [tex]62\°[/tex]

Part 2) The measure of angle AOB is [tex]56\°[/tex]

Step-by-step explanation:

step 1

Find the measure of angle C

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]

we have

[tex]arc\ AD=124\°[/tex]

substitute

[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]

step 2

Find the measure of angle AOB

we know that

In the isosceles triangle  ODC

∠D=∠C=62°

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠D+∠C+∠DOC=180°

substitute the values

62°+62°+∠DOC=180°

∠DOC=180°-124°=56°

we have that

∠AOB=∠DOC -----> by vertical angles

so

∠AOB=56°

Answer : The dimensions ​of table runner will be, 20 inch length and 4 inch width.

Step-by-step explanation :

Let the width of table runner be, x

and, the length of table runner will be, 5x

Given:

Area of table runner = [tex]80inch^2[/tex]

As we know that:

Area of rectangle = Length × Width

[tex]80inch^2=(5x)\times (x)[/tex]

[tex]80inch^2=5x^2[/tex]

[tex]x=4inch[/tex]

The width of table runner = x = 4 inch

The length of table runner = 5x = 5(4) inch = 20 inch

Therefore, the dimensions ​of table runner will be, 20 inch length and 4 inch width.

Answer:

see below

Step-by-step explanation:

If the left-side tiles are numbered 1–7 from top to bottom, their order on the right is ...

7 — denominators factored

6 — common factors canceled

5 — make the left side have the same denominator as the right

3 — express the sum over the common denominator

2 — collect numerator terms

To calculate how many cups of flour Genise will need for 2 1/2 batches, multiply the amount of flour for one batch (1 1/2 cups) by the number of batches (2 1/2). This results in 3 3/4 cups of flour needed.

To find how many cups of flour Genise will need, we start by writing an equation that reflects the amount of flour needed for one batch times the number of batches she plans to make. Since she needs 1 1/2 cups of flour for one batch and she wants to make 2 1/2 batches, we set up the multiplication:

flour_needed = (cups of flour per batch) * (number of batches)

So the equation will be:

flour_needed = 1 1/2 * 2 1/2

Converting mixed numbers to improper fractions for easier multiplication, we have:

flour_needed = 3/2 * 5/2 = 15/4 cups

Then, we convert the improper fraction back to a mixed number, which is:

flour_needed = 3 3/4 cups of flour

Answer:

ok what is tthe question

Step-by-step explanation:

Answer:

How many solution does ++=11

x

+

y

+

z

=

11

have where ,,

x

,

y

,

z

are non-negative integers. In light of the restrictions, its clear that ,,∈{0,1,2,..11}

x

,

y

,

z

∈

{

0

,

1

,

2

,

.

.11

}

. So, at face value I would assign a value for

x

and determine the different combinations that

y

and

z

can hold. For example,

For =0

x

=

0

, we have +=11

y

+

z

=

11

. With writing them out I found that there are 12

12

different assigned combinations for

y

and

z

that satisfy the equation. For =1

x

=

1

, I got 11

11

. Consequently, the pattern becomes clear whereby each one takes a value less by one. Hence, the number of solutions is 1+2+3+4+5+6+7..+12=78

1

+

2

+

3

+

4

+

5

+

6

+

7..

+

12

=

78

. I was wondering if there is an easier method perhaps with combinations equation (,)

C

(

a

,

b

)

..?

Step-by-step explanation:

Answer:  [tex]\bold{\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\dfrac{DF}{AK}=\dfrac{4}{20}=\large\boxed{\dfrac{1}{5}}[/tex]

Answer:

  C.  0.366

Step-by-step explanation:

In this stemplot, it is apparent that the number on the right is the least-significant digit (thousandths digit) of the batting average. The two most-significant digits are to the left of the vertical line.

Hence the value 0.36 | 6 represents an average that is 36 hundredths plus 6 thousandths: 0.366.

Answer:

The two consecutive positive integers are 7 and 8

Step-by-step explanation:

Let

x ----> the first positive integer

x+1 ----> the second consecutive positive integer

we know that

[tex]x^{2} -17=4(x+1)[/tex]

Solve for x

[tex]x^{2} -17=4x+4\\ \\x^{2}-4x-21=0[/tex]

Solve the quadratic equation by graphing

The solution is x=7

see the attached figure

Find the value of x+1

x+1=7+1=8

therefore

The two consecutive positive integers are 7 and 8

To find two consecutive positive integers, we can set up an equation and solve for the values of x and x + 1.

Let's assume the first positive integer is x. Since we need to find two consecutive positive integers, the second positive integer would be x + 1. According to the given condition, the square of the first decreased by 17 should be equal to 4 times the second. This can be written as:

x^2 - 17 = 4(x + 1)

Now, we can solve this equation to find the values of x and x + 1.

x^2 - 17 = 4x + 4

x^2 - 4x - 21 = 0

By factoring or using the quadratic formula, we can find the solutions for x. Once we have the values of x, we can calculate x + 1 to find the two consecutive positive integers.

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Answer:

Robert is 7 years old and Maria is 14 years old.

Step-by-step explanation:

You can use 2 variables: m and r and write 2 equations:

m = r +7

m + 2 = 4( r -3)

So 3 * r = 21 or r= 7

Maria and Robert are currently with present ages as 14 and 7 years old, respectively.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It demonstrates that the expressions on the left and right sides are connected in the same way.

An equation has components like as coefficients, variables, operators, constants, terms, expressions, and the equal to sign. The "=" sign and terms on both sides are required when generating an equation.

The information is ,

Let's say the equation looks like this: A

Right now, A is valued at

Let Maria's age be x.

Let Robert's age be y.

Maria now has a 7-year age gap with Robert.

Hence, the equation x = 7 plus y (1)

Also, in two years she will be four times Robert's age from the previous three years.

The equation is (x + 2) = 4 (y - 3). (2)

We obtain (7 + y + 2) = 4y - 12 y + 9 = 4y - 12 after simplifying.

We obtain 3y = 21 by subtracting y and adding 12 on both sides.

We obtain y = 7 years old by dividing both sides by 3.

Robert is therefore 7 years old.

And , x = 14 years old

And , the age of Maria is 14 years old

As a result, Maria and Robert are currently 14 and 7 years old, respectively.

Click here to learn more about equations.

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Answer:

23-5≥3.25n

18≥3.25n

Answer:

Step-by-step explanation:

The range is the difference between the highest and the lowest values in a set of data.  The interquartile range, the IQR, is what's "inside" the box in a box plot, which consists of the difference between the central measures, which are the first and the third quartiles.

Range is the difference between the maximum and minimum values in a dataset, while the Interquartile Range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3), representing the spread of the middle 50% of the data.

It is calculated by subtracting the minimum value from the maximum value.

For example, if the highest score in a test is 95 and the lowest score is 55,

the range is 95 - 55 = 40.

To find the IQR, we first need to determine the first quartile (Q1) and the third quartile (Q3).

Q1 is the median of the lower half of the data, while Q3 is the median of the upper half.

The IQR is then calculated by subtracting Q1 from Q3.

For example, in a dataset:

If Q1 = 70 and Q3 = 90, then

IQR = 90 - 70 = 20.

The IQR is useful in identifying potential outliers and understanding the spread of the central data.

Answer:

a) The other root is -2

   The coefficient c = -106

b) q = 35

c) c = -8.75

Step-by-step explanation:

* Lets study the general form of the quadratic equation

* ax² + bx + c = 0

- Their roots are x1 and and x2

- The sum of them = -b/a ⇒ x1 + x2 = -b/a

- The product of them = c/a ⇒ (x1)(x2) = c/a

a) * Assume that the roots of the equation 10x² - 33x + c = 0

     are m and n

∵ m + n = -b/a

∵ a = 10 and b = -33

∴ m + n = -(-33)/10 = 3.3

∵ m = 5.3

∴ 5.3 + n = 3.3 ⇒ n = 3.3 - 5.5 = -2

∴ n = -2

* The other root is -2

∵ m × n = c/a

∵ m = 5.3 , n = -2 , a = 10

∴ (5.3)(-2) = c/10

∴ -10.6 = c/10 ⇒ Multiply both sides by 10

∴ c = -106

* The coefficient c = -106

b) * Assume that the roots of the equation x² - 12x + q = 0

     are m and n

∵ The difference between the roots is 2

∴ m - n = 2 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = -12

∴ m + n = -(-12)/1 = 12

∴ m + n = 12 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 14 ⇒ divide both sides by 2

∴ m = 7

* Substitute the value of m in (1) or (2)

∴ 7 - n = 2 ⇒ 7 - 2 = n ⇒ 5 = n

∴ n = 5

∵ mn = c/a

∵ c = q , a = 1

∴ mn = q/1 = q

∴ q = 7 × 5 = 35

* q = 35

c) * Assume that the roots of the equation x² + x + c = 0

     are m and n

∵ The difference between the roots is 6

∴ m - n = 6 ⇒ (1)

∵ From the equation m + n = -b/a

∵ a = 1 , b = 1

∴ m + n = -(1)/1 = -1

∴ m + n = -1 ⇒ (2)

* Lets solve the two equation

- Add the two equation to eliminate n

∴ 2m = 5 ⇒ divide both sides by 2

∴ m = 2.5

* Substitute the value of m in (1) or (2)

∴ 2.5 + n = -1 ⇒ n = -1 - 2.5 = -3.5

∴ n = -3.5

∵ mn = c/a

∵ c = c , a = 1

∴ mn = c/1 = c

∴ c = 2.5 × (-3.5) = -8.75

* c = -8.75

Final answer:

To find the exponential function that passes through (-3, 80) and (-1, 20), we use the general form y = abˣ. By solving a system of equations using these points, we find that the exponential function is y = 40*2ˣ.

Explanation:

To write an exponential function that passes through the points (-3, 80) and (-1, 20), we can use the general form of an exponential function, which is y = abˣ. Here, a and b are constants we need to find. Given two points, we can set up a system of equations to solve for a and b.

Using the first point (-3, 80):
80 = a*b⁻³

Using the second point (-1, 20):
20 = a*b⁻¹

Dividing the second equation by the first gives us:
b2 = 4 which simplifies to b = 2 or b = -2. However, in exponential functions, b is positive, so we choose b = 2.
Substituting b = 2 into the second equation gives a = 40. Thus, the exponential function is y = 40*2ˣ.

Answer:

  1/96

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

Then ...

[tex]6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}[/tex]

Answer:

10$ an hour

Step-by-step explanation:

1/2c=6-1

c=2(6-1)

c=10

Answer:

Carey's hourly rate to babysit is $10.

Step-by-step explanation:

Given is -

For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate.

Let Carey's hourly rate to babysit be represented by 'c'

So, Anderson's hourly rate will be = [tex]\frac{c}{2}+1[/tex]

Also given that Anderson earns $6 per hour.

So, equaling both, we get;

[tex]6=\frac{c}{2}+1[/tex]

[tex]6=\frac{c+2}{2}[/tex]

[tex]c+2=12[/tex]

[tex]c=10[/tex]

Hence, Carey's hourly rate to babysit is $10.

Answer:

  $111

Step-by-step explanation:

The bank balance is ...

  $700 × (1 + 0.05) = $735

The cost of the computer is ...

  $750 × (1 -0.20) × (1 +0.04) = $624

The remaining bank balance after paying for the computer is ...

  $735 -624 = $111

_____

When you add a percentage, you effectively multiply by the sum of 1 and that percentage. The same is true if the amount "added" is negative (as for a discounted price).

  (original amount) + (percentage)×(original amount)

Use the distributive property to factor out the original amount:

 = (original amount)×(1 + percentage)

Answer:

(x, y, z) = (-2, -1, 2)

Step-by-step explanation:

Your graphing calculator can usually solve systems of linear equations easily.

Answer:

[tex]a^{2b}=x^{2}[/tex]

Step-by-step explanation:

we know that

[tex]a^{b}=x[/tex] ----> equation A

Find the value of [tex]a^{2b}[/tex]

Remember that

[tex]a^{2b}=(a^{b})^{2}[/tex]

[tex](a^{b})^{2}[/tex] ----> equation B

substitute equation A in the equation B

[tex](a^{b})^{2}=x^{2}[/tex]

therefore

[tex]a^{2b}=x^{2}[/tex]

The equations for the two machines are y = 5x and y = 8x, which represent their respective production rates. Over an 8 hour period, the first machine produces 40 miles of ribbon and the second produces 64 miles, resulting in a difference of 24 miles.

The two machines described in the question produce ribbon at different rates, which can be represented with two linear equations in slope-intercept form (y = mx + b) where m is the rate of production (slope) and b is the initial amount of ribbon (y-intercept, in this case 0 as the machine starts with no ribbon).

The first machine can produce 5 miles of ribbon in an hour, so its rate is 5 miles/hour. This gives the equation y = 5x.

The second machine can produce 8 miles of ribbon in an hour, leading to the equation y = 8x.

In an 8 hour period, the first machine will produce y = 5*8 = 40 miles of ribbon, while the second machine will produce y = 8*8 = 64 miles of ribbon. The difference is 64 - 40 = 24 miles.

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The first machine will make 40 miles of ribbon in 8 hours, and the second machine will make 64 miles of ribbon. The difference in length for an 8-hour period between the two machines is 24 miles.

To graph the length of ribbon each machine will make in 8 hours, we can start by determining the length each machine can make in one hour.

The first machine can make 5 miles of ribbon in an hour, so in 8 hours, it will make 8 times 5 = 40 miles of ribbon.

The second machine can make 8 miles of ribbon in an hour, so in 8 hours, it will make 8 times 8 = 64 miles of ribbon.

The slope-intercept form of an equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept. For the first machine, the equation would be y = 5x + 0, and for the second machine, the equation would be y = 8x + 0.

The difference in length between the two machines for an 8-hour period is 64 - 40 = 24 miles.

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Answer:

True, True , False , False , False

Step-by-step explanation:

Let us see the correction for the rest of the three False Statements

3) p→q represent the original conditional statement.

4) ~q → ~p represents the contrapositive of the original conditional statement

5) contrapositive of the original conditional statement will be ~q → ~p

There is one more implication called Converse of the original conditional statement . It is represented as q→p

Answer:

less than

Step-by-step explanation:

The multiplying fraction (5/7) is less than 1 so its product with 6 will be less than 6.

___

5/7·6 = 30/7 = 4 2/7 < 6

The expression 5/7×6 results in a value that is less than 6. This is because the value of 5/7 is less than 1, and multiplying it by 6 gives a result that is consequently less than 6.

To determine whether 5/7×6 is less than, greater than, or equal to 6, we perform the multiplication. Multiplying 5/7 by 6 can be viewed as 5 multiplied by 6, which equals 30, and then that result divided by 7. So the calculation is 30÷7, which equals approximately 4.29. Since 4.29 is less than 6, we can conclude that 5/7×6 is less than 6.

When solving mathematical problems involving multiplication and fractions, it's important to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable. Comparing the original fraction to 1 before the multiplication can help us understand whether the result will be greater or less than the number we're multiplying. In this case, since 5/7 is less than 1, multiplying it by 6 will give a result that is less than the original number, which is 6.

Answer:

B

Step-by-step explanation:

Theta is found using the sin-1 function. Start off with the sin of theta.

sin(theta) = opposite over hypotenuse.

sin(theta) = 3/8 = 0.375

Theta = Sin-1 (0.375)

Theta = 22.02 degrees.

Answer: B

Answer:

The equation of the perpendicular bisector is  2x + 3y - 3 = 0

Step-by-step explanation:

* How to find the equation of a line from two points (x1 , y1)

 and (x2 , y2) lie on it

- Find the slope of the line using the rule

 The slope (m) = (y2 - y1)/(x2 - x1)

- Use the rule of the equation y - y1 = m (x - x1), where m is

 the slope of the line and (x1 , y1) is a point on the line

* Remember if two line are perpendicular, then the product of

 their slopes = -1, that means one of them is an additive inverse

 and multiplicative inverse to the other

 # Ex: if the slope of a line is a/b, then the slope of the

   perpendicular to it is -b/a

* Now lets read the problem, we need the equation of the

 perpendicular bisector to the line that passes through the

 points (2 , 4) and (-2 , -2)

- Find the slope of the line in the graph by using the given points

 # m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2

∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative

   inverse and additive inverse of it

* Bisector means intersect it in the mid-point of the given line

- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]

∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)

* Now we have the slope and a point on the line, to find the

 equation of the perpendicular bisector its slope is -2/3 and

 a point (0 , 1)

∴ The equation: y - 1 = -2/3 (x - 0)

  The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3

  The equation : 3y - 3 = -2x ⇒ collect x , y in the same side

  The equation : 2x + 3y - 3 = 0

* The equation of the perpendicular bisector is  2x + 3y - 3 = 0

Answer:3/2

Step-by-step explanation:

Answer:

  [-1, 7]

Step-by-step explanation:

If you mean ...

  y = 4sin(2x) +3

then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.

The range of sin( ) is [-1, 1], so the range of y is ...

  4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]

_____

Comment on the problem statement

The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.

Answer:

-1,7

Step-by-step explanation:

got it right on odessyware

Answer:

The correct answer is 2 23/63

Step-by-step explanation:

To determine how much the plant grew, start by subtracting the starting whole number value from the ending whole number value.

4 - 1 = 3

Now do the same with the fractions. Use common denominators.

2/9 - 6/7

14/63 - 54/63

-40/63

Now add the two numbers together.

3 - 40/63 = 2 23/63

Answer:

  c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down

Step-by-step explanation:

You want to know the transformations that map ΔABC onto ΔDEF.

The answer choices would ask us to consider some combination of the following transformations:

We can apply these relations to the answer choices to see if they provide the desired mapping ...

a) Reflection across the y-axis, translation (1, 2)

  A(-4, 1) ⇒ A'(4, 1) . . . reflection

  A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point

b) Rotation CW 90°, translation (4, 4)

  A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW

  A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point

c) Reflection across the x-axis, translation (1, -1)

  A(-4, 1) ⇒ A'(-4, -1) . . . reflection

  A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D

d) Reflection across y=x, rotation CCW 270°

  A(-4, 1) ⇒ A'(1, -4) . . . reflection

  A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point

The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.

Answer:

a= 84.83

Step-by-step explanation:

so remember this: my teacher taught me this amazing strategy to remember the formulas

C=πd : cherry pie delicious

a=πr² : apple pie are too

and to find the area of the saded area, we need to find the area of the big circle and subtract that by the smaller circle area.

so, area of the big circle:

fill in the variables for a=πr²

you get: a=π6²

follow the pemdas, the order of operations. now on the state test don't write pemdas as your answer because people are stupid and they dont take that answer

you do the exponent first then multiply by pie.

you get: 6²=36

36xπ=113.09733552923255658465516179806

round that answer to the nearest tenths and get: 113.1

now time to find the area of the smaller circle!!!

fill in a=πr² and get: a=π3²

its not 6 this time because that was the radius for the bigger circle. the smaller circles radius is half the size as the bigger circle so divide that by two and get 3.

now solve:

a=π3²

a=π9

a=28.274333882308139146163790449516

round and get: 28.27

now subtract the the bigger circles area and the smaller circles area:

113.1 is the bigger circles area

28.27 is the smaller circles area.

113.1 - 28.27 = 84.83

a=84.83

plz give me brainliesttt