The function h(x) is defined as shown.

h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout

What is the range of h(x)?

–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥

Answer:

C

Step-by-step explanation:

Answer:

10ab + 4a + 5b + 2

= 10ab + 5b + 4a + 2

= 5b(2a+1) + 2(2a+1)

= (5b+2)(2a+1)

Answer:

C. Starting with a given set of rules and figuring out what must be  true . TRUE

Step by step explanation:

Mathematical Induction

Mathematical Induction is a mathematical technique which we can use to prove any given mathematical statement, result, theorem or corollary with help of induction.

Here, we assume the statement to be true for a smaller natural number            (Usually 1) and then prove the statement to be true for ANY ARBITRARY NUMBER say k.

Now, from the given options:

A. Writing down the steps to solve a complicated math problem .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.

B. Forming rules based upon observations and experiences .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  We need to induce the needed  statement or Result.

C. Starting with a given set of rules and figuring out what must be  true .

TRUE as the induction method is based on ASSUMPTION and INDUCTION.

We try and find out  the result with the given existing data.

D. Reducing the solution to a problem in lowest terms.

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  

Answer:

a) Given in attachment.

b) Quadrilateral formed is a rhombus. Because length of all the sides are equal and angle between adjacent sides is not 90°.

c) 24 unit².

Step-by-step explanation:

Let rectangle be ABCD with length 8 and width 6

And mid-points be E,F,G,H

Now, join the mid-points .

we know that angle between adjacent sides in a rectangle is 90°.

⇒ ΔFAE forms a right angle triangle with 90° at A.

By, pythagoras theorem , EF² = AF² + AE²

⇒ EF² = 3² + 4² = 25

⇒ EF = 5;

In the same way, FG = GH = HE = 5

⇒ the quadrilateral is either square or rhombus.

Now, from ΔFAE,   sin(∠AEF) = [tex]\frac{4}{5}[/tex]

(sinФ = opposite side / hypotenuse)

⇒ ∠AEF = 53°;

In similar manner;

∠DEH = 53° . Now ∠FEH = 180 - 53 - 53 = 74° (sum of angles on a straight line is 180°)

⇒ the quadrilateral is rhombus has angle between adjacent sides is 53° and not 90°.

Now, to find the area of rhombus, join EG and FH. And name the intersection point as J.

consider ΔEJF,

it is a right angled triangle at J, and also quadrilateral AFJE forms rectangle, as diagonals intersect perpendicular in a rhombus.

⇒ FJ = 3 and EJ = 4.

⇒ area of this triangle = 1/2 × base × height

                                     = 1/2 × EJ × JF = 1/2 × 3 ×4 = 6

similarly triangles FJG, GJH, HJE.

⇒ area of rhombus = 6+6+6+6 = 24.

Answer:

∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation:

we know that

Two angles are Adjacent when they have a common side and a common vertex

Two angles are supplementary if their sum is equal to 180 degrees

In this problem we have that

[tex]m\angle ZPB=90^o[/tex] ----> given problem

[tex]m\angle APZ=90^o[/tex] ----> given problem

so

[tex]m\angle ZPB+m\angle APZ=180^o[/tex]

∠ZPB and ∠APZ are supplementary angles

and

∠ZPB and ∠APZ have a common side (ZP) and a common vertex (P)

therefore

∠ZPB and ∠APZ are two adjacent supplementary angles

Answer: ∠ZPB and ∠APZ are two adjacent supplementary angles

Step-by-step explanation: Its the way the cookie crumbles.

Answer: [tex]S_{29}[/tex] = 2001

Step-by-step explanation:

Since the sequence is an arithmetic sequence , it means that a common difference must exist.

Let the terms in the sequence be [tex]T_{1}[/tex] , [tex]T_{2}[/tex] , [tex]T_{3}[/tex] , [tex]T_{4}[/tex] , ...

Then common difference = [tex]T_{2}[/tex] - [tex]T_{1}[/tex] = [tex]T_{3}[/tex] - [tex]T_{2}[/tex] = 8

That is , the common difference (d) = 8

The formula for calculating sum of  n terms is given by :

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a + (n-1)d ]

Where ;

n = number of terms

a = first term

d = common difference

From the question :

n = 29

a = -43

d = 8

Substituting into the formula , we have

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] [ 2{-43} + (29-1)(8) ]

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] (-86 +224)

[tex]S_{29}[/tex] = [tex]\frac{29}{2}[/tex] ( 138)

[tex]S_{29}[/tex] = [tex]\frac{4002}{2}[/tex]

[tex]S_{29}[/tex] = 2001

Answer:

December 1st

Step-by-step explanation:

Apex

Answer: December 1st

Step-by-step explanation:

Mathematics of personal finance sem 1

Answer:

please include more info

Step-by-step explanation:

Final answer:

To maintain the same weekly revenue after reducing her pot price from $24 to $16, a potter working 4 days a week must increase her daily production from 14 pots to 21 pots, which is an increase of 7 pots per day.

Explanation:

The question involves a potter who initially makes 14 pots per day and works 4 days a week, charging $24 per pot. To find out by how many pots per day she must increase her production after lowering her price to $16 per pot, to make the same amount of money, we first calculate her current weekly revenue:

After reducing the price to $16 per pot, we need to determine how many pots per day she needs to sell to maintain the same weekly revenue of $1,344:

Therefore, she needs to sell 7 more pots per day (21 pots - 14 pots) to maintain her weekly revenue.

The first link is for the first question, and the second one is to the second question I hope this helps!

Answer: [tex]4\ feet[/tex]

Step-by-step explanation:

The exercise provides you the following Quadratic function:

[tex]h(t)=4+60t-16t^2[/tex]

You know that it represents the height (in feet) of the ball as a function of the time (in seconds) since the ball hit the bat.

Based on this, you can conclude that when the ball strikes the bat the time in seconds is:

[tex]t=0[/tex]

Therefore, in order to calculate the height in feet of the ball when it strikes the bat, you need to subsititute [tex]t=0[/tex] into the function and    then evaluate.

So, you get:

 [tex]h(0)=4+60(0)-16(0)^2\\\\h(0)=4[/tex]

Answer:

78

Step-by-step explanation:

600 times 13%

The gardeners should buy 48 white and 116 pink hydrangeas altogether

Step-by-step explanation:

The given is:

We need to find how many white and how many pink hydrangeas the gardeners should buy altogether

Assume that the number of white hydrangeas is x and the number of pink hydrangeas in the first bed

∵ The first bed has x white hydrangeas

∵ The first bed has y pink hydrangeas

∵ The total of white and pink hydrangeas in 1st bed is 45

- Equate the sum of x and y by 45

∴ x + y = 45 ⇒ (1)

∵ In the 2nd bed the number of the white hydrangeas is 2 times

   as in the 1st bed

∵ The number of the pink hydrangeas is 3 times as in the 1st bed

∵ The number of the hydrangeas in the 2nd bed is 119

- Multiply x by 2 and y by 3, then add the products and equate

  the sum by 119

∴ 2x + 3y = 119 ⇒ (2)

Now let us solve the system of equations

Multiply equation (1) by -3 to eliminate y

∵ -3x - 3y = -135 ⇒ (3)

- Add equations (2) and (3)

∴ -x = -16

- Divide both sides by -1

∴ x = 16

- Substitute the value of x in equation (1) to find y

∵ 16 + y = 45

- Subtract 16 from both sides

∴ y = 29

∵ The number of the white hydrangeas in the 1st bed is x

∵ The number of the white hydrangeas in the 2nd bed is 2x

∴ The total number of the white hydrangeas = x + 2x = 3x

∵ x = 16

∴ The total number of the white hydrangeas = 3(16) = 48

∵ The number of the pink hydrangeas in the 1st bed is y

∵ The number of the pink hydrangeas in the 2nd bed is 3y

∴ The total number of the pink hydrangeas = y + 3y = 4y

∵ y = 29

∴ The total number of the pink hydrangeas = 4(29) = 116

The gardeners should buy 48 white and 116 pink hydrangeas altogether

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

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Answer:

Anna is incorrect.

Step-by-step explanation:

Find lengths of diagonals SQ and OM.

1. Consider right triangle SQR. By the Pythagorean theorem,[tex]SQ^2=SR^2+RQ^2\\ \\SQ^2=14^2+7^2\\ \\SQ^2=196+49\\ \\SQ^2=245\\ \\SQ=\sqrt{245}=7\sqrt{5}\ units[/tex]

2. Consider right triangle OML. By the Pythagorean theorem,

[tex]OM^2=OL^2+LM^2\\ \\OM^2=7^2+7^2\ [\text{In square LMNO, side } OL \text{has the same length as side }LM]\\ \\OM^2=49+49\\ \\OM^2=98\\ \\OM=\sqrt{98}=7\sqrt{2}\ units[/tex]

Since [tex]7\sqrt{5}\neq 2\cdot 7\sqrt{2}=7\sqrt{8},[/tex] diagonal SQ is not two times diagonal OM. Thus, Anna is incorect.

Answer:

Anna is not correct

Step-by-step explanation:

 Part A: No, anna is not correct because first the rectangle (PQRS) its says that the length of (SR) is 14 inches and if cut in half at the diagonal a rectangle or a square would have 2 triangles so if A2 + B2 = C2 then if C = the length of the diagonal and A would = 14 in ( the length of the rectangle) and then B would = 7 inches which is the width of the rectangle. It concludes that 14 to the power of 2 + 7 to the power of 2 = 245 which its square root is 15.65 ( if rounded to the hundredth place) 

Part B: Next, is the square (LMNO) if its length and width are both 7 inches then A2 = 7 to the power of 2 and also B2 will also = 7to the power of 2 and C2 will = will be the length of the diagonal.So, all of that 7 to the power of 2 + 7 to the power of 2 = 98 and its square root is 9.89 ( if rounded to the hundredth place) so lets just say 9.9.

Then you can see that 9.9 times 2 does not equal 15.65 so Anna was wrong.  

Good evening ,

Answer:

Look at the photo below for the Answer.

:)

Answer:

431547619  / 12500000000

0.03452380 …

Step-by-step explanation:

Both are the simplified versions of 3452380952/100000000000.

The answer above is also correct! I hope this helps you!

- sincerelynini

Answer:

28

Step-by-step explanation:

The height of the trapezoid and the base length from point S to the height makes a right triangle. In fact, it is a 3, 4, 5 triangle and a pyth. triplet. So...

QS = 5 cm

And...

perimeter = 5+3+6+3+4 = 21 cm

answer: B

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

Let "p" be the cost of one peppermint cookies

Let "c" be the cost of one cinnamon sugar cookies

To find: cost of each cookie

We can frame a equation as:

120  peppermint cookies x cost of one peppermint cookies + 30  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 81

[tex]120 \times p + 30 \times c = 81[/tex]

120p + 30c = 81  --------- eqn 1

70  peppermint cookies x cost of one peppermint cookies + 60  cinnamon sugar cookies x cost of one cinnamon sugar cookies = $ 60

[tex]70 \times p + 60 \times c = 60[/tex]

70p + 60c = 60 --------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "p" and "c"

Multiply eqn 1 by 2

240p + 60c = 162  --- eqn 3

Subtract eqn 2 from eqn 3

240p + 60c = 162

70p + 60c = 60

(-) -------------------------

170p = 102

Substitute p = 0.6 in eqn 1

120p + 30c = 81

120(0.6) + 30c = 81

72 + 30c = 81

30c = 9

Summarizing the results:

cost of one peppermint cookies = $ 0.6

cost of one cinnamon sugar cookies = $ 0.3

Answer:

Andrew did not reason that he could save the $10 per hour he would make cutting lawns by preparing his own meal

Step-by-step explanation:

If Andrew cuts lawns for $10 per hour, he would have $4 more to save by preparing his own meal rather than spending the $4 at Taco Bell

Answer:

Instead of spending time making food, he drives and buys food by a total of $4.

Now, he is not considerating the amount of gas that he is spending by going to buy food and returning.

Also, he was not working, so he is not producing money at the beginning, so making his own lunch actually does not implies that he stops working and loses money.

First, do distributive property:

2(5+3x)+(x+10)  Distribute the 2 to the 5 and the 3x; multiply them

10+6x+x+10      Since (x+10) would be 1 times x and 10, it's just x+10

Then, do communitive property:

10+6x+x+10     What we found in the last step, now combine the like terms

20+7x              This is what you get since 10+10=20 and 6x+x=7x

The answer:

20+7x or 7x+20

Hope that helps!

Answer:

D

Step-by-step explanation:

The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.

The entry in the [tex]n^{th}[/tex] row (start counting rows from 0) and [tex]k^{th}[/tex] column (start counting columns from 0) of Pascal's triangle is denoted by

[tex]C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)[/tex]

Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.

Hence,

[tex]20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}[/tex]

Answer:

2.133333

Step-by-step explanation:

He didn't simplify it

Answer:

Step-by-step explanation:

She might have not moved the decimal point in the right direction/right spaces

Answer:

y = - 3x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, - 4) and (x₂, y₂ ) = (1, 2)

m = [tex]\frac{2+4}{1-3}[/tex] = [tex]\frac{6}{-2}[/tex] = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 2), then

2 = - 3 + c ⇒ c = 2 + 3 = 5

y = - 3x + 5 ← equation of line

Answer:

y=-3x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(2-(-4))/(1-3)

m=(2+4)/-2

m=6/-2

m=-3

y-y1=m(x-x1)

y-(-4)=-3(x-3)

y+4=-3(x-3)

y=-3x+9-4

y=-3x+5

Answer:

3

Step-by-step explanation:

For this question, you need to make change the denominators of the fractions to be equal, making them the same lowest common denominator.

8/9 -> 40/45

4/15 -> 12/45

Since 12 goes into 40 3 1/3 times, he can patrol that many neighborhoods in 8/9's of an hour, which is rounded to 3 because he doesn't have enough time for 4.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value. The answer is 10/3, which means the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour.

To determine if the sheriff can patrol 2, 3, 4, or 6 neighborhoods in 8/9 of an hour, we need to calculate the time it takes to patrol a single neighborhood and then divide the given time by that value.

Given that it takes 4/15 of an hour to patrol a single neighborhood, we can divide 8/9 by 4/15.

To divide fractions, we multiply by the reciprocal, so 8/9 ÷ 4/15 becomes 8/9 × 15/4. Multiplying across, we get (8 × 15) / (9 × 4) = 120 / 36 = 10 / 3.

To find the solution to the system of equations 5x - 8y = -45 and 9x - 8y = 49, you can solve by elimination. The solution is x = 23.5 and y = 20.3125.

To find the solution to the system of equations:

5x - 8y = -45

9x - 8y = 49

Answer:

B. 3x² – 10x + 13

Step-by-step explanation:

given:

f(x) = 3x² – 8x + 5

g(x) = 2x – 8

f(x) - g(x)

= (3x² – 8x + 5) - (2x – 8)

= 3x² – 8x + 5 - 2x + 8

= 3x² – 10x + 13

Polar form: (r,θ)

Using these formulas:

x²+y²=r²

tan(θ)=y/x

We have the point (1,1) in cartesian coordinates. We need to find r and θ to get it in polar form.

r²=1²+1²

r²=2

r=±√2

tan(θ)=1/1

tan(θ)=1

θ=π/4 radians or 45 degrees

Polar coordinates: (√2,π/4)

Those answer choices look strange. Are you sure these are the right answer choices?

Answer:

Step-by-step explanation:

The way I see it, (1, 1) corresponds to a point which is √2 units from the origin and has an angle of 45° (or π/4 radians).

Answer:

12/5-2p

Step-by-step explanation:

2/5(6-5p)

12/5-10/5p

12/5-2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

2/5 (6 -5p)

Simplify the expression by solving bracket term,

(2/5) x 6 - (2/5) x 5p

12 / 5 - 2p

The simplified form of the expression 2/5 (6 -5p) is 12 / 5 - 2p.

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Answer:

9 pizzas

Step-by-step explanation:

Maria is planning a party. She should order 3 pizzas for every 7 people. Let x be the number of pizzas Maria will order for 21 people, then

3 pizzas - 7 people

x pizzas - 21 people

Write a proportion:

[tex]\dfrac{3}{x}=\dfrac{7}{21}[/tex]

Cross multiply:

[tex]7\cdot x=21\cdot 3\\ \\7x=63\\ \\x=\dfrac{63}{7}=9\ pizzas[/tex]

For this case we must simplify the following expressions:

[tex]m ^ 3 + m ^ 3\\10 + 3c + 5d-7c + d[/tex]

Expression 1:

[tex]m ^ 3 + m ^ 3 =[/tex]

They are similar terms so we can add.

[tex]2m ^ 3[/tex]

Expression 2:

[tex]10 + 3c + 5d-7c + d =[/tex]

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

[tex]10 + 3c-7c + 5d + d =\\10-4c + 6d[/tex]

Answer:

[tex]m ^ 3 + m ^ 3 = 2m ^ 3\\10 + 3c + 5d-7c + d = 10-4c + 6d[/tex]