Factor the algebraic expression.
24 a+27

Solution:

Given that equation is:

[tex]x^2 - kx + 28 = 0[/tex]

Roots are:

[tex]\alpha\\\\\alpha + 3[/tex]

To find: value of x

The general quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

[tex]\text{ Product of roots } = \frac{c}{a}\\\\\text{ Sum of roots } = \frac{-b}{a}[/tex]

From given,

[tex]x^2 - kx + 28 = 0[/tex]

a = 1

b = -k

c = 28

Therefore,

[tex]Product\ of\ roots = \frac{28}{1} = 28[/tex]

[tex]Sum\ of\ roots = \frac{-k}{1} = -k[/tex]

Given roots are:

[tex]\alpha\\\\\alpha + 3[/tex]

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, sum of roots are:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11

Answer:

81

Step-by-step explanation:

All you have to do is times 9*9=81

Answer:

A=40.5

Step-by-step explanation:

A=pq /2

A= 9x9/2

A=81/2

A=40.5

Answer:

Theta=38° to the nearest degree

Step-by-step explanation:

Answer:

-4 and +6

Step-by-step explanation:

The signs of 4 and 6 that will get you to a 2 are

[tex] - 4[/tex]

and

[tex] + 6[/tex]

Putting the two together gives

[tex] - 4 + 6 = 6 - 4 = 2[/tex]

This means that, starting from -4 on the number line , move 6 units to the right.

This will land you on 2

Answer:

vertex is 4

Step-by-step explanation:

y = (x-4)^2 + 7

(x-4) (x-4)

x * x = x^2

x * -4 = -4x

-4 * x = -4x

-4 * -4 =16

x^2 - 8x + 16

y = x^2 -8x + 16 + 7

y =  x^2 -8x + 23

       a     b     c

formula to find vertex: -b / 2a

= -b / 2a

= - (-8) / 2 (1)

= 8 / 2

= 4

vertex = 4

(what i did was work out the exponent outsite the parentesis then i got the equation i wanted, and from that equation i used the formula to find the vertex and i just plugged the numbers of the equation into the formula and work it out)

Answer:

(4,7)

Step-by-step explanation:

The equation for a parabola can be written as

y = a(x-h)^2 +k  where (h,k) is the vertex

given f(x) = (x-4)^2+7

The vertex is (4,7)

Answer:

depend on watching action movies

Step-by-step explanation:

because most watch action

Based on the given data, watching romantic movies and watching action movies are independent events, as the probability of both occurring matches the product of their individual probabilities.

We need to determine if the events of watching romantic movies and watching action movies are independent or dependent. The definition of independent events in probability is that the outcome of one event does not change the probability of the outcome of another event.

If watching romantic and action movies were independent events, we would expect the percentage of people who watch both to be the product of the individual probabilities. That would be 0.40 (the probability of watching romantic movies) times 0.60 (the probability of watching action movies), which equals 0.24 or 24%.

However, we are told that 24% of people watch both romantic and action movies. This matches our calculation exactly, so we can infer that the event of watching romantic movies is independent from the event of watching action movies. This means that watching a romantic movie does not affect the likelihood of watching an action movie, and vice versa.

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Answer:

9.45 (rounded)

Step-by-step explanation:

- The formula is to divide the centimeters by 2.54, and this will give you the amount of inches.

Answer:

9.45 inches

Step-by-step explanation:

2.54cm in 1 inch

Answer:

The answer is C) Unlikely.

Step-by-step explanation: This is because the likelihood of you rolling a 3 on a six-sided die is approximately 3/36.

It is unlikely to roll a 3.

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Possible outcomes of rolling a six-sided die.

= {1, 2, 3, 4, 5, 6}

We can say that,

If the probability of an event is 50% or above it is likely.

If the probability of an event is less than 50% it is unlikely.

If the probability of an event is 100% it is certain.

If the probability of an event is less than 0% it is impossible.

Now,

Probability of rolling a 3.

= 1/6 x 100

= 16.67%

This means,

Unlikely.

Thus,

It is unlikely to roll a 3.

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Answer:

The number is 5

Step-by-step explanation:

I like to do the equation backwards, so x*7+1/4=9 becomes:

9*4=36

36-1=35

35/7=5

And there is your answer!!!

To simplify the expression xz^3*4x^4z^5, the exponents of the like bases are added together resulting in 4x^5z^8. This application of exponent rules shows that the exponents on the same base are summed during multiplication.

To simplify the expression xz^3*4x^4z^5, we need to apply the rules of exponents. Specifically, when multiplying two expressions with the same base, we add their exponents.

Beginning with the variable x, we have an implied exponent of 1 on the standalone x, so when combined with x^4, we get x^(1+4), which simplifies to x^5.

Next, we apply the same rule to the variable z.

The expression z^3 multiplied by z^5 becomes z^(3+5), which simplifies to z^8. Finally, we multiply these results by the constant 4 to get our simplified expression:

4x^5z^8.

As an example to clarify this process, imagine a simpler case like (5^3)^4.

This could be written out as multiple fives multiplied by each other, illustrating that the exponents are indeed added together when multiplying like bases, just as we did with x and z in our original expression.

Answer:

u < 4

Step-by-step explanation:

Step 1:  Subtract 8 from both sides

8 - u - 8 > 4 - 8

-u > -4

Step 2:  Divide both sides by -1

-u / -1 > -4 / -1

Since you divide by a negative, you flip the sign.

u < 4

Answer:  u < 4

Answer:

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Step-by-step explanation:

Let

x ----> Siw's age

y ---> Mona's age

z ---> Mother's age

we know that

Siw is a fourth as old as mother

so

[tex]x=\frac{1}{4}z[/tex] ----> equation A

Mona is a fifth as old as mother

so

[tex]y=\frac{1}{5}z[/tex] ----> equation B

Mother is 22 years older than the two girls together.

so

[tex]z=x+y+22[/tex] ----> equation C

substitute equation A and equation B in equation C

[tex]z=\frac{1}{4}z+\frac{1}{5}z+22[/tex]

solve for z

Multiply by 20 both sides to remove the fraction

[tex]20z=5z+4z+440[/tex]

[tex]20z-9z=440\\11z=440\\z=40\ years[/tex]

Find the value of x

[tex]x=\frac{1}{4}(40)=10\ years[/tex]

Find the value of y

[tex]y=\frac{1}{5}(40)=8\ years[/tex]

therefore

Siw's age is 10 years old

Mona's age is 8 yers old

Mother's age is 40 years old

Answer:

Step-by-step explanation:

1/2(-9+n)=20

n=40+9

n=49

Answer:

49

Step-by-step explanation:

Sum means add

-9+n

Multiply this by 1/2

1/2(-9+n)

This is equal to 20

1/2(-9+n) = 20

Solve

Multiply each side by 2 to get rid of the fraction

2*1/2(-9+n) = 20*2

-9+n = 40

Add 9 to each side

-9+9 +n = 40+9

n = 49

Answer:

A turkey sandwich would cost $6.50 and the salads would be $5.50

Step-by-step explanation:

The cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the employees at a bank ordered 4 turkey sandwiches and 2 salads at a local deli. The total cost of the order was $25.

The cost will be calculated as,

4t + 2s = 25

s = t - 1

Substitute the value of s in the first equation,

4t + 2s = 25

4t + 2(t - 1)= 25

4t + 2t - 2 = 25

6t - 2 = 25

t = $4.5

The cost of salad will be,

S = t - 1

S = 4.5 - 1

S = $3.5

Therefore, the cost of a turkey sandwich is $4.5 and the cost of a salad is $3.5.

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Answer:

$224.

Step-by-step explanation:

If the packages cost $4 each then 56 packages will cost 56 * 4 dollars.

56 * 4 = $224.

Answer:

Step-by-step explanation:

1 day -------------- $12

cost = 2(1 day) + 10

2 days ------------ $14

cost = 2(2 days) +10

3 days -------------$16

cost = 2(3)+10

and so on

Answer:

∠EGB= 68°

Step-by-step explanation:

∠EGB= ∠AGF ( vert. opp. ∠s)

∠EGB= 68°

If 2 straight lines intersect, then the angles facing opposite each other are equal. In this case, the 2 lines are AB and EF.

-r + 8(-5r -2).

Multiply 8 by -5r - 2

- r - 40r - 16.

Combine -r and -40r

-41r - 16 is a simplified equivalent expression of -r + 8(-5r - 2)

Answer:

-41r - 16

Step-by-step explanation:

-r + 8 (-5r - 2)

-r - 8*5 r -8*2

-r - 40r - 16

-41r - 16

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

Question 1:

The given formula is

[tex]I=\frac{PTR}{100}[/tex]

To make T, the subject we multiply both sides by 100:

[tex]100I=\frac{PTR}{100} \times 100[/tex]

This becomes

[tex]100I=PTR[/tex]

Divide both sides by PR

[tex]T=\frac{100I}{PR}[/tex]

b) Amanda's principal is , P=€2565

The interest rate is 3.5% p.a. that is R=3.5

We want to find how many years, her money will gain an interest of I=€718.20

We substitute into the formula for T,

[tex]T=\frac{100 \times 718.20}{2565 \times 3.5}[/tex]

This simplifies to:

T=8

Therefore it will take 8 years

2) Percentage profit

[tex] = \frac{profit}{cost \: price} \times 100\%[/tex]

The cost price of the 80 articles €200

The selling price is 3.5×80=€280

The profit =€280-€200=€80

The percentage profit is now

[tex] = \frac{80}{200} \times 100\%[/tex]

[tex] = 0.4 \times 100\%[/tex]

[tex]40\%[/tex]

The percentage profit is 40%

Question 3)

Let the original price of the calculator be x.

Then 85% of this price will be:

[tex] \frac{85}{100} \times x[/tex]

This is the same as€32.89

We equate and solve for x.

[tex] \frac{85}{100} x= 32.89[/tex]

[tex]0.85x = 32.89[/tex]

[tex]x = \frac{32.89}{0.85} [/tex]

[tex]x = 38.69[/tex]

The original price is €38.69

Answer:

x = -2 , y = -3 , z = 3

Step-by-step explanation:

Solve the following system:

{-x - 5 y - 5 z = 2 | (equation 1)

4 x - 5 y + 4 z = 19 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Swap equation 1 with equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

-x - 5 y - 5 z = 2 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Add 1/4 × (equation 1) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - (25 y)/4 - 4 z = 27/4 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Multiply equation 2 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

x + 5 y - z = -20 | (equation 3)

Subtract 1/4 × (equation 1) from equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+(25 y)/4 - 2 z = -99/4 | (equation 3)

Multiply equation 3 by 4:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+25 y - 8 z = -99 | (equation 3)

Add equation 2 to equation 3:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y - 24 z = -72 | (equation 3)

Divide equation 3 by -24:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y - 16 z = 27 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 16 × (equation 3) to equation 2:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x - 25 y+0 z = 75 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 2 by -25:

{4 x - 5 y + 4 z = 19 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Add 5 × (equation 2) to equation 1:

{4 x + 0 y+4 z = 4 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Subtract 4 × (equation 3) from equation 1:

{4 x+0 y+0 z = -8 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Divide equation 1 by 4:

{x+0 y+0 z = -2 | (equation 1)

0 x+y+0 z = -3 | (equation 2)

0 x+0 y+z = 3 | (equation 3)

Collect results:

Answer: {x = -2 , y = -3 , z = 3

Answer:

90 sheep?

Step-by-step explanation:

1 sheep= 1 pound

1 cow= 10 pounds

total amount made= 100 pounds

100 ÷ 1 (the cost for sheep) = 100 sheep

100 - 90 (the cost of cows) = 10

10 sheep

Answer:

21 sheep

Step-by-step explanation:

100 = x + y + 8z

10x + y + z = 100

x = 1

y + 8z = 99

y + z = 90

x = 2

y + 8z = 98

y + z = 80

x = 3

y + 8z = 97

y + z = 70

x = 4

y + 8z = 96

y + z = 60

x = 5

y + 8z = 95

y + z = 50

x = 6

y + 8z = 94

y + z = 40

x = 7

y + 8z = 93

y + z = 30

7z = 63

z = 9

y = 30 - 9 = 21

x = 7 (7 cows)

y = 21 (21 sheep)

z = 9 (9×8 = 72 chicken)

Answer: 14

Step-by-step explanation:

100% of 14

= 100/100 × 14/1

14

Answer:14

Step-by-step explanation:

Percent= 100%

From= 14

Value= [tex]\frac{100}{100}[/tex] x 14= 1x 14 =14

Answer:

4p-6

Step-by-step explanation:

distribute within parenthesis:

-4+8p-4p-2

Combine like terms

4p-6

i hope this helps u

please give thx and a brainliest to level up

Answer:

2(-2-4p)+2(-2p-1)

-4-8p -4p-2

-12p-6

Step-by-step explanation:

Answer:

Yes it will be greater, he is moving back 3 feet so what you are doing is taking the leg (a2) and multiplying it by 3. Once you do, you see triangle 1 has double and so did triangle 2. Triangle 1 was originally 5.6 (rounded to 6) than went up to 26.1. Triangle 2 was originally 24 and went up to 74.7 (or 75)

Step-by-step explanation:

Triangle 1 (when multiply by 3)

a2+b2=c2

7(square to 2)+b2=27(square to 2)

49+b2=729

-49       -49

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

b2=680

(square root it)

b=26.1 Rounded to nearest tenth

Triangle 2:

a2+b2=c2

7(square to 2)+b2=75(square to 2)

49+b2=5625

-49      -49

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

b2=5576

(square root it)

b=74.7 (or 75 rounded to nearest tenth)

Hope this helps anyone who needs it :)

Yes, the distance from his eyes to the top of the tree will also be greater.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that Javier moves backward so that his horizontal distance from the tree is greater.

Before moving backward, the distance from Javier's eyes to the top of the tree can be written as -

cosФ = b/h

h = b/cosФ

Now, we can see that -

h [tex]\alpha[/tex] b

As base increases, the hypotenuse length or the distance from Javier's eyes to the top of the tree will increase.

Therefore, yes, the distance from his eyes to the top of the tree will also be greater.

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y/(5 + 3) = 5/y

y/8 = 5/y

y² = 40

y = 2√10

5/x = x/3

15 = x²

√15 = x

Answer:

  3.9

Step-by-step explanation:

The right triangles are all similar, so the ratio of short side to long side is the same for all:

  3/x = x/5

  15 = x^2 . . . . . . . . multiply by 5x

  x = √15 ≈ 3.9

Answer:

374

Step-by-step explanation:

Answer:6750

Step-by-step explanation:

Final answer:

The jumbo-sized box, created by tripling each dimension of a regular-sized box that holds 250 toothpicks, will have a volume 27 times greater. Therefore, it will hold 250 × 27 = 6,750 toothpicks.

Explanation:

The question is asking how many toothpicks a jumbo-sized box can hold if it is created by tripling the length, width, and height of a regular-sized box that holds 250 toothpicks. To find the answer, we need to consider the volume of the boxes because the toothpicks are arranged in three-dimensional space.

The volume of a box is calculated by multiplying its length by its width by its height. If we triple each of these dimensions for the jumbo box, the new volume will be 27 times the volume of the original box (since 3 × 3 × 3 = 27). Therefore, if the original box holds 250 toothpicks, the jumbo box will hold 250 × 27 toothpicks.

To find the total number of toothpicks:

Multiply the number of toothpicks in the original box (250) by 27.

Calculate 250 × 27 to get 6,750 toothpicks.

Thus, the jumbo-sized box would be able to hold 6,750 toothpicks.