Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.



If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.

Answer:

A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution

Step-by-step explanation:

==========================================================

Explanation:

x = width

y = length

both x and y are positive real numbers, and the units of which are in cm.

The perimeter of any rectangle is found by saying

P = 2*(length+width)

P = 2*(x+y)

Plugging in P = 14 leads us to

P = 2*(x+y)

14 = 2*(x+y)

14/2 = x+y

7 = x+y

Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.

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

Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.

Use the pythagorean theorem to help solve for x

a^2 + b^2 = c^2

x^2 + y^2 = 5^2

x^2 + (7-x)^2 = 25 ... plug in y = 7-x

x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule

2x^2-14x+49 = 25

2x^2-14x+49-25 = 0

2x^2-14x+24 = 0

2(x^2-7x+12) = 0

x^2-7x+12 = 0

(x-3)(x-4) = 0

x-3 = 0 or x-4 = 0

x = 3 or x = 4

If x = 3, then y = 7-x = 7-3 = 4

If x = 4, then y = 7-x = 7-4 = 3

We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).

Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.

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

Check:

P = perimeter

P = 2*(length+width)

P = 2*(x+y)

P = 2*(3+4)

P = 2*7

P = 14

That helps confirm the answer.

Answer:

The function is always Decreasing

Step-by-step explanation:

By graphing the polyminal in order to determine the intervals over which it is increasing or decreasing we find that it always decreasing.

Answer: 25 feet of wood

40 wheels and 2.5 cans of paints

Step-by-step explanation:

Answer:

25 feet of wood

40 wheels and

2.5 cans of paints

Step-by-step explanation: I did this before Also can i get brainlyist please

Answer:

m <5 = 71 degrees.

m <8 = 109 degrees.

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]

[tex]\\ \sf\longmapsto 9x=7(27)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]

[tex]\\ \sf\longmapsto x=21[/tex]

Answer:

the answer is 10

Step-by-step explanation:

900 ÷ 90

=> 10 [tex]\sf{}[/tex]

Answer:

The answer is 10.

Step-by-step explanation:

900/90=cut 0 of numerator and denominator then 90 divide by 9 is 10.

Answer:

-27

Step-by-step explanation:

Let x = 6 and y = -3

[tex]-(6)+7(-3)\\-6-21\\-27[/tex]

Answer:

72.47

Step-by-step explanation:

FV cos 43 = TV

FV (0.73135370161 ) = 53

FV = 72.468 = 72.47

Answer:

A

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos43° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TV}{FV}[/tex] = [tex]\frac{53}{FV}[/tex] ( multiply both sides by FV )

FV × cos43° = 53 ( divide both sides by cos43° )

FV = [tex]\frac{53}{cos43}[/tex] ≈ 72.47 ( to 2 dec. places )

Answer: y = 30x

Step-by-step explanation:

Because we are talking about over 8 hours. The question states that you get 30$ per hour for overtime hours. That means if you work over 8 hours your dollars per hour increases to 30. So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation. Except you put 30 making it y = 30x.

Answer:

The answer is D. Y is -3 times x

The phrase which describes the linear relationship between the values of x and y is y is -3 times x.

A linear relationship is any relationship between two variables that creates a line when graphed in the x y -plane.

According to the given question.

We have a linear relationship between x and y.

From the first we can see that

When,

x = -3 and y = 9

⇒ y = -3x = -3 × (-3) = 9

when,

x = 0, and y = 0

⇒ y = -3x = -3 × 0 = 0

when,

x = 3, and y = -9

⇒ y = -3x = -3 × 3 = -9

Hence, this shows that  y is -3 times x.

Thus, option D is correct.

Find out more information about linear relationship between two variables here:

https://brainly.com/question/15262646

#SPJ2

It would take 17 months and 14 days for the investment to grow to $1545.

To determine the time in months it would take for a $ 1500 dollar investment in a TFSA to grow to $ 1545 if the simple interest at a rate paid was 2% per annum, the following calculation must be performed:

First, you must obtain 2% of 1545 to determine the interest generated per year.

Then, a cross multiplication must be carried out considering the number of months it took to generate said interest, and compare it with the interest that arises from the subtraction of 1545 - 1500, that is, 45.

Therefore, it would take 17 months and 14 days for a $ 1500 dollar investment in a TFSA to grow to $ 1545.

Learn more about interest in https://brainly.com/question/19903178.

Answer:

2775

Step-by-step explanation:

Well of course since the problem is not restricted, the smallest number is 3. I'm almost sure that's not what you mean. The next smallest number is 2775. I found that using a  programing language. I'm sure as well that does not satisfy the question, either.

I think you are intended to do this by finding the lowest common multiple and adding 3.

21: 3 * 7

28: 2 * 2 * 7

36: 2 * 2 * 3 * 3

44: 2 * 2 * 11

LCM = 2 * 2 * 3 * 3 * 7 * 11 = 2772

Now add 3 and the number you want is 2775

Answer:

The Answer is 28.........

Answer:

10 wide 30 long

Step-by-step explanation:

1. Start guess and check.

2. When you get to 10 follow this:

10x3=30. 30+30+10+10=80

80=80

Answer:

Hence, data does not suggest the true average gap detection threshold for CTS subjects exceeds that for normal subjects.

Step-by-step explanation:

H0 : μ1 = μ2

H1 : μ1 < μ2

Given :

m = 8 ; x1 = 1.71 ; s1 = 0.53

n = 10 ; x2 = 2.53 ; s2 = 0.87

The test statistic :

(x1 - x2) / √(s1²/m + s2²/n)

(1.71 - 2.53) / √(0.53²/8 + 0.87²/10)

-0.82 / √0.1108025

Test statistic = - 0.82 / 0.3328700

Test statistic = - 2.463

The degree of freedom using the conservative approach :

Smaller of (10 - 1) or (8 - 1)

df = 7

TCritical value(0.01, 7) = 2.998

Decision region :

Reject H0 if |Test statistic| > |critical value|

Since, 2.463 < 2.998 ; WE fail to reject H0 ; Hence result is not significant at α = 0.01

Answer:

the correct answer is 3 m............

Answer:

1st option

Step-by-step explanation:

Evaluate f(- 5) then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6

9514 1404 393

Answer:

  y = 4x/(x -2)

Step-by-step explanation:

Subtract 1/x

  2/y = 1/2 -1/x

Combine terms

  2/y = (x-2)/(2x)

Cross multiply

  4x = y(x -2)

Divide by the coefficient of y

  y = 4x/(x -2) . . . . simplest

  y = 2^2/(x -2) . . . . in terms of x and 2

Answer:

16 once is the better one.

Answer: 12-ounce bag is better by $0.02 per ounce

Concept:

When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].

In finding [price per object], simply do [Total price / number of objects].

Solve:

A 12-ounce bag of rice costs $4.08

Total price / number of objects = 4.08 / 12 = $0.34 per ounce

A 16-ounce bag of rice costs $5.76

Total price / number of objects = 5.76 / 16 = $0.36 per ounce

$0.36 - $0.34 = $0.02

$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Agency C offers the least expensive overall fee

Step-by-step explanation:

Alone from gross salary, you would make 24000 a year.

Agency A

24000 - ( 2000 x 0.5)

= 23,000

$1000 fee

Agency B

24000 - ( 2000 x 0.1 ) x 6

= 24000 - 200 x 6

= 24000 - 1200

= 22,800

$1200 fee

Agency C

24000 - (500 + 100)

= 24000 - 600

= 23,400

$600 fee

Answer:

2) Add 21 to both sides

Step-by-step explanation:

When solving [tex]16x-21=52[/tex] for [tex]x[/tex], our goal to isolate [tex]x[/tex] such that we have [tex]x[/tex] set equal to something.

Therefore, we want to start by adding 21 to both sides. This leaves us with [tex]16x=73[/tex] and we are one step closer to isolating [tex]x[/tex].

Answer:

x = -4/3

Step-by-step explanation:

6x + 11 = -6x - 5

12x = -16

x = -4/3

Answer:

x = -4/3

Step-by-step explanation:

6x + 11= - (6x + 5)

Distribute the minus sign

6x+11 = -6x-5

Add 6x to each side

6x+11 +6x = -6x-5+6x

12x+11 = -5

Subtract 11 from each side

12x+11-11 = -5-11

12x = -16

Divide by 12

12x/12 = -16/12

x = -4/3

Answer:

A 59

Step-by-step explanation:

Higher sample size is generally always more accurate

Answer:

A. $15

B. $25

C. 84 peaches

Answer:

a)3dozenx$5=$15

b)60=5 dozen 5x$5=$25

c)35/5=7,7 dozen, 7 x 12= 84

Step-by-step explanation:

Bola will be 8 years old.

Let Bola's age be x

Dada's age be y

Ayo's age be z

If the sum of ages of Bola, Dada, and Ayo is 32 years, then;

x + y + z = 32

If they share a sum of money in the ratio of their ages, then the ratio of their ages will be x: y: z

Also if Bola gets N400, Dada get-N400 and Ayo get N800, then the total amount of money shared will be expressed as:

T = 400 + 400 + 800

T = N1600

Next is to get the age of Bola

[tex]\frac{age \ of \ bola}{32}* Total \ amount \ shared = Bola's \ Share[/tex]

Substitute the required variables and values into the formula;

[tex]\frac{x}{32}*1600= 400\\50x=400\\x=\frac{400}{50}\\x=8[/tex]

This shows that Bola is 8 years old

Learn more on ratio here: https://brainly.com/question/19473677

Answer:

1500000

Step-by-step explanation:

1 metre = 100 cm

15000metre =15000*100

=1500000

Answer:

10%

Step-by-step explanation:

3/30 × 100 = 100

Therefore 3 is 10% of 30

3 is 10 percent of 30.

To determine what percent of 30 is 3, we can use the concept of finding a proportion or ratio.

The proportion can be set up as follows:

3 is what percent of 30?

Let x represent the unknown percentage.

Using the formula for finding the percentage, we can write:

x/100 = 3/30

To simplify the equation, we divide both sides by 3:

x/100 = 1/10

To isolate x, we multiply both sides by 100:

x = (1/10)100

Simplifying the expression, we have:

x = 10

Therefore, 3 is 10% of 30.

To understand this calculation, we can interpret it as follows: If we consider 30 as the whole or 100%, then 3 is a fraction of that whole. By dividing 3 by 30 and multiplying by 100, we find that 3 is equivalent to 10% of 30.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ6

Answer:

No

Step-by-step explanation: Bye

9514 1404 393

Answer:

Step-by-step explanation:

The reflection over the x-axis is ...

  (x, y) ⇒ (x, -y)

The shift left 3 units is ...

  (x, y) ⇒ (x -3, y)

So, the two transformations together will be ...

  (x, y) ⇒ (x -3, -y)

  A(4, 2) ⇒ A"(1, -2)

  B(7,0) ⇒ B"(4, 0)

  C(9, 3) ⇒ C"(6, -3)

Answer:

Step-by-step explanation:

 L = 4 + w

A = 2P - 4

lw = 2(2l +2w) - 4

lw = 4(l + w) - 4

(w+4)w = 4 ( w+4+w) -4

(w +4)w = 4(2w + 4) - 4

w^2 + 4w = 8w + 16 - 4

w^2 + 4w = 8w + 12

w^2 - 4w - 12 = 0

( w      -       6 )( w  +       2  ) = 0

w - 6 = 0 ----> w = 6 ----> L=10  ---> P = 32  and A = 60

w + 2 = 0 ---> w = -2 <--- width cannot be negative; disqualified/rejected