Factor completely 81x2 − 100. (1 point) (10x − 9)(10x − 9) (10x − 9)(10x + 9) (9x − 10)(9x + 10) (9x − 10)(9x − 10)

Answer: (5,1)

Step-by-step explanation:

Adding the equations gives 2d=10, and thus d=5.

So, it follows e=1.

Therefore, the solution is (5,1).

The solution is (5,1)

Given that d+e =6 and d-e =4

We need to find the solution of the given equations

Elimination method is used to eliminate a variable in an equation to find the value of another variable

Now here ,

We we will solve the equation i.e

d+e = 6

d-e = 4

Solving this equation We get,

2d = 10

Therefore,

d= 5

Now substituting the value of d in equation d+e =6

therefore,

5+e =6

Therefore e = 1

Hence the solution is (5,1)

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Answer:

x = - 1

Step-by-step explanation:

the equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

the line passes through the x- intercept of - 1 , then

x = - 1 ← equation of vertical line

Answer:

D. 6

Step-by-step explanation:

Let's first find x :-

[tex]\sf 3 + 2x + 22 = x + 17[/tex]

Now that we found x, let's find QR :-

QR = 2x + 22

Therefore, QR = 6 !!!

The line segment which represents 2 7/16 inches should first be drawn with the use of a ruler.

This is referred to an instrument which is used to measure distances between points or draw straight lines and also usually graduated in inches.

On the inches graduation, the zero mark should be located and the 1/16 inch which is found before the half-inch mark between 2 and 3 inches. When this is done, a line should be drawn to meet both points which will therefore measure 2 7/16 inches long.

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Step-by-step explanation:

in a rhombus (not rumbus !) all sides are equally long.

that means

7x - 4 = 3x + 12

4x = 8

x = 2

Answer:

Step-by-step explanation:

The sides of a square are equal to each other, it is with the same with rhombus.

With this information, we can Say that [tex]DE[/tex] is equal to line [tex]GD[/tex], with
[tex]DE =7x-4GD=3x+12[/tex]
[tex]7x-4=3x+12\\[/tex]
Take [tex]3x[/tex] from both sides.
[tex]4x-4=12[/tex]
Add 4 to isolate X
[tex]4x=16[/tex]
Divide by 4
[tex]x=4\\[/tex]

So we can say that the value of [tex]x[/tex] is 4

Answer:

The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)

Answer:

-14

Step-by-step explanation:

[tex]16+22+x=24\\38+x=24\\x=-14[/tex]

the value of sin ∅ is 12/ 13

From the given question,

We have,  cos ∅= 5/13

From the trigonometric identities, we have that

[tex]sin^2\alpha + cos^2\alpha = 1[/tex]

Then , let's substitute the value of cos ∅

[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]

Let make sin the subject of formula and find the squares of the fraction

sin²∅ = [tex]1 - \frac{25}{169}[/tex]

Find the LCM

sin²∅ = [tex]\frac{169 - 25}{169}[/tex]

Find the difference

sin²∅ = [tex]\frac{144}{169}[/tex]

Find the square root

sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]

sin∅ = [tex]\frac{12}{13}[/tex]

In quadrant II , sin is positive, so we have

sin ∅ = 12/ 13

Thus, the value of sin ∅ is 12/ 13

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keeping in mind that the range is vertical values covered by the function, Check the picture below.

The probability that all 3 books would be nonfiction is 0.1846.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

A function assigns the value of each element of one set to the other specific element of another set.

The function given in the problem is:

f(x) = x³ + x² – 3x + 4

The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.

The second function given in the problem is:

g(x) = 2x – 4

The highest degree (power) of this function is 1. Thus, this function is a type of linear function.

Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).

Thus, the first function is a type of cubic function  and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

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Solving a quadratic equation, the correct option is given by:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are:

x1 = (-b + sqrt(Delta))/2a

x2 = (-b - sqrt(Delta))/2a

In which:

Delta = b² - 4ac

The equation for this system if:

-x² + 9x + 8 = 3x + 8

x² - 6x = 0

x(x - 6) = 0

Then:

Which means that the correct option is:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

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Answer:

x = 30 degrees

Step-by-step explanation:

angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees

KNL = 30 degrees

angle KLN is 90 degrees, a triangle is equal to 180 degrees

2x+30+90 = 180

2x = 60

x = 30 degrees

The surface area of the trapezoidal prism is: 4,190 in.².

Surface area = (b1+b2)h + PH, where:

Plug in the values

Surface area = (b1+b2)h + PH = (20 + 60)15 + (130)(23)

Surface area = 4,190 in.²

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1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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Answer: B. 9 hours

Step-by-step explanation:

Question analysis (Optional if you can understand the question)

Since they are 1170 miles apart, with their speed, the question is asking how long would it take them to travel 1170 miles together.

In other words, the distance that Jo and Jan together add up to 1170 miles.

Given information

Total distance = 1170 miles

Jo's rate = 60 mph

Jan's rate = 70 mph

Set variables

Let x be the time they took to meet each other

Set equation

60x + 70x = 1170

Solve equation

130x = 1170

Divide 130 on both sides

130x / 130 = 1170 / 130

[tex]\boxed{x=9 \: hrs}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(-oo, -8/3) U (-8/3, oo)

Step-by-step explanation:

Hope this helps.

The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)

From the question, we have the following parameters that can be used in our computation:

f(x) = 2/(3x + 1)

The above equation is a rational function

The rule of a function is that

The domain is the set of all input numbers

For the domain, we set the denominator not equal to 0

So, we have

3x + 8 ≠ 0

Evaluate

x ≠ -8/3

When represented as interval notation, we have

Domain = (-∝, -8/3) U (-8/3, ∝)

Hence, the domain is (-∝, -8/3) U (-8/3, ∝)

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Answer: 54

Step-by-step explanation:

So I helped 54 customers in 7.5 hours yesterday.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

You helped 3.6 customers per half hour yesterday.

That means,

for one hour:

Using multiplication

(3.6) x 2 per 1/2 x 2 hours

7.2 per hour.

Therefore,

if n hours so,

(7.2) per n hours

Here, n = 7.5

(7.2) x (7.5) per 7.5 hours

54 customers per 7.5 hours.

Therefore, I helped 54 people in 7.5 hours.

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The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

The expression is given as:

1/2 * 1/2 *1/2

Apply the product law of indices

1/2 * 1/2 *1/2 = (1/2)^3

Apply the power law of indices

1/2 * 1/2 *1/2 = (2^-1)^3

This gives

1/2 * 1/2 *1/2 = 2^-3

Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

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Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:

p = 5/25 = 0.2 = 20%.

20% probability that a customer ordered a large given that he or she ordered a cold drink.

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The real engine is 65.25 feet long

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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The value of the car after 5 years is 8527.02 dollars

Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.

The value after 5 years can be found as follows:

Rate = 18% = 18 / 100 = 0.18

Initial Value  = $23,000

time = 5 years

Therefore,

y = 23000(1 + 18%)⁵

y = 23000(1 - 0.18)⁵

y = 23000(0.82)⁵

y = 23000 × 0.3707398432

y = 8527.0163936

y = 8527.02 dollars

Therefore, the value of the car after 5 years is 8527.02 dollars

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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the initial cost and the decay rate are given as follows:

A(0) = 23000, r = 0.18.

Hence the value of the boat after t years is given as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 23000(1 - 0.18)^t[/tex]

[tex]A(t) = 23000(0.82)^t[/tex]

The value after 5 years will be of:

[tex]A(5) = 23000(0.82)^5 = 8527[/tex]

The value of the car after 5 years will be of $8,527.

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The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.

Total animals = 5 × 47

= 235

235 = d + (d + 20) + 1/2(d + 20) - 5

235 = d + d + 20 + 1/2d + 10 - 5

235 = 2 1/2d + 25

235 - 25 = 2 1/2d

210 = 2 1/2d

d = 210 ÷ 2 1/2

d = 210 ÷ 5/2

= 210 × 2/5

= 420/5

d = 84 dogs

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After the tax and the tip are counted, we conclude that each friend must pay $30.

We know that the meal cost is $72.50.

Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).

Then the total meal cost is:

C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39

Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:

C' = $77.39*(1 + 15%/100%) = $88.998 = $90

(Where we rounded up).

Then, if there are 3 friends, each one must pay:

$90/3 = $30

Each friend must pay $30.

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Presumably you mean the equation

[tex]\dfrac{13z}{z+1} = 11-3i[/tex]

Observe that for [tex]z\neq-1[/tex],

[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]

so we can simplify the equation to

[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]

Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].

[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]

Rationalize the denominator by introducing its complex conjugate.

[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]

Answer:

119°

Step-by-step explanation:

the angles of a triangle make 180° (so does a straight line) therefore

180 (triangle) = a + c + 51

to find c:

180 (straight line) = 112 + c

c = 180 - 112

c = 68°

now we have

180 (triangle) = a + 68 + 51

to find a:

a = 180 - (68 + 51)

a = 180 - 119

a = 61°

to find b:

180 (straight line) = 61 + b

b = 180 - 61

b = 119°

A. The distance moved by the effort is 100 m

B. The workdone by the effort in lifting the load is 8000 J

C. The losses in energy involve the operating in machine 1800 J

Velocity ratio = Effort distance / Load distance

5 = Effort distance / 20

Cross multiply

Effort distance = 5 × 20

Effort distance = 100 m

Workdone = force × distance

Workdone by effort = 80 × 100

Workdone by effort = 8000 J

We'll begin by calculating the workdone in lifting the load. This is illustrated below:

Workdone = mgh

Workdone = 50 × 9.8 × 20

Workdone = 9800 J

Now, we can determine the energy lost as follow:

Energy lost = 9800 - 8000

Energy lost = 1800 J

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The number of years it would take the investment to double in value is 13.2 years.

When the amount doubles, the interest earned would be $6200.

Time = interest earned / (amount invested x simple interest)

$6200 / (6200 x 0.076) = 13.2 years

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The length of the line segment SR is 15 units.

In Δ SRQ as seen in the attached image, we see that;

∠SRQ is a right angle

SQ is the hypotenuse

RT ⊥ SQ

Thus, by triangular rules, we know that;

(RQ)² = TQ × SQ

RQ = 20 units and TQ = 16 units

Thus;

(20)² = 16 × SQ

400 = 16 × SQ

SQ = 400/16

SQ = 25 units

By using Pythagoras theorem in Δ SRQ, we have;

(SR)² + (RQ)² = (SQ)²

RQ = 20 units and SQ = 25 units

Thus;

(SR)² + (20)² = (25)²

(SR)² + 400 = 625

(SR)² = 225

SR = √225

SR = 15 units

The length of the line segment SR is 15 units.

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