If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

Answer:

(2,3) ; (-2.11)

Step-by-step explanation:

Answer:

(2, 3); (-2, 11)

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = -2x + 7

f(x) = f(x)

x² - 2x + 3 = -2x + 7

x² = 4

x = ±2

x = 2

f(2) = -2(2) + 7 = -4 + 7 = 3

x = -2

f(-2) = -2(-2) + 7 = 4 + 7 = 11

Answer: (2, 3); (-2, 11)

Step-by-step explanation:

a vertical asymptote goes up and down.

the horizontal ones (like the horizon) go left and right.

A

1 vertical asymptote at x = 0

B

2 vertical asymptotes at x = -1 and x = +1

C

no vertical asymptote (whatever vertical line you can think of, it will always really cross the graph in finite space)

D

1 vertical asymptote at x = 3

E

like A

F

2 vertical asymptotes at x = -1 and x = +4

Answer:

a) The third term is 19
b) The new term-to-term rule is subtract 13 and then divide by 6.

Step-by-step explanation:

First term: -2
Second term: 1 (-2 * 6 = -12 + 13 = 1)
Third term: 19 (1 * 6 = 6 + 13 = 19)

Our reversed sequence is now 19, 1, -2

First term: 19

Second term: 1 (19 - 13 = 6 / 6 = 1)

Third term: -2 (1 - 13 = -12 / 6 = -2)

It's term is -3 it can be divided into 6 points +79

Answer:

option B, -(4x - 3)(x - 2)

Step-by-step explanation:

-4x^2 + 11x - 6

4x * x = 4x^2

x * -3x = -3x

-4x * -2 = -8x

-3 * -2 = -6

Using proportions, it is found that:

a) 5 people are needed.

b) Yes.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Item a:

Each person works for 32 hours, and 150 hours are needed, hence the number of people needed is given by:

150/32 = 4.6875.

However, an integer number is needed, hence 5 people are needed.

Item b:

With 30 hours, the number of people needed is given by:

150/30 = 5.

Which remains the same.

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We make use of the row percentage for comparisons

From the question, we have:

The data represented by the independent variable is always used to make comparison

Since this variable is on the rows, then the row percentage would be used for comparisons

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The time it takes = 3 hours 12 minutes

Rate is a ratio which compares two quantities of different units.

Analysis:

Speed = 5 miles/hour

distance covered = 16 miles

speed taken = distance covered/time taken

time taken = 16/ 5 = 3.2 hours = 3 hours 12 minutes

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Answer:

a. t = 3 + √15  or  t = 3 - √15

b. t =  6.87  or  t = -0.87

Step-by-step explanation:

a.

Given : t² = 6t + 6

t² = 6t + 6 ⇔ t² - 6t + 6 = 0

USING THE QUADRATIC FORMULA:

[tex]t=\frac{6\pm \sqrt{\left( -6\right)^{2} -4\left( 1\right)(-6) } }{2}[/tex]

Then

[tex]t=\frac{6\pm \sqrt{36 +24 } }{2}[/tex]

Then

[tex]t=\frac{6\pm \sqrt{60 } }{2}[/tex]

Then

[tex]t=\frac{6\pm 2\sqrt{15 } }{2}[/tex]

Then

t = 3 ± √15

Then

t = 3 + √15  or  t = 3 - √15

…………………………………………………

b.

t = 3 + √15 = 6.872983346207 ≈ 6.87

or  t = 3 - √15 = -0.872983346207 ≈ -0.87

Answer:

X=10

Step-by-step explanation:

1. Subtract 10 from both sides

2. Simplify

3. Divide both sides by the same factor

4. Simplify

Answer:

Kathy and Lilly

Step-by-step explanation:

Because they both are nearest to the leader distance of 5 meters

Answer:

transitive property

Step-by-step explanation:

Generally proofs flow naturally from one step to the next.  Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.

From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]

For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]

What changed between line 8 and 9?  The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.

So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?

Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].

The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).

Recall that the transitive property states:

[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

There are three parts,

1. the first part needs a=b

2. the second part needs b=c

3. the third part produces a=c

Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.

Statement 8 is like the second part, and statement 9 is like the third part.

Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:

Original transitive property:  [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

Updated transitive property:  [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]

In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true.  The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.

The scale factor for triangle ABC to A'B'C' is 2

The complete question is in the attached image

From the attached image, we have the following corresponding sides

AC = 4 cm

A'C' = 8 cm

The scale factor is then calculated as:

Scale factor = A'C'/AC

This gives

Scale factor = 8cm/4cm

Evaluate the quotient

Scale factor = 2

Hence, the scale factor for triangle ABC to A'B'C' is 2

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Answer:

y=8+10x that then answer I guess

The range of possible heights is given by the inequality:

d ≥ 300.125 m

We know that the time that it takes for an object to fall from a distance d is:

[tex]t = \frac{\sqrt{2d} }{4.9}[/tex]

In this case, we know that t ≥ 5s.

Then we can solve for the minimum distance, which is given when t = 5s.

[tex]5 = \frac{\sqrt{2d} }{4.9}\\\\(5*4.9)^2/2 = d = 300.125[/tex]

So the minimum height of the building is 300.125 meters, then the range of possible heights is:

d ≥ 300.125 m

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Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

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Answer:

when multiply with exponents you add so

(3a^2b^7)(5a^3b^8)=15a^5b^13

Hope This Helps!!!

Answer:

HI i no  answer of this quetion but what grade are in school

Answer:

Point Form:

(9,12)

Equation Form:

x = 9

y = 12

Step-by-step explanation:

Answer:

[tex]\fbox{x = 9, y = 12}[/tex]

Step-by-step explanation:

[tex]\textsf {Let's solve by substitution.}[/tex]

[tex]\rightarrow \mathsf {-5x + 4y = 3}\\\rightarrow \mathsf {x = 2y - 15}[/tex]

[tex]\textsf {Substitute for x in the first equation of the system.}[/tex]

[tex]\implies \mathsf {-5(2y-15)+4y=3}[/tex]

[tex]\implies \mathsf {-10y+75+4y=3}[/tex]

[tex]\implies \mathsf {-6y=-72}[/tex]

[tex]\implies \textbf {y = 12}[/tex]

[tex]\implies \mathsf {x = 2(12) - 15}[/tex]

[tex]\implies \mathbf {x = 9}[/tex]

[tex]\textsf {The solution is : x = 9, y = 12}[/tex]

Answer:

6x^2 + 17x + 5

Step-by-step explanation:

(2x + 5)(3x + 1)

= 6x^2 + 2x + 15x + 5

= 6x^2 + 17x + 5

The expression (2x+5)(3x+1) is a product of two binomials. To expand this product, we multiply each term in the first binomial by each term in the second binomial, using the distributive property of multiplication.

When we multiply 2x by 3x, we get 6x^2.

Then we multiply 2x by 1, which gives us 2x.

Next, we multiply 5 by 3x, which gives us 15x.

Finally, we multiply 5 by 1, which gives us 5.

Putting these terms together gives us the expanded form of the expression:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying, we can add the 2x and 15x terms to get 17x, giving us the final simplified expression:

(2x+5)(3x+1) = 6x^2 + 17x + 5.

The number of hours that students have to work on homework will be 1/3 hours.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

Mr. K's maths class is 1 and 1/4 hours long.

After working problems on the board for 55 minutes  or 11 / 12 hour.

He gave the students the rest of the class period to work on homework.

Then the number of hours that students have to work on homework will be

⇒ 1 + 1/4 - 11/12

⇒ 5 / 4 - 11/ 12

⇒ (15 - 11) / 12

⇒ 4/12

⇒ 1/3 hours

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Answer:

b

Step-by-step explanation:

when u plug in -6 u get the equation equal to 0 which means x+6 is a factor of that function.

Answer:

each bottle of juice was $1.71

Step-by-step explanation

first, subtract the cost of the chips from the total cost

$16.62 - $2.94 = $13.68

now we know the price of all 8 juice bottles. To find the price of each bottle of juice, divide the total price of all 8 juice bottles by 8

$13.68 / 8 = $1.71

$16.62 - $2.94 = $13.68

$13.68/8 = $1.71

Each bottle of juice is $1.71

The solution to the given quadratic expression is x = -1 and x = 5

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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The height of the pole is 12.5 feet.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Cindy's shadow is 5 feet.

length of the shadow of the pole at the same time, she finds it to be 12.5 feet.

So,

12.5/5=x/5,

62.5=5x

x= 12.5 feet.

Hence, the height of the pole is 12.5 feet.

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Answer:

1.   won 50 games and lost 32 games

2.  233 Democrats and 202 Republicans

3.  360 miles

4.  6 hours

5.  18 miles

Step-by-step explanation:

Question 1

From the given information:

Substitute Equation 2 into Equation 1 and solve for y:

⇒ y - 18 + y = 82

⇒ 2y - 18 = 82

⇒ 2y = 100

⇒ y = 50

Substitute found value of y into Equation 2 and solve for x:

⇒ x = 50 - 18

⇒ x = 32

Therefore, the team won 50 games and lost 32 games.

Question 2

From the given information:

Substitute Equation 2 into Equation 1 and solve for d:

⇒ r + 31 + r = 435

⇒ 2r + 31 = 435

⇒ 2r = 404

⇒ r = 202

⇒ d = 233

Substitute found value of d into Equation 2 and solve for r:

⇒ 233 = r + 31

⇒ r = 202

Therefore, there were 233 Democrats and 202 Republicans.

Question 3

Given:

Distance (d) = vt

⇒ d = 180 × 2

⇒ d = 360 miles

Question 4

Given:

Time (t) = d ÷ v

⇒ t = 420 ÷ 70

⇒ t = 6 hours

Question 5

If the velocity of the bus is 12 mph less than the car then:

⇒ c = b + 12

Given journey times:

Distance (d) = vt

Create two equations for distance:

Bus

⇒ d = b × 0.75 = 0.75b

⇒ d = 0.75b

Car

⇒ d = (b + 12) × 0.5

⇒ d = 0.5b + 6

Distance for both vehicles is the same. Equate the two equations for d and solve for b (velocity of bus):

⇒ d = d

⇒ 0.75b = 0.5b + 6

⇒ 0.25b = 6

⇒ b = 24 mph

Substitute the value of b into one of the distance formulas and solve for d:

⇒ d = 0.5(24) + 6

⇒ d = 18 miles

The inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Ms. Jerome wants to buy identical boxes of art supplies for her 25 students. If she can spend no more than $375 on art supplies

Let's suppose b is the price of each box of supplies.

Total cost for a 25 number of boxes = $25b

25b ≤ 375

Thus, the inequality 25b ≤ 375 describes the price she can afford for each individual box of supplies.

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Construct OD and BD. Then, in quadrilateral ABOD, angles ODA and OBA are right angles and thus angle DOB is 130 degrees (since angles in a quadrilateral add to 360 degrees).

So, this means arc DB also measures 130 degrees. Hence, by the inscribed angle theorem, angle BCD is 65 degrees.

Answer:

The exponent is 2, so the degree is 2