(x^2−1)(3x−4)(3x+4) what is the product

Answer:

√85 or 9.22

Step-by-step explanation:

For this, you'd want to use the distance formula, which is just something you'd eventually memorize.

Distance = [tex]\sqrt{(x_{2}- x_{1})^{2} + (y_{2}- y_{1})^{2}}[/tex]

Then, you'd plug in the values. Something to keep in mind is the coordinate that is farther right will be ([tex]x_{2} ,y_{2}[/tex]), since [tex](x_{2}- x_{1})[/tex] is supposed to represent the change in x (and same with the y).

d = √( (7 - (-2))² + (9 - 7)²)

= √( (9²) + 2²)

= √(81 + 4)

= √85

= 9.22

I hope this helps!

The distance between point (7, 9) and point (-2, 7) is √85 units.

To find the distance between two points, you can use the distance formula:

[tex]\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\][/tex]

In this case, the coordinates of the two points are:

Point 1: (7, 9)

Point 2: (-2, 7)

Now, plug these coordinates into the distance formula:

[tex]\[d = \sqrt{(-2 - 7)^2 + (7 - 9)^2}\][/tex]

Simplify inside the square root:

[tex]\[d = \sqrt{(-9)^2 + (-2)^2}\][/tex]

[tex]\[d = \sqrt{81 + 4}\][/tex]

[tex]\[d = \sqrt{85}\][/tex]

So, the distance between point (7, 9) and point (-2, 7) is[tex]\(\sqrt{85}\)[/tex] units, which is an irrational number and cannot be simplified further as a whole number or fraction.

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Answer: A. 50 miles per hour

Step-by-step explanation:

in between the lines if you look at the number it goes 25,50,75,100 etc.

FInd the height of the box by dividing the volume by 7 x 5 ( length x width)

Height = 105 / 35

Height = 3cm

There are 6 sides to a box.

Surface area = 2 x length x width + 2 x length x height + 2 times height x width

SA = 2*7*5 + 2*7*3 + 2*5*3

SA = 70 + 42 + 30

SA = 142 cm^2

Answer:

300 g. of chocolate.

75 g. of flour

3 people.

Step-by-step explanation:

These are proportion problems.  I'll just give you the first formula.

[tex]\frac{200}{4} =\frac{x}{6} \\\\(200)(6)=4x\\1200=4x\\x=300[/tex]

Can you do the rest? I'll be waiting in the comments.

:)

Answer:

i think it is E

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

Wrong theories the passageway

Answer:

Cost of living is the amount of money needed for fixed expenses such as housing, food, taxes, and health care, as well as variable expenses. Big cities tend to have a higher cost of living than smaller cities.

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

Explanation:

The number 4 shows up 14 times

The number 3 shows up 6 times

This is a total of 14+6 = 20 times we get a 3 or a 4 on the dice

This is out of 64 total rolls

Use a calculator to find that 20/64 = 0.3125

Move the decimal point over 2 spots to the right to get 31.25%

Lastly, round this to the nearest whole number percent to get 31%

Keep in mind that this only works for experimental probability. Theoretical probability is going to be different.

Answer:

31 percent on edgunity

Step-by-step explanation:

Answer:

6750

Step-by-step explanation:

There are 1000g in a single kilogram. Therefore, [tex]\frac{6.75kg}{1}\cdot \frac{1000}{1kg}=6750g[/tex]. Hope this helps!

Answer:

6750

Step-by-step explanation:

Answer:

The solution is given by s=9 because it makes the value of 3s+12 equal to 21.

Step-by-step explanation:

If you replace s with 9 you will get 21

Answer:

b. The solution is given by s = 3 because it makes the value of 3 s + 12 equal to 21.

Explanation:

I took the test and got it right.

Step 1: Substitute s for 3. You get 3(3) + 12 = 21.

Step 2: 3(3) + 12 = 21 is converted to 9 + 12 = 21.

Step 3: 9 + 12 equals 21.

Step-by-step explanation:

firstly you will add

the red cars and non red cars together and which is 65

probability of the red car = 25/65

to the lowest form is the 5/13(D)

Answer:

its D

Step-by-step explanation:

The algebraic expression for the cost of entering a state park and camping for n nights, with an entry fee of $6.00 and a nightly fee of $7.50, is Cost = $6.00 + ($7.50 times n).

The algebraic expression to represent the cost in dollars of entering a state park and camping for n nights, when the state park charges a $6.00 entry fee plus $7.50 per night of camping, is calculated as follows:

Cost = Entry fee + (Cost per night times Number of nights)

Here, the entry fee is $6.00, and the cost per night is $7.50. Therefore, the expression becomes:

Cost = $6.00 + ($7.50 times n)

Where n represents the number of nights spent camping.

Answer:

After 21.28  minutes will the coffee be only lukewarm (30∘C)

Step-by-step explanation:

Given -

A travel mug of 87∘C coffee is left on the roof of a parked car on a cold winter day . The temperature of the coffee after t minutes is given by

                 [tex]H = 87(2)^{\frac{-t}{14}}[/tex]

Let after [tex]t_{1}[/tex] time  H will be [tex]$30^\circ$[/tex]C

put t = [tex]t_{1}[/tex]  ,  H = [tex]$30^\circ$[/tex]C

       [tex]30 = 87(2)^{\frac{-t_{1}}{14}}[/tex]

       [tex]\frac{30}{87} = (2)^{\frac{-t_{1}}{14}}[/tex]

      .3448275 = [tex](2)^{\frac{-t_{1}}{14}}[/tex]

     Taking logarithm both side  

     [ [tex]log(2^{x}) = xlog2[/tex] ]

      log.3448275 = [tex]{\frac{-t_{1}}{14}}[/tex] log 2

      -.4581  =  [tex]{\frac{-t_{1}}{14}} \times.3010[/tex]

       [tex]{\frac{-t_{1}}{14}}[/tex]  =  -1.52

       [tex]t_{1}[/tex] = 21.28 minutes

To find the time it will take for the coffee to cool to 30 degrees Celsius, we need to solve the equation 30=87(2)−t/14 for the variable 't', which represents time.

The subject of this problem is a mathematical application of heat transfer. To answer this question thoroughly, we need to solve the given equation H=87(2)−t/14 for 't' when H (the temperature of the coffee) is 30 degrees Celsius.

When we set H equal to 30, we can rearrange the equation to solve for 't':

While this equation primarily pertains to heat transfer, it is also fundamentally about solving algebraic expressions, the core focus of high school Mathematics.

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Answer:

The answer is left

Step-by-step explanation:

Answer:

Left

Step-by-step explanation:

Took it on edg

Answer:

The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth

The common value of the investments is approximately $2358.05

Step-by-step explanation:

The formula of the compound interest including the principal is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where

Hector invests $800 in an account that earns 6.96% annual interest compounded semiannually

∵ P = 800

∵ r = 6.96 = [tex]\frac{6.96}{100}[/tex] = 0.0696

∵ n = 2 ⇒ semiannually

- Substitute all these values in the formula to find future value

∴ [tex]A=800(1+\frac{0.0696}{2})^{2t}[/tex]

∴ [tex]A=800(1.0348)^{2t}[/tex]

Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly  

∵ P = 1,000

∵ r = 5.44 = [tex]\frac{5.44}{100}[/tex] = 0.0544

∵ n = 12 ⇒ monthly

- Substitute all these values in the formula to find future value

∴ [tex]A=1000(1+\frac{0.0544}{12})^{12t}[/tex]

∴ [tex]A=1000(1.004533333)^{12t}[/tex]

∵ Rebecca's investment equals the value of Hector's investment

- Equate the two equations

∵  [tex]1000(1.004533333)^{12t}[/tex] = [tex]800(1.0348)^{2t}[/tex]

- Insert ㏑ in both sides and remember ㏑(ab) = ㏑(a) + ㏑(b)

∴ ㏑( [tex]1000(1.004533333)^{12t}[/tex] ) = ㏑( [tex]800(1.0348)^{2t}[/tex] )

∴ ㏑(1000) + ㏑( [tex](1.004533333)^{12t}[/tex] ) = ㏑(800) + ㏑( [tex](1.0348)^{2t}[/tex] )

- Remember [tex]ln(a)^{n}[/tex] = n ㏑(a)

∴ ㏑(1000) + 12t [㏑(1.004533333)] = ㏑(800) + 2t [㏑(1.0348)]

- Subtract ㏑(800) and 12t [㏑(1.004533333)] from both sides

∴ ㏑(1000) - ㏑(800) = 2t [㏑(1.0348)] - 12t [㏑(1.004533333)]

- Take t as a common factor from the right hand side

∴ ㏑(1000) - ㏑(800) = t(2[㏑(1.0348)] - 12[㏑(1.004533333)])

- Divide both sides by (2[㏑(1.0348)] - 12[㏑(1.004533333)])

∴ 15.8 = t

The value of Rebecca's investment equals the value of Hector's investment after approximately 15.8 years to the nearest tenth

Let us find this value using Hector or Rebecca equations

∵  [tex]A=800(1.0348)^{2t}[/tex]

- Substitute t by 15.8

∴  [tex]A=800(1.0348)^{2(15.8)}[/tex]

∴ A = 2358.05

The common value of the investments is approximately $2358.05

Answer:

2 inch

Step-by-step explanation:

The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 1 x 2= 2 inch)

The radius of a circle is 1/2 inch with a diameter of 1 inch.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r and the radius of a circle is half if the diameter which is r.

Given, A circle has a diameter of 1 inch.

As we know the radius of a circle is half of the diameter,

∴ A circle with a diameter of 1 inch will have a radius of 1/2 inch.

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Answer:

48 in each bus

Step-by-step explanation:

divide 192 by 4

Answer: 48

Step-by-step explanation:

If there are 4 buses and 192 students you divide 192 by 4 and get 48

Answer:

Step-by-step explanation:

35x + 10 = 190

35x = 190 - 10

35x = 180

x = 180 / 35

Therefore x = 5.14

Answer:

x=5 1/7 or 5.14

Step-by-step explanation:

35x+10=190

35x=190-10

35x=180

x= 180÷35

x=5 1/7 or 5.14

Answer:

68

Step-by-step explanation:

Answer:

The horizontal shift from point A to point A’ is -2. The vertical shift from point A to  point A’ is 5. Since in a translation all points shift the same distance, the coordinates of  point B’ are (5, 7 ).

Step-by-step explanation:

A moved two units to the left.

1 - 3 = -2

A also moved 5 units up.

12 - 7 = 5

The translation rule is: [tex](x,y) -> (x - 2, y + 5)[/tex]

Apply the translation rule to point B.

[tex](7 -2, 2+5) = (5,7)[/tex]

B' should be (5,7).

Answers and Step-by-step explanations:

1. The horizontal shift from point A to point A' will simply be the difference in the x-coordinates. The x-coordinate of A is 3 and the x-coordinate of A' is 1. So, we take 1 - 3 = -2. The horizontal shift is 2 units to the left.

2. The vertical shift is the difference in the y-coordinates. The y-coordinate of A is 7 and the y-coordinate of A' is 12. So, we take 12 - 7 = 5. The vertical shift is 5 units up.

3. Basically, we want to move the coordinates of B 2 units to the left and 5 units up. B is currently (7, 2). When we move 2 units to the left, we subtract 2 from the x-coordinate 7, and when we move 5 units up, we add 5 to the y-coordinate 2: B' = (7 - 2, 2 + 5) = (5, 7)

Hope this helps!

Answer:

3/6

Step-by-step explanation:

there are 3 white slice, two grey slice and 1 black slice. in total there are six slices. so the answer is 3/6.

hope it helps

In the equation, 29x + 92 = 29x - 11, subtracting 29x from both sides cancels out the variable and leaves 92 = -11, which is a contradiction. Therefore, the equation has no solution.

In the given equation, 29x + 92 = 29x - 11, you can see that the variable x is on both sides. The first step in solving this equation is by canceling out same terms on both sides.

When you subtract 29x from both sides, the equation will become 92 = -11 since the 29x cancels out on both sides. This equation doesn't make sense because 92 is not equal to -11. Therefore, the equation has no solution. This situation is known as a contradiction, because the variable cancels out and leaves us with a false statement.

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"The correct answer is C. The statement If these probabilities are correct, 12%is the probability that it will rain both days

To find the probability that it will rain both days, we need to multiply the probability of rain on Saturday by the probability of rain on Sunday, assuming that the events are independent.

The probability of rain on Saturday is 30%, which can be expressed as 0.30 or[tex]\(\frac{30}{100}\)[/tex].

The probability of rain on Sunday is 40%, which can be expressed as 0.40 or[tex]\(\frac{40}{100}\)[/tex].

Now, we multiply these two probabilities to find the probability of both events occurring:

[tex]\[ P(\text{Rain on Saturday}) \times P(\text{Rain on Sunday}) = \frac{30}{100} \times \frac{40}{100} \][/tex]

[tex]\[ \frac{30}{100} \times \frac{40}{100} = \frac{30 \times 40}{100 \times 100} \] \[ \frac{30 \times 40}{100 \times 100} = \frac{1200}{10000} \] \[ \frac{1200}{10000} = \frac{12}{100} \] \[ \frac{12}{100} = 0.12 \][/tex]

Converting this decimal to a percentage, we get 12%.

Therefore, the probability that it will rain both days is 12%."

Answer:

A : The height of the prism is is 10 cm

B : DFG is  a base

D : The appropriate unit of measure for the volume is cubic centimetres

Step-by-step explanation:

In the given right triangular prism, ADFG constitutes one of the bases, and the appropriate unit for volume is cubic centimeters. However, details about the height and the specific area of the base are not conclusively determined. (2 and 4 are correct)

Let's analyze each statement:

1. The height of the prism is 10 cm.

  - This statement is not necessarily true. The height of a right triangular prism is typically measured perpendicular to the base. The provided information about AC and AD doesn't directly determine the height.

2. ADFG is a base.

  - This statement is true. A base of the right triangular prism can be identified by the vertices, and ADFG forms one of the bases.

3. ADFG is a lateral side.

  - This statement is not true. ADFG is a base, not a lateral side.

4. The appropriate unit of measure for the volume is cubic centimeters.

  - This statement is true. Volume is measured in cubic units, and in this context, cubic centimeters is appropriate.

5. The area of the base is 45 square centimeters.

  - This statement is not necessarily true. The area of the base cannot be determined solely from the information given.

So, the true statements are 2 and 4.

Answer:

x² + y² = 144

Step-by-step explanation:

The general equation of a circle is given as

(x - a)² + (y-b)² = r²

where a and b are the center of the circle along the x and y axis respectively and r is the radius of the circle.

Hence a circle that has its center at the origin and has a diameter of 24 units, we can deduce that the values of a,b are 0,0. Also,

radius = diameter/2

= 24/2

= 12 units

Hence the standard equation of the circle

(x - 0)² + (y - 0)² = 12²

x² + y² = 144

a = (1+0.2)p

This equation is used to calculate the quantity of lemonade.

Step-by-step explanation:

Let the quality of lemonade in lans glass be 'a'

Quantity of lemonade in patricias glass = p ounces

Lan pours 20% more than Patricia

a = (1+0.2)p

This equation is used to calculate the quantity of lemonade

Answer:

Patricia poured P ounces of lemonade in her glass. Ian poured 20% more than P ounces in his glass; that is, he poured 0.20p or .2p ounces more than Patricia.

ANSWER: 0.20p

Step-by-step explanation: