Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.

Answer: The given quadratic expression is -3x²+172x-20. To factor this expression, we look for two numbers that multiply to -20 and add to 172.

We can start by dividing -20 by different numbers and checking if the product and the sum of the divisors equals -20 and 172 respectively.

-20/1 = -20, 1+-20 = -19

-20/2 = -10, 2+-10 = -8

-20/4 = -5, 4+-5 = -1

-20/-1 = 20, -1+20 = 19

-20/-2 = 10, -2+10 = 8

-20/-4 = 5, -4+5 = 1

We can see that the divisors that multiply to -20 and add to 172 are (x+8)(x-5)

So, we can factor the quadratic expression as:

-3x²+172x-20 = -3(x+8)(x-5)

Hope this helps!

Step-by-step explanation:

Answer: x > -5

Step-by-step explanation:

-1.5x < 7.5

x > -5 (When multiplying both sides by a negative, the inequality is flipped)

[tex]-1.5x < 7.5[/tex]

Divide both sides by -1.5:

[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]

When dividing by a negative number, the inequality sign will reverse.

Answer:

[tex]x > -5[/tex]

The revenue is maximized when the derivative of R(p) is equal to 0.

R'(p) = -80p + 400 = 0

p = 5

A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.

Therefore, the maximum revenue is achieved when the price of each ticket is $5.

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No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.

We have 2(12 ÷ 2)2 – 14 + 6

Here according to the BODMAS rule which stands for Brackets  Of  Division  Multiplication  Addition  Subtraction, we will first solve the brackets.

Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.

12 ÷ 2 = 6

Hence we get

2 X 6 X 2  -  14  +  6

Now we need to multiply.

2 X 6 X 2 = 12 X 2 = 24

Hence we get

24 - 14 + 6

Now we need to add the numbers up.

24 + 6 = 30 hence we get

30 - 14

= 16

Hence Chase's work is not correct.

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The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45

The definition of the function is given as

a₁= 0

aₙ = aₙ₋₁ + 15

The above definitions imply that we simply add 15 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 0 + 15

a₂ = 15

Also, we have

a₃ = 15 + 15

a₃ = 30

Lastly, we have

a₄ = 30 + 15

Evaluate the equation

a₄ = 45

Hence, the value of a₄ is 45

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The third angle of  acute scalene triangle is  41°

Now, According to the question:

The first angle of acute scalene triangle is 93°

The second angle of  acute scalene triangle is 46°

Let the third angle of  acute scalene triangle is x

We know that:

The sum of the interior angles is always equal to 180 degrees.

Now, 93° + 46° + x = 180°

139° + x = 180°

x = 180° - 139°

x = 41°

Hence, the third angle of  acute scalene triangle is  41°

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The numerical value of x in the function f(x) = -9x + 13 when f(x) = -41 is 6.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To find the value of x, replace the occurrence of f(x) with -41 in the function and simplify.

f(x) = -9x + 13

-41 = -9x + 13

Collect like terms

9x = 41 + 13

Add 41 and 13

9x = 54

Divide both sides by 9

9x/9 = 54/9

x = 54/9

x = 6

Therefore, the input value x is 6.

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We can assume linear inequality 8x>40 for x>8 for an indirect proof.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given,

Quinn ran total distance>40 mile

No. of times he ran=5

average distance for each run>8

also let x>8 where x=average distance for each run

Hence,

           We can assume linear inequality 8x>40 for x>8

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Answer: To find the total weight of the bags of topsoil, you can multiply the number of bags by the weight of each bag.

18 bags * 36 pounds/bag = 648 pounds

So, Elayna bought 18 bags of topsoil which is 648 pounds in total.

Step-by-step explanation:

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

What is null hypothesis ?

The null hypothesis is a arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test the null hypothesis, we can use a one-sample t-test. The t-statistic for this test is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population mean (6.7 lbs/square inch in this case), s is the population standard deviation (assumed to be 1), and n is the sample size (280 engines).

The p-value for this test can be calculated using the t-distribution table or a t-test calculator. If the p-value is less than the significance level of 0.1, then we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs below the specifications.

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

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By trigonometric functions and trigonometric formulas, the exact value of cot (3π / 2) is equal to 0.

In this problem we have the case of trigonometric function whose exact value must be found by means of trigonometric functions and trigonometric formulas. Now we proceed to present the entire procedure:

cot (3π / 2)

1 / tan (3π / 2)

Rewrite the function in terms of fundamental trigonometric functions: (sine, cosine)

1 / [sin (3π / 2) / cos (3π / 2)]

cos (3π / 2) / sin (3π / 2)

Then, we get the following exact value:

0 / (- 1)

0

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Answer: $10=2.30p

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

23.37

Step-by-step explanation:

There ya go

:)

The number of months when the total cost is $1700 is 48 months

A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.

These variables are;

From the information given, we have that;

Now, substitute the values, we have;

1700 = 35x + 20

collect like terms

35x = 1700 - 20

subtract the like terms

35x = 1680

Make 'x' the subject of formula

x = 48 months

Hence, the value is 48 months

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Answer:

We can use algebra to find the two consecutive even integers whose product is 168.

Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:

x * (x+2) = 168

We can solve for x by simplifying the equation:

x^2 + 2x = 168

x^2 + 2x - 168 = 0

We can factor the left side of the equation:

(x-14)(x+12) = 0

So the two solutions for x are -12 and 14.

The negative integers are -12 and -14.

The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.

Answer:

Step-by-step explanation:

that a huge prob but yah

The distance between the tennis balls and the cans is 49.46 cubic inches.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Given: Each ball has a diameter of three inches.

Three tennis balls are contained in each can, which is how they are sold.

Each can has a cylindrical shape.

We start by determining each tennis ball's volume.

Because of their spherical shape, their volume is determined by

[tex]$V=\frac{4}{3} \pi r^3$[/tex]

Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in

Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have

[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]

Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.

Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by

[tex]$V=\pi r^2 h$[/tex]

Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.

[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]

Therefore, the volume of each can exists 63.59 cubic inches, approximately.

The complete question is:

Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder

A)what is the volume of one tennis ball ?

B)what is the volume of the cylinder ?

C)how much space is not occupied by the tennis balls in the can?

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Answer: X has to be greater than or equal to 15/7 for the inequality to be true.

Step-by-step explanation:

here are the steps to solve the inequality 25-2x≤5(2-x):

Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x

Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x

Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10

Now we'll add 7x to both sides: 25 ≤ 10 + 7x

Subtract 10 from both sides: 15 ≤ 7x

Finally, divide both sides by 7: 15/7 ≤ x

The solution set is x ≥ 15/7.

So x has to be greater than or equal to 15/7 for the inequality to be true.

Answer:

-5 ≥ x  or x ≤ -5

Step-by-step explanation:

25 - 2x ≤ 5(2 - x)

distribute the 5 to eliminate the parentheses:

25 - 2x ≤ 10 - 5x

now combine like terms:

15 - 2x ≤ -5x

15 ≤ -3x

-5 ≥ x  or x ≤ -5

the inequality symbol gets switched whenever you multiply or divide by a negative value

The statement below about the rocket is true:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A rocket travels at an approximate speed of 7.9 kilometers per second.

Since, some unit conversion:

1 kilometer = 1000 meteres

1 kilometer = 100000 centimeteres = 10⁵ cm

1 kilometer = 10000000 milimeteres = 10⁷ mm

thus we can say that from the given options only "f" is correct that states:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

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Answer:

12.  & 2.5mins

Step-by-step explanation:

2 hours = 120 mins for 48 baguettes.  so 120/48 = 2.5 mins per baguette

30 mins is 1/4 of 2 hours. so 12  baguettes

Ariana earned $708 in 24 hours, so $312 more Ariana earn per hour than Jacob.

We have to find how much more Ariana earn per hour than Jacob.

The equation y = 16.5x represents Jacob's earnings in dollars and cents, y, for working x hours.

Ariana earned $708 in 24 hours.

So the value of x = 24

Now putting the value of x in equation y = 16.5x

y = 16.5 × 24

y = 396

Jacob's earnings = $396

Difference between the Ariana earning and Jacob earning = $708 - $396

Difference between the Ariana earning and Jacob earning = $312

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Two  cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652

Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of possible ways the event A occurs

n(S) = total possible outcomes

In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.

First drawn: number of diamond = 13

Hence, P1(diamond) = 13/52

In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.

Hence, the probability of the second card will be a diamond is:

P2(diamond) = 12/51.

Since those 2 events are independent, the probability that both cards are diamonds is:

P(diamonds) = P1 (diamond) x P2 (diamond)

                     = (13/52) x (11/51) = 143/2,652

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Steven will have to pay $127. 50 for the insurance per year.

The correct answer is an option (C)

First, we need to find the corresponding value for the all-wood building in the city suburbs.

From given table, we will use the value 0.85 because he wishes to ensure his belongings.

Here, the value of the belongings in the apartment is about $15,000

Steven wants to insure his belongings while renting.

Now we can calculate the amount of money he will have to pay  for insurance per year as follows:

15000 × (0.85 / 100)

= 127. 50 dollars

Therefore, he will have to pay 127. 50 dollars for insurance.

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The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

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Answer:

125b+2

Step-by-step explanation:

5^3b+2

5x5x5=125

125b+2

Cannot be simplified any futher

The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,

we shall evaluate for the height of the antenna AB as follows:

tan 44° = AB/18m {opposite/adjacent}

AB = 18m × tan 44° {cross multiplication}

AB = 18m × 0.9657

AB = 17.3826m

Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.

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Answer:
2 meters

I got it correct in my hw (check the photos)

also mark me brainleist

Answer:

11/3 or 11/3x

Step-by-step explanation:

Another term for "Rate of change" is slope.

The usual slope equation is (y2-y1)/(x2-x1)

Plugging in the points we get

(3 - (-8)) / (3 - 0)

(3+8)/(3-0)

(11)/(3)

Which makes the slope 11/3 or 11/3x