write y=3x-5 in function notation

Answer:

Answer is x=7

Step-by-step explanation:

[tex]given \: that \: triangle \: stu \: is \: \\ similarto \: triangle \: plm \\ by \: similarity \: theorem \\ \frac{st}{pl} = \frac{tu}{lm} = \frac{su}{pm} \\ \frac{x + 1}{72} = \frac{2x - 3}{99} \\ cancelling \: by \: 9 \: which \: is \: common \\ \frac{x + 1}{8} = \frac{2x - 3}{11} \\ 11(x + 1) = 8(2x - 3) \\ 11x + 11 = 16x - 24 \\ 11 + 24 = 16x - 11x \\ 35 = 5x \\ therefore \: x = 7[/tex]

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Given:

Funnel is in the shape of a cone.

Radius = 4 inches

Height = 10 inches

To find:

a) The volume of the funnel

b) How many quarts of oil are in the funnel.

Solution:

Volume of cone:

[tex]$V=\frac{1}{3}\pi r^2 h[/tex]

[tex]$V=\frac{1}{3}\times 3.14 \times 4^2 \times 10[/tex]

[tex]$V=167.47[/tex] in³

The volume of the funnel is 167.47 in³.

1 qt ≈ 58 in³

To convert cubic inch to quarts divide by 58.

[tex]$167.47in^3=\frac{167.47}{58}[/tex]

               = 2.9 quarts

Therefore 2.9 quarts of oil are in the funnel.

Answer:

8 and -8

Step-by-step explanation:

The definition of a square root is 'a number which produces a specified quantity when multiplied by itself.' Though a negative number cannot have a square root or be a perfect square, it can be a square root.

8 is the only positive square root, but every number that has a square root, also has a second one, the negative version.

-8 is also the square root because it can be multiplied by itself to get 64 :D

The real square roots of the integer 64 will have 8 and -8.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Let's say the square root of 64 is x.

x = √64

Square both sides

x² = (√64)² = 64

x² = 64

Now, find two equal number that gives 64 by multiplying.

Consider, 8 and 8 → 8² = 64

Thus, x = 8

Another could be -8 and -8 → (-8)² = 64

Hence "The real square roots of the integer 64 will have 8 and -8".

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Answer:

P(A and B) = P(A) + P(B) - P(A or B)

                 = 0.6 + 0.45 - 0.66

                 = 0.39

The value of P(A AND B), given the probabilities of P(A), P(B), and P(A OR B),  is found to be 0.39.  

To find the probability of both events A and B occurring, we use the formula for the probability of the union of two events, which is P(A OR B) = P(A) + P(B) \'96 P(A AND B). We rearrange this formula to find P(A AND B) by subtracting P(A) and P(B) from P(A OR B):

P(A AND B) = P(A) + P(B) \'96 P(A OR B)

Substituting the given values:

P(A AND B) = 0.6 + 0.45 \'96 0.66 = 0.39

So, the probability of A and B occurring together, P(A AND B), is 0.39, which rounds to the nearest thousandth as required.

Answer:

Step-by-step explanation:

The oxidation state of O in H₃O⁺ is -2

From the question, the given ion is  H3O+.

This can be written properly as H₃O⁺

To determine the oxidation state of O (that is Oxygen) in H₃O⁺,

The oxidation state of H (Hydrogen) here is +1

∴ We can form the equation

(+1 × 3) + O = +1

(NOTE: The expression is equated to +1 because the overall charge on the given ion is +1)

Then, we have

+3 + O = +1

Now, subtract 3 from both sides

+3 -3 + O = +1 -3

∴ O = -2

Hence, the oxidation state of O in H₃O⁺ is -2

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Answer:

114.5 in³

Step-by-step explanation:

Volume of cone:

⅓ × 3.14 × 8² × 12

= 803.84 cm³

Volume of hemisphere:

⅔ × 3.14 × 8³

= 1071.786667 cm³

Total = 803.84 + 1071.786667

= 1875.626667 cm³

1 cm = 0.393701 inches

1 cm³ = 0.393701³ inches

Volume in in³:

1875.786667/0.393701³

= 114.4579471 in³

Answer:

48/51

Step-by-step explanation:

The probability of not choosing a king after you've chosen the first king is 48/51 since there are 48 cards in the deck that are not kings and there are 51 cards left in the deck, including king cards.

Answer: Their are 4 kings in a deck of cards, so the answer would be P( Cards that aren't Kings/Total cards) so the probability is .92 or 92%.

Answer:

Additive inverse property

Step-by-step explanation:

-1/3 + 1/3 =0

We are adding opposites to get to zero

a+ -a =0

The maximum height that the dolphin reaches is 5 units, which occurs at a horizontal distance of 5 units. The dolphin's total horizontal jump distance is 10 units.

The maximum height the dolphin reaches (the vertex of the parabola) is found by the formula -b/(2a) for the maximum or minimum of a parabola ax^2 + bx + c. In your equation, a = -0.2 and b = 2. Therefore, the horizontal distance, d, at the maximum height is d = -b/(2a) = -2/(-0.4) = 5 units. Substituting d = 5 into the original equation gives h = -0.2*5^2 + 2*5 = 5 units. Thus, the maximum height the dolphin reaches is 5 units.

The dolphin's horizontal distance (the 'd' value when h = 0) specifies the full length of the jump. Solving the equation -0.2*d^2 + 2*d = 0 gives d = 0 (the start of the jump) and d = 10 (the end of the jump). Thus, the dolphin jumped 10 units horizontally.

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The maximum height reached by the dolphin is 5 meters, and it jumps a horizontal distance of 10 meters. This is determined by analyzing the quadratic equation for maximum height and the point where the dolphin returns to the water surface.

To determine the maximum height (h) the dolphin reaches, we need to analyze the given quadratic equation h = -0.2d² + 2d. Because the coefficient of d² is negative, the parabola opens downward, indicating that the vertex of the parabola will give us the maximum height. The vertex of a parabola in the form of h = ad² + bd + c is given by the formula d = -b/(2a). In this case, a = -0.2 and b = 2, so the horizontal distance (d) at the vertex is d = -2/(2 × (-0.2)) = 5 meters. Plugging this back into the equation, we get h = -0.2(5)² + 2(5) = -0.2(25) + 10 = -5 + 10 = 5 meters.

So, the maximum height reached by the dolphin is 5 meters.

The dolphin jumps until it returns to the water surface, which means the height h becomes 0. We solve the quadratic equation 0 = -0.2d² + 2d by factoring out d: 0 = d(-0.2d + 2). This gives us two solutions: d = 0 (the starting point) and -0.2d + 2 = 0 which leads to d = 10.

Therefore, the dolphin jumped a horizontal distance of 10 meters

Answer:

y≥ 5+5/3x

Step-by-step explanation:

5x-3y≤-15

-5x .     -5x

-3y≤-15 -5x

/-3 .     /-3 .(flip inequality when dividing or multiplying by a negative number)

y≥ 5+5/3x

Answer:35%

Step-by-step explanation:

The percentage decrease in the value of the book is 35%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Cost of the book = £19.80

Selling price of the book = £12.87

The percentage decrease in the value of the book.

= (19.80 - 12.87)/19.80 x 100

= 6.93/19.80 x 100

= 35%

Thus,

The percentage decrease is 35%.

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Answer: 8? What are the answer choices??

Explanation: C= 2(3.14)r

50= 2(3.14)r

First do 50 divided by 2 which equals 25. Then divide 25 by 3.14 to equal 7.96.... Or 8

Step-by-step explanation:

[tex] {b}^{2} + 8b - 6 \\ {5}^{2} - 8 \times 5 - 6 \\ 25 - 40 - 6 \\ = - 21[/tex]

Answer:

59

Step-by-step explanation:

This is a substitution question

So we will have to solve by substituting the given value into the equation

So let's solve

b^2-8b-6

And b is given to be-5

So let's substitute

(-5)^2-8(-5)-6

25+40-6

65-6

59

Therefore the final answer is 59

Answer:

if you subscride to my yotube i will tell you it is ytmonkey do now if you want help

Step-by-step explanation:

Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.

Step-by-step explanation:

The coin is tossed 3 times. We need to find the tree diagram that shows all the possible outcomes of the coin landing heads up or tails up

Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.

Answer:

the first one is 8 then the seconed one is 3

Step-by-step explanation:

i just took the quiz

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

[tex]t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex]t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)} [/tex]

[tex]t = \frac{32 \pm 30.98}{2} [/tex]

[tex]t_1 = \frac{32 + 30.98}{2} [/tex]

[tex]t_1 = 31.49 [/tex]

[tex]t_2 = \frac{32 - 30.98}{2} [/tex]

[tex]t_2 = 0.51 [/tex]

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

Answer:

a) Alice starts first, b) Briana gets the finish line first, c) [tex]t \approx 0.509\,min[/tex]

Step-by-step explanation:

a) Alice starts first, since binomial inside the squared root is equal to zero when [tex]t = \frac{1}{2}\,min[/tex], whereas Alice begins at [tex]t = 0\,min[/tex].

b) The instant when each competitor reach finish line is:

Alice

[tex]5\,km = \frac{t}{4}[/tex]

[tex]t = 20\,min[/tex]

Briana

[tex]5\,km = \sqrt{2\cdot t - 1}[/tex]

[tex]25\,km^{2} = 2\cdot t - 1[/tex]

[tex]t = 13\,min[/tex]

Briana gets the finish line first.

c) Alice and Briana are side by side when [tex]a(t) = b(t)[/tex]. Then:

[tex]\frac{t}{4} = \sqrt{2\cdot t - 1}[/tex]

[tex]\frac{t^{2}}{16} = 2\cdot t - 1[/tex]

[tex]t^{2} - 32\cdot t + 16 = 0[/tex]

The roots of the second order polynomial are:

[tex]t_{1} \approx 31.492\,min[/tex] and [tex]t_{2} \approx 0.509\,min[/tex]

Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.

Answer:

b = ± 28

Step-by-step explanation:

Given

96² + b² = 100² ( subtract 96² from both sides )

b² = 100² - 96² = 10000 - 9216 = 784 ( take the square root of both sides )

b = ± [tex]\sqrt{784}[/tex] = ± 28

Answer:

Find the infinite geometric sum, if possible: 50 150 + 450 +... -75 25 1000000 Does not exist and

Step-by-step explanation:

Answer:

total cost = 50 + 0.15 * x

Step-by-step explanation:

We have a fixed charge and a variable charge, which would be the number of miles you travel with the car. Therefore, the expression that represents this, would be the following:

x = is the number of miles traveled in a given period

total charge = 50 + 0.15 * x

This total charge corresponds to the cost of renting a car in any amount of time (weeks)

Answer:

12/26, 1/2, 18/25, 4/7

Step-by-step explanation:

-3 (2a - 1) (4a + 3)

Answer:

80.4672kmh

22.352m/s

43.4488 knots

73.3333 fps

Step-by-step explanation:

Answer:

4 dollars

Step-by-step explanation:

5 minus 1 equals 4

Answer:

4 and 10

Step-by-step explanation:

To solve this problem, we need to find all the numbers between 1 and 13 that have a sum of 14. The list is shown below:

1 + 13,   2 + 12,   3 + 11,   4 + 10,   5 + 9,   6 + 8,   7 + 7

Now we must figure out which set of numbers include one number that is 2/5 of the value of the other. We can do that by turning the sets of numbers into fractions as shown below:

[tex]\frac{1}{13}\neq \frac{2}{5}[/tex]

[tex]\frac{2}{12}\neq \frac{2}{5}[/tex]

[tex]\frac{3}{11}\neq \frac{2}{5}[/tex]

[tex]\frac{4}{10}= \frac{2}{5}[/tex]    (answer)

[tex]\frac{5}{9}\neq \frac{2}{5}[/tex]

[tex]\frac{6}{8}\neq \frac{2}{5}[/tex]

[tex]\frac{7}{7}\neq \frac{2}{5}[/tex]

The first number is 4, and the second number is 10, and their sum is indeed 14, as given in the problem.

Let's call the first number "x" and the second number "y." According to the information given:

The sum of the two numbers is 14, so we can write the equation:

x + y = 14

The first number (x) is 2/5 of the second number (y), which can be expressed as:

x = (2/5)y

Now, we can solve this system of equations using substitution. First, we'll substitute the expression for x from the second equation into the first equation:

(2/5)y + y = 14

To make the equation easier to solve, we can get rid of the fraction by multiplying both sides of the equation by 5 (the denominator of 2/5):

5(2/5)y + 5y = 5 * 14

This simplifies to:

2y + 5y = 70

Now, combine like terms:

7y = 70

To solve for y, divide both sides by 7:

y = 70 / 7

y = 10

Now that we've found the value of y, we can find the value of x using the second equation:

x = (2/5)y

x = (2/5) * 10

x = 4

So, the two numbers are:

x = 4

y = 10

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Answer: 25 meters.

Step-by-step explanation:

The missing figure is attached.

Draw a Right triangle as the one shown in the second picture, where "a" is the smallest length of rope  (in meters) that Ryan could buy, which would stretch from one tree to the other tree.

You need to use the Pythagoream Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" are "c" are the legs of the Right triangle.

In this case you can identify that:

[tex]b=25-10=15\\\\c=20[/tex]

Knowing those values, you can susbtitute into  [tex]a^2=b^2+c^2[/tex] and then solve  for "a" in order to find its value.

You get:

[tex]a^2=15^2+20^2\\\\a=\sqrt{15^2+20^2}\\\\a=25[/tex]

Answer:

B, 36 degrees

Step-by-step explanation:

Because AB and CB are congruent, so are arcs AB and CB. Therefore, 3x+12=6x-12

24=3x

x=8

3x+12=3(8)+12=24+12=36 degrees, or answer choice B. Hope this helps!

Answer:

1. 5

2. 66/25

3. -7.2

4. 25/24

Answer:

C

By substuting x=- 3 the answer will be negative