The total points scored in a basketball game can be calculated using the expression 3c + 3.

If c = 41, how many points total were scored?

Answer:

The correct answer would be 9! hope this helped you

Answer:

5.21

Step-by-step explanation:

3.21x+4=10.3041+2x

1.21x=6.3041

x=5.21

Answer:

6 units

Step-by-step explanation:

The formula for a trapezoid is ((b1+b2)/2)h.

Here, we see b1 = 8 and b2 = 17.

If the area of the trapezoid is 75, we can make the equation :

75 = ((8+17)/2)x , where we would solve for x.

First, we simplify the right side of the equation :

75 = (25/2)x

Multiply both sides by 2 to get rid of the "/2"

150 = 25x

Then divide both sides by 25.

6=x

Answer:

9/10

Step-by-step explanation:

To divide by 5/6, invert 5/6, obtaining 6/5, and then multiply:

 3         6

------ *  ----- = 18/20 = 9/10 (same as the 2nd possible answer)

  4        5

The solution of the given equation 1080 = 15³ˣ⁻⁴ is (x = 2.19), round to the nearest hundredth.

A logarithmic term represents a number in logarithmic form. A log term is another name for it.

A quantity can also be the sum of two or even more quantities. As a result, a term can consist of the product of two or more quantities, one of which must be in logarithmic form. For such cases, this same terms are known as log terms.

A quantity can also be defined as the quotient of two quantities. But, if a term includes a quotient of quantities, or at least one of the quantities can also be expressed in log form, this same terms are known as log terms.

Now, consider the given equation given in the question;

1080=15³ˣ⁻⁴

Take log on the both sides;

㏒1080 = ㏒15³ˣ⁻⁴

Using the power rule on the second side of the equation;

㏒1080 = (3x - 4)㏒15

Taking log on one side and other variables on other side.

3x - 4 = ㏒1080/㏒15

Use calculator to find the values of both log.

3x - 4 = 2.57

3x = 6.57

x = 2.19

Therefore, the solution of the given function 1080=15³ˣ⁻⁴ is (x = 2.19), rounded up to nearest hundredth.

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In a circle, 5 ones and 4 zeros are arranged randomly. Between any two equal digits, you write 0, and between any two different digits, you write 1.

To understand the process, consider the arrangement of the digits around the circle. Let's start with the first digit and compare it with the next digit. If they are the same, we write 0 in between them. If they are different, we write 1.

We continue this process for all adjacent pairs of digits around the circle until we reach the starting point again. This creates a new arrangement of zeros and ones based on the original arrangement of the digits.

By following this rule, we ensure that between any two equal digits, we have a 0, and between any two different digits, we have a 1. The resulting arrangement reflects the pattern described in the problem statement.

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The inequality that models this problem is as follows:

7x + 5y ≤ 30

She budgeted $30 per month for entertainment.

Movies cost $7 and sport games cost $5.

Let

x = number of movies she attended in a given month

y = The number of sport games she attended in the same month.

Therefore, the inequality that model this problem is as follows:

7x + 5y ≤ 30

Note her expenses must be less than or equals to 30 dollars.

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At equilibrium, the electric field due to the charges of the bottom sphere must point downward in the wire. The charges of the system must be arranged such that the top sphere is positively charged and the bottom sphere is negatively charged.

When the positively charged sphere is placed next to the first sphere, the charges in the system redistribute themselves to achieve equilibrium. Since like charges repel each other, the positive charges in the bottom sphere will experience a repulsive force from the positive charges in the top sphere. In order to counteract this repulsion, negative charges will migrate towards the bottom sphere.

The electric field lines always point in the direction of the force experienced by a positive test charge. In this case, a positive test charge placed in the wire near the bottom sphere would experience an attractive force towards the negatively charged bottom sphere. Therefore, the electric field due to the charges of the bottom sphere must point downward in the wire.

To achieve equilibrium, the charges of the system must be arranged in such a way that the top sphere is positively charged and the bottom sphere is negatively charged. This charge distribution creates an electric field that counteracts the repulsive force between the positive charges, allowing the system to reach a stable state.

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Answer:

\(\bold{\dfrac{9}{11}}\)

Step-by-step explanation:

I will use the dot notation for multiplication

We have
\(\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4\)

Convert 4 to a fraction:
\(4=\dfrac{4}{1}\)

Therefore

\(\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4 \\\\= \dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \dfrac{\cancel {4}}{1}\\\\\)

Cross-cancel common factor 4
\(=\dfrac{3}{11}\cdot \dfrac{3}{1}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\:\cdot \:c}{b\:\cdot \:d}\)
\(=\dfrac{3\cdot \:3}{11\cdot \:1}\)

\(=\bold{\dfrac{9}{11}}\)

One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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Answer:

y = 3/2x + 2

Step-by-step explanation:

Step 1: Write original equation into slope-intercept form

3y = -2x + 3

y = -2/3x + 1

Step 2: Find slope of perpendicular line

Take the negative reciprocal of the other slope.

m = 3/2x

Step 3: Find b

y = 3/2x + b

-4 = 3/2(-4) + b

-4 = -6 + b

b = 2

Step 4: Rewrite perpendicular equation

y = 3/2x + 2

Answer:

b. y = -3/2x + 1

Step-by-step explanation:

A parallel line has the same slope as the line in question. The only difference is the y-intercept, which you calculate by plugging in the given point.

The original line: y = -3/2x + 3

The parallel line: -5 = -3/2(4) + y-intercept

-5 = -6 + y-intercept. So, y-intercept = 1

This means that the parallel line is b, y = -3/2x + 1.

Answer:

mine is correct

Given

a line is giving as

y-3=3/2x

and the point is(4-5)

To Find

the equation of the line parallel line (I) and passing through the point (4-5)

Explanation

let. be the equation of the required line be

y=mx+c

since it is parallel to equation o

m=3/2

hence the equation of the required line is

y= -3/2X+X

since it passes through the point (4-5)

-5=-3/2×4+c

=C=1

thus the equation of the required line is

y= -3/2x+1

=y+3/2x=1

=2y+3x=2

=3x+2y=2

therefore the correct option is (a)

pls follow me for more answers

Answer:

Simple interest after 2 year = $36

Step-by-step explanation:

Given:

Amount invested = $300

Number of year amount invested = 2 year

Rate of interest per year = 6% = 6/100 = 0.06

Find:

Simple interest after 2 year

Computation:

Simple interest formula;

Simple interest = [Amount invested][Rate of interest][Number of year]

Simple interest after 2 year = [300][0.06][2]

Simple interest after 2 year = [18][2]

Simple interest after 2 year = $36

A) The exact cost of producing the 31st food processor is $3771.70. B)  Using the marginal cost, the approximate cost of producing the 31st food processor is $3741.40.

(A) To find the exact cost of producing the 31st food processor, we substitute x = 31 into the cost function C(x) = 1900 + 60x - 0.3x^2:

C(31) = 1900 + 60(31) - 0.3(31)^2

C(31) = 1900 + 1860 - 0.3(961)

C(31) = 1900 + 1860 - 288.3

C(31) = 3771.7

Therefore, the exact cost of producing the 31st food processor is $3771.70.

(B) The marginal cost represents the rate of change of the cost function with respect to the quantity produced. Mathematically, it is the derivative of the cost function C(x).

Taking the derivative of C(x) = 1900 + 60x - 0.3x^2 with respect to x, we get:

C'(x) = 60 - 0.6x

To approximate the cost of producing the 31st food processor using the marginal cost, we evaluate C'(x) at x = 31:

C'(31) = 60 - 0.6(31)

C'(31) = 60 - 18.6

C'(31) ≈ 41.4

The marginal cost at x = 31 is approximately 41.4 dollars.

To approximate the cost, we add the marginal cost to the cost of producing the 30th food processor:

C(30) = 1900 + 60(30) - 0.3(30)^2

C(30) = 1900 + 1800 - 0.3(900)

C(30) = 3700

Approximate cost of producing the 31st food processor ≈ C(30) + C'(31)

≈ 3700 + 41.4

≈ 3741.4

Therefore, using the marginal cost, the approximate cost of producing the 31st food processor is $3741.40.

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Answer: 1/2 , I tried to help you but you kept insisting it was subtraction

Step-by-step explanation:

the keyword “of” means multiplication

so we do 3/4 x 2/3 and it will give us 1/2

If I’m wrong I’m sorry

Answer:

18π

Step-by-step explanation:

ANSWER

(-4, 2)

(Option D)

EXPLANATION

The triangle in the picture is dilated with scale factor 2.

This simply means that the size of the triangle was increased by 2.

To do this, first, let us write out the cordinates of the vertices of the original triangle:

M(-2, 1)

P(2, -2)

A(3, 5)

To dilate this, we will multiply the cordinates by 2, they become:

M' (-4, 2)

P' (4, -4)

A' (6, 10)

Therefore, the vertex M on the image after the dilation is (-4, 2).

(Option D)

Step-by-step explanation:

What you do pretty much is combine the parts with f and combine the regular numbers

\( - 2.6f + 0.3f = - 2.3f\)

\( - 15 - 4 = - 19\)

\( - 2.3f - 19\)

Answer:

59.) 80 smokers, 280 nonsmokers.

61.) 240 men, 200 women

Step-by-step explanation:

59.)

Start with:

\(\frac{2}{7}= \frac{x-100}{x+100}\)

Cross product.

\(2x+200=7x-700\)

Subtract \(2x\) from both sides of the equation.

\(200=5x-700\)

Add \(700\) to both sides of the equation.

\(900=5x\)

Divide by \(5\)

\(x=180\)

Substitute in your x-value.

\((180)-100 = 80\)

\((180)+100= 280\)

61.)

Start with:

\(6x+5x=440\)

Combine like terms.

\(11x=440\)

Divide by the coefficient of \(x\), which is \(11\)

\(x=40\)

Substitute.

\(6(40)=240\)

\(5(40)=200\)

Points of discontinuity for the rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4) are x = -1 and x = -4.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In the case of the given rational function y=(x+3)(x-5)(x+7)/(x+1)(x+4), the numerator is a polynomial of degree 3, and the denominator is a polynomial of degree 2.

To find any points of discontinuity for a rational function, we need to determine where the denominator is equal to zero. Division by zero is undefined, so any value of x that makes the denominator equal to zero will be a point of discontinuity for the function.

In this case, we set the denominator (x+1)(x+4) equal to zero and solve for x:

(x+1)(x+4) = 0

This equation is true if either (x+1) = 0 or (x+4) = 0. So we have two solutions:

x+1 = 0 or x+4 = 0

x = -1 or x = -4

These values of x make the denominator of the function equal to zero, which means that the function is undefined at these points. These points are known as vertical asymptotes of the function, since the function approaches infinity as x approaches these points from either side.

It's important to note that the numerator of the function does not affect the points of discontinuity, since it is always defined for any value of x. Therefore, the points of discontinuity only depend on the denominator of the function.

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Answer:

None of the following

Step-by-step explanation:

Answer:

Radius duh

Step-by-step explanation:

Answer: 6q +  2

Step-by-step explanation:

The given compound logical proposition is a tautology.

To prove that the given compound logical proposition is a tautology, we need to show that it is always true regardless of the truth values of its individual propositions.

The given compound proposition is:

(asp) →→→ (r^-p)

Let's break it down and analyze it step by step:

The expression "asp" represents the conjunction of the propositions "a" and "sp". We don't have the exact definitions of "a" and "sp," so we cannot make any specific deductions about them.

The expression "(r^-p)" represents the implication of "r" and the negation of "p". This means that if "r" is true, then "p" must be false.

Now, let's consider different scenarios:

Scenario 1: If "r" is true:

In this case, "(r^-p)" is true because if "r" is true, then "p" must be false. Therefore, the compound proposition evaluates to true, regardless of the truth values of "asp".

Scenario 2: If "r" is false:

In this case, "(r^-p)" is also true because the implication "r → ¬p" is true when the antecedent is false. Again, the compound proposition evaluates to true, regardless of the truth values of "asp".

Since the compound proposition is true in both scenarios, regardless of the truth values of its individual propositions, we can conclude that it is a tautology.

Note: It's important to have the exact definitions of the individual propositions and their logical relationships to provide a more precise analysis.

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Answer:

To find the area of the stage, we need to use the formula for the area of a trapezoid, which is:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides, and h is the height (or distance between the parallel sides).

In this case, we know that:

a = 80 feet

b = 50 feet

h = 40 feet

Plugging these values into the formula, we get:

Area = (80 + 50) * 40 / 2

Area = 130 * 20

Area = 2600 square feet

Therefore, the area of the stage is 2600 square feet.

9514 1404 393

Answer:

  a)  θ = 14°

  b)  θ = 62°, A = 28°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relation ...

  Tan = Opposite/Adjacent

This is the useful relation in each case.

__

a) tan(θ) = 43/172

  θ = arctan(43/172) ≈ 14°

__

b) tan(θ) = 32/17

  θ = arctan(32/17) ≈ 62°

  A = complement of θ = 90° -62° = 28°

Answer:

5.5/3 - 3/1 = 2.5/3

The rate at which the distance between the cars is increasing two hours later is approximately 64.03 miles per hour.

To determine the rate at which the distance between the cars is increasing, we can use the Pythagorean theorem and differentiate it with respect to time.

Let's denote the distance traveled by the southbound car as Ds and the distance traveled by the westbound car as Dw. After two hours, the southbound car will have traveled 60 miles/hour * 2 hours = 120 miles (Ds = 120 miles), and the westbound car will have traveled 25 miles/hour * 2 hours = 50 miles (Dw = 50 miles).

According to the Pythagorean theorem, the distance (D) between the two cars is given by D^2 = Ds^2 + Dw^2. Substituting the values, we have D^2 = 120^2 + 50^2 = 14400 + 2500 = 16900. Taking the square root of both sides, we get D ≈ 130 miles.

To find the rate at which the distance is increasing, we differentiate D with respect to time (t) using implicit differentiation. The equation becomes 2D * (dD/dt) = 2Ds * (dDs/dt) + 2Dw * (dDw/dt). Since dDs/dt = 60 mi/h (the rate of the southbound car) and dDw/dt = 25 mi/h (the rate of the westbound car), we can substitute these values into the equation.

2D * (dD/dt) = 2 * 120 mi * (60 mi/h) + 2 * 50 mi * (25 mi/h) = 240 * 60 + 50 * 25 = 14400 + 1250 = 15650. Solving for dD/dt, we have dD/dt = 15650 / (2 * 130 mi) ≈ 60.1923 mi/h.

Therefore, the rate at which the distance between the cars is increasing two hours later is approximately 60.1923 miles per hour.

After two hours, the distance between the cars is increasing at a rate of approximately 60.1923 miles per hour. This calculation takes into account the speeds and directions of both cars and applies the Pythagorean theorem to determine the distance between them.

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Answer:

y = -3x + 3

Step-by-step explanation:

So, basically I can't remember how to do this the long way but I used a calculator on Desmos (the graphing one to be specific). You should be able to find tutorials on how to use it and graph problems to find their answers but if not, you can just message me and I'll walk you through how to use it.

As for the form it asked for in the question, slope-intercept form is just:

y = mx + b

m is the slope, and b is the y-intercept (the place where the line crosses the y-axis)

Car A has the best fuel efficiency as it gives 80 km/liter which is far better than car B and car C.

Fuel efficiency is expressed as a measurement of how much a car will transform power in fuel into kinetic energy to travel. Fuel efficiency indicates how distant your car can travel with a specific amount of fuel.

To determine fuel efficiency, we need to calculate the number of kilometers toured for each car.

Car A =  80 km / 1 liter

Car A = 80 km/liter

Car B = 110110110 km / 101010 liters

Car B = 1.089 km/liter

Car C =727272 km / 666 liters

Car C = 1.092 km/liter

Therefore we can conclude that Car A has the best fuel efficiency.

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The complete question is-

Select the car that has the best fuel efficiency.

Car A's journey is 80km to 1 liter.

Car B's journey is  110110110 km to 101010 liters

Car C's journey is  727272  km to 666 liters