Which point is a solution to the inequality?
O (-2, 1)
0 (-1,1)
0 (0, 1/2)
0 (3, 1/2)

Answer: -4

Step-by-step explanation: Después de resolver la equación, la respuesta es x = -4

Answer:

X = -4

Step-by-step explanation:

X + 7 = 3

X + 7 - 7 = 3 - 7 ==> subtract 7 on each side to isolate x

X = -4

The rigid motion of the solid line figure is translated to the dotted line figure.

Translation describe a function that moves an object a certain distance.

In a translation, every point of the object must be moved in the same direction and for the same distance.

In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.

Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation

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Answer:

b

Step-by-step explanation:

Therefore, the solution to the inequality 3(y + 1/4) > 3/4 is y > 0.

An inequality is a mathematical statement that shows a relationship between two values, which are not necessarily equal. Inequalities are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are commonly used in algebra and other areas of mathematics, as well as in real-world applications such as finance, economics, and science. They can be used to represent constraints or limits on a variable, such as the maximum or minimum value that it can take.

Here,

We can solve the inequality 3(y + 1/4) > 3/4 by first distributing the 3 to the expression inside the parentheses:

3y + 3/4 > 3/4

Next, we can simplify by subtracting 3/4 from both sides:

3y > 0

Finally, we can solve for y by dividing both sides by 3:

y > 0/3

y > 0

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Answer:n=9

Step-by-step explanation:

\(\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}\)

Option B is the answer.

Answer: C

i hope you can see my handwriting

The heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, a cone a volume of 37 units³, we need to find the heights for given radii,

We know that, the volume of a cone = π×radius²×height/3

Therefore,

1) If the cone's radius is 1, then its height =

37 = π×1×h/3

h = 37×3/3.14

h = 35.35 units

2) If the cone's radius is 2, then its height =

37 = π×4×h/3

h = 37×3/3.14×4

h = 8.83 units

3) If the cone's radius is 5, then its height =

37 = π×25×h/3

h = 37×3/3.14×25

h = 1.41 units

4) If the cone's radius is 1/2, then its height =  

37 = π×1×h/3×4

h = 141.40 units

Hence, the heights for the given radius and volume are 35.35 units, 8.83 units, 1.41 units and 141.40 units

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Answer:

G

Step-by-step explanation:

When you go left or down you subtract

WHen you go right or up you add

Answer:

Step-by-step explanation:

(x-8, y-13) to move left 8 and down 13

Answer: ......... 14.85

Step-by-step explanation:

4.95 × 3

...

14.85

bros lazy lol

\(\huge\boxed{\boxed{\bold{1.5\ \bftext{km/min}}}\ \boxed{\bold{3\ \bftext{km}}}}\)

\(\hrulefill\)

To convert from kilometers per hour to kilometers per minute, we simply divide by \(60\) as there are \(60\) minutes in an hour.

\(\frac{90}{60}=\frac{90\div30}{60\div30}=\frac{3}{2}=\large\boxed{1.5}\)

To find how far the car will travel in a certain time, just multiply the speed by the time.

\(1.5\ \text{km/min}*2\ \text{min}\)

\(\large\boxed{3\ \text{km}}\)

If the equation for every x and x in the domain of f holds, then a function f is odd.  −f(x)=f(−x) − f ( x ) = f ( − x )

If the equation for every x and x in the domain of f holds, then a function f is odd. −f(x)=f(−x) − f ( x ) = f ( − x ) An odd function has a graph that, geometrically speaking, is rotationally symmetric with respect to the origin, meaning that the graph is unaffected by a 180° rotation of the origin.

An even function exists if an expression is obtained that is equivalent to f(x); an odd function exists if an expression is obtained that is equivalent to -f(x); and neither occurs, in which case it is neither.

An odd function is a function having a symmetrical graph about the origin. If a function doesn't display either symmetry, it cannot be either even or odd.

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

\(\frac{1}{12}\) probability of getting a head on the coin and the number 2 on the die

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Independent events:

If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:

\(P(A \cap B) = P(A)P(B)\)

Probability of getting a head on the coin:

Head or tails, fair coin, so:

\(P(A) = \frac{1}{2}\)

Probability of getting the number 2 on the die:

6 numbers, one of which is 2, so:

\(P(B) = \frac{1}{6}\)

What is the probability of getting a head on the coin and the number 2 on the die?

\(P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}\)

\(\frac{1}{12}\) probability of getting a head on the coin and the number 2 on the die

While problem and solution essays are considered expository (writing that exposes facts) in nature, they are persuasive in nature because they call for a solution to a problem.

What is the problem?

A mathematical problem is one that can be modeled, examined, and potentially resolved using mathematical techniques. This can be a practical issue, like figuring out the orbits of the planets in our solar system, or a more theoretical issue, like Hilbert's problems.

The expository essay is a type of essay that calls for the student to research a topic, assess the evidence, elaborate on the topic, and present an argument about the topic in a clear and succinct manner. This can be done by using examples, definitions, comparisons, cause and effect analyses, and more.

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(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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The best option is bank 2. You would have $40,325.26 in the bank after three years at 2.1 monthly. You would have 44,295.81 in interest after two years at 5.4 semiannual.

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Answer:  192 oz

Step-by-step explanation:

thats the answer

Answer:

The median is the middle number; found by ordering all data points and picking out the one in the middle.

You want to put the numbers in order:

47, 49, 49, 50, 52, 57, 57, 57, 61

Then you go one number at a time from both ends until you get into the middle:

47, 49, 49, 50, 52, 57, 57, 57, 61

47, 49, 49, 50, 52, 57, 57, 57, 61

47, 49, 49, 50, 52, 57, 57, 57, 61

47, 49, 49, 50, 52, 57, 57, 57, 61

47, 49, 49, 50, 52, 57, 57, 57, 61

So the answer is 52.

Tip: when you do this and you are left with two numbers that are in the middle, add them and divide them by 2.

Answer:

52

Step-by-step explanation:

Arrange your numbers in numerical order.

Count how many numbers you have.

47, 49, 49, 50, 52, 57, 57, 57, 61

Median = Middle

52 is the number in the middle

Answer:

yes

Step-by-step explanation:

f(x) = 4x/5 + 8/3 can be written as

f(x) = 4/5 x + 8/3

which is in the form

y = mx + b

The form y = mx + b is the slope-intercept form of the equation of a line, so

f(x) = 4x/5 + 8/3 is a linear function.

Answer:

She can play a total of 7 games.

Answer:

No

Step-by-step explanation:

I don't think it is proportional

Here it is not proportional.

What is proportional?

Proportional relationships are relationships between two variables where their ratios are equivalent.

Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.

Here given that,

\(y=-\frac{5}{9x}\)

Here it is not proportional.

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Answer: C

she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.

System of equations:

x - y = 3

x + 2y = 21

solving using substitution:

1. isolate one of the variables in one of the equations

x - y = 3

x = 3 + y

2. substitute 3 + y into the other equation

3 + y + 2y = 21

3. simplify

3 + 3y = 21

3y = 18

y = 6

4. substitute 6 back into one of the equations and solve for x

x - 6 = 3

x = 9

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

Answer:

A. -1.8

Step-by-step explanation:

If x is the independent variable and y is the dependent variable, therefore constant of proportionality would be:

k = y/x

Using any pair of values from the table, we can find k. Let's use (3, -5.4):

k = y/x = -5.4/3

k = -1.8

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

18

Step-by-step explanation:

Since 7×3=21

Then 6×3=18

We times top and bottom by 3 to make it equivalent.

Answer:

6/7 = 18/21

Step-by-step explanation:

Least Common Multiple

7, 14, 21 = 3

-

6 x 3 = 18

6/7 = 18/21

Answer:

88.88% or 8/9 of the yard is mowed

Step-by-step explanation:

First step is to get the denominator to the same number. Both denominators have a least common multiple of 12.

3/4 * 3/3 = 9/12

2/3 * 4/4 = 8/12

9/12 hours is how long it takes Evan to mow his backyard. He has 8/12 hours of work already done. If we divide the time already passed by the time still needed to mow the backyard, we can get how much of the yard is already mowed.

(8/12) / (9/12)

8/12 * 12/9  

96/108 = 88.88

Answer:

X = 33°

Step-by-step explanation:

I hope you understood from the pic but if you have further questions do let me know