Which choice is the correct graph of |x|< 3

The rocket will hit the ground after 19.09 seconds.

a) The height of the rocket can be describe as:

h(t) = -16t² + 210t + 75

where

t = time in seconds

h(t) = height of the rocket in feet

b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:

t = -b/(2a)

where

a = -16

b = 210

Substituting these values, we get:

t = -210/(2(-16)) = 6.5625 seconds

To find the maximum height, we substitute this value of t back into the equation for h(t):

h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet

This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.

c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:

-16t² + 210t + 75 > 721

-16t² + 210t - 646 > 0

Solving for t using the quadratic formula, we get:

t < 2.975 or t > 14.038

Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.

d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:

-16t² + 210t + 75 = 0

Solving for t using the quadratic formula, we get:

t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]

a = -16, b = 210, c = 75

t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]

t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]

t = [tex]\frac{-210 \± 149}{-32}[/tex]

t = 2.53125 or t = 13.53125

Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:

t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds

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Answer:

f'(x) = 2x, so f'(x) = f'(3) = 2(3) = 6.

The percentage decrease of the TV from $900 to $837 is 7%

Percentage decrease = Difference in price / original price × 100

[tex]=\dfrac{(900-837)}{900} \times 100[/tex]

[tex]=\dfrac{63}{900} \times 100[/tex]

[tex]= 0.07 \times 100[/tex]

[tex]= 7\%[/tex]

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Complete question-

An electronics store reduced the price of a TV from $900 to $837. What was the percent of decrease?

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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Answer:

---------------------------

The number is basically a combination in the form of:

Hence the possible digits:

So possible telephone number combinations:

Answer:

Step-by-step explanation:

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

Using the Pythagorean theorem we know that the third side is 15 units.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b², are equal to the squares on the legs.

To determine c, use the Pythagorean Theorem as follows:

a² + b² = c²

9² + 12² = c²

81 + 144 = c²

225 = c

c² = 225

c = √(225)

c = 15

Therefore, using the Pythagorean theorem we know that the third side is 15 units.

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Correct question:

Find the length of the third side. If necessary, round to the nearest tenth.

12 and 9

The station earned $1485 in revenue from selling the gas.

In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.

To find the dot product of v and w, we will use the formula:

Vw = v . w = (210)(2.8) + (300)(2.99)

Vw = 588 + 897 = 1485

Therefore, the value of Vw is 1485.

Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.

The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.

Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.

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Answer:

5 baby goats

Step-by-step explanation:

4 + 1 = 5 pints total

each baby goat gets 1 pint

The dimensions of the region which enclose the maximal area will be  40.5 feet in length by width 27 feet.

Given that the farmer has 162 feet of fencing, we will have:

2L + 3W = 162 feet

2L = 162 - 3W

L = 162 - 3W\2

L = 81 -3/2W  Eqn 1

Given that the area of a rectangle is A = L × W we will call this equation 2

Now we substitute the first equation in the second one to give

A = (81 -3/2W) × W

A = 81W -3/2W²

When we take the derivative W will equal

81/3 = 27

Now we substitute in the second equation, we will have:

= 81 - 3/2(27)

= 81 - 40.5

= 40.5.

So the length will be 40.5 feet while the width will be 27 feet.

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Answer:

Step-by-step explanation:

The size of each interior angle of the polygon is 4x+28 °

The value of x is 34 degree and y is 56 degree.

Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.

here, we have,

We have, BOA is an isosceles triangle.

< CBO = 90°

So, < DBO = 90 - 56

<DBO = 34

and, <ODB = 34°

Now, let the angle ODB be x

As, from the figure < EBD is also 90°

So, <y = 180 - (90+34)  (Angle sum property)

<y = 56

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complete question:

Work out the size of angle x and work out the size of angle y

The value of,

Given function f(x) = cx for 1 ≤ x ≤ 2

a) To find the value of constant x, we have to use the following p.d.f condition as shown below,

[tex]\int\limits^a_b {x} \, dx =1[/tex]

here, a is -∞ and b is ∞.

From the above condition to find the value of c,

[tex]\int\limits^2_1{cx^2} \, dx[/tex] = 1

c * [[tex]\frac{x^3}{3}[/tex]]²₁ = 1

c * [8/3 - 1/3] = 1

c * 7/3 = 1

c = 3/7.

b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²

f(3/2) = 3/7 * (3/2)²

         = 3/7 * 9/4

         = 27/28.

From the above solution, we solved both problems.

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Answer:

No, i do not believe i have learned this yet so good luck bestiee

We have proven that m∠C = m∠A.

We have,

We are given that m∠A + m∠B = m∠B + m∠C.

We want to prove that m∠C = m∠A.

Using algebra,

We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.

This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.

We can also use the transitive property of equality to show that

m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that

m∠A = m∠C.

Therefore,

We have proven that m∠C = m∠A.

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The given operation of the matrix is expressed as: -9y + 2z = 12

Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.

The simultaneous equations formed by the matrix are:

x + 2y + z = -5

    4y - 2 = 3

4x - y + 6 = -8

We are told to Multiply row 1 by -4 and this gives us:

-4x - 8y - 4z = 20

Adding it to row 3 gives us:

-9y + 2z = 12

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Answer:

Step-by-step explanation:

-9+6-1-2-3-4+5-6

-3-3-7-1

-6-8

-14

Answer:

The answer is -14.

Step-by-step explanation:

-(9 - 6) + (-1 -2) - (3 + 4) + (5 - 6)

Subtract 6 from 9 to get 3.

-3 -1 -2 - (3 + 4) + 5 - 6

Subtract 1 from -3 to get -4.

-4 - 2 - (3 + 4) + 5 - 6

Subtract 2 from -4 to get -6.

-6 - (3 + 4) + 5 - 6

Add 3 and 4 to get 7.

-6 - 7 + 5 - 6

Subtract 7 from -6 to get -13.

-13 + 5 - 6

Add -13 and 5 to get -8.

-8 - 6

Subtract 6 from -8 to get -14.

-14.

Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,

1/9 = 2/9, 3/9, 4/9,5/9         ......so on.

Here, we have,

To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.

We have,

Multiple of fraction is the number which is n times of the original function. Here  can be any whole or fraction number.

The given number in the problem is the fraction number which is,

The above number is the unit fraction.

Unit fraction-

Unit fractions are the fraction in which the value of numerator is 1.

The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,

1/9 = 2/9, 3/9, 4/9,5/9            .......so on.

Hence the multiple of the given fraction are,

1/9 = 2/9, 3/9, 4/9,5/9             ......so on.

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Answer:

Step-by-step explanation:

y=-3x-1

format for formula:

y=mx+b

b=1  that is your y-intercept.  where it hits the y-axis

m= -3    this is your slope    [tex]\frac{rise}{run} =\frac{-3}{1}[/tex]  

from a point you have, the y-intercept, you go down 3 (because of the negative in front of it), this is your rise,
and to the right 1, this is your run

The graph of the piecewise function is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.

The definitions are given as follows:

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The probability of picking a senator from at least one out of Georgia, South Carolina, or Florida is equal to 3/50 or 0.06.

Determining the probability of selecting a senator from either Georgia, South Carolina, or Florida is merely a summation of the individual probabilities of drawing one from each state.

There are 100 senators in all and two representatives from each region, thus resulting in an addition of 2 x 50 which equals to 100 senators altogether.

Subsequently, selecting a senator from Georgia has a chance of 1/50,

1/50 + 1/50 + 1/50 = 3/50

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The image point of the coordinate X after the rotation is (-1, 5).

When a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.

So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).

Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).

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The total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark is 720 liters.  

The amount of fluid that moves through a pipe or other container over a given amount of time.

The amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated using the equation for the rate at which the water is flowing.

Given that the rate at which the water is flowing at time t is r(t)=200-4t liters per minute and that 0≤t<50, the total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated as follows:

Total amount of water = ∫r(t)dt  

                   = ∫(200 - 4t)dt  

                   = (200t - 4t²)  

                   = (200(37) - 4(37²)) - (200(7) - 4(7²))  

                   = 1924 - 1204  

                   = 720 liters

The rate of flow decreases linearly with time, which means that the total amount of water flowing from the tank at any given time is equal to the area under the graph of the rate of flow.

This means that the total amount of water that flows from the tank between the 7 minute mark and the 37 minute mark can be calculated by integrating the rate of flow function over the given time interval.

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Answer: 2.303

Explanation: In image

There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

To test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.

Let p be the true proportion of mathematics research published by U.S. authors.

The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).

sample proportion, x/n = 62/130 = 0.477

The test statistic for a two-tailed test is given by:

z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)

= 2.41

Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.

Since  0.016 < 0.05

, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

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Question: What are the two possible angles of a triangle with sides of 100 and 75 with a 40° as marked in the triangles above? Solution: Use the law of sines formula where the 75 length is opposite of 40°, and 100 is opposite of θ. Answer: The two possible angles for this triangle is 58.97° and 121.03°.

Answer:

A B

Step-by-step explanation:

Is between A or B

Answer:  A yes

Step-by-step explanation:

The answer is A because they divided both sides by 5

Not by variable and they didn't add/sub  

This equations are  equivalent

Step-by-step explanation:

58 g = 660 g * ( 1/2)^n

58 / 660 = (1/2) ^n       LOG both sides

-1.056 = n log 1/2

n = 3.508 half lives  

     3. 508  x 10 min = ~ 35.1 min

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]

[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]

Answer: 3t(9t + 5)

Step-by-step explanation:

Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.

To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.

So we start by factoring out the 3t:

27t² + 15t = 3t(9t + 5)

Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:

3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t

Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).

In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.

Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.

Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.

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So it would take A 10 days to do the whole job alone.

An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.

Here,

Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:

In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).

If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.

We can simplify the second equation by multiplying out the brackets and collecting like terms:

8a + 2b = 1

Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:

5(a + b) = 1

5b = 1 - 5a

b = (1/5) - a

Now we can substitute this expression for "b" into the second equation:

8a + 2b = 1

8a + 2((1/5) - a) = 1

8a + (2/5) - 2a = 1

6a = (3/5)

a = (1/10)

So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:

time = amount of work / rate

Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:

time = 1 / (1/10)

= 10 days

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