PLEESE HELP
If someone who is 5 feet tall uses a potato gun to shoot a potato in the air at 100 feet per second, we can use the function ℎ()=−162+100+5 to calculate how far the potato will be from the ground at any given second (t).



What is the value of h(1)?

The general solution of the homogeneous system is given as:

x = t * [1, -2, -1] + s * [3, 3, 1],

where t and s are arbitrary constants.

To find the general solution of the given homogeneous system, we start by setting up an augmented matrix using the coefficients of the variables:

[1  2  -3  |  0]

[4  7  -9  |  0]

[-1 -3  6  |  0]

Next, we perform row operations to bring the matrix into row-echelon form or reduced row-echelon form. After applying the necessary row operations, we obtain:

[1  2  -3  |  0]

[0  1   1  |  0]

[0  0   0  |  0]

From the row-echelon form, we can observe that the system has infinitely many solutions. This is because there is at least one free variable (in this case, x3). We can express the solution in terms of this free variable.

Let x3 = t, where t is an arbitrary constant. By back-substitution, we can find the values of x1 and x2 in terms of t:

From the second row: x2 + x3 = 0, we have x2 = -t.

From the first row: x1 + 2x2 - 3x3 = 0, substituting the values of x2 and x3, we get x1 + 2(-t) - 3t = 0. Simplifying, we have x1 - 5t = 0, which gives x1 = 5t.

Therefore, the general solution can be expressed as:

x = t * [1, -2, -1] + s * [3, 3, 1],

where t and s are arbitrary constants.

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Answer:

A. Cos S

Step-by-step explanation:

Recall: SOH CAH TOA

Sin W = Opp/Hyp

Opposite = 4

Hypotenuse = 5

Sin W = 4/5

Let's find the ratio for each option given to determine which gives us the same ratio as Sin W.

Option A: Cos S

Cos S = Adj/Hyp = 4/5

Option B: tan W

Tan W = Opp/Adj = 4/3

Option C: cos W

Cos W = Adj/Hyp = 3/5

Option D: sin S

Sin S = Opp/Hyp = 3/5

✔️Thus, sin W = cos S = 4/5

The correct option is A

The Option 1 has a lower interest rate and a lower monthly payment but the total cost of the vehicle is slightly higher than Option 2. So, i will choose Option 1.

OPTION 1:

Principal amount (P) = $24,000

Annual interest rate (r) = 2.9% = 0.029

Years (n) = 4 (quarterly)

Time(t) = 6

Using the formula, we will calculate total amount:

A = $24,000(1 + 0.029/4)^(4*6)

A = $28,543.4107

A = $28,543.41

Monthly payment = $28,543.41 / (6*12)

Monthly payment = $396.43625

Monthly payment = $396.44

OPTION 2:

Principal amount (P) = $22,000

Annual interest rate (r) = 5.9% = 0.059

Time = 4 (quarterly)

Time in years (t) = 6

A = $22,000(1 + 0.059/4)^(4*6)

A = $31,263.681

A = $31,263.68

Monthly payment = $31,263.68 / (6*12)

Monthly payment = $434.22.

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Both of the following forms of the SVD are equivalent because both are related spectroscopic data.

Singular value decomposition (SVD)

Singular value decomposition (SVD) is a technique commonly used in the analysis of spectroscopic data that both acts as a noise filter and reduces the dimensionality of subsequent least-squares fits.

The singular value decomposition (SVD) of a matrix A is the process of factorizing A into the  product of three matrices A = U DV^{T} where the columns of U and V are orthonormal and  the matrix D is diagonal with positive real entries. Data matrix A is useful to find a low rank matrix which is a good approximation  to the data matrix.

spectroscopic data

spectrographs collect data that tell scientists how much light comes out at each wavelength. These data reveal important details about the makeup of atmospheres on exoplanets, the compositions of stars and nebulas, the motion of galaxies and more.

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A commission also will order someone to be done as well as the artist received a commission for a new color to hang in the constructing lobby, as well as a committee, is a commander in the military or a special commission that also controls or investigates stuff, and the further calculation can be defined as follows:

Solution:

Calculating the commission value for Justin:

\(\to (100000 \times 6\%)\\\\\to (100000 \times \frac{6}{100})\\\\\to (1000 \times 6)\\\\\to 6000\)

Calculating the commission value for Blake:

\(\to (80000 \times 5\%)+ (20000 \times 6\%)\\\\\to (80000 \times \frac{5}{100})+ (20000 \times \frac{6}{100})\\\\\to (800 \times 5)+ (200\times 6)\\\\\to (4000 )+ (1200)\\\\\to 5200\\\\\)

Therefore, the final answer is "Justin makes 800 than Blake".

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To make a table of values using multiples of π/4 for x with the function y = cos x, we will calculate the cosine values for the given x values. Here's the table:

x | y
-------
0 | cos(0) = 1
π/4 | cos(π/4) = √2/2 ≈ 0.71
π/2 | cos(π/2) = 0
3π/4 | cos(3π/4) = -√2/2 ≈ -0.71
π | cos(π) = -1
5π/4 | cos(5π/4) = -√2/2 ≈ -0.71
3π/2 | cos(3π/2) = 0
7π/4 | cos(7π/4) = √2/2 ≈ 0.71
2 | cos(2) ≈ -0.42

Your answer:
x | y
-------
0 | 1
π/4 | 0.71
π/2 | 0
3π/4 | -0.71
π | -1
5π/4 | -0.71
3π/2 | 0
7π/4 | 0.71
2 | -0.42

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The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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Answer:

24/45 or 9/15

Step-by-step explanation:

none of these is equivalent to 6:10

Answer:

1.25

Step-by-step explanation:

125/100 = 1.25

Answer:

it's 1.25

Step-by-step explanation:

125 ÷100 = 1.25

Given :

The store sells gasoline for .25 per gallon below it's regular cost per gallon.

Suppose the store sells 5,750 gallons that day.

To Find :

the stores profit or loss in comparison to the amount the store would had made without the special offer.

Solution :

Since, store is selling gasoline for lower amount than regular so they will be in loss.

Loss =$ 0.25 × 5750

Loss = $1437.5

Therefore, loss of store in comparison to the amount the store would had made without the special offer is $1437.5 .

Hence, this is the required solution.

Answer:

19

Step-by-step explanation:

14 ) x + 37 + 37 = 180

or , x + 74 = 180

or , x = 180 - 74

or , x = 106

Answer:

An expression

Step-by-step explanation:

The constant in this case would be 6 because it never changes.

The variable would be x because the value of x can change.

A formula is a mathematical rule, which 6 +x is not.

Therefore, 6+x is an expression.

The probability of getting a number whose product is even when rolling two unbiased dice is 18/36 or 1/2.

To find the probability of getting a number whose product is an even number when rolling two unbiased dice, we need to first determine the total number of possible outcomes. When rolling two dice, each die has six possible outcomes, so the total number of possible outcomes is 6 x 6 = 36.

Next, we need to determine the number of outcomes where the product is even. An even number can be obtained by either rolling an even number or by rolling an odd number and an even number. We can break this down into two cases:

Case 1: One even and one odd number. There are three even numbers on a die (2, 4, 6) and three odd numbers (1, 3, 5). So, the number of outcomes where one die is even and one is odd is 3 x 3 = 9.

Case 2: Both numbers are even. There are three even numbers on a die (2, 4, 6), so the number of outcomes where both dice are even is 3 x 3 = 9.

Therefore, the total number of outcomes where the product is even is 9 + 9 = 18.

So, the probability of getting a number whose product is even when rolling two unbiased dice is 18/36 or 1/2.

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By using a trigonometric relation, we will see that the value of x is 60.57°

On the image, we can see a right triangle where x represents one of the angles.

We can see that the length of the two catheti are shown, such that the adjacent cathetus is 2.2, and the opposite cathetus is 3.9, then we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Then we can write:

tan(x) = 3.9/2.2

Using the inverse tangent function in both sides, we will get:

Atan( tan(x)) = Atan(3.9/2.2)

x = Atan(3.9/2.2) = 60.57°

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Step-by-step explanation:

c = cost per person

p = number of people

The cost per person is 1500/p, where 

is the number of people. A larger p creates a smaller value of c since they are INVERSELY RELATED.

I believe the inverse variation function is

c = 1500 × 1/p

make sure to ask if you need anything else. :)

Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

Answer:

x = -1

Step-by-step explanation:

(x1,y1) = (1,4) and m = 2

(y-y1)/(x-x1) = m

derive the linear function first before finding the zero.

(y-4)/(x-1) = 2

cross multiply

y-4 = 2(x-1)

y-4= 2x - 2

y = 2x - 2+4

y. = 2x + 2 is the linear equation

at y = 0 gives the zero

2x + 2 = 0

2x = -2

x = -2/2

x = -1 is the zero

Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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The required solution to the given statement is 14/15.

The least common multiple is defined as the least positive integer that is dividable by both given numbers.

A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers. For example, the LCM of 4 and 5 is 20; 20 is the smallest number that is both a multiple of 4 and a multiple of 5

The statement is given in the question below as:

-2/5 plus 4/3

Here "plus" represents the addition sign (+)

So, the algebraic form of the above statement will be as:

⇒ -2/5 + 4/3

Take the LCM between the fractions, we get

⇒ ( -6 + 20)/15

⇒ 14/15

This means 14/15 is obtained from -2/5 plus 4/3.

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Answer:

v = 3.483

Step-by-step explanation:

-6v -15v -19 = -91

-21v = -91 +19

-21v = -72

-21v/-21 = -72/-21

v = 3.483

\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_2(x)=-5\implies 2^{-5}=x\)

Answer:

y=mx+b

Step-by-step explanation:

Answer: 72

Step-by-step explanation:

The average is 90.

To calculate the average, you add the grades and divide by the total amount of them. The number of grades is 5. We need to know what value of x satisfies the following equation:

\(90 = \frac{96+90+87+95+x}{5}\)

To solve the equation, we first multiply each side by 5, netting:

450 = 96 + 90 + 87 + 95 + x.

Then we subtract each grade from each side.

450 - 378 = 378 - 378 + x

72 = x

Answer:

4

Step-by-step explanation:

4*3=12

12*3=36

36*3=108

Answer:

\(\boxed{\mathrm{4}}\)

Step-by-step explanation:

Hi student, let me help you out!

......................................................................

First, let's take a look at the common ratio, which is 3.

Common ratio ===> the amount we multiply or divide by to obtain the next term in a geometric sequence.

Now that we know the common ratio, let's divide 12 by the common ratio, 3. This gives us 4, which is the missing term

Hope this helped you out, ask in comments if any queries arise.

Best Wishes!

\(\star\bigstar\underline{\overline{\underline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star\)

\(\underline{\rule{300}{4}}\)

Answer: She should run 1 1/3 miles 5 times a week.

Step-by-step explanation:  I converted 3/4 to a decimal to have 1.75 and I multiplied it by 5 because that is how many times she will be running 1.75 miles in a week, I got 8.75. So that means if she runs 1.75 miles for 5 days she will run a total of 8.75 miles. Then I converted 1/4 into a decimal and now have 2.25, then I multiplied 2.25 by 3 and got 6.75. So I saw that 8.75 is greater than 6.75,

So the correct answer is: she should run 1 3/4 miles 5 times a week

Answer:

B; the angles of the triangle and the hypothnuse can be multiplied.

Answer:

c

Step-by-step explanation:

x=1 g(x)=-10

x=2 g(x)=-12

x=3 g(x)=-14

f(x)=x+4

=＞ g(x)=-2·(x+4)

Answer:

Scatter plots

Pie graph

graph

in words

Answer:

Step-by-step explanation: