Find the area (in square inches) of the shape shown below.

Answer:

b

Step-by-step explanation:

Point (0,4) slope (3/4) form would be

y-4 = 3/4 ( x-0)     re-arrange to y = mx + b form

y = 3/4x + 4

Answer:

D

Step-by-step explanation:

(f(g(x))' = g'(x)×f'(g(x))

so,

4×e^(-7x) = g'(x)×f'(g(x)

we know that

(e^x)' = e^x

and the integral vice versa (+ C of course).

4×(e^(-7x))' = 4×(-7x)'×e^(-7x) = 4×-7×e^(-7x)

so, in order for

(f(g(x))' = 4×e^(-7x)

we need to have an additional -1/7 factor in f(g(x)) (which is the integral of (f(g(x))'):

-1/7 × 4 × e^(-7x) = -4/7×e^(-7x)

so, D is the correct answer

On solving the provided question, we can say that the derivative will be y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0

The derivative of a function with real variables in mathematics gauges how sensitively the function's value will change in response to changes in its arguments. Calculus's fundamental tools are derivatives. Differentiation (in mathematics, the rate of change of a function with respect to a variable) (in mathematics, the rate of change of a function with respect to a variable). Calculus and differential equation problem-solving depend heavily on derivatives. Finding the "slope" of a specific function is the definition of "derivative" or "taking a derivative" in calculus. Because it is often the slope of a straight line, the slope should be enclose in quotations. While applying to practically every function, derivatives are measures of rate of change.

Linear second-order differential equation F(x, y, y′, y″) = 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0  

differential equation

y = c₁x + c₂x⁴  ...(i)

Differentiating equation (i)

y¹ = c₁(1) +  c₂ ( 4 x³ ) ...(ii)

Differentiating equation (ii)

y¹¹ =   c₂ ( 12 x² )

12 x² y = (y¹12 x³ - 4 x⁴ y¹¹) + x⁴ y¹¹

x⁴ y¹¹ - 4 x⁴ y¹¹ + y¹12 x³ - 12 x² y= 0

y¹¹( -3 x⁴ )+ y¹12 x³ - 12 x² y= 0

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Answer:

[tex]a (5)[/tex]

[tex]b (0,5)[/tex]

[tex]c (-3,0,5)[/tex]

[tex]d (1/3, 5/8, 66/67, -1.27)[/tex]

[tex]e( \sqrt{2} \: \sqrt{7} \: )[/tex]

[tex]f( - 3 \: 5 \: \frac{1}{3} \: \frac{5}{8} 0 \: \sqrt{2 \:} \sqrt{7} - 1.27 \: \frac{66}{67} )[/tex]

A. 5 feet is the length of bookshelf C.  

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

this is a Pythagorean theorem problem, and it involves right triangles.

If this is the case, then we can use the formula: a² + b² = c².

In this case, it gives us the values of a and b,

so we have 3² + 4² = c².

This is equal to 9 + 16 = c², and further simplified, 25 = c².

So we can then find the square root of 25,

written as √25, which would equal 5,

as 5² = 5 * 5,

and 5 * 5 = 25.

So therefore your answer would be A. 5 feet.

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Answer: 11,923

Step-by-step explanation:

The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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The answer is (A) because -6a -12 +3a is the expression that equals 3 (-2a-4) +3a.

A group of numbers or variables coupled with the operations +, -,/, or form an expression.

Algebraic expressions with variables, numbers, and mathematical operators, as opposed to arithmetic expressions that simply contain numbers and mathematical operators.

So, we have the expression:
3 ( -2a-4) +3a

There is just one variable in this expression: a.

The bracket will be opened using the distributive property.

The Distributive property states that multiplying a number by the sum of two other numbers will have the same outcome as multiplying the number by each addend separately.

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

When addressing the brackets:

-6a -12 +3a

Putting like phrases together:

Similar phrases are grouped together using the Associative feature.

The associative property states that even if the order of the numbers is changed, the total of two or more remains the same:

-6a +3a -12

+3a -12

Therefore, the answer is (A) because -6a -12 +3a is the expression that equals 3 (-2a-4) +3a.

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Complete question:

Which expressions are equivalent to 3(-2a-4)+3a3(−2a−4)+3a3, left parenthesis, minus, 2, a, minus, 4, right parenthesis, plus, 3, a ? Choose all answers that apply: Choose all answers that apply: (Choice A) A -6a-12+3a−6a−12+3aminus, 6, a, minus, 12, plus, 3, a (Choice B) B 3a+123a+123, a, plus, 12 (Choice C) C None of the above

Yes, it is possible to have a graph of a function that is symmetric about both the y-axis and the origin. This means that if (x, y) is a point on the graph, then (-x, y) and (x, -y) are also points on the graph.

In other words, the function has both reflectional symmetry about the y-axis and rotational symmetry about the origin. An example of such a function is y = x², which is a parabolic function that opens upwards and is symmetric about both the y-axis and the origin.

A graph is symmetric about the y-axis if the graph is unchanged when reflected over the y-axis. This means that for any point (x,y) on the graph, the corresponding point (-x,-y) will also be on the graph. A graph is symmetric about the origin if the graph is unchanged when reflected over the origin.

Therefore, This means that for any point (x,y) on the graph, the corresponding point (-x,y) will also be on the graph. When a graph is symmetric about both the y-axis and the origin, it means that the graph is unchanged when reflected over either the y-axis or the origin.

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Coach Yamada can make fewer than 10 full teams.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each team can have 8 players.

and, not more than 80 players can the Coach take.

let x be the number of teams formed then the inequality is

8x < 80

Now, solving the inequality

x< 80/8

x < 10.

Hence, Fewer than 10 full teams can be made.

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Answer:

(2s,0)

Step-by-step explanation:

since there are no numbers at point M to help find point L answer should be (2s,0)

Answer:

(2s,0)

Step-by-step explanation:

because it's isosecle triangle so do a line from M to x axis, it should be the mid point of L. so L =2s

L is on x-axis, so y=0

Given the problem:

What is 32% expressed as a decimal?

To convert percentages to decimals, simply divide the percentage by 100. Or move the percentage sign two places to the left and change it to a decimal point.

So the answer is 0.32

The 25th percentile of radiation levels is given as follows:

P25 = 0.905 W/kg.

A measure is said to be in the xth percentile of the data-set if it the bottom separator of the bottom x% of measures of the data-set and the top (100 - x)% of measures, that is, it is greater than x% of the measures of the data-set.

In this problem, the data-set has 50 elements, hence the position of the element at the 25th percentile is given as follows:

0.25 x 50 = 50/4 = 12.5.

Meaning that the 25th percentile is the mean of the 12th and 13th elements, as follows:

P25 = (0.9 + 0.91)/2

P25 = 0.905 W/kg.

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Each month, the interest for the current balance is calculated as:

$3,287.90 * 14.5% / 12 = $48.22

How Do Interest Rates Work?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

The new balance after each payment is:

$3,287.90 + $48.22 - $1,200.00 = $2,147.12

Repeat the calculation until the balance is zero:

Month 1:

Balance: $3,287.90

Interest: $48.22

New Balance: $2,147.12

Month 2:

Balance: $2,147.12

Interest: $31.14

New Balance: $1,178.26

...

Month 26:

Balance: $0.00

So, it takes 26 months to pay off the credit card, and the total amount paid including interest is $31,622.68.

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Based on the information provided, the area of this triangle is 44.17 square centimeters.

The area of a triangle  (surface occupied by the triangle) can be calculated using the three lengths of the sides of the triangle or using two sides and one angle as it is shown below:

Based on this, the area of the triangle given is 44.17 square centimeters.

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Answer:

$773.55

Step-by-step explanation:

To find the total cost of the camera with the sales tax included, you need to calculate the amount of sales tax and add it to the listed price of the camera.

The sales tax rate is given as 9.75%. To convert this to a decimal, divide the percentage by 100: 9.75/100 = 0.0975

To find the amount of sales tax, multiply the listed price of the camera by the sales tax rate as a decimal: $704.95 x 0.0975 = $68.60

To find the total cost of the camera, add the amount of sales tax to the listed price: $704.95 + $68.60 = $773.55

So the total cost of the camera with the sales tax included is $773.55

Answer:

Step-by-step explanation:

Let r be the cost of each juice bottle.

The total cost of the juice bottles is 10 * r = 10r.

The total cost of the apples and the juice is $1.59 + 10r = $7.39.

We can set up an equation using the above information:

$1.59 + 10r = $7.39

10r = $7.39 - $1.59 = $5.80

r = $5.80 / 10 = $0.58

Therefore, each juice bottle costs $0.58.

Answer:

gyyvggghhbbdsdgbnkkk

When 75°30' converted into radian it will be 1.309 radians.

A radian is a unit of measurement for angles in mathematics. It is defined as the angle formed at the center of a circle by an arc that is equal in length to the radius of the circle. In other words, a radian is the angle that subtends an arc equal in length to the radius of the circle.

The radian is used as a unit of measurement because it provides a convenient and natural way to describe angles in terms of their relationship to circles. It allows for the calculation of angles in terms of lengths, making it easier to solve problems involving circular motion and trigonometry. The conversion between degrees and radians is given by the formula: 1 radian = 180/π degrees, where π is the mathematical constant pi.

To convert degrees to radians, use the formula: radians = (degrees × π) / 180.

For 75° 30', the conversion to radians is:

radians = (75° 30' * π) / 180 = (75 + 30/60) * π / 180 = 1.309 radians.

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The power function, h(x) = [tex]$$3x^{0.5[/tex] then the domain for h(x) is [0, ∞).

A power function is a single-term function that has a real number, a coefficient, and a variable raised to a specified real number as its product. Coefficients are numbers that multiply a variable by itself when it is increased to an exponent.

A variable base raised to a fixed power is a component of a power function. This function is raised to a variable power from a constant base. Not a power function, but an exponential function is what this is.

The power function in statistics is a function that connects the likelihood of rejecting a null hypothesis on the value of a parameter to its true value. An exponential function has its variable in its exponent, whereas a power function has its variable in its base. This is the key distinction.

Therefore, the correct answer is option a) The domain for h(x) is [0, ∞).

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Answer: $3.50

Step-by-step explanation:

20.00 - 16.49 = 3.51

3.51 rounded to the nearest 10 is 3.50

Answer: 3.50

The solution of given system of equations is (10, 4).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of equations are 3x+4y=38 -----(I) and 5x-5y=30 -------(II)

x-y=6 -------(III)

x=6+y

Substitute x=6+y in equation (I), we get

3(6+y)+4y=38

18+1y+4y=38

5y=20

y=4

Substitute y=4 in equation (III), we get

x=10

So, the solution is (10, 4)

Therefore, the solution of given system of equations is (10, 4).

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Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem! (see explanation)

Step-by-step explanation:

[tex]7x/5x^2-x\\= \frac{-5x^2+7x}{5x^2} \\=\frac{-5x^2+7}{5x}[/tex]

(Hope this helps!)

The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour is 6 = 0.15 gallons per hour and  2 R(t) dt using the average Riemann sum with four equal length partitions is 383.04 gallons.

(a)  R'(7), you can use the mean rate of change formula.

R'(7) ≈ [R(10) - R(4)] / [10 - 4]

With the data from the table it looks like this:

R(10) = 11.3 gallons per hour

R(4) = 10.4 gallons per hour

For this,

R'(7) ≈ (11.3 - 10.4) / 6 = 0.15 gallons per hour

The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour squared.

(b) To approximate 2 R(t) dt using the average Riemann sum with four equal length partitions, we can use

Δt = (24 - 0) / 4 = 6

2 R(t) dt ≈ 2Δt [R(1.5Δt) + R(4.5Δt) + R(7.5Δt) + R(10.5Δt)]

With the data from the table it looks like this:

R(1.5Δt) = R(4.5) = 10.4 gallons/hour

R(4.5Δt) = R(10.5) = 11.3 gallons per hour

R(7.5Δt) = R(16.5) = 10.2 gallons/hour

R(10.5Δt) = R(22.5) = 9.6 gallons per hour

For this,

2 R(t) dt ≈ 2(6) [10.4 + 11.3 + 10.2 + 9.6] = 383.04 gallons

The approximate unit of integral is the gallon. 

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An initial value differential equation is S(t) = 10 * e^(-0.005t).

The initial value differential equation for the amount of sugar in the tank can be modeled as:

dS/dt = (0.2 kg/L) * 10 L/min - (S/400 L) * 10 L/min

        dS/S = -0.005 dt

        ln(S) = -0.005t + C

        ln(10) = C

        S(t) = 10 * e^(-0.005t)

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The value of a is 31/3 in the equation (a+8)/5 + (a-8)/7 = 4.

Two or more expressions with an Equal sign is called as Equation.

The given equation is (a+8)/5 + (a-8)/7 = 4

Multiply with the LCM

7(a+8)+5(a-8)=140

Apply distributive property

7a+56+5a-40=140

Add the like terms

12a+16=140

12a=124

Divide both sides by 12

a=124/12

a=31/3

Hence, the value of a is 31/3 in the equation (a+8)/5 + (a-8)/7 = 4.

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By 17.77 percent this stock price rises.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, In one day, the stock price for Warbeck's Coffee rose from $5 to $6 per share.

From the general formula of percentage:

Percentage = difference value/ total value * 100

In our case,

Difference value = 6-5

Difference value = 1

total value = 6

thus,

Percentage change = 1/6 * 100

percentage change = 17.77%
Therefore, By 17.77 percent this stock price rises.

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