can the sides of a triangle have lengths 3, 4, and 7?​

a) The linear equation is:

y = 25 + x

b) When the daughter's is one third of her mother's age​ we will have x = 12.5

We know that the mother is 25 years older than the daughter, so, if the daughter's age is x, the mother's age can be defined as the linear equation:

y = 25 + x

b) When the daughter's age is one third of her mother's, we have:

x = (1/3)*y

3x = y

Replacing that in the equation above we will get:

3x = 25 + x

3x - x = 25

2x = 25

x = 25/2 = 12.5

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If "function-f" is defined by f(x) = √(x³+2) and "g" is an "anti-derivative" of "f" such that g(3) = 5, then g(1) = -1.585.

The "Anti-derivative" of a "function-f(x)" is a function, F(x) whose derivative is equal to f(x).

The function is defined as f(x) = √(x³+2),

The "function-g" is an anti-derivative of function-f, such that g(3) = 5 ,

Which means,

⇒ g(a) = \(\int\limits^x_0\)f(t) dt + c,

⇒ g(a) = \(\int\limits^x_0\)√(t³+2)dt + c,

⇒ 5 = \(\int\limits^x_0\)√(t³+2)dt + c,

⇒ c = 5 - \(\int\limits^x_0\)√(t³+2)dt,

So, the function g(x) = \(\int\limits^x_0\)√(t³+2)dt + 5 - \(\int\limits^3_0\)√(t³+2)dt,

⇒ g(1) =  \(\int\limits^x_0\)√(t³+2)dt + 5 - \(\int\limits^3_0\)√(t³+2)dt,

On Simplifying further ,

We get,

⇒ g(1) = 1.4971 + 5 - 8.0817,

⇒ g(1) = -1.5846 ≈ -1.585.

Therefore, the value of g(1) is -1.585.

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The given question is incomplete, the complete question is

If the function f is defined by f(x) = √(x³+2) and "g" is an antiderivative of "f" such that g(3) = 5, then g(1) = ?

Answer:

Step-by-step explanation:

Dilating with a scale factor of 3 centered at the origin means we multiply all the coordinates by 3.

Therefore, the answers are the second option and the sixth option.

Answer:

0.5 + 0.5, 0 + 1, 0.6 + 0.4, etc etc

Step-by-step explanation:

Answer:

b is 40

Step-by-step explanation:

Answer:

I think b = 40

Step-by-step explanation:

Answer:

is there any more details?

Step-by-step explanation:

Answer:

any more details please?

Answer:

120 cm. .here u go..

Step-by-step explanation:

Circumference: 2πr

C=18 so r= 18/2π= 9π

Arc length = rθ 6=(9π)θ θ=6/9π

Convert to degrees by multiplying by 180/π



6/9π x 180/π = 120 degrees

Hope it helps!

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TYSM!

Answer:Use the calculator above to calculate height, radius or volume of a cylinder. Enter any two values and the missing one will be calculated.

Step-by-step explanation: I dont know

Answer:

We need the values to help you, but I think I can get you started.

Step-by-step explanation:

To find the volume of a cylinder, you find the area of the base, then multiply by height. The formula is v=(πr²)(h), pi times the radius squared, times height. Plug in your values, and you should be good to go.

If the function f be defined by f(x) =5x – 2a, then the value of a is 5.

Let the function f be defined by f(x) =5x – 2a

The value of f(10)

f(x) =5x – 2a

f(10) = 5(10) - 2a

f(10) = 50 - 2a

The value of f(10)

f(x) =5x – 2a

f(5) = 5(5) - 2a

f(5) = 25 -2a

f (10) + f (5) = 55,

50 - 2a + 25 - 2a = 55

-4a = 55 - 75

4a = 20

a = 5

Therefore, if the function f be defined by f(x) =5x – 2a, then the value of a is 5.

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Answer: i got a for your answer choice

Step-by-step explanation:

Answer:

24.15

Step-by-step explanation:

I think

Answer:

x = 22.93 feet

Step-by-step explanation:

Given that,

The sun is 70° above the horizon.

We need to find the length of the shadow cast by a building 63ft tall.

Let the length of the shadow be x. We can find it using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan(70)=\dfrac{63}{x}\\\\x=\dfrac{63}{\tan(70)}\\\\x=22.93\ ft\)

So, the length of the casted shadow is equal to 22.93 feet.

Answer:

 2 • (x2 - 2y)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 2x2 -  4y

Step  2  :  See below

Step  3  :  See below

Pulling out like terms :

3.1     Pull out like factors :

Answer:  2 • (x2 - 2y)

Hope this helps.

1. The area formula to use for each of the faces and base is the area of triangle

2. The surface area is 139.5 square yards

From the question, we have the following parameters that can be used in our computation:

The triangular pyramid

The above means that

The faces and the base of the figure are triangles

So, the area formula to use for each of the faces and base is the area of triangle formula

This is the sum of the areas of the shapes

So, we have

Surface area = 3 * 1/2 * 9 * 8 + 1/2 * 7 * 9

Evaluate

Surface area = 139.5

Hence, the surface area is 139.5 square yards

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The value of the equation ( 3x²y⁴)³ is  A = 27x⁶y¹²

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the value of A is

Value of A = ( 3x²y⁴)³

Now , let us simplify each terms of the equation as

( x )³ = x³

So , A = ( 3x²y⁴)³ is simplified as

Value of the expression ( 3 )³ = 3 x 3 x 3

Value of the expression ( 3 )³ = 27

And ,

Value of the expression ( x² )³ = x²ˣ³

Value of the expression ( x² )³ = x⁶

And ,

Value of the expression ( y⁴)³ = y⁴ˣ³

Value of the expression ( y⁴)³ = y¹²

So , the value of equation A is

A =  27x⁶y¹²

Hence The value of the equation ( 3x²y⁴)³ is  A = 27x⁶y¹²

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:

60%

Step-by-step explanation:

Answer:

Step-by-step explanation:

a = 5 ft, b = 8 ft, c = 9 ft

semiperimeter s =  (a+b+c)/2

=  (5 + 8 + 9)/2

=  11 ft

area = √(s(s-a)(s-b)(s-c))

 = √[11(11-5)(11-8)(11-9)]

 = √396 ft²

area = ½(9)h = √396

4.5h = √396

h = √396/4.5 ≅ 4.42 ft

Answer:

b

Step-by-step explanation:

Answer:

i am pretty sure the answer is d

Step-by-step explanation:

let me know if this is wrong

a. 6a - 40 = <-16, -58, -4>

b. ||a|| = sqrt(61)

c. b = <7, 5, -2>

d. Unit vector in the direction of 7 = 1

e. a x b = <12, 50, 47>

f. projac = (-41) / sqrt(29)

g. Area of the parallelogram determined by a and b = sqrt(4853)

Let's determine the values as requested:

a. 6a - 40:

To find 6a - 40, we multiply each component of vector a by 6 and subtract 40 from each component.

6a = 6 * <4, -3, 6> = <24, -18, 36>

6a - 40 = <24, -18, 36> - <40, 40, 40> = <-16, -58, -4>

b. ||a||:

The magnitude (or length) of vector a can be found using the formula:

||a|| = sqrt(a1^2 + a2^2 + a3^2)

Plugging in the values of vector a, we have:

||a|| = sqrt(4^2 + (-3)^2 + 6^2) = sqrt(16 + 9 + 36) = sqrt(61)

c. b:

Vector b is already given as <7, 5, -2>.

d. Unit vector in the direction of 7:

To find the unit vector in the direction of vector 7, we divide vector 7 by its magnitude.

Magnitude of vector 7, ||7|| = sqrt(7^2) = sqrt(49) = 7

Unit vector in the direction of 7 = 7/7 = 1

e. a x b:

To find the cross product of vectors a and b, we use the formula:

a x b = <a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1>

Plugging in the values, we have:

a x b = <(-3)(-2) - 6(5), 6(7) - 4(-2), 4(5) - (-3)(7)> = <12, 50, 47>

f. projac:

The projection of vector a onto vector c is given by the formula:

projac = (a . c) / ||c||

where "." denotes the dot product.

Plugging in the values, we have:

projac = (<4, -3, 6> . <-2, 3, -4>) / ||<-2, 3, -4>||

= (-8 + (-9) + (-24)) / sqrt((-2)^2 + 3^2 + (-4)^2)

= (-41) / sqrt(4 + 9 + 16)

= (-41) / sqrt(29)

g. Area of the parallelogram determined by a and b:

The area of a parallelogram determined by vectors a and b is given by the magnitude of their cross product:

Area = ||a x b||

Plugging in the values, we have:

Area = ||<12, 50, 47>||

= sqrt(12^2 + 50^2 + 47^2)

= sqrt(144 + 2500 + 2209)

= sqrt(4853)

Therefore:

a. 6a - 40 = <-16, -58, -4>

b. ||a|| = sqrt(61)

c. b = <7, 5, -2>

d. Unit vector in the direction of 7 = 1

e. a x b = <12, 50, 47>

f. projac = (-41) / sqrt(29)

g. Area of the parallelogram determined by a and b = sqrt(4853)

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Answer and Step-by-step explanation:

To find the length of AB, we have to use Distance Formula.

Distance Formula takes two points on a graph, and puts it into the following formula to calculate the distance between those two points.

The formula:

D = \(\sqrt{(x_{2} - x_1)^2 + (y_2 - y_1)^2 }\)

Where:

D = The Distance between two points

\(x_2\) = The x value of the second point

\(x_{1}\) = The x value of the first point

\(y_2\) = The x value of the second point

\(y_{1}\) = The x value of the first point

Point A will be the first point and point B will be the second point. All we have to do now is plug those points into the formula and solve.

\(\sqrt{(10 - 5)^2 + (0 - 10)^2 }\\\\\\\\\sqrt{(5)^2 + (- 10)^2 }\\\\\\\\\sqrt{25 + 100 }\\\\\\\\\sqrt{125}\\\\\\\\\sqrt{125} = 5\sqrt{5}\)

The length of side AB is \(5\sqrt{5}\) units, or 11.18 units.

I hope this helps!

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Identify which number??

Answer:

8 feet and 9 inches

Step-by-step explanation:

I just divided 105 by 12.

Then did 12 x 8 which = 96.

Then I did 105 - 96 which = 9

Answer:

y=3x+10

Step-by-step explanation:

We can use standard form to write the equation of this line.

y=mx+b

where m=the slope (or gradient) of the line

and where b= the y-intercept

now to solve...

we know the slope (gradient) or m=3

so we can put this in the equation.

y=3x+b

now we must solve for b.

in order to this we can subsitute the coordinate (-2,4) into x and y since

a coordinates values/variable representation is (x,y) -> (-2,4)

So subsituting the coordinate in...

y=3x+b

4=3(-2)+b

simplify.

4=-6+b

b=10

This means the y-intercept=10

so...

y=3x+10

is the equation of the line.

The correct option is: 1 = ∫∫∫r dz dr dθ

By converting the given expression into an equivalent triple integral in cylindrical coordinates, we obtain:

1 = ∫∫∫r dz dr dθ

This option represents the correct conversion of the integral into cylindrical coordinates. The integral is taken over the region defined by the limits of integration for z, r, and θ, which are not provided in the given question.

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