The shorter leg of a right triangle is 1414 feet less than the other leg. find the length of the two legs if the hypotenuse is 3434 feet.

The given arithmetic series is

[tex] \sum_{t=1}^{18} (3t-4) [/tex]

When t =1, we will get the first term,a, which is

[tex] 3(1)-4 =3-4=-1 [/tex]

When t =18, we will get the last term,l , which is

[tex] 3(18)-4 = 50 [/tex]

Now we use the formula of sum of n terms which is

[tex] S = \frac{t}{2} (a+l) [/tex]

Substituting the values of t,a and l, we will get

[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]

Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]

Let t=1 in the given series, we get

first term = [tex] a_{1} [/tex] = 3-4 = -1.

Let t=2 in the given series, we get

second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]

Let t=3 in the given series, we get

third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]

Now, let t=18 in the given series, we get

last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]

We get the series as

-1, 2, 5,..... 50

Sum = [tex] \frac{n}{2}(a+l) [/tex]

= [tex] \frac{18}{2}(-1+50) [/tex]

= [tex] = 9 \times 49 [/tex]

= 441

Therefore, the sum of the given arithmetic series is 441.

In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.

As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.

Therefore, Option A, minor arc is the correct answer.

The time it takes to cook a turkey is a function of the turkey’s weight. Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Choose the situation that represents a function.

An intake and an outlet are both present in a function. Each unique supply is converted into a result as per the concept of a function.

The amount of the turkey determines how long it will take to cook.

Oversized turkeys will take longer to prepare than smaller turkeys, and vice versa.

The time it takes to cook a turkey is a function of the turkey’s weight.

Then the correct option is C.

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A(2/7:5)

B(10:39)

The slope is 7/2.

The slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation of line is y=3.5x+4

When we compare this with slope intercept form y=mx+b.

slope m=3.5

We need to find the value of x when y is 5

5=3.5x+4

1=3.5x

Divide both sides by 3.5

x=0.28

So a coordinates are (0.28, 5)

Now let us find y value when x is 10

y=3.5(10)+4

y=39

So b coordinates are (0.28, 39)

Hence, the slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)

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The zero of the quadratic function is therefore x = 1. Since both factors give the same zero, we have a repeated zero and f(x) only touches the x-axis at one point, x = 1.

The zeros of the quadratic function f(x) = 4x^2 - 12x + 8 are the values of x that make f(x) = 0. In this function, we can factor by finding two numbers that multiply to give the constant term (8 times 4, the coefficient of x^2) and add to give the coefficient of x (-12). Here, those numbers are -4 and -4, so we rewrite the middle term -12x as -4x - 4x, and factor by grouping:

4x^2 - 4x - 4x + 8 = 0

4x(x - 1) - 4(x - 1) = 0

(4x - 4)(x - 1) = 0

Now we have two factors equal to zero, which gives us two equations to solve:

4x - 4 = 0 or x - 1 = 0

x = 1

Answer:

The value of the given function is 25 for x = 2.

Step-by-step explanation:

Given function is,

[tex]F(x) = 4x^3 - x^2 - 5x + 7[/tex]

At x = 2,

The value of the function is,

[tex]f(2)=4(2)^3-(2)^2-5(2)+7[/tex]

[tex]=4(8)-4-10+7[/tex]

[tex]=32 - 7[/tex]

[tex]=25[/tex]

Hence, the value of the given function is 25 for x = 2.

Answer:

[tex](x+6)^{2}+2x=189[/tex]  

and

[tex]x^{2}+14x+36=189[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represent the situation is

[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]

therefore

The equations that could be used are

[tex](x+6)^{2}+2x=189[/tex]  and [tex]x^{2}+14x+36=189[/tex]

Answer:

(x+6)^{2}+2x=189  

and

x^{2}+14x+36=189

Step-by-step explanation:

APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX

More than $0 but less than $4100

The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Given the standard form of the equations :

The General form of a slope - intercept equation :

For equation (1) :

3x - 4y = 28

Make y the subject

-4y = 28 - 3x

Divide both sides by - 4 to isolate y

y = -7 + 3/4x

[tex]y = \frac{3}{4} x - 7 [/tex]

For equation (2) :

4x + 10y = 20

Make y the subject

10y = 20 - 4x

Divide through by 10 to isolate y

y = 2 - 2/5x

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

Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

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Final answer:

The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)

Explanation:

The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.

Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.

C. 31 pi over 5

~sbcardinals :)

hello there

your answer would be

C, 31 pi over 5

hope it helps

thank you

best regards Queen Z