f(4)

Help me with this please

The current height of the bird is 8 2/3 feet.

A fraction represented with its quotient and remainder is a mixed fraction. For example:

2 1/3 is a mixed fraction.

where,

2 =quotient

1 = remainder

We have,

Bird initial height = 15 feet.

The bird drops down to 6 1/3 feet.

The current height of the bird is:

= 15 - 6 1/3

We can write the mix fraction 6 1/3 in a proper fraction

6 1/3 = 19 / 3

= 15 - 19/3

= (45 - 19) / 3

= 26 / 3

= 8 2/3 feet

Thus the current height of the bird is 8 2/3 feet.

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The quadratic function to represent the given situation is                         y=-(1/312)x²+x+3

A quadratic function is of the form y=g(x) where g(x) is a polynomial in x with degree 2.

The baseball is hit at a initial height of 3 feet. The baseball follows a path of a parabola.

Maximum height=81 feet

Distance from home plate =156 feet

So, (156,81) is the vertex of the parabolic path.

We know that when vertex is at (h,k) then the vertex form of the parabola is  y=a(x-h)²+k

So the quadratic equation is of the form

y=a(x-156)²+81

Now the initial height is given as 3 feet.

So at x=0, y=3

Putting the values in the equation we get:

3=a(0-156)²+81

or, -78=a×156²

or, a=-(78÷156²)

or, a=-(1/312)

So the quadratic equation can be written as

y=-(1/312)(x-156)²+81

Simplifying we get : y=-(1/312)x²+x+3

The quadratic function to represent the path of the baseball is given by y=-(1/312)x²+x+3

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the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.

First, let's define the natural logarithm.

We know that the natural logarithm is the inverse of the exponential function, then:

[tex]e^{ln(x)} = x\\ln(e^x) = x[/tex]

So the natural logarithm of x tells us the value of the exponent y of e such that e^y is equal to x.

And the logarithmic function is a logarithm on base 10, which is written as:

log(x) = log₁₀(x) = ln(x)/ln(10)

If we say that this is equal to e^y for some value of y, we get:

ln(x) = ln(10)*y

If now we apply the exponential function in both sides, we get:

expo(ln(x)) = exp(ln(10)*y) = 10^y

x = 10^y

So, the logarithm of x ells us the value of the exponent y of 10 such that 10^y is equal to x.

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The value of x in the angle is 15

The given parameters are

m < CDF = (3x + 14), m < FDE = (5x -2), and m < CDE = (10x - 18)

The above means that

Line FD divides angle CDE

So, we have

CDE = CDF + FDE

This gives

10x - 18 = 3x + 14 + 5x - 2

Evaluate the like terms

2x = 30

Divide both sides by 2

x = 15

Hence, the value of x in the angle is 15

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Answer:

A wouldn now be at -4, -1

B would be at -1, -1

C would be placed at -1, -5

D would be located at -2, -2

Step-by-step explanation:

Hope it helps!

Answer:

5

Step-by-step explanation:

Factor- 5

[tex]Domain: x - R[/tex]

[tex]Range : y - R[/tex]

[tex]Zeros - 0[/tex]

[tex]Y - intercept \: \: y = 5[/tex]

[tex]Horizontal \: asmptotes \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5, x > + \infty [/tex]

[tex]Parity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: The \: function \: is \: even[/tex]

[tex]Monotonicity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( - \infty , \: \infty \: \: ) constant[/tex]

.

.

Answer:

Step-by-step explanation:

this is clearly not a linear sequence (the terms don't have the same difference).

so, it has to be a geometric sequence.

the common ratio is r.

s2 = s1 × r

16 = 64 × r

r = 16/64 = 1/4

control :

s3 = s2×r

4 = 16 × 1/4 = 4

correct.

Step-by-step explanation:

Answer:

if ur adding them that would be 12cm for all

Step-by-step explanation:

hope it helped

34 = -2x

Divide through by -2

x = -17

you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

Let's define the variable x as the number of liters of the 30% that you need to use.

The concentration of the mixture then will be:

1*x +  0.1*12

Where the concentration for the x liters is 100%, because this is pure alcohol, and for the 12 liters we use a concentration of 10%.

Now, that must be equal to a mixture with a concentration of the 30%, then we can write:

x + 0.1*12 = (x + 12)*0.3

Now we just need to solve this linear equation for x.

x + 1.2 = x*0.3 + 12*0.3

x - x*0.3 = 12*0.3 - 1.2

x*0.7 = 12*0.3 - 1.2

x = (12*0.3 - 1.2)/0.7 = 3.43

This means that you need to add 3.43 liters of pure alcohol to reach a concentration of 30%.

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The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.

Given data

B2 is changed from 7 to 9

C3 contains the formula =B2*2

Finding the increment in B2

= 9 - 7

= 2

The effect on C3

C3 = B2 * 2

C3 = 2 * 2

C3 = 4

We can therefore say that The value of C3 will increase with a factor of 4 because the value of B2 increased with a factor of 2 and C3 is multiplying B2 by 2.

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Answer:

16,000

Step-by-step explanation:
Because,
I know it :)

The percent increase in temperature between 9:00 am and 4:00 pm is 25%

The first step is calculate the percentage change

= 85-68

= 17

The percent increase can be calculated as follows

= 17/68 × 100

= 0.25 × 100

= 25%

Hence the percent increase is 25%

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We use a property from an earlier question of yours [27174924], that

[tex]\displaystyle \int_a^b f(x) \, dx + \int_{f(a)}^{f(b)} f^{-1}(x) \, dx = b\,f(b) - a\, f(a)[/tex]

Note that

[tex]f(x) = \log_2(x^3+1) \implies f^{-1}(x) = \left(2^x - 1\right)^{1/3}[/tex]

[tex]a = 1 \implies f(a) = \log_2(1^3 + 1) = \log_2(2) = 1[/tex]

[tex]b = 2 \implies f(b) = \log_2(2^3 + 1) = \log_2(9)[/tex]

so that the exact value of the integral is

[tex]\displaystyle \int_1^2 \log_2(x^3 + 1) \, dx + \int_1^{\log_2(9)} \left(2^x - 1\right)^{1/3} = 2\log_2(9) - 1[/tex]

Now, observe that

[tex]8 = 2^3 < 9 < 2^{7/2} = 8\sqrt2 \approx11.3 \\\\ \implies 3 < \log_2(9) < \dfrac72 \\\\ \implies 6 < 2\log_2(9) < 7 \\\\ \implies 5 < 2\log_2(9) - 1 < 6[/tex]

so that

[tex]\left\lfloor 2\log_2(9) - 1 \right\rfloor = \boxed{5}[/tex]

There are total 100 candidates that sat for the exam.

A set is a group of items (referred to as members or elements) that are taken to be one object. Writing x A denotes that an item x is a member of the set A, whereas writing x A denotes that x is not a member of A.

Using the formula of sets,

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C),

n(A) = 60                                             n(B∩C) = 16

n(B) = 50                                              n(C∩A) = 22

n(C) = 48                                              n(A∩B∩C) = 10

n(A∩B) = 30

The total students sat for the class are -

n(A∪B∪C) = 60 + 50 + 48 - 30 - 16 - 22 + 10

n(A∪B∪C) = 100

So, In total 100 candidates appeared for the exam.

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The inequality will be given by 0 < x + 5 < 12 or -5 < x < 7 which meant value of number x will lie between -5 and 7.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that the sum of a number and 5 is between 0 and 12. This can be represented by an inequality.

Let's assume the number is x.

So , the sum of number x and 5 will be :

= x + 5

Also , given that,  this value is between 0 and 12 .

This meant the inequality will be given by :

0 < x + 5 < 12

Let's subtract 5 from every term of inequality.

0 - 5 < x + 5 - 5 < 12 - 5

or

-5 < x < 7

The value of x lies between -5 and 7.

Therefore , the inequality will be given by 0 < x + 5 < 12 or -5 < x < 7 which meant value of number x will lie between -5 and 7.

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Answer:

see below

Step-by-step explanation:

The figure 0.12 represents in this context the D. the fraction of the books in the library that are how-to books on electronics.

From the information, three-tenths of the books in the school library are how-to books and 0.2 deal with carpentry and 0.4 deal with electronics.

Therefore, the figure 0.12 represents in this context the fraction of the books in the library that are how-to books on electronics.

This was calculated as:

= 0.4 × 0.3

= 0.12

Therefore, the correct option is D.

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The set A’ using the roster method is A' = {5, 6, 8}

The sets are given as

Universal set, U = {5, 6, 7, 8, 9, 10, 11}

Set A, A = {7, 9, 10, 11}

The elements of the set A’ are the elements that are in the universal set but not in set A

Using the above as a guide, we have the following values

A' = {5, 6, 8}

The above is in roster method or form

Hence, the set A’ using the roster method is A' = {5, 6, 8}

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Answer:

She has completed [tex]\frac{8}{17}[/tex] laps.

She has [tex]\frac{9}{17}[/tex] laps remaining

Hope that helps

Answer:

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

Step-by-step explanation:

The value of the function is f(−1)=6.

A function is defined as a relation between a set of inputs having one output each.

In this problem, we are given a function f(x) = x+7 and we are asked to evaluate f(-1)

Recall that f(x) = y.

When we evaluate functions, we substitute the given x-value to find the corresponding y-value of the functionWhen evaluating functions using function notation the number in place of the "x" in "f(x)" is the number that you plug into the x of your function.

So, if f(x)=x+7 then

f(−1)=(−1)+7

Therefore, f(−1)=6

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Answer:

D) 3 - (-5) = 8

Step-by-step explanation:

A. [tex]-3 + 5 \to 5 - 3 \to 2[/tex]

B. [tex]-3 - (-5) \to -3 + 5 \to 5 - 3 \to 2[/tex]

C. [tex]3 - 5 \to -2[/tex]

D. [tex]3 - (-5) \to 3 + 5 \to 8[/tex]

Answer:

-25

Step-by-step explanation:

3(x+7)+4=2x

3x+25=2x

x= -25

[tex] \bf\implies x = - 2 \\ [/tex]

[tex]25 = 5x + 35 \\ 25 - 35 = 5x \\ - 10 = 5x \\ - \frac{ \cancel{10}}{ \cancel5} = x \\ - 2 = x \\ \implies \boxed{ x = - 2} \: ans.[/tex]

Answer:

35.45

Step-by-step explanation:

Answer:

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Answer:

Step-by-step explanation:

DCCCXXIV

The correct answer is 1x+7y=-15.

Finding an equation in standard form for a line with the points (-8, -1) and (-1, -2) is what we're after.

Since a, b, and c are integer coefficients in standard form, a and b CANNOT equal 0 or be negative.

It is helpful to first put the line in a different form, such as slope-intercept form, which is represented by the equation y=mx+b, where m is the slope and b is the y intercept.

Let's start by calculating the slope using the equation, which can be done from two points.

(y_2-y_1)/(x_2-x_1)

x1 = -8

y1 = -1

x2 = -1

y2 = -2

Substituting the value = (-2-(-1 ))/((-1-(-8))

= -2+1/-1+8

= -1/7

Thus the slope is -1/7

y=mx+b

y=(-1/7)x+b

-1=(-1/7)(-8)+b

-1=8/7+b

-1-8/7=b

-7-8/7=b

-15/7 = b

substituting the value in equation,

y = (-1/7)x-15/7

7y=-1x-15

Thus the equation is,

1x+7y=-15

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