(x² + 8x + 1) ÷ (x −4)

Answer:

For part a you would decompose the fraction into two independent fractions with the following form:

() = ()/( x^2+5)(x ^2+3x−4)  = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)

Combining these fractions we get:

((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)

Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()

You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().

You would follow a similar process for part b as well.

Step-by-step explanation:

The three domains are the Archaea, the Bacteria, and the Eukary.

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==========================================

Explanation:

If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.

Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.

Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.

The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one  blue point.

The Probability of an odd number = 0.5.

What is Probability?

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using probability, we can calculate everything from the possibility of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two occurrences coming together, are essential to understand in order to properly appreciate this field of mathematics.

In the given question, we have:

The odd numbers on the given spin are 1,3,5,7 and 9;

So, The number of odd numbers is 6;

That is, n(odd) = 6;

and,

Total number of Spin = 12;

So, The probability of an odd number = [tex]\frac{odd number}{total number}[/tex]

The probability of an odd number = [tex]\frac{6}{12}[/tex]

Hence, The Probability of an odd number = 0.5.

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a)4

so it's seven factorial divided by 7-5 factorial

The value of function is positive so the function have maximum value at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value at x=3.

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Solution of the equation 3x-2y = 5 for domain {-3} is (-3,-7).

Given,

Eq => 3x - 2y = 5

Domain = x = -3

Put x = -3 in equation

3(-3) - 2y = 5

   -9 - 2y = 5

     -9 - 5 = 2y

         -14 = 2y

            y = - 14 / 2

               = -7

Hence, solution is (-3,-7).

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The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.

Given,

Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)

The normal distribution's standard deviation, s = 3000 pounds

95% confidence interval

N = 20 observations were made.

Mean = 30,800

Margin of error :

z₇ × √3000².20

±1.314.8079

Confidence interval

= Mean + Margin of error

= 30,800 ±1.314.8079

= 29,485.192 , 32,114.8

The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).

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Check the picture below.

so the rocket will hit the ground when y = 0, so hmmm, there's no simple factoring that'd give us integers, so we'll plug the quadratic into the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+240}x\stackrel{\stackrel{c}{\downarrow }}{+115} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (240) \pm \sqrt { (240)^2 -4(-16)(115)}}{2(-16)} \implies x = \cfrac{ -240 \pm \sqrt { 57600 +7360}}{ -32 }[/tex]

[tex]x= \cfrac{ -240 \pm \sqrt { 64960 }}{ -32 }\implies x=\cfrac{ -240 \pm 8\sqrt { 1015 }}{ -32 }\implies x=\cfrac{ 240 \mp 8\sqrt { 1015 }}{ 32 } \\\\\\ x=\cfrac{ 30 \mp \sqrt { 1015 }}{ 4 }\implies x\approx \begin{cases} -0.46\\\\ 15.46 ~~ \textit{\large \checkmark} \end{cases}[/tex]

now, let's notice, "x" cannot be negative, so the negative value is tossed.

Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Given,

In the question:

Why are the tops of mountains round and the soil often rough, rocky, and thin in many places in the Northeast?

Now, According to the question:

The correct answer is:

Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

Other question is

4 + 2

By addition:

4 + 2 = 6

Hence, Glaciers scoured the landscape, grinding the high places and mixing the soil with rocks.

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Answer:

Step-by-step explanation:

Answer:

Note: A percentage is always a number over 100.      (34% = [tex]\frac{34}{100}[/tex])

Cost of meal = 100%

Cost of tip = 34%

Total = 134%

134% = [tex]\frac{134}{100}[/tex]

To find the total and the tip, you must multiply it by [tex]\frac{134}{100}[/tex]

Answer:

Bill times the 0.34 percent equals the price of the tip. After you find what the tip is, you add the base price (the bill price) to the tip and you get the total number paid. However, another way you can solve (in one step) this is by adding 1.00 to the percent you are multiplying by which in this case we add 0.34 by 1.00 and this gives us 1.34. Suppose we set the bill to 4 dollars and use the normal way (2-step equation) by doing 3(0.34) which is 1.02 and 1.02 + 3 = 4.02 as our final answer / final bill. However, when we do our one-step equation, we can write this as 3x(1.34) and this is equal to 4.02.

1st Step

Bill(0.34) = tip

tip + bill = total

2nd Step (one-step equation)

Note: we are going to set the bill in this equation as $4

4(1.34) = total; Total = 4.02 ← We added 1.00 to the tip percentage in decimal form.

The total number of cupcakes ordered, using proportions, is of:

5.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.

These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.

In this problem, the amounts are given as follows:

The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:

3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.

The problem is:

I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?

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The equation of the line in slope intercept form is y = (-4/3)x   .

In the question ,

a line graph is given ,

we need to find the equation of that line .

the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,

the equation of the line passing from the points (x₁ , y₁) with slope m  in the slope intercept form is given by

(y - y₁) = m(x - x₁) .

we first need to find the slope .

So , m = (0 - 4)/(0 + 3)

m = -4/3

The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is

(y - 4) = (-4/3)(x -(-3))

y - 4 = (-4/3)(x + 3)

y - 4 = (-4/3)x - 4

y = (-4/3)x - 4 + 4

y = (-4/3)x

Therefore , The equation of the line in slope intercept form is  y = (-4/3)x  .

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Eplaination of algebraic rules with equation of line is describe below

Algebraic rules are maths expression of two variable that can be written in the form of equation.

Now we will understand by the equation of line given in the question,

we have Y = mx + c

where y is the intercept on y-axis, m is the slope of line, x is intercept on x-axis, and c is the point where line cuts y-axis.

This equation represent the line which follows algebraic rules.

Graph of equation:

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Compatible numbers are close in value to the real numbers, which simplifies problem-solving and estimation of the solution. 1,7,10/32 has a quotient (integer division) of 53 and a remainder ("leftover") of 14. The dividend is 1,7,10, while the divisor is 32.

Compatible numbers are those that divide equally into each other and are near to the numbers they are replacing. The outcome of a division is the quotient. 55,304 is not too far away from 56,000. 800 splits equally into 56,000 and is reasonably near to 875.

Our minds can occasionally spin when we are asked to find the total (in addition), difference (in subtraction), product (in multiplication), or quotient (in division). By rounding each number to the closest ten, twenty, fifty, or hundred, we employ suitable numbers to make the problem simpler to figure out mentally.

Numbers that are simple to mentally add, subtract, multiply, or divide are said to be compatible. To estimate a calculation, substitute compatible numbers for the actual numbers. Since it is simple to mentally calculate the sum of 800, the numbers 500 and 300 can be added together.

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Answer:

x-4<12 x<-4

-3x<12

-3x/-3=x

12/-3=-4

x-4+4=x

8+4=12

Answer: -1/3

Step-by-step explanation:

The formula for slope =y1-y2/x1-x2. You first subtract the numbers for the y coordinate which is -6-(-5), and thats -1. Then you subtract the x coordinates. -6-(-9)=3. So the slope is -1/3

The total interest that Magdalena's parents would have to pay to repay the loan is  $864.50

The interest that Magdalena's parents will pay per year is:

= Value of loan x Simple interest rate per year

= 2, 600 x 7%

= $182

To find the total interest paid, this amount should then be multiplied by the number of years it would take Magdalena's parents to repay the loan. 4 years and 9 months in years is:

= 4 + 9/12 months in a year

= 4 + 3 / 4

= 4 + 0.75

= 4.75 years

The total interest is:

= 4.75 x 182

= $864.50

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Step-by-step explanation:

if the solution has "nice" numbers, we can split the expression into 2 factors in the form

(x + a)(x + b) = x² + (a+b)x + ab

as this is equal to x² + 4x - 21.

ab = -21

so, one is positive and one is negative.

and 4 = a + b

we know the typical factors of 21 : 3×7

and then we see easily : 7-3 = 4

so,

we have

(x + 7)(x - 3) >= 0

this has 2 x-intercepts (x-values when y = 0) :

x = -7

x = 3

because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.

that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.

so, the solution are the intervals

x <= -7 and x >= 3

in these areas is the expression x² + 4x - 21 >= 0.

Answer: x= 9

Step-by-step explanation:

I just checked that its right!

Answer:

The correct answer would be 9

Step-by-step explanation:

The congruency can be proved using SAS rule.

What are congruent triangles?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles is slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of harmoniousness is’ ≅’.

Main Body:

In ΔPQR and ΔRST

PR = RT           ---(1)

as both the sides are congruent , the third sides of triangles is also equal.

QR = RS          ----(2)

∠PRQ = ∠SRT   ----(3)

Hence by side- angle -side

ΔPQR and ΔRST are congruent.

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The rate at which length of shadow of person changing is 3 ft /sec.

H = Height of streetlight; 16 ft

h = Height of man; 6 ft

x = Length of man's shadow.

s = Distance from streetlight to man.

Using the similarities of the triangles.

H/h = (s + x)/x

Hx = h(s + x)

Differentiate with respect to 't' on both sides.

H(dx/dt) = h(ds/dt + dx/dt)

Put the values.

16(dx/dt) = 6(5 + dx/dt)

16(dx/dt) = 30 + 5dx/dt

10dx/dt = 30

dx/dt = 3 ft /sec

Thus, the rate at which length of shadow of person changing is 3 ft /sec.

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To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.

What is balanced hanger?

Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.

adding a circle to the left and a square to the right. To both sides, add two triangles.

Hence the option 1, 2, and 5 are correct.

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We can actually deduce here that the statement, "base of an isosceles triangle can be right angles" is false.

An isosceles triangle is actually known to be a triangle which has two sides equal and opposite angles of the sides also equal. In other words, an isosceles triangle must have at least two equal triangles.

Some of the properties of an isosceles triangle are:

We see here that the base of an isosceles triangle cannot be a right angles. It is still to have one side as a right angle but not the two sides as right angles.

The complete question is:

True or false: Base angles of an isosceles triangle can be right angles.

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The maximum area is 640,000.

Given fencing yards = 3200

let the length be x and the width be y

The parameter of the rectangle is given as;

2(L + B),that is

2(x + y) = 3200

x + y = 1600

y = 1600-x

let the area of the rectangle be A, then

A = x y

A = x(1600-x)

A = 1600x - x^2

finding the maximum derivative of A with respect of x

da/dx = 1600 - 2x

set da/dx to zero,

1600 - 2x = 0

1600 = 2x

x = 1600/2

x =800

substitute the value of x = 800 in to y

y = 1600 - 800

y = 800

The maximum area is 800 x 800

Therefore Maximum area = 640,000.

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The midrange of the data set shown is 85 is true about the box-and-whisker plot below. The middle is the number in question. The least and greatest values should be added together, divided by two, or, in other words, the mean of the least and biggest values should be determined.

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Answer:

The answer is 80