Graph the line that represents this equation:
y = -5.1 +2

Answer:

the scores on her last test is x (x > 0)

because on her last tests she scored 4 points lower than she did on her fifth test

=> the scores in the 5th test is x + 4

because Angela’s average for six math tests is 87, we have:

[tex] \frac{93 + 87 + 82 + 86 + x + x + 4}{6} = 87 \\ \\ < = > \frac{352 + 2x}{6} = 87 \\ \\ < = > 352 + 2x = 522 \\ \\ < = > 2x = 170 \\ \\ < = > x = 85[/tex]

=> on her last test, she had 85

=> on her 5th test, she had 85 + 4 = 89

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Answer:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Step-by-step explanation:

A

Let's start with the first function:

[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 3, 7, 11, 15...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.

so let's put the two things together:

[tex](-1)^{n}x^{4n+3}[/tex]

Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

So now we can build the whole series:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

B

Now, let's continue with the next function:

[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 5, 9, 13, 17...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.

so let's put the two things together:

[tex](-1)^{n}x^{4n+5}[/tex]

Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

So now we can build the whole series:

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Answer:

I started by dividing 2940 by the smallest prime that would fit into it, being 2. This left me with another even number, 1470, so I divided by 2 again. The result, 735, is divisible by 5, but 3 divides in also, and it's smaller, so I divided by 3 to get 245. This is not divisible by 3 but is divisible by 5, so I divided by 5 and got 49, which is divisible by 7.

Answer:

0.2

Step-by-step explanation:

The total number of points in PS is a sum of the number of points in :

PQ + QR + RS ;

PQ = 7 ; QR = 13 ; RS = 5

PS = (7 + 13 + 5) = 25

Probability that point selected at random is in RS ;

Required outcome = point in RS

Total possible outcomes = points in PS

Probability = RS / PS = 5 / 25 = 0.2

Answer:

pixxer

Step-by-step explanation:

please pick inside please

Answer:

I dont now

Step-by-step explanation:

plz conprendation

Step-by-step explanation:

I suspect we don't see the full information for the problem here.

all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).

I guess there is a diagram with 2 triangles and what is known about them.

and since we cannot see them, we cannot tell you which method would apply here.

just remember

SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.

SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.

ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.

Answer:

y = x + 6

Step-by-step explanation:

rise = 1

run = 1

slope = rise/run = 1

y-intercept = 6

y = mx + b

y = x + 6

Answer:

Hypergeometric

Kindly check explanation

Step-by-step explanation:

For a hypergeometric distribution, the following conditions must be met :

1.) The total number of samples must be fixed.

2.) Sample size will be a portion of the population

3.) The probability of success changes per trial. This is because sampling is done without replacement

The above scenario meets the condition described:

Total number of samples = 210

Sample size, n = 10

Blue balls = 200 ; red balls = 10

P(10 red balls)

Using the hypergeometric distribution function and the calculator :

X ~ H(n, N, M)

X ~ (10, 200, 210) = 0.6072

Answer:

domain:-16,-8,0,12

range:0,-11,12,14

Answer:

Total earning last month with x articles is:

This is same amount as 2000

The equation is:

Answer:

The numbers are 65, 67, and 69

Step-by-step explanation:

Hi there!

We need to find 3 consecutive odd integers.

Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)

We're given that 5 times the first number + 4 times the second + 3 times the third = 800

Let's make the first number x

Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)

Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)

5 times the first number is 5x

4 times the second is 4(x+2)

3 times the third is 3(x+4)

And of course, that equals 800

As an equation, it'll be:

5x+4(x+2)+3(x+4)=800

open the parenthesis

5x+4x+8+3x+12=800

combine like terms

12x+20=800

Subtract 20 from both sides

12x=780

Divide by 12 on both sides

x=65

The first number is x, so the first number is 65

The second number is x+2, or 65+2=67

The third number is x+4, or 65+4=69

Hope this helps!

Answer:

8.75 or 8 3/4

Step-by-step explanation:

To do this question, many do it differently. But for now, we will convert the fractions into decimals.

1/4 = 0.25

11/2= 5.5

0.25 + 3 + 5.5

3.25 + 5.5 =

8.75

The answer is 8.75 or 8 3/4

Answer:

Decimal form :

8.75

Step-by-step explanation:

Hope it is helpful....

Answer:

Step-by-step explanation:

012345678910

'yl\f[pt;]p;d[k;ell-=;q'[;

Answer:

see explanation

Step-by-step explanation:

Assuming you mean

secθ × [tex]\sqrt{1-cos^20}[/tex]

= [tex]\frac{1}{cos0}[/tex] × sinθ [ sin²θ + cos²θ = 1 , so sinθ = [tex]\sqrt{1-cos^20}[/tex] ]

= [tex]\frac{sin0}{cos0}[/tex]

= tanθ

= right side , thus verified

Answer:

y - 2 = 2/3 (x-1)

y - 4 = 2/3(x-4)

Step-by-step explanation:

With this graph,the equation can be found on a straight line as the graph is .

So the formula is

[tex]y - y1 = m(x - x1)[/tex]

where your m is your gradient or slope as already said,the equation can be used by this formula (note;after finding your normal slope (not on a straight line ) firstly)

When you are done take any of the points connecting to the x axis and y axis directly as in (4,-4) or (2,1)

Let your first number be x1 and second y1 and place it in the formula .

where m is still your normal slope.

Answer:

Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3

Step-by-step explanation:

First, we can graph these inequalities out. As you can see in the picture, the three vertices where the inequalities all connect form a triangle. We can check each of these vertices to find our minimum and maximum.

First, we have (3,7). 4y-3x = 4(7)-3(3)=28-9=19

Next, for (3, -3), we have 4y-3x = 4(-3)-3(3) = -12-9=-21

Finally, for (0.5, 2), we have 4y-3x=4(2)-3(0.5)=8-1.5 = 6.5

Our maximum is 19 when x=3 and y=7 and our minimum is -21 when x=3 and y = -3

Answer:

19.14

Step-by-step explanation:

You have a half circle and a square, look at them separate then add for the area.

Circle

Your radius is half the diameter, so 4/2

Radius  = 2

[tex]A = 3.14 * radius\\A = 3.14 * 2\\A = 6.28[/tex]

This is for the entire circle, half of that would be 3.14

Square

[tex]A = 4^{2} \\A = 16[/tex]

Add them both together for a total area of 19.14 square miles

Answer:

The right solution is "0.5".

Step-by-step explanation:

According to the question,

P(pay with the sponsored credit card | order exceeds $110)

= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]

= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]

By putting the values, we get

= [tex]\frac{0.17}{0.34}[/tex]

= [tex]0.5[/tex]

Thus, the above is the right solution.

Answer:

6

Step-by-step explanation:

y = -7(-13)

=> y = -7 × (-13)

= y = 91

Answer:

[tex]x=-1\text{ or }x=11[/tex]

Step-by-step explanation:

For [tex]a=|b|[/tex], we have two cases:

[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]

Therefore, for [tex]18=|15-3x|[/tex], we have the following cases:

[tex]\begin{cases}18=15-3x,\\18=-(15-3x)\end{cases}[/tex]

Solving, we have:

[tex]\begin{cases}18=15-3x, -3x=3, x=\boxed{-1},\\18=-(15-3x), 18=-15+3x, 33=3x, x=\boxed{11}\end{cases}[/tex].

Therefore,

[tex]\implies \boxed{x=-1\text{ or }x=11}[/tex]

Answer:

c

Step-by-step explanation:

when we take the 5 inside the root the 5 vil be 5^2 times 2 which is equal to 50

9514 1404 393

Answer:

  44°

Step-by-step explanation:

The sum of the marked angles on the right is equal to the sum of the marked angles on the left:

  ? + 74 = 92 + 26

  ? = 92 +26 -74 = 44

The missing angle is 44°.

_____

Additional comment

The vertical angles in the center of the figure are v = 62°, the measure required to bring the total to 180° in each triangle. We have shortcut the equation(s) ...

  ? + 74 + v = 180 = 92 + 26 + v

by subtracting v from both sides, giving ...

  ? +74 = 92 +26

Division yields

[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]

Now for partial fractions: you're looking for constants a, b, and c such that

[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]

[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]

Now, in the integral we get

[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]

Answer: Is reinforced with other material

Step-by-step explanation:

The options are:

A is expensive to build.

B usually cracks under heavy weights.

C looks like any other road.

D is reinforced with other material.

The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.

Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.

Answer:

Step-by-step explanation:

On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.

That means all the points which lie in this area will satisfy both the inequalities.

From the graph attached,

Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.

Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.