The graph shows the functions f(x), p(x), and g(x):

Part A: What is the solution to the pair of equations represented by g(x) and p(x)? (3 points)

Part B: Write any two solutions for p(x). (3 points)

Part C: What is the solution to the equation g(x) = f(x)? Justify your answer. (4 points)

Answer:

Step-by-step explanation:

[tex](3m^2+2mn-n^2)+(m^2+4mn-n^2)\\\\=3m^2+2mn-n^2+m^2+4mn-n^2\qquad\text{combine like terms}\\\\=(3m^2+m^2)+(2mn+4mn)+(-n^2-n^2)\\\\=\boxed{4m^2+6mn-2n^2}[/tex]

Based on the available information, the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

To simplify the expression (3m² + 2mn - n²) + (m² + 4mn - n²), we can combine like terms.

Like terms have the same variables and the same exponents.

Let's group the like terms together:

(3m² + m²) + (2mn + 4mn) + (-n²- n²)

Combining like terms within each group, we get:

4m² + 6mn - 2n²

Therefore, in this case, it is concluded that the expression (3m² + 2mn - n²) + (m² + 4mn - n²) is equivalent to 4m² + 6mn - 2n².

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Answer:

615

Step-by-step explanation:u make $20 a week and u worked 40 hours u jus do 40*20=$800

800-185=615 im pretty sure hope this helps

Answer:

Weekly net pay is $36790

Weekly gross pay is  $41600

Step-by-step explanation:

Net pay  is the gross pay minus taxes

Net pay = gross pay - taxes

Gross pay =  hours worked * hourly rate

Net pay = hours worked * hourly rate - taxes

We know the  

hours worked = 40

Hourly rate = 20

tax rate = 185 bi weekly  = 185/2 = 92.5 weekly

Net pay = 40 * 20 - 92.5

Net pay = 800-92.5

Net pay = 707.5

This is the weekly net pay

Assuming we work 52 weeks a year

Weekly net pay is 52* 707.5 = 36790

Weekly gross pay is  40*20 * 52 = 41600

Answer:

The answer is B. Step 2; 8x − 16 = 16 + 2x

Hope This Helps!

Answer:

31.020

Step-by-step explanation:

Multiply the fraction by 4/4 to get the denominator to 1000. Simplify to a denominator of 100 if you like. Then use place value to write your number.

... 31 + 5/250 = 31 + 20/1000 . . . . thirty-one and twenty thousandths

... = 31 + 0.020 =  31.020 . . . or . . . 31.02

12 in

If the dilation is uniform, both height and width will be multiplied by 4.

New height = (1 in) × 4 = 4 in

New width = (3 in) × 4 = 12 in

Answer:

The solution for u is:

[tex]u = \frac{mpq}{q+p}[/tex]

Step-by-step explanation:

The first step to solve this problem is finding the least common multiplicator between p and q, that is pq, so:

[tex]\frac{u}{p} + \frac{u}{q} = m[/tex]

[tex]\frac{uq + up}{pq} = m[/tex]

[tex]uq + up = mpq[/tex]

[tex]u(q + p) = mpq[/tex]

[tex]u = \frac{mpq}{q+p}[/tex]

The required solution of the given equation for u is equal to

(m(p × q)) / (q + p).

Given that:

Equation: u/p + u/q = m, if p ≠ -q

To solve for u in the equation u/p + u/q = m, use the method of finding a common denominator and simplifying the expression.

First, need to find a common denominator for the fractions u/p and u/q. The common denominator in this case would be (p × q).

Multiplying the equation by (p × q) to get,

u(q) + u(p) = m(p × q)

Next, combine the terms with u as:

u × q + u × p = m(p × q)

Now, factor out u as:

u(q + p) = m(p × q)

To solve for u, divide both sides of the equation by (q + p):

u = (m(p × q)) / (q + p)

Therefore, the solution for u is u = (m(p × q)) / (q + p).

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f(x) = 11.93·1.42^x

I entered the data into a graphing calculator and made use of its exponential regression function to find the coefficients of ...

... y = a·b^x

It told me ...

... a ≈ 11.9304, b ≈ 1.41885

In accordance with the problem statement, these values are rounded to hundredths to get the answer.

_____

Comment on the graph

The given points and two curves are show. The solid red curve is the exponential regression curve produced by the calculator. The dotted blue curve is the one you get when you round the numbers to the nearest hundredth.

Answer:

36

Step-by-step explanation:

The length of 1 1/2 units is equivalent to 3/2 = 6/4 = 6×(1/4) = 6 cubes.

The width of 1/2 units is equivalent to 2/4 = 2×(1/4) = 2 cubes.

The height of 3/4 units is equivalent to 3×(1/4) = 3 cubes.

Then, in terms of cubes, the dimensions are 6 × 2 × 3. The volume is the product of these dimensions, so is ...

... 6 × 2 × 3 = 36 . . . . cubes

Answer:

Step-by-step explanation:

Answer:

3/√2

Step-by-step explanation:

find the details in the attachment (this is not the shortest way).

The shortest way is: to prove ED=AB, then to calculate x=AB/√2=3/√2.

Answer:

Step-by-step explanation:

a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero

b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...

... p(x) = (x -1)(x² -2x +0) -1

_____

Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.

Answer:

21

Step-by-step explanation:

Simplify 5^2 to 25

25-2^2

Simplify 2^2 to 4

25-4

Answer

21

The value of the expression will be 21.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 5²- 2²

Simplify the expression, then the value of the expression will be given as,

⇒ 5²- 2²

⇒ 25 - 4

⇒ 21

The value of the expression will be 21.

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Answer: The total cost will be $156.85.

Step-by-step explanation:

Since we have given that

Time taken by labor to assemble the each skateboard is given by

[tex]1\frac{6}{7}\ hours\\\\=\frac{13}{7}\ hours[/tex]

Time taken by labor to finish and stain each skateboard is given by

[tex]2\frac{1}{2}\ hours\\\\=\frac{5}{2}\ hours[/tex]

Cost of labour to the company per hour = $36.00

According to question,

We will use "Distributive Property":

[tex]a\times (b+c)=a\times b+a\times c[/tex]

[tex]36(\frac{13}{7}+\frac{5}{2})\\\\=36\times \frac{13}{7}+36\times \frac{5}{2}\\\\=\frac{468}{7}+18\times 5\\\\=\frac{468}{7}+90\\\\=\frac{468+630}{7}\\\\=\frac{1098}{7}\\\\=\$156.85[/tex]

Hence, the total cost will be $156.85.

Answer:

x ≈ 0, x ≈ 2.5

Step-by-step explanation:

The left point of intersection is very near the y-axis, where x=0.

The right point of intersection is somewhat below the midpoint between x=2 and x=4. It seems to be just about at the midpoint between that midpoint (x=3) and the line at x=2. We estimate the value at about x=2.5.

_____

If we knew the actual function definitions, we could solve for the points of intersection.

Answer:

0.471

Step-by-step explanation:

The mnemoic SOH CAH TOA reminds you that ...

... Sin = Opposite/Hypotenuse

... sin(S) = 32/68 ≈ 0.471

Answer:

12% chance of 22

35% chance of 21, 22, or 23

55% chance of 20, 21, 22, 23, or 24

How can 22 be a good prediction when it's wrong 88% of the time?

I'd say from 20 to 24 is a good prediction without being trivial.

Step-by-step explanation:

C(n,k) = n Choose k = n! / (k! (n-k)!)

aka binomial coefficient

aka from n things choose k

To get probability of getting heads 22 times in 44 tries, you divide number of ways to get heads 22 times by number of ways to assign heads or tails to each throw.

Two ways to assign H or T to first, times two ways for second throw,

gives 2^44. That's the denominator.

Number of ways to get heads 22 times is the same as number of ways to choose which 22 flips of 44 are to be heads, or C(44,22)

To get 12% calculate C(44,22)/2^44

To get 55% calculate C(44,20)/2^44 + ... + C(44,24)/2^44

Final answer:

The best prediction for the number of times a coin will land on heads after 44 flips is 22 times, as each flip has a 50-50 chance of resulting in heads.

Explanation:

When you flip a coin 44 times, the best prediction for the number of times it will land on heads is that it will land on heads about 22 times. This is because each flip is independent, and the probability of landing on heads is 50%, or a 50-50 chance.

When a coin is tossed multiple times, despite the possibility of getting streaks of either outcome, as the number of flips increases, the overall distribution of heads and tails tends to even out and approach a 50% split due to the law of large numbers. For example, if you tossed a coin 100 times, the number of heads and tails would be close to 50 each, although not exactly due to the randomness of each flip.

Answer:

Step-by-step explanation:

The simple answer is that logs cannot be negative and if you insert a 2 where the x is located you get a negative. Logs have to be >= 0

[text]log_5 (3x-10) = log_5 (-4)[tex]

It all has to do with logs being tied to exponents and exponents being tied to logs. Actually an inverse of an exponent is a log.

f(x) = -(x -2)² +3

We can fill in the vertex (h, k) values immediately in the vertex form ...

... f(x) = a(x -h)² +k

To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:

... -1 = a(0 -2)² +3

... -4 = 4a . . . . . . . . . subtract 3, simplify

... -1 = a . . . . . . . . . . . divide by 4

Now, we know the function is ...

... f(x) = -(x -2)² +3

Answer:

We are given:

[tex]SSx = 4[/tex]

[tex]SSy=25[/tex]

[tex]Sp=6[/tex]

We know that the Pearson's correlation coefficient is:

[tex]r=\frac{S_{p}}{\sqrt{SS_{x} \times SS_{y}} }[/tex]

     [tex]=\frac{6}{\sqrt{4 \times 25} }[/tex]

     [tex]=\frac{6}{\sqrt{100} }[/tex]

     [tex]=\frac{6}{10}[/tex]

Therefore, the option 6/10 is correct

Answer:

y =293(1.06) ^x

y = 370  after 4 years

Step-by-step explanation:

If we are using the model for growth

y = a ( 1+b)^x

a is the initial population

b is  the increase rate

We can substitute the values into the equation

y =293 (1+.06) ^ x

y =293(1.06) ^x

Let x equal 4 for the 4 years

y = 293(1.06)^4

y=369.9

400%

Suppose sales in 1994 were 100 of some unit. Then in 1995, they were ...

... 100 - 80% × 100 = 100 × (1 - 0.80) = 100 × 0.20 = 20 . . . . units

Then the percent increase to sales of 100 units in 1996 can be found from ...

... percent change = ((new value) - (old value))/(old value) × 100%

... = (100 -20)/20 × 100%

... = 80/20 × 100%

... = 400%

The increase from 1995 to 1996 was 400%.

We know that :

✿  [tex]\mathsf{Cos\theta = \frac{Adjacent\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Sin\theta = \frac{Opposite\;Side}{Hypotenuse}}[/tex]

✿  [tex]\mathsf{Tan\theta = \frac{Opposite\;Side}{Adjacent\;Side}}[/tex]

From the Figure :

✿  [tex]\mathsf{Cosx = \frac{4}{5}}[/tex]

✿  [tex]\mathsf{Sinx = \frac{3}{5}}[/tex]

✿  [tex]\mathsf{Tanx = \frac{3}{4}}[/tex]

Only 1st Statement is True

1st Option is the Answer

Answer:

Number of girls in PE class is 20

D.  20 girls

Step-by-step explanation:

We are given

Number of girls in 6th grade =120

Number of boys in 6th grade =102

so, firstly we will find ratios of girls and boys

[tex]\frac{G}{B}=\frac{120}{102}[/tex]

now, we have

17 boys are in the first PE class

Let's assume number girls in PE class as 'x'

we know that

ratios of boys and girls must be equal

so, we get

[tex]\frac{G}{B}=\frac{120}{102}=\frac{x}{17}[/tex]

now, we can solve for x

[tex]\frac{120}{102}=\frac{x}{17}[/tex]

[tex]x=17\times \frac{120}{102}[/tex]

[tex]x=20[/tex]

So,

Number of girls in PE class is 20

Answer:

Step-by-step explanation:

The question will look like (3b)/(a^-2)

To simplify, note the (a^-2). It is a negative, so flip the placement of the monomial. Note that the term is located in the decimal, so when it is flipped, it goes to the numerator (vice versa if it is opposite)

(3b)/(a^-2) = (3b)(a²)

3a²b, or (A) is your answer choice

~

Answer:

Option A) 3a2b

Step-by-step explanation:

Let x represent the number of adults who swam at the pool. Then (262-x) is the number of children. Multiplying these numbers by the corresponding admission charge will give the associated receipts. We are given the total of receipts, so we can write the equation ...

... 2.00x +1.50(262-x) = 470.00

... 0.50x +393.00 = 470.00 . . . . . simplify

... 0.50x = 77.00 . . . . . . . . . . . . . . .subtract 393

... 77.00/0.50 = x = 154 . . . . . . . . . divide by the coefficient of x

... (262-x) = 108 . . . . . . . . . . . . . . . .find the number of children admitted

Answer:

-3367 1/9

Step-by-step explanation:

This is what calculators are for.

Perform the multiplication and division before the addition.

... = 10000/-9 -2256

... = -1111 1/9 -2256

... = -3367 1/9

_____

If you don't have a calculator, the Google and Bing search boxes can be relied upon to use the correct order of operations.

Answer:

The difference is 18.7 degrees

Step-by-step explanation:

To find the difference in the temperature, we take the high temperature and subtract the low temperature.

Difference = high - low

                   = -3.6 - (-22.3)

                   = -3.6+22.3

                   = 18.7

The difference is 18.7 degrees

Answer:

Step-by-step explanation:

∠1 is complementary to 15°, so is 90° -15° = 75°

∠2 completes the triangle with angles 49° and 75°, so is 180° -49° -75° = 56°

∠3 is supplementary to ∠2, so is 180° -56° = 124°

∠4 is complementary to 49°, so is 90° -49° = 41°

34

KM is a transversal relative to parallel lines LM and KN. Thus ∠2 = ∠MKN ≅ ∠KML and ∠KML = ∠1. The two base angles of ΔKLM are equal, so that triangle is isosceles.

Then the ratios of all the sides are ...

... KL : LM : MN : KN = 8 : 8 : 8 : 9

The sum of these ratio units is 33, so each one stands for 132/33 = 4 perimeter length units. Then segment LM is 8×4 = 32 perimeter length units, and KN is 9×4 = 36 permeter length units.

The midsegment is the average of lengths LM and KN, so is ...

... (32 +36)/2 = 34 . . . . perimeter length units

The length of midsegment is 34 units.

Given data:

The trapezoid KLMN, Such that KL = MN.

And [tex]m\angle1 = m\angle2[/tex], LM/KN = 8/9

Also, perimeter of KLMN = 132 units.

To find:

The length of midsegment (KM).

In the given problem, we can observe that KM is a transversal relative to parallel lines LM and KN. Which means,

[tex]\angle MKN = \angle KML\\\angle 2=\angle 1\\[/tex]

Clearly, two base angles are equal. So, the triangles KLM and KMN are isosceles.

Taking the ratios of sides of two triangles as,

= KL : LM : MN : KN

= 8 : 8 : 8 : 9

The sum of ratio units is, 8 + 8 +8 +9 = 33. Then, the value of each ratio is,

[tex]= \dfrac{perimeter}{33} \\\\=\dfrac{132}{33} \\\\=4[/tex]

Then the length of segment LM is,

[tex]LM = 8 \times 4 = 32 \;\rm perimeter \;\rm length \;\rm units[/tex]

And, length of segment KN is,

[tex]KN = 9 \times 4 = 36 \;\rm perimeter \;\rm length \;\rm units[/tex]

Then, the length of midsegment KM is obtained by taking the average of LM and KN as,

[tex]KM = \dfrac{LM+KN}{2} \\\\KM = \dfrac{32+36}{2}\\KE = 34[/tex]

Thus, the length of midsegment is 34 units.

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the answer is

1.  x=28

2. p=7