2. Write an expression for the perimeter of a rectangle with a length of
(3x² + x + 2) and a width of (-x² – 5x + 1).

Answer:

x < 4

Step-by-step explanation:

3x - 3 < 9

3x - 3 + 3 < 9 + 3

3x < 12

\(\frac{3x}{3} <\frac{12}{3}\)

x < 4

Answer:

the answer is x is less than 4

Step-by-step explanation:

3x-3<9

3x-3+3<9+3

-3deleted by +3

so we get 3x<12. over 3 over 3 and we got

x<4

Answer:

-1/10

Step-by-step explanation:

after (.) we put zero in the denominator according to how many numbers are after .

-0.1= -1/10

hope this will help you

plz mark me as braniliest

To find the point P on the line y=3x that is closest to the point (50,0), we need to use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where A, B, and C are the coefficients of the equation of the line in the form Ax + By + C = 0.

In this case, the equation of the line y=3x can be written as -3x + y = 0. So we have:

A = -3, B = 1, C = 0

Now we can plug in the values of (50,0) and solve for x and y to find the point P that is closest to it:

distance = |-3x + y| / sqrt((-3)^2 + 1^2)
distance = |-3x| / sqrt(10)

To minimize the distance, we need to minimize |-3x|. This occurs when x = 0. So the point P that is closest to (50,0) is the point (0,0).
To find the point P on the line y = 3x that is closest to the point (50, 0), we need to minimize the distance between P and (50, 0).

Let P(x, y) be a point on the line y = 3x. The distance between P and (50, 0) is given by the distance formula:

D = sqrt((x - 50)^2 + (y - 0)^2)

Since y = 3x, we can rewrite the distance formula as:

D = sqrt((x - 50)^2 + (3x)^2)

To minimize the distance, we can minimize the square of the distance (D^2), as it avoids dealing with the square root:

D^2 = (x - 50)^2 + (3x)^2

Now, we can find the derivative of D^2 with respect to x and set it to 0 to find the critical points:

d(D^2)/dx = 2(x - 50) + 2(3x)^2 * 6x = 0

Solve this equation to find the x-coordinate of the point P. Then, use y = 3x to find the corresponding y-coordinate. Finally, you'll have the coordinates of the point P that is closest to (50, 0).

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The time Billy should get up to be right on time for school is 6:52 am.

The formula to calculate the time Billy should get up to be right on time for school is as follows: Time Billy Should Get Up = School Start Time - (Time to Get Dressed + Time to Eat Breakfast + Time to Walk to School). In this case, the formula is: Time Billy Should Get Up = 8:35 am - (32 minutes + 13 minutes + 17 minutes). In order to solve this equation, first we must convert the minutes to hours. 32 minutes is equal to 0.53 hours and 13 minutes is equal to 0.22 hours. 17 minutes is equal to 0.28 hours. Thus, the formula is: Time Billy Should Get Up = 8:35 am - (0.53 hours + 0.22 hours + 0.28 hours). Now, we can solve for the time Billy should get up. 8:35 am minus 0.53 hours is 7:42 am. Then, 7:42 am minus 0.22 hours is 7:20 am. Finally, 7:20 am minus 0.28 hours is 6:52 am. Therefore, the time Billy should get up to be right on time for school is 6:52 am.

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Answer:

0

Step-by-step explanation:

Here, given the function f(x), we want to calculate f(1)

Mathematically, this means we shall substitute 1 for the value of x in that function.

Thus, given F(x) = 1-x

Then F(1) would be = 1-1 = 0

Total length of wire = 8.33 + 6.67 + 5.33 + ...20 terms= 100[2 - 0.8^20] / [1.2]≈ 80.99 feet Since the total length of wire required is less than the available wire, Sonja will have enough wire.

Given, Sonja cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. We need to find the explicit formula for the nth piece.We can see that Sonja is cutting wire in decreasing order of 20%.So, the explicit formula for the nth piece can be given by an = a1 * r^(n-1)where a1 = 100 and r = 0.8 Thus, the explicit formula for the nth piece can be given byan = 100 * (0.8)^(n-1)Now, we need to find if Sonja has enough wire for the mobile as she only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern.We know that 1 inch = 0.0833 feet 100 inches = 100 * 0.0833 feet = 8.33 feet80 inches = 80 * 0.0833 feet = 6.67 feet64 inches = 64 * 0.0833 feet = 5.33 feet Now, we can find the total length of wire Sonja needs to cut 20 pieces. Therefore, she can complete the mobile using the given pattern.

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Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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Answer:

53.88 or [54.0]

Step-by-step explanation:

Answer:

3.7

Step-by-step explanation:

The value of the probability P(z < -2.6) is 0.0046612

From the question, we have the following parameters that can be used in our computation:

To calculate the probability P(z < -2.6), we make use of a graphing calculator

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

P(z < -2.6) = 0.0046612

Hence, the value is 0.0046612

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Answer:

(a) 2x + x + 39 = 90

(b) m<1 = 34°; m<2 = 56°

Step-by-step explanation:

Use the angle addition postulate. Angles 1 and 2 add to a right angle. A right angle has a measure of 90°.

(a) m<1 + m<2 = 90

2x + x + 39 = 90

(b)

Solve the equation for x.

2x + x + 39 = 90

3x = 51

x = 17

Use the value of x to find the angle measures.

m<1 = 2x = 2(17) = 34

m<2 = x + 39 = 17 + 39 = 56

Answer:

a.) 3x+39=90

b.) ∠1=34°

    ∠2=56°

Step-by-step explanation:

According to the graph, ∠1 + ∠2=90°.

∠1=2x and ∠2=x+39

So,

\(2x+(x+39)=90\\2x+x+39=90\\3x+39=90\\3x=51\\x=17\)

Rewrite the equations for the two angles substituting 17 for x.

∠1=[2(17)]°=34° and ∠2=[(17)+39]°=56°

Answer:uhhhh im not sure i would help if i knew TvT

Step-by-step explanation:

Answer:

(-2,8) (0,4) (2,3) (4,2)

Step-by-step explanation:

Answer:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Step-by-step explanation:

Given:

92÷5

Hailey's workings:

92 divided by 5.

5 goes into 9 1 time.

9 minus 5 = 4.

5 goes into 42 8 times.

42 minus 40 = 2.

The answer is 18 R 2.

The true statements about Hailey's work are:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

8 teams will remain in the 4th round of the tournament.

It is given that there are total of 64 teams in the tournament. Each team plays only 1 game per round. The winning team advances to the next round and the losing team gets eliminated and since a game is played between 2 teams, This means for the first round, total number matches are 32 and only 32 teams goes to Round 2.

⇒64 ÷2 = 32

Similarly , for Round 2 there are only 16 matches between 32 teams. If we keep repeating the same process for  Round 3 and Round 4 , we get :

⇒32 ÷ 2 = 16

⇒16 ÷ 2  = 8

Therefore, only 8 teams will remain for the 4th Round of the tournament.

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Sum of coordinates, S + T = (9 , -7)

A coordinate is an address, which helps to locate a point in space. For a two-dimensional space, the coordinates of a point are (x, y). Here let us take note of these two important terms.

Abscissa: It is the x value in the point (x, y), and is the distance of this point along the x-axis, from the origin

Ordinate:  It is the y value in the point (x, y)., and is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.

Given,

S = (4 , -6)

T = (5 , -1)

S + T = (4 , -6) + (5 , -1)

        = (4 + 5 , -6 + -1)

        = (9 , -7)

Hence, S + T = (9 , -7) is sum of coordinates of point S and T

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Answer:

\(\frac{88\pi}{35}\) m/s

Step-by-step explanation:

The circumference is \(8.8(2)(\pi)=17.6\pi\) meters.

So, the speed is \(\frac{17.6\pi}{7}=\frac{88\pi}{35}\) m/s.

Answer:

97 inches

Step-by-step explanation:

We know that sum of all angles of a triangle is 180°,

So,

\( \sf2x + 1 + 5x + 5 + 90 = 180 \\ \sf7x + 96 = 180 \\ \sf7x = 180 - 96 \\ \sf7x = 82 \\ \tt \: x = 12\)

Now,

\( \tt∠1 = 2x + 1 \\ \tt = 2(12) + 1 \\ \tt = 24 + 1 \\ \tt= 25 \degree\)

&

\( \tt∠ 2 = 5x + 5 \\ \tt = 5(12) + 5 \\ \tt = 60 + 5 \\ \tt = 65 \degree\)

The required measure of the angles ∠A and ∠C is 25° and 65° respectively.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Consider the given triangle ABC,

Since we know that the sum of the interior angle of a triangle is equal to 180°.

∠A + ∠B + ∠C = 180,
2x + 1 + 90 + 5x + 5 = 180

7x + 6 = 90
7x = 84
x = 12

Now,
∠A = 2(12) + 1 = 25°
∠C = 5(12) + 5 = 65°

Thus, the required measure of the ∠A and ∠C is 25° and 65° respectively.

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Yoink:

hey imma yoink your points  and not answer the question ok?

Jk:

jk, number 1 is b

number 2 is a

number 3 is d

and number 4 is c

The relationship between the corresponding sides of similar triangles indicates that the height of the tree is 60 feet. The correct option is therefore;

Similar triangles are triangles in which the ratio of the corresponding sides of the triangles are equivalent for the three sides of the triangle.

The location of the tree divides the hypotenuse side and the base of the triangle formed by the building into two parts of the same length, therefore;

The length of the hypotenuse side to the building = 2 × 108 ft = 216 ft

The length of the base to the building = 2 × 90 ft = 180 ft

The ratio of corresponding sides of similar triangles and the trigonometric ratio of sines, indicates that we get;

Height of the tree/108 = 120/216

Height of the tree = 108 × (120/216) = 60 feet

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Answer:

C. c = -4

Step-by-step explanation:

you must get c by itself. you have to divide both sides by 10. this gets rid of the 10c and keeps both sides equal

-40/10 = c

c = -4

The derivative of the function y = ln(7 + x²) is found as dy/dx = 2x/(7 + x²).

To find the derivative of the function

y=ln(7+x²),

we use the chain rule of differentiation which states that if we have a composite function f(g(x)) .

we can find its derivative by differentiating the outer function f and then multiplying by the derivative of the inner function g.

In this case, the outer function is ln(x) and the inner function is (7+x²).

Thus:

dy/dx = 1/(7 + x²) × d(7 + x²)/dx

      = 1/(7 + x²) × 2x

          = 2x/(7 + x²)

Hence, the derivative of the function y = ln(7 + x²) is given as dy/dx = 2x/(7 + x²).

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The probability is 7/72 that each of the final three rolls is at least as large as the roll preceding it.

Let \(N_{i}\) represent the number appearing on die when die is rolled ith time,

i=1,2,3,4

Given that \(N_{1}\)≤\(N_{2}\)≤\(N_{3}\)≤\(N_{4}\)

Each time when a die is rolled, six options are there.

Let we have four equal sets

{1,2,3,4,5,6}, now we have to select four numbers such that, exactly one number is selected from each set

Case 1: All four are same

Number of ways:⁶C₁ =6

Case 2: Three are same but one is different

Number of ways: ⁶C₁ ⁵C₁ =30

Case 3: Two are same of one kind and two are same of second kind

Number of ways: \(\frac{1}{2}\) ⁶C₁ ⁵C₁=15

Case 4: Two are same and two are different

Number of ways: ⁶C₁ ⁵C₂=60

Case 5: All four are different

Number of ways: ⁶C₄=15

Required probability:

=\(\frac{6+30+5+60+15}{6*6*6*6}\)

=\(\frac{126}{36*36}\)

=\(\frac{72}{7}\)

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Answer:

Step-by-step explanation:

Given that the circumference  of the frame is 56in

we can proceed to obtain the radius of the frame

we know that

circumference= 2πr

56= 2*3.142*r

56= 6.284r

divide both sides by 6.284

r= 56/6.284

r=8.9

approximately radius is 9in

therefore the area of the mirror that is largest would be

Area=  πr^2

Area= 3.142*9^2

Area= 3.142*81

Area= 254.5 in^2

The largest area is 254.5 in^2

Answer:

I'm not completely sure but...I believe Samuel factored out a 2 when he should have factored out a 4.

Step-by-step explanation:

First:

You have to factor the equation...

12xyz^2+(162)(y2)z−32x^2yz

     =−32x^2yz+12xyz^2+256y^2z

          =4yz(−8x^2+3xz+64y)

Answer:

He factor 2 instead of 4

Step-by-step explanation:

4xyz (3z + 4xy - 8x)

Answer:its a extra 1.23 so 1658 would be your total

Step-by-step explanation:

Mr. Baker must pay $3.15 in sales tax, and the total amount he needs to pay for his purchases is $48.15. To calculate the amount of sales tax Mr. Baker needs to pay and the total amount he must pay for his purchases, we need to consider the prices of the goods and the sales tax rate.

Let's assume the prices of the goods Mr. Baker bought are as follows:

- Item 1: $10.00

- Item 2: $20.00

- Item 3: $15.00

To calculate the sales tax, we multiply the total purchase amount by the sales tax rate. The total purchase amount is the sum of the prices of all the items.

Total purchase amount = $10.00 + $20.00 + $15.00 = $45.00

Sales tax amount = Total purchase amount * Sales tax rate

               = $45.00 * 0.07

               = $3.15

Therefore, Mr. Baker must pay $3.15 in sales tax.

To calculate the total amount he must pay, we add the sales tax amount to the total purchase amount.

Total amount to pay = Total purchase amount + Sales tax amount

                  = $45.00 + $3.15

                  = $48.15

Therefore, Mr. Baker must pay a total of $48.15 for his purchases, including the sales tax.

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Answer:

43

Step-by-step explanation:

250-35(from Monday)=215

215/5=43

Hope this helps!