7. If the length of the side of a table is 3 more than twice its width, what is the expression
of its perimeter?
a. Draw an image and show all your work to demonstrate your thinking and
understanding of this problem.
b. If the perimeter is 30, what is the width of the table? Show your work

Answer:

x = 5, -6

Step-by-step explanation:

Step 1: Write out equation

x² + 2x - 25 = x + 5

Step 2: Move everything to one side

x² + x - 30 = 0

Step 3: Factor

(x - 5)(x + 6) = 0

Step 4: Find roots

x - 5 = 0

x = 5

x + 6 = 0

x = -6

Answer:

You shoulda showed us the diagram but corresponding angles are the 2 angles on the diagram which are the same, look closely and you could tell which 2 are the same, they also have to be on THE SAME SIDE, right or left

Hope that helps!

Step-by-step explanation:

Answer:

C, Angle 3 and Angle 7

Step-by-step explanation:

heres the full question

In the diagram, which pair of angles are corresponding angles?

Angle 1 and Angle 8

Angle 4 and Angle 6

Angle 3 and Angle 7

Angle 2 and Angle 4

Answer:

There are 9 llamas.

Step-by-step explanation:

For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.

As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.

If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.

If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.

We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.

9 ÷ 3 = 3.

This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6,  because she has twice the amount of lambs.

Billy has 2 lambs and 6 llamas.

Milly has 6 lambs and 3 llamas.

The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.

Answer:

Billy: Has 4 lots of animals

Milly: Has 3 lots of animals

17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total

Answer: Rita has $25 saved.

Step-by-step explanation:

You could think about it this way: $69 is $6 less than 3 times the amount of money that she has. So, let's solve this:

1) First you would add $6 to the $69 that the skateboard costs because you     need to know what her savings would be if she multiplied it by 3.

      $69+$6=$75  

2) Now that we know that if we tripled her savings, we would have $75. We can now find out how much she actually has saved up by dividing the total of $75 by 3.

      $75÷3=$25

I hope this helped you with your question!

Answer:

she saved $25

Step-by-step explanation:

Answer:

The height of the tree is about 30 feet.

Step-by-step explanation:

tan(55) = h/21

*21          *21

21*tan(55)=h

29.99=h

h=29.99=30 feet

The height of the tree will be 30 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Given; A tree casts a shadow 21 m long.

The angle of elevation of the sun is 55°.

Let h be the height of tree.

Then the height of the tree will be;

tan(55) = h/21

21*tan(55)=h

29.99=h

h = 29.99 = 30 feet

Therefore, The height of the tree will be 30 feet.

More about the right-angle triangle link is given below;

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Answer:

×=19

Step-by-step explanation:

90-22=68

3x+11=68

68-11=57

3x=57

57÷3=19

x=19

Answer:

median: 90

mode: 91

mean: 84.2 or round it to 84

Step-by-step explanation:

Let me know if this helps! have a great day! :)

Answer:

a) Median = 91

b) mode = 91

c)Mean 84.2

Step-by-step explanation:

a) Median is the middle term. So, 6th term

Median = 91

b) Mode is the score which occurs more number of times

91 occurs 3 times

Mode = 91

c) Mean= sum of all data's/Number of data's

            = 85 + 91 + 48 +98 + 99 /5

            = 421/5

  Mean = 84.2

Answer:

336 cm3

Step-by-step explanation:

Using Cavalieri’s principle, this volume is the same as for a right rectangular prism with these dimensions. Apply the formula for volume of a rectangular prism:

V = lwh

V = (6)(4)(14)

V = 336 cm3

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Circles.

thus the, Equation of circle with centres as (h, k) is given as,

(y-k)^2 + (x-h) ^2 = r^2

where, r is the radius if the circle.

so here, we can see that,

[tex] {r}^{2} = 100 \\ r = 10 \\ [/tex]

thus , we can say that, 2r = d

thus diameter = 20 units

Answer:

x >5

Step-by-step explanation:

-4(3-X) > 8

Divide by -4, remembering to flip the inequality

-4/-4(3-X) < 8/-4

3-x < -2

Subtract 3 from each side

3-x-3 < -2-3

-x <-5

Divide by -1, remembering to flip the inequality

x >5

Answer:

[tex]c.[/tex] [tex]5<x[/tex]

Step-by-step explanation:

[tex]-4(3-x)>8\\3-x>-2\\-x>-5\\x>5[/tex]

Answer:

[tex]\frac{13}{3}[/tex] ÷ [tex](-\frac{5}{6})[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}/(-\frac{5}{6})=\\\\\frac{13}{3}/(-\frac{5}{6})[/tex]

Answer:

13/3  ÷ - 5/6

Step-by-step explanation:

4 1/3 ÷ - 5/6

Change the mixed number to an improper fraction

4 1/3 = (3*4 +1)/3 = 13/3

13/3  ÷ - 5/6

Answer:

1. The train is will cross the tunnel in 2 minutes.

The train is traveling at 30 km every hour or 60 minutes, so it will move 1 km every 60/30 minutes, or every 2 minutes.

2. Explanation here first: 22 free throws means 22 points and 22 field goals.

184-22=162 points they still needed to get, and

85-22=63 goals they still needed to score

We can now use a system of equations, (where x is 3-point goals, and y is 2-point goals) to solve the problem:

3x+2y=162

x+y=63 (-2)

-------------------------------------------------------------

3x+2y=162

-2x-2y= -126

-------------------------------------------------------------

x=36, and y=27 so the NBA players got 36 3-point goals, and 27 2-point goals

We can check this:

(36*3) + (27*2) + 22 = 108+54+22 = 184 total points

Step-by-step explanation:

Hope this helps!

Answer:

Length = (x^2-6x-7)m²/ (x-7)m

Step-by-step explanation:

let L =length

let W= width

let A = area of the rectangle.

if A = L × W

making L the subject, divide both side by W

A/W= L×W/W

therefore, L =A/W

L= (x²-6x-7)m²/(x-7)m

Answer:

Option A.

Step-by-step explanation:

Note: The given function should be [tex]f(x)=\dfrac{2}{5}(10)^x[/tex] instead of [tex]f(x)=(10)^x[/tex].

Consider the given function is  

[tex]f(x)=\dfrac{2}{5}(10)^x[/tex]

We need to find the function which represents a reflection of f(x) across the x-axis.

If a function f(x) is reflected across the x-axis, then the new function is

[tex]g(x)=-f(x)[/tex]

Using this rule, we get

[tex]g(x)=-\dfrac{2}{5}(10)^x[/tex]        [tex][\because f(x)=\dfrac{2}{5}(10)^x][/tex]

Therefore, the correct option is A.

Answer:

See the explanation

Step-by-step explanation:

The function given to us is:

f(x) = (1/3)⁻ˣ

We can convert the negative power into positive one by interchanging the numerator and denominator.

f(x) = (3/1)ˣ

f(x) = 3ˣ

Substitute value for x= -3 , -2, -1, 0, 1, 2, 3

f(-3) = 3⁻³ = 0.037

f(-2) = 3⁻² = 0.111

f(-1) = 3⁻¹ = 0.333

f(0) = 3⁰ = 1

f(1) = 3¹ = 3

f(2) = 3² = 9

f(3) = 3³ = 27

f(4) = 3⁴ = 81

and so on

The table of the found values of f(x) or y for the corresponding values of x, along with their graph is given below.

Answer:

a = 6

Step-by-step explanation:

10a - 41 = 19

10a = 19 + 41

10a = 60

a = 60/10

a = 6

Answer:

a=  6

Step-by-step explanation:

10a - 41=19

+41         +41

10a = 60

÷10    ÷10

a=  6

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Answer:

H = 0.95 feet

Step-by-step explanation:

The circumference of Earth = 2πR

My belt = 2πR    (Where R is the radius of the Earth)

Peter's belt = 2πR+6

We have to find the Height "h" so the radius of the circle for Peter's belt becomes R+h So the expression becomes 2π(R+h)

But we already know,

Peter's belt = 2πR+6

So,

2πR+6 = 2π(R+H)

2πR + 6 = 2πR + 2πH

Subtracting 2πR to both sides

=> 6 = 2πH

OR

=> H = 6/2π

=> H = 3/π

Where π = 3.14

=> H = 0.95 feet

Answer: 0.00016 miles

Step-by-step explanation:

According to Google, the circumference of the Earth is 24,901.461 miles. Using the formula 2*pi*r = circumference, the radius of your belt is around 3963.19061 miles. Now, 6 feet is 0.001 miles. So his belt is 24,901.461+0.001 = 24,901.462 miles. Use 2*pi*r to get 3963.19077 miles, a full 0.00016 miles above the surface!

Answer:

The answer would be A. because AB/EF=BC/DE

Step-by-step explanation:

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF=BC/DE is correct. All of the others are not.

The slope of line segment AC the same as the slope of line segment DF in the figure below because AB/EF = BC/DE.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We need to find the proportionality statement for the ratio of the sides of the triangles.

If two triangles are similar, then the corresponding sides are proportional.

ABC ≈ DEF,

Here AB, BC, and AC are corresponding sides of DE, EF, and DF respectively.

Using the definition of similarity we ge

AB = 2

EF = 5

BC = 1

DE = 2.5

2/5 = 0.4

1/2.5 = 0.4

The equation AB/EF = BC/DE is correct. All of the others are not.

Learn more about a triangle;

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Answer:

The probability that the combined sample tests positive  for the virus is 0.083

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability that the combined sample will test positive is 0.083

Step-by-step explanation:

Given that:

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

Therefore; the probability that the combined sample tests positive  for the virus is 0.083

Is it unlikely for such a combined  sample to test positive?

P(combined  sample test positive  for the virus ) = 0.0834

Since the probability that combined sample test positive for the virus is greater than 0.05, it is not likely for such a combined  sample to test positive.

The probability of a randomly selected adult in one country being infected with a certain virus is 0.003.

P = 0.003

number of blood sample size n = 29

The probability mass function of X is as follows;

[tex]P(X=x) = \left[\begin{array}{c}{29}&x\\\end{array}\right] (0.003)^x (1-0.003)^{29-x}[/tex]

Thus; the required probability is;

[tex]P(X \geq 1) = 1 - P ( X < 1)[/tex]

[tex]P(X \geq 1) = 1 - P ( X =0)[/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} \dfrac{29!}{0!(29-0)!} \ \ \times 0.003)^0 \times (1-0.003)^{29-0}}\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - \left[\begin{array}{c} 1 \times 1 \times ( 0.9166)\end{array}\right][/tex]

[tex]P(X \geq 1) = 1 - 0.9166[/tex]

[tex]P(X \geq 1) = 0.0834[/tex]

The probability that the combined sample will test positive is 0.083

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer:

6 sq units, 4 sq units, 6 sq units

Step-by-step explanation:

Method:

count dots inside ...(a)

the ones on the border of the polygon and divide by two ...(b)

(a)+(b)-1 = area

use this method for the red, green, and yellow polygons.

Red:

(a): 2

(b): 10/2 = 5

2+5-1 = 6 sq units

Green:

(a): 0

(b): 10/2 = 5

0+5-1 = 4 sq units

Yellow:

(a): 3

(b): 8/2 = 4

3+4-1 = 6 sq units

I hope this helps, and plz mark me brainliest!!!!

Answer:

The number is 5250

Step-by-step explanation:

5/6 * x = 4375

Multiply each side by 6/5 to isolate x

6/5 * 5/6 x = 4375 * 6/5

x =5250

Answer:

5250

Step-by-step explanation:

5/6x= 4375

x= 4375*6/5

x= 5250

Answer: B

Step-by-step explanation:

Makes the most sense out of all the options because it’s the most random or unpredictable

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y = -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

Answer:

12 rational

Step-by-step explanation:

2√3×√12 =

= 2√3×√2²·3

= 2√3×2√3

= 2×2×√3×√3

= 4×3

= 12

Answer:

y = x + 16

Step-by-step explanation:

Step 1: Find slope of perpendicular line

Take the negative reciprocal of the 1st line

m = 1

Step 2: Find b

y = x + b

14 = -2 + b

b = 16

Step 3: Write equation

y = x + 16

Answer:

y = x + 16

Step-by-step explanation:

Given the equation y = -x - 1, we see that the slope (the coefficient of the x term) is -1.  A line perpendicular to this one has a slope which is the negative reciprocal of the given equation:   +1.

Using the point-slope formula for the equation of a straight line, we get:

y - 14 = +1(x + 2), or y - 14 = x + 2, or y = x + 16

Answer:

A: There is only one solution since the two lines meet up. If it was parallel or the two lines where on top of each other there would be either an infinite amount of solutions or zero.

B:(3,5)

Step-by-step explanation:

Answer:

The answer is option c.

There are no x-intercepts

Hope this helps