Write an equation for the sentence "The product of a number n and 7.7 equals 112.42." Solve for the variable.

Answer:

49b^2 -36 = (7b -6)(7b +6)

so because there you missed some signs in these wrote choices  

hope helped  

Step-by-step explanation:

Answer:

[tex](b+1)^2(b+6)[/tex]

Step-by-step explanation:

The given rational expression is:

[tex]\frac{b}{b^2+2b+1}-\frac{6}{b^2+7b+6}[/tex]

We factor the denominators to get:

[tex]\frac{b}{(b+1)^2}-\frac{6}{(b+1)(b+6)}[/tex]

The least common denominator is the product of the highest powers of the common factors of the denominators.

Therefore the least common denominator is:

[tex](b+1)^2(b+6)[/tex]

Answer:

1/4(x+y)(x-y)

Step-by-step explanation:

We can first factor out the shared 1/4 and it now looks like,

1/4(x^2-y^2)

Since x^2-y^2 is a difference of squares, which is a^2-b^2 = (a+b)(a-b), we can change x^2-y^2 to (x+y)(x-y). So our answer is:

1/4(x+y)(x-y)

Answer:

144ft^2

Step-by-step explanation:

since it's a kite, there are two pairs of congruent (exactly the same shape) triangles

bc of this you can find one triangle from each pair and double it

e.g.

[tex] \frac{6 \times 8}{2}=24[/tex]

[tex] \frac{12 \times 8}{2}= 48[/tex]

so you would do 2(24+48)=144

Answer:

-2

Step-by-step explanation:

The team skipped 8 times, causing them to lose 8 points. They also guessed correctly 6 times, causing them to gain 6 points. 6 points won - 8 points lost = -2 points total.

Answer: y= -6

Step-by-step explanation:

because you know the slope is 0, you simply plug in from there

y=mx+b

y=0x (no slope) -6 (where it intersects the y axis)

y= -6

The answer is:   " y = - 6 " .

_________________________________________________

Step-by-step explanation:

_________________________________________________

To start, We find the equation of the given line ;  (in "blue" ; within the "image attached");

in the slope-intercept form:  

  " y = mx + b " ;

in which:

   "m = the slope = 0 " ; since there is no "slope";

   "b" = the "y-intercept" ;  or more precise, the value of the "y-coordinate" of the [point of the "y-intercept" — that is; the point at which the graph crosses the "y-axis" .].

    Note:  From the graph shown (Refer to image attached);  the "y-intercept" is:  " (0, 4) " ;  

    As such:  " b = 4 " .

_____________________________

So,  the equation;  in "slope intercept format" ; that is:  " y = mx + b " for the original line;  is:   "y = 0x + 4 " .

Let us simplify this equation:

    " y = 0x + 4 " ;    Note:  " 0x = 0 " ;

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

_____________________________

We are are left with " y = 4 " ;  

_____________________________

Now, we are asked to find the equation of the line that is "parallel" to this line and that passes through the point:  " (-4, 6) ".

If such a line is "parallel" to the original line, the slope would be the same, which is "0" .

So, " y = 0x + b" ;

_____________________________

Also, note the formula:

 y - y₁  = m(x - x₁) ;

in which we consider the point:  " (- 4, - 6) " ;

 in which:  " y₁ = -6 " ;  and:  " x₁ = -4 " ;

→  y - (-6) = m (x - (-4)) ;

→  y + 6  = m (x + 4) ;

Note:  " m = 0" ;

  So;  " m(x + 4) " =  (0)* (x + 4) = "0" ;  

      {since:  "0" ; multiplied by "any value" ;  results in:  "0" .}.

→  We have:

    y + 6 = 0 ;  

→ Let us subtract "6" from each side of the equation;

          to isolate "y" on one side of the equation;

          & to write the equation for the 'perpendicular line' ; as follows:

→   y + 6 - 6 = 0 - 6 ;

to get:  

→   y  =  - 6  ;

____________________________________________

The answer is:   " y = - 6 " .

____________________________________________

Hope this helps!

    Wishing you the best in your academic endeavors

             — and within the "Brainly" community!

____________________________________________

Answer:

d+e =6       d=5 and e=1

d-e=4

Step-by-step explanation:

5+1=6

5-1=4

simple math you have to think hard to get it right might look easy but it is not

Answer:

the solution is (1, 5)

Step-by-step explanation:

If d - e = 4, then d = e + 4.  Substitute e + 4 for d in the first equation:

d + e = 6 →  e + 4 + e = 6.  Then 2e = 2, and e = 1.

Subbing 1 for e in the second equation, we get d + e = 6, or d + 1 = 6.

Thus, d = 5, and the solution is (1, 5)

Answer:

I think D would be the answer.

Step-by-step explanation:

The most people would see it on the website, making it, if you ask me, the most likely answer.

The sampling method "He asks three random households from each street in his neighborhood" option (a) is correct.

It is defined as the group of data having the same entity which is related to some problems. The sample is a subset of the population, it is a part of the population.

We have a sampling method:

From the provided statement, the best sampling method would be he asks three random households from each street in his neighborhood.

Thus, the sampling method "He asks three random households from each street in his neighborhood" option (a) is correct.

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ANSWER

9cm

EXPLANATION

The volume of a square pyramid is calculated using the formula;

[tex]V = \frac{1}{3} {l}^{2}h[/tex]

where h=12cm is the height of the pyramid and l is the length of each side of the square base.

The volume is V=324.

We substitute the values in to the formula and solve for l.

[tex]324 = \frac{1}{3} {l}^{2} \times 12[/tex]

[tex]324 = 1 {l}^{2} [/tex]

[tex] {l}^{2} = \frac{324}{4} [/tex]

[tex] {l}^{2} = 81[/tex]

[tex]l = \sqrt{81} = 9[/tex]

The length of each side of the square base is 9 cm.

Answer:

2x < 600 or x < 300

Step-by-step explanation:

x = Johnny's current amount of records.

ANSWER

B. 4

EXPLANATION

The numbers on the first die are;

{1,2,3,4,5,6}

The numbers on the second die are;

{1,2,3,4,5,6}

The events of getting a sum of 5 are

2+3

3+2

1+4

4+1

There are four events.

The correct choice is B .

Answer:

5-7=-2

Step-by-step explanation:

positive integers: 5 and 7

Subtraction 5-7 is equal to a negative answer: -2

If two positive integers are 5 and 3. Then the subtraction of the positive integers will be negative 2.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The subtraction problem that involves two positive integers and has a negative value

Let x and y be the two integers.  ​And y is greater than x.

Then we have

Then the difference between x and y should be negative

Then subtract y from x.

x - y = negative value

Let y be 5 and x be 3. Then we have

x - y = 3 - 5

x - y = -2

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For this case we have the following system of two equations with two unknowns:

[tex]-2x + y + 6 = 0\\2x + y-8 = 0[/tex]

Adding both equations we have to eliminate the variable "x":

[tex]y + y + 6-8 = 0[/tex]

Adding common terms, keeping in mind that different signs are subtracted and the sign of the major is placed:

[tex]2y-2 = 0\\2y = 2[/tex]

Answer:

[tex]2y = 2[/tex]

Option A

Answer:

Total surface area = 154 in²

Step-by-step explanation:

The prism has a total of 6 surfaces:  top and bottom, 2 sides, and 2 ends.

We have to find the area of each top, side, end, and then add these together, and then multiply the result by 2 to finish the job.

Area of top:  (5 in)(3.5 in) = 17.5 in²

Area of side:  (5 in)(7 in) = 35 in²

Area of end:  (3.5 in)(7 in) = 24.5 in²

Now add these three results together and multiply the sum by 2:

2( 17.5 in² + 35 in² + 24.5 in²) = total surface area = 154 in²

To answer the other part of this question:  find the volume of this prism:

V = length · width · ht = (5 in)(3.5 in)(7 in) = 122 in³.  

Yes, this box can definitely hold 22 in³ of packing peanuts.

Eli's box has a surface area of 154 square inches, and this is the total area he will need to paint. The box has a volume of 122.5 cubic inches, thus it is large enough to hold 22 cubic inches of packing peanuts.

To calculate the total area Eli will paint on his wooden box, we need to find the surface area of the rectangular prism. The box has a length (L) of 5 inches, width (W) of 3.5 inches, and height (H) of 7 inches. The surface area (SA) of a rectangular prism is given by the formula:

SA = 2(LW + LH + WH)

Plugging in the dimensions, we get:

SA = 2(5 × 3.5 + 5 × 7 + 3.5 × 7) = 2(17.5 + 35 + 24.5) = 2(77) = 154 square inches

So, the total area Eli will paint is 154 square inches.

The volume of the box is calculated using:

Volume = L × W × H

Volume = 5 × 3.5 × 7 = 122.5 cubic inches

Since 122.5 cubic inches is greater than 22 cubic inches, the box can indeed hold 22 cubic inches of packing peanuts.

ANSWER

12 ft

EXPLANATION

The volume of a cylinder is calculated using the formula

[tex]V=\pi {r}^{2} h[/tex]

From the question, the volume was given as 540π ft³ .

The height is given as 15 ft.

We substitute the values to obtain:

[tex]540\pi=\pi {r}^{2} \times 15[/tex]

This implies that;

[tex] {r}^{2} = \frac{540\pi}{15\pi} [/tex]

We simplify to get;

[tex] {r}^{2}=36[/tex]

Take positive square root to obtain:

[tex]r = \sqrt{36} [/tex]

[tex]r = 6ft[/tex]

The diameter is twice the radius.

Hence the diameter is 12ft

The answer is:

The diameter of the cylinder is equal to 12 feet.

Why?

To find the diameter of the cylinder we need to use the formula to calculate its volume.

So,  we have:

[tex]Volume=\pi *r^{2}*h[/tex]

We are given the following dimensions of the cylinder:

[tex]Volume=540\pift^{3}\\\\Height=15ft^{3}[/tex]

Now, using substituting and isolating the radius in order to find the diameter, we have:

[tex]Volume=\pi *r^{2}*h\\\\r^{2}=\frac{Volume}{\pi *h} \\\\r=\sqrt{\frac{Volume}{\pi *h} }[/tex]

Therefore, we have:

[tex]r=\sqrt{\frac{Volume}{\pi *h}}\\\\r=\sqrt{\frac{540\pi ft^{3}}{\pi *15ft}}\\\\r=\sqrt{36ft^{2} }=6ft[/tex]

We know the radius, then, calculating the diameter we have:

[tex]diameter=2*radius=2*6ft=12ft[/tex]

Hence, we have that the diameter of the cylinder is equal to 12 feet.

Have a nice day!

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are close to the average. A high standard deviation means that the numbers are more spread out.

It is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.

So, good standard deviation is 5 = Very Good, 4 = Good, 3 = Average, 2 = Poor, 1 = Very Poor, The mean score is 2.8 and the standard deviation is 0.54.

Hope this helps :)

For this case we have that the figure shown is composed of three triangles and a square. By definition, the area of a triangle is given by:

[tex]A = \frac {1} {2} b * h[/tex]

Where:

b: It's the base

h: It's the height

We have 3 triangles, then the sum of their areas will be:

[tex]A = \frac {1} {2} (9 * 3.5) + \frac {1} {2} (2 * 2) + \frac {1} {2} (5 * 2)\\A = 15.75 + 2 + 5\\A = 22.75 \ units ^ 2[/tex]

On the other hand, the area of a square is given by:

[tex]A = l ^ 2[/tex]

Where:

l: It's the side of the square

According to the figure we have:

[tex]A = 2 ^ 2\\A = 4 \ units ^ 2[/tex]

So, the total area is:

[tex]A_ {t} = 22.75 + 4\\A_ {t} = 26.75 \ units ^ 2[/tex]

Answer:

[tex]A_ {t} = 26.75 \ units ^ 2[/tex]

356,000 would be the answer I believe

Answers:

4668.

Step-by-step explanation:

355790

3 +1 5 +1 5 +1 7+1 00

466800

=4668

The scale is simply the ratio between the distances in the plan and the actual distances. So, first of all, let's convert all lengths to the same unit measure:

[tex]18\text{ ft} = 216\text{ in}[/tex]

So, the scale is

[tex]\dfrac{216}{6.4} = 33.75[/tex]

which means that one inch in the plan is the same as 33.75 inches in the real world.

Answer:

1 : 33.75

Step-by-step explanation:

6.4 inches ⇒ 18 feet

6.4 inches ⇒ 18 x 12 = 216 inches

scale used

= 6.4 : 216

= 1 : 216 ÷ 6.4

= 1 : 33.75

Answer:

If the function is [tex]y=\sqrt{x+6} -7[/tex] , the domain are all values of x  greater than or equal to -6

If the function is [tex]y=\sqrt{x+6-7}[/tex] , the domain are all values of x  greater than or equal to 1

Step-by-step explanation:

First case

we have

[tex]y=\sqrt{x+6} -7[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x+6 \geq 0[/tex]

[tex]x\geq-6[/tex]

the solution is the interval---------> [-6,∞)

therefore

The domain are all values of x  greater than or equal to -6

Second case

we have

[tex]y=\sqrt{x+6-7}[/tex]

so

[tex]y=\sqrt{x-1}[/tex]

we know that

The radicand  of the function must be greater than or equal to zero

so

[tex]x-1 \geq 0[/tex]

[tex]x\geq 1[/tex]

the solution is the interval---------> [1,∞)

therefore

The domain are all values of x  greater than or equal 1

Answer:

1)m=9ft and n=10ft

2) p=10cm and r=18cm

3) s=4mi and t=8mi

Step-by-step explanation:

1)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides m and n

m/sinD = 5/sinF

m= sin60(5/sin30)

  = 8.66

   = 9

n/sinE= 5/sin30

n= sin90(5/sin30)

  = 10

hence m=9ft and n=10ft

2)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides p and r

p/sinF = 21/sinE

p= sin30(21/sin90)

  = 10.5

   = 10

r/sinD= 21/sin90

r= sin60(21/sin90)

  = 18.18

  =18

hence p=10cm and r=18cm

3)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides s and t

s/sinF = 3√6/sinD

s= sin30(3√6/sin60)

  = 4.24

   = 4

t/sinE= 3√6/sinD

t= sin90(3√6/sin60)

  = 8.48

  = 8

hence s=4mi and t=8mi !

$275*.15(15%)=41.25 (this is the amount of the discount)

$275-$41.25=$233.75 (cost of jacket after discount)

$233.75* .0725=$16.946(round to $16.95, this is the amount of the sales tax).

If you want to know the total cost after tax just add $16.95 to the discounted price of $233.75. The price you pay for the jacket is $250.70.

Answer:

$16.95

Step-by-step explanation:

A department store is having a 15% off sale on all winter coats.

The cost of the winter coat that you purchased = $275

The price after discount of 15% = 275 -(15% × 275)

                                                    = 275 - (0.15 × 275)

                                                    = 275 - 41.25

                                                    = $233.75

Sales tax rate on that location = 7.25%

Sales tax which you would pay = 7.25% × 233.75

                                                    = 0.0725 × 233.75

                                                    = $16.9468 ≈ $16.95

You have to pay $16.95 sales tax.

The surface area of the smaller solid will be 144 m².

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The volumes of two similar solids are 1,331 m² and 216 m². The surface area of the larger solid is 484 m².

The sides length  will be

a³ = 1331

 a = 11 m

Then the surface area will be

SA = 4(11²)

SA = 484 m²

Then the surface area of the smaller solid will be

Let x be the surface area of the smaller solid. Then we have

b³ = 216

 b = 6 m

Then the surface area will be

x = 4 (6²)

x = 144 m²

Thus, the correct option is C.

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Answer:

x = -3 , y = -6

Step-by-step explanation:

Solve the following system:

{4 x - 3 y = 6 | (equation 1)

{x + 2 y = -15 | (equation 2)

Subtract 1/4 × (equation 1) from equation 2:

{4 x - 3 y = 6 | (equation 1)

{0 x+(11 y)/4 = (-33)/2 | (equation 2)

Multiply equation 2 by 4/11:

{4 x - 3 y = 6 | (equation 1)

{0 x+y = -6 | (equation 2)

Add 3 × (equation 2) to equation 1:

{4 x+0 y = -12 | (equation 1)

{0 x+y = -6 | (equation 2)

Divide equation 1 by 4:

{x+0 y = -3 | (equation 1)

{0 x+y = -6 | (equation 2)

Collect results:

Answer:  {x = -3 , y = -6

The probability that a student doesn't have lice, given that the student tested negative is 99.40%.

Correct option is (D).

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

As per the given diagram:

The probabilities of different events is given in the diagram.

Probability that a student doesn't have lice, given that the student tested negative P(B):

[tex]\frac{P(Test \: shows \: negative) \times P(Student \:has\: no\: lice)}{P(Test\: shows \:negative) \times P(Student\: has\: no\: lice) + P(Test\: shows\: positive) \times P(Student\: has\: no\: lice)}[/tex]

= [tex]\frac{0.94 \times 0.72}{0.94 \times 0.72 + 0.06 \times 0.72}[/tex]

= 0.994

Which is equal to 99.40%

Hence, the probability that a student doesn't have lice, given that the student tested negative is 99.40%.

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Answer:

My guess is

Mary:7

Ed:5

Step-by-step explanation:

Mary present age is 7 years while Ed present age is 5 years.

An equation is an expression that shows the relationship between two or more variables and number.

Let x represent Mary present age and y represent Ed present age, hence:

x = y + 2   (1)

And:

x - 3 = 2(y - 3)    (2)

x = 7, y = 5

Mary present age is 7 years while Ed present age is 5 years.

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Answer:

Hence final answer is [tex]x \leq -3[/tex] or [tex]2 \leq x<7[/tex]

correct choice is A because both ends are open circles.

Step-by-step explanation:

Given inequality is [tex]\frac{x^2+x-6}{x-7}\leq 0[/tex]

Setting both numerator and denominator =0 gives:

[tex]x^2+x-6=0[/tex],  x-7=0

or  [tex](x+3)(x-2)=0[/tex],  x-7=0

or x+3=0, x-2=0,  x-7=0

or x=-3, x=2,  x=7

Using these critical points, we can divide number line into four sets:

[tex](-\infty,-3)[/tex], (-3,2), (2,7), [tex](7,\infty)[/tex]

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for [tex](-\infty,-3)[/tex].

Clearly x=-4 belongs to [tex](-\infty,-3)[/tex] interval then plug x=-4 into [tex]\frac{x^2+x-6}{x-7}\leq 0[/tex]

[tex]\frac{(-4)^2+(-4)-6}{(-4)-7}\leq 0[/tex]

[tex]\frac{6}{-11}\leq 0[/tex]

Which is TRUE.

Hence [tex](-\infty,-3)[/tex] belongs to the answer.

Similarly testing other intervals, we get that only [tex](-\infty,-3)[/tex] and [tex](2,7)[/tex] satisfies the original inequality.

Hence final answer is [tex]x \leq -3[/tex] or [tex]2 \leq x<7[/tex]

correct choice is A because both ends are open circles.

Answer and explanation:

a) the equation would be:

          w=55m

*w= words

*m=minutes

b) w=55(20)

   w=1,100

There are 1,100 typed in 20 minutes.

hope this helps :)

The variable expression representing the number of words an office assistant types in 'm' minutes can be depicted as '55m'. When evaluated for 20 minutes, the assistant types 1100 words.

The subject of the question is Mathematics, which covers the aspect of forming expressions and evaluating them. This is a practical application of Algebra.

Here, the office assistant types 55 words per minute. We can represent the number of words typed in 'm' minutes as a variable expression, using multiplication. The expression is '55m', implying the assistant types '55m' words in 'm' minutes.

To evaluate the expression for 20 minutes, substitute 'm' with '20'. So, 55*20 = 1100. Therefore, the assistant types 1100 words in 20 minutes.

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ANSWER

y=x+5

EXPLANATION

We can observe the following pattern among the x and y-values.

9=4+5

12=7+5

18=13+5

22=17+5

24=19+5

Hence, in general, the function rule is

y=x +5

Answer: Third option.

Step-by-step explanation:

You need to substitute a value of "x" (input value) provided in the table into each function and observe in the value of "y" obtained (output value) matches with the coorresponding output value shown in the table.

For [tex]x=4[/tex]

First option:

[tex]y = 5x\\y = 5(4)\\y=20[/tex]

Second option:

 [tex]y = x + 3\\y = 4 + 3\\y=7[/tex]

Third option:

 [tex]y = x + 5\\y = 4 + 5\\y=9[/tex]

(This one matches with the function table)

Fourth option:

 [tex]y = 3x\\y = (3)(4)\\y=12[/tex]

Then the answer is: [tex]y = x + 5[/tex]

Answer:

The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation:

In the real world, length and width only make sense when they are positive. For that to be the case, the width must be greater than 2. There is nothing in the description that restricts the values to integers.

Answer:

C) the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2

Step-by-step explanation: