Mathematics College

There are a total of 26 students in Tom's class. There are 4 more boys than girls.

Which system of equations represents this situation? Let g be the number of girls, and let b be the number of boys.

A
g+b=26

g=4+b

B
g+b=26

b=4+g

C
g+b=26

g=4b

D
g+b=26

b=4g

Answers

Answer 1
The answer is B
4 more boys than girls so:
b = g + 4
And the total number of student is 26 so:
g + b = 26

Related Questions

the city is planning to build a new park by enlarging the current park by a scale factor of 4. The current park has an area of 37,625 yd squared. what is the area of the new park

Answers

The new area would be 602,000 yd².

When you enlarge a shape (or a park) by a factor, you are multiplying the length of its sides by that factor.  In this case, we are multiplying its length and width by 4.

Let l be the old length and w be the new length.  The old area would be given by A=lw.

Enlarging this by a factor of 4 would make the new length 4l and the new width 4w.  The new area would be 4l(4w)=16lw.  The new area is 16 times larger than the old area, so:

37,625(16)=602,000.

Solve this derivative using the quotient rule

Answers

[tex]\bf y=\cfrac{(-x+5)^5}{3x-4}\implies y=\cfrac{(5-x)^5}{3x-4} \\\\\\ \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{5(5-x)^4(-1)(3x-4)~~-~~(5-x)^5(3)}{(3x-4)^2}} \\\\\\ \cfrac{dy}{dx}=\cfrac{-5(5-x)^4(3x-4)-3(5-x)^5}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\stackrel{common~factor}{-(5-x)^4}[5(3x-4)+3(5-x)]}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[15x-20+15-3x]}{(3x-4)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{-(5-x)^4~~[12x-5]}{(3x-4)^2}\implies \cfrac{dy}{dx}=\cfrac{(5-x)^4~~[5+12x]}{(3x-4)^2}[/tex]

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.

A; an = 2 • 3n - 1
B; an = 2 • (-3)n - 1
C; an = 2 • 3n
D; an = 2 • (-3)n + 1

Answers

5th term / 2nd term  = r^4 / r  = r^3

r^3 =  162/-6 = -27

so r = -3

a1 * r-3 = -6  so  first term = 2

an = 2. (-3)^(n-1)  Answer 

Its B

The answer is B, I have just confirmed it.

Find the value of x so that line m is parallel to line n.
A. 57
B. 51
C. 50
D. 49

Answers

I think you have to set 3x + 11 equal to 161 because they are alternate interior angles, hence they are congruent.

3x + 11 = 161
3x = 150
x = 50

Answer:

,C) x =50

Step-by-step explanation:

Given : Parallel line m and n in figure.

To find : Find the value of x

Solution : We  have given

Two parallel line with traversal line

Alternate interior angle property :  The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles are equal.

3x + 11  and angle 161 are alternate angle .

3x + 11 =161.

On subtracting both sides by 11

3x = 161 -11

3x = 150

On dividng both sides by 3

x =50

Therefore,C) x =50

which collection of three side lengths will not form a triangle



6, 10 18
10, 12 ,15
10, 15, 6
10, 18 ,12 please tell me how you figured it out.

Answers

To construct a triangle, the sum of any 2 sides of the triangle should be greater than the third side of the triangle.
lets calculate the sums of all the given choices to find out which three lengths given do not form a triangle.

A.
 6,10,18
6 + 10 = 16 
16 is smaller than the third side-18
Therefore these 3 lengths do not form a triangle

B.10,12,15
10 + 12 = 22                  15+12 = 27                         15 + 10 = 25
22>15 (3rd side)            27>10 (3rd side)                    25>12 (3rd side)
In this triangle, sum of all the possible pairs of sides are greater than the third side therefore these lengths can form a triangle 

C.10,15,6
10 + 15 = 25                      15 + 6 = 21                              10+6 = 16
25 >  6                                 21>10                                      16>15
in this too, sum of all the possible pairs of sides are greater than the third side. These lengths can be used to form a triangle

D.10,18 ,12
10 + 18 = 28                      18 + 12 = 30                             10 +12 = 22
28> 12                                    30>10                                      22> 18
Therefore these lengths can also be used to form a triangle

correct answer is 6,10 and 18 these cannot form a triangle
Final answer:

To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem to each collection of side lengths given, we can determine which ones will form a triangle.

Explanation:

A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For the collection 6, 10, 18, the sum of the two smaller sides (6 + 10) is less than the largest side (18), so this collection will not form a triangle.For the collection 10, 12, 15, the sum of the two smaller sides (10 + 12) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 15, 6, the sum of the two smaller sides (6 + 10) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 18, 12, the sum of the two smaller sides (10 + 12) is greater than the largest side (18), so this collection will form a triangle.

what does x=? I know it is vertical

Answers

the angles are supplementary

7x + x + 20 = 180
8x = 160
x = 20
Hello there!

We know a vertical line = 180 degrees


x + 20 + 7x = 180

we can simplify this

20 + 8x = 180

To solve this, we can work backwards.

180 - 20 = 160

8x = 160

160/8 = 20

x = 20 degrees


Hope I helped!

Let me know if you need anything else!

~ Zoe 

A sandwich shop has 30 stores and 60% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California amd bow many are in Nevada?

Answers

60% of 30 = 0.6 x 30 = 18

There are 18 stores in California.

30 - 18 = 12

Theee are 12 stores in Nevada.

Answer:

18

Step-by-step explanation:

Which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5

Answers

m<1 +m<2 = 180° is the answer

Answer:

Third option is the right choice.

Step by step explanation:

We have been given an diagram and we are asked to choose the true statement about the diagram.

Let us see our all choices one by one.

1. [tex]m\angle5+m\angle6=m\angle1[/tex]

We can see that [tex]\angle5[/tex] and [tex]\angle6[/tex] are supplementary and there measure should be equal to 180 degrees. [tex]\angle1[/tex] is exterior angle of our triangle and its measure must be equal to sum of measures of [tex]\angle5[/tex] and [tex]\angle3[/tex].

Therefore, 1st option is incorrect.  

2. [tex]m\angle3+m\angle4+m\angle5=180^{o}[/tex]

We can see that [tex]\angle3[/tex] and [tex]\angle4[/tex] are supplementary and they must be equal to 180 degrees.  Therefore, 2nd option is also incorrect.

3. [tex]m\angle1+m\angle2=180^{o}[/tex]

We can see from our diagram that [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary. Therefore, 3rd option is the correct choice.

4. [tex]m\angle2+m\angle3=m\angle5[/tex]

We can see that [tex]\angle2[/tex], [tex]\angle3[/tex] and [tex]\angle5[/tex] are interior angles of our triangle and their measure should be equal to 180 degrees. By exterior angle theorem sum of measures of [tex]\angle2[/tex] and [tex]\angle3[/tex] will be equal to measure of [tex]\angle6[/tex] instead of [tex]\angle5[/tex].

Therefore, our 4th option is also incorrect.

Ms. Romero is buying a scrapbook and sheets of designer paper. She has $30 and needs at least $15.75 to buy the scrapbook. Each sheet of paper costs $0.29. 30−0.29x≥15.75 to find the number of sheets of paper, x, she can buy. How many sheets of paper can she buy?

Answers

we need to solve the inequality to find what x could be
solving inequalities is similar to solving unknowns in an equation, the same set of steps are followed, except that x could be equal to the final answer or more or less than that value depending on the sign .
30−0.29x ≥ 15.75 
-0.29x ≥ -14.25
when dividing by a negative number (-0.29) the inequality side should change its direction 
In this case ≥ changes to ≤
x ≤ -14.25/-0.29
x ≤ 49.13
since they are asking for number of sheets of paper it should be the nearest whole number that is less than or equal to 49.13
since 49.13 is not a whole number we should round it off to the nearest whole number that is less than that.
x ≤ 49
she can buy maximum 49 sheets of paper and have enough money to buy the scrapbook.
49 x $ 0.29 + 15.75 = 14.21 + 15.75 = $29.96

Ms. Romero can buy up to 49 sheets of paper.

To determine the number of sheets of paper \( x \) that Ms. Romero can buy, we start with the inequality:

[tex]\[ 30 - 0.29x \geq 15.75 \][/tex]

First, isolate the term involving \( x \) by subtracting 15.75 from both sides:

[tex]\[ 30 - 15.75 \geq 0.29x \][/tex]

Simplify the left side:

[tex]\[ 14.25 \geq 0.29x \][/tex]

Next, solve for \( x \) by dividing both sides by 0.29:

[tex]\[ \frac{14.25}{0.29} \geq x \][/tex]

Calculate the value:

[tex]\[ x \leq \frac{14.25}{0.29} \]\[ x \leq 49.13793103448276 \][/tex]

Since \( x \) must be a whole number, we take the greatest integer less than or equal to 49.13793103448276, which is 49. Therefore, the maximum number of sheets of paper she can buy is:

[tex]\[ x = 49 \][/tex]

Thus, Ms. Romero can buy up to 49 sheets of paper.

PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Exponential Growth/Decay Function
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years. (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answers

Did you get the answer for part b?

Call a household prosperous if its income exceeds $100,000. call the household educated if the householder completed college. select an american household at random, and let a be the event that the selected household is prosperous and b the event that it is educated. according to a survey, p(a) = 0.132, p(b) = 0.227, and the probability that a household is both prosperous and educated is p(a and
b.= 0.082. what is the conditional probability that a household is prosperous, given that it is educated? (round your answer to four decimal places.) .3612 explain why your result shows that events a and b are not independent. if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(a), and p(a and
b.would equal the sum p(a) + p(b). if a and b were independent, then p(a|b) would equal p(a and b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the product p(a)p(b). if a and b were independent, then p(a|b) would equal p(b), and p(a and
b.would equal the sum p(a) + p(b). submit answer save progress

Answers

p(a|b) = p(a&b)/p(b)
.. = 0.082/0.227
.. ≈ 0.3612

If these events were independent, p(a|b) = p(a) and p(a&b) = p(a)*p(b). (Looks like your 1st selection.)

0.5x+78.2=287 whats the value of x

Answers

0.5x+78.2=287
-78.2 -78.2 SUBTRACT 78.2

0.5x=208.8
/.5 /.5 DIVIDE BY .5

x=417.6 ANSWER

Joan and Ernie are earning money for summer camp. Joan receives a $7 weekly allowance plus $6 for each hour she helps her father paint. Ernie writes the equation y = 5x + 7 to represent the relationship between the number of hours he helps his father with yard work and his weekly allowance. Which statement best describes the graphs of their earnings for one week?

Answers

The Correct statement are:

Joan has more money in 10 weeks

Their y-intercepts are the same

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Joan:

Joan receives a $7 weekly allowance plus $6 for each hour

so, the Equation for Joan Earning, y= 6x+ 7

Ernie Earning y = 5x + 7

So, the slope for Joan is 7 and Ernie's slope is 7.

Then, the Correct statement is:

Joan has more money in 10 weeks

Their y-intercepts are the same

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ3

Jake needs to put gas in the delivery van. Regular gasoline is $3.20 per gallon. He only had a $ 20 bill on him. How many gallons can he buy

Answers

Hello,

The answer is "6 gallons".

Reason:

Just divide 20 by 3.20.....

20/3.20=6.25

Round to the nearest whole number will be 6.

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

he can buy 6 galons and he got 58 extra

What is the slope of the line that goes through (2, 5) and (-6, -2) ?

Answers

Answer:
slope = 7/8

Explanation:
Slope of the line can be calculated using the following equation:
slope = [tex] \frac{y2 - y1}{x2 - x1} [/tex]

The two points given are:
(2,5) representing (x1 , y1)
(-6,-2) representing (x2 , y2)

Substitute with the points in the above equation to get the slope as follows:
slope = [tex] \frac{-2 - 5}{-6 - 2} [/tex] = 7/8

Hope this helps :)

A right triangle has one leg that is 17 centimeters shorter then the other. If the hypotenuse is 25 what is the length of the two legs

Answers

Let x represent the shorter leg. Then the Pythagorean theorem tells us
  x^2 +(x +17)^2 = 25^2
  2x^2 +34x +289 = 625
  x^2 +17x -168 = 0
  (x -7)(x +24) = 0 . . . . . the zero product rule tells you x=7 is the solution

The shorter leg is 7 cm; the longer one is 24 cm.

Nolan bought 26 yards of rope, the rope costs 2 dollars per foot, how much did Nolan play for the rope?

Answers

He played 78 dollars
$78 for 26 yards of rope

The bookstore marked some notepads down from ???$ 3.00 but still kept the price over ???$ 2.00. It sold all of them. The total amount of money from the sale of the pads was ???$ 27.95. How many notepads were??? sold? What was the price of each??? notepad?

Answers

The answer is 13. To figure this out I used 10 notebooks sold as a guide. I knew the answer could not be 10, because $27.95/10 was not a number stopping in the hundredths place (or a true money amount).

I tried numbers greater than 10 using a trial and error strategy until I got to 13 notebooks sold and found that it $27.95 was divisible by 13 to get an answer between $2 and $3 ($2.15 exactly).

Expand the log as a sun or difference

Answers

27. (1/2*log(9) -(4*log(x) +1/3*log(3))/log(a)
  = ((1/2)*2*log(3) -4*log(x) -1/3*log(3))/log(a)
  = ((2/3)*log(3) -4*log(x))/log(a)
  = [tex]\frac{2}{3}\log_a{(3)}-4\log_a{(x)}[/tex]
[tex]\bf \textit{logarithm of factors} \\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\\\ \textit{Logarithm of rationals} \\\\ log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y) \\\\\\ \textit{Logarithm of exponentials} \\\\ log_a\left( x^b \right)\implies b\cdot log_a(x)\\\\ -------------------------------[/tex]

[tex]\bf log_a\left( \cfrac{9^{\frac{1}{2}}}{x^43^{\frac{1}{3}}} \right)\implies log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^43^{\frac{1}{3}} \right) \\\\\\ log_a\left( 9^{\frac{1}{2}} \right)-\left[ log_a\left( x^4 \right)+log_a\left( 3^{\frac{1}{3}} \right) \right] \\\\\\ log_a\left( 9^{\frac{1}{2}} \right)-log_a\left( x^4 \right)-log_a\left( 3^{\frac{1}{3}} \right)\\\\\\ \cfrac{1}{2}log_a(9)-4log_a(x)-\cfrac{1}{3}log_a(3)[/tex]

or more expanded so as 

[tex]\bf \cfrac{1}{2}log_a(3^2)-4log_a(x)-\cfrac{1}{3}log_a(3) \\\\\\ \cfrac{1}{2}\cdot 2log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3) \\\\\\ log_a(3)-4log_a(x)-\cfrac{1}{3}log_a(3)[/tex]

A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets an a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets?

Answers

The best expression would be 9.50c + 9.50a. 

Question

A theater company charges $9.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets an a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets?

Answer:

10.50c + a

PLZ GIVE BRAINLYEST!!!

Find the general solution of the differential equation y'' +4y = 3sin2t

Answers

Consider, pls, this option. Make a design according to local requirements.

Find the points on the surface 4 x^2 + 4 y^2 + 1 z^2 = 1 at which the tangent plane is parallel to the plane -4 x - 4 y + 4 z = -8.

Answers

i dont know i will tell you when i find out

Use the information below to find EF such that triangle ABC is congruent to triangle DEF

AB=36 BC=24 DE=48 m<B=110 m<E=110 EF=?

Answers

check the picture below.

notice, the green numbers are the given ones, and the red ones are the implicit ones.

since we know both triangles are congruent, then all their sides as well as angles are congruent as well.

so if triangle ABC has sides of 24 and 36, so does triangle DEF, and if triangle DEF has a side of 48, so does triangle ABC.

Which ordered pair represents the x-intercept for the linear equation, 3y + 4x = 8?

Answers

3y + 4x = 8 represents a line on the x-y plane, looking like the image I attached.

To find the x-intercept means to find the place where the line intersects the x-axis. If the line is intersecting the x-axis, then the point where it intersects the x-axis must be a place where y = 0. If y didn't equal 0, then that point wouldn't be on the x-axis.

So, to find the x-intercept, we set y in the given equation to 0, like this:
[tex]3y + 4x = 8 [/tex]
[tex]3(0) + 4x = 8[/tex]
[tex]4x = 8[/tex]
[tex]x = \frac{8}{4}[/tex]
[tex]x=2[/tex]
So, [tex]x=2[/tex]. We assumed that [tex]y=0[/tex] to find the x-intercept at the beginning. Then, our ordered pair in the usual order [tex](x,y)[/tex] is [tex](0,2)[/tex]. You can see this is correct by looking at the attached graph.

Final answer:

To find the x-intercept for the equation 3y + 4x = 8, set y to 0 and solve for x, which results in x = 2. Thus, the ordered pair for the x-intercept is (2, 0).

Explanation:

The question is asking to determine the x-intercept of the linear equation 3y + 4x = 8. The x-intercept occurs where the graph of the equation crosses the x-axis, which is when y is equal to 0. To find the x-intercept, you set y to 0 and solve for x:

3(0) + 4x = 8

4x = 8

x = 8/4

x = 2

Therefore, the ordered pair that represents the x-intercept is (2, 0). This is the point on the graph where the line crosses the x-axis.

For the number -5/8 name the opposite, reciprocal and absolute value

opposite:
Reciprocal:
Absolute value:

Answers

opposite-   5/8
reciprocal-   -8/5
absolute value-   5/8

Giving brainiest+points need explanation on this one my answer is 25 is it right?

Answers

yes, the answer of 25 is correct.

Multiply x^2-8x+15/3x * 8x/x-3

Answers

You must follow the steps below:

 1. First, you should apply the dstributive property:

 =(x²-8x+15/3x)(8x/x-3)
 =(8x³-64x²+120x)/3x(x-3)

 2. As you can see, the common factor in the numerator is: "8x". So, you have:

 =8x(x²-8x+15)/3x(x-3)

 3. Then, when you simplify, you obtain:

 =8(x²-8x+15)/3(x-3)

 Therefore, the solution is: 8(x²-8x+15)/3(x-3)
 

Hi! can someone please answer this question

Answers

The perimeter of a rectangle is twice the sum of length and width, so the sum of length and width is 360 meters.

360 m - 160 m = 200 m

The width of the garden is 200 meters.


_____
Of course, you know that 1 km = 1000 m, so 0.72 km = 720 m.
Hello! 

In order to find the answer to the question, we can begin by converting the measurements into one common unit. In this case, we can convert 0.72km to 720 meters, which will make the final calculation a bit easier. 

The formula to find the perimeter of the garden is L2+W2. 

The length is 160 meters, so we can multiply this by two to find a portion of the rectangle. 

160 x 2 = 320

Now, we can subtract 320 from the total number: 720

720 - 320 = 400

To find the width, we simply now need to divide 400 by 2. 

[tex] \frac{400}{2} [/tex] = 200

The width of the garden is 200 meters. 

I hope this helps you! Have a wonderful day!
-MMMski

Richard goes to the electronics store. He buys 2 memory cards that cost $8.99 each and 3 packages of batteries that are on sale for $7.47 each. He also buys a case for his cell phone for $2.99 and a wireless headset for $29.99. What is the total cost of Richard’s items, before sales tax?

Answers

2*8.99 +3*7.47 +2.99 +29.99 = 73.37

Richard's items cost $73.37 before sales tax is added.

how to we get radius

Answers

Just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation
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