Answer:
7x + 15x= 21x
Step-by-step explanation:
7x + 15x
= (7 + 15)x
= 22x
Answer: 22x
Step-by-step explanation: +7x and +15x are called terms and the numbers in front of the variables, +7 and +15 are called coefficients.
Because the variables, x and x, are identical, the two terms in this problem are called like terms. Like terms can be added together by simply adding their coefficients. So in this problem, since 7 + 15 is 22, 7x + 15x is simply 22x.
You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 13 of one section of the fence.
What fraction of the fence did you paint?
Question:
You have a 32-foot fence around a square garden. There are 4 equal sections. You paint 1/3 of one section of the fence. What fraction of the fence did you paint?
Answer:
The fraction of the fence painted is [tex]\frac{1}{12}[/tex]
Solution:
Given that:
You have a 32-foot fence around a square garden. There are 4 equal sections
Find the length of each section:
4 sections = 32 foot
[tex]\text{ 1 section } = 32 \div 4 = 8 foot[/tex]
Find the length that is painted:
[tex]\text{ Fence painted }= \frac{1}{3} \text{ of one section }\\\\\text{ Fence painted }= \frac{1}{3} \times 8 = \frac{8}{3} \text{ foot }[/tex]
Therefore [tex]\frac{8}{3}[/tex] foot of fence is painted
Find the fraction that that is painted:
Total length of fence = 32
[tex]\text{ Fraction of the fence painted } = \frac{8}{3} \div 32 = \frac{8}{3} \times \frac{1}{32}\\\\\text{ Fraction of the fence painted } = \frac{1}{12}[/tex]
Therefore [tex]\frac{1}{12}[/tex] fraction of the fence is painted
A surveyor wants to find the distance from points A and B to an inaccessible point C. These three points form a triangle. Because point C can be sighted from both A and B, he knows that the measure of < A= 53 degrees and the measure of < B = 61 degrees. In addition, the distance from A to B is 142 meters. Find AC and BC. Draw a diagram.
Answer:
Part a) [tex]AC=135.95\ m[/tex]
Part b) [tex]BC=124.14\ m[/tex]
The diagram in the attached figure
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]
substitute the given values
[tex]53^o+61^o+m\angle C=180^o[/tex]
[tex]114^o+m\angle C=180^o[/tex]
[tex]m\angle C=180^o-114^o[/tex]
[tex]m\angle C=66^o[/tex]
step 2
Find the distance AC
Applying the law of sines
[tex]\frac{AB}{sin(C)}=\frac{AC}{sin(B)}[/tex]
see the attached figure to better understand the problem
substitute the given values
[tex]\frac{142}{sin(66^o)}=\frac{AC}{sin(61^o)}[/tex]
[tex]AC=\frac{142}{sin(66^o)}(sin(61^o))[/tex]
[tex]AC=135.95\ m[/tex] ---> rounded to the nearest hundredth
step 3
Find the distance BC
Applying the law of sines
[tex]\frac{AB}{sin(C)}=\frac{BC}{sin(A)}[/tex]
substitute the given values
[tex]\frac{142}{sin(66^o)}=\frac{BC}{sin(53^o)}[/tex]
[tex]BC=\frac{142}{sin(66^o)}(sin(53^o))[/tex]
[tex]BC=124.14\ m[/tex] ---> rounded to the nearest hundredth
If distinct planes R and S are both perpendicular to line L , which is always true?
1. Plane R is parallel to plane S
2. Plane R is perpendicular to plane S
3. Planes R and S and line L are all parallel
4. The intersection of planes R and S is perpendicular to line L
Answer:
Option 1 is correct.
Step-by-step explanation:
Let there is a line A which is perpendicular to line L at point O.
Now, rotating line A about point O by 360° will give the plane R.
So, plane R is perpendicular plane to line L.
Again, let there is a line B which is perpendicular to line L at point P.
Now, rotating line B about point P by 360° will give another plane S.
So, plane S is perpendicular plane to line L.
Since line A and line B are parallel (As they are perpendicular to the same line L) so, plane R containing line A and plane S containing line B will also be parallel to each other.
Hence, option 1 is correct. (Answer)
A book is 15 centimeters long and 6 centimeters wide. What are the length and width of the book in inches.Round your answer to the nearest hundredth.
Length and width of book is 5.91 inches and 2.36 inches respectively
Solution:
Given that a book is 15 centimeters long and 6 centimeters wide
To find: length and width of book in inches
From given question,
Length of book = 15 cm
Width of book = 6 cm
The conversion factor used is:
1 cm = 0.393701 inches
Therefore, length of book in inches is:
[tex]15 \text{ cm} = 15 \times 0.393701 \text{ inches }= 5.905515 \text{ inches }[/tex]
Rounding off rules:
First look at the digit to immediate right of rounding off digit
If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.
If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.
On rounding to nearest hundredth, ( two decimal places )
[tex]5.905515 \text{ inches } = 5.91 \text{ inches }[/tex]
Width of book in inches:
[tex]6 \text{ cm} = 6 \times 0.393701 \text{ inches } = 2.362206 \text{ inches }[/tex]
On rounding to nearest hundredth, we get 2.36 inches
Final answer:
The book measures approximately 5.91 inches in length and 2.36 inches in width.
Explanation:
To convert the dimensions of the book from centimeters to inches, we use the conversion factor that 1 inch is equal to 2.54 centimeters.
The length of the book in inches is calculated as follows:
Length in inches = Length in centimeters ÷ 2.54Length in inches = 15 cm ÷ 2.54Length in inches ≈ 5.91 inches (rounded to the nearest hundredth)Similarly, the width of the book in inches is:
Width in inches = Width in centimeters ÷ 2.54Width in inches = 6 cm ÷ 2.54Width in inches ≈ 2.36 inches (rounded to the nearest hundredth)Therefore, the book measures approximately 5.91 inches in length and 2.36 inches in width.
3.6x - 12.2=-1.5x + 8.2
Answer:
x = 4Step-by-step explanation:
[tex]3.6x-12.2=-1.5x+8.2\qquad\text{multiply both sides by 10}\\\\36x-122=-15x+82\qquad\text{add 122 to both sides}\\\\36x-122+122=-15x+82+122\\\\36x=-15x+204\qquad\text{add}\ 15x\ \text{to both sides}\\\\36x+15x=-15x+15x+204\\\\51x=204\qquad\text{divide both sides by 51}\\\\\dfrac{51x}{51}=\dfrac{204}{51}\\\\x=4[/tex]
Haddie makes and sells knit scarves. Next week she will pay a $25 fee for the use of a booth at a craft fair. She will charge $12 for each scraft fair. Write an expression to determine Haddie’s profit for selling s scarves after paying the fee for the use of the booth.
The profit Haddie makes from selling scarves at a craft fair can be represented by the algebraic expression P = 12s - 25. Here, P represents profit, s represents the number of scarves sold, 12 represents the price of each scarf, and 25 represents the cost of booth rental.
Explanation:The subject of the question deals with the concept of profit in a business transaction, which falls under Mathematics, specifically algebra and economics. It's a High School level problem since it involves creating a basic algebraic expression.
Haddie's profit can be determined by subtracting her costs (the booth fee) from her earnings (the sale of the scarves). She earns $12 for each scarf sold, represented as 12s (where s is the number of scarves sold), and she has a fixed cost of $25 for the booth rental.
Therefore, the expression for Haddie's profit, P, for selling s scarves is: P = 12s - 25. This expression represents the total amount Haddie will earn from selling s scarves after deducting her cost for the booth rental.
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I just need help factoring or solving this one
Answer:
v = 1/2(1 + i√23) , 1/2(1 - i√23).
Step-by-step explanation:
-2v^2 - v + 12 = -3v^2 + 6
-2v^2 + 3v^2 - v + 12 - 6 = 0
v^2 - v + 6 = 0
This will not factor so we could use the quadratic formula to solve it:
For the equation ax^2 + bx + c = 0 the roots are:
x = [ - b +/- sqrt(b^2 - 4ac) ] / 2a.
So here we have:
v = [-(-1) +/- sqrt((-1)^1 - 4*1*6)] / 2
v = [ 1 +/- sqrt (-23)] / 2
= 1/2 + i√23/2 , 1/2 - i√23/2
= 1/2(1 + i√23) , 1/2(1 - i√23).
Find the midpoint of RS
Answer:
The midpoints of the given graph are ( - 1, 3 ).
Step-by-step explanation:
By the graph we have to given that the endpoints are R ( -5, 4) and S (3, 2)-
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex]) and ( [tex]x_{2}, y_{2}[/tex] ) then the mid points C are-
C = ( [tex]\frac{x_{1} + x_{2} }{2}[/tex], [tex]\frac{y_{1} + y_{2} }{2}[/tex] )
Here,
R ( - 5, 4 ) and S ( 3, 2 )
then the midpoints C are-
C = ( [tex]\frac{ - 5 + 3}{2}[/tex] , [tex]\frac{4 + 2}{2}[/tex]
C= ( - 2/2 , 6/2 )
C = ( -1, 3 )
Hence the midpoints are ( - 1, 3 ).
Olive's solar powered scooter travels at a rate of 30 miles per hour. What equation can she use to calculate her distance with relation to the time she is traveling?
m = miles
h = hours
A: h = 30m
B: h = m + 30
C: m = h + 30
D: m = 30h
Answer:
The equation to represent the distance traveled by Olive in here solar powered scooter can be given as:
D: [tex]m=30h[/tex]
Step-by-step explanation:
Given:
Speed of Olive's solar powered scooter = 30 miles/hour
[tex]m\rightarrow[/tex] miles traveled
[tex]h\rightarrow[/tex] hours of travel
To find the distance traveled by Olive.
Solution:
Distance traveled = [tex]Speed\ \times \ Time[/tex]
Thus, the equation to represent the distance traveled by Olive in here solar powered scooter can be given as:
[tex]m=30\times h[/tex]
∴ [tex]m=30h[/tex]
answer pleaseeeeeeeeee
Answer:
The answer is 50.
Step-by-step explanation:
The answer is 50 because, the line that the Exterior angle is on is equal to 180. So you take the two interior angels and add them. Then subract that from 180 and you get 50.
Hope this helps :))
Answer:
The correct answer is 110°.
Step-by-step explanation:
The Exterior Angle Theorem states, "the exterior angle of a triangle is equal to the sum of its non-adjacent angles".
This means we would add 50 + 60 to get 110°.
Or we could look at the exterior angle and the adjacent angle to it. The two angles form a supplementary angle - this equals 180°. To find our answer this way, we subtract the known angle form 180:
180 - 70 = 110°
Hope this helps,
♥A.W.E.S.W.A.N.♥
100 POINTS PLEASE ANSWER AND DO ASK DIRECTED
In 5-7 sentences RAFTED PARAGRAPH, create a well-organized paragraph with a claim and evidence that answers the question below. Is it better to text or call? Justify
Answer:
Brainly User: eletricblu3s@*********.com
Should college be free? It’s a classic question with a complicated and arguably unclear answer. The affordability of college education, as well as the current student debt crisis, is always one of the center-stage issues for presidential political seasons. In fact, many candidates build their platforms around college costs as a key issue.
As with any major decision, especially relating to higher education, there are pros and cons to consider. Let me help break down the positives and negatives of tuition-free college.
The PROS of Tuition-Free College
More Lower-Income Students Might Reach Graduation if There’s No Tuition
Some students drop out because they do not have the ability to pay for tuition all four years. Getting rid of tuition would eliminate this reason for not graduating. This would also serve to improve college graduation rates, as fewer students would feel the need to drop to part-time status or take a break from education for financial reasons.
Student Debt Will No Longer Crush the Younger Generations
If an American college student is able to graduate with less than $10,000 in student loan debt, they are considered lucky (the average is $37,000). However, students from other countries that don’t have tuition already have that luxury; most of their loans come from living expenses and books. Without the weight of student loan debt, more college graduates might buy houses rather than renting apartments. They might buy cars, spend more on healthy food, travel more: In essence, they could contribute more to the economy.
Students Might Have More Freedom to Choose a Major They Enjoy
Whether it is the influence of parents or knowing you need to pay loans back as quickly as possible, current students are often guided toward “practical” majors that have a more lucrative post-graduation income. If shelling out thousands upon thousands of dollars is no longer a factor, parents and students might feel more relaxed about studying for majors that don’t necessarily have a large paycheck associated with them. Interest and enjoyment from a field of study goes a long way in helping students stick with it and avoid burning out.
More People Would Go to College
By negating the large bill of a college education, we could see an increase in the number of students able to attend college. This then creates a more well-educated workforce and a population that has better critical thinking skills. This could lead to more innovation in all areas of society. This would also help people with financial need to earn an education
Write an equation of the line containing the given point and perpendicular to the given line:
(4, - 7); 9x+5y=3
Answer:
[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]
Step-by-step explanation:
Given equation of line:
[tex]9x+5y=3[/tex]
To find the equation of line perpendicular to the line of the given equation and passes through point (4,-7).
Writing the given equation of line in standard form.
Subtracting both sides by [tex]9x[/tex]
[tex]9x-9x+5y=3-9x[/tex]
[tex]5y=3-9x[/tex]
Dividing both sides by 5.
[tex]\frac{5y}{5}=\frac{3}{5}-\frac{9x}{5}[/tex]
[tex]y=\frac{3}{5}-\frac{9x}{5}[/tex]
Rearranging the equation in standard form [tex]y=mx+b[/tex]
[tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex]
Applying slope relationship between perpendicular lines.
[tex]m_1=-\frac{1}{m_2}[/tex]
where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of perpendicular lines.
For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex]can be found by comparing [tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex] with standard form.
∴ [tex]m_2=-\frac{9}{5}[/tex]
Thus slope of line perpendicular to this line [tex]m_1[/tex] would be given as:
[tex]m_1=-\frac{1}{-\frac{9}{5}}[/tex]
∴ [tex]m_1=\frac{5}{9}[/tex]
The line passes through point (4,-7)
Using point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where [tex](x_1,y_1)\rightarrow (4,-7)[/tex] and [tex]m=m_1=\frac{5}{9}[/tex]
So,
[tex]y-(-7)=\frac{5}{9}(x-4)[/tex]
Using distribution.
[tex]y+7=(\frac{5}{9}x)-(\frac{5}{9}\times 4)[/tex]
[tex]y+7=\frac{5}{9}x-\frac{20}{9}[/tex]
Subtracting 7 to both sides.
[tex]y+7-7=\frac{5}{9}x-\frac{20}{9}-7[/tex]
Taking LCD to subtract fractions
[tex]y=\frac{5}{9}x-\frac{20}{9}-\frac{63}{9}[/tex]
[tex]y=\frac{5}{9}x+\frac{(-20-63)}{9}[/tex]
[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]
[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]
Thus, the equation of line in standard form is given by:
[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]
Find the number, if 3 1/3 of it is 10
Answer:
3
Step-by-step explanation:
You want a number that if it is multiplied by 3 1/3 the result will be 10. Let the number be x
3 1/3 * x = 10 Change to a mixed number
10/3 * x = 10 Multiply by 3/10
(10/3)*x * 3/10 = 10 * 3/10 Combine
x = 10*3 / 10 Simplify
x = 30/10 = 3
Answer:
3
Step-by-step explanation:
20 POINTS BRAINLIEST
Answer:
D
Step-by-step explanation:
Using the rule of logarithms
log x - log y = log([tex]\frac{x}{y}[/tex])
Given
[tex]log_{7}[/tex]([tex]\frac{n}{2}[/tex])
= [tex]log_{7}[/tex] n - [tex]log_{7}[/tex] 2 → D
Answer:
yoink im eating them points nomnomnom
Step-by-step explanation:
Round 832 to the nearest hundreds place.
Answer:
800
Step-by-step explanation:
Look at the tens if it's 0-4 keep the number the same if 5-9 go up one number
PLEASE MARK BRAINLIEST!
Answer:
832 --> ???
832 - we must round the underlined digit
832 --> ???
832 --> 800
The rounding rule is:
4 and below, stay down low! [Round down]. 5 and above, soar like a dove! [Round up].
So with that rule, 832 becomes 800.
800 is your answer.
I hope this helps!
The dimensions of a rectangle are given in
ectangle are given in terms of s as shown below.
-s+ / -
[not drawn to scale)
Select all expressions that represent the perimeter of the rectangle.
+
4s + 1
* 2s + 1
© 4s + 2
© 2/5 + 1)
© 2s +
® 22s +
Option A and Option F
The expressions that represent the perimeter of rectangle are 4s + 1 and [tex]2(2s + \frac{1}{2})[/tex]
Solution:
From figure,
Length = s
Width = [tex]s + \frac{1}{2}[/tex]
The perimeter of rectangle is given as:
perimeter = 2(length + width)
Substituting the values we get,
[tex]perimeter = 2(s + s + \frac{1}{2})\\\\perimeter = 2(2s + \frac{1}{2})[/tex]
Thus option F is correct
On further simplification,
[tex]perimeter = 2(2s + \frac{1}{2})\\\\perimeter = 4s + 2(\frac{1}{2})\\\\perimeter = 4s + 1[/tex]
Thus Option A is correct
31. In a Mathematics competition, there are 10 questions of equal marks. You get 10 marks for a correct
answer, lose 8 marks for a wrong answer, or no mark for each blank answer. If Jimmy answered 3
questions correctly, 6 questions wrongly, and left 1 question unanswered, how many marks could he
get?
Jimmy can get -18 marks in the Mathematics competition based on his correct, incorrect, and unanswered answers.
Explanation:To calculate the marks Jimmy can get, we need to consider the number of questions he answered correctly, incorrectly, and left unanswered. Since each question carries 10 marks for a correct answer and deducts 8 marks for a wrong answer, we can calculate his marks as follows:
Number of correct answers: 3 * 10 = 30 marksNumber of incorrect answers: 6 * (-8) = -48 marksNumber of unanswered questions: 1 * 0 = 0 marks
To get the total marks, we add up his scores from each category:
Total marks = 30 - 48 + 0 = -18 marks.
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Which number is in the solution set of the inequality 4x + 4 > 36
Step-by-step explanation:
4x > 36-4
4x > 32 (divide both sides of the inequality by 4 )
4x ÷ 4 > 32 ÷ 4
x > 8
Final answer:
To determine the solution set of the inequality 4x + 4 > 36, subtract 4 from both sides to get 4x > 32 and then divide by 4 to find x > 8. Any number greater than 8 is part of the solution set.
Explanation:
To find which number is in the solution set of the inequality 4x + 4 > 36, we need to solve for x by performing a series of steps:
Subtract 4 from both sides of the inequality to get 4x > 32.
Divide both sides of the inequality by 4 to solve for x, resulting in x > 8.
Thus, any number greater than 8 is in the solution set of the given inequality.
1. Which of the following could be
the measurements of two
complementary angles?
A. 7º and 830
B. 83° and 830
C. 97º and 83°
D. 117° and 83°
Step-by-step explanation:
I don't know if this helps, but none of the above.
first of all, complementary angles mean that the 2 (or more) angles add up to 90 degrees. so, if you were to combine the angles, you'll get an angle that's way larger than 90 degrees. (a and b won't work cause 830 isn't an angle)
P.S. but 83 degrees and 7 degrees would be complementary...
hope you at least know why i say none of the above
Jerome's credit card has an APR of 18%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. His credit card record for the last 7 months is shown in the table
below.
End of
month
Previous
balance
$0.00
$2200.00
$2189.00
$2178.06
$2167 16
$2156.33
$2145.55
Now
charges
$2200.00
$0.00
50.00
S0.00
$0.00
$0.00
50.00
Payment
recolved
S000
$44.00
$43.78
$43.56
$43.34
$43.13
$42.91
chere
30.00
$33.00
532.84
$32.67
$3251
$32,34
$32.18
Principal
pald
30.00
$11.00
$10.95
$10.89
$10.84
$10.78
$10.73
balance
$2200.00
$2189.00
$2178.06
$2167.16
$2156.33
$2145.55
$2134.82
What is the total amount that Jerome has paid in interest over the 7 months?
Answer: 11,056.1
Step-by-step explanation: Because you have to add the first 7
Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.
To find the total amount that Jerome has paid in interest over the 7 months, we need to sum up the interest paid each month. The interest for each month is calculated as follows:
[tex]\[ \text{Interest for the month} = \text{Previous balance} \times \text{APR} / 12 \][/tex]
Let's calculate the interest for each month:
1. For the second month:
[tex]\[ \text{Interest} = \$2200.00 \times 0.18 / 12 = \$33.00 \][/tex]
2. For the third month:
[tex]\[ \text{Interest} = \$2189.00 \times 0.18 / 12 = \$32.84 \][/tex]
3. For the fourth month:
[tex]\[ \text{Interest} = \$2178.06 \times 0.18 / 12 = \$32.67 \][/tex]
4. For the fifth month:
[tex]\[ \text{Interest} = \$2167.16 \times 0.18 / 12 = \$32.51 \][/tex]
5. For the sixth month:
[tex]\[ \text{Interest} = \$2156.33 \times 0.18 / 12 = \$32.34 \][/tex]
6. For the seventh month:
[tex]\[ \text{Interest} = \$2145.55 \times 0.18 / 12 = \$32.18 \][/tex]
Now, sum up these monthly interest amounts:
[tex]\[ \$33.00 + \$32.84 + \$32.67 + \$32.51 + \$32.34 + \$32.18 = \$195.54 \][/tex]
So, Jerome has paid a total of [tex]\$195.54[/tex]rest over the 7 months.
A shrub in Pam's back yard is about 1 3\8 feet tall. A small tree in her back yard is about 7 times as the shurd. About how tall is the tree
The height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]
Solution:
Given that shrub in Pam's backyard is about [tex]1\frac{3}{8}[/tex] feet tall
A small tree in her back yard is about 7 times as the shurd
To find: height of tree
From given information,
Height of shrub = [tex]1\frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8} \text{ feet}[/tex]
Given that small tree in her back yard is about 7 times as the shurb
So we get,
height of tree = 7 times the height of shrub
[tex]\text{ height of tree } = 7 \times \text{ height of shrub}\\\\\text{ height of tree } = 7 \times \frac{11}{8}[/tex]
Therefore on solving we get,
[tex]\text{ height of tree } = \frac{77}{8} = 9\frac{5}{8} \text{ feet}[/tex]
Thus the height of tree is [tex]9\frac{5}{8} \text{ feet}[/tex]
If f (x)= 5x -7, then what is the solution to f (x) = 4?
Answer:
11/5
Step-by-step explanation:
5x-7=4
5x=4+7
5x=11
x=11/5
The required solution of the function at x = 4 is f(4) = 13.
Given that,
A function is given f(x) = 5x - 7, the value of the function at x = 4 is to be determined.
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given function,
f(x) = 5x - 7
put the value x = 4 in the above equation,
f(4) = 5 * 4 - 7
f(4) = 20 -7
f(4) = 13
Thus, the required solution of the function at x = 4 is f(4) = 13.
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1
Select the correct answer.
What is the area of the cross section that is parallel to side PQRS in this rectangular box?
A.
12 square units
B.
16 square units
C.
30 square units
D.
40 square units
Answer:
12 square units.
Step-by-step explanation:
I just took the test.
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect$96, selling a total of 36 jewelry items. how many of each type did you sell?
Answer:
I sell 12 bracelets and 24 necklaces.
Step-by-step explanation:
The selling price of each bracelet is $2 and that of each necklace is $3.
I collect $96, selling a total of 36 jewelry items.
Let us assume that I sell x bracelets and y necklaces.
So, x + y = 36 ........ (1) and
2x + 3y = 96 .......... (2)
Now, solving equations (1) and (2) we get, 3y - 2y = 96 - 72
⇒ y = 24
Hence, from equation (1) we get x = 36 - y = 36 - 24 = 12
Therefore, I sell 12 bracelets and 24 necklaces. (Answer)
Jessica used 2/3 yard of fabric to make a scarf. Can she make 2 of these scarves with 1 3/4 yards of fabric
Answer:
Yes
Step-by-step explanation:
2 × 2/3 = 4/3 yards of fabric needed for 2 scarves. This amount is less than 1 1/2 yards. The amount of fabric that Jessica has is more than 1 1/2 yards, so is more than enough.
Jessica can make 2 scarves.
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day.
C(x) = 4x³+7x²-14x-6
Step-by-step explanation:
Given that the amount of water used in normal days is given by the equation;
W(x) = 5x³ +9x²-14x +9 -----(i)
The amount of decrease in water used is modeled by the equation;
D(x)= x³+2x² +15--------(ii)
To get the function C(x) that models the water used by the car wash on shorter day you subtract equation (ii) from equation(i)
5x³ +9x²-14x +9
- x³+2x² +15
-------------------------
4x³+7x²-14x-6
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Answer:
C(x) = 4x³ + 7x² − 14x - 6
Step-by-step explanation:
In a shorter day the water used by the car wash is computed as the difference between the original usage and the decrease, that is:
C(x) = W(x) - D(x)
Replacing with data:
C(x) = 5x³ + 9x² − 14x + 9 - (x³ + 2x² + 15)
C(x) = 5x³ + 9x² − 14x + 9 - x³ - 2x² - 15
C(x) = (5-1)x³ + (9-2)x² − 14x + (9-15)
C(x) = 4x³ + 7x² − 14x - 6
Write the equation of a line that passes through the two points (4,-2) and (12,4).
Answer:
y+2=3/4(x-4)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-(-2))/(12-4)
m=(4+2)/8
m=6/8
m=3/4
----------
y-y1=m(x-x1)
y-(-2)=3/4(x-4)
y+2=3/4(x-4)
Rita has a container with a liter of milk and is wondering how many fluid ounces of milk are in the container. She knows that 1 gallon is about 3.785 liters, and she sets up the expression below to convert 1 liter to fluid ounces.
1 liter ×
gallon
liter ×
fluid ounces
gallon
Answer:
1 liter × 0.2642 gallons liter × 33.817 fluid ounces gallon.
Step-by-step explanation:
Given:
1 gallon = 3.785 liters
We need to find how many fluid of ounce are there in 1 liter.
First we will find number of gallons in 1 liter.
We know that;
3.785 liters = 1 gallons
1 liters = number of gallons in 1 liter.
By using Unitary method we get;
number of gallons in 1 liter = [tex]\frac{1}{3.785}= 0.2642\ gallons[/tex]
Now we know that:
1 gallons = 128 fluid ounce
So 0.2642 gallons = Number of fluid ounce in 0.2642 gallons
Again by using Unitary method we get;
Number of fluid ounce in 0.2642 gallons = [tex]128 \times 0.2642\approx 33.817\ oz[/tex]
Hence we can say,
1 liter ×0.2642 gallons liter × 33.817 fluid ounces gallon.
Henry and Gavin are marking exam papers. Each set takes Henry 36 minutes and Gavin 1 hour. Express the times Henry and Gavin take as a ratio.
Give your answer in its simplest form.
The ratio of time taken by Henry to time taken by Gavin is 3:5
Step-by-step explanation:
Time taken by Henry for each set = 36 minutes
Time taken by Gavin for each set = 1 hour
We will convert Gavin's time into minutes.
Time taken by Gavin for each set = 60 minutes
Ratio;
Time taken by Henry : Time taken by Gavin
[tex]36:60[/tex]
Dividing by 6
[tex]\frac{36}{6}:\frac{60}{6}\\6:10[/tex]
Dividing by 2
[tex]\frac{6}{2}:\frac{10}{2}\\3:5[/tex]
The ratio of time taken by Henry to time taken by Gavin is 3:5
Keywords: ratio, division
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Sue lives 6 miles from Gill. She also lives 1 mile closer to Taco Town restaurant than Gill does. Write an equation that shows this statement: the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.
Answer:
The equation representing the statement is [tex](x-1)+x=6[/tex].
Step-by-step explanation:
Given:
Distance from Sue house to Gill house = 6 miles.
Let the distance from Gill to Taco Town restaurant be 'x'.
Also Given:
Sue lives 1 mile closer to Taco Town restaurant than Gill does.
Hence Distance from Sue to Taco Town restaurant will be = [tex]x-1[/tex]
We need to write the equation for the below statement.
the distance from Sue's to Taco Town plus the distance from Taco Town to Gill's equals the distance from Sue's house to Gill's house.
Framing in equation form we get;
[tex](x-1)+x=6[/tex]
Hence the equation is [tex](x-1)+x=6[/tex].