Answer:
c
Step-by-step explanation:
Let 1/x = a &
1/y = b
So, now the equation:
2a +3b = 13 --------------------(i)
5a - 4b = -2 --------------------(ii)
To eliminate a, Multiply equation (i) by 5 and multiply (ii) by (-2)
(i)*5 10a + 15b = 65
(ii)*(-2) - 10a + 8b = 4 ( Now add, a will be eliminated}
23b = 69
b= 69/23
b = 3
Plug in the value of b in equation (i)
2a + 3*3 = 13
2a + 9 = 13
2a = 13 - 9
2a = 4
a= 4/2
a = 2
Now a = 1/x ------>x = 1/a = 1/2
b = 1/y ----------->y = 1/b = 1/3
[tex]x+y=\frac{1}{2}+\frac{1}{3}\\\\=\frac{1*3}{2*3}+\frac{1*2}{3*2}\\\\=\frac{3}{6}+\frac{2}{6}\\\\=\frac{5}{6}[/tex]
Find the exact area of a triangle with two sides that measure 6 yd and 2 yd with an included
angle of 10°
Answer:
1 yd^2
Step-by-step explanation
A=1/2(2)(6)Sin(10)
Final answer:
The area of a triangle with sides of 6 yd and 2 yd and an included angle of 10° is approximately 1.0439 square yards.
Explanation:
To find the exact area of a triangle with two sides measuring 6 yd and 2 yd and an included angle of 10°, you can use the formula for the area of a triangle when two sides and the included angle are known: A = ½ ab × sin(C), where a and b are the sides and C is the included angle.
The calculation will be: A = ½ × 6 yd × 2 yd × sin(10°). Using a calculator with the sine function set to degrees, we find that sin(10°) ≈ 0.17365. Therefore, the area A is approximately: A = ½ × 6 yd × 2 yd × 0.17365 ≈ 1.0439 yd².
Thus, the exact area of the given triangle is approximately 1.0439 square yards.
A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units. Which expression represents the volume, in cubic units, of the shaded region of the composite figure?
The expression is 1/2(14)* 10*8- π (2.5)² *8.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
Prism: side length base= 14 units and 10 units
Cylinder d= 5 units
So, Volume of prism
=1/2(14)* 10*8
and, Volume of cylinder
= π (2.5)² *8
As, the cylinder is cut out then the expression would be
=1/2(14)* 10*8- π (2.5)² *8
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emma was given a system of equations to solve by graphing. which statement correctly identifies Emma’s error?
Please help me. i’m struggling a lot on this question and only have a bit of time left
Answer:
A The first line should have an intercept at 2 not at 1
Step-by-step explanation:
The first line should have an intercept at 2 not at 1. The graph is 1 unit too low
The intercept should be at x=3 and y = 1
Answer:
First one
Step-by-step explanation:
Line 1:
When x = 0
y = -(1/3)(0) + 2
y = 2
y-intercept is 2
Which scenario is the BEST example of how the government would act in a mixed market economy?
The government requires a factory to produce surplus goods for the use of
the military.
The government stops a factory from producing imitations of an expensive
type of purse.
The government allows only two competitors to offer goods for sale on the
country's highways.
The government imposes a limit on the number of television sets that can
be exported annually.
In a mixed market economy, which typically combines elements of both market and government intervention, the BEST example is the government imposes a limit on the number of television sets that can be exported annually. Here option D is correct.
This scenario reflects a government intervention aimed at managing international trade and protecting domestic industries. By imposing export limits on television sets, the government can regulate the flow of goods, balance trade, and potentially safeguard local industries from excessive foreign competition.
This intervention allows for a controlled market environment while still allowing private enterprises to operate. Unlike the other options, this scenario demonstrates a strategic use of government intervention to achieve economic objectives without completely dominating the market or infringing on individual business operations.
It showcases a balance between free-market principles and government oversight, characteristic of a mixed market economy. Here option D is correct.
Complete question:
Which scenario is the BEST example of how the government would act in a mixed market economy?
A - The government requires a factory to produce surplus goods for the use of the military.
B - The government stops a factory from producing imitations of an expensive type of purse.
C - The government allows only two competitors to offer goods for sale on the country's highways.
D - The government imposes a limit on the number of television sets that can be exported annually.
According to one survey, 25% of high school
students reported that they would not get summer
jobs. Predict how many of the 948 students at
Mohawk High School will not get summer jobs.
Answer:
237
Step-by-step explanation:
25/100 = x/948, simplify to get 1/4 = x/948
cross multiply and get 948=4x
swap the sides and get 4x=948
divide both sides by 4 and get x=237
in conclusion 237 students won't get summer jobs.
About 237 students at Mohawk High School are predicted not to get summer jobs based on applying the survey percentage of 25% to the total student population of 948.
Explanation:To predict how many students at Mohawk High School will not get summer jobs, we use the percentage from the survey and apply it to the total number of students at the school. According to the survey, 25% of high school students reported that they would not get summer jobs. Mohawk High School has a total of 948 students.
To find the number of students who will not get summer jobs, we perform the following calculation:
Percentage not working = 25%Total students = 948 studentsStudents not working = Total students × Percentage not working = 948 × 0.25Students not working = 237 studentsThus, we predict that about 237 students at Mohawk High School will not get summer jobs.
Samuel and Randi are placemat weavers. Samuel can weave 7 placemats in 8 hours. Randi can weave 5 placemats in 4 hours. How many placemats can they make in 5 days if they worked 8 hours each day?
Answer: 85 placemats
Step-by-step explanation:
Let’s split it into three parts: how much Samuel can weave, how much Randi can weave, and how much they can weave in total
Part 1: Samuel
First, let’s figure out how much Samuel can weave!
First, we know that Samuel can weave 7 placemats in 8 hours (1 day). So, if he weaved placemats for 5 days, then:
= 7 x 5
= 35
Therefore, Samuel weaved 35 placemats in 5 days if he worked 8 hours each day.
Part 2: Randi
We know that Randi makes 5 placemats in 4 hours, which is half, a day. But lets figure out how many placemats he can make it a day.
All we have to do is multiply by two.
= 5 x 2
= 10
So, we now know that he can make 10 placemats in a day. Now, let’s see how many placemats he can make in five days.
= 10 x 5
= 50
Therefore, Randi weaved 50 placemats in 5 days if he worked 8 hours each day.
Part 3: Adding Them
Now, we have 35 placemats from Samuel and 50 placements from Randi. So, we have to add them.
= 35 + 50
= 85
Therefore, Randi and Samuel can make 85 placemats in 5 days together if they work 8 hours each day.
Samuel and Randi can make a total of 85 placemats in 5 days.
Explanation:To find out how many placemats Samuel and Randi can make in 5 days, we need to calculate how many placemats each of them can make in one hour. Samuel can weave 7 placemats in 8 hours, so he can weave 7/8 placemats in one hour. Randi can weave 5 placemats in 4 hours, so she can weave 5/4 placemats in one hour. To find out how many placemats they can make in 5 days, we need to multiply their rates by the number of hours they work in 5 days. Samuel can make (7/8) * (8 * 5) = 35 placemats in 5 days. Randi can make (5/4) * (8 * 5) = 50 placemats in 5 days. Therefore, Samuel and Randi can make a total of 35 + 50 = 85 placemats in 5 days.
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You are in charge of the city carnvial committee. You have $8,096.35 to spend. You have already purchased: Decorations $894.60. Tent rental
$1.009.99, new popcorn and cotton candy machines $658.50
How much money do you have left to spend to rent carnival rides for the kids?
Step-by-step explanation:
Total amount to spend = 8096.35
Amount already spent = 894. 60 + 1009.99 + 658.50 = 2563.09
Amount left to spend = 5533.26
Find the interest on $5,200 at 6% for 2 and a half years. Which of the following equations would be used to solve this problem?
i put this before but forgot to put the equations sorry
A: I = (5200)(6)(2.5)
B: 5200 = P(0.06)(2.5)
C: I = (5200)(0.06)(2.5)
D: I = (5200)(0.6)(2.5)
hidoes anybody know answer please
Answer:
0,1,2,3,4 any of those would work and be less then 50
Step-by-step explanation:
9600 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 37800 dollars?
Answer: lt will take 28.09 years for the account value to reach $37800
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r) t
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Annual Nominal Interest Rate (decimal form)
Replacing with the values given
37800= 9600 (1+0.05)^t
Solving for t (years)
37800/9600 = 1.05^t
3.9375 = 1.05^t
log 3.9375 = log 1.05^t
log 3.9375 = t (log 1.05)
log 3.9375/log 1.05 = t
t = 28.09 years
Written as a simplified polynomial in standard form, what is the result when
(2x-8)^2 is subtracted from 3x?
Answer:
- 2x² + 3x + 64
Step-by-step explanation:
3x - (2x-8)² Write the equation and distribute the exponent
3x - 2x² + 64 Write the equation in order of degree of exponents, or standard form
- 2x² + 3x + 64
the result of the polynomial when [tex](2x-8)^2[/tex]is subtracted from [tex]3x[/tex] is
[tex]-4x^2+35x-64[/tex]
Given :
We need to simplify when [tex](2x-8)^2[/tex]is subtracted from [tex]3x[/tex]
Lets subtract[tex](2x-8)^2[/tex] is subtracted from [tex]3x[/tex]
we write the expression as
[tex]3x-(2x-8)^2[/tex]
Now we expand the square
[tex]3x-(2x-8)^2\\3x-(2x-8)(2x-8)\\3x-(4x^2-16x-16x+64)\\3x-4x^2+16x+16x-64\\-4x^2+35x-64[/tex]
The simplified polynomial is
[tex]-4x^2+35x-64[/tex]
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How could you find the area of the parallelogram
Answer:
24
Step-by-step explanation:
Multiply the base by the height
Base:8
Height:3
To find the base..... Count the amount of grid squares on the bottom of the parallelogram.
To find the height.... Count the amount of grid squares on the side of the parallelogram.
I hope I've helped! Please leave a Thanks and Vote.
Factor the expression below.
4x2 - 20x + 25
Answer: (2x+5)^2
Step-by-step explanation:
Answer:
(2x-5)^2 ITS A MINUS NOT A PLUS I JUST. DID HIS ANSWER HES WRONG APEX VERAFIED
Step-by-step explanation:
Find the value of x in ⊙Q .
Answer:
x= 5
Step-by-step explanation:
both lines are the same length
5x-6=2x+9
-2x -2x
3x-6= +9
+6 +6
3x = 15
÷3 ÷3
x= 5
The value of x is 5.
To find the value of [tex]\(x\)[/tex] in the given circle, we need to use the properties of the circle and the given information about the segments.
1. Given:
PM is a chord of the circle with center [tex]\(Q\)[/tex].
[tex]\(NL\)[/tex] is the perpendicular bisector of [tex]\(PM\)[/tex].
[tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], and [tex]\(T\)[/tex] lies on [tex]\(NL\)[/tex].
[tex]\(MT = 5x - 6\)[/tex] and [tex]\(TP = 2x + 9\)[/tex].
2. Key Properties:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have [tex]\(PT = TM\)[/tex].
The perpendicular bisector of a chord passes through the center of the circle, so [tex]\(NL\)[/tex] passes through [tex]\(Q\)[/tex].
3. Equating the Segments:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have:
[tex]\[ PT = TM. \][/tex]
Using the given expressions for [tex]\(MT\)[/tex] and [tex]\(TP\)[/tex]:
[tex]\[ MT = 5x - 6 \quad \text{and} \quad TP = 2x + 9. \][/tex]
Because [tex]\(T\)[/tex] is the midpoint, [tex]\(PT = TM\)[/tex].
Therefore, we have:
[tex]\[ PT = TM = 2x + 9. \][/tex]
Since [tex]\(MT = 5x - 6\)[/tex], and [tex]\(PT = TM\)[/tex], we have:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
4. Solving for [tex]\(x\)[/tex]:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
[tex]\[ 3x - 6 = 9. \][/tex]
[tex]\[ 3x = 15. \][/tex]
[tex]\[ x = 5. \][/tex]
If 5 friends want to share 1.25 of pizza evenly, how much pizza would each person get?
Answer:
0.25
Explanation: To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.
pls help! will give brainlist!
Answer:
Since this is a transversal, I am using certain rules to figure this out.
For example, angles 1 & 2 should equal 180 when added together, in the same way angles 11 & 12 should do the same thing!
Therefore, since angle 1 is 140°, angle 2 should be 40°, to complete it. This is the same for the other side!
Answer:
Angle2: 40
Angle11: 60
Step-by-step explanation:
ang1+ang2=180 (Linear pair)
140+ang2=180
ang2=40
ang2+ang9+ang11=180 (angle sum property)
40+80+ang11=180
ang11=180-120
ang11=60
Hope this helps...Pls mark as Brainliest!!
-1.5x + 2.5y + 3 = 0 6x - 10y + 6 = 0
Which statement about the pair of equations is true?
A) The equation pair has no solutions.
B) The equation pair has exactly 1 solution.
C) The equation pair has exactly 2 solutions.
D) The equation pair has infinitely many solutions.
Answer:
c
Step-by-step explanation:
hope it help
Answer:
i think the answer is B
Step-by-step explanation:
Lindsay bought 3 shirts for $15 each. The sales tax in Indiana is 7%. What is the total cost of her purchase?
Answer:
$48.15
Step-by-step explanation:
To work this out you will first need to work out the cost of the shirts. You can do this by multiplying 15 by 3, which gives you 45. The next step is to work out the percentages, however there are two methods you can use. Method 1 is easier and involves directly calculating the total. While Method 2 is to use the traditional method of working out the percentage and then adding it to the price of the shirts.
1) Multiply 15 by 3.
[tex]15*3=45[/tex]
Method 1:
The first step for method 1 involves converting the percentage into a decimal. You can do this by dividing 7 by 100, which gives you 0.07. This is because percentages are out of 100. the next step is to add 1 to 0.07, which is 1.07. This is because we are increasing the amount by 7%. You would then multiply 45 by 1.07, which gives you $48.15.
1) Divide 7 by 100.
[tex]7/100=0.07[/tex]
2) Add 1 to 0.07.
[tex]0.07+1=1.07[/tex]
3) Multiply 45 by 1.07.
[tex]45*1.07=48.15[/tex]
Method 2:
The first step for the second method you would first need to divide the percentage of 7 by 100, which gives you 0.07. Then you would multiply that by the amount of 45, which gives you 3.15. Then you would add 3.15 to 45, which gives you $48.15
1) Divide 7 by 100.
[tex]7/100=0.07[/tex]
2) Multiply 0.07 by 45.
[tex]0.07*45=3.15[/tex]
3) Add 3.15 to 45.
[tex]3.14+45=48.15[/tex]
One period of y= cos(2x) is graphed below.
What is the domain of y=cos(2)
A
[-2, 2]
B. [0,infinity)
C. (-infinity, infinity)
D. [0, pi]
Answer:
-oo, oo
Step-by-step explanation:
what is the greatest common factor of the expression below?
22x^5 + 20x
Answer:
the answer is 2x
Step-by-step explanation:
The greatest common factor of the expression 22x^5 + 20x is 2x. Both the numerical values and the variable components are considered to determine this.
Explanation:To find the greatest common factor of the expression, we need to identify the highest number and the highest power of variable that evenly divides both terms. In the case of the expression 22x^5 + 20x, the numerical part of the greatest common factor can be found by examining 22 and 20. The greatest common factor of 22 and 20 is 2. Next we need to look at the variables in each term, in this case 'x'. The highest power of 'x' that will divide both 'x^5' and 'x' is 'x' itself.
So, combining these two elements, the greatest common factor of the expression is 2x.
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there are 150 students in the marching band, and 30 of them play the trumpet. Which number line represents the percent of the srudents in the marching band who play the trumpet?
Answer:
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet.
Step-by-step explanation:
Draw two number lines:
One number line to represent number of students from 0 to 150. For convenience, divide the number line into intervals of 15 so that 30 is also present on the line.Second number line to represent percentage and divide it in intervals from 1 to 100.Now, place the other number line just below the other number line and draw a vertical line as shown the attached figure.
We find out that 30 is at 20% of 150.
It means that 20% (30 of total 150) of total 150 students in the marching band, play trumpet.
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet. Step-by-step explanation:
A bag contains 20 marbles of the same size that are blue, green, and red. The probability of picking a blue marble is 20%. The probability of picking a green marble is 50%. Determine the probability of picking a red marble from the bag and then classify the probability of picking a red marble as likely or not likely to occur.
:) Find the area of the triangle.
please, solve for x!
Answer:
I want brainliest!!! :)
Step-by-step explanation:
That angle is 90 degrees
x+18+x=90
2x=72
x=36
Factorize completely :
4x² - y² + 4y - 4
Answer:
(2x-y+2)(2x+y-2)
Step-by-step explanation:
4x² - y² + 4y - 4=
=(2x)²-(y²-4y+4)
=(2x)²-(y-2)²
= [2x-(y-2)][2x+(y-2)]
=(2x-y+2)(2x+y-2)
a²-b²=(a-b)(a+b)
Step-by-step explanation:
the answer is (2x-y+2) (2x+y-2)
Noah scores n points in a basketball game.
a. What does 15 < n mean in the context of the basketball game?
Answer: Noah scores more than 15 points.
Step-by-step explanation:
Hi, to answer this question we have to analyze the inequality:
15 < n
Where n are the scored points on a basketball game.
< means greater than.
So, in the context of the basketball game, it means that Noah scored more than 15 points.
Feel free to ask for more if needed or if you did not understand something.
The correct interpretation of 15 < n in the context of the basketball game is that Noah scores more than 15 points.
The inequality 15 < n indicates that the number of points Noah scores, represented by n, is greater than 15. This means that the actual number of points Noah scores must be any number that is a increment above 15, but cannot be 15 itself. For example, if Noah scores 16 points, 17 points, or any number of points greater than 15, the inequality 15 < n would be satisfied. It is a mathematical way of stating that Noah's score exceeds 15 points.
Fill in the blank.
A rectangular prism has a length of 11 centimeters, a width of 9 centimeters, and a height of 3 centimeters. Its volume is
a0 cubic centimeters.
Answer:
297 cubic centimeters
Step-by-step explanation:
volume is LWH
11*9*3 = 297
Answer:
297 cubic centimeters
Step-by-step explanation:
mark me brainy plz!
The perimeter of a rectangular Swimming pool is 70 yards.It's length Is 21 yards Which of the following Can be used to find the width? A. Width = ( 70 yd + 42 yd ) ÷ 2
B. Width = (70 yd + 42 yd ) ÷4
C. Width= (70 yd - 42 yd ) ÷4
D. Width= ( 70 yd - 42 yd ) ÷ 2
The width of the rectangular swimming pool is 14 yards.
Explanation:To find the width of the rectangular swimming pool, we can use the formula for the perimeter of a rectangle, which is P = 2(length + width). Given that the perimeter is 70 yards and the length is 21 yards, we can rearrange the formula to solve for the width:
P = 2(21 + w)
70 = 2(21 + w)
Divide both sides by 2:
35 = 21 + w
Subtract 21 from both sides:
14 = w
Therefore, the width of the swimming pool is 14 yards.
A stadium holds a total of 7,500 people. A random survey of 150 people finds that 17 of them are under 21 years old.
Enter the total number of people predicted to be in the stadium under 21.
Answer: 850 people
Step-by-step explanation:
Stadium capacity = 7,500 people.
A random survey was done for 150 people and it was found out that 17 of them are under 21 years old. This can be expressed as a fraction as:
= 17/150
The total number of people that are predicted to be in the stadium of under 21 will be:
= 17/150 × 7500
= 17 × 50
= 850 people
10.
The ratio of boys to girls in Mrs. Harrison's math classes is 5:7. If there are 120 students in an
of her classes, how many are boys.
Answer:
50 Boys
70 Girls
Step-by-step explanation:
Lets take the no. of boys = 5x
and girls = 7x
Total no. of students in ratio = 12x
Total no of students = 120
Therefore, 12x = 120
x = 10
So, no. of boys = 5x = 5*10 = 50
No. of girls = 7x = 7*10 = 70