Answer:
the sum of all possible values of x is: 2+6 = 8
Step-by-step explanation:
Assume the two points in your question are:
A [tex](x_{1},y_{1})[/tex] = (x,21)B [tex](x_{2}, y_{2})[/tex] = (4,7)=> The distance between the points A(x,21) and B(4,7) is [tex]10\sqrt{2}[/tex]
As we know, the distance of two points can be determined by this formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Apply this formula in this situation to find all possible values of x, we have:
[tex]\sqrt{(4-x)^{2} + (7-21)^{2} }[/tex] = [tex]\frac{10}{\sqrt{2} }[/tex]
<=> [tex](4-x)^{2} + 196 = 200[/tex]
<=> [tex](4-x)^{2} = 4[/tex]
<=> (4-x) = 2 or (4-x) = -2
<=> x = 2 or x = 6
=> the sum of all possible values of x is: 2+6 = 8
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
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
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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In a particular game, a spinner with four equally-sized sectors labeled 1, 3, 5, and 6 is spun twice. One turn is considered 2 spins of the spinner. If the sum of the spins is even, you move backward 6 spaces. Otherwise, you move forward 2 spaces. What is the mathematical expectation for the number of spaces moved in one turn? *
Answer:
3 spaces backwards, if you still need it.
Step-by-step explanation:
The mathematical expectation for the game described is -3 spaces, indicating that on average, a player will move 3 spaces backward per turn.
Expected Value Calculation:
To calculate the mathematical expectation for the number of spaces moved in one turn in the game described, we must consider all possible sums of the two spins and their outcomes. These outcomes are moving backward 6 spaces if the sum is even, or moving forward 2 spaces if the sum is odd. With a fair four-segment spinner that has equal likelihood for landing on numbers 1, 3, 5, and 6, we can calculate each possible sum and its associated probability.
Even sum outcomes: (1+3), (1+5), (3+5), (5+1), (3+1), (5+3), (1+6), (3+6), (5+6), and (6+6).Odd sum outcomes: (1+1), (3+3), (5+5), (6+1), (6+3), and (6+5).The probability of spinning an even sum is the number of even outcomes divided by the total number of outcomes (10/16). Similarly, the probability of spinning an odd sum is the number of odd outcomes divided by the total number of outcomes (6/16).
The expected value of moving spaces is therefore calculated by multiplying each sum outcome probability by the spaces moved for that outcome, and then summing these products:
Expected value = (Probability of even sum * -6 spaces) + (Probability of odd sum * 2 spaces)
= (10/16 * -6) + (6/16 * 2)
= (-60/16) + (12/16)
= (-48/16)
= -3
Thus, the mathematical expectation for the number of spaces moved in one turn is -3 spaces.
multiply 3x^2-2x and 2x^2+3x-1
Answer:
6[tex]x^{4}[/tex] + 5x³ - 9x² + 2x
Step-by-step explanation:
Given
(3x² - 2x)(2x² + 3x - 1)
Each term in the second factor is multiplied by each term in the first factor, that is
= 3x²(2x² + 3x - 1) - 2x(2x² + 3x - 1) ← distribute both parenthesis
= 6[tex]x^{4}[/tex] + 9x³ - 3x² - 4x³ - 6x² + 2x ← collect like terms
= 6[tex]x^{4}[/tex] + 5x³ - 9x² + 2x
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.
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.
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.
Can someone please help me with this?
Answer:
a. 3, 100 degrees
- I know 6 is 100 degrees and angle 3 is identical to angle 6. Therefore, angle 3 is 100 degrees.
b. 6, 100 degrees
- Angle 3 and 6 are identical. This means angle 6 is 100 degrees.
c. 4, 80
- Knowing a straight line is 180 degrees and all other angles are 100 degrees, I subtracted 180-100 = 80 degrees
Step-by-step explanation:
Everything was explained above, but be sure to know...
N
W E
S
- Hope that helps! Please let me know if you need further explanation.
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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Does the point (5, 10) satisfy the inequality y>x+5
What is the solution to the equation 2x+4 – 12 = 20?
N
X=2
X=9
Answer:
x=1 .
Step-by-step explanation:
b on edge 2020
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:
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:
Evaluate 1/2 t + 3/8 when t = 1/4
Answer:
1/2
Step-by-step explanation:
1/2 of 1/4 is 1/8
so 1/8 + 3/8 is 4/8
4/8 = 1/2
Answer:
1/2
Step-by-step explanation:
1/2t +3/8
Replace t with 1/4
1/2 x 1/4 + 3/8 (the x is the multiplication symbol)
Then multiply 1/2 and 1/4
1/8 +3/8
Then add.
4/8 = 1/2
P.S.
Hope this helps you and explains the answer! Have a great day and stay safe!
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.
:) Find the area of the triangle.
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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evalulate 3*5-2*(3+2)
Answer:
5
Step-by-step explanation:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Following the order, first is parenthesis:
3 · 5 - 2(5)
Multiplication:
15 - 10
5
A company mixes two kinds of cleansers to get a blend they sell for 59 cents a liter. One of the cleansers costs 50 cents per liter, and the other 80 cents per liter. How much of each kind should be mixed to get 2,000 liters of the blend?
Answer:
Cleanser that costs 50 cents is 1400 liters, Cleanser that costs 80 cents is 600 liters.
Step-by-step explanation:
We can solve this by using simultaneous equations:
Let us express the question in terms of equationsLet a be cleanser at 50 cents and let b be the cleanser at 80 cents.
Equation 1: 0.5a + 0.8b = 0.59(a+b)
Equation 2: a + b = 2000
From equation 2, a = 2000 - b (Let's call this equation 3)
2. Substituting equations 2 and 3 in Equation 1:
0.5a + 0.8b = 0.59(a+b)
0.5(2000 - b) + 0.8b = 0.59(2000)
1000 - 0.5b + 0.8b = 1180
0.3b = 180
b = 600
Substitute in equation 3:
a = 2000 - 600
a = 1400
As a note, I formed equation 1 because I know for a fact the cost per liter of a and b. I also know it is sold at 0.59 cents per liter. We are selling 2000 liters in this instance, therefore 0.59(2000) = 1180, which in this case is the selling price.
Final answer:
To create 2,000 liters of a cleanser blend sold at 59 cents per liter, the company should mix 800 liters of the 50-cent cleanser with 1,200 liters of the 80-cent cleanser, using a system of equations.
Explanation:
How to Mix Cleansers for a Desired Cost
To solve this problem, we need to set up a system of equations that reflects the cost and the quantity of the blend we want to obtain. Let's assign x to represent the amount in liters of the 50 cents per liter cleanser and y to represent the amount in liters of the 80 cents per liter cleanser.
Following the premise of the problem, we have two equations:
The total amount of the mixture should be 2,000 liters:
x + y = 2,000
The cost for the blend per liter is 59 cents, so the total cost for 2,000 liters would be 2,000 * $0.59. The sum of the individual costs of cleansers multiplied by their respective volumes should equal this total cost:
0.50x + 0.80y = 2,000 * $0.59
Solving this system of equations, we find that:
x = 800 liters of the 50 cents cleanser
y = 1,200 liters of the 80 cents cleanser
Thus, the company should mix 800 liters of the 50-cent cleanser with 1,200 liters of the 80-cent cleanser to obtain 2,000 liters of the blend sold for 59 cents a liter.
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.
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)
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:
-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:
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)
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]
A square with diagonals is shown. The distance from one point to the middle point is 3. The length from the center point to another point is 3. What is the approximate side length of the square?
Answer:
4.24
Step-by-step explanation:
Since it is the midpoint, it means that the entire diagonal will measure twice, that is 3 * 2 = 6
To calculate the length of the sides, we can do it by means of Pythagoras, since it is a square a = b
c ^ 2 = a ^ 2 + b ^ 2
c ^ 2 = 2 * a ^ 2
6 ^ 2 = 2 * a ^ 2
a ^ 2 = 36/2
a = 4.24
therefore, it means that the sides of the square measure 4.24
Answer:
Answer: C (3rd option)
Step-by-step explanation:
E2020
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.
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
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