The Distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.
The distance between two points in a coordinate plane. The distance formula is based on the Pythagorean theorem and calculates the straight-line distance between two points.
The coordinates of the first point as (x1, y1) = (4, -2) and the coordinates of the second point as (x2, y2) = (7, -9).
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
d = sqrt((7 - 4)^2 + (-9 - (-2))^2)
d = sqrt((3)^2 + (-7)^2)
d = sqrt(9 + 49)
d = sqrt(58)
Hence, the distance between the points (4, -2) and (7, -9) is sqrt(58) or approximately 7.62 units.
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The volume V, of a cylinder is V=pie times radius to the power of 2 h, where r is the radius of the cylinder and h is the height. Using rounding to the nearest whole number, which of the following is an estimate of the volume of a cylinder with a radius of 3.75 inches and height of 6.21 inches
Answer:
[tex]274\,\text{in}^3[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3[/tex]
Lasting Company purchases a computerized manufacturing machine for $60,000 to use in operating activities for the next five years. It estimates the equipment’s salvage value at $5,000. The machine is estimated to produce 220,000 units over its useful life. In year 1 it produced 36,000 units, in year 2: 44,000 units, in year 3: 52,000 units, in year 4: 60,000 units and in year 5: 32,000 units.
Prepare a table showing depreciation expense, accumulated depreciation and book value for each year assuming units of production depreciation.
The deprecation expenditure for each time is calculated by multiplying the number of units produced in that time by the deprecation per unit($0.25).
Time Units Produced deprecation expenditure Accumulated Depreciation Book Value
1 36,000$ 9,000$ 9,000$ 51,000
2 44,000$ 11,000$ 20,000$ 40,000
3 52,000$ 13,000$ 33,000$ 27,000
4 60,000$ 15,000$ 48,000$ 12,000
5 32,000$ 8,000$ 56,000$ 4,000
To calculate deprecation expenditure using the units of product system, we need to determine the deprecation per unit produced. Then is how we can calculate it deprecation per unit = ( original cost- Salvage value)/ Total estimated units produced = ($ 60,000-$ 5,000)/ 220,000 = $ 55,000/ 220,000 = $0.25 per unit
Now we can prepare the table showing deprecation expenditure, accumulated deprecation, and book value for each time Time Units Produced deprecation expenditure Accumulated Depreciation Book Value
1 36,000$ 9,000$ 9,000$ 51,000
2 44,000$ 11,000$ 20,000$ 40,000
3 52,000$ 13,000$ 33,000$ 27,000
4 60,000$ 15,000$ 48,000$ 12,000
5 32,000$ 8,000$ 56,000$ 4,000
The deprecation expenditure for each time is calculated by multiplying the number of units produced in that time by the deprecation per unit($0.25). Accumulated deprecation is the sum of the deprecation charges from all former times. Book value is calculated by abating the accumulated deprecation from the original cost($ 60,000).
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Can someone answer this question?
Between 40 and 60 minutes the target heart rate strictly increasing then strictly decreasing. Therefore, option B is the correct answer.
From the given graph, in the first curve between the interval 0-10 speed is increasing, between the interval 10-30 speed is constant and between the interval 30-40 speed is decreasing.
In the second curve between the interval 40-50 speed is increasing, between the interval 50-60 speed is decreasing, between the interval 60-65 speed is increasing and between the interval 65-73 speed is constant.
In the third curve between the interval 73-85 speed is increasing, between the interval 85-92 speed is constant and between the interval 92-100 speed is decreasing.
Therefore, option B is the correct answer.
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Can someone answer this question?
The graph that best represents a quadratic function that has only one zero is Option C.
We are given that;
The four graphs of the function
Now,
A quadratic function has only one zero if its graph intersects the x-axis at only one point. This occurs when the discriminant of the quadratic equation is equal to zero:
b^2 - 4ac = 0
x = (-b ± sqrt(b^2 - 4ac)) / 2a
If the discriminant is equal to zero, then there is only one solution to the quadratic equation, which means that the graph of the quadratic function intersects the x-axis at only one point.
Therefore, by the given graphed function the answer will be Option C.
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A grocer purchased 75kg of sugar at Rs.30 per kg and mixed it with 25 kg of sugar at Rs.36 per kg. At what rate should he sell the mixture to gain 10%.
Select one:
Rs.32.20
None of these
Rs.32.85
Rs.32.45
Rs.32.60
Answer:
None of these
Step-by-step explanation:
Step 1:
75 kg x Rs.30 = 2250
25 kg x Rs.36 = 900
Total Cost Price = 2250 + 900 = Rs.3150.
Cost Price per Kg = 3150 / 100 = 31.5
Gain of 10% will be;
31.5 x 10 / 100 = 3.15
Cost Price with gain of 10% will be = 31.5+3.15 = Rs. 34.65.
Answer:
Hence, The correct option is (B), NONE OF THESE
Step-by-step explanation:
Make a plan:
In this question, we need to calculate the cost price and selling price of the mixture.Then we can get the selling price of the mixture by adding 10% profit to the cost price.Finally, we can calculate the rate of the mixture.Solve the Problem:
The cost price of 75 kg of sugar at Rs30 per kg is:
75 * 30 = 2250
The cost price of 25 kg of sugar at Rs
36 per kg is:
25 * 36 = 900
The total cost price of the mixture is:2250 + 900 = 3150
To gain 10% profit, the selling price of the mixture is:3150 * 1.1 = 3465
The total weight of the mixture is:75 + 25 = 100 kg
The rate of the mixture is:3465 / 100 = 34.65
Draw the conclusion:
The rate at which he or she should sell the mixture to gain 10% is:Rs 34.65
Hence, The correct option is (B) NONE OF THESE.
Hope this helps!
Can someone answer this question?
The second one is the answer just think of symmetry and if its symmetrical or not.
Answer:
The answer is A
Step-by-step explanation:
Odd symmetry is like the opposite of one side
What is the Cubed root of -108
Answer:
about -4.7622
Step-by-step explanation:
You want the cube root of -108.
CalculatorYour calculator will tell you the cube root of -108 is about -4.7622.
__
Additional comment
Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.
The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...
∛-108 = -3∛4
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When asked their favorite color, 20 students said red, 23 students said blue,
25 students said green, and 28 students said yellow. Students with which
favorite color would be represented by the largest wedge in a pie chart?
OA. Blue
OB. Yellow
OC. Green
D. Red
Answer: B. Yellow
Step-by-step explanation: Yellow has the largest number of students out of the entire data set, so it will consume the largest area on a pie chart.
Answer:
A pie chart is a type of graph that shows the relative sizes of different categories of data by dividing a circle into sectors or slices. Each sector represents a fraction of the whole circle, which is equal to 100%. The angle of each sector is proportional to the percentage of the data it represents. To answer a question based on a pie chart, we need to compare the sizes of the sectors and find the one that matches the given condition.
For example, consider the following question:
When asked their favorite color, 20 students said red, 23 students said blue,
25 students said green, and 28 students said yellow. Students with which
favorite color would be represented by the largest wedge in a pie chart?
To answer this question, we need to find the total number of students who participated in the survey. We can do this by adding up the numbers of students who chose each color:
20 + 23 + 25 + 28 = 96
Next, we need to find the percentage of students who chose each color by dividing the number of students by the total and multiplying by 100:
Red: (20 / 96) x 100 = 20.83%
Blue: (23 / 96) x 100 = 23.96%
Green: (25 / 96) x 100 = 26.04%
Yellow: (28 / 96) x 100 = 29.17%
Finally, we need to compare the percentages and find the largest one. In this case, it is yellow with 29.17%. Therefore, students who chose yellow as their favorite color would be represented by the largest wedge in a pie chart.
The answer is B. Yellow.
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The rational function has an x-intercept at (-2,0) and vertical asymptotes at x = 5 and x = 1.
Write an equation that could represent this function.
The equation f(x) = k * (x + 2) / [(x - 5) * (x - 1)] could represent the given rational function with an x-intercept at (-2, 0) and vertical asymptotes at x = 5 and x = 1.
To write an equation that represents the given rational function with an x-intercept at (-2, 0) and vertical asymptotes at x = 5 and x = 1, we can start by considering the factors in the numerator and denominator of the function.
Since the function has an x-intercept at (-2, 0), it means that the numerator of the function has a factor of (x + 2).
Since the function has vertical asymptotes at x = 5 and x = 1, it means that the denominator of the function has factors of (x - 5) and (x - 1).
Putting these factors together, the equation that could represent this function is:
f(x) = k * (x + 2) / [(x - 5) * (x - 1)]
Here, k represents a constant multiplier that scales the function, and it can be any non-zero constant value.
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All of these top 3 areas that the federal goverment spends tax money on except
All of these are top 3 areas that the federal government spends tax money on EXCEPT: Option B: Education
What is the tax money?The three primary sectors where tax money is generally allocated by the federal government are Social Security, Medicaid, and the armed forces.
Nevertheless, education would be the only circumstance that deviates from the aforementioned rule. Although education is crucial for government investment, it is usually not among the primary three fields in regards to federal spending.
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See text below
All of these are top 3 areas that the federal government spends tax money on EXCEPT:
Social Security
Education
Medicaid
Military
Use the probabilities to find the missing values P(B A + 7/17
The given probability is P(B | A) = 7/17.
To find the missing values, we need additional information about the probabilities of events A and B individually. Specifically, we need either P(A) or P(B) or both.
The probability notation P(B | A) represents the conditional probability of event B occurring given that event A has already occurred. It can be interpreted as the probability of event B happening "under the condition" that event A has already taken place.
Without the probabilities of A and B individually, we cannot determine the missing values or calculate the probabilities directly.
If you have additional information or specific values for P(A) or P(B), please provide them so that I can assist you further in calculating the missing values.
A store owner want to develop a new snack mix by mixing chocolate and trail mix. How many pounds of chocolate costing $14.60 per pound should be mixed with 12 pounds of trail mix costing $4.40 per pound to create a mixture worth $9.70 per pound? (round to the nearest pound)
Answer:
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] pound chocolate
Let x be the number of pounds of chocolate that needs to be mixed.
The cost of the chocolate is $14.60 per pound, so the cost of x pounds of chocolate is 14.6x dollars.
The cost of the trail mix is $4.40 per pound, so the cost of 12 pounds of trail mix is 4.4(12) = 52.8 dollars.
The cost of the mixture is $9.70 per pound, so the cost of (x + 12) pounds of the mixture is 9.7(x + 12) dollars.
We can set up an equation based on the fact that the total cost of the mixture equals the sum of the costs of the individual components:
14.6x + 52.8 = 9.7(x + 12)
Simplifying and solving for x, we get:
14.6x + 52.8 = 9.7x + 116.4
4.9x = 63.6
x = 12.98
Rounding to the nearest pound, we get x = 13.
Therefore, the store owner should mix 13 pounds of chocolate with 12 pounds of trail mix to create a mixture worth $9.70 per pound.
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 what is the value of X in the equation when Y =3 and z=125 show and explain how you got your answer
x^3 = 125 use 125 = 5^3
x^3 = 5^3 We know that if a^n = b^n then a = bx = 5
Please help me with this question
π×2x÷2×2x÷2×v
3.14×(2x÷2)^2×v
The volume of a cylinder is base are of a circle multiplied by the height of the cylinder
.......................................................................................................
Answer:
1640
Step-by-step explanation:
Are of the square
a = [tex]s^{2}[/tex]
a = [tex]10^{2}[/tex]
a = 100
Area of a trapezoid
a = 1/2(a + b)h
a = 1/2(48 + 40)35
a = 1/2 (48 + 40)35
a = 1/2(88)35
a = 44(35)
a = 1540
100 + 1540 = 1640
Helping in the name of Jesus.
Answer:
The area is 1640 square meters
Step-by-step explanation:
the area of the short block(top right) is
[tex](10)(10) = 100\\[/tex]
Now, the total length of the top side is(of the bottom portion),
38 + 10 = 48
We can divide the bottom portion into a square and triangular part,
for the square part we get the area,
[tex](40)(35)=1400[/tex]
For the triangle, we first have to find the length of the base,
which we see from the figure that it will be,
48 - 40 = 8
(and height is 35)
so the area of the triangle is,
[tex](1/2)(8)(35)=140[/tex]
so the total area of the park is
[tex]140 + 1400 + 100 = 1640[/tex]
If f(x)=7+4x and g(x)=1/2x, what is the value of {f/g}(5)?
Answer:
the value of {f/g}(5) is 10.8.
Step-by-step explanation:
To find the value of {f/g}(5), we need to evaluate the function f(x)/g(x) at x = 5.
First, let's calculate f(5) and g(5):
f(5) = 7 + 4(5) = 7 + 20 = 27
g(5) = (1/2)(5) = 5/2 = 2.5
Now, we can find {f/g}(5) by dividing f(5) by g(5):
{f/g}(5) = f(5) / g(5) = 27 / 2.5 = 10.8
If the function f(x)=7+4x and g(x)=1/2x, the value of {f/g}(5) is 10.8.
To calculate the value of {f/g}(5), substitute x = 5 into the expression for f(x) and g(x) and then divide f(5) by g(5).
Given that:
f(x) = 7 + 4x
g(x) = (1/2)x
f(5) = 7 + 4(5)
= 7 + 20
= 27
So,
g(5) = (1/2)(5)
= 5/2
= 2.5
Hence,
{f/g}(5) = f(5) / g(5)
= 27 / 2.5
= 10.8
Thus, 10.8 is the value of {f/g}(5).
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Marsha saves $92 during her first
month at a new job. If she increases the amount she saves by 20% each month,how much will she have saved after 3 months?
Answer:
a
Step-by-step explanation:
a
If x^2+y^2=14 and xy = 5, find the value of (1/2 x+1/2 y)^2
Answer:
6
Step-by-step explanation:
The explanation is attached below.
HELP.
Solve and write the solution in interval notation
The solution in interval notation is (-∞, -8/45).
To solve the equation 12x + 77x + 22 < 1 + 6x - 8x + 5, we can simplify both sides:
12x + 77x + 22 < 1 + 6x - 8x + 5
Combining like terms:
89x + 22 < -x + 6
89x + x < 6 - 22
90x < -16
Divide both sides by 90:
x < -16/90
Simplifying the fraction:
x < -8/45
Therefore, the solution in interval notation is (-∞, -8/45).
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Please help fast! I need answers quickly.
The 3 options that are like terms are:
3x⁴ and 2x⁴
2x² and 3x²
2x and 3x
Which ones are like terms?Two terms are like terms if the powers of the variable are the same ones, so for example, if in both sides we have x², then these are like terms.
Then the options that are like terms are:
3x⁴ and 2x⁴
2x² and 3x²
2x and 3x
These are the 3 correct options.
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b) Find the least number that must be subtracted from 2120 so that the result is a perfect square.
Answer:
4
Step-by-step explanation:
2120 - 4 = 2116
[tex]\sqrt{2116} =46[/tex]
[tex]46^{2} =2116[/tex]
Hope this helps
A washer and dryer cost a total of 928$. The cost of the washer is three times the cost of the dryer. Find the cost of each item.
washer + dryer = 1104
dryer = x
washer = 3x
3x + x = 1104
4x= 1104
x = 276 = dryer
washer = 3x = 3(276)= 828
For many years, organized crime ran a numbers game that is now run legally by many state governments. The player selects a three-digit number from 000 to 999. There are 1000 such numbers. A bet of is placed on a number, say number 115. If the number is selected, the player wins $. If any other number is selected, the player wins nothing. Find the expected value for this game and describe what this means.
The average amount the player can expect to win or lose per game over the long run. In this game, the Expected value is x/1000.
The expected value for the numbers game, we need to calculate the weighted average of the possible outcomes.
In this game, there are 1000 possible numbers that can be selected, ranging from 000 to 999. If the player selects the winning number, they win a certain amount, and if they select any other number, they win nothing.
Let's assume the amount won is $x when the winning number is selected
The probability of selecting the winning number is 1/1000 because there is only one winning number out of the 1000 possible numbers.
The probability of not selecting the winning number is 999/1000 because there are 999 other numbers that can be selected.
The expected value (EV) can be calculated using the following formula:
EV = (Amount won if winning number is selected) * (Probability of winning) + (Amount won if losing number is selected) * (Probability of losing)
In this case, the EV is:
EV = (x * 1/1000) + (0 * 999/1000)
= x/1000
The average amount the player can expect to win or lose per game over the long run. In this game, the expected value is x/1000.
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the equation given: f(x) = 2/x-2 +2
sketch the following:
1. y = f(x-2)
2. y = f(x-1) - 3
To sketch the given equations, we will start with the graph of the original function f(x) = 2/(x-2) + 2 and then apply the necessary transformations.
1. y = f(x-2):
To sketch y = f(x-2), we need to shift the graph of f(x) two units to the right. This can be done by replacing x in the equation f(x) with (x-2). The equation becomes y = f(x-2) = 2/((x-2)-2) + 2 = 2/(x-4) + 2.
2. y = f(x-1) - 3:
To sketch y = f(x-1) - 3, we need to shift the graph of f(x) one unit to the right and three units downward. This can be done by replacing x in the equation f(x) with (x-1) and subtracting 3 from the result. The equation becomes y = f(x-1) - 3 = 2/((x-1)-2) + 2 - 3 = 2/(x-3) - 1.
Now, let's plot these equations on a graph:
Note: The graph of the original function f(x) = 2/(x-2) + 2 should be sketched first before applying the transformations.
Kindly Heart and 5 Star this answer, thanks!Juanita has 3 rectangular cards that are 3 inches by 6 inches. How can she arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter? How will the area of the polygon compare to the combined area of the 3 cards? what is the answer
Answer:
Step-by-step explanation:
Given
3 rectangular cards
each card is 8 inches by 9 inches
The way that she can arrange the cards, without overlapping, to make one larger polygon with the smallest possible perimeter is that:
Put 3 cards together according to the length
So the smallest possible perimeter is:
8 + 8 + 8 + 8 + 8 + 8 + 9 + 9 = 66 inches as you can see in the attached photo.
The area of the polygon is equal to the combined area of the 3 cards without overlapping or extending.
Eliminate the parameter.
x=cost, y=tant
Please give step-by-step.
We have eliminated the parameter from the given parametric equations:
x = cost,
y = tant,
To eliminate the parameter from the given parametric equations:
x = cost,
y = tant,
We can use the trigonometric identity:
tant = sint/cost.
Substitute the value of tant in terms of x and y using the trigonometric identity:
y = sint/x.
Rearrange the equation to solve for sint:
sint = y × x.
Substitute the value of sint back into the trigonometric identity to find the expression for cost:
[tex]cost = x / \sqrt{(1 + (y \times x)^2).}[/tex]
Therefore, by following these steps, we have eliminated the parameter from the given parametric equations:
x = cost,
y = tant,
and obtained the equations:
[tex]cost = x / \sqrt{(1 + (y \times x)^2),} \\sint = y \times x.[/tex]
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please please help!! i can’t find anything for this anywhere! :((
find x
The value of x in the triangle is x=3
In the given triangle a midline passing through the middle iof the triangle makes the triangle in to two triangles.
By midpoint segment theorem
x=1/2(x+3)
Apply distributive property
x=x/2+3/2
Take the variable terms on one side and constant on other side
x-x/2=3/2
x/2=3/2
We get the value of x as three
x=3
Hence, the value of x in the triangle is x=3
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4p + 4q = 1
7 = 3p + 2q
Find q, round answer to 1 decimal place.
Answer:
Step-by-step explanation:
4p+4q=1 -------- equation 1 -------*+3
3p+2q=7 --------equation 2 -------* +4
12p+12q=3 ------equation 3
( - )
12p +8q=28 -----equation 4
----------------------
4q = -25
q= -25/4
q = -6.25
substitute q = -6.25 into equation 1
4p + 4q = 1
4p + 4( - 6.25 ) = 1
4p - 25 = 1
4p = 25 + 1
4p = 26
p = 26/4
p = 6.5
therefore p = 6.5, q = -6.25
q to 1 deimal place = -6.3
Ashira bought a game system for $280 on the installment plan. She will pay $55 for 6 months.
How much is Ashira's finance charge?
$75.20
$44.88
$50
Answer:
Therefore, Ashira's finance charge is $50.
Step-by-step explanation:
To calculate Ashira's finance charge, we need to find the total amount she will pay for the game system through the installment plan and subtract the original purchase price.
Total amount paid = Monthly payment * Number of months
Total amount paid = $55 * 6
Total amount paid = $330
Finance charge = Total amount paid - Purchase price
Finance charge = $330 - $280
Finance charge = $50
Therefore, Ashira's finance charge is $50.
The equations that represent the balance in three different savings
accounts x years after 2012,
A(x) = 900(1.05)*
B(x)= 1100(1.038)*
C(x) = 5000(0.85)*
Which of the following statements are TRUE? Check all that apply.
The balance of Account A is growing at a rate of 5% per year.
Account C had the largest balance in the year 2012.
Account A is growing faster than account B.
The balance of Account C is decreasing at a rate of 85% per year.
The true statements are: The balance of Account A is growing at a rate of 5% per year. Account A is growing faster than Account B.
Let's analyze each statement one by one:
The balance of Account A is growing at a rate of 5% per year.
This statement is true. The equation for Account A is A(x) = 900(1.05)^x, where x represents the number of years after 2012. The term (1.05)^x accounts for the growth rate of 5% per year.
Account C had the largest balance in the year 2012.
This statement cannot be determined based on the given information. The equations only provide the balance after a certain number of years, but they do not provide the balances in the year 2012. Without the initial balances, we cannot determine which account had the largest balance in 2012.
Account A is growing faster than Account B.
This statement is true. Comparing the growth rates in the equations, we can see that the growth rate of Account A is 5% per year (multiplied by 1.05), while the growth rate of Account B is 3.8% per year (multiplied by 1.038). Therefore, Account A is growing faster than Account B.
The balance of Account C is decreasing at a rate of 85% per year.
This statement is false. The equation for Account C is C(x) = 5000(0.85)^x, where x represents the number of years after 2012. The term (0.85)^x represents a decrease of 15% per year, not 85% per year. Therefore, the balance of Account C is decreasing at a rate of 15% per year, not 85% per year.
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