Answer
CD is 17,0
The point -2,19
Step-by-step explanation:
In a 30-60-90 triangle, the hypotenuse is 20 feet long. Find the length of the length of the long leg and the short leg
An illusionist needs up to 10 volunteers for a show. She needs no fewer than 4 female volunteers. Let x represent the number of female volunteers and y represent the number of male volunteers.
Which inequalities model the situation?
Choose exactly three answers that are correct.
A- x + y < 10
B- x + y ≤ 10
C- x > 4
D- x ≥ 4
E- y > 0
G- y ≥ 0
The answer is
x ≥ 4
x + y ≤ 10
y ≥ 0
Find the length of arc XPY.
Answer:
Arc length XPY =28.26 m.
Step-by-step explanation:
Given : A circle with two arc XY and XPY and radius 6 m.
To find : Arc length XPY.
Solution : We have given that arc XY and XPY .
Radius = 6 m.
Central angle formed by arc XPY = 360 - 90 = 270.
Arc length = 2 *pi* r ( [tex]\frac{central\ angle}{360}[/tex].
Plugging the values
Arc length = 2 *3.14 * 6 ( [tex]\frac{270}{360}[/tex].
Arc length =37.68 ( [tex]\frac{3}{4}[/tex].
Arc length =37.68 * 0.75
Arc length XPY =28.26 m.
Therefore, Arc length XPY =28.26 m.
Answer:
The length of arc XPY=28.26 m
Step-by-step explanation:
We are given that a circle in which
Radius=6 m
Central angle made by arc XPY=[tex]360-90=270^{\circ}[/tex]
We have to find the length of arc XPY.
We know that
Arc length formula:[tex]\frac{central\;angle}{360^{\circ}}\times 2\pi r[/tex]
Substitute the value in the formula then we get
Length of arc XPY=[tex]\frac{270}{360}\times 2\times 3.14 \times 6=28.26 m[/tex] ([tex]\pi=3.14[/tex])
Hence, the length of arc XPY=28.26 m
1. 8q + 6; q = 2
10
14
20
22
2. 9 + 4g; g = −3
–3
3
21
13
3. 7x – 7; x = 4
0
21
35
28
4. 10 – 3.2n; n = 2
6.8
3.6
13.2
16.4
5. 12p + 4; p = 1.5
14
16
18
22
For questions 6–10, solve the equation using number sense.
6. 5w + 10 = 40
6
10
30
50
7. 4y – 12 = 60
12
18
48
72
8. 10k + 5 = 65
6
7
60
70
9. 2b – 15 = 33
4
9
24
48
10. 3d + 18 = 21
–1
1
3
13
help
Ann worked 20 hours and made $200. how much money does she make per hour?
Find (fg)(-4) when f(x) = x + 5 and g(x) = 5x2 + 10x - 5.
Grandpa's age is 6 yrs less than 6 times junior's age. The sum of their age is 78. find each of their ages?
6/7 times 5/6 simplest form
Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation? a. {−12, −2} b. {−7, 7} c. {−6, −4} d. {−5, 5}
First, rearrange the equation so that only zero will be on the right side:
x^2 + 14x +24 = 0
Let the coefficients be:
a = 1
b = 14
c = 24
To complete the square, add (b/2)^2 to both sides of the equation:
(b/2)^2 = 49
x^2 + 14x + 49 + 24 = 49
x^2 + 14x + 49 = 25
(x+7)^2 = 25
Therefore, the solution set of the equation is {-12, -2}
The solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
x² + 14x = −24
It is required to solve the equation by completing the square.
First, arrange the quadratic equation
x² + 14x + 24 = 0
x² + 14x + 7² - 7² + 24 = 0
(x + 7)² -25 = 0
(x + 7)² = 25
x + 7 = ±5
Taking positive sign:
x + 7 = 5
x = -2
Taking negative sign:
x + 7 = -5
x = -12
The solution set is [-12, -2]
Thus, the solution set of the quadratic equation x² + 14x = −24 is [-12, -2] option (a) is correct.
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How do you express a mass of 5.712 grams in miligrams and in kilograms???
A manufacturer of mountain bikes has found that when 20 bikes are produced per day, the average cost is $200 and the marginal cost is $150. Based on the information, approximate the total cost of producing 21 bikes per day. ...?
Lara Otero is employed by Parks Inc. She is on a single plan with a PPO annual premium of $6,009. Lara's employer pays 75% of the total cost. Her contribution is deducted from her paycheck. What is Lara's semimonthly deduction?
The answer is $62.59
Which is greater 77% or 3/5
To compare 77% and 3/5, we convert them to the same format. 77% is equivalent to 77/100 and 3/5 is equivalent to 60/100, or 60%. Therefore, 77% is greater than 3/5.
Explanation:
In order to compare 77% and 3/5, you should convert them both to the same format. Percentages are a way of expressing a number as a fraction of 100. Hence, 77% can be written as 77/100.
Similarly, the fraction 3/5 remains as is, which is equivalent to 60/100, or 60% when converted into a percentage.
Comparing these values, it is clear that 77% is greater than 3/5, or 60%.
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Final answer:
After converting 3/5 to a percent (60%), we can see that 77% is greater than 60%, making 77% the greater value.
Explanation:
To determine which is greater, 77% or 3/5, we need to compare them either as percentages or as decimals. First, let's convert 3/5 to a percent. To do this, we divide the numerator by the denominator to get the decimal: 3 ÷ 5 = 0.6. Then, we convert the decimal to a percent by multiplying by 100: 0.6 × 100 = 60%.
Now that we have both numbers as percentages, we can easily compare them: 77% is greater than 60%. Therefore, 77% is greater than 3/5.
A light bulb consumes 18900 watt-hours in 5 days and 6 hours. How many watt-hours does it consume per day?
Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years. Approximately what is the minimum simple interest rate Maggie needs to reach her goal? a. 2.89% b. 3.55% c. 4.95% d. 5.18%
Answer
Find out the what is the minimum simple interest rate Maggie needs to reach her goal .
To proof
Formula
[tex]Simple\ interest = \frac{principle\times rate\times time}{100}[/tex]
As given
Maggie has $14,100 to invest, and wishes to gain $4,000 in interest over the next eight years.
put all the values in the formula
[tex]4000 = \frac{14100\times rate\times 8}{100}[/tex]
Solving
[tex]rate = \frac{4000\times 100}{14100\times8}[/tex]
solving the above
[tex]rate = \frac{400000}{112800}[/tex]
rate =3.55% (approx)
the minimum simple interest rate Maggie needs to reach her goal is 3.55% .
Option (b) is correct .
Hence proved
Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.
For a rectangle with a given area, the smallest possible perimeter is achieved when the rectangle is a square. Hence, for a rectangle with an area of 343 m², the dimensions that give the smallest perimeter are approximately 18.5 m x 18.5 m.
Explanation:The subject of this question is related to the optimization problems in Calculus. Given that the area of a rectangle is 343 m², we are looking for the smallest possible perimeter. The area of a rectangle can be defined as the product of its length and width (l*w), and the perimeter is defined as the sum of all sides (2l + 2w).
According to the properties of rectangles, a rectangle will have the smallest possible perimeter if it is a square, because rectangles with the same area have larger perimeters as their shapes become more elongated.
So, if the rectangle is a square, its area is side² or s². Given that the area is 343 m², s² = 343, thus the side s equals the square root of 343, which is approximately 18.5202591775 meters. Therefore, the dimensions of the rectangle with the smallest possible perimeter are approximately 18.5 m × 18.5 m.
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A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b.
The moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]
To find the moment of inertia I of the thin rectangular sheet of metal about an axis passing through its center and parallel to the side with length b, we can use the parallel axis theorem.
This theorem states that the moment of inertia about any axis parallel to the axis passing through the center of mass can be found by adding the moment of inertia about the center of mass and the product of the mass and the square of the perpendicular distance between the two axes.
The moment of inertia of a thin rectangular plate about its center and perpendicular to its plane is given by:
[tex]\[ I_c = \frac{M}{12}(a^2 + b^2) \][/tex]
where M is the mass of the plate, a and b are the lengths of the sides of the rectangle.
Now, let's denote d as the perpendicular distance between the axis passing through the center and the axis parallel to the side with length b. Since the axis is passing through the center of the rectangle, d is half the length of side a, so [tex]\( d = \frac{a}{2} \)[/tex].
Using the parallel axis theorem, the moment of inertia about the desired axis is:
[tex]\[ I = I_c + Md^2 \][/tex]
[tex]\[ I = \frac{M}{12}(a^2 + b^2) + M\left(\frac{a}{2}\right)^2 \][/tex]
[tex]\[ I = \frac{M}{12}(a^2 + b^2) + \frac{M}{4}a^2 \][/tex]
[tex]\[ I = \frac{Ma^2}{12} + \frac{Mb^2}{12} + \frac{3Ma^2}{12} \][/tex]
[tex]\[ I = \frac{Ma^2}{4} + \frac{Mb^2}{12} \][/tex]
Thus, the moment of inertia of the thin rectangular sheet of metal about the specified axis is[tex]\( \frac{Ma^2}{4} + \frac{Mb^2}{12} \).[/tex]
Which row of Pascal’s triangle would you use to expand (2x 10y)15?
The correct answer is:
Row 15.
Explanation:
Each row of Pascal's triangle corresponds with the exponent of a binomial. The first row is a binomial to the first power; the second row, to the second power; the third row, to the third power; etc.
For the 15th power, we would want the 15th row of the triangle.
Why can't quadrilaterals have four obtuse angles?
Describe a strategy for converting a rate measured in one pair of units to rate measured in a diferrent pair of unit. for example how would you convert ounces per cup to pound per gallon
Final answer:
One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. The conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.
Explanation:
One strategy for converting a rate measured in one pair of units to a rate measured in a different pair of units is to use unit analysis. This involves setting up conversion factors to cancel out the unwanted units. Here's an example:
Given the rate of ounces per cup, we know that there are 8 fluid ounces in 1 cup.To convert to pounds per gallon, we need to find the conversion factor between ounces and pounds, which is 16 ounces per pound.We also need to find the conversion factor between cups and gallons, which is 16 cups per gallon.Now, set up the conversion factor using unit analysis: 8 fl oz × 1 lb / 16 fl oz × 16 cups / 1 gal.Cancel out the unwanted units: 8 lb / 16 gal.Simplify the expression: 1 lb / 2 gal.Therefore, the conversion from ounces per cup to pounds per gallon is 1 lb / 2 gal.
If x<0 and y>0, determine the sign of the real number x-y/xy ...?
The real number resulting from the expression x-y/xy is positive when x is negative and y is positive. This is determined by following the rules of signs in arithmetic where subtracting a positive number from a negative results in a negative and dividing a negative number by another negative results in a positive.
Explanation:The given expression in question is x-y/xy. To understand the sign of the resulting real number we have to discern the signs of x, y and the result of subtraction, x-y.
As mentioned, x is less than 0 and hence negative and y is greater than 0, thus positive. So when you subtract a positive number y from the negative number x, the result will obviously be negative. This is due to the 'rules of signs' in arithmetic.
Then, for the division, when you divide this negative result by the multiplication of x (which is negative) and y (which is positive), the answer will be positive. This is again because of the 'rules of signs' for division - a negative number divided by a negative number yields a positive number.
So, the sign of the result of the real number expression x-y/xy is positive when x<0 and y>0.
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Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales. If Jamie makes $475 in one week, what are her sales for that week?
Jamie made $2375 of sales on one week and earns 20% of it as a commission.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Jamie is a salesperson in a shoe store and earns $95 per week, plus 20% of her weekly sales.
Jamie makes $475 in one week which is 20% of the total sale assuming he made $x worth of sales.
∴ (20/100)×x = 475.
0.2x = 475.
x = 475/0.2.
x = $2375
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Find the solution.
(x - 3)(x + 2) = 0
Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: -2x + 5 < 1 (Subtraction)
Step 3: -2x < 6 (Addition)
Step 4: x > -3 (Division)
Mia is trying to find her mistake in the problem shown. In which step did she first make a mistake?
A) Step 1
B) Step 2
C) Step 3
D) Step 4
Answer:
C) Step 3
Step-by-step explanation:
We are given that
[tex]4x+5< 6x+1[/tex]
We have to find the mistake made by Mia in her solution.
Step 1:[tex]4x+5<6x+1[/tex]
Reason: Given
Step 2: [tex]4x-6x+5<+1[/tex]
[tex]-2x+5<1[/tex]
Reason: Subtraction property of inequality
Step 3: [tex]-2x <1-5[/tex]
[tex]-2x<-4[/tex]
Reason: Using subtraction property of inequality
Step 4:[tex]-x<-2[/tex]
[tex]x>2[/tex]
Reason: Division property of inequality
Mia did mistake in step 3 .She using addition property instead of subtraction property.
Option C is true.
Felix buys a carpet for $230. The price is $3.50 per square foot. If Felix had a special discount coupon for $50 off, which linear equation could be used to find the area, A, of the carpet?
The linear equation to find the area of the carpet after applying Felix's $50 discount is 3.50 × A = 180, where A represents the area in square feet. After solving the equation, we find that the area is 51.43 square feet.
To find the area, A, of the carpet that Felix buys, we can set up a linear equation based on the total cost after the discount and the cost per square foot. The original price of the carpet is $230, but Felix has a coupon for a $50 discount, reducing the cost to $180. Since the cost per square foot of the carpet is $3.50, we can denote the area of the carpet as A, and set up the equation:
3.50 × A = 180
To solve for A, we divide both sides of the equation by 3.50:
A = 180 / 3.50
A = 51.43 square feet
Part 1: Write the equation of the line that passes through the points (–1, –4) and (2, 5).
Part 2: Using complete sentences, explain whether or not it matters which point is used in the final answer. Also explain why you chose the point you did. ...?
the car was 28000 the car value go down at the rate of 7.25% what would its value be after 5 years
Eliminate y to solve for x. Plug in x into the second equation to solve for y
A gardener is planting two types of trees: type a is 3 feet tall and grows at a rate of 16 inches per year. type b is 4 feet tall and grows at a rate of 13 inches per year. algebraically determine exactly how many years it will take for these trees to be the same height.
what is d for 3 4d–14=15–5d–4d
To solve the equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d. The value of d is 29/21.
Explanation:To find the value of d in equation 3(4d) – 14 = 15 – 5d – 4d, we need to simplify the equation and isolate d on one side of the equation. Let's start:
Expand the brackets: 12d - 14 = 15 - 9dCombine like terms: 12d + 9d = 15 + 14Combine the d terms: 21d = 29Isolate d by dividing both sides of the equation by 21: d = 29/21Therefore, the value of d in the equation is 29/21.