To determine the value of x for the right triangle, we applied the Pythagorean theorem to the side lengths and solved the resulting quadratic equation, revealing x to be -1.
Explanation:To find the value of x for the side lengths of a right triangle with side lengths x + 9, x + 2, and x + 10 as the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the two other sides.
Here's the step by step solution:
Write the Pythagorean theorem with the given side lengths: (x + 2)² + (x + 9)² = (x + 10)².Expand the squares: x² + 4x + 4 + x² + 18x + 81 = x² + 20x + 100.Combine like terms and move all terms to one side: x² + 22x + 85 = 0.Solve the quadratic equation, which yields x = -1 or x = -85. However, since side lengths cannot be negative, the only logical value of x is -1.
Final answer:
To find the value of x in a right triangle with sides x + 9, x + 2, and hypotenuse x + 10, the Pythagorean theorem is used. After applying the theorem, we simplify and solve the resulting quadratic equation, which gives us a positive value of x = 3.
Explanation:
The student is asking how to find the value of x in a right triangle with sides x + 9, x + 2, and x + 10, where x + 10 is the hypotenuse. To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
For this particular triangle:
Identify the legs and the hypotenuse of the triangle: Leg 1 is x + 9, Leg 2 is x + 2, and the Hypotenuse is x + 10.Apply the Pythagorean theorem: (x + 9)² + (x + 2)² = (x + 10)².Simplify and solve for x. Expand the squares: x² + 18x + 81 + x² + 4x + 4 = x² + 20x + 100.Combine like terms and move all terms to one side of the equation:(2x² + 22x + 85) - (x² + 20x + 100) = 0x² + 2x - 15 = 0Factor the quadratic equation: (x + 5)(x - 3) = 0Find the possible values for x: x = -5 or x = 3. Since a side length can't be negative, the value for x must be 3.Therefore, the value of x is 3.
Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in the school rode their bikes toschool
Write the quadratic function in vertex form. y = x2 + 8x + 18
Which rule represents R0, 180
Answer:
[tex](x, y) \rightarrow (-x, -y)[/tex]
Step-by-step explanation:
Rotation of any point in the form of (x, y) about the origin O through 180 degree in anticlockwise or counterclockwise direction, it will takes the new position (-x, -y)
i.e,
The rule of rotation about the origin through 180 degree is given by:
[tex](x, y) \rightarrow (-x, -y)[/tex]
For example:
Let the point A(-4, 6) rotate by the rule [tex]R_{0, 180^{\circ}}[/tex]
then;
[tex]A(-4, 6) \rightarrow (4, -6)[/tex]
⇒the coordinate of image of the point A is, (4, -6)
Therefore, the rule represents [tex]R_{0, 180^{\circ}}[/tex] is, [tex](x, y) \rightarrow (-x, -y)[/tex]
Answer:
B
Step-by-step explanation:
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train?
Which equation could be used to find the number of miles the trains will travel?
A. 30x = 55(x + 300)
B. x÷30 = (x - 300)÷55
C. x÷30 = (x + 300)÷55
Answer:
The answer is C. x÷30 = (x + 300)÷55
Step-by-step explanation:
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph.
The equation will be
Total speed = Total distance / time taken
x ÷ 30 = (x + 300) ÷ 55
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
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Geometry- You are designing a poster that will be 3yd wide and 8ft high. How much paper do you need to make the poster? Give your answer in square feet. My answer was 72ft^2, but the textbook says 74ft^2. Can someone please check to see if my answer is correct and the textbook is wrong.
Dependent events can best be described as. A= two or more events that have the same probabilities. B= two or more events that do not have the same probabilities. C= a group of events whose later outcomes are not affected by previous outcomes.D= a group of events whose later outcomes are affected by previous outcomes.
Option: D is the correct answer.
D = a group of events whose later outcomes are affected by previous outcomes.
Step-by-step explanation:We know that two events Event A and event B are said to be dependent if the occurrence of one outcome affects the occurrence of the other outcome.
For example--
If we have a bag containing 5 blue marbles, 2 red marbles and 3 green marbles then if we draw first marble and then draw second without replacement.
Then the event of drawing a blue marble first and then a green marble are dependent events.
If a baker doubles a recipe that calls for 6 3/4 cups of flour, how many cups of flour will be needed in all
If the interest rate on a savings account is 0.018%, approximately how much money do you need to keep in this account for 1 year to earn enough interest to cover a single $9.99 Below-Minimum-Balance Fee?
$55,555
$55
$555
$5,555
What is the solution of the system of equations ? 2x-y=7 y=2x+3
Answer:
Step-by-step explanation:
I forgot
Matching 1. protects against loss from automobile accidents of insured malpractice 2. protects against loss to insured's home and furnishings automobile 3. protects against loss from fire on insured's property liability 4. protects against loss from injury to others on insured's property fire 5. protects against loss from lawsuits against insured life 6. protects against loss from death of insured homeowners
1. protects against loss from automobile accidents of insured - Automobile insurance.
2. protects against loss to insured's home and furnishings - Homeowners insurance
3. protects against loss from fire on insured's property - Fire insurance
4. protects against loss from injury to others on insured's property - Liability insurance
5. protects against loss from lawsuits against insured - Malpractice insurance
6. protects against loss from death of insured - Life insurance
Chris is trying to find the volume of a pool. What unit will he use?
When measuring the volume of a swimming pool, larger units of capacity like liters and gallons are used. For an Olympic-sized pool, the volume is often measured in megaliters or cubic meters.
When measuring the volume of a swimming pool, we are dealing with a very large capacity, therefore using small capacity units like milliliters would not be practical due to the large numbers it would involve. In cases such as filling a pool, larger units of capacity are more appropriate. Common units of measure for such large volumes are liters and gallons. For very large swimming pools, like Olympic-sized ones, volume is often expressed in megaliters (ML) because one megaliter equals one million liters. For instance, an Olympic-sized swimming pool holds about 2,500,000 liters, which can also be expressed as 2.5 megaliters (ML).
Additionally, when working with the volume of a pool, it would also be possible to measure in cubic meters (m³). This is particularly common in scientific contexts or in regions where the metric system is standard for all measurements.
A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
Answer:
The restaurant needs to earn $839 on Sunday.
Step-by-step explanation:
Consider the provided information.
Let $x needs to earn on Sunday, to average $1000 per day .
It is given that the average earn should be $1000
[tex]Average=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]
[tex]Average= \frac{1240+921+x}{3}[/tex]
[tex]Average= \frac{2161+x}{3}[/tex]
The average should be $1000, so substitute 1000 for average and solve for x.
[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex]
Thus, the restaurant needs to earn $839 on Sunday.
The required equation is [tex]\frac{1240+921+x}{3}=1000[/tex].
I have a 20 question geometry diagnostic due at 1 pm
find the rate in the following problem Round the answer to the nearest hundredth of a percent. What percent of 85 is 10?
To find the percent of 85 that is 10, divide 10 by 85 and multiply by 100. The answer is 11.76%.
Explanation:To find the percent of 85 that is 10, we divide 10 by 85 and multiply by 100.
10 / 85 = 0.1176
0.1176 * 100 = 11.76%
Roundin the answer to the nearest hundredth of a percent, we get 11.76%.
a toy manufacturer estimates that 6% of its products are defective. if it produces 550 toys in one day, how many will be defective?
Answer:
33
Step-by-step explanation:
We need to find 6% of 550.
We can calculate with a direct rule of 3. If the 100% is 550, how much is the 6%?
[tex]100 -\!\!\!-\!\!\!- 550\\ 6 -\!\!\!-\!\!\!- x[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {6 * 550}{100} \\ \\ x = \frac {3300}{100}\\ \\ x = 33[/tex]
33 toys will be defective.
If a toy manufacturer produces 550 toys in one day, then the number of toys that would be defective is 33 toys.
Let the defective toys be D.Let the total toys be T.Given the following data:
Total number of toys produced in a day = 550 toys.To find the number of toys that would be defective from a production:
[tex]D = \frac{6}{100}[/tex] × [tex]T[/tex]
Substituting the given parameters into the formula, we have;
[tex]D = \frac{6}{100}[/tex] × [tex]550[/tex]
[tex]D = 0.06(550)[/tex]
Defective toys, D = 33 toys.
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A table is 3 feet and 2 inches wide and a chair is 25 inches wide how much wider is the table then chair in inches
Answer:
junko enishima
Step-by-step explanation:
What is the abbreviation for SI unit of mass
A map is drawn to scale such that 1/8 inch represents 65 feet. if the shortest route from the dorm to the grocery store measures 23 ¼ inches on the map, how many miles is it to the grocery store? round to the nearest tenth.
Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
$22 AUD ×
$22 AUD ×
$1.20 AUD ×
$1.20 AUD × pls help need awnwer quick
Answer:
[tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text {AUD}}[/tex]
Step-by-step explanation:
We are told that 1.2 Australian dollars equals to 1 US dollar. We are supposed to write an expression that can be used to convert 22 Australian dollars to US dollars.
To find the amount of US dollars in 22 Australian dollars we will divide 22 by amount of Australian dollars that is equal to 1 US dollar (1.2 AUD).
[tex]22\text{ AUD}=\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text{ AUD}}[/tex]
Australian dollars will cancel out with Australian dollars from unit parts and our unit will be in American dollars.
[tex]22\text{ AUD}=\frac{22\cdot 1\text{ USD}}{1.20}[/tex]
Therefore, our desired expression that can convert 22 Australian dollars to US dollars will be [tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text { AUD}}[/tex].
Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work. *
Please help!! Explain how you got the answer!
multiply 3.5 x 3 = 10.5
add -5 +-10 = -15
so you have 10.5 x 10^15
then you need to move the decimal point 1 place to the left to get 1.05
since you move the decimal point 1 place to the left you add 1 to the -15 to get -14
so answer = 1.05 x 10^-14
3c+2d=2;d=4 step by step
Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let h represent the number of hats.
What is the minimum number of hats Jason will need to sell to make a profit?
Which inequality models this problem?
A.) 15h>750+3.5h
B.) 3.5h>750+15h
C.) 15h<750+3.5h
D.) 3.5h≥750+15h
Answer:
the answer is A. 15h>750+3.5h
Im 100% sure. Good luck!
A ski jacket costing $160 is $20 less than twice the cost of the matching ski pants. Find the total cost of the ski jacket and matching ski pants.
The total cost of the ski jacket and matching ski pants is $250.
Given that, a ski jacket costing $160 is $20 less than twice the cost of the matching ski pants.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the cost of matching ski pants be x.
Now, 2x-20=160
⇒ 2x=180
⇒ x=90
So, the cost of the matching ski pants is $90.
Total cost = 160+90 = $250
Therefore, the total cost of the ski jacket and matching ski pants is $250.
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find the missing data item given the following values
25, 28, 21, x, 32
Pablo simplified the expression(2^-4)^-2 as shown.
(2^-4)^-2=2^-4*^-2=2^-8
Which statement explains Pablo’s error?
A. He should have added the exponents instead of multiplying them.
B. He should have divided the exponents instead of multiplying them.
C. He should have found 8 as the exponent, not –8.
D. He should have written mc014-3.jpg as mc014-4.jpg.
Answer:
C. He should have found 8 as the exponent, not –8.
Step-by-step explanation:
We have been given an expression [tex](2^{-4})^{-2}[/tex]. We are asked to find the Pablo's error in simplifying the expression.
Let us check steps done by Pablo.
In first step Pablo has simplified [tex](2^{-4})^{-2}[/tex] to [tex](2)^{(-2*-4)}[/tex] using power rule property of exponents which states that to raise a power to a power we have to multiply the exponents. Therefore, his first step is correct.
Now let us check Pablo's second step. We can see that Pablo multiplied -2 by -4 and simplified to [tex]2^{-8}[/tex].
Since we know that multiplying a negative number with another negative number gives a positive result, therefore, Pablo made mistake in second step. He should have found 8 instead of -8 as the exponent.
The correct steps for simplifying the given expression will be [tex](2^{-4})^{-2}=2^{(-2*-4)}=2^{8}[/tex].
Upon looking at our given option we can see that option C is the correct statement about Pablo's error.
Simplify −0.5i−i
Enter your answer in the box.
Answer: -1.5i
Step-by-step explanation: This was correct
HELP PLEASE!!!!!!! 10 POINTS!!!
How do the rules for adding and subtracting signed decimals compare with the rules for adding and subtracting integers? please explain
The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class population. What is the value of the numerator of the calculation of the variance?
The value of the numerator of the calculation of the variance= 258
and Variance= 51.6
Step-by-step explanation:We know that in order to calculate the variance we need to follow following steps:
First calculate mean.Then subtract each of the data points from means and square the difference quantity.Lastly calculate the mean of these squared quantity.The data points are:
90, 75, 72, 88, 85
The mean of these data points are:
[tex]Mean=\dfrac{90+75+72+88+85}{5}\\\\\\Mean=\dfrac{410}{5}\\\\\\Mean=82[/tex]
Now on finding the difference terms i.e.
90-82=8
75-82= -7
72-82= -10
88-82=6
and 85-82=3
The square of these difference term is:
8²=64
(-7)²=49
(-10)²=100
6²=36
and 3²=9
Hence, the mean of these squared quantity i.e. Variance is:
[tex]Variance=\dfrac{64+49+100+36+9}{5}\\\\\\Variance=\dfrac{258}{5}\\\\\\Variance=51.6[/tex]
What is another name for like r.