Answers
the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
The image depicts a right-angled triangle with a hypotenuse of length 10 and one leg of length 6, with the other leg labeled as [tex]\( a \)[/tex]. There is also a smaller right-angled triangle within it, sharing the leg of length 6 with the larger triangle, with the hypotenuse of the smaller triangle labeled as 8 and the other leg labeled as [tex]\( b \).[/tex]
To find the lengths of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse [tex](\( c \))[/tex] is equal to the sum of the squares of the lengths of the other two sides [tex](\( a \)[/tex] and [tex]\( b \)[/tex]): [tex]\( c^2 = a^2 + b^2 \).[/tex]
For the larger triangle:
[tex]\[ 10^2 = 6^2 + a^2 \][/tex]
For the smaller triangle:
[tex]\[ 8^2 = 6^2 + b^2 \][/tex]
We will solve these two equations to find [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. Let's start with the calculations for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] using the Pythagorean theorem.
Using the Pythagorean theorem for each triangle, we find:
For the larger triangle:
[tex]\[ a^2 = 10^2 - 6^2 \][/tex]
[tex]\[ a^2 = 100 - 36 \][/tex]
[tex]\[ a^2 = 64 \][/tex]
[tex]\[ a = 8 \][/tex]
For the smaller triangle:
[tex]\[ b^2 = 8^2 - 6^2 \][/tex]
[tex]\[ b^2 = 64 - 36 \][/tex]
[tex]\[ b^2 = 28 \][/tex]
[tex]\[ b = \sqrt{28} \][/tex]
[tex]\[ b = 2\sqrt{7} \][/tex]
So, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
Related Questions
Ming says that 0.24 > 1414 because 0.24 = 2424
Answers
Final answer:
To compare numbers, we look at their values from left to right. In this case, 1414 is greater than 0.24 due to the magnitude of the numbers.
Explanation:
The student's statement is incorrect. To compare numbers, you look at the digits from left to right, so 0.24 is less than 1 as it's closer to zero. Meanwhile, 1414 is a much larger number because it's in the thousands range.
Therefore, 1414 > 0.24, not the other way around. The student's reasoning based on the equality with 2424 is inaccurate in the context of comparing these two numbers.
The following table gives values of the differentiable function .
x
0
1
2
3
4
5
6
7
8
9
10
y
3
1
-2
-5
-4
2
-1
-2
-4
-6
-7
Now assume that the table gives values of the continuous function y=f'(x) (instead of f(x) ). Estimate and classify critical points of the function f(x).
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y=-x+3
Find the equation of the ellipsoid passing through the points (±7,0,0),(0,±1,0)(±7,0,0),(0,±1,0) and (0,0,±4)
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5.6 times what equals to -19.04
Answers
/5.6. /5.6
-3.4 = x
just divide -19.04 by 5.6 and you get -3.4
The given equation can be rearranged as a division problem: -19.04 divided by 5.6. The solution to this is -3.4. Thus, 5.6 times -3.4 equals -19.04.
Explanation:To answer the question, we must find the unknown variable in your given equation, where you are multiplying a number (5.6) by some unknown figure to get -19.04. This type of math problem is a division problem arranged differently. Instead of saying '5.6 times what equals to -19.04', we can rearrange it to say '-19.04 divided by 5.6 equals what'.
To get the answer, simply divide -19.04 by 5.6, which equals -3.4. So 5.6 times -3.4 equals -19.04.
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Jayson takes a total of 5 hours of swimming lessons per week.if each lesson is 5/6 of an hour how many lessons does he take per week
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( 5/6 hour / lesson ). "hour" and "hours" will drop out, leaving you with the # of lessons:
5 hours
----------------- = 6 lessons (answer)
5/6 hour
------------
1 lesson
What is 600000-347201
Answers
Which equivalent expression demonstrates the commutative property? Check all the apply.
13 + 2 + 9 = 2 + 13 + 9
8 + 0 = 8
9(8 + 45) = 9(8) + 9(45)
[29(14)] + 45 = [14(29)] + 45
29(14 + 45) = 14(29) + 45
Answers
Answer:
13+2+9=2+13+9
[29(14)]+45=[14(29)]+45
Step-by-step explanation:
The equivalent expressions 13 + 2 + 9 = 2 + 13 + 9 and [29(14)] + 45 = [14(29)] + 45 demonstrate the commutative property, according to which the order in which numbers are added or multiplied does not change the result.
Explanation:The commutative property in mathematics is the property that states the order in which numbers are added or multiplied does not change the result. So, looking at the given options, the expressions that demonstrate the commutative property are:
13 + 2 + 9 = 2 + 13 + 9 [29(14)] + 45 = [14(29)] + 45
The other options do not represent the commutative property.
The operation 8 + 0 = 8 is an instance of identity property of addition because any number added to zero gives that number. The expression 9(8 + 45) = 9(8) + 9(45) is an application of the distributive property (where a(b + c) = ab + ac), and 29(14 + 45) = 14(29) + 45 is not a valid mathematical equation since it doesn't balance equally on both sides.Learn more about Commutative Property here:https://brainly.com/question/5637942
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The product P of two consecutive natural numbers, the first of which is N
Answers
The product of two consecutive natural numbers, with the first being [tex]\( N \),[/tex]is [tex]\( N \times (N + 1) \).[/tex]
The product [tex]\( P \)[/tex] of two consecutive natural numbers can be expressed as the product of a number and its consecutive number. So, if the first number is [tex]\( N \),[/tex] then the second number would be [tex]\( N + 1 \).[/tex] Therefore, the product [tex]\( P \)[/tex] can be written as:
[tex]\[ P = N \times (N + 1) \][/tex]
Expanding this, we get:
[tex]\[ P = N^2 + N \][/tex]
This represents the product of two consecutive natural numbers where [tex]\( N \)[/tex] is the first number.
georgia is making sock puppets.each pair of sock puppets cost $2 georgia bought six pairs of sock puppets.how much did she spend
Answers
Georgia spent a total of $12 on six pairs of sock puppets, with each pair costing $2.
Georgia is calculating the total cost of sock puppets she purchased. The cost per pair is $2, and she bought six pairs. To find out how much she spent, we need to multiply the cost per pair by the number of pairs she bought.
Calculation:
Cost per pair of sock puppets = $2
Number of pairs = 6
Total cost = Cost per pair * Number of pairs
Total cost = $2 * 6
Total cost = $12
Therefore, Georgia spent $12 on sock puppets.
Find 1112+(−712)1112+(−712). Write your answer as a fraction in simplest form.
Answers
Name the property illustrated be each statement. (3x+2)-5=(3x+2)-5
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5x + 20 = y 5x + 20 = 70 5x = 50 x = 10 Jack has a business mowing lawns and charges a flat fee of $20 per yard, plus an additional $5 an hour. He wants to make sure that he makes at least $70 doing yard work for a client with a very large yard. He sets up and solves the equation above. What does his solution of 10 mean? A) He needs to mow at least 10 yards. B) He needs to work for at least 10 days for this client. C) He needs to work at least 10 hours in the client's yard. D) He needs to charge and additional $10 an hour for this client.
Answers
Answer:
C
Step-by-step explanation:
Find the product. Type your answer in the provided space. Do not use spaces in your answer. To demonstrate an exponent, use the ^ key. For example, x 2should be typed in as x^2.
3x 3 y · 5x 2 y
Answers
Final answer:
To find the product of [tex]3x^{3y}[/tex] and [tex]5x^{2y}[/tex], multiply 3 and 5 to get 15, then add exponents of x (3 and 2) and y (1 and 1, because y = [tex]y^{1}[/tex]) to get [tex]15x^{5y^{2} }[/tex].
Explanation:
The student's question involves the multiplication of exponentials. When multiplying variables with exponents, we multiply the coefficient (numerical part) and add the exponents of like bases.
Given the expression [tex]3x^{3y}[/tex].[tex]5x^{2y}[/tex], we multiply the coefficients (3 and 5) and add the exponents of like bases (“3” for x and “1” for each y, since no exponent means 1).
The result is [tex]15x^{(3+2)y^{1+1} }[/tex], which simplifies to [tex]15x^{5y^{2} }[/tex].
Fred Johnson's total insurance premium is $1,200. His employer pays 60% of the total premium. How much does Fred pay? $480 $720 $2,000 $3,000
Answers
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
Amount of Fred Johnson's total insurance premium = $1200
Percentage of total premium his employer pays = 60%
Remaining percentage of total premium he pays is given by
[tex]100\%-60\%=40\%[/tex]
So, amount of insurance premium Fred Johnson pay is given by
[tex]\frac{40}{100}\times 1200\\\\=40\times 12\\\\=\$480[/tex]
Hence, First option is correct.
How many more equal angles does a square have than a rectangle
Answers
The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l, of a cone with a surface area of 500π ft2 and a radius of 15 ft. l = ft
Answers
The slant height (l) of this cone is equal to 18.33 feet.
Given the following data:
Surface area of cone = 500π [tex]ft^2[/tex].Radius of cone = 15 ft.To calculate the slant height (l) of this cone:
How to calculate surface area.Mathematically, the surface area (SA) of a cone is given by this formula:
[tex]SA = \pi r(l + r)[/tex]
Where:
l is the slant height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]500 \pi = \pi \times 15(l + 15)\\\\500=15(l + 15)\\\\500=15l+225\\\\15l=500-225\\\\15l=275\\\\l=\frac{275}{15}[/tex]
Slant height, l = 18.33 feet.
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The slant height of a cone with a surface area of 500π square feet and a radius of 15 feet is 275 feet.
Explanation:The question asks for the slant height of a cone, given that the surface area (S) is 500π square feet and the radius (r) is 15 feet. No explicit formula for the slant height is provided.
We know the formula for the surface area of a cone is S = πrl + πr², where r is the radius, l is the slant height, and π is a constant (approximately 3.14).
By rearranging this equation, subtracting the base area from the surface area and then dividing by πr, we can solve for l: l = (S - πr²)/πr.
Plugging in the provided numbers: l = (500π - π*(15 ft)²)/(π * 15 ft). Simplifying this equation gives: l = (500 - 225) ft = 275 ft. Therefore, the slant height of the cone is 275 feet.
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Nate went on a trip, and he used a table of values to repeatedly record the time he had been traveling and the distance from his destination. The function represented by the table of values is linear, and the rate of change is 50 miles per hour. Which of these statements is correct?
Answers
Answer: b. with any pair of values for time and distance, it is possible for Nate to determine the initial value by repeatedly subtracting 50, if necessary.
Step-by-step explanation: i took the unit test. hope this helps<33
Answer:
B
Step-by-step explanation:
edge 2021
Information about a shipment of mirrors to a local store is shown.
Of all of the medium mirrors that were shipped, how many of them were broken?
A. 68
B. 78
C. 164
D. 208
Answers
480-214-102= 164
From here, subtract the number of mirrors that are not broken.
164-96= 68
Final answer: 68 broken medium mirrors, A
The table is an illustration of a two-way table
The number of medium mirrors that were not broken are 68
Start by calculating the number of medium mirrors
Medium = 480 - 214 - 102
Evaluate the difference
Medium = 164
From the question 96 mirrors are not broken.
So, the number of broken mirror is:
Broken = 164 - 96
Evaluate the difference
Broken = 68
Hence, the number of medium mirrors that were not broken are 68
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Let f(x) represent a function. Which descriptions match the given transformations? Drag and drop the answers into the boxes.
f(x−3.5) -->
3.5f(x)-->
f(x)
is translated 3.5 units down.
f(x)
is translated 3.5 units left.
f(x)
is vertically compressed by a factor of 3.5.
f(x)
is translated 3.5 units up.
f(x)
is vertically stretched by a factor of 3.5.
f(x)
is translated 3.5 units right.
Answers
You can figure that out by thinking that for x = 3.5 (which is 3.5 units to the right of x = 0, f(3.5 - 3.5) is the same that f(0), ... for x = 10.5 (which is 3.5 units to the right of x = 7, f(10.5 - 3.5) = f(7) ... and so for every value of x.
For 3.5 f(x) the answer is that f(x) is vertically stretched by a factor of 3.5 which you figure out from a table like this:
f(x) 3.5 f(x)
0 0
1 3.5
2 7
10 35
And from that you can see the 3.5 f(x) is horizontally compressed and vertically stretched respect to f(x).
Answer:
3.5f(x) is vertically streched and f(x-3.5) is transaleted 3.5 units up
Step-by-step explanation:
In a certain school, course grades range from 0 to 100. Adrianna took 4 courses and her average course grade was 90. Roberto took 5 courses. If both students have the same sum of course grades, what was Roberto's average?
(I want to know the most easiest way to do it)
Answers
which expression is represented by the model below?
Answers
you are a geologist assigned to estimate the density of the Earth. look at picture for the full question:
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[tex]\bf g=\cfrac{GM}{R^2}\implies R^2=\cfrac{GM}{g}\implies R=\sqrt{\frac{GM}{g}}\quad \begin{cases} G=6.67\cdot 10^{-11}\\ M=5.97\cdot 10^{24}\\ g=9.81 \end{cases} \\\\\\ R=\sqrt{\cfrac{{(6.67\cdot 10^{-11})(5.97\cdot 10^{24})}}{9.81}} \\\\\\ R=\sqrt{\cfrac{{6.67\cdot 5.97\cdot 10^{13}}}{9.81}} \\\\\\ R\approx 6371116.97~m\\\\ -------------------------------\\\\ V=\cfrac{4\pi R^3}{3}\implies V=\cfrac{4\pi 40591131498470.95^3}{3} \\\\\\ V\approx 1083266582306022184268.1~m^3[/tex]
The graph of g(x) is the graph of f(X) = x + 6 reflected across the x-axis. Which equation describes g? Question 3 options: g(x) = -x + 6 g(x) = -6x - 6 g(x) = -x - 6 g(x) = x - 6
Answers
f(x) = x + 6
What is the equation for the reflection across the x-axis? since the y-value is the opposite of its normal value at every point, g(x) = -f(x)
g(x) = -f(x)
g(x) = -(x+6)
g(x) = -x - 6
Third choice is the answer
Fred worked on Monday and Tuesday, earning $109.30 total for the two days. He had Wednesday off, made $67.89 on Thursday, had a half day on Friday making $35.12, and made $87.34 on Saturday. What is the total amount of money he made that week?
Answers
Algebraic expression of 25 less than a number d
Answers
The algebraic expression for 25 less than a number is y = 25-x
What is an algebraic expression?An algebraic expression is a set of terms that have been combined using operations like addition, subtraction, multiplication, and division.
An algebraic expression is formed by a single term or by a group of terms.
For example, in the expression 4x + y, the two terms are 4x and y.
Given that, we need to construct an expression for a number 25 less d,
Let the number be y,
The algebraic expression for 25 less than a number is;
y = 25-x
That we give, all the obtained value of y is less than 25.
Hence, the algebraic expression for 25 less than a number is y = 25-x.
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What point on the unit circle corresponds to an angle of 173º
Answers
The point on the unit circle that corresponds to an angle of 173º is approximately (-0.9917, 0.1288), derived by converting the angle to radians, then calculating the cosine and sine for the x and y coordinates respectively.
Explanation:To find the point on the unit circle that corresponds to an angle of 173º, we first need to convert the angle from degrees to radians. We use the conversion factor of π/180 radians per degree, so 173 degrees is equal to (173)*(π/180) = 3.02 radians.
On the unit circle, the x-coordinate of a point corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle. In this case, the x-coordinate would be cos(3.02) ≈ -0.9917, and the y-coordinate would be sin(3.02) ≈ 0.1288.
So, the point on the unit circle that corresponds to an angle of 173º is approximately (-0.9917, 0.1288).
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Solve the following equations. Some equations will have a single answer, others will have no solution, and still others will have infinite solutions
1. 2x + 2x + 2 = 4x + 2
2. 3(x − 1) = 2x + 9
3. 2x + 8 = 2(x + 4)
4. 2x − x + 7 = x + 3 + 4
Answers
3(x − 1) = 2x + 9 = x=9
All values of x are solutions
All values of x are solutions
Quick i need help! (includeing pic)
Answers
Most evenings after dinner Duarte spends 30 minutes playing chess with his dad. Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together e evenings.
Answers
number of evening playing chess: e
number of minutes = 30 minutes / play * number of evening playing chess
=> m = 30e
Answer: m = 30e
The airport garage charges $5 to park for the first hour and then $3.50 an hour for any additional hours. Ben paid $57.50 to park there one day when he flew to another city. How many hours was he parked at the airport?
Answers
Final answer:
Ben was parked at the airport for a total of 16 hours, after calculating the initial cost for the first hour and then dividing the remainder by the hourly rate for additional hours.
Explanation:
The student's question asks how many hours Ben was parked at the airport, given that the parking cost is $5 for the first hour and $3.50 for each additional hour, with a total fee of $57.50.
First, we subtract the initial $5 from the total cost to determine the cost of additional hours:
$57.50 - $5 = $52.50 for additional hours
Next, we divide the remaining cost by the hourly rate for additional hours to find the number of additional hours Ben parked:
$52.50 ÷ $3.50/hour = 15 hours
Finally, we add the first hour to the additional hours to calculate the total hours parked:
15 hours + 1 hour = 16 hours
Thus, Ben was parked at the airport for a total of 16 hours.