=GEOMETRYPythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.
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From the triangle, we have:
c = 13
b = 7
Let's solve for a.
The triangle is a right triangle.
To find the length of the missing sides, apply Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]We are to solve for a.
Rewrite the equation for a:
[tex]a^2=c^2-b^2[/tex]Thus, we have:
[tex]\begin{gathered} a^2=13^2-7^2 \\ \\ a^2=169-49 \\ \\ a^2=120 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{120} \\ \\ a=10.95 \end{gathered}[/tex]ANSWER:
[tex]10.95[/tex]Related Questions
Evaluate (3√2-1) (3√2+1)
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Answer:
9√3 converted is 15.58845727
<1 and <2 are complementary angles. the measure of <1 is 55°. the measure of <2 is 5(x+1)°.find the value of x.
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Answer:
Step-by-step explanation:
Answer 29
A ladder that is 55 meters in length is resting on a branch of a tree, and the base of the ladder is 33 meters from the tree on the level ground. How high up is the branch on which the ladder is resting?
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the diagram of situation is given as follows
so by using the right-angle property.
[tex]x^2+33^2=55^2[/tex][tex]\begin{gathered} x^2=3025-1089=1936 \\ x=\sqrt[]{1936} \end{gathered}[/tex][tex]x=44[/tex]so the height of the tree is 44
Solve the direct variation problemsJohn is working at a bank and receives 25 dollars an hour. a. Write an equation that relates x and y.b. what is the constant of proportionality?
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Let "x" represent the number of hours that John works and "y" represent John's earnings after working x hours.
b) John receives $25/hour → this value represents the change in John's earnings for every unit increase of x, which is, the constant proportionality (k) of the relationship.
a) If x and y have a direct relationship, you can express it as follows:
[tex]y=25x[/tex]A-32-10A. 20-C?LBDIn the similaritytransformation of AABCEto AEDF, AABC was dilated bya scale factor of [?], reflectedacross the [ ], and movedthrough the translation [ ].B. 1/23 4F 5 Find the answer to all three missing boxes
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To find the scale factor use the next formula:
[tex]sf=\frac{dimension\text{ }new\text{ }shape}{dimension\text{ }original\text{ }shape}[/tex]Use dimension of corresponding sides AB and ED:
[tex]sf=\frac{2}{4}=\frac{1}{2}[/tex]Then, the scale factor is 1/2___________After the dilation the figure is reflected across the y-axis_____________
Then, the triangle is translated one unit to the right and 3 units up [+1,+3] or [1,3]A satellite dish is the shape of a paraboloid. The dish is 42 inches wide, and 10 inches
deep. How many inches should the receiver be located from the vertex for optimal
reception? (round to the nearest thousandth)
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The receiver is situated 44.24 inches from the vertex, is the correct response.
Define parabola.Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Observe the illustration below. It depicts the paraboloid's vertical cross-section through its axis of symmetry.
Make the origin of the parabola the vertex.
Then, it has the equation y = bx².
The parabola crosses via (21,10), therefore
10 = b(21²)
= 0.0226
because
Its equation is y =0.0226²
For best reception, the receiver should be positioned at the paraboloid's focus point.
The focus has a y-coordinate of
a = 1/(4b)
= 1/0.0226
= 44.24 in
The receiver is situated 44.24 inches from the vertex, is the correct response.
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Y=-x^2+x+12 write in intercept form and show work
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Given that y= x^2+x+12, to write the expression in an intercept form we need to factorize the expression.
[tex]y=-x^2+x+12[/tex]The intercept form is of the format
[tex]y=a(x\pm p)(x\pm q)_{}[/tex]This is obtained by factoring the quadratic equation above
[tex]\begin{gathered} y=-x^2+4x-3x+12 \\ y=-x(x-4)-3(x-4) \\ y=(x-4)(-x-3) \\ y=-1(x+3)(x-4) \end{gathered}[/tex]Hence, the intercept form of the equation is y= -1 (x + 3) ( x - 4 )
Cory has 20 crayons. He wants to give the same number of crayons to eachof his friends.Part A Write two different questions about Cory's crayons that can be answeredusing division.
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He has 20 cranyons.
Part A Write two different questions about Cory's crayons that can be answered using division.
Question 1:
He divided the cranyons among 5 of his friends. How many cranions did each of them get?
Answer: 20/5 = 4
Question 2:
One of his friends got 8 cranyons. The remaining cranyons, he divided among 4 other friends. How many each of those got?
20 - 8 = 12
12/4 = 3
A library give every employee a $500 bonus. What effect, if any does it have on(a) mean (b) median (c) mode (d) Standard division
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The mean is the
sum of salaries/number of employees
Assuming the salaries of 5 employees were
1000, 2000, 3000, 4000, 4000
Mean = (1000 + 2000 + 3000 + 4000, 4000)/5 = 2800
If we add a bonus of $500 to each, we have
1500, 2500, 3500, 4500, 4500
Mean = (1500 + 2500 + 3500 + 4500 + 4500)/5 = 3300
Thus, the mean increases
The median is the middle value
The middle value was 3000, the new median is 3500
The median increases
The mode is the value with the highest frequency. The former mode is 4000. The new mode is 4500
the mode increases
The standard deviation is how far the values are from the mean
Standard deviation = Square root of the square of (each value - mean)/ number of values. Thus, we have
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1/4×3/2×8/9 whats the answer?
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Multiply the given fractions to find the answer, use the given example:
Now, solve the given multiplication:
[tex]\frac{1}{4}\cdot\frac{3}{2}\cdot\frac{8}{9}=\frac{1\cdot3\cdot8}{4\cdot2\cdot9}=\frac{24}{72}=\frac{1}{3}[/tex]The answer is 1/3.
Please help! ♥️I have to get it done by the end of today thank youu sm♥️
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The center of circle is P, diameter of circle is RQ and three radii are PR, PQ, PS.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
From the given figure:
P = Center of circle
RQ = diameter of circle
PQ,PS,PR = radii of circle
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Select your answer to the question below: * AABC is shown below. Suppose the triangle is translated 5 units to the right and 7 units down. What are the coordinates of the image of vertex B after this transformation? : Y 6 B'C 2 A C. 8 G 2 4 A (8-6) B (2-6) c (-3.-6) D (2.0)
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From the given graph,
The coordinates of point B are (-3, 7)
The triangle ABC has translated 5 units to the right and 7 units down
That means the x coordinate of B must add by 5 and the y-coordinate must subtract by 7
The rule is (x + 5, y - 7)
The image of point B is B'
B' = (-3 + 5, 7 - 7)
B' = (2, 0)
The image of point B is (2, 0)
A car has 34,000,miles on its odometer and accumulates an average of 100 more each week. What is the function rule that represents the total m miles the car will have on the odometer after w weeks?
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Answer:
Step-by-step explanation:
M= 100m +34,000w
Answer: it would be A. for you, but for me it was C.:
m = 34,000 + 100w
what I mean is the answers were jumbled around.
1) After the rise in popularity of the Croc shoe, a competitor brand will launch in January called “Srocs.” The company spends $9 to manufacture each pair of Sroc shoes. They also spend $8,000 on their Sroc-making machine and $4,000 on ads. One of the founders wants to sell each pair for $49 because that is the retail price for Crocs, but the other founder says they should sell the Srocs for $39.Write an equation for the company’s costs:Determine which price option you would choose and why.How much of the product must be sold to break even (using your chosen selling price)?
Answers
Company's costs:
Sroc's making machine = $8000
Ads = $4000
For each manufactured pair of Sroc shoes = $9
We add them to find the cost equation in terms of x manufactured pair of Srocs:
[tex]\begin{gathered} C(x)=8000+4000+9x \\ \\ \Rightarrow C(x)=9x+12000 \end{gathered}[/tex]There are two options for the selling price:
[tex]\begin{gathered} P_1(x)=49x \\ P_2(x)=39x \end{gathered}[/tex]We use each of them to find out how many Srocs we need to sell in order to have a null profit:
[tex]\begin{gathered} 49x=9x+12000 \\ 40x=12000 \\ x=300 \end{gathered}[/tex][tex]\begin{gathered} 39x=9x+12000 \\ 30x=12000 \\ x=400 \end{gathered}[/tex]As we can see, we need to sell only 100 pairs of Srocs more to recover the investment. Therefore, we choose the selling price P₂:
[tex]\text{ Selling price: \$39}[/tex]Finally, we have already found how much of the product must be sold to break even:
[tex]\text{ Answer: 400 pairs of Srocs}[/tex]I need help, I don’t know which one would have factors of 5x-8
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
factor:
5x - 8
Step 02:
difference of squares:
(5x - 8)(5x + 8) = 25x² - 64
The answer is:
25x² - 64
A machine can fill 5,400 bottles in 3 hours. How many bottles can it fill in 8 hours?
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Answer:
14400
Step-by-step explanation:
A store manager records a positive number to show when a deposit is made to the store's bank account and a negative number to show withdrawals.
Which equation could represent how the store manager records making 3 withdrawals of $36 each?
O 3 x 36 108
O 3x-36= -108
-3 x 36 108
O-3 x-36= -108
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Answer:
03*36 108 the positive number
you have torn a tendon and is facing surgery to repair it. the surgeon explains the risks to you: infection occurs in 3% of such operations, the repair fails in 17%, and both infection and failure occur together in 2%. what percentage of these operations succeed and are free from infection? give your answer as a whole number.
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Our required probability is 99.82% or a 100%
%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.
What is the definition of percentage in statistics?
Percentages. The use of percentages to express statistics is one of the most popular. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By dividing the whole or whole number by 100, one percent (or 1%) is equal to one hundredth of the total or whole.
Given that P(operational infection occurs at a 3% rate)
P(operational repair failures) = 17%
P(infection and failure happen simultaneously) = 2%
The first thing we'll discover is that P(infection or failure) is given by 0.03 + 0.17 - 0.02 = 0.18 = 0.18%.
Therefore, the probability that these procedures will be successful and infection-free is given by 100 - 0.18 = 99.82%.
Consequently, 99.82% of a probability is needed.
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John recently purchased $4,106.00 worth of a stock that is expected to grow in value by 8% each year for the next ten years.Assuming this growth forecast holds, which function will show the value of John's stock in tyears?A(t) = 1.08(54,106)A(O) = 54,106(1.1)A(0) = 54,106(1.08)A(t) = $4,106(1.08)
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The exponential growth formula:
[tex]A(t)=A_0(1+r)^t[/tex]Given:
[tex]\begin{gathered} A_0=\text{ \$4106} \\ t=10yrs \\ r=8\%=\frac{8}{100}=0.08 \end{gathered}[/tex]Therefore,
[tex]A(t)=4106(1+0.08)^t=4106(1.08)^t[/tex]Hence, the answer is
[tex]A(t)=\text{ \$}4106(1.08)^t[/tex]How do I Graph the line with the given slope m and y-intercept b.
M=-4/3,b=2
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Then look at your slope “m” and the top is the vertical movement and the denominator is the horizontal movement. So to solve this, you start at (0,2) and you have two choices, to go down 4 and right three OR up 4 left 3.
Remember: if the slope a integer, the denominator is one so you can move left or right one according
Find the degree of the polynomial.2x6 − 4x2 + 3x − 1
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Given:
There are given the equation:
[tex]f(x)=2x^6-4x^2+3x-1[/tex]Explanation:
According to the question, we need to find the degree.
So,
From the concept of degrees:
The degree is the largest exponent of the variable.
Final answer:
Hence, the value of the degree is 6.
the radius of a circle is 3 inches long. what is the circumference?
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Given:
a.) A circle with a radius of 3 inches long.
To be able to get the circumference of the circle, we will be using the following formula:
[tex]\text{ C = 2}\pi r[/tex]Where,
C = Circumference
r = radius
We get,
[tex]\begin{gathered} \text{ C = 2}\pi r \\ \text{ = 2(3.14)(3)} \\ \text{ = 6 x 3.14} \end{gathered}[/tex][tex]\text{ C = 18.84 in.}[/tex]Therefore, the circumference of the circle is 18.84 in.
Using the Distributive Property, which of the following expressions are equivalent to 7 x 6? Select all that apply. A. (6 x 7)+(6 x 7)
B. (5×6) + (2 × 6)
C. (7 x 6) + (1 x 6)
D. (7 x 6) + (2 x 6)
E. (2 x 6)+(5 x 6)
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By using the Distributive Property, the equivalent expression to 6 x 7 is option (B) (5 x 6) + (2 x 6) and option (E) (2 x 6) + (5 x 6).
Distributive property:
The distributive Property defines that when a factor is multiplied by the addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
This property can be stated symbolically as:
A ( B+ C) = (A x B) + (A x C)
Where A, B and C are three different values.
Given,
Here we have the expression 7 x 6.
Now, we need to find the equivalent expression by using the distributive expression.
AS per the definition of distributive property,
First we have o identify in which term is got separated,
Here they separated the term 7.
So, there three way for dividing it,
They are,
6 + 1 = 7
2 + 5 = 7
3 + 4 = 7
Based on these, we have two way to write the expression,
one is,
(5 x 6) + (2 x 6)
Another way is,
(2 x 6) + (5 x 6)
So, the correct options are option (B) and (E).
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In the similaritytransformation of AABCto ADEF. ABC was dilatedby a scale factor of 1/2reflected across the !? 1,and moved through thetranslation [1.
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Solution: C. Y-Axis
Analysis: In this case, the triangle is reflected across the Y-Axis. That's the reason why the triangle changes the orientation of the initial triangle.
Example: Point B reflects Point E. X=2 to X=-2. And the value of Y stands.
In health class, Leslie is learning about making healthy food choices. For a lesson on digestive health, her teacher asks everyone to track how much fiber they eat daily. At breakfast, Leslie has a banana. She also has raisin bran cereal, which contains 3.8 grams of fiber. In all, Leslie eats 6.7 grams of fiber at breakfast.
Use an equation to find the amount of fiber in the banana.
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The amount of fiber in the banana is 2.9 grams of fiber.
What is a equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the. information, she has raisin bran cereal, which contains 3.8 grams of fiber and in all, Leslie eats 6.7 grams of fiber at breakfast.
Let the fiber in banana be b. This will be illustrated as:
b + 3.8 = 6.7
Collect like terms
b = 6.7 - 3.8
b.= 2.9
The fiber is 2.9 grams
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Using the conjugate zeros theorem to find all zeros of a polynomial
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We know that 1+i is a root of the polynimial. This also implies that 1-i is also a root of the polynomial. In other words, the term
[tex](x-1+i)(x-1-i)[/tex]is a factor of our polynomial. This last expression can be written as
[tex](x-1+i)(x-1-i)=x^2-2x+2[/tex]so, in order to find the remaining zero, we can compute the following division of polynomials,
which gives
Therefore, the remaining root is x=1.
In summary, the answer is:
[tex]1+i,1-i,1[/tex]In 2002, the population of Isosceles City was 200,000. If expected growth is 10% per year, what will the expected population be in 2010?
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The expected population in [tex]2010[/tex] will be [tex]428,717.762[/tex].
In [tex]2002[/tex] the population of Icosceles city was [tex]200,000[/tex].
The expected growth per year [tex]=10%[/tex]%
We have to find the expected population in [tex]2010[/tex].
From [tex]2002[/tex] to [tex]2010[/tex] the total years are [tex]8[/tex].
Since the population is increased every year so the population of previous year added. So we can see that the population is increased compound. We can find the total population by multiplying the population in 2002 with the rate assembled by one. So we can use the formula
Total population in [tex]2010=[/tex]Population in [tex]2002(1+\frac{rate}{100})^{year}[/tex]
Total population in [tex]2010=[/tex] [tex]2010=200,000(1+\frac{10}{100})^{8}[/tex]
Total population in [tex]2010=200,000(1+\frac{1}{10})^{8}[/tex]
Total population in [tex]2010=200,000(\frac{11}{10})^{8}\\[/tex]
Total population in [tex]2010=200,000(\frac{214,358,881}{100000000} )[/tex]
Total population in [tex]2010=200,000(2.14,358,881)[/tex]
Total population in [tex]2010=428717.762[/tex]
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If two lines intersect to form a right angle, then they are
..(perpendicular, parallel, obtuse
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I just need someone to show how to brake down and solve this?
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help meeeeeeeeee pleaseee !!!!!
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The total number of toys sold if the daily sales of the toy is $6.50 is 2750 toys.
Functions and valuesEach element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The independent values are known as the domain while the dependent are the codomain.
Given the function that represents the price-sales relationship for number of toys as;
y = 6000 - 500x
If the daily sales of the toy is $6.50, the total toys sold will be:
y = 6000 - 500 (6.50)
y = 6000 - 3250
y = 2750 toys
This gives the total number of toys sold.
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