SLV is a 45°-45°-90° triangle with leg SV. If SV = m, determine the length ofthe other leg and the hypotenuse.
Answers
Since angles S and L are congruent, the triangle SLV is isosceles with base SL, that means SV = LV.
Since SV = m, we have LV = m
Now, to calculate the hypotenuse, we can use Pythagorean theorem:
[tex]\begin{gathered} SL^2=SV^2+LV^2 \\ SL^2=m^2+m^2 \\ SL^2=2m^2 \\ SL=m\cdot\sqrt[]{2} \end{gathered}[/tex]Related Questions
Donna got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 21 cents per yard. If after that purchase there was $21.22 left on the card, how many yards of ribbon did Donna buy?
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Given data:
Initial amount of money: $25.00
Final amount of money: $21.22
Price of ribbon: $0.21 per yard
1. Find the money Donna spend in the craft store: Subtract the final amount of money from the initial amount of money:
[tex]25.00-21.22=3.78[/tex]2. Divide the result of step 1 by the price per yard of the ribbon:
[tex]\frac{3.78}{0.21}*\frac{100}{100}=\frac{378}{21}[/tex]Then, Donna bought 18 yards of ribbonIn this activity, you’ll use the inspection method to rewrite a rational expression, a(x)/b(x), in the form q(x) + r(x)/b(x).Answer these questions to step through the process of rewriting x^2-5x+7/x-9Part ACan the polynomial in the numerator of the expression x^2-5x+7/x-9 be factored to derive (x-9) as a factor?Answer is noPart DWhat number must be added to the numerator to get the new constant term you identified in Part C?Part EAdd the number you calculated in part D to the numerator, and then subtract the number to keep the value of the expression unchanged.Part F Rewrite the numerator so it contains a trinomial that can be faced with x-9 as a common factor, and then write it in the factored formPart GRewrite the expression you found in part F as the sum of two rational expressions with (x-9) as their common denominator Part HReduce the first fraction and write the expression in this format:A(x)/b(x) = q(x)+ r(x)/b(x)
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The expression is:
[tex]\frac{x^2-5x+7}{x-9}[/tex]Part B
To get -9 to -5, we need to add 4. This is important because the factored form will be something like this:
[tex]x^2-5x+7=(x-9)(x+a)[/tex]And when we distribute it, the middle term will be the sum of -9 and a, so we if we want it to be -5 (as the given expression) a has to be 4.
Part C
Now, looking to the constant part, it will be the multiplication of -9 and a, since we know that a is 4, the constant term is:
[tex]-9\cdot4=-36[/tex]So, we need a constant term of -36 in the numerator.
Part D
Since we already got 7 in the numerator, we have to add -43 to get it to -36.
Part E
[tex]\frac{x^2-5x+7}{x-9}=\frac{x^2-5x+7+(-43)-(-43)}{x-9}=\frac{x^2-5x-36+43}{x-9}[/tex]Part F
[tex]\frac{x^2-5x+-36+43}{x-9}=\frac{(x-9)(x+4)+43}{x-9}[/tex]Part G
[tex]\frac{(x-9)(x+4)+43}{x-9}=\frac{(x-9)(x+4)}{x-9}+\frac{43}{x-9}[/tex]Part H
[tex]\frac{(x-9)(x+4)}{x-9}+\frac{43}{x-9}=x+4+\frac{43}{x-9}[/tex]So:
[tex]\frac{x^2-5x+7}{x-9}=x+4+\frac{43}{x-9}[/tex]2h-3(3-h)+_=5h-8 Solve
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ANSWER
1
EXPLANATION
We have the equation:
2h - 3(3 - h) + _ = 5h - 8
We need to find the missing number.
Let us expand the bracket and simplify the equation. We have:
2h - 9 + 3h + __ = 5h - 8
Collect like terms:
__ = 5h - 2h - 3h - 8 + 9
=> __ = 1
Therefore, the missing number is 1.
What are the critical points of f prime = 2x -2/x
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The critical points of f prime are at x = ± 1
What are critical points?Critical points of a function are the points at which the function changes direction.
How to find the critical points of f prime?Since we have the function f'(x) = 2x - 2/x
Since the functionis f'(x), this implies that it is a derivative of x.
So, to find the critical points of f'(x), we equate f'(x) to zero.
So, we have that
f'(x) = 0
⇒ 2x - 2/x = 0
⇒ 2x = 2/x
cross-multiplying, we have that
⇒ 2x² = 2
Dividing through by 2, we have that
⇒ x² = 2/2
⇒ x² = 1
Taking square root of both sides, we have that
⇒ x = ±√1
⇒ x = ± 1
So, the critical points are at x = ± 1
Learn more about critical points here:
https://brainly.com/question/26978374
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I need help.on a problem
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the equation
[tex]-1.26\times n=-10.08[/tex]total days
we solve n dividing all expression by -1.26
[tex]\begin{gathered} \frac{-1.26\times n}{-1.26}=\frac{-10.08}{-1.26} \\ \\ n=8 \end{gathered}[/tex]then the total number of days is 8
Explain the Pythagorean Theorem, and provide two additional examples (other than football) of how it can it apply to sports
Answers
Given:
The objective is to explain Pythagorean Theorem with two examples by applying it to sports.
Explanation:
The Pythagorean Theorem states that. in a right triangle the sum of the squares of a two perpendicular legs will be equal to the square of the largest side of the triangle.
Consider a right triangle ∆ABC right angled at B.
By applying the Pythagorean Theorem to the above right triangle,
[tex]AC^2=AB^2+BC^2\text{ . . . . . .(1)}[/tex]Example 1:
Consider a tennis player standing striking the ball to the service line of opponent field.
Let the height of the tennis player will be h = 3m.
The distance between the tennis player and the opponent service line is x = 18m.
Then, the distance at which the tennis player strikes the ground can be calculated as,
From the above diagram the distance d can be calculated using equation (1) as,
[tex]d^2=h^2+x^2\text{ . . . . . . (2)}[/tex]On plugging the values in equation (2),
[tex]\begin{gathered} d^2=3^2+18^2 \\ d^2=9+324 \\ d=\sqrt[]{333} \\ d\approx18.25m \end{gathered}[/tex]Example 2:
Consider a basket ball player ready to take a free throw standing at a horizontal distance of 20 ft from the ring and holding the ball at with distance of 10ft below the ring.
Then, the hypotenuse distance of the ring can be calculated using equation (1) as,
[tex]\begin{gathered} x^2=10^2+20^2 \\ x^2=100+400 \\ x=\sqrt[]{500} \\ x\approx22.36ft \end{gathered}[/tex]Hence, the explanation for Pythagorean Theorem with two examples are provided.
graph the equation y= -x² + 10x - 16. you must plot 5 points including the roots and the vertex
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Given the function:
[tex]y=-x^2+10x-16[/tex]The graph of the function is plotted and attached below:
From the graph:
• The roots are (2,0) and (8,0).
,• The vertex is a maximum that occurs at (5,9)
,• The graph intersects the y-axis at (0,-16).
The other points are added as a guide when plotting your own graph.
Hi, I have no clue how to do proportions and can you explain how to do this? If you can't that's alright.
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___________________
Please, give me some minutes to take over your question
______________________________________
Rate = miles / time
8/t = 7/ 35
Dividing by 7
8/t = 7/ 35
8/ 7t = 1/ 35
Multiplying by t
8/7 = t/35
_____________
Options
1) 8/t = 35/ 7 (False, t/8 = 35/ 7 )
2) t/8 = 7/ 35 (False, t/8 = 35/ 7 )
3) 8/7 = t/ 35 (TRUE)
4) 7/8 = t/35 (False, 8/7 = t/ 35 )
__________________
Answer
3) 8/7 = t/ 35 (TRUE)
Todd mowed 1/3 of his yard in the morning and then 3/6 of his yard in the
afternoon. How much of his yard has Todd mowed so far?
1 point
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Answer: 5/6 of the yard mowed
Step-by-step explanation:
We will add 1/3 to 3/6 to find the total amount of yard mowed so far.
1/3 + 3/6 = 2/6 + 3/6 = 5/6 of the yard mowed
If a regular polygon has exteriorangles that measure approximately17.14° each, how many sides doesthe polygon have?
Answers
To answer this question we will set and solve an equation.
Recall that the exterior angle of an n-gon has a measure of:
[tex]\frac{360^{\circ}}{n}.[/tex]Let n be the number of sides that the polygon that we are looking for has. Since the regular polygon exterior angles with a measure of approximately 17.14 degrees, then:
[tex]\frac{360^{\circ}}{n}\approx17.14^{\circ}.[/tex]Therefore:
[tex]n\approx\frac{360^{\circ}}{17.14^{\circ}}[/tex]Simplifying the above result we get:
[tex]n\approx21.[/tex]Answer: 21 sides.
Find the slope of the line that passes through (-31, 26) and (4, 36).
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The slope of a line can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You know that the line passes through the following points:
[tex]\mleft(-31,26\mright);(4,36)[/tex]For this case, you can set up that:
[tex]\begin{gathered} y_2=36 \\ y_1=26 \\ x_2=4 \\ x_1=-31 \end{gathered}[/tex]Then, knowing the coordinates shown above, you can substitute them into the formula in order to find the slope of the line. This is:
[tex]\begin{gathered} m=\frac{36-26}{4-(-31)} \\ \\ m=\frac{10}{35} \\ \\ m=\frac{2}{7} \end{gathered}[/tex]The answer is:
[tex]m=\frac{2}{7}[/tex]What is the simplified form of each expression?a. 10^8b. (0.2)^5
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Answer:
(a)100,000,000
(b)0.00032
Explanation:
(a)To determine the simplified form of 10^8
[tex]\begin{gathered} 10^8=10\times10\times10\times10\times10\times10\times10\times10 \\ =100,000,000 \end{gathered}[/tex](b)To determine the simplified form of (0.2)^5
[tex]\begin{gathered} 0.2^5=(0.1\times2)^5 \\ =0.1^5\times2^5 \\ =0.00001\times32 \\ =0.00032 \end{gathered}[/tex]2 (4k + 3)- 13 = 2 (18 - k) 13
Answers
Given the expression:
[tex]2(4k+3)-13=2(18-k)-13[/tex]solve for k :
[tex]2\cdot4k+2\cdot3-13=2\cdot18-2k-13[/tex][tex]8k+6-13=36-2k-13[/tex]combine the like terms:
[tex]undefined[/tex]-sqrt-50 in radical form
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We have the following expression:
[tex]-\sqrt[]{-50}[/tex]The prime factorization of 50 is
[tex]\begin{gathered} 50=2\times5\times5 \\ 50=2\times5^2 \end{gathered}[/tex]Then, we can rewritte our expression as
[tex]-\sqrt[]{-50}=-\sqrt[]{-(2\times5^2})=-i\sqrt[]{2\times5^2}[/tex]because the square root of -1 is defined as the complex i. Then, we have
[tex]\begin{gathered} -\sqrt[]{-50}=-i\times\sqrt[]{2}\times\sqrt[]{5^2} \\ or\text{ equivalently,} \\ -\sqrt[]{-50}=-i\times\sqrt[]{2}\times5 \end{gathered}[/tex]Therefore, the answer is
[tex]-\sqrt[]{-50}=-5\sqrt[]{2}\text{ i}[/tex]Is anyone able to assist with this complex question? Thanks
Answers
Solution
Step 1:
A finite discontinuity exists when the two-sided limit does not exist, but the two one-sided limits are both finite, yet not equal to each other. The graph of a function having this feature will show a vertical gap between the two branches of the function.
ms or mr could you please help me out with this problem?
Answers
The coordinates of the triangle after reflection over the line x= 1 will be A'(5,0), B' (2,4) and C'(2,0)
The first thing we need to do here is to label the coordinates of the vertices of the triangle
What we need here is to know the coordinates of the points A,B and C on the graph
Let us have our scale as 1 cm representing 1 unit on both axes
We have the coordinates of the vertices as follows;
A = (-3, 0)
B = (0,4)
c = (0,0) ; it is at the origin
Now, we will perform a reflection on these coordinates over the line x= 1
To perform a reflection over the line x = 1,
Matematically given that we want to reflect over a line with equation x = b,
The coordinates of the reflected point will be;
(2b-x, y)
So for A (-3,0); A' will be (2(1)-(-3), 0) = (5,0)
For B (0,4), B' will be (2(1)-0, 4) =(2,4)
C' will be (2(1)-0, 0) = (2,0)
So the coordinates of the reflected image will be;
A'(5,0) , B' (2,4) , C (2,0)
Hence, we proceed to get these points on the graph.
After locating them, we join them together to form a triangle
What is the equation of the line that passes through the point (-5, -3) and
has a slope of -3/5?
Answers
Answer:
y = (-3/5)x - 6
Step-by-step explanation:
m = slope: (-3/5); (-5, -3)
(x₁, y₁)
y - y₁ = m(x - x₁)
y - (-3) = (-3/5)(x - (-5)
y + 3 = (-3/5)(x + 5)
y + 3 = (-3/5)x - 3
-3 -3
-------------------------
y = (-3/5)x - 6
I hope this helps!
15. Find the volume of the figure below.20 yd15 yd9 yd12 yd- 20.9
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The volume of a triangular prism is the following equation:
[tex]V=Ah[/tex]where A represents the area of the base and h represents the height of the prism.
In this case, the area of the base is the following:
[tex]A=\frac{12\cdot9}{2}=\frac{108}{2}=54yd^2[/tex]then, the volume of the prism is:
[tex]V=54(20)=1080yd^3[/tex]if you could draw the graph, that would be great!!
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The functions we have are:
[tex]\begin{gathered} F(x)=x^2 \\ G(x)=3x+1 \end{gathered}[/tex]And we need to graph F-G
Step 1. Find the expression for F-G.
We subtract the expressions for F(x) and G(x):
[tex]F-G=x^2-(3x+1)[/tex]Simplifying this expression:
[tex]F-G=x^2-3x-1[/tex]Step 2. Graph the expression.
In the following image, we can thee the graph for F-G:
will send image 8.2 + x + 2; x= 3.1
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For x = 3.1
10) 8.2 + x
Yellow chip = +1 Red chip = -1Find the sum of 4 + -5 using the counter chips.4=-5=4 + -5 =
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Notice that 5 is greater than 4.
To find 4-5, remember that when a greater number is subtracted from another, the result is a negative number. Then, the result is the same as the result of 5 minus 4 but with a negative sign.
Since 5-4 is equal to 1, then:
[tex]4-5=-1[/tex]Therefore, the answer is: -1.
Gemma had $2, 054 in her checking account. She wrote acheck for $584 to pay the rent on her apartment. After thelandlord cashed the check, how much money did Gemmahave left in her checking account?
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Solution
Given that Gemma had $2, 054 in her checking account.
She wrote a check for $584 to pay the rent on her apartment.
That means she would have $2, 054 - $584 = $1, 470 left in her checking account
Option C
Suppose that ABC is isosceles with base BA.Suppose also that mZ B=(5x+24)° and mC = (2x + 72).Find the degree measure of each angle in the triangle.с(2x + 72)m 2A =0D9Хm ZB =Аm LC =BT(5x + 24)口。
Answers
1) The best way to tackle questions like these is to sketch out:
2) We were told that this is an isosceles triangle therefore at least 2 of their angles are congruent to themselves. Therefore we can write down the following equation also considering the Triangle Sum Theorem:
[tex]\begin{gathered} 5x+24+5x+24+2x+72=180 \\ 12x+48+72=180 \\ 12x+120=180 \\ 12x+120-120=180-120 \\ 12x=60 \\ \frac{12x}{12}=\frac{60}{12} \\ x=5 \end{gathered}[/tex]Note that now, we can find the measure of each angle by plugging x=5:
[tex]\begin{gathered} m\angle A=m\angle B=5x+24=5(5)+24=49^{\circ} \\ m\angle A=m\angle B=49^{\circ} \\ m\angle C=2(5)+72 \\ m\angle C=82^{\circ} \end{gathered}[/tex]3) Thus the answer is:
[tex]m\angle A=49^{\circ},m\angle B=49^{\circ},m\angle C=82^{\circ}[/tex]suppose cos(0) = -3/7 and 0 is in quadrant 2. What is the value of sin(0)?
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In the second quadrant, the sine function is positive while the cosine function is negative.
[tex]\Rightarrow\cos \theta<0,\sin \theta>0[/tex]Furthermore, we can use the following trigonometric identity.
[tex]\cos ^2\theta+\sin ^2\theta=1[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow\sin ^2\theta=1-\cos ^2\theta \\ \Rightarrow\sin \theta=\pm\sqrt[]{1-\cos ^2\theta} \\ \Rightarrow\sin \theta=\sqrt[]{1-\cos^2\theta} \end{gathered}[/tex]Because sin(theta) has to be positive, as stated before; thus,
[tex]\begin{gathered} \Rightarrow\sin \theta=\sqrt[]{1-(-\frac{3}{7})^2}=\sqrt[]{1-\frac{9}{49}}=\sqrt[]{\frac{40}{49}}=\frac{\sqrt[]{40}}{7}=\frac{2\sqrt[]{10}}{7} \\ \Rightarrow\sin \theta=\frac{2\sqrt[]{10}}{7} \end{gathered}[/tex]Thus, the answer is sinθ=2sqrt(10)/7
Find the Area of the figure below. Round to the nearest tenths place
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The Figure contains a trapezium and a semicircle. The area of the figure would be the sum of the area of the trapezium and the area of the semicircle. The formula for finding the area of a trapezium is expressed as
Area = 1/2(a + b)h
where
a and b are the length of the parallel sides of the trapezium
h = height of trapezium
From the diagram,
a = 13
b = 6
h = 8
Area = 1/2(13 + 6)8
Area = 76
The formula for finding the area of a semicircle is expressed as
Area = 1/2 x pi x radius^2
pi = 3.14
diameter = 6
radius = diameter/2 = 6/2
radius = 3
Area = 1/2 x 3.14 x 3^2
Area = 14.13
Area of figure = 76 + 14.13
Area of figure = 90.1
the graph shows that school's profit P for selling x lunches on one day.The school wants to change the price for lunch so that when it sells more than 30 lunches in one day, it begins to make a profit.How much would the school need to charge for each lunch situation?
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Find the slope of the line. That will give us the present price for each lunch.
Use the points (0,-150) and (50,0):
[tex]\begin{gathered} m=\frac{0--150}{50-0} \\ \Rightarrow m=3 \end{gathered}[/tex]Then, the current profit equation is given by:
[tex]y=3x-150[/tex]We want to change the price of each lunch so that the point (30,0) belongs to the graph (that means that when selling 30 lunches, it begins to make profit).
Let M be the new price. Then:
[tex]\begin{gathered} 0=30M-150 \\ \Rightarrow30M=150 \\ \Rightarrow M=\frac{150}{30} \\ \therefore M=5 \end{gathered}[/tex]Therefore, the school should charge 5 dollars for each lunch.
Translate the sentence into an inequality.The sum of a number times 6 and 18 is at least -28.Use the variable b for the unknown number.
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Traslating the sentence into an inequality, we get:
[tex]6b+18\ge-28[/tex]Find the point of intersection of the following pair of equations, then sketch your solutions indicating all point where the equations intersect both sets of axes: a) y = 2x – 1 and x + 2y = 5b) ^2 + ^2 = 4 and 3x + y = 2
Answers
Answer:
a) Intersection of the equations (1.4, 1.8)
b) Intersection of the equations (0, 2) and (1.2, -1.6)
Explanation:
Part a) y = 2x – 1 and x + 2y = 5
To find the intersection point, let's replace the first equation on the second one, so
x + 2y = 5
x + 2(2x - 1) = 5
Now, we can solve the equation for x
x + 2(2x) - 2(1) = 5
x + 4x - 2 = 5
5x - 2 = 5
5x - 2 + 2 = 5 + 2
5x = 7
5x/5 = 7/5
x = 1.4
Then, replace x = 7/5 on the first equation
y = 2x - 1
y = 2(1.4) - 1
y = 2.8 - 1
y = 1.8
Then, the graph of the lines is:
Where the intersection points with the axes for y = 2x - 1 are (0, -1) and (0.5, 0) and the intersection points with the axes of x + 2y = 5 are (0, 2.5) and (5, 0)
Part b) ^2 + ^2 = 4 and 3x + y = 2
First, let's solve 3x + y = 2 for y, so
3x + y - 3x = 2 - 3x
y = 2 - 3x
Then, replace y = 2 - 3x on the first equation and solve for x
x² + y² = 4
x² + (2 - 3x)² = 4
x² + 2² - 2(2)(3x) + (3x)² = 4
x² + 4 - 12x + 9x² = 4
10x² - 12x + 4 = 4
10x² - 12x + 4 - 4 = 0
10x² - 12x = 0
x(10x - 12) = 0
So, the solutions are
x = 0
or
10x - 12 = 0
10x = 12
x = 12/10
x = 1.2
Replacing the values of x, we get that y is equal to
For x = 0
y = 2 - 3x
y = 2 - 3(0)
y = 2 - 0
y = 2
For x = 1.2
y = 2 - 3(1.2)
y = 2 - 3.6
y = -1.6
Therefore, the intersection points are (0, 2) and (1.2, -1.6)
Then, the graph of the functions are:
Since ^2 + ^2 = 4 is a circle with radius 2, the intersection points with the axes are (2,0), (0, -2), (-2, 0) and (0, 2). Additionally, the intersections potins with the axis of the line 3x + y are (0, 2) and (0.667, 0)
match each vertex in triangle EFG to it corresponding vertex in the dashed triangle
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The matching is as following:
[tex]\begin{gathered} E\rightarrow H \\ F\rightarrow E \\ G\rightarrow G \end{gathered}[/tex]it’s a system of equation graph and they need to be matched with its solution
Answers
Explanation
Step 1
[tex]\begin{gathered} f(x)=2^x-3 \\ j(x)=x+2 \end{gathered}[/tex]a) to graph f(x) , we start from the function
[tex]\begin{gathered} f(x)=2^x \\ then,\text{ we shift the graph 3 units down, so} \end{gathered}[/tex]b) j (x) is a line, so we need 2 points
[tex]\begin{gathered} j(0)=0+2=2 \\ P1(0,2) \\ and \\ j(1)=1+2=3 \\ P2(1,3) \end{gathered}[/tex]then, draw a line that passes through P1 and P2
finally, the solution is the point where the graph intersect each other, so
so, we can conclude that
the answer is