Find the length of the third side. If necessary, round to the nearest tenth. 4 5
Answers
Solution :
We'll solve this using the Pythagorean TheoremLet,
Let AB be Base.4 be BC, where BC is the Perpendicular.5 be AC, where AC is the Hypotenuse.We know that,
[tex]{ \longrightarrow \bf \qquad \: (AB) {}^{2} +( BC) {}^{2} = (AC) {}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: (AB) {}^{2} +( 4) {}^{2} = (5) {}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: (AB) {}^{2} = (5) {}^{2} - ( 4) {}^{2} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: AB = \sqrt{(5) {}^{2} - ( 4) {}^{2}} }[/tex]
[tex]{ \longrightarrow \sf \qquad \: AB = \sqrt{25 - 16 }}[/tex]
[tex]{ \longrightarrow \sf \qquad \: AB = \sqrt{9 }}[/tex]
[tex]{ \longrightarrow {\pmb {\bf\qquad \: AB = 3}}}[/tex]
Therefore,
The length of the third side is 3 .
Related Questions
All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
4
6
Answers
The area of shaded region is 32 square units.
What is area ?"The area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. The area is measured in square units such as square centimeters, square feet, square inches, etc."
To find the area of the shaded region
1. Find the area of the biggest square ([tex]A_{1}[/tex])
Formula for area of a square
[tex]A_{1}[/tex] = side × side
⇒[tex]A_{1}[/tex] = 10×10
⇒[tex]A_{1}[/tex] = 100 square units.
2. Find the area of the unshaded region ([tex]A_{2}[/tex])
[tex]A_{2}[/tex] = X(biggest square)+ 2.Y(smallest square)
⇒[tex]A_{2}[/tex] = [tex](6[/tex]×[tex]6)[/tex] + [tex]2(4[/tex]×[tex]4)[/tex]
⇒[tex]A_{2} =36+2.(16)[/tex]
⇒[tex]A_{2}=68[/tex] square units
3. Find the difference of [tex]A_{1}[/tex] and [tex]A_{2}[/tex]
Area of the shaded part = [tex]A_{1}[/tex] - [tex]A_{2}[/tex]
= 100-68
= 32 square units.
Hence, The area of shaded region is 32 square units.
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If m(x) = x2 3 and n(x) = 5x 9, which expression is equivalent to (mn)(x)? 5x3 9x2 15x 27 25x2 90x 84 x2 5x 12 5x2 24
Answers
The expression that is equivalent to m(n(x)) is [tex]25x^{2} +90x+84[/tex].
It is given that
[tex]m(x) = x^{2} +3\\n(x) = 5x+9[/tex]
If there are two functions f(x) and g(x), how f g(x) will be calculated?If there are two functions f(x) and g(x), f(g(x)) will be obtained by replacing x by g(x) into f(x).
So, [tex]m (n(x))= (5x+9)^2+ 3[/tex]
[tex]m (n(x))= 25x^{2} +81+90x +3[/tex]
[tex]m (n(x))= 25x^{2} +90x+84[/tex]
Therefore, the expression that is equivalent to m(n(x)) is [tex]25x^{2} +90x+84[/tex].
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Answer:
b
Step-by-step explanation:
What is the solution set for 2x^2+15=-11x
Answers
Answer:
x = {-3, -2.5}
Step-by-step explanation:
Simplifying
3 + x = 0
Solving
3 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3
Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3
Combine like terms: 0 + -3 = -3
x = -3
Simplifying
x = -3
Simplifying
5 + 2x = 0
Solving
5 + 2x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5
Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5
Combine like terms: 0 + -5 = -5
2x = -5
Divide each side by '2'.
x = -2.5
Simplifying
x = -2.5
Answer: 11
Step-by-step explanation:
by the way need to show the work.
Answers
Answer:
angle 2 is 85
Step-by-step explanation:
since its facing the 85
Answer:
Answer:1 is 95°
2 is 85°
3 is 95°
Step-by-step explanations
opposite angles are equal so 2 is 85° 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180°
Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°
Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°then 3 is directly opposite to 1 so both are 95
Answer:1 is 95°2 is 85°3 is 95°Step-by-step explanation:directly opposite angles are equal so 2 is 85angles on a straight line add up to 180° so 3 is 180-85=95°then 3 is directly opposite to 1 so both are 95 I hope you're helped?
What is 30% of 20? Please help
Answers
Answer:
the answer is x=6
Step-by-step explanation:
A triangle has an area of 2400cm^2. The angle between two adjacent sides of the triangle is 150°. If the length of one of the adjacent sides is 65cm, calculate the length of the other side correct to 3 significant figures.
Answers
Answer: 73.9
Step-by-step explanation:
Antonio has just graduated from four years of college. For the last two years, he took out a Stafford loan to pay for his tuition. Each loan had a duration of ten years and interest compounded monthly. Antonio will pay each of them back by making monthly payments, starting as he graduates. Antonio’s loans are detailed in the table below. Year Loan Amount ($) Interest Rate (%) Subsidized? Junior 5,894 6. 9 Y Senior 5,258 7. 5 N Once all of his loans are paid off, what will Antonio’s total lifetime cost be? Round all dollar values to the nearest cent. A. $16,246. 80 b. $17,804. 40 c. $7,593. 16 d. $9,874. 76 Please select the best answer from the choices provided A B C D.
Answers
Antonio’s total lifetime cost will be $11680.99 after calculating all loans
What will be Antonio’s total lifetime cost?Given that
Loan Amount ($)
5,894$
5,258$
Interest Rate (%)
6.9%
7.5%
Now for the loan amount 5,894$ at 6.9% interest, the amount will be
[tex]A=P(1+\dfrac{r}{h} )^{n\times t}[/tex]
[tex]A=5894(1+\dfrac{0.069}{12} )^{12\times 10}[/tex]
[tex]A=5894\times(1.00575)x^{120} =11727.76[/tex]
Now for the loan amount 5.258$ at 7.5% interest, the amount will be
[tex]A=5258(1+\dfrac{0.075}{12} )^{12\times 10}[/tex]
[tex]A=5258\times2.1120=111105.23[/tex]
So the total lifetime cost will be
[tex]=11727.76-5894+111105.23-5258=11680.99[/tex]
Thus Antonio’s total lifetime cost will be $11680.99 after calculating all loans
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Answer:
a. $16,246.80
Step-by-step explanation:
EDGE
In a highway building project, 32 miles of a new highway have been
completed. This is three miles less than one third of the entire length.
How long will the new highway be when completed?
Answers
Answer: 105 miles
Step-by-step explanation:
You can write an equation for this problem and solve it.
32 miles=1/3x-3, where x is equal to the total length of the highway.
35=1/3x, and then you multiply by 3, to get x=105
Convert 80 gallons into liters. Round your answer to the nearest whole number.
Answers
Write a real word situation that would require an exact answer
Answers
Answer:
Julie has 5 bunnies. She looses 2. How many bunnies does she have now?
Answer: 3 bunnies left
RIP BUNNIES!!
If you wanted a harder one, then please, be more specific.
HELP O_O
Find the Roots of the polynomial equation!!!
2x^3+2x^2-19x+20=0
Answers
Answer:
Your given polynomial has only one real root which is x= -4
Step-by-step explanation:
find any zero of the polynomial.
x-a divides the polynomial where a is a zero of polynomial:
So x+4 divides [tex]2x^{3} +2x^{2} -19x+20[/tex]
If we factor out a two, we can use the quadratic formula.
2(x^2-3x+2.5) so we have x = (-(-3)+/-(9-4*1*2.5)^(1/2))/2*1)=(3+i) or (3-i)/2 .
Final answer:
[tex]2x^{3} +2x^{2} -19x+20=0[/tex]
then x=-4, (3+i)/2, or (3-i)/2
Graph attached
Zeros are the x intercepts
Only one real zero -1.047Mr.Maar received 18 packages contained 5 crayons for his classroom. Each package 5 crayons. Write an equation that show the total amount of crayons (t) Mr. Maar has.
Answers
Which is not a way to find 9/16
Answers
Answer:
a way to not find the answer is to do anything but divide 9 by 16
Step-by-step explanation:
hope this helps, brainliest appreciated :)
If Event A is "the card is a face card" and Event B is "the card is a spade," demonstrate the equation holds true.
/ 52 = / 13 × / 52
Answers
The demonstration of the equation is an illustration of probability
The complete demonstration of the equation is:
3/52 = 3/13 * 13/52
How to demonstrate the equationIn a standard deck, we have the following parameters:
Event A = Face card = 12
Event B = Spade =13
Number of cards = 52
So, the probability that a card is a spade and a face card is:
P(A and B) = P(A) * P(B)
This gives
P(A and B) = 12/52 * 13/52
Simplify
P(A and B) = 3/13 * 13/52
Further simplify
P(A and B) = 3/1 * 1/52
Multiply
P(A and B) = 3/52
So, the complete demonstration of the equation is:
3/52 = 3/13 * 13/52
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please help! I need to get my grade up before I get put in lunch detention.
Answers
Answer:
it is a pattern. 8: add 1. 9: multiply m by 3 to get n
Construct a quadrilateral MINT such that MI= 5cm, IN = 6cm, NT = 7cm, TM=3cm and MN =9cm
Answers
From the given dimensions, of MI, IN, NT, TM, and MN, the quadrilateral
MINT can be drawn as shown in the attached image.
What are the steps for the construction of MINT?The given dimensions of the quadrilateral MINT are;
MI = 5 cm
IN = 6 cm
NT = 7 cm
TM = 3 cm
MN = 9 cm
The side MN is a diagonal of MINT, therefore;
ΔMIN, and ΔMTN are triangles with a common base = MN
The steps to construct MINT are therefore;
Step 1; Draw the line MN = 9 cm.Step 2; Place the compass at point M and with a radius MI = 5 cm, draw an arc on one side of MN.Step 3; Place the compass at N and with radius IN = 6 cm, draw an arc to intersect the arc dawn in step 1 above.Step 4; Place an arc at point M and with radius TM = 3 cm draw an arc on the other side of MN.Step 5; Place the compass at point N and with radius NT = 7 cm, draw an arc to intersect the arc drawn in step 3.Step 6; Join the point of intersection of the arcs to points M and N to complete the quadrilateral MINT.Please find attached the drawing (showing the construction arcs) of the
quadrilateral MINT created with MS Word.
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Factor the following polynomials by finding a GCF.
Answers
Answer:
5mn(2m + 6n + 1)
Step-by-step explanation:
Look at the coefficients (the numbers): 10, 30, 5
The greatest common factor of 10, 30, and 5 is 5.
Now look at the variable parts of the three terms.
Start with the variable m.
There is m², m, and m.
The GCF of m², m, and m is m.
Now look at the variable n.
There is n, n², n.
The GCF on n, n², and n is n.
The GCF for the entire polynomial is 5mn.
Now we factor out 5mn from all terms.
To factor out 5mn, you divide each term by the GCF, 5mn.
10m²n + 30mn² + 5mn = 5mn(2m + 6n + 1)
The model represents a perfect square monomial. an algebra tile configuration showing only the product spot, which has 4 tiles in 2 columns with 2 rows. first row: 2 x squared. second row: 2 x squared. what equation is represented by the model? (2x)2 = 4x2 (2x2)2 = 4x4 (4x)2 = 8x2 (4x2)2 = 8x8
Answers
A perfect square is an expression that factors into two other expressions that are identical. The equation that represents this model is (2x)²=4x².
What is a perfect square monomial?
A perfect square is an expression that factors into two other expressions that are identical. A monomial is a single phrase made up of a product of constants, variables, and their positive integer powers. As a result, a perfect square monomial is a monomial that factors into two monomials that are identical.
As given to us that the first row consists of tile 2x², and the second row also consists of tile 2x². Thus, the expression can be written as,
[tex]2x^2+2x^2\\\\=(2x)^2=4x^2[/tex]
Hence, the equation that represents this model is (2x)²=4x².
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Answer:
A
Step-by-step explanation:
2022
Let f(x)=x^2−2x−4.
What is the average rate of change for the quadratic function from x=−1 to x = 4?
Enter your answer in the box.
Answers
Solve the system of equations using elimination.
Answers
Answer:
(69/40 , 7/11)
Step-by-step explanation:
multiply the bottom equation by 2
-4x + 8y = 12
4x+3y=-5
cancel out both 4x
8y+3y=11y
12+ -5 = 7
11y=7
divide both sides by 11
y=7/11
substitute that in for y
4x + 3(7/11) = -5
4x + 21/11 = -5
4x = -69/10
x= 69/40
Guys, I’m giving you at least 86 points for you to answer to my last month of my math word problem homework package from The Hung Vuong Learning Centre Incorporated! So guys, please listen up and pay attention to me without ignoring my last month’s math homework package from The Hung Vuong Learning Centre Incorporated for no reason! :D
The question #7 is the difference between the number of the girls and the number of the boys in the outdoors club is 12. There are 4 times the number of the girls decreased by 25 equals 3 times the number of the boys. Please help me as soon as possible to find the number of the girls and the number of the boys in the club.
Please answer to my math word problem question as soon as possible with the best efforts and the best step-by-step explanations in order to get the Brainliest award of all the time! :D
Well anyways, guys, good luck on answering my math word problem question of my last month of my math word problem homework package from The Hung Vuong Learning Centre Incorporated in order to get the best Brainliest award of all of the time, and I will check the answers to see if it’s appropriate for me. :)
Answers
Answer:
girls = 61
boys = 73
Step-by-step explanation:
Let x = number of girls
Let y = number of boys
Given the difference between the number of the girls and the number of the boys in the outdoors club is 12:
⇒ y - x = 12
Given there are 4 times the number of the girls decreased by 25 equals 3 times the number of the boys:
⇒ 4x - 25 = 3y
Rearrange x - y = 12 to make y the subject:
⇒ y = 12 + x
Substitute x = 12 + y into 4x - 25 = 3y and solve for y:
⇒ 4x- 25 = 3(12 + x)
⇒ 4x- 25 = 36 + 3x
⇒ x = 61
Now we have found the value of x, substitute this into y = 12 + x and solve for y:
⇒ y = 12 + 61
⇒ y = 73
HELPPP!!! QUICK
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. You must use the fact that opposite angles in a quadrilateral are supplementary.
Show me:
(a) supplementary equation used to solve for x (1 point)
(b) all math used to calculate for x (1 point)
(c) correct value for x (1 point)
(d) plugging x into expressions for angles A, C, D (1 point)
(e) show all math used to calculate the measures of angles A, C, D (2 points)
(f) all math used to calculate the measure of angle B (1 point)
Answers
Answer:
see image
Step-by-step explanation:
Supplementary means the angles add up to 180°.
Add the given angles and set equal to 180°
To solve, combine like terms, add 10, divide by two to get x all by itself.
Replace x with 95 to find the measures of Angles A, C, D.
Use the supplementary definition a second time to find the measure of Angle B.
see image.
An $80 printer is selling for 37.5% off, find the final price of the printer if sales tax is 5.5%
PLEASE SHOW HOW TO DO IT
Answers
Answer: $54.40
Step-by-step explanation: 37.5%-5.5% = 32% off $80-32% = $54.40
please help, its easy :)
Answers
Answer:
1: 5/20 2: 1 2/20
Step-by-step explanation:
multiply ti to get 20 and multiply the numerator with it
Kelly invested $5,000 in a cd at charter bank. the annual rate is 4.9% compounded monthly. how much is her investment at the end of 8 years? round to the nearest hundredth.
Answers
The investment of the kelly at the end of 8 years is $7393.78.
What will be the investment of kelly at the end of 8 years?It is given that
The principle P= $5000
rate of interest R=4.9%
The rate is compounded monthly so
[tex]CI=P(1+\dfrac{R}{12}^{12t} )[/tex]
By putting the value
[tex]CI= 5000\times (1+\dfrac{0.049}{12}^{12\times8} )[/tex]
[tex]CI=7393.78[/tex]
Thus the investment of the kelly at the end of 8 years is $7393.78.
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Please help! I will give brainliest.
Answers
Step-by-step explanation:
= a_(n-1) x 1.5
1.5a_(n-1)
The age of the father is 42, the age of the son is 9. After how many years will the father be twice as the age of the son?
Answers
Answer:
24 years
Step-by-step explanation:
First, I will set up an equation.
2(9 + x) = 42 + x
18 + 2x = 42 + x
x = 24
9 + 24 = 33
42 + 24 = 66
66 is 2 times 33.
On a trip Joel drove 25 miles more than half the number of miles
Rita drove. Together they drove 340 miles. How many miles did
Joel drive?
Answers
Answer:
194
Step-by-step explanation:
you would do 340 divided by 2 and that gets you 170 then you would subtract 24 from Rita and that is 146 so Rita drove 146 miles. then for Joel you add 170 +24 = 194. So Joel drove 194 miles.
Solve the equations for the given variable then place the equations in the table under the correct solution
Answers
Step-by-step explanation:
X = 3
-14x=-42
-3/5 + x=12/5
X-5=-2
X/4=6/8
X= -3
-6+x=-9
X/3=9
Toby thinks of a number less than 15. He divides it by 2 and then he adds 4. He then divides it by 3. His answer is 3.5
Answers
Answer:
13
Step-by-step explanation:
For this problem, work backwards to determine what the starting number was. Take 3.5 and multiply it by 3 to get 10.5, then subtract 4 to get 6.5. Finally, multiply 6.5 by 2 to get the starting number, which is 13. To check your work, you can always take 13 and perform the operations to make sure you end up with 3.5.
Hopefully this helps- let me know if you have any questions!