Answer:
9
Step-by-step explanation:
shorter leg = x
longer leg = x + 3
Hypotenuse = x + 6
x² + (x + 3)² = (x + 6)²
x² + x² + 6x + 9 = x² + 12x + 36
2x² + 6x + 9 = x² + 12x + 36
x² - 6x - 27 = 0
(x - 9) ( x + 3) = 0
x = 9 or x = -3 (rejected)
The length of the shorter leg of the right angles triangle is 9.
What is a right-angle triangle?
A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle. The right triangle or 90-degree triangle is another name for this triangle.
A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse
The right triangle's three sides are interconnected. The Pythagorean Theorem explains this connection. This theorem states that in a right triangle, [tex]h^{2} = x^{2} + y^{2}[/tex];
where, h = hypotenuse; x = perpendicular side; y = base side;
Given that:
shorter leg = x
longer leg = x + 3
Hypotenuse = x + 6
⇒x² + (x + 3)² = (x + 6)²
⇒x² + x² + 6x + 9 = x² + 12x + 36
⇒2x² + 6x + 9 = x² + 12x + 36
⇒x² - 6x - 27 = 0
⇒(x - 9) ( x + 3) = 0
⇒x = 9 or x = -3.
x=-3 is not possible;
Hence, The length of the shorter leg = 9.
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Mary and Jane are trying to set up their marmalade selling business. They started off by peeling the oranges. Mary peels 8 oranges in 10 minutes while Jane peels 3 oranges in 5 minutes. If they need to peel 500 oranges for their first batch of marmalade, how long (in hours) will it take them to finish peeling? (round off to nearest hr)
Answer:
6.0 hours
Step-by-step explanation:
1 hour is the same as 60 minutes.
"Mary peels 8 oranges in 10 minutes"
1 hour = 60 minutes = 6 * 10 minutes
In 1 hour, she peels 6 times as many oranges, so Mary peels 48 oranges in 1 hour.
"Jane peels 3 oranges in 5 minutes"
1 hour = 60 minutes = 12 * 5 minutes
In 1 hour, she peels 12 times as many oranges, so Jane peels 36 oranges in 1 hour.
Combined, the peel 48 + 36 = 84 oranges in 1 hour.
(500 oranges)/(84 oranges/hour) = 5.952 hours
Answer: 6.0 hours
What is the measure of ∠JSM?
A) 12°
B) 17°
C) 23°
D) 31°
I think it would be “B”
Answer:
Option B.
Step-by-step explanation:
Given information: [tex]m\angle A=48^{\circ},\angle E=90^{\circ},\angle EMS=59^{\circ}[/tex].
According to the angle sum property of a triangles, the sum of interior angles of a triangle is 180°.
Apply angle sum property on triangle AEJ.
[tex]\angle A+\angle E+\angle J=180^{\circ}[/tex]
[tex]48^{\circ}+90^{\circ}+\angle J=180^{\circ}[/tex]
[tex]138^{\circ}+\angle J=180^{\circ}[/tex]
Subtract 138 from both sides.
[tex]\angle J=180^{\circ}-138^{\circ}[/tex]
[tex]\angle J=42^{\circ}[/tex]
The measure of angle J is 42°.
According to exterior angle property, the sum of two interior angles of a triangle is equal to the third exterior angle.
Apply exterior angle property on triangle JMS.
[tex]\angle EJA+\angle JSM=\angle EMS[/tex]
[tex]42^{\circ}+\angle JSM=59^{\circ}[/tex]
Subtract 42 from both sides.
[tex]\angle JSM=59^{\circ}-42^{\circ}[/tex]
[tex]\angle JSM=17^{\circ}[/tex]
The measure of ∠JSM is 17°.
Therefore, the correct option is B.
The leg of a right triangle is 3 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle . need help !!
Answer:
[tex]\sqrt{7}[/tex]
Step-by-step explanation:
let the other leg be x
Then using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 3² = 4²
x² + 9 = 16 ( subtract 9 from both sides )
x² = 7 ( take the square root of both sides )
x = [tex]\sqrt{7}[/tex]
Answer:
Square root of 7
Step-by-step explanation:
Find the area of the trapezoid.
75
15×6÷2+10×6÷2
90÷2+60÷2
45+30
75
The answer is 75.
Hope this helps!
The denominator of the seventh term is
125
216
343
512
343 will be your answer
Answer: Thus, Third option is correct.
Step-by-step explanation:
Since we have given that
[tex]1,\dfrac{1}{8},\dfrac{1}{27},\dfrac{1}{64},...............\dfrac{1}{n^3}[/tex]
So, we can see the pattern:
General term of the series is given as
[tex]\dfrac{1}{n^3}[/tex]
So, we just put the value of n = 7, to get the required denominator:
[tex]\dfrac{1}{7^3}=\dfrac{1}{343}[/tex]
Hence, the denominator of the seventh term is 343.
Thus, Third option is correct.
11. Determine whether the triangles are similar. If so, what is the similarity statement and the
postulate or theorem used?
(please answer ASAP if you have the all of the questions for the semester exam I'll take them too please)
A.>TRS~>TPQ;SSS~
B.>TRS~>TPQ;SAS~
C.>TRS~>PQR;SAS~
D.The triangles are not similar
Answer:
Option B
Step-by-step explanation:
we know that
SAS Similarity Theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
In this problem
∠STR is congruent with ∠QTP
Verify if the corresponding sides are proportional
[tex]\frac{42}{42+6}=\frac{28}{28+4}[/tex]
[tex]\frac{42}{48}=\frac{28}{32}[/tex]
[tex]42*32=48*28[/tex]
[tex]1,344=1,344[/tex] ----> is true
therefore
The triangles TRS and TPQ are similar by SAS
which of these is the best definition of a circle?
Answer:
C
Step-by-step explanation:
It is all the points on a plane that are the same distance away from 1 fixed point.
That makes C the answer. There are definitions here for a parabola (B), an ellipse (A) and a Hyperbola (D).
Only C is correct for the circle.
Answer: C just did it
The area of a playground is 160 yd2. The width of the playground is 6 yd longer than its length. Find the length and width of the playground.
Answer:
length=10\ yd, width=16\ yd
Answer:
Length of the playground is 10 yd and the Width of the playground is 16 yd .
Step-by-step explanation:
Formula
Area of a rectangle = Length × Width
As given
The area of a playground is 160 yd².
The width of the playground is 6 yd longer than its length.
Let us assume that the length be x .
Thus
Width = x + 6
Put all the values in the formula
160 = x × (x + 6)
160 = x² + 6x
x² + 6x - 160 = 0
x² + 16x - 10x - 160 = 0
x (x + 16)-10 (x + 16) = 0
(x -10)(x + 16) = 0
Thus
Either (x - 10) = 0 or (x + 16 ) = 0
x = 10 or x = -16
(Negative value is neglected because sides cannot be negative.)
Thus
x = 10
Length = 10 yd
Width = 10 + 6
= 16 yd
Therefore the length of the playground is 10 yd and the width of the playground is 16 yd .
Does anyone know this?! Pls help
Answer:
Step-by-step explanation:
we are given the angles of XYR = 40, ZXY = 130, and SRY = 40 degrees.
angle ZXY is half of angle ZAY, so angle ZXY is 65 degrees.
imagine a line XA (not on the diagram). then ZXA is 32.5 degrees since it is half of YXZ. Angle XZA and ZXA are equal, so XZA is 32.5 degrees. RZA = XZA + RZX = 32.5 + 40 degrees (assuming the upper left stated degree belongs to angle XZA), or simply RZA is 72.5 degrees.
since ZRA = RZA, then ZRA is 72.5 degrees. since angle ZRS = SRY + ZRA, finally ZRA = 40 + 72.5 degrees or simply, ZRS = 112.5 degrees. which visually is blantantly wrong as it appears to be less than 90 degrees.
A right rectangular prism has a length of 10 in., a width of 12 in., and a height of 16 in. The dimensions of the prism are halved. What is the surface area of the reduced prism? Enter your answer in the box. in²
Answer:
[tex]S.A=236in^2[/tex]
Step-by-step explanation:
The given prism has dimension;
[tex]L=10in.,W=12in.,H=16in.,[/tex]
If the dimensions of the prism are halved then;
[tex]l=5in.,w=6in.,h=8in.,[/tex]
The surface area of the reduced prism will be;
[tex]S.A=2(lw+lh+wh)[/tex]
[tex]S.A=2(5(6)+5(8)+6(8))[/tex]
[tex]S.A=2(30+40+48)[/tex]
[tex]S.A=2(118)[/tex]
[tex]S.A=236in^2[/tex]
Answer:
236in²
Step-by-step explanation:
Given in the question,
length of rectangular prism = 10 in
width of rectangular prism = 12 in
height of the prism = 16 in
Since the dimensions are reduced to half so the new dimensions are
length of rectangular prism = 5 in
width of rectangular prism = 6 in
height of the prism = 8 in
Formula to calculate the surface area
2(lw + lh + wh)
2 ((5x6) + (8x5) + 2(6x8))
236 in²
Plz help me with this
Answer: A) 13
Step-by-step explanation:
Mean - 1 SD: 20.2 - 2.4 = 17.8 --> (18)
Mean + 1 SD: 20.2 + 2.4 = 22.6 --> (23)
Now, find the values on the histogram for 18 through 23:
2 + 3 + 4 + 3 + 1 + 1 = 13
I’m thinking of a number. The square of this number is the same as the number times 4. What could my number be?
Answer:
4
Step-by-step explanation:
4 squared equals 16 and 4 times 4 equals 16
Write the equation 4x + 2y = 5 in the form y = mx + b.
Answer:
4x+2y-5=0
Step-by-step explanation:
since you have to put the problem in that order you take 5 from both sides
Answer:
The correct answer is y = -2x + 5/2
Step-by-step explanation:
y = mx + b. is the y intercept form of a line.
To find the y = mx + b. form
It is given that,
4x + 2y = 5
2y = -4x + 5
Dividing both sides by 2 we get,
2y/2 = (-4x + 5)/2
y = -4x/2 + 5/2
y = -2x + 5/2
Here m = -2 and b = 5/2
Could someone check over me? Thanks!
Answer:
Yes, I agree with A. :)
Step-by-step explanation:
A toy manufacturer uses 1,000 plastic wheels to make 250 toy trucks. If they use 3,584 plastic wheels in an 8 hour shift, how many toy trucks are made per hour?
Answer:
112 trucks
Step-by-step explanation:
so you take ratio:
1000-250
3584-x
x=896
and after you divide 896 by 8 hours and get 112
hope it helped you
Helpppppp PLZZZZZZZZZZZZ
Answer:
Final answer is m∠D = 61°.
Step-by-step explanation:
Given that m∠C = 98°,
m∠B = 140°,
m∠A = m∠D ,
Using those information we need to find the value of m∠D.
We know that sum of all 4 interior angles of a quadrilateral is always 360°.
So we can write equation:
m∠A +m∠B +m∠C +m∠D = 360°
m∠A + 140° + 98° +m∠D = 360°
m∠D + 140° + 98° +m∠D = 360°
2(m∠D) + 140° + 98° = 360°
2(m∠D) + 238° = 360°
2(m∠D) = 360° - 238°
2(m∠D) = 122°
m∠D = 122°/2
m∠D = 61°
Hene final answer is m∠D = 61°.
Answer:
the answer is 61°
Step-by-step explanation:
360- 98- 140 = 122 ÷2 = 61
!HELP!
I need to write an expression for the shaded region in its simplest form, showing all of my steps!
But it's late at night and I'm not entirely sure how to do this, so thank you so much in advance!!!
Answer:
x² + 23x + 49
Step-by-step explanation:
Area of the big rectangle
= (x + 10)(2x + 5)
= 2x² + 5x + 20x + 50
= 2x² + 25x + 50
Area of the small white rectangle
= (x + 1)(x + 1)
= x² + x + x + 1
= x² + 2x + 1
Area of the shaded area
= (2x² + 25x + 50) - (x² + 2x + 1)
= 2x² + 25x + 50 - x² - 2x - 1
= x² + 23x + 49
Lesson 4 practice problems.
Answer:
which is the question yours asking help for
Which of the following are solutions to2x^2-8x-90? Select all that apply. 2
-5
-7
9
15
5
7
Answer:
9,-5
Step-by-step explanation:
2x^2-8x-90
Factor by 2
2(x^2 -4x-45)
What two numbers multiply to -45 and add to -4
-9*5 = -45
-9+5 = -5
2(x-9) (x+5)
Set this equal to zero
2(x-9) (x+5) =0
Divide by 2
(x-9) (x+5) =0
Using the zero product property
x-9=0 x+5=0
x=9 x=-5
A(n) ____ is NOT an example of an agreement.
A) Lease
B) Month-to-month
C) Annual
D) Fine Print
Answer:
D) Fine Print
Fine print is part of an agreement but technically isnt one.
Final answer:
The correct answer is D) Fine Print. Fine Print is not an agreement but refers to the small, often hard-to-read text in a contract that contains important legal provisions.
Explanation:
The correct answer is D) Fine Print. A lease is a contractual agreement between a lessor and a lessee that gives the lessee the right to use a property owned by the lessor for a specific period in exchange for payment. A month-to-month agreement is a type of lease which automatically renews each month until either party decides to terminate it. An annual agreement typically refers to a contract or lease that is renewed once per year.
The perimeter of the triangle below is 4x + 3y. Find the measure of the missing side. (Picture of triangle)
Answer: 2x+3y
Step-by-step explanation: look at picture
To find the missing side in a triangle with a given perimeter, subtract the lengths of the known sides from the total frame. This is based on the sum of the lengths of all sides of a triangle, which equals its circumference.
Explanation:We need to understand a simple rule about triangles to find the missing side of a triangle where the perimeter is 4x + 3y. The sum of all sides of a triangle equals its edge. So, if we know the length of the other two sides, we can subtract their sum from the total circumference to find the size of the missing side.
For example, if we know that the other two sides of the triangle are 2x and y, respectively, the missing side would be calculated by subtracting the sum of these sides from the given perimeter.
4x + 3y = perimeter
2x + y = known sides
missing side = (4x + 3y) - (2x + y)
Note: This method assumes that x and y values are provided. If they're unknown, we will require additional equations to solve for x and y before calculating the length of the missing side.
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Which of the following terms appear in the expansion of (x+y)^10? The letter "a" in each term represents a real constant.
Choices are:
ax^4y^6
ax^5
ax^3y^7
ax^6y^4
Can be multiple
ANSWER
[tex]ax^4y^6[/tex]
[tex]ax^3y^7[/tex]
[tex]ax^6y^4[/tex]
EXPLANATION.
The given binomial is
[tex]( {x + y)}^{10} [/tex]
One property about all the terms in this binomial expansion is that:
The degree of each term is 10.
[tex]ax^4y^6[/tex]
degree=4+6=10
[tex]ax^3y^7 [/tex]
degree=3+7=10
[tex]ax^6y^4[/tex]
degree=6+4=10
[tex]ax^5[/tex]
degree=5+0=5
All the terms with degree 10 are the correct options
Answer:All of them except for ax^5
Step-by-step explanation:
You add what it’s being squared too and if it equals ten then it’s correct since we’re trying to find (x+y)^10
calculate the slope of the given points (6,2) and (8,2)
Answer:
0
Step-by-step explanation:
Since both points are on the the line (0,2) there is no slope/the slope is 0
There is no slope it just a straight line
Find the area of the trapezoid by decomposing it into other shapes.
A) 35 cm2
B) 39 cm2
C) 40 cm2
D) 48 cm2
Answer:
A) 35 cm2
Step-by-step:
Answer:
A- 35 cm2
Step-by-step explanation:
a refund of $3.15 on a $8.64 bill
8.64 - 3.15 = $5.49 if this is what you are asking
Answer:
Step-by-step explanation:
3.15-8.64 is5.49 hope this helps
What does this equal to in standard form? (A+bi)
[tex]
3i(-7+11i)=-28i+33i^2=\boxed{-33-28i}
[/tex]
Answer:
-33 - 21i
Step-by-step explanation:
3i (-7 + 11i)
= -21i + 33i^2 (i^2 = -1)
= -21i + 33(-1)
= -33 - 21i
[WILL GIVE BRAINLIEST ANSWER] f(x)=(x-5)(5x+2) write the smaller solution first and the smaller solutuon second
Answer:
x = - [tex]\frac{2}{5}[/tex], x = 5
Step-by-step explanation:
Given
f(x) = (x - 5)(5x + 2)
To obtain the solutions set f(x) = 0, that is
(x - 5)(5x + 2) = 0
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5 ← larger x
5x + 2 = 0 ⇒ 5x = - 2 ⇒ x = - [tex]\frac{2}{5}[/tex] ← smaller x
A game is played with a deck of 50 cards numbered from 1 to 50. At the end of each round, players calculate their score by adding the numbers on their cards.
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
Answer:
28, 329, 11
Step-by-step explanation:
What is the least score a player could have if he or she has 7 cards remaining at the end of a round?
28 pointsWhat is the greatest score a player could have if he or she has 7 cards remaining at the end of a round?
329 pointsGlenna needs to get 60 points in the next round to win the game. What is the least number of cards Glenna needs to be guaranteed a win?
11The least score a player could have is if he or she has 7 cards remaining at the end of round 28.
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
Calculation:-
Addition of the first 7 natural number (out of 50 cards)
In order to get the minimum value
⇒1+2=3+4+5+6+7=28
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Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?
Answer:
1 dollar.
Step-by-step explanation:
"Chris spent $8 on lunch. 75% was spent on a sub ad the rest was used to buy two cookies. How much was each cookie?"
.75=75%
8*.75=cost of sub=6
total cost- cost of sub=cost of cookies
8-6=2
The cost of 2 cookies is 2 dollars
Now to find the cost per cookie we take the total cost of the cookies, and divide it by the amount of cookies-
2/2=cost per cookie=1
It cost $1 for each cookie.
Use the distributive property to remove the parentheses.
-5(6y - u - 2)
Answer:
-30y+5u+10
Hope this helped