Answers
You only have to apply the theorem of Pythagoras here. Remember the square on the hypotenuse (the longest side) is equal to the sum of the squares on the other two sides :
1. AB is the hypotenuse, so, according to the theorem we can write :
AB² = AC² + CB²
c² = 5² + 4²
c²= 25 + 16
c² = 41
applying the square root of 41 we get :
c ≈ 6.40 rounded to the hundred
The next cases are exactly the same thing so there is no need for explanation :
2.
AB is the hypotenuse here because it is the biggest side clearl :
AB² = AC² + CB²
25² = 15² + b²
Thus
b² = 25² - 15²
we just subtracted 15² on each side of the equation
b² = 625 - 225
b² = 400
applying the square root of 400 we get
b = √400 = 20
So AC = 20
3. The longest side is clearly AB = 60
So
AB² = AC² + CB²
60² = 40² + a²
subtracting 40² on each side of the equation we get :
a² = 60² - 40²
I let you finish this using your calculator and doing exactly like the previous cases
4.
AB is the hypotenuse,
AB² = AC² + CB²
23² = b² + 14²
Subtracting 14² from each side of the equation we get
b² = 23² - 14²
5.
AB is the biggest side :
AB² = AC² + CB²
29² = 23² + a²
We subtract 23² on each sides of the equation :
a² = 29² - 23²
You can finish with your calculator
6.
AB² = AC² + BC²
78² = b² + 30²
subtraction...
b² = 78² - 30²
Good luck :)
Related Questions
Please help with this question and if you can explain because I’m confused. - thank you
Answers
y = 32, x = 43
To figure this out, you have to use what you know to find all sorts of measures.
Lets start with the 75 degree angle. We know that the opposite side is a vertical angle, so that is also equal to 75 degrees. Since the angle to the big triangle is a supplementary angle, we know that the sum of 75 degrees and that angle is 180 degrees. Do the math and we get 180 - 75, or 105 degrees. The angles of a triangle always add up to 180, so 105 + 43 + y = 180. Solve for y: [tex]148+y=180=148-148+y=180-148=y=32[/tex]. So y is equal to 32 degrees. Now to find x, we know that the bases of the triangles are parallel, and that there is a line that goes straight from angle y to one of our unknown angles. Because the triangle bases are parallel and the y to unknown line does not change, we can tell that those are the same. So y = unknown angle 1, or 32 = 32. So, we know the measure of one angle. The other unknown angle is vertical to the other angle we found earlier, 105. So, we get 105 + 32 + x = 180. Evaluate: [tex]32+105+x=180=137+x=180=137-137+x=180-137=x=43[/tex]. So x is equal to 43.
a) Solve the system by substitution.
y = 5x – 3
-X – 5y = -11
Answers
Answer:
Step-by-step explanation:
the answer 4x-5y +2 = 0. 5y =-4x-2. y = -4x/5 -2/5 slope = -4/5
Answer:
{y,x} = {2,1}
Step-by-step explanation:
// Solve equation [1] for the variable y
[1] y = 5x - 3
// Plug this in for variable y in equation [2]
[2] -5•(5x-3) - x = -11
[2] - 26x = -26
// Solve equation [2] for the variable x
[2] 26x = 26
[2] x = 1
// By now we know this much :
y = 5x-3
x = 1
// Use the x value to solve for y
y = 5(1)-3 = 2
Mike has $84 less than three times as much as Dave. Together they have $132. How much money does Mike have?
I have to use either the system of equation strategy of elimination or substitution to solve this. I realize that the first equation is
m + d = 132. But I don’t get what the second equation should be!
Answers
Answer: $48
Step-by-step explanation:
132 - 84 = 48
Evaluate. [2−∣∣−1/4−2(−3/5)∣∣]÷(−6) What is the value of the expression? Enter your answer as a simplified fraction in the box.
Answers
Answer:
-7/40
Step-by-step explanation:
I hope this helps!
The sides of a rectangle are in the ratio of 5:6. If its longer side is 7.2 in., find the shorter side, the perimeter, and the area of this rectangle.
Answers
Answer:
The shorter side is 6.
The perimeter is 26.4 inches.
The area is 43.2 inches[tex]^{2}[/tex]
Step-by-step explanation:
The ratio 5;6 and the given longer side is 7.2 in.
Since it is the longer side, the '6' in the ratio is 7.2 in.
Let x be the shorter side
5:6 = x : 7,2
Divide 7.2 to 6.
7.2 ÷ 6 = 1.2
Then multiply 1.2 to 5.
1.2 * 5 = 6
So the shorter side is 6.
L = 7.2
W = 6
Now to find the perimeter, let's use the formula
P = 2L + 2W
Let's put the values in the formula
P = 2(7.2) + 2(6)
P = 14. 4 + 12
P = 26.4
The perimeter is 26.4 inches
To find the area, let's use the formula
A = LW
A = (7.2)(6)
A = 43. 2 inches[tex]^{2}[/tex]
Answer:
shorter side= 6
p= 26.4
a= 43.2
Step-by-step explanation:
blank as 9 hundred is 9 thousand
Answers
Answer:
x = 10
Step-by-step explanation:
x × 900 = 9000
=> 900x = 9000
=> x = 10
Find the 66th term of the arithmetic sequence 3, 13, 23, ...3,13,23,...
Answers
Answer:
[tex]a_{66}[/tex] = 653
Explanation:
General formula: [tex]a_{n}[/tex] = ([tex]a_{1}[/tex] + ((term) - 1) · (common difference)
[tex]a_{66}[/tex] = 3 + (66 - 1) · (10)
[tex]a_{66}[/tex] = 653
arsene wenger pushes a box with a force of 60N over a distance 10m calculate the work done
Answers
Answer:
600J
Step-by-step explanation:
work done = force x distance
= 60 x 10
= 600J
The workdone by arsene wenger in joules is 600J
What is workdone?Work doneis defined as product of the force and the distance over which the force is applied. It is a scalar quantity and it is measured in Joules.(J)
Workdone is expressed as;
Workdone = f × d
where do is the force and d is the distance.
The force he uses on the box is 60N and the distance he pushes the box is 10m. All quantities in their SI unit.
Therefore, the workdone by arsene wernger is
W = 60 × 10
W = 600J
learn more about workdone from
https://brainly.com/question/25573309
#SPJ3
Jenny drove 335 miles in 5 hours at the same rate how long would it take her to drive 871 miles?
Answers
Answer: x = 13 hours
Step-by-step explanation:
335 miles/5 hours = 67 mi/hr
(67 mi/hr)x = 871 miles
x = 13 hours
Solve the system by substitution. x=-y-9 6x-5y=1
Answers
Answer:
x= -64, y= 55
Step-by-step explanation:
x=-y-9
6(y-9)-5y=1
6y-54-5y=1
y=55
x=-55-9
x=-64
Answer:
{x=-4
{x= -5
Step-by-step explanation:
Substitute into one of the equations:6(- y -9) - 5y=1
Apply Multiplicative Distribution Law:- 6y-54-5y=1
Rearrange unknown terms to the left side of the equation:-6y -5y = 1+54
Combine like terms:- 11y= 1+54
Calculate the sum or difference:-11y=55
Divide both sides of the equation by the coefficient of variable:y= 55÷(-11)
Remove the parentheses:y = -55÷11
Calculate the product or quotient:y=-5
Substitute into one of the equations:x=-(-5)-9
Remove the parentheses:x=5-9
Calculate the sum or difference:x=-4
The solution of the system is:{x=-4
{x=-5.
amara needs $624 for her budget every week. She works 40 hours a week.CLEARCHECKWhat is the minimum amount Tamara needs to earn per hour?$per hour
Answers
15.6 or
Step-by-step explanation:
Based on the given conditions, formulate:
624 ÷ 40
Reduce the fraction:
get the result:
15.6 or
Answer:
15.6 or
(Hope this helps can I pls have brainliest
You bought for hamburgers you gave the cashier $50 bill and get $22 change how much was each hamburger
!!!!!!!!5 step plan please!!!!!!!!
Answers
$28/4hamburgers=$7
Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and
potatoes. His plan for the field layout in feet is shown in the figure below. Use the figure and your
knowledge of polynomials, perimeter and area to solve the following questions.
1. Write a polynomial expression that represents the area of the potato field.
2. Simplify a polynomial expression that represents the area of the potato field.
3. Explain why the calculated area would be useful to Farmer Bob.
Answers
The simplified polynomial expression that represents the area of the potato field is x^3 + 13x^2 + 54x + 72
From the diagram shown, we can see that the area of the potato field can be represented as a scaled factor of the area of the farm because they are both rectangular in nature.
Area of the potato field = length * width
Length = x^2 + 7x + 12
Width = x + 6
Substitute into the formula to get the required polynomial
Area of the potato field = (x^2 + 7x + 12)(x+6)
Area of the potato field = x^3+6x^2+7x^2+42x+12x+72
Area of the potato field = x^3 + 13x^2 + 54x + 72
Hence the simplified polynomial expression that represents the area of the potato field is x^3 + 13x^2 + 54x + 72
Learn more on polynomial expression here: https://brainly.com/question/21534285
Carlos spent 1 1/4 hours doing his math homework. He spent 1/4 of this time practicing his multiplication facts.
How many hours did Carlos spend practicing his multiplication facts?
____ of an hour
A: 1/4 of an hour
B: 3/8 of an hour
C: 1/16 of an hour
D: 5/16 of an hour
Answers
Please help i attached a link below to the graph
Write the linear inequality shown in the graph. The gray area represents the shaded region.
y ≥ –x – 4
y ≥ –x + 4
y ≤ –x – 4
y ≤ –x + 4
Answers
Answer: y ≤ -y+4
Step-by-step explanation:
The line in the graph:
Taking two points, we can calculate the slope of the line. I'll pick (0,4) and (4,0)
Rise/Run (slope): Rise (0-4) = -4, Run = (4-0) = 4. Slope is -4/4 or -1.
The y-intercept is 4 (the value of y when x is zero).
The equation for the line is y = -x + 4. The shades area includes all points on and under this line, so y ≤ -y+4.
Given: SR is the perpendicular bisector of QT; QR is the perpendicular bisector of SP
Prove: PQ=TS
Answers
Two lines are said to be perpendicular if they are at right angle to each other. The prove that PQ = TS is as stated below:
SR ⊥ QT (given)
QR ⊥ PS (given)
Comparing Δ PQS and ΔQST, we have:
Points Q and T are equidistant to bisector SR (bisection property of a line)
Points P and S are equidistant from QR (bisection property of a line)
QS is a common side to the triangles
Then,
PS ≅ QT (similar property of triangles)
Thus,
PQ ≅ ST (Side-Side-Side (SSS) property of triangles)
Therefore by Side-Side-Side (SSS) theorem, PQ = ST.
Visit: https://brainly.com/question/8691470
A line passes through the points (-4,5) and (1,-5). Write the equation of the line in slope-
intercept form.
A.y = - 2x - 3
B. y= - 2x + 3
C. y = 2x - 3
D. y = 2x +3
Answers
Answer:
y = -2x - 3
Step-by-step explanation:
Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2
y-intercept= 5 - (-2)(-4) = 5 - 8 = -3
What is the
leasure of Z?
x
У
4.
9
Z=
=
= [?]V
Give your answer in simplest form.
Answers
Answer:
z = 3√13
Step-by-step explanation:
The length of z is the geometric mean of the segments of the longest side that share a common point with z. The shorter of those is 9; the longer one is 4+9 = 13. Then ...
z = √(9(13))
z = 3√13
__
Additional comment
In like fashion, ...
x = √(4(13)) = 2√13y = √(4·9) = 6.__
These relations come about because all of these right triangles are similar. That means their side lengths are proportional.
long side/hypotenuse = z/13 = 9/z ⇒ z = √(9·13)
short side/hypotenuse = x/13 = 4/x ⇒ x = √(4·13)
short side/long side = 4/y = y/9 ⇒ y = √(4·9)
State if the triangles are similar. If so, how do you know they are similar and complete the similarity
statement
STU ~
Answers
Answer:
b. not similar
Step-by-step explanation:
Side SC of the smaller triangle is ...
96 -57 = 39
So, the side lengths of the small triangle, shortest to longest, are ...
39, 40, 44
Side ST of the larger triangle is ...
44 +64 = 108
So, the side lengths of the large triangle, shortest to longest, are ...
96, 96, 108
These lengths do not have the same ratios as the lengths of the sides in the smaller triangle, so the triangles are not similar.
_____
Additional comment
The larger triangle is isosceles. The smaller triangle is not.
what is 3x-4y= -24 answer
Answers
Answer:
The answer will be ( [tex]x=\frac{-24+4y}{3}[/tex] )
What is the Slope of the equation y = x - 2
Question 4 options:
1
-2
2
0
Answers
Answer:
1
Step-by-step explanation:
Answer:
The slope for the equations y = x - 2 is answer A - 1
Step-by-step explanation:
Graph attached Below
Hope I helped,
Brainliest is always appreciated.
A packet of Hobnobs claims to be 24% bigger!!
It now contains 31 biscuits. How many did it have before?
Answers
Answer:
25
Step-by-step explanation:
124% = 31
1% = 0.25
100% = 25 biscuits
...YUMMY!
Answer:
24
Step-by-step explanation:
Find the range of the following group of numbers: 1, -8, -10, 11, 19
Answers
helpppp me pleaseee
Answers
Answer:
C
Step-by-step explanation:
What is the measure of
Answers
Answer:
45 degrees
Step-by-step explanation:
90+45+45=180 degrees
:))
Answer:
[tex]m\angle A=45\textdegree[/tex]
Step-by-step explanation:
All triangles have a sum of 180°. The problem shows us that two of the angles are 90° and 45°. Therefore, the last angle is 45°.
[tex]m\angle A+45+90=180\\m\angle A+135=180\\m\angle A=45[/tex]
PLS HURRY ONLY CORRECT ANSWERS 50 POINTS NEED THIS IN ONE HOUR
Part A: Rhett made $250 washing cars with his mobile car wash company. He charges $70 per car and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car wash. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
Answers
Part A: 70x+50=$250
Part B: 75x-5x+$35=$250
They differ because in Part A they don't lose any money and just gain it, while in part B they lose money, while gaining more in part A.
not 100% sure on Part B
7.802 divided by 2.1
Answers
Answer:
3.715
Step-by-step explanation:
7.802/2.1 = 3.715
=
3.71
it costs $20 per day to board a dog and $16 per day to board a cat. The kennel needs to make at least $800 per day to cover expenses, but can hold no more than 80 total animals. Write a systems of inequalities, graph , and give two possible solutions to the number of dogs and cats they can board each day
Answers
Answer:
Step-by-step explanation:
the anwer is r=dog y=cat 20r+16y>800-->y>-5/4 r+50 20r-16y<r+80 40 dogs+20 cats 15+55 cats
How do you solve the following equation: n+2*0.5n+1
Answers
Answer:
[tex]n=-\frac{1}{2}[/tex]
Step-by-step explanation:
The order of operators is the next:
ParenthesisExponentsMultiplication and divisionAddition SubtractionSo the first step is multiply and later add up the rest terms ([tex]0.5 = \frac{1}{2}[/tex]).
[tex]n+\frac{2}{2}n + 1 = 0\\n + n + 1 = 0\\2n = -1\\n = -\frac{1}{2}[/tex]
multiply first, add n terms
(2n + 1 = 0)
2n = -1
n = -1/2
Olivia works at a travel agency. She earns 7% commission her sales of airline tickets. How much does she earn when she sells 4 airline tickets, each costing $359.50
Answers
Answer:
$100.66
Step-by-step explanation:
First you have to figure out how much she is making from all four tickets, so 4 x 359.50 is $1,438
She makes 7% commission. In decimal form, that is .07. In order to find what she made, multiply .07 by $1,438.
Olivia makes $100.66