Answer:
The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.
Step-by-step explanation:
Let the shorter leg be x.
Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (x + 7).
Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the side lengths and c is the hypotenuse.
The hypotenuse is 13 and the legs are x and (x + 7). Substitute:
[tex](x)^2+(x+7)^2=(13)^2[/tex]
Square:
[tex]x^2+x^2+14x+49=169[/tex]
Simplify:
[tex]2x^2+14x-120=0[/tex]
We can divide both sides by two:
[tex]x^2+7x-60=0[/tex]
Factor:
[tex](x-5)(x+12)=0[/tex]
Zero Product Property:
[tex]x-5=0\text{ or }x+12=0[/tex]
Solve for each case:
[tex]x=5\text{ or } x=-12[/tex]
Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:
[tex]x=5[/tex]
The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.
A vase is shaped like a rectangular prism with a square base of length 11 cm. It has 2 litres of water poured into it. To what height (to 1 decimal place) does the water reach in the vase?
Answer:
x=16.53cm
Step-by-step explanation:
1 liter = 1000 cm^3
The volume of water in the rectangular prism will be 11*11*x = 2000
121x=2000
x=2000/121
x=16.53cm
How many kiloliters are there in 19,000 milliliters?
A. 19
B. 1.9
C. 0.019
D. 0.0019
Answer:
C
Step-by-step explanation:
To convert milli- to kilo-, move the decimal point six places to the left
Sung Lee invests $3,000 at age 18. He hopes the investment will be worth $9,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
.169
Step-by-step explanation:
I hoped I helped you solve sorry if I'm wrong
3(7x)-2(4-x) simplify the expression
Answer:
23x - 8 is the answer in simplify that expression
Answer:
[tex]3(7x)-2(4-x)[/tex]
[tex]21x-2(-x+4)[/tex][tex](21x+2x)-8[/tex][tex]23x-8[/tex]-------------------------
hope it helps...
have a great day!!
lab scale known to have a standard deviation of 0.001gram, speimen weghtted 8 times. average weiht is 4.1602 gram. what is 99% confidence interval
Answer:
[tex]99\% CI=4.1602 \pm 0.0009[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=8[/tex]
Mean [tex]\=x=4.1602[/tex]
Standard deviation [tex]\sigma=0.001gram[/tex]
Generally 99\% confidence from table is mathematically given by
[tex]99\% CI=4.1602 \pm *2.576*\frac{0.001}{\sqrt{{8}}}[/tex]
[tex]P(-z<x<z)=0.99[/tex]
[tex]Z_{\alpha/2}=2.576[/tex]
Generally the equation for 99\% confidence level (CI) is mathematically given by
[tex]99\% CI=\=x \pm Z_{\alpha/2*\frac{\sigma}{\sqrt{{n}}}[/tex]
[tex]99\% CI=4.1602 \pm 0.0009[/tex]
Given the function f(x) = 4x - 2, explain and show how to find the average rate of change between x = 2 and x = 4.
Answer:
The average rate of change between x = 2 and x = 4 is of 4.
Step-by-step explanation:
Average rate of change:
The average rate of change of a function f(x) in an interval [a,b] is given by:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
In this question:
[tex]f(x) = 4x - 2, b = 4, a = 2[/tex]
Thus:
[tex]f(b) = f(4) = 4(4) - 2 = 16 - 2 = 14[/tex]
[tex]f(a) = f(2) = 4(2) - 2 = 8 - 2 = 6[/tex]
Average rate of change:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
[tex]A = \frac{14-6}{4-2}[/tex]
[tex]A = \frac{8}{2}[/tex]
[tex]A = 4[/tex]
The average rate of change between x = 2 and x = 4 is of 4.
Determine the value of x
1)70
2)140
3)40
4)280
5х – 4 y = -10
3х + 2y = 16
Answer:
x= 2, y= 5
Step-by-step explanation:
5x -4y= -10 -----(1)
3x +2y= 16 -----(2)
(2) ×2:
6x +4y= 32 -----(3)
(1) +(3):
5x -4y +6x +4y= -10 +32
11x= 22
x= 22 ÷11 (÷11 on both sides)
x= 2
Substitute x= 2 into (2):
3(2) +2y= 16
6 +2y= 16
2y= 16 -6
2y= 10
y= 10 ÷2
y= 5
A salesperson at DHL Department Store earns $415 per hour and is paid biweekly. FOr the last pay cycle, a sales rep earned 5% commission on sales amounting to $89,500. Calculate their basic wage if they worked for 40 hours each week. please help me, Thanks
Answer:
=$21075
Step-by-step explanation:
Given data
Earnings =$415 per hour
Commission =5%
Sales =$89500
Time =40 hours
Let us find the commission
5/100*89500
0.05*89500
=4475
Let us find the amount earned in 40 hours
40*415
=16600
Total
=16600+4475
=21075
Can someone please help me with this problem?
Answer:
C 6
Step-by-step explanation:
Pythagoras
c² = a² + b²
117 = x² + (x+3)² = x² + x² + 6x + 9 = 2x² + 6x + 9
=>
108 = 2x² + 6x
54 = x² + 3x
0 = x² + 3x - 54 = (x-6)(x+9)
just think by what numbers can we divide 54 without any remainder (so that when multiplying we get 54) ? and which pair of these have a difference of 3 (so that with +/- combination we get "3x" in the multiplication)?
the solutions for x are the 2 numbers that would make one of the bracket expressions 0, as this turns the whole expression to 0.
x = 6 and x = -9
a negative number does not make any sense for a side length.
so, the only possible solution is x = 6
PLEASE HELP ASAP PLSSSSS!!!
Answer:
143 degrees
Step-by-step explanation:
First find angle ACB which is 180-83=97
Then angle ABC which is 180-134=46
Then angle CAB (97+46)-180=37
Finally angle HAB 180-37=143
What is the area and perimeter of the triangle
Answer:
Area = 20yd
Perimeter = 23 yd
Step-by-step explanation:
Area = 1/2 ×bh
b, which I the base = 10yd
h, which is the height = 4yd
Note: 5yd is the base because when you turn the triangle you will see that 10yd is the base and 5yd is the height not 8yd because 8 yd is not a straight line at a right angle
Therefore;
Area = 1/2× 10 × 4
= 1× 5 × 4
= 20yd
Perimeter = 8yd +5yd +10yd
= 13yd + 10yd
= 23yd
What is the sum of the polynomials?
(6x+7+x2)+(2x2-3)
-x^2 +6x+4, 3x^2 +6x+4, 9x+4, 9x^2 +4
9514 1404 393
Answer:
(b) 3x^2 +6x+4
Step-by-step explanation:
(6x+7+x^2)+(2x^2-3)
= (1 +2)x^2 +(6)x +(7 -3) . . . . combine like terms
= 3x^2 +6x +4
Answer:
3x ² + 6x + 4
Step-by-step explanation:
( 6x + 7 + x² ) + ( 2x² -3 )
Remove unnecessary parantheses6x + 7 + x² + ( 2 x² - 3 )
6 x + 7 + x² + 2x ² - 3
subtract the numbers6 x + 7 - 4 + x² + 2x²
collect like terms6x + 4 + 3x²
use the commutative property to reorder the terms3x ² + 6x + 4
Determine if the two triangles are congruent. If they are State how you know. NO LINKS!!!
Problem 25
These triangles are congruent.
The reasoning is the AAS congruence theorem. We have two pairs of congruent angles, as shown by the arc markings, and a pair of congruent sides. The sides are not between the angles. That means AAS is slightly different from ASA. The order matters.
=====================================================
Problem 26
The triangles are not congruent
Why not? Well it all comes down to the angle placement. For the triangle on the right side, the arc is between the shared segment and the segment with the double tickmarks. The other arc is not in the proper corresponding location to be able to use SAS. It would need to be adjacent to the arc on the right for us to use SAS.
If it's hard to visualize what I mean, refer to the diagram below.
=====================================================
Problem 27
The triangles are congruent by SAS
The angles aren't marked, but recall that vertical angles are always congruent. So you could add in angle markers if you wanted, to help complete the diagram. The tickmarks of course tell us which segments are the same length. The angles are between the segments.
====================================================
Problem 28
The triangles are congruent by SSS
Like before, the tickmarks tell us which sides are the same length. So the tickmarks say that we have two pairs of congruent sides. The overlapping sides or shared sides are the third pair of congruent segments. So in reality, we have three pairs of congruent sides. It might help to break up the figure into two separate triangles.
Could someone help please I'm stuck and need desperate help???
Answer:
9/64π
Step-by-step explanation:
The area of a circle is given as :
Area = πr²
The diameter of the circle = 3/4 in
Radius of circle = diameter / 2 = (3/4) ÷ 2 = (3/4) * 1/2 = 3/8 in
Area = π(3/8)²
Area = π * 9/64
Area = 9/64π
H Н
Which two statements are both true?
Di Ta and KFT
EH I TĞ and KT | TG
Di I K and Di 1 ET
ET I TĞ and KF | DI
Ryan rides his bicycle 5 miles in 34 hour. How many miles can he ride at the same rate in 1 hour?
(2x-3)(x+4)=2x2+_-12
Answer:
_ = 5
Step-by-step explanation:
This is the last one thank u !
Answer and Step-by-step explanation:
The answer is that A'C' will be 1.5 times longer than AC.
This is because you are dilating the figure by a scale of 1.5.
#teamtrese #PAW (Plant and Water)
Need help for this please
Answer:
i think 471.24cm³?
i just found the volume for both the cylinder and cone and added them together.
I need more help with 21 questions
Answer:
45
Step-by-step explanation:
9 ÷ 1/5
9 × 5/1
9 × 5
45
Joseph leans a 20-foot ladder against a wall so that it forms an angle of 69° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest hundredth of a foot if necessary.
Answer:
18.67 ft
Step-by-step explanation:
|\
| \
| \
h | \ 20 ft
| \
| \
|-- 69° \
---|----------------
For the 69° angle, h is the opposite leg, and 20 ft is the hypotenuse.
sin A = opp/hyp
sin 69° = h/20
h = 20 * sin 69°
h = 18.67
Answer: 18.67 ft
Deborah finds that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 times, she calculated that she flipped "heads" 45 times. What is the percent difference in theoretical and experimental probability?
Answer:
I have the same doubt so pls answer
Step-by-step explanation:
Nathan is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1978 cans.
What is the mass, in kilograms, of these cans?
Answer:
33.5 kg
Step-by-step explanation:
Each 59 cans are about 1 kg.
He collected 1978 cans.
How many times 59 cans did he collect?
1978/59 = 33.5
He collected 1978 cans which is 33.52 times 59 cans, so he collected 33.5 kg
Simplify by combining like terms. − 5 p + 4 m − 2 p + m
Answer:
-7p +5m
Step-by-step explanation:
− 5 p + 4 m − 2 p + m
Combine like terms
-5p -2p +4m +m
-7p +5m
Answer:
-7p+5m
Step-by-step explanation:
See image below:) :)
[tex] \frac{9}{11} = 0. |?| |?| [/tex]
list the digits that repeat
Step-by-step explanation:
9/11=0.81818181....
the digits that repeat is 81
Answer:
.81 repeating
Step-by-step explanation:
9/11 = 0.81 repeating.
Find lim PLEASE I NEED HELP ASAP !!!!
Computing the limit directly:
[tex]\displaystyle\lim_{h\to0}\frac{f(2+h)-f(2)}h=\lim_{h\to0}\frac{((2+h)^2+(2+h)+1)-7}h\\\displaystyle=\lim_{h\to0}\frac{5h+h^2}h\\=\displaystyle\lim_{h\to0}(5+h)=\boxed{5}[/tex]
Alternatively, you can recognize the limit as being equivalent the derivative of f(x) at x = 2, in which case differentiating and plugging in 2 gives
f'(x) = 2x + 1 => f' (2) = 5
A card deck for a board game has 20 cards, of which 4 are red, 6 are blue, and 10 are purple.
What is the probability of randomly selecting a blue card, then a purple card, without replacement?
Answer:
6/20 or in simplification, 3/10 would be the correct answer.
30% would also be correct :)
And 0.3
need help asap! The graphs below have the same shape. what is the equation of the red graph?
no links
Answer:
B. [tex]g(x) = x^{3} - 5[/tex]
Step-by-step explanation:
The graph of f(x) is the graph of g(x) translated 5 units downwards.
Can y’all help on question 29?!
Answer:
Option C: 20 cm^2
Step-by-step explanation:
Essentially, surface area is just area added up. In this question, there are 4 same rectangles and 2 squares with the areas given. So you have to figure out the total.
Since there are 4 rectangles and each of them has an area of 4cm just multiply 4 by 4 to get 16.
Then, since there are 2 squares with an area of 2 cm each just multiply 2 by 2 to get 4.
Add both numbers, 16 + 4 = 20 and you get your answer.
The total surface area would be 20cm^2.