Mathema
8. Leg XY of the right triangle shown in the
diagram below is twice as long as
leg YZ.
Z
Y
х
If the area of the triangle is 36 cm?, what
is the length, in cm, of leg XY?
(1)
6
(2)
9
(3)
12
(4)
18
(5)
24
Answers
9514 1404 393
Answer:
(3) 12
Step-by-step explanation:
Let x represent the length of leg XY. Then the length of YZ is x/2 and the area of the right triangle is ...
A = 1/2bh
A = 1/2(x)(x/2) = x²/4
36 = x²/4 . . . . . use the given value for area
144 = x² . . . . . . multiply by 4
√144 = 12 = x . . . . . take the square root
The length of leg XY is 12 cm.
Related Questions
PLEASE HELP ASAP WILL GIVE BRAINLEIST FOR AN ACTUAL ANSWER
Answers
Answer:
<V = 40
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
20x = 60+7x+5
Combine like terms
20x = 7x+65
Subtract 7x from each side
20x -7x = 7x+65-7x
13x = 65
Divide each side by 13
13x/13 = 65/13
x = 5
<v = 7x+5 = 7*5+5 = 35+5 = 40
answer:
it's U = 60°
V = 50°
T = 70°
The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
х
4
Answers
Answer:
x = 2√2
Step-by-step explanation:
Since the triangle is isosceles, it means 2 of the angles are equal and 2 of the sides are also equal.
Now, since we see that it is also a right angled triangle, it means one angle is 90°.
Let the equal angles be a.
Thus;
a + a + 90 = 180 (since sum of angles in a triangle is 180)
2a + 90 = 180
2a = 180 - 90
2a = 90
a = 90/2
a = 45°
Now, using sine rule, we can find x. Thus;
x/sin 45 = 4/sin 90
sin 90 = 1
sin 45 = 1/√2
Thus;
x = (4 × 1/√2)/1
x = 4/√2
Let's rationalize the denominator to get;
x = (4/√2) × √2/√2
x = (4√2)/2
x = 2√2
tank contains 250 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answers
Solution :
Given data :
[tex]c_{in}[/tex] = 1 g/L
[tex]r_{in}[/tex] = 5 L/min
[tex]r_{out}[/tex] = 5 L/min
[tex]$v_0$[/tex] = 250 L
[tex]A_0[/tex] = 20 g
∴ [tex]r_{net} = r_{in}- r_{out}[/tex]
= 5 - 5
= 0
[tex]c_{out} = \frac{A}{250} \ g/L[/tex]
Now, [tex]\frac{dA}{dt}=(r_{in} \times c_{in}) - (r_{out} \times c_{out})[/tex]
[tex]$\frac{dA}{dt} = 5-5\left(\frac{A}{250}\right)$[/tex]
[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5[/tex]
[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5 \text{ with} \ A_0 = 20[/tex]
Integrating factor = exp(5 t/250)
Therefore,
[tex]A \times \exp (5t \ /250) = \text{integral of}\ 5 \times \exp (5t / 250) + C[/tex]
Put [tex]A_0=250+C[/tex]
C = -230
[tex]A \times \exp(5t/250) = 250 \exp(5t/250) + (-230)[/tex]
[tex]A(t) = 250-230 \exp(-5t/250)[/tex]
[tex]A(t) = 250-230e^{\left(\frac{-t}{50}\right)} \ g[/tex]
what would be the integer for this problem
???+-8=-2
Answers
Answer:10
Step-by-step explanation:
10 because 10 minus 8 would be 2
Or 6-8= -2
PLEASE HELP!! Please answer all if you can and show answer clearly thankyou sm if u do
Answers
Answer:
Below:
Step-by-step explanation:
A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)
B) 0.45
C) 0.40
A) the total probability has to equal 1.
To find the probability of rat subtract the other animals from1:
Rat = 1 - 0.35-0.4-0.1 = 0.15
Rat = 0.15
B) probability of cat or hamster equals the sum of their probabilities:
Cat = 0.35 + hamster = 0.1 = 0.45
Answer = 0.45
C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16
Answer = 0.16
A construction crew is lengthening a road that originally measured 47 miles. The crew is adding one mile to the road each day. Let L be the length (in miles) after D days of construction. Write an equation relating L to D. Then use this equation to find the length of the road after 31 days.
Answers
Answer:
78 miles
Step-by-step explanation:
Given that:
Original length, L = 47 miles
Additional length (miles) added per day, = 1 mile
Representing as an equation :
L(D) = original length + additional length per day * number of days
Let, D = number of days
L(D) = 47 + D
Length after 31 days :
L(31) = 47 + 31
= 78 miles
In some country the budget for defense exceeded the budget for education by $629.1 billion. If x represents the budget for education, in billions of dollars, how can the budget for defense
be represented?
If x represents the budget for education, in billions of dollars, the budget for defense can be represented by
Answers
Answer:
y = defence
Step-by-step explanation:
x^2 + ( 47y (7 + 6) + 18.1) is a starter point
x^2 + (47y (7+6) + 3(6+ 1/30))
x^2 + (611y + 3(6+1/30))
x^2 + (611y + 18.1)
x^2 + 629.1y
With x representing x billion and y representing y billion for defence
The budget for defense can be represented by the algebraic expression $ (x + 629.1) billion.
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.
Let x represents the budget for education.
Given that the budget for defense exceeded the budget for education by $629.1 billion.
The budget for defense can be represented by (x + 629.1).
Learn more about algebraic expression here
https://brainly.com/question/953809
#SPJ2
What is the area of the triangle centimeters squared 23 CM 16 CM 14 CM
Answers
Answer:
Step-by-step explanation:
82
Answer:
Step-by-step explanation:
.5(half) x 14(base) x 16(height)=112cm
Help pleaseeeee will give brainliest
Answers
Answer:
q.12
angle ACB=180-123
therefore ACB=57
again 5x-15+7x+6+57=180
or,12x+48=180
or,x=132/12
or x=11
Find the volume of each shape. Round your answer to two decimal places.with clear explanation.
Answers
Answer:
Volume = 111.33 in.³
Step-by-step explanation:
The volume of the shape = volume of the rectangular prism part + volume of the triangular prism part
✔️volume of the rectangular prism part:
V = L*W*H
Where,
L = 5.1 in.
W = 3.4 in.
H = 5.9 in.
V = 5.1*3.4*5.9
V = 102.306 in.³
✔️volume of the triangular prism part:
V = ½*b*h*l
b = 6 - 5.1 = 0.9 in.
h = 5.9 in.
l = 3.4 in.
V = ½*0.9*5.9*3.4
V = 9.027 in.³
✅Volume of the shape = 102.306 + 9.027
= 111.333 in.³
≈ 111.33 in.³ (approximated to 2 decimal places)
PLEASE HELP ILL MARK BRAINLIEST
Answers
3,-30,300,-3000 is it geometric or not geometric if so whats the common ratio r=?
Answers
Step-by-step explanation:
everything can be found in the picture
The sum of two numbers in 106 and the greater exceeds the lesser in 8. Find the numbers.
Answers
Step-by-step explanation:
51 and 51
maybe
hope it help uI'm Stuck and need help please). The table shows the test scores and the sleep averages of several students. A) Write the least squares regression equation that models the data. Let x = the test score and y = average sleep. B) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. Show Your Work. ( Will Mark Brainliest but no Links or nonsense answers please). Answer A and Answer B.
Answers
Answer:
a
you should take values of x and y that are similar or they are close to each other like 8 is close to 8.5
b
u will take the average of all the scores with 8hr sleep
42.
A toy store's percent of markup is 45%. A model train costs the store $100. Find the markaup.
(First gets brainliest)
Answers
Answer:
$68.97
Step-by-step explanation:
The equation you have to use is I=p(1.45)
If you have a 45% increase to 100, the original price was $68.97.
The following condensed information was reported by Peabody Toys, Inc., for 2021 and 2020: ($ in thousands) 2021 2020 Income statement information Net sales $ 6,900 $ 5,900 Net income 374 158 Balance sheet information Current assets $ 970 $ 920 Property, plant, and equipment (net) 2,630 2,280 Total assets $ 3,600 $ 3,200 Current liabilities $ 1,660 $ 1,310 Long-term liabilities 920 920 Common stock 700 700 Retained earnings 320 270 Liabilities and shareholders’ equity $ 3,600 $ 3,200 Required: Determine the following ratios for 2021: (Round your percentage answers to 1 decimal place.) Determine the amount of dividends paid to shareholders during 2021. (Enter your answers in whole dollars, not in thousands. For example, $150,000 rather than 150.)
1a. Profit margin on sales 5.4 %
1b. Return on assets %
1c. Return on equity %
2. Dividends paid ?
Answers
Answer:
The answers are given below.
Step-by-step explanation:
The computation is shown below:
1.a.
Profit Margin = Net Income ÷ Sales × 100
= $374 ÷ $6,900 ×100
= 5.4%
1-b:
Average Assets = (Beginning Assets + Ending Assets) ÷ 2
= ($3,200 + $3,600) ÷ 2
= $3,400
Now
Return on Assets = Net Income ÷ Average Assets
= $374 ÷ $3,400
= 11%
1-c
Average Equity = ($700 + $700 + $320 + $270) ÷ 2
= $995
Now
Return on Equity = Net Income ÷ Average Equity *100
= $374 ÷ $995
= 37.59%
2:
Dividends Paid = Beginning Retained Earnings + Net Income – Ending Retained Earnings
= $270 + $374 - $320
= $324
(1/2)5 standard form
Answers
Answer:
[tex]\frac{5}{2}[/tex] or 2.5
Hope that this helps!
Carrie walked 6 miles per day. Which table represents y, the number of miles Carrie walked in x days.
D. Says 1. 18
2. 36
3. 54
4. 72
Answers
Answer:
C
Step-by-step explanation:
Since Carrie walked 6 miles her day, the function that best suits this relationship is given by [tex]y=6x[/tex] where [tex]x[/tex] is the number of days she walked and [tex]y[/tex] is the number of miles.
Table C represents this function [tex]y=6x[/tex] because all y values are exactly 6 times the x value.
Answer:
The answer is C.
Step-by-step explanation:
18 ÷ 3 = 6 miles a day
36÷6 = 6 miles a day
54÷9 = 6 miles a day
72÷12 = 6 miles a day
Question 3
Simplify
4x² × 2x³
Answers
Step-by-step explanation:
[tex]4 {x}^{2} \times 2 {x}^{3} = 8 {x}^{5} [/tex]
Answer:
Step-by-step explanation:
4x^2 * 2x^3
(2)^2 *x^2 *2*x^3
(2)^2+1 *x^2+3
(2)^3 *x^5
8*x^5
8x^5
another method
4*x^2*2*x^3
multiply 4 and 2
8*x^2+3
8x^5
in multiplication if the bases are same we add their power(exponent).In division if the bases are same we subtract their power(exponent).
What is the solution to the following system of equations?
[3x-2y = 12
16x-4y = 24
O It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0).
Answers
Answer:
(0, -6)
Step-by-step explanation:
Given the following systems of linear equations;
3x - 2y = 12 ...... equation 1
16x - 4y = 24 ........ equation 2
We would solve for the solution using the elimination method;
Multiplying eqn 1 by 2, we have;
2 * (3x - 2y = 12)
6x - 4y = 24
16x - 4y = 24
Subtracting the two equations, we have;
(6x - 16x) + (-4y -[-4y]) = (24 - 24)
-10x - 0 = 0
-10x = 0
x = -0/10 = 0
Next, we would find the value of y;
3x - 2y = 12
3(0) - 2y = 12
0 - 2y = 12
-2y = 12
y = -12/2
y = -6
Check:
3x - 2y = 12
3(0) - 2(-6) = 12
0 - (-12) = 12
12 = 12
Note: the options provided for this questions are incorrect or inappropriate.
x over 3 add 5 = 5
Pls help someone
Answers
Answer:
x=0
Step-by-step explanation:
0/3 = 0
0+5=5
Explanation: Plugged it into a calculator to check!
A man bought a car for $8200 and sold it for 80% of the price two years later. How much did he lose?
Answers
Answer:
I don't know for sure, but I'm pretty sure its 1,640.
Step-by-step explanation:
80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
According to question, The price at which it was sold is equal to :
[tex]80 \% \: \: of \: \: 8200[/tex][tex] \dfrac{80}{100} \times 8200[/tex][tex]80 \times 82[/tex][tex]6560[/tex]The car was sold at $ 6560
Now, loss is equal to :
[tex]8200 - 6560[/tex][tex] \$ \: 1640[/tex]The ratio of winners to losers was 7 to 5. If the total number of winners and losers was 1260, how many more winners were there than losers?
Answers
Answer:
210
Step-by-step explanation:
7:5
First add the ratios
7+5=12
Put each ratio over the denominator 12 then multiply each by the total
7/12×1260= 735
5/12 × 1260 = 525
To find how many more winners than losers
735-525= 210
de acuerdo a la sucesion 11,18,25,32... encuentra el término que se ubica en la posición 50
Answers
Answer:
354.
Step-by-step explanation:
De acuerdo a la sucesión 11,18,25,32..., para encontrar el término que se ubica en la posición 50 se debe realizar el siguiente razonamiento lógico-matemático:
32 - 25 = 7
25 - 18 = 7
18 - 11 = 7
Así, los números van subiendo de 7 en 7. Por lo tanto, para determinar el número que se ubica en la posición 50 debe realizarse el siguiente cálculo:
(7 x 49) + 11 = X
343 + 11 = X
354 = X
Por lo tanto, el término que se ubica en la posición 50 es 354.
What is the median of 6, 7, 3, 15, 4, 4.
Answers
Answer:
5
Step-by-step explanation:
The median is the middle when the numbers are lined up from smallest to largest
3,4,4,6,7,15
There are 6 number so the middle is the between the 3rd and 4th number
3,4,4, 6,7,15
Take the 3rd and 4th numbers and average
(4+6)/2 = 10/2 = 5
Answer:
median = 5
Step-by-step explanation:
Arrange the data in ascending order :
3 , 4 , 4 , 6 , 7 , 15
Choose the middle number.
Here there are even number of data. Take the average of the middle
numbers .
4 and 6 are the middle number. average of 4 and 6 = ( 4 + 6 ) /2 = 5
Therefore , median = 5
How long is 20 yards?
A. 600 in.
B. 720 in.
C. 840 in.
D. 900 in.
Answers
Answer:
B) 720 in
Step-by-step explanation:
1 yard is equal to 36 inches.
So, we just have to multiply 20 by 36:
20 × 36 = 720
20 yards is 720 inches.
6,12,24,48 Find the 11'th term
Answers
Answer:
614
Step-by-step explanation:
This pattern is being multiplied by 2
keep multiplying by two till you get to the 11th term
6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144
6144 is the 11th term.
(8,9); x+3y=2 in y=mx+b form
Answers
Answer:
use photo math. it will help
A department store manager noted that the sales of furniture contributed 20% of the store's profits in the year 2015 and 29% in the year 2016.
Of the following choices, which two statements about furniture sales are true?
a.) There was a 45% increase in furniture sales.
b.) Furniture sales rose by 45 percentage points.
c.) There was a 31% increase in furniture sales.
d.) There was a 9% increase in furniture sales.
e.) Furniture sales rose by 31 percentage points.
f.) Furniture sales rose by 9 percentage points.
Answers
Answer:
There was a 45% increase in furniture sales.
Furniture sales rose by 9 percentage points.
Step-by-step explanation:
absolute difference = new - old
29-20= 9 percentage points
absolute difference / initial value = 9/20 = .45 * 100 = 45%
Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.
What is percentage ?Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]
We have,
Sales of furniture in [tex]2015=20\%[/tex]
Sales of furniture in [tex]2016=29\%[/tex],
So,
Change in Percentage [tex]=29-20=9\%[/tex]
i.e.
Sales rise by [tex]9\%[/tex] points,
And,
Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]
Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.
To know more about Percentage click here
https://brainly.com/question/24159063
#SPJ3
Kate lanes a letter against her house to get to the roof. The house is 25 feet tall and I put a ladder is 15 feet away from the side of the house. What is the angle that the latter makes with the ground?
Answers
Answer:
this is the correct answer
