Answer:
29
Step by step explanation.
You add them together then you minus the 8 then you get 29 .
In a right triangle, the measures of the legs are x and x + 14 and the measure of the hypotenuse is x + 16. Find the measure of x.
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
We can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
The two legs are x and (x + 14) and the hypotenuse is (x + 16). Therefore:
[tex](x)^2+(x+14)^2=(x+16)^2[/tex]
Expand:
[tex]\displaystyle x^2+(x^2+28x+196)=x^2+32x+256[/tex]
Combine like terms:
[tex]2x^2+28x+196=x^2+32x+256[/tex]
Subtract the right from the left:
[tex](2x^2+28x+196)-(x^2+32x+256)=0[/tex]
Subtract:
[tex]x^2-4x-60=0[/tex]
Factor:
[tex](x-10)(x+4)=0[/tex]
Zero Product Property:
[tex]x-10=0\text{ or } x+4=0[/tex]
Solve:
[tex]\displaystyle x = 10 \text{ or } x = -4[/tex]
The x cannot be negative since a side cannot measure -4. So, our only answer is:
[tex]x=10[/tex]
So, the legs are 10 and 24 with the hypotenuse being 26.
help plss helppppppppppppppppppppppppppppppppppppppppp
Answer:
okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk
Step-by-step explanation:
answer mujha nahi pata aaaaaaaaaàaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Please I’ll do anything I’m begging
Answer:
14√2
Step-by-step explanation:
This is a 45-45-90 triangle
Because both of the angles are the same all sides, but the hypotonouse are the same
this means that the other length is 14 too
we can use a²+b²=c² to solve
14²+14²=c²
=
392=c²
√392=c
√392=14√2
A tank is filled with 1000 liters of pure water. Brine containing 0.08 kg of salt per liter enters the tank at 6 liters per minute. Another brine solution containing 0.09 kg of salt per liter enters the tank at 5 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 11 liters per minute.
A. Determine the differential equation which describes this system. Let SG) denote the number of kg of salt in the tank after t minutes. Then ds/dt=_____.
B. Solve the differential equation for S(t).
Answer:
The answer is below
Step-by-step explanation:
Let s(t) represent the amount of salt in the tank at time t. Therefore:
ds / dt = (rate of salt flowing into the tank) - (rate of salt going out of the tank)
[tex]\frac{ds}{dt}=[(0.08\ kg/L*6\ L/min)+(0.09\ kg/L*5\ L/min)]-(\frac{s\ kg}{1000\ L}*11\ L/min ) \\\\\frac{ds}{dt}=(0.48\ kg/min+0.45\ kg/min)-(\frac{11s}{1000}\ kg/min )\\\\\frac{ds}{dt}=0.93\ kg/min-\frac{11s}{1000}\ kg/min \\\\\frac{ds}{dt}=\frac{930-11s}{1000}\ kg/min \\\\\frac{ds}{930-11s}=\frac{1}{1000}dt\\\\Integrating:\\\\\int\limits { \frac{ds}{930-11s}} \, ds=\int\limits {\frac{1}{1000}} \, dt\\\\-\frac{1}{11}ln(930-11s)=\frac{t}{1000}+C\\\\multiply\ through\ by\ -11:[/tex]
[tex]ln(930-11s)= - \frac{11t}{1000}+A\\\\Take \ exponential:\\\\930-11s=e^{ - \frac{11t}{1000}+A}\\\\930-11s=C_1e^{ - \frac{11t}{1000}}\\\\11s=930-C_1e^{ - \frac{11t}{1000}}\\\\s=\frac{930-C_1e^{ - \frac{11t}{1000}}}{11} \\\\To \ find\ C_1,s(0)=0.Hence:\\\\0=\frac{930-C_1e^{ - \frac{11(0)}{1000}}}{11} \\\\0=930-C_1\\\\C_1=930\\\\s(t)=\frac{930-930e^{ - \frac{11t}{1000}}}{11} \\\\s(t)=930(\frac{1-e^{ - \frac{11t}{1000}}}{11})[/tex]
A) So, the required value is [tex]1.01-\frac{11S}{1000}[/tex].
B) The required value is [tex]\frac{1010}{11} (1-e^{-11/1000t} )[/tex]
Differential Equation:A differential equation is an equation that contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable).
[tex]\frac{dy}{dx} =f(x)[/tex]
(A) Let [tex]S(t)[/tex] denotes the number of kg of the salt in the tank at the time [tex]t[/tex] minutes.
Then,
[tex]\frac{ds}{dt}=[/tex](rate of salt in to tank)-(rate of salt of tank)
[tex]\frac{ds}{dt}=\left ( 0.08\times 0.09\times 5 \right )-\left ( \frac{s\left (t\right )}{1000}\times 11 \right ) \\ \therefore \frac{ds}{dt}=1.01-\frac{11S}{1000}[/tex]
(B)
[tex]\frac{ds}{dt}=\frac{101}{100}-\frac{11S}{1000} \\ \Rightarrow \frac{ds}{dt}=\frac{1010-11S}{1000} \\ \Rightarrow \frac{ds}{1010-11S}=\frac{dt}{1000}[/tex]
Integrating we get,
[tex]-\frac{1}{11}I_n|1010-11S|=\frac{t}{1000}+In \ C_1 \\ \Rightarrow 1010-11S=C_1e^{-11/1000t} \\ S(t)=\frac{1010-C_1e^{-11/1000t}}{11}[/tex]
Initially, [tex]S(0)=0\\\Rightarrow C_1=1010[/tex]
Then the required solution is,
[tex]\therefore S(t)=\frac{1010}{11} (1-e^{-11/1000t} )[/tex]
Learn more about the topic of Differential Equation: https://brainly.com/question/24546081
. 32+4 X (16 X �) -2
pls help
Answer:
94
Step-by-step explanation:
r+4 at r=13 help me
The value of the expression is 17.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
r + 4
When r = 13
r + 4
= 13 + 4
= 17
Thus,
The value is 17.
Learn more about expressions here:
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Katie got a loan for $10,000. The interest rate is 5%. How much interest will she pay in one year?
Answer: 10,000 x 0.05 = $500
0.05 is equal to 5%
$500
Please brainlyist
A stapler weighs 8.82 ounces. For every 1 pound, there are 16 ounces.
How many pounds does the stapler weigh, rounded to the nearest hundredth?
Answer:
0,55
Step-by-step explanation:
1 pound= 16 ounces
8.82 ounces= 8.82/ 16= 0.55 pound
The perimeter of a rectangle is 32 meters. The length is 5 less than twice the width. Find the length and the width of the rectangle.
length:___ Width:____
Please hELLPPPPP:(((((((((((((((((
Subtract. Write your answer in simplest form.
5 1/2- 1 2/7
Answer:
5 1/2- 1 2/7
11/2-9/7
(11×7-9×2)/14
59/14
4 3/14
15/3 x 2/2= what is the answer there are more than one I need help fast
Answer:
the answer is 5
Step-by-step explanation:
15/3=5
2/2=1
5×1=5
Answer:
5
Step-by-step explanation:
First multiply the numerators and denominators.
15 x 2 = 30
3 x 2 = 6
Then divide
30/6 = 5
Which of the following could represent the question: How many 4/9s are in 6/5 as a multiplication equation?
x*4/9=6/5
x*6/5=4/9
6/5*4/9=x
4/9*6/5=x
Answer:
Step-by-step explanation:
I am pretty sure it’s 4/9 * 6/5 = x
( I think it’s this )
Katy invests £200 000 in a savings account for 4 years. The account pays compound interest
at a rate of 1.5 % per annum.
Calculate the total amount of interest Katy will get at the end of 4 years
Answer:
212272.71
Step-by-step explanation:
we have the following equation (for interesting that compound yearly)
PV(1+i)^n
200000(1+.015)^4
212272.71
The total amount of interest Katy will get at the end of 4 years is £12,272.71
Compound interestCompound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interestCompound interest refers to the phenomenon whereby the interest associated with a bank account, loan, or investment increases exponentially—rather than linearly—over time.Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periodsHow to solve this problem?The steps are as follow:
Given:p = £200 000
r = 1.5%
n = 4 years
Formula to find Amount (A) after 4 years will as follow:A = p(1+r/100)ⁿ
A = 200000(1+1.5/100)⁴
A = 212,272.71 £
The compound interest is given by:C.I. = A - p
C.I. = 212,272.71 - 200,000
C.I. = £12,272.71
So the total amount of interest Katy will get at the end of 4 years is £12,272.71
Learn more about Compound interest here:
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Find the Simple Interest
$700 deposited at an interest rate of 1.5% for 3 years
Answer:
$31.50
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 1.5%/100 = 0.015 per year,
then, solving our equation
I = 700 × 0.015 × 3 = 31.5
I = $ 31.50
The simple interest accumulated
on a principal of $ 700.00
at a rate of 1.5% per year
for 3 years is $ 31.50.
How are 4.730 and 4.73 eqivalent
Answer:
The zero means nothing, it's just being used as a placeholder, like .7 and 0.7 mean the same thing.
good luck, i hope this helps :)
4.730 and 4.73 are equivalent because 0 has no value therefore if 0 has no value and you take away the 0 than you get 4.73 and 4.73.
За + 4 = 25 whats the answer
Answer: 7
Step-by-step explanation:
3a + 4 = 21
Step 1 subtract 4 from both sides.
3a+4−4=25−4
3a = 21
Step 2: Divide both sides by 3.
3a / 3 = 1
21 / 3 = 7
a = 7
A physical education department wanted a single test of upper body strength that was easy to administer. Dips on the parallel bars and pull-ups on the horizontal bar were considered good tests. One faculty member thought that both tests were not needed because the correlation between the two was probably high. To evaluate this assumption, 141 students were tested on both criteria. The faculty member let X represent dips on the parallel bars and Y represent pull-ups and calculated the following from the data:
ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416.
Calculate the following:
a. The mean of each variable
b. The correlation between the two variables
c. The level of confidence and the p value reached by the coefficient
d. The predicted number of pull-ups for a student who performed 20 dips
e. The standard error of the estimate
f. The predicted range of possible pull-up scores at the 95% LOC for a student who performed 20 dips
Answer:
24.23 ; 13.47 ; 0.782 ; p value < 0.00001 ;7.45
Step-by-step explanation:
Given that :
ΣX = 3,416, ΣY = 1,899, SDX = 8.84, SDY = 4.70, ΣZXZY = 109.416
Sample size, N = 141
Mean of X:
£X / N = 3416 / 141 = 24.23
Mean of Y:
£Y / N = 1899 / 141 = 13.47
B.) Correlation between the 2 variables :
£ZXZY / N - 1
= 109.416 / 140
= 0.782
C.)
Level of significance and p value :
T = [Rsqrt(n-2)] ÷ sqrt(1 - R²)
T = [0.782 * sqrt(139)] ÷ sqrt(1-0.782^2)
T = 14.79
P value from Tscore calculator
Df = 141 - 2 = 139 ; α = 0.05
Pvalue = 0.00001
Pvalue < α ; Hence, a significant positive relationship exists.
To obtain regression model :
Slope = £ZXZY / SDX²
m = 109.416 / 8.84^2 = 1. 4
yintercept = meanY - slope*x
yintercept = 13.47 - 1.4*24.3
yintercept = - 20.55
Equation in slope intercept form:
y = mx + c
y = 1.4x - 20.55
For x = 20
y = 1.4(20) - 20.55
y = 7.45
The formula V equals S to the third power gives the volume V of a cube with the side length S the volume of a cube that has a side length of 3 inches is__?__ inches cubed
Answer:
27
Step-by-step explanation:
The formula for the volume of a cube is given as [tex]V=s^{3}[/tex]. if s=3in, then V=27inches cubed.
si el peso de la figura es de 80 N cuales son las tensiones en las cuerdas a y b
Answer: Can you translate for me? I don't know spanish.
Step-by-step explanation:
:)
7.88 as a percent student
788% gdkgdkgdkgdkgdkgdkgdk
HELP!!!! PLEASE SOMEONE SHOW ME HOW TO DO THIS PROBLUM!!! WILL GIVE BRAINLIST
What is the exact circumference of a circle with a radius of 3 ft?
Enter your answer in the box.
a
ft
Answer:
C≈18.85 ft
this is the answer I think
Answer:
The answer is 18.85ft
Step-by-step explanation:
To explain is the radius is 3ft and the circumference is 2nr
To show how to solve will be like this and look down here C=2πr=2·π·3≈18.84956ft
18.84956ft round to the nearest is 18.85ft
Write the following expression in simplest radical form. Plz help
Answer:[tex]4x^{3}[/tex][tex]\sqrt[3]{25x^{2} }[/tex]
Step-by-step explanation:
n
The Federal Reserve
manages the nation's currency and money supply by
manipulating interest rates and acting as a lender to banks.
overseeing bank collections and payments on loans.
dictating criteria and setting loan terms for banks.
offering investment advice and adjusting interest rates.
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Financials.
Hence,according to the statement given above, the correct answer is
option 1.)
===> Manipulating interest rates and acting as a lender to the banks.
Simplify the expression. -3(1+n)-6n
Answer:
− 3 − 9 n
Step-by-step explanation:
Simplify the expression
what is the value of x in this problem
Answer:
x = 12
Step-by-step explanation:
Based on the altitude theorem of a right triangle, since x is the altitude/height, therefore,
x = √(4*36)
x = √144
x = 12
There are several climate zones on Earth. One type of zone is identified by shading on the map below. Together, the darker shaded areas on the map form Earth's temperate zor
EARTH'S TEMPERATE CLIMATE ZONE
North
America
Europe
CV
Africa
America
stralia
Antarctica
Based on the position of the temperate zone, how would you describe its climate?
It is the driest zone because it is close to the equator.
Climate in this zone is mild, without extreme heat or cold.
It is the wettest zone because of its nearness to Earth's poles.
Temperatures in the zone are extremely cold because of the high elevation.
Answer:
s
Step-by-step explanation:
s
Evan is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The total cost of the gym membership over tt months is given by the equation C=40t+125.C=40t+125. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
the slope of the function is 40 which represents the monthly fee to remain a mrmber.
Step-by-step explanation:
THE SLOPE IS THE COEFFICIENT OF THE INDEPENDENT VARIABLE
C= 40t + 125
ME AJUDEM PFVV!!(CONTA NA FOTO)
(espero que esto ayude) La respuesta es D que es [tex]\frac{2}{3}[/tex]
2. A container of oil holds 585 gallons. How many
containers each holding 4.5 gallons will be needed if
all the oil is to be transferred to the smaller
containers?
Answer:
130
Step-by-step explanation:
585/4.5=130