Answer:
The value of [tex]f = x_{1}+10\cdot y_{1}+x_{2}+10\cdot y_{2}[/tex] is 317.
Step-by-step explanation:
Let the system of nonlinear equations be:
[tex]x\cdot (y-1) = 180[/tex] (1)
[tex]y\cdot (1+x) = 208[/tex] (2)
From (1), we clear [tex]x[/tex]:
[tex]x = \frac{180}{y-1}[/tex]
Let apply this resulting expression in (2):
[tex]y\cdot \left(1+\frac{180}{y-1} \right)= 208[/tex]
[tex]y\cdot \left(\frac{y-1+180}{y-1} \right) = 208[/tex]
[tex]y\cdot \left(\frac{y+179}{y-1} \right)=208[/tex]
[tex]y\cdot (y+179) = 208\cdot (y-1)[/tex]
[tex]y^{2}+179\cdot y = 208\cdot y-208[/tex]
[tex]y^{2}-29\cdot y+208 = 0[/tex]
By the Quadratic Formula we obtain the solution of the second order polynomial:
[tex]y_{1} = 16[/tex] and [tex]y_{2} = 13[/tex]
And the respective values of [tex]x[/tex] are, respectively:
[tex]y_{1} = 16[/tex]
[tex]x_{1} = \frac{180}{y_{1}-1}[/tex]
[tex]x_{1} = \frac{180}{15}[/tex]
[tex]x_{1} = 12[/tex]
[tex]y_{2} = 13[/tex]
[tex]x_{2} = \frac{180}{y_{2}-1}[/tex]
[tex]x_{2} = \frac{180}{12}[/tex]
[tex]x_{2} = 15[/tex]
If we know that [tex]x_{1} = 12[/tex], [tex]y_{1} = 16[/tex], [tex]x_{2} = 15[/tex] and [tex]y_{2} = 13[/tex], then the value of [tex]f = x_{1}+10\cdot y_{1}+x_{2}+10\cdot y_{2}[/tex] is:
[tex]f = 12+10\cdot (16)+15+10\cdot (13)[/tex]
[tex]f = 317[/tex]
The value of [tex]f = x_{1}+10\cdot y_{1}+x_{2}+10\cdot y_{2}[/tex] is 317.
Using the definition f'(x) = lim f(x+h)-f(x)
h→0.
h
find f'(x) when f(x) =
-2/2x-3
Answer:
Step-by-step explanation:
We will apply the definition of the derivative. Then we use algebra to expand and simplify the numerator. Next, we can cancel a factor of
h
in the numerator and denominator since
h
is approaching zero but not actually equal to zero. Finally, we can simply substitute zero for
h
to evaluate the limit.
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f
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−
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=
lim
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(
x
+
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2
−
2
(
x
+
h
)
+
3
−
(
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2
−
2
x
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3
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h
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lim
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2
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h
−
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Find the difference: 25 kg 32 g - 23 kg 83 g
The difference of the weight is 1 kg 949 g.
How to find the difference of numbers?The weight of the two items to find the difference are as follows:
25 kg 32 g23 kg 83 gDifference in mathematics is the result of subtracting one number from another.
Therefore, let's convert the weight .
1000g = 1 kg
32 g =
cross multiply
weight = 32 / 1000
weight = 0.032 kg
1000g = 1 kg
83 g = ?
cross multiply
weight = 83 / 1000 = 0.083 kg
Therefore,
25 kg + 0.032 kg = 25.032 kg
23kg + 0.083 kg = 23.083 kg
Hence,
the difference of the weight = 25.032 kg - 23.083 kg
the difference of the weight = 1.949 kg
Hence,
the difference of the weight = 1 kg 949 g
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* All of the following can be a product of a nega- tive integer and a positive integer EXCEPT (A) -6 (B)1 (C)-1 (D)-2
Answer:
B
Step-by-step explanation:
The product of a negative integer and positive integer is always negative. A, C and D are negative; Only B is positive so it is NOT a negative integer. The word EXCEPT means it is asking for non-negative answers or answers that are positive
Answer:
B
Step-by-step explanation:
A weather forecaster claimed the chance of rain next week on Monday is 50% and the chance it rains on Tuesday is 80%. Is the probability that it rains next
Monday and Tuesday equal to 40%?
O Yes, because the chance of rain on Monday and the chance of rain on Tuesday are independent.
O No, because the chance of rain on Monday and the chance of rain on Tuesday are not independent.
O No, because the chance of rain Monday and the chance of rain Tuesday are not mutually exclusive.
O Yes, because the chance of rain on Monday and the chance of rain on Tuesday are mutually exclusive,
Answer:
A: Yes, because the chance of rain on Monday and the chance of rain on Tuesday are independent.
Step-by-step explanation:
We are given;
chance of rain next week on Monday is 50%. Thus;
P(rain next Monday) = 0.5
chance it rains on Tuesday is 80%. Thus;
P(rain next Tuesday) = 0.8
From independent events, we can say that;
P(A and B) = P(A) × P(B)
A and B are independent events because the probability of A doesn't affect B as is the case for rain on Monday and Tuesday given.
Thus;
P(rain on Monday & tuesday next week) = 0.5 × 0.8 = 0.4
This can also be written as 40%
Correct answer is option A since both events are independent
Given g(x)=−x2+10x−3, find the following.
g(9)=
Question 14 options:
-174
-111
6
138
Answer:
g(9) = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
g(x) = -x² + 10x - 3
g(9) is x = 9
Step 2: Evaluate
Substitute in x: g(9) = -(9)² + 10(9) - 3Exponents: g(9) = -(81) + 10(9) - 3Multiply: g(9) = -81 + 90 - 3Add: g(9) = 9 - 3Subtract: g(9) = 6Essential Question 3-5, 7th Grade I WILL GIVE BRAINLIEST!
What does the graph of a proportional relationship look like?
Answer:
It is a straight line because the x and y values are proportional.
Step-by-step explanation:
Answer:
it looks like a straight line thru the origin
A florist has to pay $7.50 each time a customer chooses a competitor for the delivery of flowers. Which expression shows the amount that the florist earns if p people use a competitor for delivery, and the company makes $320.00 before any payment is made to their competitors?
320 minus 7.50 p
320 + 7.50 p
7.50 p minus 320
7.50 p + 320
Answer:
320 minus 7.50 p
Explanation:
the florist earned 320 dollars and then lost money due to having a competitor deliver, since we dont know the amount of people who chose competitors we use the term p next to the amount that p is worth because each time a customer uses a competitor it costs 7.50 out of the original 320.
The weekly demand for an item in a retail store follows a uniform distribution over the range of 50 to 100. What would be the weekly demand if its corresponding computer-generated value is 0.4?a. 60b. 70c. 75d. 80
Answer: 70
Step-by-step explanation:
Given that :
Uniform range of distribution = 50 to 100
50 ≤ x ≤ 100
Difference between both values = 100 - 50 = 50
Range / difference = computer generated value
(Weekly demand - lower limit) / difference = computer generated value
(Weekly demand - 50) / 50 = 0.4
Weekly demand - 50 = 20
Weekly demand = 20 + 50
Weekly demand = 70
The weekly demand if the corresponding computer-generated value is 0.4 is given by: Option B: 70
What is the property of a uniformly distributed random variable?A uniformly distributed random variable's probability is distributed uniformly in the interval in which it is defined. Thus, if X ranges from a to b, and pertains uniform distribution, then its probability density function is given by;
[tex]f(x) = \dfrac{1}{b-a}; a < x < b\\\\f(x) = 0; x < a , b < x[/tex]
For the given case, the weekly demand(let it be tracked by random variable X) is in range 50 to 100.
The computer generated value shows:
[tex]\text{Computer generated value} = \dfrac{\text{Weekly demand} - \text{Lower limit}}{\text{difference between upper and lower limit}}[/tex]
(computer generated value is showing in range 0 to 1, the part occupied by the weekly value from starting, here as it is 0.4, so it means out of 50 values, it is 0.4 = 40% of (100 -50) = 20 (from start which is 50, thus, 50 + 20 = 70) )
As we've got:
Thus, the weekly demand is obtained as:
[tex]0.4 = \dfrac{\text{Weekly demand} - 50}{50}\\\\\text{Weekly demand} = 0.4 \times 50 + 50 = 70[/tex]
Thus, the weekly demand if the corresponding computer-generated value is 0.4 is given by: Option B: 70
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Sending Paypal to whoever gets this right ( i made this question)
BE? I don't really know lol
There are 640 students who attend Washington College Prep. 75% of the students play a sport. How many students at Washington College Prep play a sport? Draw a percent bar to show your answer.
Please answer this
Answer:
D
Step-by-step explanation:
i need help with this badddddddddd
Answer:
She forgot to add the zero when she multiplied 27 x 50
Step-by-step explanation:
If you need one ask me I can try my best to explain
Which problem can be solved by dividing 3.5 divided by 5?
Answer:
3.5÷5
Step-by-step explanation:
It's asking what problem can be solved by doing 3.5 ÷ 5
the problem is 3.5 ÷ 5
first step in solving the equation 4x -8=7
Is this true? log(x) = logb(c) * log(x). For this question, first try several examples. Then prove it. See the proofs in the Basic Math lecture for ideas. (Hint: let
m = logb(x) and n=logb(c) and p = logc(x). Then use the definition of logarithms and rules of exponents to show m = np.
The logarithmic statement [tex]log_bx=log_bc \cdot log_cx[/tex] is true.
Logarithm is a mathematical operator that is used to simplify the exponential equations .
The logarithm is exponentiation's opposite function in mathematics. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.
The exponential equation logₓy=n is equivalent to xⁿ=y.
The properties of Logarithmic equations are:
log x + log y = log xylog x-log y= log (x/y)log ₙn=1n log x = log xⁿ[tex]log_ab=\frac{log_xa}{log_xb}[/tex] , x≠0Now the given expression is of the form: [tex]log_bx=log_bc \cdot log_cx[/tex]
We know that [tex]log_bc=\frac{log_nc}{log_nb}[/tex] and [tex]log_cx=\frac{log_cx}{log_nc}[/tex]
let n=[tex]log_bc=\frac{log_nc}{log_nb}[/tex] and p=[tex]log_cx=\frac{log_cx}{log_nc}[/tex]
Now for the right side of the equation we have:
n×p
[tex]log_bc \cdot log_cx[/tex]
This can be written as:
[tex]or, \frac{log_nc}{log_nb}\cdot\frac{log_cx}{log_nc}\\or, \frac{log_cx}{log_nb}\\or, log_bx[/tex]
which is equivalent to the left side of the equation.
Hence the statement [tex]log_bx=log_bc \cdot log_cx[/tex] is true.
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work out the value of 10 fourths
Answer:
10/4 equals 2 1/2 when simplified.
Step-by-step explanation:
10/4 = 2 2/4 or 2 1/2 when simplified.
This is because, 4 x 2 = 8, and 8 + 2 (or 1/2 of 4) = 10.
Hope this helps! :D
(x + 4)(x − 12) = 0 can someone help me with this
Answer:
You chose the correct option on the picture
x = -4; x = 12
Step-by-step explanation:
You solve for x by simplifying both sides of the equation, then isolating the variable.
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x + 4 = 0
x − 12 = 0
Set x + 4 equal to 0 and solve for x.
Set x+4 equal to 0.
x+4=0
Subtract 4 from both sides of the equation.
x = −4
Set x − 12 equal to 0 and solve for x.
Set x−12 equal to 0.
x−12=0
Add 12 to both sides of the equation.
x=12
The final solution is all the values that make (x+4)(x−12)=0 true.
x=−4,12
Sorry for taking a while but have a good day
pls help question 2!!!!!!!!
Answer:
2/3
Step-by-step explanation:
one hundred percent positive
Answer:
2/3
Step-by-step explanation:
The way we divide fractions like this is to take the inverse of the divisor (second fraction) and multiply. So 1/6 x 4/1 = 4/6 which reduces to 2/3.
what is the reciprocal of 4/7
The reciprocal of 4/7 is 7/4
which expression is equivalent to 18x12
Answer:
12x18
Step-by-step explanation:
Answer:
Hello, you do not give us any answers to choose from, but i can say that 18x12 is 216
Step-by-step explanation:
Graph a line with a slope of 4 that contains point (4,3)
Answer:
y-3= 4(x-4)
y-3= 4x-4
y=4x-4+3
y=4x-1
-3.1x +6x = 2+3z+8-10
=
Answer:
_
z=96x
(line on top of the nine)
Step-by-step explanation:
There are a total of 114 oak and pine trees on a piece of land. There are 26 fewer oak trees than pine trees. There is a regulation that the number of oak troos on this piece of land cannot exceed one-third of the total number of trees. Find how many oak and pine trees are on this piece of land and determine whether the solution is viable or nonviable A. There are 35 oak trees and 78 pine trees. The solution is viable. B. There are 35 oak trees and 78 pine trees. The solution is nonviable. C. There are 42 oak trees and 70 pine trees. The solution is nonviable D. There are 44 oak trees and 70 pine trees. The solution is viable
Answer:
c
Step-by-step explanation:
Answer:
There are 42 oak trees and 70 pine trees. The solution is nonviable.
Step-by-step explanation:
:)
Write the slope-intercept form of an equation that passed through the given point and is: (a) parallel, (b) perpendicular, to the graph of the equation below (-4, -5); -4x+5y=-6
Answer:
-4x+5y=-4 and 5x+4y=-40.
Step-by-step explanation:
all the details are provided in the attachment.
Tommy was trying to solve the system of a linear equation and a quadratic equation shown below. 2x – y = –1 x2 – 5x – y = –7 Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic, x2 – 7x – 1, to complete the problem. Step I: y = 2x + 1 Step II: x2 – 5x – (2x + 1) = –7 Step III: x2 – 5x – 2x – 1 = –7 Step IV: x2 – 7x – 1 = –7 Determine the step in which Tommy made his mistake and justify your reasoning.
Answer:
Step IV; Tommy must set the quadratic expression equal to 0 before factoring.
plz give brainlyest
It is found that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that the system of a linear equation and a quadratic equation.
2x – y = –1
x² – 5x – y = –7
Now Tommy had completed the following steps in his algebraic solution process but could not factor the resulting quadratic equation as;
x² – 7x – 1,
Step I: y = 2x + 1
Step II: x² – 5x – (2x + 1) = –7
Step III: x² – 5x – 2x – 1 = –7
Step IV: x² – 7x – 1 = –7
Therefore, we conclude that in Step IV; Tommy must set the quadratic equations equal to 0 before factoring and then solving.
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At a community barbecue, Mrs. Walton and Mr. Buckley are buying dinner for their families.
Mrs. Walton purchases 5 hot dog meal and 2 hamburger meals, paying a total of $15.50.
Mr. Buckley buys 1 hot dog meal and 4 hamburger meals, spending $17.50 in all.
How much does a hot dog meal cost?
Answer:
Step-by-step explanation:
5ht dogs=1.50 each
2hamburger=4.00 each
equals15.50
1 ht dog=1.50
4hamburger=16.00
total equals 17.50
hot dog dinner =1.50
Please find the value of gf(2)
Step-by-step explanation:
here is ur answer with perfect solution
There were 8 roses in the vase. Jessica cut some more roses from her flower garden and put them in her vase. There are now 13 roses in the vase. Write an equation for how many roses did she cut ?
Answer:
8+x=13
Step-by-step explanation:
Answer:
13-8=r
r=roses she cut
Step-by-step explanation:
you take away how many roses there were in the begining from the amount she started with and you get r (the amount of roses she cut).
Helpppp pleaseeeeeee
Answer:
A.
positive and negative 5 and square root of 29
In a diagram of a landscape plan, the scale is 5 cm = 12 ft. In the diagram, the
trees are 9 centimeters apart. How far apart should the actual trees be planted?
Answer:
21.6 feet.
Step-by-step explanation:
By proportion that is (9/5) * 12
= 1.8 * 12
= 21.6 feet.
[tex]8^{2}=x\\x+12=y\\y-3=n\\n=?[/tex]
Answer:
n = 73
Step-by-step explanation:
—Math8² = x ==> x = 64
x + 12 = y ==> y = 64 + 12 = 76
y – 3 = n ==> n = 76 – 3 = 73
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