Answer
{-10, 9}
Step-by-step explanation:
The above are Simultaneous equations
What are simultaneous equations?These are two or more equations that share same variables.
8X + 10Y = 10--------(1)
5X + 4Y = -14-------(2)
Multiply equation (1) by 5 and equation (2) by 840X + 50Y = 50 ---------(3)
40X + 32Y = - 112--------(4)
Subtract equation (4) from (3)18Y = 162
Divide bothsides by 18[tex] \frac{18y}{18} = \frac{162}{18} \\ y = 9[/tex]
Substitute y = 9 into equation (3)40X + 50Y = 50
40X + 50(9) = 50
40X + 450 = 50
40X = 50 - 450
40X = - 400
[tex]Dividing \: bothsides \: by \: 40 \\ \frac{40x}{40} = \frac{ - 400}{40} \\ \\ x = - 10 \\ therefore \: the \: values \: are \: -10, \: 9[/tex]{-10, 9}
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
When we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
Given two expressions be [tex]x^{3} +6x^{2} +3x+1[/tex] and (x-2).
We are required to divide the first expression by second expression.
Division means distributing parts of something. The number which is being divided is known as quotient.Divisor is a number which divides the number.
Expressions refers to the combination of numbers, fractions, coefficients, determinants, indeterminants. It expresses some relationship or show equation of line.
We know that relationship between quotient, divisor, divident and remainder is as under:
Dividend=Divisor*Quotient+Remainder
[tex]x^{3} +6x^{2} +3x+1[/tex]=(x-2)*([tex]x^{2} +8x+19[/tex])+39
Quotient=[tex]x^{2} +8x+19[/tex]
Remainder=39
Hence when we divide [tex]x^{3} +6x^{2} +3x+1[/tex] by (x-2) we will get the quotient be [tex]x^{2} +8x+19[/tex] and remainder be 39.
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Multiply each of the following(X+7)and(y-7)
Answer:
xy-49
Step-by-step explanation:
x x y is xy and -7x7 is 49 so the answer is xy- 49
the difference between 2 numbers, a and b is 21. the difference of 5 times a and 2 times b is 18. What are the values of a and b?
Answer:
Step-by-step explanation:
a-b=21
5a-2b=18
Using elimination, we have
5a-5b=105
5a-2b=18
So:
3b=-87 so b=-29
Substituting, a=-8
(a,b)=(-8,-29)
If s(x) = x - 7 and f(x) = 4x²-x + 3, which expression is equivalent to (t*s) (x)?
Answer: [tex]4x^3 -29x^2 +10x-21[/tex]
Step-by-step explanation:
[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: The mean age of students in a large statistics class is less than 31. A simple random sample of the students has a mean age of 30.4.
Choose the correct answer below.
A.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim.
B.
The sample is not unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
C.
The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
D.
The sample is unusual if the claim is true. The sample is unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
The correct option regarding the sampling is C. The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is sufficient evidence to support the claim.
What do you mean sampling?Sampling is a process that is used in statistical analysis in which a predetermined number of observations are taken from a larger population
In this case, since the claim is mean pulse rate of students in a large statistics classes is greater than 72. The sample mean pulse rate was found to be 98.9 then the sample is not unusual if the claim is true. The sample is unusual if claim is false. Therefore there is sufficient evidence to support the claim.
The correct option is C.
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(g) Every student of class IV donated as much money as their number to make a fund for landslide, If there are 68 students in class IV how much money did they collect?
Answer:$2346
Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.
Add using fraction strip. 1/2 + 5/2
Answer:
3
Step-by-step explanation:
First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.
Answer:
If you add this fraction in fraction strip instead of equivalent fraction method
Step-by-step explanation:
firstly draw 5 1/2 fraction strip
then draw 12 1/4 fraction strip
we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.
The end product will be 12/4
cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3
if you think it wrong then use the equivalent fraction method to see the answer..
1/2 + 5/2
denominators are same so we will take only one denominator and will directly add the numerators
1 + 5 = 6 so
6/2 cancel it the ans will be 3/1 and it's equal to 3.
Someone please help me with this question asap!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Correct choice = B[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = a, GH = b and GJ = c
a = b + 2 c = a + b - 17 a + b + c = 73put the value of a from equation 1 in equation 2
[tex]\qquad❖ \: \sf \:c = (b + 2) + b - 17[/tex]
[tex]\qquad❖ \: \sf \:c = 2b - 15[/tex]
now, put the value of a and c in equation 3
[tex]\qquad❖ \: \sf \:b + 2 + b + 2b - 15 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b - 13 = 73[/tex]
[tex]\qquad❖ \: \sf \:4b = 86[/tex]
[tex]\qquad❖ \: \sf \:b = 21.5 \: \: in[/tex]
Now, we need to find HJ (a)
[tex]\qquad❖ \: \sf \:a = b + 2[/tex]
[tex]\qquad❖ \: \sf \:a = 21.5 + 2[/tex]
[tex]\qquad❖ \: \sf \:23.5 \: \: in[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correctAnswer:
23.5 in
Step-by-step explanation:
To find the length of HJ in triangle GHJ, create three equations using the given information, then solve simultaneously.
Equation 1
HJ is two inches longer than GH:
⇒ HJ = GH + 2
Equation 2
GJ is 17 inches shorter than the sum of HJ and GH:
⇒ GJ + 17 = HJ + GH
Equation 3
The perimeter of ΔGHJ is 73 inches:
⇒ HJ + GH + GJ = 73
Substitute Equation 1 into Equation 2 and isolate GJ:
⇒ GJ + 17 = GH + 2 + GH
⇒ GJ + 17 = 2GH + 2
⇒ GJ = 2GH - 15
Substitute Equation 1 into Equation 3 and isolate GJ:
⇒ GH + 2 + GH + GJ = 73
⇒ 2GH + GJ = 71
⇒ GJ = 71 - 2GH
Equate the two equations where GJ is the subject and solve for GH:
⇒ 2GH - 15 = 71 - 2GH
⇒ 4GH = 86
⇒ GH = 21.5
Substitute the found value of GH into Equation 1 and solve for HJ:
⇒ HJ = 21.5 + 2
⇒ HJ = 23.5
HELP!!! A,B,or C
Eric was rock climbing. At one point, he stopped and climbed straight down 2 1/2 meters. Then he climbed straight up 6 3/4 meters.Eric was wondering what his change in elevation was after these two moves.
Suppose that the derivable functions x=x(t) and y=y(t) satisfy xcosy=2.
If dx/dt=−2, find dy/dt when y=π/4.
a-) -√2 / 2
b-) 4
c-) -2√2
d-) √2
e-) 2√2
Please, someone help me!
Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:
a-) -√2 / 2.
What is implicit differentiation?Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.
In this problem, the function is:
xcos(y) = 2.
The derivative is relative to t, applying the product rule, as follows:
[tex]\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0[/tex]
[tex]\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}[/tex]
Since dx/dt=−2, we have that:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
When y = π/4, x is given by:
xcos(y) = 2.
[tex]x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}[/tex]
Hence:
[tex]\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}[/tex]
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}[/tex]
Since cot(pi/4) = 1, we have that:
[tex]\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}[/tex]
Which means that option a is correct.
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Please help quick what is the answer thank you
Answer:
y= -3x+4
Step-by-step explanation:
y=mx+c
m= y2-y1 ÷ x2-x1
m= -3
y=-3x+c
7=-3(-1)+c
c=4
y=-3+4
if x is normally distributed with U = 283 and o = 21 find p(x) is greater than 315
The probability that the value of p(x) is greater than 315 is 0.063754
How to determine the probability that the value of p(x) is greater than 315?From the question, the given parameters about the distribution are
Mean value of the set of data = 283Standard deviation value of the set of data = 21The actual data value = 315The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (315 - 283)/21
Evaluate the difference of 315 and 283
z = 32/21
Evaluate the quotient of 32 and 21
z = 1.524
The probability that the value of p(x) is greater than 315 is then calculated as:
P(x > 315) = P(z > 1.524)
From the z table of probabilities, we have;
P(x > 315) = 0.063754
Hence, the probability that the value of p(x) is greater than 315 is 0.063754
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The coefficient of 2(3)(6)Q is
The coefficient of 2(3)(6)Q is 2(3)(6)
How to determine the coefficient?The expression is given as:
2(3)(6)Q
For an expression
AQ
Where A is a number or product of numbers and Q is a variable
The number A represents the coefficient
By comparing:
AQ and 2(3)(6)Q
We have
A = 2(3)(6)
Hence, the coefficient of 2(3)(6)Q is 2(3)(6)
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Please help, need for math hw and cant figure it out
The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
How to represent the quadratic function in standard form?The quadratic function is given as
f(x) = -3x^2 + 6x - 2
The standard form of a quadratic function is represented as:
f(x) = ax^2 + bx + c
When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form
Where
a = -3
b = 6
c = -2
Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2
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pls help
heather had some candy to give to her five children. she first took eight pieces for herself and then evenly divided the rest amount her children. each child received four pieces. with how many pieces did she start?
Answer: She started with 28 pieces of candy.
Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.
Answer:
She started with 28 candies.
Explanation:
Let the total amount of candies be c
Build equation:
heather took out 8 candies for herself→ remaining: c - 8
then divided the remaining candies to her five children→ each gets: (c - 8)/5
Here given each gets 4 candies
So,
(c - 8)/5 = 4
c - 8 = 5(4)
c - 8 = 20
c = 20 + 8
c = 28
Ellen read a book a day for 10 weeks. How many books did
she read in all?
1 week = 7 days
10 weeks = 10×7 days
= 70 days
if Ellen reads 1 book in a day
Therefore,
1 day = 1 book
70 days = 70×1
= 70 books.
Thus Ellen reads 70 books in 10 weeks.
Hope helps
Answer:
70 books
Step-by-step explanation:
Ellen reads one book per day for 10 weeks.
All we need to do to know the number of books Ellen read overall is to multiply 1 (number of books he read each day) and 10 weeks (total number of days).
Each week is 7 days, so 10 weeks is equal to 70 days.
The equation will be: 1 x 70
We can conclude that Ellen read 70 books overall within 10 weeks.
Working together a small pipe and large pipe can fill a big pool in 6 hour. It takes the smaller pipe 5 hours longer than the large pipe to fill the big pool working alone. How long does it take the smaller pipe to fill the pool by itself ?
The time taken for the smaller pipe to fill the pool by itself is 15.71 hours
Rate of workTime taken for both pipes = 6 hoursTime taken for long pipe = xTime taken for small pipe = x + 6Rate of work of both pipes = 1/6Rate of work of long pipe = 1/xRate of work of small pipe = 1/x + 61/6 = 1/x + 1/(x+6)
1/6 = (x+6)+(x) / (x)(x+6)
1/6 = (x+6+x) / x²+6x
1/6 = (2x+6)(x² + 6x)
cross product1(x² + 6x) = 6(2x+6)
x² + 6x = 12x + 36
x² + 6x - 12x - 36 = 0
x² - 6x - 36 = 0
Using quadratic formulax = 9.71 or -3.71
The value of x cannot be negative
Therefore, the
Time taken for long pipe = x
= 9.71 hours
Time taken for small pipe = x + 6
= 9.71 + 6
= 15.71 hours
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An envelope contains $1.20 in dimes and nickels. if the dimes were quarters and the nickels were dimes, there would be $1.35 more in the envelope. How many nickels are in the envelope?
The nickels in the envelope is $0. 12
How to determine the number
From the information given, we have that;
Dimes + nickels = $1. 20
1/4 dimes + dimes = $ 1. 35
Let dimes = d
Nickels = n
d + n = 1. 20 equation a
d/4 + d = 1. 35 equation b
Make 'd' subject from equation a
d = 1. 20 - n
Substitute into equation b
1. 20 - n/ 4 + 1. 20 - n = 1. 35
0. 3 - 0. 25n + 1. 20 - n = 1. 35
collect like terms
- 1. 25n = 1. 35 - 1. 5
- 1. 25 = - 0. 15
n = -0. 15/ -1. 25
n = 0. 12
Thus, the number of nickels in the envelope is $0. 12
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What is the distance from (-5,2) and (0,4)?
Answer:
d = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
The distance between two points is given by
d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex] where ( x1,y1) and ( x2,y2) are the two points
d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]
d = [tex]\sqrt{5^2 + 2^2}[/tex]
d = [tex]\sqrt{25 +4}[/tex]
d = [tex]\sqrt{29}[/tex]
Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]
Step-by-step explanation:
Given information
[tex](x_1,~y_1)=(-5,~2)[/tex]
[tex](x_2,~y_2)=(0,~4)[/tex]
Given the distance formula
[tex]Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the formula
[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]
Simplify values in the parenthesis
[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]
[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]
Simplify the exponents
[tex]Distance =\sqrt{25+4}[/tex]
Simplify values in the radical sign
[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
a chord subtend an angle of 72⁰ at the center of a circle with radius 24.5m. calculate the perimeter of the minor segment
The perimeter of the minor segment is 77. 4m
How to determine the perimeter
The formula for determining the perimeter of the minor segment is given as;
Perimeter = θ/360 × 2πr + 2r sin θ/2
where;
radius = 24. 5mθ = 72Substitute into the formula;
Perimeter = (72/360 × 2 × 3. 142 × 24. 5) +( 2 × 24. 5 × sin 72)
Perimeter = 30. 79 + 46. 60
Perimeter = 77. 4 m
Thus, the perimeter of the minor segment is 77. 4m
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How many lines can be drawn through points J and K?
Answer:
show the image because we cant answer it if there's no picture or image
Step-by-step explanation:
solve this equations 3x+4x-8=6(x-3)+x
Answer:
no solutions
Step-by-step explanation:
PLEASE HELP ME WITH THIS QUESTION
6
Answer:
45
Step-by-step explanation:
Assuming this is a trapezoid,
[tex]\frac{29+WZ}{2}=37 \\ \\ 29+WZ=74 \\ \\ WZ=45[/tex]
need heeeelp please
Answer:
Initial population: 222 fish
After 7 years: 871 fish
Step-by-step explanation:
Initial population size:
Let t=0
∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]
=[tex]\frac{2000}{1+8}[/tex]
=[tex]\frac{2000}{9}[/tex]
=222 fish
After 7 years:
Let t=7
∴P(7)=871 fish
How many three-digit multiples of 5 have three different digits and an odd tens digit?
I am getting 72. which is wrong
Answer:
68?
Step-by-step explanation:
multiples of 5 end in 5 or 0
_ _ _
last digit has 2 choices ( 5 and 0 )
1,3,5,7,9 are odd
so tens digit has 5 choices but we see that 5 is repeated so we split into more cases
when last digit is 0, tens digit has 5 choices then hundreds digit has 8 choices so 1*5*8=40
when last digit is 5, tens digit has 4 choices and hundreds digit has 7 choices (0 can't be first digit) 1*4*7=28
40+28=68
Evaluate the expression if a=2,b=-3,C=-1, and D=4
-2(b^2-5c)
Answer:
Your answer is - 28
Step-by-step explanation:
Given,
a = 2
b = - 3
c = - 1
d = 4
Now,
- 2 ( b² - 5 c )
= - 2 ( -3² - 5 ( - 1 ) )
= - 2 ( 9 + 5 )
= - 2 × 14
= - 28 ans….
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One integer is 4 times another. If the product of the two integers is 144, then find the integers.
One possible set of answers is;
Another possible set of answers is:
Divide the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x. (27x 4 - 18x 3 + 9x 2) ÷ 3x
Answer:
9x3 - 6x2 + 3x
Step-by-step explanation:
(27x 4 - 18x 3 + 9x 2) ÷ 3x
Dividing each term between 3x we have:
9x3 - 6x2 + 3x
We can check the result:
(9x3 - 6x2 + 3x) * (3x)
= (27x4 - 18x3 + 9x2)
suppose you are using a=.01 to test the claim than mu is greater than or equal to 32 using a p-value. you are given the sample statistics n=40 , x bar =33.8 and o =4.3. Find the p-value.
0.0040, 0.0211, 0.1030, 0.9960
Using the z-distribution, the p-value for the test is of 0.0040.
What is the test statistic for the z-distribution?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are given as follows:
[tex]\overline{x} = 33.8, \mu = 32, \sigma = 4.3, n = 40[/tex]
Hence the value of the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
z = (33.8 - 32)/(4.3/sqrt(40))
z = 2.65.
What is the p-value?Using a z-distribution calculator, with z = 2.65 and a right-tailed test, as we are testing if the mean is greater than a value, the p-value is of 0.0040.
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how many liters of 70% alcohol solution and 20% alcohol solution must be mixed to obtain 20 liters of 60% alcohol solution?
Answer:
16 liters of 70% alcohol
4 liters of 20% alcohol
Step-by-step explanation:
Let x = volume of 70% alcohol and y = volume of 20% alcohol. Since we need total of 20 liters, the first equation is x + y = 20. Next, calculate the amount of alcohol in the 20 liters of 60% alcohol. 60% is equivalent to 0.6, so there is 20*0.6 = 12 liters of alcohol in the 20 liter solution. Therefore the second equation is 0.7x + 0.2y = 12.
x + y = 20
0.7x + 0.2y = 12
2x + 2y = 40
7x + 2y = 120
-5x = -80
x = 16
16 + y = 20
y = 4