The solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following set of equations -
x+3y+z=-8 ..[1]
2x+y-6z=20 ..[2]
x-2y+z=-13 ..[3]
We can write eq [3] as -
z = - 13 - x + 2y
So, eq [1] and [2], will become -
x + 3y + (-13 - x + 2y) = -8
x + 3y - 13 - x + 2y = -8
5y = - 8 + 13
5y = 5
y = 1 ..Eq[4]
AND
2x + y - 6z = 20
2x + y - 6(- 13 - x + 2y) = 20
2x + y + 78 + 6x - 12y = 20
2x + 1 + 78 + 6x - 12 = 20
8x = 47
x = 5.875 ..Eq[5]
Now -
x - 2y + z = -13
5.875 - 2 + z = - 13
z = 16.875
Therefore, the solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875.
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The graph of y=f(x) is drawn on the grid.
a) Write down the coordinates of the turning point of the graph. (1)
b) Write down the roots of f(x) = 0
c) Use the graph to find an estimate for f(2.5)
The solution to the points are:
Turning point: (1, -3.2)Root: (-1, 0) and (3, 0)Estimate of f(2.5) is -1.4The coordinates of the turning pointThis is the point where the curve or curves of the graph changes direction.
In this case, the turning point in the vertex
The graph has its vertex at (1, -3.2)
This means that
Turning point = (1, -3.2)
The roots of the functionThis is the point where the curve or curves of the graph touches the x-axis i.e. f(x) = 0
In this case, the points are: (-1, 0) and (3, 0)
This means that
The roots are (-1, 0) and (3, 0)
The estimate of f(2.5)This is the point where the curve or curves of the graph passes through x = 2.5
In this case, the points are: (2.5, -1.4)
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8,40,200,...
Find the 10th term.
The sequence has the 10th term of 15625000
How to find the 10th term for the arithmetic sequence?The sequence is given as:
8,40,200,...
The above sequence has the following parameters
First term, a = 8
Common ratio, r = 5 i.e. 40/8 = 5
Number of terms , n = 10
This means that the sequence is a geometric sequence
The nth term of an geometric sequence is calculated as
f(n) = ar^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(10) = 8 * 5^(10 - 1)
Evaluate
f(10) = 15625000
Hence, the 10th term for the sequence is 15625000
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Multiply 12. 462 by 13.
Answer:
162.006
Step-by-step explanation:
The cost of a pizza varies directly as the square of its radius. If a
pizza with a 6 inch radius costs $8.00, how much should a pizza with
an 11 inch radius cost?
The cost of a pizza with an 11 inch radius is $26.86
In this question, the cost of a pizza varies directly as the square of its radius.
Let C be the cost of pizza and r be the radius of Pizza.
We have been given the direct proportionality between the cost of pizza and the radius of Pizza.
C ∝ r²
If a pizza with a 6 inch radius costs $8.00
8 = k * 6^2
where k is the proportionality constant.
8 = k * 36
k = 0.222
We need to find the cost of pizza with an 11 inch radius.
so, we get an equation,
C = k * 11^2
substitute above value of k
C = 0.222 * 11^2
C = 0.222 * 121
C = $26.86
Therefore, the cost of a pizza with an 11 inch radius is $26.86
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This shows a triangle.
What is the value of x?
43
62
105
115
Answer:
105 degrees
Step-by-step explanation:
Find angle F:
the sum of angles of triangle =180
62+43+y=180
105+y=180
y=75
straight line = 180 degrees
75+x=180
x=105 degrees
what condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?
When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:
The data values should be symmetrical in the sample.No outliers should be in sample data .If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.
A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.
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charlie has 2 fair coins. he repeatedly tosses the pair of coins simultaneously (i.e., two tosses at a time), until he has seen both sides of both coins. in expectation, how many total tosses does this take?
By using the trial method we get a total number of trials taken by Charlie to see both sides of both the coins is 4.
What is probability?Probability is the name of the area of mathematics that deals with the examination of random events. The ratio of favorable occurrences to the total number of events is used to calculate an event's probability.
P(E) = F(E)/T (E)P(E)
It stands for the probability that an event will occur.
F(E) = Amount of favorable occurrences
Total number of trials (T(E))
Given that Charlie has 2 fair coins.
If he tosses the pair of coins simultaneously, then the number of samples can be HH, HT, TH, TT.
So to see both sides of both the coins he should toss the coin four times.
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An investor borrows r11500 to buy a computer and is charged interest at an annual rate of 6 %per annum compounded quarterly. the loan has to be paid in 3 years. calculate the amount of loan that is outstanding at the end of 2 years
The loan amount at the end of 2 years is Rs. 12,127 .
In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.
compund interest is defined as the addition of interest to the principal of loan.
principal (P) = 11500
If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %
Using the formula of Amount ,
Amount = P( 1 + r / 100) ᵗ
= 11500( 1 + 2/ 300)⁸
= 12127.83 ~ 12128
compound interest = Amount - principal =
12128- 11500 = Rs. 628
So, An investor has to pay total Rs. 12128 at the end of 2- year.
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Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
Answer: Stacy is 12 years old
Step-by-step explanation:
36/4 = 12
17. Yu Yan withdrew $25 from her savings account. The next day, she withdrew another $32.75 from
her savings account.
a. Write a numerical expression to represent the changes in Yu Yan's account.
b. Evaluate your expression from part (a).
18. Evaluate 33.28 0.64 by using the standard algorithm.
Answer:
Step-by-step explanation:
a. The numerical expression representing the changes in Yu Yan's account is x = 25 + 32.75.
b. After evaluating expression (a), we see that $57.75 is the total amount changed from her account.
What is a numerical expression?
In mathematics, a numerical expression is a combination of sets of numbers and integer combined using addition, subtraction, multiplication, or division. When used with mathematical operators like addition, subtraction, multiplication, or division, it is said that a numerical expression is a combination of different integer numbers. The following are a few typical examples of numerical expressions: 5 + 10150 - 2520 × 2 + 5 40 ÷ 10 × 2 - 8 + 1 75 + 6 - 8.
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When Lily left her house in the morning, her cell phone battery was partially charged. The charge remaining in Lily's battery, as a percentage, can be modeled by the equation B=-4t+52,B=−4t+52, where t is the number of hours since Lily left her house. What is the x-intercept of the equation and what is its interpretation in the context of the problem?
The x-intercept of the equation is 13 and its interpretation in the context of the problem is the number of time in hours for which Lily left her house.
What is x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
Next, we would determine the number of time for which Lily has left her house since in the morning by substituting the value of B with zero (0) as follows:
B = -4t + 52
0 = -4t + 52
4t = 52
Time, t = 52/4
Time, t = 13 hours.
Therefore, the x-intercept of the given equation is (0, 13).
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Oliva is making granola bars. She will use 17.9 ounces of pastachios, 12.6 ounces of almonds,12.5 ounces of walnuts, and 12.5 ounces of cashews. This amount makes 25 bars. How many ounces of nuts are in each granola bar?
The required number of ounces of nuts would be 1/2 in each granola bar.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
She will use 12.5 ounces of walnuts to make 25 granola bars which is given in the question.
To determine the number of ounces of nuts in each granola bar
Let the number of ounces of nuts in each granola bar would be x
As per the given situation, we can write a ratio as
12.5 ounces : 25 bars = x ounces : 1 bars
⇒ 12.5 / 25 = x / 1
⇒ 1/2 = x
⇒ x = 1/2
Thus, the required number of ounces of nuts would be 1/2 in each granola bar.
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the probability of spinning a1 is the same for both spinners ture or false
The probability of spinning a 1 is the same for both spinners: False
How to determine the true statement?The spinners that complete the question are added as an attachment
From the attached figures, we have
Spinner 1
Number of 1 = 1
Sections = 4
Spinner 2
Number of 1 = 2
Sections = 6
The probability of obtaining 1 is calculated as
P(1) = Number of 1/Sections
So, we have
Spinner 1
Number of 1 = 1
Sections = 4
P(1) = 1/4
Spinner 2
Number of 1 = 2
Sections = 6
P(1) = 2/6
By comparison
1/4 and 2/6 do not have the same value
Hence. it is false that the probability of spinning a 1 is the same for both spinners
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What is -900+16-2^3 ?
Answer: -893
Step-by-step explanation: -900 -(+16) = 884 +(-8) = -893
Answer:
-892
-900+16-2^3=-900+16-8=-900+8=-892
Simplify the following expressions by adding the like terms: 3a² - 2a - 7 + 3a + 4 - 2a² + 9a x² + 6xy + 5y² - 6xy + 2y² 1 2
what is the most appropriate measure of central tendency to use in determining the average time it takes students to graduate from college, assuming that a few students take an extraordinary long time to finish their degree, and why it is the most appropriate?
As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.
Why is central tendency important?A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.
Where can you locate the central tendency?You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.
What use do central tendency metrics serve in evaluating student learning?The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.
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for sample size n, the margin of error is 3. how many more samples do we need to make the margin of error 0.3?
We will need 100 more samples to make the margin error of 0.3 .
What are sample errors?When the statistical characteristics of a population are estimated from a subset, or sample, of that population, sampling errors are made in statistics. Statistics of the sample (commonly referred to as estimators), such as means and quartiles, usually diverge from those of the total population because the sample does not include all individuals of the population (known as parameters). The sampling error is defined as the discrepancy between the sample statistic and the population parameter. For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million persons in the country.acc to our question-
Margin error is 3Margin error tobe 0.3 SAMPLE size ?0.3 =3/10Ratio =3/3/10=10n^2=10×10=100Samples in size of 100Hence, We will need 100 more samples to make the margin error of 0.3 .
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Solve for c. You must show ALL of your work.
6c + 14 = -5c + 4 + 9c
Answer:
c = -5
Step-by-step explanation:
6c + 14 = -5c + 4 + 9c
1) We want to first combine the c values on the right side. This would give us 6c + 14 = 4c + 4.
2) Next, we want to move the c value to one side of the equation. This means we would subtract 4c from the right side. This gives us 2c + 14 = 4.
3) We can then subtract 14 from the left side to isolate the c value. This gives us 2c = -10.
3) We can then divide both sides by 2 and get the answer for c.
This gives us c = -5.
So, anyone wann.a decorate my rrom with me? we could give decorating ideas and what not, just bore.d
Answer: sure:)
Step-by-step explanation:
Find the length and the width.
Answer:
Length would be 6ft
Width would be 4ft
Step-by-step explanation:
24ft^2 is the area as we know 6x4 = 24 and 4 is two less than 6, therefor your answer is 4 and 6.
Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $55,000, if the total monthly fixed costs are $17,363.50 and the variable cost per chair is $52.17. $72.41 $70.80 $25.38 $20.24
Answer:
A) $72.41------------------------------
Find the total cost to produce 3575 chairs. It includes the fixed costs as well as the variable cost per chair.
17363.50 + 3575*52.17 = 203871.25Add the profit we want to have
203871.25 + 55000 = 258871.25This is the minimum amount to be made from sale.
Find minimum sales price per chair:
258871.25 / 3575 = 72.41 (rounded)This is matching the first answer choice.
PLEASE HELP ASAP I WILL GIVE BRAINLIEST
Find x and y
The values of the variables x and y in the triangle are 1.25 and 1.75
How to determine the values of the variables x and y?The tringle represents the given parameter
On the triangle, we have the following equivalent ratio
5 : 8 = 5 + x : 10
7 : 8 = 7 + y : 10
These are true because the horizontal lines of the triangles are parallel
So, we have
5 : 8 = 5 + x : 10
Express as fraction
5/8 = 5 + x/10
This gives
5 + x = 6.25
Solve for x
x = 1.25
Similarly, we have
7 : 8 = 7 + y : 10
So, we have
7/8 = 7 + y/10
This gives
7 + y = 10*7/8
Evaluate
7 + y = 8.75
So, we have
y = 1.75
Hence, the values of x and y are 1.25 and 1.75
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mary invests £12000 in a savings account.
the account pays 1.5% compound intrest per year.
y is inversely proportional to x.
when y=7, x=9
a) work out an equation connecting y and x.
b) work out the value of y when x=21.
pls show step by step working out.
Using a proportional relationship, it is found that:
a) The equation is: y = 63/x.
b) When x = 21, the numeric value is of y = 3.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables are inversely proportional, we have a inverse proportional relationship, in which the output variable y is obtained by the division of k by the input variable x, as follows:
y = k/x.
For this function, when y = 7, x = 9, hence the constant is obtained as follows:
7 = k/9
k = 9 x 7
k = 63.
Hence the equation is:
y = 63/x.
The numeric value of the function when x = 21 is given as follows:
y = 63/21 = 3.
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can the sum X to the power of two plus X to the power of three be written in simpler form? explain.
The sum X to the power of two plus X to the power of three be written in simpler form is X² + X³.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, this will be illustrated as X² + X³. In this case, it illustrate the addition of exponents.
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how many ways are there to select a set of 8 donuts from 3 varieties? donuts of the same variety are indistinguishable.
There are 336 to select a set of 8 donuts from 3 varieties, where the donuts of the same variety are indistinguishable.
here the total number of 8 donuts of a set needs to make from a given variety of 3, since here the orders so, we need to use permutations.A permutation of a set is an arrangement of its individuals into a grouping or direct order, or in the event that the set is as of now ordered, a modification of its elements. It alludes to the act or preparation of changing the direct arrange of a requested set. Permutations vary from combinations, which are determinations of a few individuals of a set in any case of an order.
the formula for permutations is :
P(n,r) = n! /(n-r)! , here n i=8 and r = 3
P(8,3) = 8! /(8-3)!
= 8* 7*6= 336
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Please help!!! photo is attached.
find the value of x
x = √ [?]
The required value of x is x = [tex]\sqrt{79}[/tex]
Given : A right angled triangle
This right angles triangle is again divided in two parts
the first part has measures 3 , z and the other side can be calculated by using The Pythagoras Theorem
According to this theorem
3² + z² = y²
thus 9 + z² = y² ------------------equation 1
Also 7 + 3 = 10
thus 10² = z² + x²-----------------equation 2
And 7² + y² = x² --------------- equation 3
from equation 1 we know
9 + z² + 49 = x²
58 + z² = x²
Thus on substituting this in equation 2 we get
100 = 58 + z² + z²
42 = 2z²
21 = z²
z = [tex]\sqrt{21}[/tex]
thus x² = 58 + 21 = 79
x = [tex]\sqrt{79}[/tex]
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Four out of nine dogs weigh less than 20 pounds what is the decimal equivalent for number of dogs weighing under 20 pounds
Answer:
.444....
Step-by-step explanation:
4 out of 9 is 4/9 or 4 ÷ 9 = .444...
simplify (3^6)^5/9x3^7 give your answer as an power of 3
We are going to use these properties :
1. (a^m)^n = a^mn
2. a^m x a^n = a^(m+n)
3. a^m : a^n = a^(m-n)
Using the first property, (3^6)^5 = 3^(6x5) = 3^30
Using the second property :
9 = 3^2
-> 9 x 3^7 = 3^2 x 3^7 = 3^(2+7) = 3^9
Therefore, it is simplified down to 3^30 : 3^9
Finally, we will use the third property :
3^30 : 3^9 = 3^(30-9) = 3^21
Express as a trinomial.
(2x-8)(2x-2)
Answer:
Step-by-step explanation:
:
The answer is 4x^{2}+12x-16. correct me if im not ty!
Answer:
4x^2 - 20x + 16
Step-by-step explanation:
4x^2 - 4x - 16x + 16
4x^2 - 20x + 16
a frustum is made by removing a small cone from a similar large cone. The height of the small cone is quarter of the height of the large cone. Find the volume of the frustum.
Height of large cone =12
radius of large cone =6
The volume of a frustum is equal to 445.3785 cubic units.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
Volume of a cone = 1/3 × πr²h
Where:
h represents the height of a cone.r represents the radius of a cone.For the volume of the large cone, we have the following:
Volume of large cone = 1/3 × πr²h
Volume of large cone = 1/3 × 3.142 × 6² × 12
Volume of large cone = 3.142 × 36 × 4
Volume of large cone = 452.448 cubic units.
Since the height of the small cone is quarter of the height of the large cone, we have:
Height of small cone = 1/4 × 12 = 3 units.
Radius of small cone = 12/18 = 3/2 = 1.5 units (similar triangles by AAA).
For the volume of the small cone, we have the following:
Volume of small cone = 1/3 × πr²h
Volume of small cone = 1/3 × 3.142 × 1.5² × 3
Volume of small cone = 3.142 × 2.25
Volume of small cone = 7.0695 cubic units.
Mathematically, we know that the volume of a frustum is made by subtracting the volume of a small cone from the volume of a similar large cone cone:
Volume of the frustum = Volume of large cone - Volume of small cone
Volume of the frustum = 452.448 - 7.0695
Volume of the frustum = 445.3785 cubic units.
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