The number of touchdowns is 4.
The number of extra-point kicks is 4.
and the number of field goals is 2.
What are linear equations in three variables?
If a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables.
How to solve the system of linear equations in three variables?
Select two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. then, solve the system of the two newly obtained equations using the Addition/Subtraction method.
Let the number of touchdowns be "x", the number of extra-point kicks be "y", and the number of field goals is "z".
Total points scored in game = 20+14 =34
Now,
According to the given question,
6x + y + 3z = 34 -----------(I)
x = y ----------(II)
x = 2z
z = [tex]\frac{x}{2}[/tex] -----------(III)
Putting the values of "y" and "z" in equation (I), we get
6x + x + 3×[tex]\frac{x}{2}[/tex] = 34
[tex]\frac{17x}{2}[/tex] = 34
x = 4
Now, putting the value of "x" in equations (II) and (III), we get
y = 4.
z = 2.
Hence, The number of touchdowns is 4. The number of extra-point kicks is 4, and the number of field goals is 2.
To learn more about the system of linear equations, visit:
https://brainly.com/question/26150814
#SPJ1
-6y-18
factored expression
Population: The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and
Elise (age 5).
Sample
n = 2
Ages
Sample
range
A, B
15, 10
5
A, C
15,9
6
A, D
15,7
8
Α, Ε
15, 5
10
B, C
10,9
1
B, D B, E
00000000
10,7
3
10, 5
The last sample range in this table is missing. What is the missing value? 2
C, D
9,7
5 2
C, E
9,5
4
D, E
7,5
The last sample range in this table is missing,the missing value is 2.
Given:
The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).
Sample(n = 2) A, B A, C A, D Α, Ε B, C ........ D,E
Ages 15, 10 15,9 15,7 15, 5 10,9 ....... 7,5
Sample range 5 6 8 10 1 ...........
Let x be the sample range missing.
sample range = ages difference
= Age of D - Age of E
= 7 - 5
= 2
Therefore The last sample range in this table is missing,the missing value is 2.
Learn more about the missing value here:
https://brainly.com/question/16579022
#SPJ1
Answer:
answer is 2 i did it and got it right
Step-by-step explanation:
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $28, and the standard deviation is known to be $5.5. How large of a sample would be required in order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42? Round your answer up to the next integer.
In order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42. The sample size would be 85
How to find the size of sample when the error of at most $0.42Information form the question
the mean income is $28
the standard deviation is known to be $5.5
the mean per capita income at the 90% level of confidence
an error of at most $0.42
What is the formula for the sample size?This is given as from margin of error:
This is the term refers to the minimum error that is to be allowed
Margin of error, E = Zc * √(SD²/n)
n = sample size
n = SD x (Zc/E)²
SD = standard deviation
Zc = would be the critical value at 90 percent level of confidence = 1.65
plugging in the values
n = 5.5 x (1.65/0.42)²
n = 0.25 x 15.4337
n = 84.8854
n = 85
Read more on margin of error here:
https://brainly.com/question/13897400
#SPJ1
Please Help
(f-g)(x)if f(x)=/16x4 and g(x)=3x2-3x-5
The value of the function (f - g)(x) is x² + 3x + 5
How to solve functions?A function is defined as a relation between a set of inputs having one output each.
In a simpler terms, a function relates input and output.
Therefore, let's solve the function (f - g)(x)
f(x) = √16x⁴
g(x) = 3x² - 3x - 5
Therefore,
(f - g)(x) = f(x) - g(x)
(f - g)(x) = √16x⁴ - (3x² - 3x - 5)
(f - g)(x) = √16x⁴ - 3x² + 3x + 5
(f - g)(x) = 4x² - 3x² + 3x + 5
Therefore,
(f - g)(x) = x² + 3x + 5
learn more on function here: https://brainly.com/question/15607023
#SPJ1
math help, will mark brainliest
Answer: 1 question Solve for x
x=
3
−y−2z−10
Solve for y
y=−3x−2z−10
Step-by-step explanation: Steps for Solving Linear Equation
3x+y+2z=−10
Subtract y from both sides.
3x+2z=−10−y
Subtract 2z from both sides.
3x=−10−y−2z
The equation is in standard form.
3x=−y−2z−10
Divide both sides by 3.
3
3x
=
3
−y−2z−10
Dividing by 3 undoes the multiplication by 3.
x=
3
−y−2z−10
A rectangle has a width (3x-2) and a length of (5x). The rectangle has the same perimeter as a square with a perimeter of 44 units.
Find the value of x.
Check the picture below.
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
The inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
According to the question,
We have the following information:
The perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
Now, the expressions for the width and length of the rectangle are given below:
Width = x units
Length = (x+4) units
We know that the following formula is used to find the perimeter of rectangle:
2(length+width) < 122
2(x+4+x) < 122
2(2x+4) < 122
Dividing by 2 on both sides:
2x+4 < 122/2
2x+4 < 61
Subtracting 4 from both sides:
2x < 61-4
2x < 57
Dividing by 2 on both sides:
x < 57/2
x < 28.6
Hence, the inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
To know more about inequality here
https://brainly.com/question/10681890
#SPJ1
HELP PLEASE QUICKLY!!!!
The expression that shows the result of applying the distributive property is 21y - 7/11 (option D).
What is the expression?The distributive property states that an expression that has this form a(b + c) can be solved as a x (b + c) which becomes ab + ac.
Thus, to solve an expression using the distributive property, multiply the term in the brackets by the term outside the brackets. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.
7(3y - 1/11)
= 7 x (3y - 1/11)
= 21y - 7/11
To learn more about the distributive property, please check: https://brainly.com/question/6276874
#SPJ1
Orenda opened a savings account with $4500 that earns 0.6% simple interest
annually. After how many years will the balance of the account be $4635? Round to the nearest tenth, if necessary.
WHAT IS THE ANSWER???
The time required for for the balance to reach $4635 is 5 years.
How to solve simple interest problems?The formula for simple interest can be expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $4500Interest rate r = 0.6%Accrued amount A = $4635Time t = ?First convert the interest rate from percent to decimal
Interest rate = 0.6%
Interest rate = 0.6/100
Interest rate = 0.006
Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
t = ( 4635/4500 - 1) / 0.006
t = ( 1.03 - 1) / 0.006
t = ( 0.03) / 0.006
t = 5 years.
Therefore, the required time is 5 years.
Learn more about simple interest here: brainly.com/question/25845758
#SPJ1
Write an equation of the line that is PARALLEL to 12x - 4y = 4 and through the point (-9,-2).
Answer:
y=3x+25
Step-by-step explanation:
we need start by making slope intercept form
lets move the 12x after moving it we get
-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4
we get y=3x-1
now we can create an equation to get the parallel line
y+2=3(x+9) now distribute
y+2=3x+27 and subtract the two
y=3x+25
Simplify 2.54 + 1.5 × 4
00
Which could be the base shape of the cylinder?
Oline
O non-square rectangle
O circle
O square
Answer:
The answer is a D. a circle
The base shape of the cylinder can only be a circle.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.
The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.
A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.
Hence, the base shape of the cylinder can only be a circle.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ5
what is √3 + 1/3 and is the answer irrational or rational?
Answer:
Your answer would be 2.1.
Step-by-step explanation:
The square root of 3 is:
1.73205080757
Then since 1/3 is equal to 0.33, I added 0.33 to the square root of 3 to get:
2.06205080757
Then, I rounded it:
2.1
Chris works at an electronics store. He earns $10 per hour plus 12.5% commission on his computer sales. Today, Chris worked 5.5 hours and sold $1100 in computers. How much did Chris earn in total today?
By solving a simple equation we can see that Chris earned $192.50.
How much did Chirs earn Today?
We know that Chris wins $10 per hour plus the 12.5% of the total amount he solds in computers.
So, if he works 5.5 hours and sold $1,100 in computers, the amount that he earns is given by the equation:
E = $10*5.5 + $1,100*( 12.5%/100%)
E = $10*5.5 + $1,100*(0.125) = $192.50
Then we conclude that Chris earned $192.50 today.
Learn more about equations:
https://brainly.com/question/13763238
#SPJ1
15. Given the following measurements in
parallelogram ABCD, find the PERIMETER of
CED
AC 34 in. AB = 26 in. BD = 28 in.
P =
20 points for whoever answers
The Perimeter of CED AC is 34 in. AB is 26 in. BD is 28 in. P is 57 in.
Explain about the parallelogram?A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle. Rhombus: An equal-length parallelogram with four sides.
The diagonals of a parallelogram bisect each other AC = 2 CE
Substitute AC= 34 into AC = 2 CE 34 = 2CE
Calculate 34 = 2 CE CE = 17
The diagonals of a parallelogram bisect each other BD = 2DE
Substitute BD= 28 into BD = 2DE 28 = 2DE
Calculate 28 = 2 DE DE = 14
Opposite sides of parallelogram are congruent AB = CD
Substitute AB = 26 into AB = CD CD = 26
Perimeter of a triangle PΔCDE = CE + CD + DE
Substitute CE = 17 DE = 14 CD = 26 PΔCDE = CE + CD + DE
PΔCDE = 17+ 26 + 14
PΔCDE = 57
To learn more about parallelogram refer to:
https://brainly.com/question/970600
#SPJ1
Consider the following quadratic equation:
49x2=64
Using the standard form ax2+bx+c=0 of the given quadratic equation, factor the left hand side of the equation into two linear factors.
⇒ let us first write the given equation in the form
[tex]ax^{2} +bx+c=0[/tex]
⇒[tex]49x^{2} -64=0[/tex]
⇒ Note in this case bx=0
Let us factorize the equation...49 is a square number and 64 is also a square number ..This equation is a difference of two squares which can be written as:
[tex](7x-8)(7x+8)=0[/tex]
⇒The answer is (7x-8)(7x+8)=0
WILL GIVE BRAINLIEST
You walk 10km North then turn and walk 5km East. What is your displacement from where you started? Show your work
Answer:
A hiker walks 10 km East, then 5 km in a direction 60 degrees North of West, then 8.7 km in a direction 30 degrees South of West. Find her resultant displacement.
Since you walk 10km North then turn and walk 5km East, your displacement from where you started is approximately 11.18 km.
How to determine the displacementFrom the information given, we have that you walked 10 km north (which represents the vertical side of the triangle) and 5 km east Using the Pythagorean theorem, the displacement (d) can be determined as;
[tex]d^2 = (10 km)^2 + (5 km)^2[/tex]
Find the square values, we get
d² = 100 km² + 25 km²
add the squares, we get
d² = 125 km²
Find the square root of both sides of the equation, we have;
d = 125km²
d = 11.18 km
Therefore, your displacement from where you started is approximately 11.18 km.
Learn about displacement at:
https://brainly.com/question/14422259
#SPJ2
brainliest points whatever you want please
Annual rate of return earned when the share was sold at $50 per share is 20%
Annual rate of return earned when the share was sold at $60 per share is 40%
How to calculate annual rate of returnAnnual rate of return is given by the formula
let end of the year price = eyp
let beginning of the year price = byp
= {(eyp - byp) / byp} * 100
Annual rate of return at share price of $50 per share
when there is paying of dividends the value is added to the the eyp
eyp = 50 * 100 + 2 * 100 * 5 = 6000
byp = 50 * 100 = 5000
= {(6000 - 5000) / 5000} * 100
= 20%
Annual rate of return at share price of $60 per share
eyp = 60 * 100 + 2 * 100 * 5 = 7000
byp = 50 * 100 = 5000
= {(7000 - 5000) / 5000} * 100
= 40%
Learn more about annual rate of return here:
https://brainly.com/question/3578105
#SPJ1
or
The equation of line k is y=
–
10x–8. Perpendicular to line k is line , which passes through the point (2,2). What is the equation of line ?
Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 10x -8.
The line has a slope of 10. If you multiply the slopes of two perpendicular lines, you get –1:
10× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 10
slope perpendicular line= -1/10
The perpendicular line has a form of: y= -1/10x + b
The line passes through the point (2, 2). Then:
2= -1/10× (2) + b
2= -1/5+ b
2+ 1/5= b
11/5= b
Finally, the perpendicular line is y= -1/10x + 11/5.
Learn more about perpendicular line:
brainly.com/question/7197064
brainly.com/question/11470863
brainly.com/question/7280013
#SPJ1
A rectangular box is 12 in. x 14 in. x 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in
terms of pi.
The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²
The surface area of sphere = 324π inches²
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the surface area of the Sphere be = S
Let the dimensions of the rectangular box be L x W x H
12 inches x 14 inches x 18 inches
Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum
From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere
So , Height of the Box = Diameter of the Sphere
And , Radius of the sphere = Height of the Box / 2
= 18 / 2
Radius of the sphere = 9 inches
Now ,
Surface Area of a Sphere = 4πr²
r = 9 inches
Substituting the values in the equation , we get
Surface Area of a Sphere S = 4 x π x ( 9 )²
= 4 x π x 81
= 324π inches²
Therefore , the value of S is 324π inches²
Hence , The surface area of sphere = 324π inches²
To learn more about sphere click :
https://brainly.com/question/27933834
#SPJ1
Write an algebraic expression that represents each purchase.
a. Dr. Lin bought x number of soccer balls and 4 baseballs.
b. Nestor, Felix, Peter, and Hao are on a baseball team. They each bought a baseball and x pairs of sweat socks.
26. Suppose x has the same value in both of the expressions you wrote for 25. Are the two expressions you wrote for 25 equivalent? Explain.
27. Sophia says that the algebraic expression 4
4
5x, where x represents the cost of a baseball, describes the cost of a soccer ball. Do you agree? Explain.
1. An algebraic expression that represents each purchase is as follows:
a) 15x + 24b) 5x + 24.2. Supposing that x has the same value in both expressions written above, the two algebraic expressions are not equivalent because the slope of expression A is greater than the slope of expression B.
3. The cost of a soccer ball in relation to the cost of a baseball cannot be represented by the algebraic expression 4 + 5x because it is given that the cost of a soccer ball is $15, and no number can substitute the x variable to equate the two.
What is an algebraic expression?An algebraic expression is a combination of terms (variables and constants) using the mathematical operations of addition, subtraction, multiplication, division, etc.
a) 15x + 4(6) = 15x + 24
b) 4(6) + 5x = 24 + 5x or 5x + 24
c) Cost of a soccer ball = $15
Cost of a baseball = $6
Learn more about algebraic expressions at https://brainly.com/question/4344214
#SPJ1
Question Completion:Soccer balls = $15 each
Baseballs=$6 each
Sweat socks =$5 per pair
help for brainlest please???
Answer:
45
Step-by-step explanation:
the pattern adds 3 if you look at it care fully
Raven is taking a math test.
The test lasts for 1 hour and 35 minutes.
If they finish the test at 1:20, what time did they start the test?
If they took 1 hour and 35 minutes to complete the test and finished at 1:20 they started at 11:45.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The total time of the math test Raven took was 1 hour and 35 minutes.
Now he finishes the test at 1:20.
So, One hour before the time was 12:20.
20 minutes before that was exactly 12:00 and 15 minutes before that was
11:45 so a total of 1 hour and 35 minutes.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
A researcher collected sample data for 12 middle-aged women. The sample had a mean serum cholesterol level (measured in milligrams per one hundred
milliliters) of 189.6, with a standard deviation of 10. Assuming that serum cholesterol levels for middle-aged women are normally distributed, find a 95%
confidence interval for the mean serum cholesterol level of all women in this age group. Give the lower limit and upper limit of the 95% confidence interval.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
5
The lower and upper limit of the 95% confidence interval is 183.2 and 196.0 unit.
What is a confidence interval ?
When you run your experiment again or resample the population in the same way, you can expect your estimate to fall within a certain range of values a certain percentage of the time. This is known as the confidence interval.
Main Body:
Given in question :
x- bar = 189.6
standard deviation = 10
C.I. = 95% =0.95
N=12
so, degree of freedom (D.F) = N-1 = 11
confidence level (α) = (1- C.I.)/2
= 0.025
according to t- distribution table for d.f = 11 and α= 0.025 , my result is 2.201
Now dividing standard deviation by square root of samples, we get
= 10/√12= 2.887
Lower limit = Mean - 2.201*2.887
= 189.6- 6.354
= 183.246
Upper limit = Mean + 2.201*2.887
= 189.6 + 6.354
= 195.954
Hence the result is 183.2 and 196.
to learn more about confidence interval , visit;
https://brainly.com/question/15712887
#SPJ13
Find g(x), where g(x) is the translation 1 unit up of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
g(x)=
The value of the translated function g(x) will be x²+1.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.
Given that the function is f(x) = x². The function g(x) in the form of a(x–h)²+k will be written as below,
The function is translated to the 1 unit up which means that the value of k will be equal to the positive 1.
The function is,
g(x) = a(x–h)²+k
g(x) = 1(x-0)² + 1
g(x) = x² + 1
Therefore, the value of the translated function g(x) will be x²+1.
To know more about function follow
https://brainly.com/question/13992502
#SPJ1
Samuel is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Samuel's test score (out of 100) if he got 9 questions wrong? What would be his score if he got xx questions wrong?
If Samuel answers 9 questions wrong, his score will be 55 points, and if he answers x questions wrong his score is:
f(x) = 100 - x*5
What will be Samuel's score if he got 9 questions wrong?
We know that there are 100 points available, and each question gives 5 points, then the number of questions is given by the quotient:
100/5 = 20
There are 20 questions.
So, if you answer 9 wrong, then you answer:
20 - 9 = 11 correctly
Then your score is:
11*5 = 55
Your score will be 55 points.
And again, each answer gives 5 points, so if you answer x questions wrong your score will be the linear equation:
f(x) = (20 - x)*5
f(x) = 100 - x*5
Where x is an integer between 0 and 20.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
If the nth term of a number sequence n2-3 find the first 3 terms
Answer:
-1,-2,0
Step-by-step explanation:
n(2-3)
1st term=n(2-3)
substitute value
1(2-3)=-1
2nd term=2(2-3)=-2
3rd term=3(3-3)=0
matrix
urgent please fast
Answer:
-8, -5
Step-by-step explanation:
You want the second column of matrix B given matrices A and AB.
Matrix BMatrix B can be found by left-multiplying AB by A^-1, as shown in the attachment.
The second column of matrix B is ...
[tex]\left[\begin{array}{c}-8\\-5\end{array}\right][/tex]
Can someone please help me , thank you :)!
Answer:
a )
[tex]6 ( ? ) = 27[/tex]
b )
? = The amount of rice in each container.
So, 1 container = ( ? ) ounce.
6 containers have = 6 x ( ? ) ounces.
We know that 6 containers have 27 ounces so...
[tex]6 ( ? ) = 27[/tex]
[tex]? = \frac{27}{6}[/tex]
[tex]? = 4.5[/tex]
Final Answer: 4.5 ounces in each container
Hope this helps! :)
What is Prince William's full name?
Answer:
Depends on the gravitational force. On Earth, one pound equals 4.41N.
Step-by-step explanation:
The formula for Newton's Second Law of Motion is F=ma, which is Force = mass × acceleration.
The SI unit of mass is the kilogram (kg), so we'll have to convert one pound to kilograms. For practical purposes, one pound equals 0.45kg.
The gravitational force of the Earth is 9.8m/s^2. It is worth noting that each planetary body has its own gravitational force in respect to its mass.
Force = mass × acceleration = 0.45kg × 9.8m/s^2 = 4.41N
This number is only applicable on Earth, and may and will change on a planetary body with a mass different from Earth's.
