Answer:
b=(cd-ax)/y
Step-by-step explanation:
b=(cd-ax)/y
In a football game, Team A defeated Team B by a score of 31 to 14. The total points scored came from a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3
points, respectively. The numbers of touchdowns and extra-point kicks were equal. There were six times as many touchdowns as field goals. Find the number of touchdowns, extra-point
kicks, and field goals scored.
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.
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Please help me with these questions
The rate of change of the linear functions given in tabular form and equations are found as follows;
1. a. The rate of change of the function is 5
b. The rate of change of the function is 7
c. The rate of then function is 0.75
d. The function has a rate of change of -8
2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values
b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days
c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day
The rate of change of a function is a measure of how much the output changes per unit change in the input.
1. The rate of change of the functions are as follows;
a. The first difference of the y-values is constant, therefore the function is a linear function
The formula for the rate of change of the linear function is presented as follows;
[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{-3 - (-8)}{1 - 0} = 5[/tex]b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]
The rate of change of the function is 7 unit changes in the y-value per unit change in the x-valuesc. The function is a linear function, as the first difference is constant and equal to 0.75
The rate of change of the function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]
The rate of change of the function is 0.75d. The first difference is constant and equal to -8
The rate of change of the straight line function is therefore;
[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]
The rate of change of the function is -82. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function
The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4
The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units
b. When the number of antibodies is 360, we have;
360 = 20·d + 100
20·d = 360 - 100 = 260
d = 260 ÷ 20 = 13
It would take 13 days for the patients blood to have 360 antibodiesc. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.
3. The function that gives the amount of antibodies in the body is a = 20·d + 100
d = The number of days
a = The number of antibodies
a. The table is completed as follows;
Data for Medicine A
d [tex]{}[/tex] a
0 [tex]{}[/tex] 100
1 [tex]{}[/tex] 120
2 [tex]{}[/tex] 140
3 [tex]{}[/tex] 160
4 [tex]{}[/tex] 180
5 [tex]{}[/tex] 200
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Determine when the function is positive, negative, increasing, or decreasing.
The function is positive and increasing from 0 to 2.5, at negative and decreasing from 0 to -2.5, respectively.
How to find returns to scale?
Returns to scale involves an increase in an output more than when all the inputs increase proportionately.
Using the graph, there is a line segment from the origin to a point. at the middle of the third block making 2.5. this shows an increase which is positive and on the other hand, there is a line segment from the origin towards left hand side on the number line showing a decrease and a negative from 0 to -2.5.
In conclusion, the line pointing upwards towards right hand side shows both positive and increase while the line pointing leftward shows decrease and negative.
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8x^(3)-27=0
find the roots of x
Answer:
[tex] \sf Root \: of \: x \: are \: \dfrac{3}{2} \: and \: \dfrac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
Step-by-step explanation:
[tex] \rm \implies 8 {x}^{3} - 27 = 0 \\ \\ \rm \implies (2 \times 2 \times 2) {x}^{3} - (3 \times 3 \times 3) = 0 \\ \\ \rm \implies {(2x)}^{3} - {3}^{3} = 0 \\ \\ \boxed{ \rm {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )} \\ \\ \rm \implies (2x - 3)( {(2x)}^{2} + (2x)(3) + {3}^{2} ) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: and \: 4 {x}^{2} + 6x + 9 = 0 \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{36 - 144} }{8} \\ \\ \rm \implies x = \frac{3}{2} \: and \: x = \frac{ - 6 \pm \sqrt{ - 108} }{8} [/tex]
7. Wanda's Widgets used market surveys and linear regression to develop a demand function based on the wholesale price. The demand function is q = -140p + 9,000. The expense function is E = 2.00q + 16,000.
a. Express the expense function in terms of p.
b. At a price of $10.00, how many widgets are demanded?
c. How much does it cost to produce the number of widgets from part b?
I am so confused on how to answer these 3 sections, so if anyone could help I would really appreciate it!!
a. The expense function in terms of p is - 280p + 34, 000
b. At a price of $10.00, 7, 600 widgets are demanded
c. It costs $31, 200 to produce the number of widgets from part b
How to determine the valuesWe have that;
The demand function is q = -140p + 9,000The expense function is E = 2.00q + 16,000To express the expense function in terms of p, we have to take the following steps;
Substitute the value of q in the demand function into the function for the expense, we get;
Expense function = 2( -140p + 9,000) + 16, 000
Now, expand the bracket, we get;
Expense function = - 280p + 18, 000 + 16, 000
collect and add like terms
Expense function = - 280p + 34, 000
If p = $10. 00
Then,
Demand function is q = -140(10) + 9,000
expand the bracket
q = - 1400 + 9, 000
q = 7, 600
Substitute q in expense function
E = 2.00q + 16,000
E = 2. 00(7600) + 16, 000
E = $31, 200
Hence, the expense function is - 280p + 34, 000
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The face value of a simple discount note is $17,000. The discount is 4% for 160 days. Calculate the following. a. Amount of interest charged for each note. (Round your answer to the nearest cent.) b. Amount borrower would receive. (Round your answer to the nearest cent.)
The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.
The amount the borrower would receive is $16, 697. 78.
How to find the interest charged?The interest charged on the simple discount note can be found by the formula:
= Face value of note x discount rate x number of days / total days in a year
= 17, 000 x 4% x 160 / 360
= $302. 22
The amount that the borrower would receive is then:
= Face value of note - Interest charged on note
= 17, 000 - 302.22
= $ 16, 697. 78
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George invest $500 in his friend's startup company. his friend agrees to give him 8% of the original investment each year for the next 3 years. write a linear function for this situation.
The linear function for the situation is :-
Amount at the end of 3 years = Original investment + original investment*Rate*Time/100
It is given in the question that:-
Investment of George's friend in startup company = $ 500.
Interest percent = 8 %
Time period of investment = 3 years
We have to find the linear function for this situation.
As this interest is on original investment, the interest will be simple.
Hence,
The linear function for the situation will be :-
Amount at the end of 3 years= Original investment + original investment*Rate*Time/100
Amount at the end of 3 years = 500 + 500*8*3/100 = 500 + 120 = $ 620
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What is tan 67 degrees
How do I calculate the area and perimeter of this triangle?
Step-by-step explanation:
to find the perimeter first:
13×3=39
13×3=39
5×3=15
5×3=15
39+39+15+15=108
P=108
i hope it's useful
Two times the sum of a number and 3 is 8.
Use the variable c for the unknown number.
My answer is : 2(c+3)=8
The " is" throwing my brain off, thanks so much
Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.
Let the value of the unknown number or variable be c.
Given,
"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.
If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.
The equation will be:
2(c + 3) = 8
=> 2c + 6 = 8
=> 2c = 8- 6
=> 2c = 2
=> c = 2/2
=> c = 1.
Hence, the value of the unknown number c will be 1.
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Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
quotient of 2÷ 3/7 iready
Answer:
6/7
Step-by-step explanation:
2÷3/7=2*3/7
6/7
WILL GIVE BRAINLIEST PLEASE HELP!!!!
A cat runs 10 meters north, sees a dog and runs 2 meters back south. It then runs 6 meters west. What is the displacement of the cat and the total distance it ran?
Answer:
The cat is at at 8 north 6 west
Step-by-step explanation:
The cat ran a total of 14 meters
For which value of x is line n parallel to line m?
Answer:
x is 70°
hopefully this will help u
A number x is such that dividing the number by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10. Write down and solve an equation satisfied by x. Enter your answer in the box below as a number, rounded to one decimal place if necessary.
Answer:
x = 2
Step-by-step explanation:
You want x such that dividing by 5 and then adding 2 gives the same outcome as adding 22 and then dividing by 10.
Setup(x/5) +2 . . . . the value after dividing by 5 and adding 2
(x +22)/10 . . . . the value after adding 22, then dividing by 10
These two outcomes are the same:
x/5 +2 = (x +22)/10
SolutionMultiplying the equation by 10 gives ...
2x +20 = x +22
x = 2 . . . . . . . . . . . . subtract x+20
The number is x = 2.
__
Additional comment
The outcome in each case is 2.4.
What is 4/5 ÷ 1/3? The quotient is 2 and
Answer:4/5 : 1/3=4/5 x 3/1=12/5
Step-by-step explanation:
Answer:
12/5
Step-by-step explanation:
If you set it in the calculator 4/5 ÷ 1/3 you get = 12/5
was it helpful?
How do I solve this question
Answer: [tex]6/(x-7) +( -5)/(x-5)[/tex]
Step-by-step explanation:
Let
[tex](x+5)/(x-7)(x-5) = A/(x-7) +B/(x-5)[/tex]
⇒[tex](x+5)/(x-7)(x-5)=( A(x-5) +B(x-7))/(x-7)(x-5)[/tex]
Comparing both the sides
[tex](x+5)= A(x-5)+B(x-7)\\x+5=Ax-5A+Bx-7B\\x+5= (A+B)x + (-5A-7B)\\[/tex]
Comparing both sides of the equation we get,
[tex]A+B= 1[/tex] ....eq(1)
[tex]-5A-5B=5[/tex] ..... eq(2)
solving eq(1) and eq(2),
we get B=-5 and A=6.
Hence the solution is [tex]6/(x-7) +( -5)/(x-5)[/tex]
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suppose v varies directly as g,and v=36 when x=4.Find v when g=11
Answer:
v = 99
Step-by-step explanation:
given v varies directly as g then the equation relating them is
v = kg ← k is the constant of variation
to find k use the condition v = 36 when g = 4 , then
36 = 4k ( divide both sides by 4 )
9 = k
v = 9g ← equation of variation
when g = 11 , then
v = 9 × 11 = 99
CLASSIFYING A FUNCTION. Is the function represented by the ordered pairs linear or nonlinear? Explain your reasoning.
Car A is travelling east at a steady speed .......
Answer:
for 20 miles per hour
Step-by-step explanation:
.
Plot the following numbers on the number line: -3 1/2 1 3/4
A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.
In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.
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Which expression is equivalent to 3x – 5?
Answer:
2x – 4 – 1 + x
Step-by-step explanation:
Answer:
Step-by-step explanation: -15
QUESTION 1
1 POINT
To study whether there is a correlation between regular exercise and sleep, a researcher randomly selected 100 people who
exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on
average.
Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Select the correct answer below:
The study is an experiment. The controlled factor is the amount of sleep.
O The study is an experiment. The controlled factor is the amount of exercise.
The study is an observational study.
O The study is an experiment. The controlled factor is the survey.
Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.
What is an observational study?An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).
In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.
In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.
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For what value of x is g(x) = 2
Answer:
x = 2
Step-by-step explanation:
For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.
Hope this helps!
Contains the points (5, 3) and (8, 12); slope-intercept form
Answer:
y = 3x + 12
Step-by-step explanation:
y = mx + b
The m is the slope and the b is the y intercept.
Slope:
Change in y over the change in x. The ordered pair is written in the form (x,y)
[tex]\frac{12-3}{8-5}[/tex] = [tex]\frac{9}{3}[/tex] = 3
The slope is 3.
Use the slope of the 3 and the x and y from one of the ordered pairs given. I am going to use the point (5,3), but either point will work
slope 3
x = 5
y=3 Plug these all in and solve for b
y = mx + b
3 = (3)5 + b
3 = 15 + b Subtract 15 from both sides
-12 = b
This is the y intercept
y = 3x - 12
Answer:
Slope-intercept form,
→ y = 3x - 12
Step-by-step explanation:
Formula we use,
→ y = mx + b
The value of slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (12 - 3)/(8 - 5)
→ m = 9/3
→ [ m = 3 ]
Then the value of b will be,
→ y = mx + b
→ 12 = (3)8 + b
→ b + 24 = 12
→ b = 12 - 24
→ [ b = -12 ]
Now the slope-intercept form is,
→ y = mx + b
→ [ y = 3x - 12 ]
Hence, the answer is y = 3x - 12.
Pls help me, giving brainliest 50 POINTS!
Pls show your work and not only your answers pls
If you can’t answer it then don’t answer but if you can thank you
You will be reported if you put links
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]
[tex] \textsf{36 = 2 × 2 × 2 × 2 × 2 × 1} [/tex][tex] \textsf{3 = 3 × 1 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]
[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]
Similarly,
[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]
[tex] \textsf{6 = 2 × 3 } [/tex][tex] \textsf{54 = 2 × 3 × 3 × 3 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 3 = 6 } [/tex]
[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]
[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]
[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]
[tex] \textsf{16 = 2 × 2 × 2 × 2} [/tex][tex] \textsf{8 = 2 × 2 × 2 } [/tex][tex] \textsf{12 = 2 × 2 × 3 } [/tex][tex] \textsf{GCD = 2 × 2 = 4 } [/tex]
[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]
Answer:
Numbers are : 36, 3, 12
36 = 2 × 2 × 2 × 2 × 2 × 1
3 = 3 × 1
12 = 2 × 2 × 3
HCF = product of total common factors of all three numbers, i.e : 2
LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96
Similarly,
2. Numbers are : 6, 54, 12
6 = 2 × 3
54 = 2 × 3 × 3 × 3
12 = 2 × 2 × 3
GCD = 2 × 3 = 6
[ 2 and 3 are the only ones common among all three ]
LCM = 2² × 3³ = 4 × 27 = 108
3. Numbers are : 16, 8, 12
16 = 2 × 2 × 2 × 2
8 = 2 × 2 × 2
12 = 2 × 2 × 3
GCD = 2 × 2 = 4
LCM = 2⁴ × 3 = 16 × 3 = 48
I need help please answer
Drag each expression to the correct location on the table.
Match each expression to its simplified form.
Answer:
3x-3:
(1/3)(9x-9)
(9/2x - 2) -(3/2x +1)
(3/2x-2) + (3/2x-1)
2x-1:
(7/2 x -2) - (3/2 x - 1)
1/2(4x-2)
Step-by-step explanation:
(7/2 x -2) - (3/2 x - 1)
7/2 x -2 -3/2 x +1 Distribute the negative sign to both terms
4/2 x -1 Combine like terms
2x-1
(1/3)(9x-9)
3x-3 Distributive property
(9/2x - 2) -(3/2x +1)
9/2x -2 -3/2x -1 Distribute negative sign
6/2x -3
3x-3
(3/2x-2) + (3/2x-1)
3/2x -2 +3/2x -1 Can just get rid of parenthesis since everything is added.
6/2x -3
3x-3
1/2(4x-2)
2x-1 Distribute the 1/2 to both numbers
write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
The 10 forms 1/8 can be written is as follows;
1/81 ÷ 81/2³1/√64[tex]{8}^{ - 1} [/tex][tex]{√64}^{ - 1} [/tex]1 : 8[tex]{2}^{ - 3} [/tex]2/164 : 32How to write 1/8 in different forms?A fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper value of a fraction.
A denominator is the lower value of a fraction.
1 over 8 can be written in the following ways;
1/8
1 ÷ 8
1/2³
= 1 / 2×2×2
= 1/8
1/√64
= 1/8
[tex]{8}^{ - 1} [/tex]
= 1/8
1 : 8
= 1/8
[tex]{√64}^{ - 1} [/tex]
= 1/√64
= 1/8
[tex]{2}^{ - 3} [/tex]
= 1/2³
= 1/8
2/16
= 1/8
4 : 32
= 4/32
= 1/8
In conclusion, 1/8 can be written in different forms including using square root and ratios.
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The slide at the playground has a height of 9 feet. The base of the slide measured onthe ground is 12 feet. What is the length of the slide?
O 15 feet
O 45 feet
21 feet
36 feet
Step-by-step explanation:
this creates a right-angled triangle, with the length of the slide being the Hypotenuse (the side opposite of the 90° angle), and height and base are the legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse, a and b being the legs.
length² = 9² + 12² = 81 + 144 = 225
length = sqrt(225) = 15 ft
