Answer: Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(5,−2),(−3,−10)
Equation Form:
x=5,y=−2x=5,y=-2
x=−3,y=−10x=-3,y=-10
Maybe want something different then here:
X intercepts- (7,0)
Y intercepts- (0, -7)
A 9-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
(Pls help)
Answer: 0.75 inches per hour
Step-by-step explanation:
9/12=0.75
0.75 x 12 = 9
0.75 inches per hour
Answer: 4.5 hours.
Step-by-step explanation:
Use a proportion.
3 3/8 = 3.375
9 inch is to 12 hours as 3.75 inches is to x hours.
9/12 = 3.375/x
3/4 = 3.375/x
3x = 4 * 3.375
x = 4 * 1.125
x = 4.5
Answer: 4.5 hours
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What is the sum of the series sum from n equals 1 to infinity of negative 3 times three eighths to the n power question mark
The required sum of the series sum from n equals 1 to infinity is -9/5
What is geometric series of infinity?geometric series, in science, a infinite series of the structure a + ar + ar^2 + ar^3+⋯, where r is known as the common ratio. A basic model is the mathematical series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +⋯, which joins to an amount of 2 (or 1 on the off chance that the initial term is barred).
According to question:We have,
GP; -3(3/8), -3(3/8)^2,................ -3(3/8)^∞
Common ratio(r) = 3/8, a = -9/8
S(1 to ∞) = a/(1 - r)
S(1 to ∞) = -9/8(1 - 3/8)
S(1 to ∞) = -9/8/5/8
S(1 to ∞) = -9/5
Thus, sum of geometric series is -9/5.
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Using the simplex tableau solve for the LPP.
Objective function z=x1+2x2
Constraints
2x1 + x2<8
X1 + x2 <5
X1,x2>0
The values of the objective function obtained for the given set of equation is 7.
Define the term LPP?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.For the stated question-
Objective function z = x1+2x2
Constraints
2x1 + x2<8 ....eq 1x1 + x2 <5 ....eq 2x1, x2>0 .....eq 3Subtract equation 2 from 1.
x1 = 8 - 5
x1 = 3
Put value if x1 in eq 2
x1 + x2 = 5
x2 = 5 - 3
x2 = 2
Put the values of x1 and x2 in Objective function
z = x1 + 2x2
z = 3 + 2x2
z = 7
Thus, the values of the objective function obtained for the given set of equation is 7.
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What is the sum of the infinite geometric series?
25 minus 10 plus 4 minus eight fifths plus continuing
The series diverges.
five halves
fifty sevenths
one hundred twenty-five sevenths
eighty-seven fifths
Answer: [tex]C. \frac{125}{7}[/tex]
Step-by-step explanation:
1. Find the sum of the infinite geometric sequence:
[tex]S = \frac{125}{7}[/tex]
2. Find the correct option:
C
Lisa received 20% discount on a video game she bought. The discount was $5. What is the
regular price of the video game?
-2x+7y=-16
-x-8y = 15
Answer:
y = -2
x = 1
Step-by-step explanation:
what is the equation for a line that passes through (3.4) and 4,9
The equation of the line in slope-intercept form that passes through (3, 4) and (4, 9) is: y = 5x - 11.
How to Find the Equation of a Line?The equation of a line can be written in point-slope form as y - b = m(x - a), if we know the slope (m) and a point (a, b) on the line. It can be rewritten to the slope-intercept form as y = mx + b.
Given the points on a line:
(3, 4) and (4, 9)
Slope of the line (m) = change in y / change in x = (9 - 4)/(4 - 3)
Slope of the line (m) = 5/1
m = 5
To write the equation of the line, substitute m = 5 and (a, b) = (3, 4) into y - b = m(x - a):
y - 4 = 5(x - 3)
Rewrite in slope-intercept form:
y - 4 = 5x - 15
y = 5x - 15 + 4
y = 5x - 11 [equation of the line]
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Find the values of x and y.
x + 2 = 3y
The number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'. The solution is (1, 1).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given below.
x + 2 = 3y
There is only one equation, so we have to assume 'x'.
If x = 1, then the value of the variable 'y' is given as,
3y = 1 + 2
3y = 3
y = 3 / 3
y = 1
Similarly, the number of solution of the equation x + 2 = 3y will be infinite for the infinite value of 'x'.
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Carson measured a line to be 2.2 inches long. If the actual length of the line is 2.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage error of the measurement is 47.8%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The actual length of the line = 2.3 inches
The measured length of the line = 2.2 inches
The error length of the line.
= 2.3 - 2.2
= 1.1 inches
The percentage error of the measurement.
= 1.1/2.3 x 100
= 47.8%
Thus,
The percentage error of the measurement is 47.8%.
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What is the solution of this inequality?
r−6>−11
Drag and drop the choices to correctly complete the inequality.
help
The solution to the given linear inequality, r - 6 > -11, is r > -5
Solving Linear InequalitiesFrom the question, we are to determine the solution of the given inequality
The given inequality is
r - 6 > -11
To determine the solution of the inequality, we will solve the inequality for the unknown variable.
In the inequality, the unknown variable is r.
Solving the inequality for r
r - 6 > -11
Add 6 to both sides
r - 6 + 6 > -11 + 6
r > -5
Hence, the solution is r > -5
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A new corporation has established itself and is set to start selling shares of stock. On the first day, you purchase 100 shares of stock at $23.00 per share. Three years later, you sell the stock for $45.00 per share.
a. How much did you net from the sale?
b. Was this a capital gain or a capital loss?
a) The net for the sale is: $4,500
b) The capital gain is $2,200
How much did you net from the sale?
We know that you had 100 shares, now the value of each of these is $45.00, then the amount that you make if you sell the 100 shares is:
S = 100*$45.00 = $4,500
How to get the capital gain?The capital gain is the difference between the amount we found above and the amount you paid for the shares.
The price of the shares was $23.00, then the amount you paid is:
C = $23.00*100 = $2,300
Then the capital gain is:
g = $4,500 - $2,300 = $2,200
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Select all the equations that represent a line passing through the point (5,-2) with a slope of 4.
Answer:
y = 4x - 22
Step-by-step explanation:
y = 4x + b
-2 = 4(5) + b
-2 = 20 + b
b = -22
y = 4x - 22
help pls
What is the average rate of change of the function on the interval from x = 3 to x = 5?
f(x)=10(2)x
Answer: 1560
Step-by-step explanation: The average rate of change of a function over an interval is the total change in the value of the function divided by the length of the interval. In this case, the function is f(x) = 10(2)^x and the interval is [3, 5].
To find the average rate of change of the function over the interval, we can first evaluate the function at the two endpoints of the interval, which are x = 3 and x = 5. At x = 3, the function has a value of f(3) = 10(2)^3 = 80. At x = 5, the function has a value of f(5) = 10(2)^5 = 3200.
The total change in the value of the function over the interval is then the difference between the values at the two endpoints, which is f(5) - f(3) = 3200 - 80 = 3120.
The length of the interval is 5 - 3 = 2, since it goes from x = 3 to x = 5. Therefore, the average rate of change of the function over the interval is the total change in the value of the function divided by the length of the interval, which is (3120) / 2 = 1560.
Therefore, the average rate of change of the function f(x) = 10(2)^x on the interval [3, 5] is 1560.
When Max moved to a
new school in 6th
grade, there were
only 3 other kids he
knew at the entire
school. There were
367 kids in the school.
What percentage of
kids did Max know?
What is 31+4 × [11-(1+3)] =
Answer:
59
Step-by-step explanation:
31+4 × [11-(1+3)]
31+4*[11-4]
31+4*(7)
31+28
59
The easy Answer is 59. When doing these types of questions remember:
Parentheses
Exponents
Multiplication
Divionsion
Add
Subtract
p. Determine which of the values in the set {-5, -1, 0, 3}, if any, make the equation 4 = m +5 - 2m true.
Answer:
None of the values.
Step-by-step explanation:
Simplify the given equation.
First, simplify by combining like terms. Like terms are terms that share the same amount of the same variables:
4 = m + 5 - 2m
4 = (m - 2m) + 5
4 = -m + 5
Next, isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
-
First, subtract 5 from both sides of the equation:
4 = -m + 5
4 (-5) = -m + 5 (-5)
4 - 5 = -m
-1 = -m
Next, isolate the variable m. Remove the negative sign by dividing -1 from both sides of the equation:
(-1)/-1 = (-m)/-1
m = -1/-1 = 1
None of the values will make the equation true, as 1 is not a given value.
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Evaluate 25 - 4x when x = 2 and when x = 3. Which gives you the larger value and
what is that value?
O x = 2 will give you the larger value of 17.
O x = 3 will give you the larger value of 63.
O x = 2 will give you the larger value of 42.
O x = 3 will give you the larger value of 13.
Answer:17
Step-by-step explanation:
Substitute: 25-4x2
Calculate the product or quotient: 25-8
Calculate the sum or difference: 17
Answer: 17
what is the volume of the composite figure 16 7 3 5 3 6
The total volume of the composite figure is; 381 m³
How to find the volume of the composite figure?The formula for volume of a prism is;
V = Bh
where;
B is area of triangular base
h is height of prism
Thus;
V = (¹/₂ * 3 * 5) * 6
V = 45 m³
Volume of bottom cuboid is given by the formula;
V = Length * width * height
Thus;
V = 16 * 7 * 3
V = 336 m³
Total volume of composite figure = 45 m³ + 336 m³
Total volume of composite figure = 381 m³
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This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
Using an exponential function, the rate of growth is 20.482%, the number of bacteria after two hours is 12048.21 and the doubling time of the bacteria is 3.7 hours
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function.
A) The rate of growth can be calculated as
Data;
P = 8300A = 10000r = ?x = 1 hourWriting this in an exponential function;
A = P(1 + r)ˣ
10000 = 8300(1 + r)¹
r = 0.2048
r = 20.482%
B)
Substituting the values into the function above
x = 2
A = 8300(1 + 0.2048)²
A = 12048.21
C)
For the bacterial to double, the time will be
2 = (1 + 0.2048)ˣ
x = 3.7 hours
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Please nswer this question.
Answer:
4.75 megabytes per second
Step-by-step explanation:
500-25 = 475
475 / 100 = 4.75
The graph of x=6(y+6)^2+1 is a parabola with vertex (−6,1) and opening to the right.
answer options:
By the definition of the vertex form of the quadratic equation x - 1 = 6 · (y + 6)² has its vertex at (h, k) = (- 6, 1) and opens to the right. (Correct choices: A, B)
How to determine the features of a quadratic equation
In this problem we find the definition of a quadratic equation in vertex form, whose axis of symmetry is parallel to the x-axis. This form of quadratic equation is described below:
x - h = C · (y - k)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.
Please notice that the parabola opens to the right (+ x direction) when the vertex constant is greater than 0. By direct inspection, we have the following conclusions:
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can anyone help me? I don't know the answer.
Answer: 27/70
the area of the shaded rectangle
Step-by-step explanation:
9/10 and 3/7 of the rectangle are shaded on top and bttom. So you multiple this together and you will get 27/70
9/10 x 3/7 = 27/70
When you apply the method to complete the square to find the solution to the equation
2x^2 +3x +3=4
What term should we sum/add on both sides of the equation?
A. 9
B. 9/4
C. 3/2
D. 9/16
Answer:
B
Step-by-step explanation:
x² + 3x + 3 = 4 ( subtract 3 from both sides )
x² + 3x = 1
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2( [tex]\frac{3}{2}[/tex] )x + ([tex]\frac{3}{2}[/tex] )² = 1 + ( [tex]\frac{3}{2}[/tex] )²
(x + [tex]\frac{3}{2}[/tex] )² + [tex]\frac{9}{4}[/tex] = 1 + [tex]\frac{9}{4}[/tex]
that is [tex]\frac{9}{4}[/tex] is added to both sides
If the change in velocity of a car is 30 m/s and the time interval is 5 seconds, the acceleration of the car is ________ m/s2
The acceleration of the car is 6m/s²
What is acceleration?Acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. Acceleration is measured in meter per second squared
It can also be defined as the ratio of the change in velocity to the time
Therefore acceleration is given as (v-u)/t
where v is the final velocity and u is the initial velocity, t is the time
therefore a= 30-0/5
a= 30/5
a= 6m/s²
therefore the acceleration of the car is 6m/s²
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The table shows the lowest and highest record temperatures for three cities.Which city had the greatest change in the record temperature?
The city that had the greatest change in the recorded temperature is; 115°F
How to find the change in the function table?We are given the following as the table showing the lowest and highest recorded temperatures for three cities
City: Barrow Budapest Prague
Highest Temperature: 73 103 98
Lowest Temperature: -42 -10 -16
The temperatures are given in Fahrenheit.
We have to find the cities with difference between their highest and lowest temperatures .
Change in temperature for the city of barrow = (73 - (42)) = 115°F
Change in temperature for the city of Budapest = (103 - (-10)) = 113°F
Change in temperature for the city of Prague = (98 - (-16)) = 114°F
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Complete question is;
The table gives the highest and lowest recorded temperatures for six cities. Which cities recorded a difference between their highest and lowest temperatures that is greater than or equal to 115°F? Select two answers.
A.Barrow
B.Budapest
C.Prague
D.Tehran
E.D e a t h Valley
F.London
Dan reads his favorite series of books at a rate of 19
pages per hour. If Dan has already read the series for
34 hours but still has 1193 pages left, how many pages
are in the series altogether?
Answer:
Step-by-step explanation:
mult 19 buy 34 to find total number of page read then add page left = 1839
What is good IQ for an 11-year-old?
And adult plate costs $8
A child plate costs $5
Total plates sold is 272
Total value is $1,933
How many of each plate were sold?
191 of adult plates and 81 child plates were sold.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Adult plate costs A= $8
Child plate costs C=$5
Total plates sold is 272
A+C=272..(1)
8A+5C=1,933..(2)
C=272-A
Substitute in equation 2
8A+5(272-A)=1933
8A+1360-5A=1933
1360+3A=1933
Subtract 1360 on both sides
3A=1933-1360
3A=573
Divide both sides by 3
A=191
Now substitute A value in 1
191+C=272
Subtract 191 on both sides
C=272-191
C=81
Hence, 191 of adult plates and 81 child plates were sold.
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PLEASE PLEASE HELP ASAP WILL GIVE BRAINLIEST
A regular polygon is shown, with one of its angle measures labeled a.
If ma = (5z + 65)°, find the value of z.
Oz=15
Oz=20
Oz=23
Oz=41
a
Answer:
z = 15
Step-by-step explanation:
I got it right on my exam ( i luckily guessed it, but trust me.)
Evaluate the expression 9x - 5 for the values of x given in the first column.
Value of x Value of expression
5
4
129
6
7
Answer:
Step-by-step explanation:
To fill the table using the expression
you have to replace each value with x and solve the expression
Answer:
Step-by-step explanation:
Expression : 9x - 5
To fill the table using the expression, you have to replace each value with x and solve the expression.
The answer is attached to the picture.