The solution for the system of linear equations y = 5 − x and 4x + 2y = 10 are x = 0 and y = 5
What are linear equations?Linear equations are equations that have constant average rates of change.
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y = 5 − x
4x + 2y = 10
Substitute y = 5 − x in the equation 4x + 2y = 10
So, we have the following equation
4x + 2(5 - x) = 10
Open the brackets
4x + 10 - 2x = 10
Evaluate the like terms
2x = 0
Divide through by 0
So, we have
x = 0
Substitute x = 0 in y = 5 - x
y = 5 - 0
Evaluate the like terms
y = 5
Hence, the solution of the equations are x = 0 and y = 5
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Multiply.
(2.75 x 10-%) • (4.6 x 10-3)
Answer:
1.265 x 10-10
Step-by-step explanation:
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1210 1331
Option 2 (amount in dollars) 1100 1200 1300
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.
B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;
Option 1; f(n) = n + 100
Option 2; f(n) = n + 100x
C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900
How to solve Linear functions?A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.
For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.
B) For option 1, the function is;
f(n) = n + 100
For option 2, the function is;
f(n) = n + 100x
C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.
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8^x = 2 Write down the value of x.
Answer:
x = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex]8^{x}[/tex] = 2
[tex]2^3)^{x}[/tex] = 2 , that is
[tex]2^{3x}[/tex] = [tex]2^{1}[/tex]
since the bases on both sides are equal, both 2, then equate the exponents
3x = 1 ( divide both sides by 3 )
x = [tex]\frac{1}{3}[/tex]
find the value of x. Show your steps.
Answer:
x=8
Step-by-step explanation:
83+(12x+1)=180
It equal to 180 because the line measures to 180.
Then write out the equation and solve.
answer choices:
6cm by 1.5cm
10cm by 2cm
13cm by 4cm
18cm by 4.5cm
80cm by 20cm
worth 23 points! and i will give brainly , pls hellpppp
Answer:
6cm by 1.5cm
18cm by 4.5cm
80cm by 20cm
Step-by-step explanation:
**#5.) Use the diagram below to answer the questions.
Answer:
a) ∠13
b) ∠13
c) ∠2
Step-by-step explanation:
a) ∠ 8 + ∠13 = 180°
Co - interior angles are supplementary, when m // l
b) ∠5 ≅ ∠13
If m // l, the corresponding angles are congruent.
c) ∠5 + ∠2 = 180°
∠5 and ∠2 are co interior angles and they are supplementary if a // b.
11. Aviation The number of active certified commercialpilots has been declining since 1980, as shown inthe table.a. Find a linear equation that can be used as a modelto predict the number of active certified commercialpilots for any year. Assume a steady rate of decline.
a. The line equation is given by:
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y intercep.
In this case y is the number of active pilots and x is the year.
In order to obtain the line equation of the function, you use the information about a pair of years in the given table, in order to calculate the slope of the line. You can select whichever two years with its number of active pilots.
For example, for years 1980 and 1990, you have that the pilots were 182,097 and 149,666 respectively.
To calculate the slope of the line, you use the following formula:
[tex]m=\frac{149,666-182,097}{1990-1980}=-3,243.1[/tex]Then, the slope of the line is negative.
If you consider the zero point of the year axis, as the year 1980, the y intercept of the function will the value of the active pilots in that years, which is 182,097.
Finally, the line equation is:
[tex]y=-3,243.1x+182,097[/tex]b. For the year 2003, you have that x is:
x = 2003 - 1980 =23
You replace this value of x into the linear equation:
[tex]y=-3,243.1(23)+182,097=107506[/tex]The number of active pilots for 2003 is 107,506
boiling an egg physcal or chemcal
Answer:
it's a chemical change.
Step-by-step explanation:
a raw egg is converted into a hard boiled one by chemical changes happening inside it. Its also an irreversible change
30 POINTS!! HELP ASAP!
Answer: Hi this would be the arrow that goes to the left and the dot on the right, so something like ← and dot. Hope this helps, I know this is confusing but try your best.
Step-by-step explanation:
Answer:
After solving the inequality, we get:
[tex]x\leq -10[/tex]
With the plotted inequality given.
Step-by-step explanation:
Step 1: Manipulate and solve the inequality
The inequality is given as:
[tex]\frac{1}{2}x+8\leq 3[/tex]
Make [tex]x[/tex] the subject of the inequality to solve it:
[tex]\frac{1}{2}x+8\leq 3\\\\\text{Subtract 8 from both sides of the equation:}\\\frac{1}{2}x+8-8\leq 3-8\\\\\text{Simplify:}\\\frac{1}{2}x\leq -5\\\\\text{Multiply by 2 on both sides of the inequality:}\\2\times \frac{1}{2}x\leq -5\times 2\\\\\text{Simplify:}\\x\leq-10[/tex]
Step 2: Plot the inequality
After solving the inequality, we get:
[tex]x\leq -10[/tex]
Which means that [tex]x[/tex] consists of all values that are equal to and less than [tex]-10[/tex].
On a number line, when the inequality includes the value, it is denoted by a closed circle.
With all this information, let's plot the number line:
which domain would be the most appropriate set to use for a function that predicts the total weight of pounds
Accurate Whole numbers .
What is accurate whole number?
Accuracy is defined by the number of significant digits while precision is identified by the location of the last significant digit. For instance the number 1234 is more accurate than 0.123 because 1234 had more significant digits.
What does function mean?
Each element of x is given exactly one element of y via a function from a set x to a set y. The sets x and y are collectively referred to as the function's domain and codomain, respectively.
The following details must to be taken into account:
The term "whole number" refers to a number that is free of fractions and decimals.
It calculated the number of household online devices in relation to the number of occupants.
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Find f (0) please help me. I need this turned in by 11:59 tonight
The value of the function f(0) = 1, obtained from the graph.
What is meant by the function?A function is defined as the interaction between a set of inputs that each have one output. A function is a relation between inputs where every input is related to accurately one output. Each function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), in which x is the input. A function's general representation is y = f. (x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input does have exactly one output and the output can be linked directly to its input.For the given question;
The graph for the function is given.
For finding the value of function f(0), simply see the value of y with respect to x = 0.
f(0) = 1, taken from graph.
Thus, the value of function f(0) is found as 1.
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the linear function
The equation of the linear function is: 3x + y = 1.
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y - y₁ = m(x - x₁), where m is the slope and c is the y-intercept.
Given, the line passes through the points (-2, 7) and (2, -5).
Now, using the formula established in the literature, we get:
Slope = m = (y₂ - y₁)/(x₂ - x₁) = (-5 - 7)/(2 - (-2)) = -12/4 = -3
Equation of the linear function: y - 7 = (-3)(x - (-2)) ⇒ y - 7 = (-3)(x + 2)
⇒ y - 7 = -3x - 6 ⇒ 3x + y = 1
Thus, the equation of the linear function is: 3x + y = 1.
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What is the slope of the line?
⇒The line passes through the points (3,0) and (1,-3) I will use them to find the gradient of the line. Note this information is from the graph.
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{-3-0}{1-3} \\m=\frac{3}{-2} \\m=-\frac{3}{2}[/tex]
3) Calculate the area of this trapezium
D
A
11 cm
¹9 cm
19 cm
B
10 cm
C
Answer:
A = 135 cm²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 9 , b₁ = 19 , b₂ = 11 , then
A = [tex]\frac{1}{2}[/tex] × 9 × (19 + 11) = 4.5 × 30 = 135 cm²
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist?
The car will catch up the cyclist 3 hours after it starts moving.
In how many hours the car will catch up the cyclist?The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:
C(t) = 9*4 + 9*t = 36 + 9*t
And the car moves at 21 miles per hour, then the position is:
P(t) = 21*t
The car will catch the cyclist when:
C(t) = P(t), this gives:
36 + 9*t = 21*t
36 = 21*t - 9*t = 12*t
36/12 = t
3 = t
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is m parallel to n. if so what theorem can you use.
You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.
write an equation for the line parallel to y 3x - 8 through the point (-2,-7)
Answer:
y = 3x - 1
Step-by-step explanation:
In order for lines to be parallel, they must have the same slope.
The slope of y = 3x - 8 is 3.
Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:
y − y₁ = m(x − x₁)
y - (-7) = 3(x - (-2))
y + 7 = 3(x + 2)
Distribute 3 and isolate y:
y + 7 = 3x + 6
y = 3x - 1
100x20x10+2=
pls iam doing a test and the calculator is blocked
Answer:
20002
Step-by-step explanation:
100*20=2000
2000*10=20000
20000+2=20002
At an amusement park, a new thrill ride was introduced. It costs $7.50 for 3 rides on the Wild Slider. a) What is the Wild Slider’s unit rate per ride? b) At this rate, what would it cost for 18 rides on Wild Slider? Determine the answer two different ways.
Answer:
The stadium’s seating options will include premium seats (boxes closest to the action), medium-priced seats, and budget-friendly bleachers. Your design calls for 4,500 upper-deck premium seats and 7,500 lower-deck premium seats. The team’s policy is to have a 3:2 ratio of premium seats to bleacher seats. How many bleacher seats will the stadium include?
Answer: 8,000 bleacher seats. 4,500 + 7,500 premium seats = 12,000. 12,000/x = 3/2. x = 8,000.
Triangle HIJ is similar to triangle KLM. Find the measure of side MK. Round your
answer to the nearest tenth if necessary.
MK = 50
to get from 13 to 53
times 1 plus 40
10 times 1 plus 40 =50
Red letters and blue letters are used in a game. Some of the letters are X. All the other letters are Y. X Y X Y The ratio of the number of red letters to the number of blue letters is 2:5 The ratio of the number of red Xs to the number of red Ys is 1: 3 The ratio of the number of blue Xs to the number of blue Ys is 3:1 Work out what fraction of all the letters are Xs.
17/28 of all the letters are X's.
2/3 + 1/4 + 1/2 = x/12 , so what is x?
Answer:
Solve for x by simplifying both sides of the equation, then isolating the variable.
x=17
Step-by-step explanation:
a movie ticket used to cost $4.25 back in 1990. inflation exist because products increase in value over time. the inflation rate is about 3.5% in what year can we expect the price of a movie ticket to exceed $5.50
In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].
What is an equation?
Math can be used to analyze an equation or a set of equations. An equation is a sentence that maintains the equivalence of two expressions. Most of the time, it is easy to solve the arithmetic equations given in an exact manner. While perfect solutions can occasionally be found, it is more typical to find approaches that are just as accurate. It speaks to the particular guidelines for quadratic mathematical equations.A movie ticket cost $4.25 in 1990.
The inflation rate is about 3.5%
Rate increased ,r=100%+3.5%=103.5%=1.035
equation generated is,
y=4.25[(1.035)^x]
Solving the equation for each year, we get the following data:
Tabulating the data
Year cost
1990 4.25
1991 ....
.... ....
1998 5.5964~ 5.6
In the year 1998, the will be greater than $5.50.
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Miranda did a survey of what time people
get to their office on Monday morning.
The table shows her results for
150 people.
+
35/40 Marks
Time
before 7 am
7am to 7:59 am
8am to 8:59 am
9am to 9:59 am
+
No of people
15
39
a) What percentage of the people surveyed arrive at their office before 7am?
Optional working
75
21
Answer:
b) What percentage of the people surveyed arrive at their office after 7:59 am?
Optional working
Answer:
%
a) 10 percent people arrive before 7 am.
b) 64 percent of the people arrive after 7:59 am.
Here, we are given the following data-
Time No. of people
before 7 am 15
7am to 7:59 am 39
8am to 8:59 am 75
9am to 9:59 am 21
a) the number of people who arrive at the office before 7am = 15
The total number of people in the office = 150
Thus, the percentage of people surveyed who arrived before 7 am = (15/150)*100
= (1/10)*100
= 10
Thus, 10% people arrive before 7 am.
b) The number of people who arrive after 7:59 am = 75 + 21
= 96
Thus, the percentage of people surveyed who arrived after 7:59 am =
(96/150)*100
= (0.64)*100
= 64
Thus, 64 percent of the people arrive after 7:59 am.
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Mon. Tues. Wed. Thurs. Fri. 9. 60° 800 650 75° 70° Find the mean temperature in Eagletown for the past 5 days. help me
Which two identify the same sequence
The correct answer is options A and E.
f(x) = 6x + 4
f(1) = 6(1) + 4 = 10
f(2) = 6(2) + 4 = 16
f(3) = 6(3) + 4 = 22
[tex]\begin{gathered} \text{When n=1,} \\ a_1=10 \\ a_{n+1}=a_{1+1}=a_2=a_1+6\text{ = 10+6=16} \\ _{}when\text{ n=2} \\ a_{n+1}=a_{2+1}=a_3=a_2+6=16+6=22 \end{gathered}[/tex]Clearly, options A and E are the same sequences.
s equivalent to 2x + 3?
Answer:
Step-by-step explanation:
2x+3
x=3divides2
Name the marked angle in 2 different ways.
Answer:
Acute angle
OLN angle
Step-by-step explanation:
f (x)=√x + 9. Find ¹(x) and its domain.
The inverse and domain of the function are y = x²-9 and all real numbers.
Inverse of a functionA function's inverse is a function that reverses the action of a function, such as g(x). If and only if g(x) is bijective, then the inverse of g(x) exists, and if it exist.
If the function f(x)=√x + 9, find the inverse;
y = √x+9
x = √y+9
x² = y+9
y = x²-9
The domain of the inverse function will exist on all real numbers.
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A shipping company packs boxes at the rate shown in the graph below.
14. Based on the data shown in the graph, how many boxes can the shipping company pack in an 18-hour period?
*
0/1
110
A unit rate means a rate for one of something.
The number of boxes packed in 18 hours is 216 boxes.
What is a unit rate?A unit rate means a rate for one of something.
We write this as a ratio with a denominator of one.
We have,
From the graph, we see that,
In 5 hours, there are 60 boxes packed.
This can be written as:
5 hours = 60 boxes
Similarly,
1 hour = 12 boxes
3 hours = 36 boxes
The number of boxes packed in 18 hours:
1 hour = 12 boxes
Multiply both sides by 18.
18 hours = 18 x 12 boxes
18 hours = 216 boxes
Thus,
The number of boxes packed in 18 hours is 216 boxes.
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