Given the equation:
\(y=-\frac{1}{2}(x+5)+1\)To be able to graph the line, the first step is to determine the coordinates of two points.
To determine the coordinates of the points, you have to choose two values of x, replace them in the formula and calculate the corresponding value of y.
For example, you can use the values x=1 and x=3
For x=1
\(\begin{gathered} y=-\frac{1}{2}(x-5)+1 \\ y=-\frac{1}{2}(1-5)+1 \\ y=(-\frac{1}{2})\cdot(-4)+1 \\ y=2+1 \\ y=3 \end{gathered}\)The first ordered pair is (1,3)
For x=3
\(\begin{gathered} y=-\frac{1}{2}(x-5)+1 \\ y=-\frac{1}{2}(3-5)+1 \\ y=(-\frac{1}{2})(-2)+1 \\ y=1+1 \\ y=2 \end{gathered}\)The second ordered pair is (3,2)
Once you have determined the coordinates of both points, you have to plot them on the coordinate system:
Link both points with a line to graph it.
Factor.
8xy - 54x^2 how to solve this
i need help with the answer i also need to explain this question
Answer: B: 20
Step-by-step explanation: We can take 40% as a fraction to make it 4/10, simplifying gives 2/5. 2/5 of 50 is 20!
Hope this Helps!
A store buys 15 sweaters for $165 and sells them for $405. If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, write a proportional equation for p in terms of s that matches the context.
A proportional equation for p in terms of s that matches the context is p = 16s.
How to write a proportional equation?Mathematically, a proportional equation can be represented by the following equation:
y = kx
For this exercise, we would have:
Let the total profit be represented by p.Let the number of sweaters be represented by s.Next, we would determine the cost price and sales price per sweater as follows:
Cost price = $165/15
Cost price = $11.
Sales price = $405/15
Sales price = $27
Therefore, an equation for the total profit is given by:
Total profit, p = Cost price - Sales price
Total profit, p = 27s - 11s
Total profit, p = 16s
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Please find missing side length!
Answer:
The missing side length is 24.98 units
Step-by-step explanation:
Given
The attached right-triangle
Required
The length of the missing length
Let the missing length be x.
Apply Pythagoras theorem
\(Hyp^2 = Opp^2 + Adj^2\)
This gives
\(43^2 = 35^2 + x^2\)
\(1849 = 1225 + x^2\)
Collect like terms
\(x^2 = 1849 - 1225\)
\(x^2 = 624\)
Take square roots of both sides
\(x = \sqrt{624\)
\(x = 24.98\) --- approximated
how do i solve 1-(1+.04/12)^-12x10
To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.
Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).
Step 3: Add 1 to 0.0033333 to get 1.0033333.
Step 4: Raise 1.0033333 to the power of -120.
Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.
Step 6: Subtract the value obtained in Step 5 from 1.
1 - 0.742657 = 0.257343 (approximately).
Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.
It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.
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Which statements apply to the expression 3/5 ? Check all that apply
Answer:
See below.
Step-by-step explanation:
I assume the fraction 3/5 is raised to the 3rd power.
I assume this is the given expression.
\( (\dfrac{3}{5})^3 \)
The base is 3/5 True
The base is 3 False
The exponent is 3 True
The expanded form is \( \dfrac{3}{5} \times \dfrac{3}{5} \times \dfrac{3}{5} \) True
The expanded form is \( \dfrac{3 \times 3 \times 3}{5} \) False
\( (\dfrac{3}{5})^3 = \dfrac{9}{15} \) False
\( (\dfrac{3}{5})^3 = \dfrac{27}{125} \) True
21x - 56 = -2 what is x?
Answer:
About 2.57
Step-by-step explanation:
\(21x-56=-2 \\\\21x=54 \\\\x\approx 2.57\)
Hope this helps!
Answer:
I got 2.5
Step-by-step explanation
1) add 56 to both sides to get 21x = 54
2) divide both sides by 21
3) you should get 2.5
HELP URGENT! LIMITED TIME TEST!!!
An ice cream truck tracks its sales for a year. They create a scatter plot using the data with the average monthly temperature temperature on the x-
axis and the sales along the y- axis.
The data in the graph (the photo added) suggest a linear association. Which of the functions best represents the equation of the line of best fit?
[Pay attention to the scale of the x and y axis]
Choose one,
y= 0.01x + 152
y= 0.5x + 100
y= x + 100
y = 30x - 159
A linear relationship between two quantities can be modeled using a mathematical function.
What is function?Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.
The form of the function is generally expressed as y = mx + b, where y is the dependent variable, m is the slope of the line, x is the independent variable, and b is the y-intercept. The slope of the line, m, can be calculated from two points on the line using the formula m = (y2-y1)/(x2-x1). The y-intercept, b, can be calculated by substituting any point into the equation y = mx + b and solving for b.
Once the slope and y-intercept are known, the equation can be used to predict the value of the dependent variable given a certain value of the independent variable. For example, if the equation is y = 3x + 4, then for any given value of x, the corresponding value of y can be calculated. For x = 5, the corresponding value of y is 19 (5 x 3 + 4 = 19). This equation can also be used to graph the linear relationship between the two variables; by plotting the equation, a straight line is produced.
By using a function to model a linear relationship between two quantities, it is possible to calculate the relationship between them and predict values for either one given the other. This can be a useful tool for understanding the data and for making predictions about the data.
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Consider the following equation:
cos x = x^3
Use your calculator to find an interval of length 0.01 that contains a root. (Enter your answer using interval notation.)
If the equation is cos x = x^3, the interval of length 0.01 that contains a root is [0.86, 0.87]
The given equation is
cos x = x^3
Move the term x^3 to the left hand side of the equation
cos x - x^3 = 0
Therefore the equation will be
f(x) = cos x - x^3
Here to find the interval of length 0.01 that contains a root, we have to use the intermediate value theorem
Plot the function in the graph
From the graph, we can see that the value of
x = 0.865
The interval of length = 0.01
Then the intervals will be 0.86 and 0.87
Therefore, the interval of length 0.01 that contains a root will be [0.86, 0.87]
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A delivery up to 1 mile costs $10. For any distance over 1 mile, there is an additional charge at the rate of $5 per mile, with a limit of 5 miles. Which graph represents this scenario?
Answer:
its c
Step-by-step explanation:
Answer:
Its the 3rd chart
Step-by-step explanation:
Just got it correct on edge 2020
please help simplify !
Answer:
B
Step-by-step explanation:
using the rule of exponents
\(a^{m}\) ÷ \(a^{n}\) = \(a^{(m-n)}\) , then
\(6^{9}\) ÷ 6³ = \(6^{(9-3)}\) = \(6^{6}\)
Select the correct answer.
What is this expression in simplest form?
1/2x^2-4x - 2/x
A. 4x-7/2x(x-2)
B. -4x+9/2x(x-2)
C. -1/2x(x-2)
D. -3x-8/2x(x-2)
Answer:a A. 4x-7/2x(x-2)
got it right on the test
Step-by-step explanation:
In ΔWXY, w = 320 inches, y = 740 inches and ∠Y=169°. Find all possible values of ∠W, to the nearest 10th of a degree.
After simplification, how many terms will be there in 4x3 + 9y2 - 3x + 2 - 1?
3
6
5
4.
Answer:
Correct answer is 4 because the last 2 terms can be combined:
Step-by-step explanation:
4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.
Find the number of 4-digit numbers that contain exactly two even and two odd digits.
Answer:
There are six possible forms of 4-digit numbers consisting of two odd digits and two even digits:
OOEE
OEOE
OEEO
EEOO
EOEO
EOOE
Each of the three forms starting with (O)dd digits can form 5^4 = 625 numbers, since there are 5 odd and 5 even digits.
Each of the three forms starting with (E)ven digits can form 4*5^3 = 500 numbers, since the first digit cannot be zero.
Therefore, the total numbers possible is 3*(625+500)
= 3,375
Step-by-step explanation:
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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Select the correct answer.
Evaluate the following expression when x = -4 and y = 4.
x
6
−
x
4
y
A.
1
,
025
4
B.
1
,
023
4
C.
16
,
385
4
D.
−
1
,
023
4
Answer:
1023/4
Step-by-step explanation:
shown in the picture
Is this right? Pls help
Answer:
A
Step-by-step explanation:
DE is the shortest side because it's is opposite to the smallest angle (<F)
180 - 60 = 3X +2X + 5,
X = 23
<F = 2*(23) +5 = 51
Help me
I will mark is the most brilliant answer
Answer:
Number one is D/12.5
Step-by-step explanation:
correct me if im wrong plz
Simplify the following fractions.
Please Slove this 2 question
Answer:
b)14/3 or 4 2/3 C) 256/15 or 14 1/15
Step-by-step explanation:
In the second fraction, the "of" means to multiply
Answer:
#b
\( \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}\)
\(\frak{SOLUTION:}\)
\(\displaystyle \frak{Here,}\)
\(\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }\)
Convert mixed fractions into improper fractions:\( = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }\)
\(=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }\)
\(\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }\)
\(\displaystyle{ = \frac{8 \times 7}{12} }\)
\( =\displaystyle{} \frac{56}{12} \)
\(\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }\)
\(\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } \)
#c
\(\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}\)
\(\displaystyle{ \frak{SOLUTION:}}\)
\(\displaystyle \frak{Here,}\)
\( \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }\)
\(\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}\)
\( = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }\)
\(\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }\)
\(\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }\)
\(\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }\)
\( = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }\)
Answered by :
\(\frak{\pink{seolleaphrodite}}\)
what is the missing number if the mean of 48,33 is 41
Answer:
42
Step-by-step explanation:
let's make the missing number x
\(mean = \frac{sum \: of \: numbers}{how \: many \: numbers \: there \: are} \)
\(41 = \frac{48 + 33 + x}{3} \)
multiply 3 on both sides to get rid of the fraction, 41 × 3 = 123
\(123 = 48 + 33 + x\)
simplify the right side, 48 + 33 = 81
\(123 = 81 + x\)
subtract 81 on both sides
\(123 - 81 = x\)
\(x = 42\)
Anyone know how to do this?
Answer:
They cannot form a triangle.
Step-by-step explanation:
A triangle can only be formed if the sum of the lengths of any 2 sides are greater than the 3rd side. 2 + 7 is less than 15, so this cannot be a triangle.
Plz help me this is 7th grade math
Answer:
D=52
E=77
F=61
Step-by-step explanation:
What is the equation of the line that passes through the points (-4,-6) and (-8,4) need help ASAP
Answer: When x = 6 (point A), y = 1/2*6 -8 = 3 -8 = -5✔
When x = 8 (point B), y = 1/2*8 - 8 = 4 - 8 = -4 ✔
Answer:
y=-5/2x-16
Step-by-step explanation:
If it is Slope-Intercept Form
A 2-yard piece of brass wire costs $21.96. What is the price per foot?
Answer:
$3.66.
Step-by-step explanation:
1 yard is equal to 3 feet. So, a 2-yard piece of brass wire is equivalent to 6 feet of brass wire. To find the price per foot, we need to divide the total cost by the total length. So, the price per foot is
Caroline went to the cafeteria. She bought
two pieces of pizza for $1.50 each, some fries for $3.25, and a drink for
$2.50. How much money did she spend total?
A. $7.25
B.$8.75
C. $8.77
Answer:
hehebbshdbwbsbdhebnjhabshshahsbbdhsu
I will give brainlist need answer thx
Answer:
1288
Step-by-step explanation:
S = n/2(2a+(n-1)d)
S = 23/2(2(23)+(23-1)3)
S = 1288
How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixed nuts that cost $10.25 per pound.
9514 1404 393
Answer:
5 pounds
Step-by-step explanation:
The target price is the average of the other two prices, so equal quantities of each kind of nut will go into the mix. (14+6.50)/2 = 20.50/2 = 10.25
5 pounds of cashews
_____
Let c represent the number of pounds of cashews. Then the cost of the mix will be ...
14c + 5(6.50) = 10.25(c +5)
14c +32.50 = 10.25c +51.25
3.75c = 18.75 . . . . . . . subtract (10.25c +32.50)
c = 5 . . . . . . . . . . . . . divide by 3.75
5 pounds of cashews must be mixed with the peanuts.
Marta simplified this expression.
4 logs x+logs 2x log, 3x
In which step did she incorrectly apply a property of logarithms?
Answer:
step 1
Step-by-step explanation:
You want to know which step in Marta's simplification of 4·log₅(x) +log₅(2x) -log₅(3x) contains an error in application of properties of logarithms.
Properties of logslog(a^b) = b·log(a)
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
Simplification\(4\log_5(x)+\log_5(2x)-\log_5(3x)\\\\=\log_5(x^4)+\log_5(2x)-\log_5(3x)\qquad\text{Step 1. Mistake: $4x$ instead of $x^4$}\\\\\log_5(x^4\cdot2x)-\log_5(3x)=\log_5\left(\dfrac{2x^5}{3x}\right)\\\\=\boxed{\log_5\left(\dfrac{2x^4}{3}\right)}\)
Amadi is three times as old as Chima. The sum of their ages is 24
Answer:
Amadi: 20 years old
Chima : 4 years old