Answer:
The equation of the line with slope = 4 and point (-5, -13)
will be:
\(y=4x+7\)Step-by-step explanation:
Given
slope = m = 4point = (-5, -13)As the point-slope form of the equation of line is
\(y-y_1=m\left(x-x_1\right)\)
where m is the slope.
substituting the values m = 4 and the point (-5, -13)
\(y-y_1=m\left(x-x_1\right)\)
\(y-\left(-13\right)=4\left(x-\left(-5\right)\right)\)
\(y+13=4\left(x+5\right)\)
subtract 13 from both sides
\(y+13-13=4\left(x+5\right)-13\)
\(y=4x+7\)
Therefore, the equation of the line with slope = 4 and point (-5, -13)
will be:
\(y=4x+7\)
Beth went shopping and withdrew an anverage of 25$ from her account every hour for 6 hours. What was the change in her account
Answer:
To solve this question we are going to multiply. So lets say that h represents hours, in this equation we have 6 hours, so 6h Beth spent 25 dollars per hour for 6 hours so we can substitute the h in 6h with 25, which will result in us multiplying,
6h
6(25)
= 150
Step-by-step explanation:
I hope this helps!
Type the correct answer in the box
A new clothing store uses advertising through social media to draw customers and increase the number of transactions each month. The
number of transactions, n), for n months is shown in the table below.
Month, n No. of Transactions, f(n)
1
10
2
20
3
40
4
80
If the number of transactions per month continues to increase in this way, fill in the values for a and rto create the function that
describes this situation.
The function that represent the number of transactions per month is aₙ=10×2ⁿ⁻¹.
Given that,
Month, n Number of Transactions, f(n)
1 10
2 20
3 40
4 80
Here, in the number of transactions 10, 20, 40, 80.
First term =a=10, common ratio = r = 20/10 =2, 40/20 =2 and 80/40 =2.
Use the formula aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.
Now, aₙ=10×2ⁿ⁻¹
Therefore, the function that represent the number of transactions per month is aₙ=10×2ⁿ⁻¹.
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Please help me pretty please I been stuck on this for a while now
Use the fact that for points (a1, b1) and (a2, b2) in the coordinate plane, we can calculate the slope of the line through these points using the following formula. Slope = Δy Δx = b2 − b1 a2 − a1 Find the point where the line through (5, 2) with slope 4 crosses the vertical axis. (x, y) =
The values: y - 2 = 4 * (x - 5) Now, set x = 0 and solve for y: y - 2 = 4 * (0 - 5) y - 2 = -20 y = -18 So, the point where the line crosses the vertical axis is (0, -18).
To find the point where the line through (5, 2) with slope 4 crosses the vertical axis, we first need to use the given formula to find the equation of the line.
Using the point-slope form of a line, we have:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point (5, 2).
Plugging in m = 4 and (x1, y1) = (5, 2), we get:
y - 2 = 4(x - 5)
Simplifying, we get:
y = 4x - 18
To find the point where this line crosses the vertical axis, we set x = 0 and solve for y:
y = 4(0) - 18
y = -18
So the point where the line crosses the vertical axis is (0, -18).
Therefore, the answer is (x, y) = (0, -18).
To summarize, we used the given formula to calculate the equation of the line through (5, 2) with slope 4, and then found the point where this line crosses the vertical axis by setting x = 0 and solving for y.
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Someone help ASAP plssss
Answer:
49
Step-by-step explanation:
you are given the hypotenuse of 60 and a leg of 35
a^2 + b^2 = c^2
35^2 + b^2 = 60^2
1225 +b^2 = 3600
-1225 -1225
2375
B^2 = square root 2375
48.73 round up to 49
please help I don't get it
2. Using proportion, the value of x = 38, the length of FC = 36 in.
3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.
What is the Angle Bisector Theorem?The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.
2. The proportion we would set up to find x is:
(x - 2) / 4 = 27 / 3
Solve for x:
3 * (x - 2) = 4 * 27
3x - 6 = 108
3x = 108 + 6
Simplifying:
3x = 114
x = 114 / 3
x = 38
Length of FC = x - 2 = 38 - 2
FC = 36 in.
3. The proportion we would set up to find x based on the angle bisector theorem is:
13 / 3x = 7 / (2x - 5)
Cross multiply:
13 * (2x - 5) = 7 * 3x
26x - 65 = 21x
26x - 21x - 65 = 0
5x - 65 = 0
5x = 65
x = 65 / 5
x = 13
Length of CD = 3x = 3(13)
CD = 39 cm
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Given b(x) - 1X+4. what is b(-10)?
-10
-6
6
14
Answer:
D. 1×10⁻⁸ M
Explanation:
[H⁺] [OH⁻] = 10⁻¹⁴
(1×10⁻⁶) [OH⁻] = 10⁻¹⁴
[OH⁻] = 1×10⁻⁸
HYRIGH fararefant et fanter i In a class of 25 student,
17 like volleyball, 15 like basketball and 10 like both games.
Illustrate it with a Venn-diagram and find the number of
students who don't like any of the games. (Ans: 3]
Given:
Total students in a class = 25
Students who like volleyball = 17
Students who like basketball = 15
Students who like both = 10
To find:
The students who don't like any of the games.
Solution:
We have,
Total students in a class = 25
Students who like volleyball = 17
Students who like basketball = 15
Students who like both = 10
Now,
Students who like only volleyball = 17-10
= 7
Students who like only basketball = 15-10
= 5
Students who don't like any of the games is the difference of total number of students and number of students who like at least one game.
Students who don't like any of the games = 25 - (7+5+10)
= 25 - 22
= 3
Therefore, 3 students don't like any of the games.
Two positive numbers have a sum of 8 and a product of 13. Algebraically determine the value of the larger of the two numbers to the nearest hundredth
The value of the larger of the two numbers is 5.73.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Two numbers = M and N
M + N = 8 _____(1)
M = 8 - N _____(2)
MN = 13 _____(3)
Putting (2) in (3) we get,
(8 - N)N = 13
8N - N² = 13
N² - 8N + 13 = 0
This is in the form of ax² + bx + c = 0
a = 1, b = -8 and c = 13
Using the determinant we have,
N = -b ± √(b² - 4ac) / 2a
N = 8 ± √(64 - 52) / 2
N = 8 ± √12 / 2
N = 8 ± 2√3 / 2
N = 4 ± √3
N = 4 + √3 and N = 4 - √3
[√3 = 1.73]
N = 5.73
N = 2.27
Now,
When N = 5.73, M = 8 - 5.73 = 2.27
When N = 2.27, M = 8 - 2.27 = 5.73
Now,
The two numbers are 5.73 and 2.27
Thus,
The larger of the two numbers is 5.73.
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To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
It is TRUE that If you want to calculate the total magnification, take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
If you want to get the total magnification of a microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. The objective lens typically has a magnification of 4X, 10X, or 40X, and the eyepiece lens usually has a magnification of 10X. So, for example, if you are using a 10X objective lens and a 10X eyepiece lens, the total magnification would be 10 × 10 = 100X.
On the other hand, these numbers may be the total magnification for a lower powered stereomicroscope. 10X and 40X are achievable with 10X eyepieces and 1X or 4X objective lenses. Or it can be a zoom stereomicroscope with zoom set to 1X and 4X and 10X eyepieces. To get a total of 4X, you can use the 0.8X zoom setting (which is common) plus the 5X eyepiece. Or you can use the 0.5x auxiliary lens, 0.8x zoom and 10x eyepieces.
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Complete Question:
True, or False
To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.
50 POINTS!! Are the sums rational or irrational?
Answer:
rational
irrational
irrational
rational
rational
irrational
Step-by-step explanation:
sqrt(16) + (-21/5) = 4 + (-21/5) = 4+(-4 1/5)= rational both can be written as fractions
pi +24 irrational pi is irrational
sqrt(8) + pi = 2 sqrt(2) + pi irrational because both are irrational
sqrt(4) +5 = 2+5 = 7 rational
sqrt(36) + cuberoot(27) =6+3 = 9 rational
3/4+ sqrt(27) = 3/4 + 3sqrt(3) = irrational sqrt(3) is irrational
Answer:
rational
irrational
irrational
rational
rational
irrational
Step-by-step explanation:
√16 = 4 is rational.
-21/5 is rational it can be expressed as a fraction.
\(\pi\) is irrational.
√4 = 2 is rational.
5 is a rational number.
√36 = 6 is rational.
∛27 = 3 is rational.
3/4 is rational.
√27 is irrational.
do the three lines 2x1−4x2=8, 4x1 6x2=−40, and −2x1−10x2=48 have a common point of intersection? explain.
No, the three lines 2x1 − 4x2 = 8, 4x1 + 6x2 = −40, and −2x1 − 10x2 = 48 do not have a common point of intersection. They form a system of linear equations that is inconsistent.
To determine if the three lines have a common point of intersection, we need to check if there is a solution to the system of linear equations. We can rewrite the system of equations in matrix form as:
| 2 -4 | | x1 | | 8 |
| 4 6 | * | x2 | = | -40 |
|-2 -10 | | x3 | | 48 |
If we attempt to solve this system using Gaussian elimination or any other method, we will find that it leads to an inconsistent system, meaning there is no solution that satisfies all three equations simultaneously.
This can be seen by examining the matrix formed by the coefficients of the variables. The second row is a linear combination of the first row, and the third row is a multiple of the first row. Inconsistent systems occur when the rows of the coefficient matrix are linearly dependent or when one row is a multiple of another.
Therefore, the given system of equations does not have a common point of intersection.
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HELPPPPPPP PLZZZZZZZ
Answer:
lets pray
Step-by-step explanation:
...
Find the volume of a locker that is 50 cm wide, 40 cm long, and 250 cm tall. V=lwh
Answer:
56
Step-by-step explanation:
Answer:
its 56 i think but tell me if its right or no Arigatōgo
Step-by-step explanation:
Jeff saw 7 identical
withdrawals on his bank
statement that came to a total
of $315. By how much did each
withdrawal change Jeff's
account?
Answer:
$45
Step-by-step explanation:
solve 2/x-1=16/x^2+3x-4
The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)
To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:
1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)
2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:
\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)
3. Simplify the equation:
\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)
4. Combine like terms:
-x^3 - x^2 + 14x - 8 = 16x
5. Move all terms to one side of the equation:
\(-x^3 - x^2 - 2x - 8 = 0\)
6. Rearrange the equation in descending order:
-x^3 - x^2 - 2x + 8 = 0
7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.
8. Divide the equation by (x - 2):
\(-(x - 2)(x^2 + x - 4) = 0\)
9. Apply the zero product property:
x - 2 = 0 or x^2 + x - 4 = 0
10. Solve each equation separately:
x = 2
11. Solve the quadratic equation:
For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:
\(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)
Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)
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2x + 5 /3x + 7 = 3/5 find X plz
Answer:
x = -96/55
Step-by-step explanation:
Given that 2x + (5 /3)x + 7 = 3/5
Firstly, we have to multiply through out the expression by the common denominator. We can see that the denominators are 3 and 5, hence the common denominator is 15. Multiplying through by 15 gives:
2x * 15 + (5 /3)x * 15 + 7 * 15 = (3/5) * 15
30x + 25x + 105 = 9
Collect like terms:
30x + 25x = 9 - 105
55x = -96
Dividing through by 55:
x = -96/55
1,(-2/5 +-6/5) .2/9
2, 5: 3/4 - 24/5 :3/4
Answer:
1: 0.3555556
2: 2 > 3/4 Or 2.75
Step-by-step explanation:
Not sure if they are correct my bad if it is
The exercise price on one of Flanagan Company's options is $16, its exercise value is $25, and its time value is $4. What are the option's market value and the price of the stock? Round your answers to the nearest dollar; Opton's market value: $ Price of the stock: 5
The Option's market value is $29, and the price of the stock is $45.
The given exercise price of one of Flanagan Company's options is $16. The exercise value is $25 and the time value is $4.
We have to find the market value of the option and the price of the stock.
The market value of the option can be calculated as follows:
Market value = Exercise value + Time value= $25 + $4= $29
Price of the Stock:
We know that Exercise price = $16.
Let's assume the price of the stock is x.
Therefore, we have the following equation:
Exercise price + Option Price = Stock Price
$16 + $29 = x
Price of the stock = $45
Therefore, the correct answer is:
Option's market value: $29
Price of the stock: $45
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What is the opposite of 8.5?
Answer:
-8.5
Step-by-step explanation:
If I'm not mistaken this is true because the opposite of a whole number (That isn't 0) is always the negative
find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = 11 tan−1(x), a = 1 t3(x) =
To find the Taylor polynomial \(\(t_3(x)\)\) for the function \(\(f(x) = 11 \tan^{-1}(x)\)\) centered at \(\(a = 1\)\) , we can use the Taylor series expansion of the function. The Taylor series expansion for \(\(\tan^{-1}(x)\)\) centered at \(\(a = 1\)\) is:
\(\[\tan^{-1}(x) = \tan^{-1}(a) + \frac{1}{1+a^2}(x-a) - \frac{1}{2(1+a^2)}(x-a)^2 + \frac{1}{3(1+a^2)}(x-a)^3 + \ldots\]\)
Now we substitute \(\(a = 1\)\) and \(\(f(x) = 11 \tan^{-1}(x)\)\) into the series:
\(\(t_3(x) = 11 \tan^{-1}(1) + \frac{1}{2}(x-1) - \frac{1}{4}(x-1)^2 + \frac{1}{6}(x-1)^3\)\)
Simplifying:
\(\(t_3(x) = 11 \cdot \frac{\pi}{4} + \frac{1}{2}(x-1) - \frac{1}{4}(x-1)^2 + \frac{1}{6}(x-1)^3\)\)
Thus, the Taylor polynomial \(\(t_3(x)\) for \(f(x) = 11 \tan^{-1}(x)\)\) centered at
\(\(a = 1\) is \(t_3(x) = 11 \cdot \frac{\pi}{4} + \frac{1}{2}(x-1) - \frac{1}{4}(x-1)^2 + \frac{1}{6}(x-1)^3\).\)
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Maryanne invests $500 into an account that earns 4% annual interest compounded quarterly.
What is her account balance after 5 years if she makes no withdrawals or deposits?
Enter your answer in the box.
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10\)
help me please i have to pass it
Answer:
<
_
Step-by-step explanation:
Just some basic logic.
Apply the properties of operations to find an equivalent expression for 4x + 2y
Answer:
2(2x + y)
Step-by-step explanation:
We can distribute a 2 out and we would get the same expression when we multiply it back out.
Answer:
2(2x + y)
Step-by-step explanation:
It said that after I answered it on Edmentum.
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as.
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as small as that provided by the sample
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
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Apply the Gauian elimination method to olve the following ytem of linear equation. 2x – y 3z = 5
2x 2y 3z = 7
-2x 3y = -3
The solution is (x,y,z) =(1,2,3)
How to apply Gauian elimination method?It takes three row operations to transform an augmented matrix into its row-echelon form. by Gaussian elimination These involve row switch, multiplication of a row by a constant and addition of rows.
[R2 -2R1 -----R2]
1 2 3 14
2 -3 - 3 -15
2 3 1 11
[R3 -2R1 -----R3]
1 2 3 14
0 -3 - 3 -15
0 -1 -5 17
[R3 -(1/3R2 -----R3]
1 2 3 14
0 -3 - 3 -15
0 0 -4 -12
The result above may be expressed as a system of linear equations:
2x+2y+3z=14
-3y-3z=-15
-4z=-12
From the first equation and using y=−2 and z=3:
x+2y+3z=14
x+2(2)+3(3)=14
x+4+9=14
x+13=14
x=1
[substract 13 from both side]
The solution is (x,y,z) =(1,2,3)
The complete question is : Use the Gaussian Elimination Method to solve:
x+2y+3z=14
2x+y+3z=13
2x+3y+z=11
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What do you notice about these two triangles? What's
the same? What's different?
10
Share w
10
15
Answer:
They are the same shape and ratio, but are in different scales/size
Step-by-step explanation:
Please help me,Please I have a class in 2 hours Please help me
To find the perimeter of a shape you add all the side lengths together.
Perimeter of A is 20cm because 7+7+3+3=20
Perimeter of B is 27cm because 9+8+10=27
Perimeter of C is 17cm because 6+6+5=17
Perimeter of D is 34cm because 10+10+4+4+3+3=34
On shape E there is one side length that we do not know. To find that do 8-3=5 because 5+3 would be the opposite side of the 8. Now do 5+8+8+4+12+3=40 cm which is the perimeter of shape E.
I hope this helps you have a good day
8. Alvin purchased $1,300,000 worth of videogame set and made a $150,000 down payment. He agreed to pay the balance by making equal payments at the end of each month for 20 years. What is the size of the monthly payment if the interest charged is 16% compounded quarterly?
We have a purchase of $1,300,000.
The downpayment is $150,000 and the rest is financed.
We can calculate the amount that is owed as:
\(\begin{gathered} C=1,300,000-150,000 \\ C=1,150,000 \end{gathered}\)This amount will be paid in equal amounts, monthly for 20 years.
The interest rate is 16% compounded quarterly.
We have to start by converting the interest rate in a monthly-compounded equivalent rate.
A rate of 16% compounded quarterly (m=3) will be equivalent to a monthly rate r. We can calculate r as:
\(\begin{gathered} (1+r)^{12}=(1+\frac{0.16}{3})^3 \\ (1+r)^4=1+\frac{0.16}{3} \\ (1+r)^4\approx1+0.05333 \\ 1+r\approx1.0533^{\frac{1}{4}} \\ r\approx1.013-1 \\ r\approx0.013 \end{gathered}\)We then can calculate the payments as an annuity with r = 0.013 and 20*12 = 240 payments.
We can calculate the amount he will pay each month as:
\(\begin{gathered} P=\frac{r\cdot PV}{1-(1+r)^{-n}} \\ P=\frac{0.013\cdot1150000}{1-(1+0.013)^{-240}} \\ P=\frac{14950}{1-1.013^{-240}} \\ P=\frac{14950}{1-0.045} \\ P=\frac{14950}{0.955} \\ P=15654.45 \end{gathered}\)Answer: the monthly payment is approximately $15654.45.
The family-size bottle holds 12 fluid ounces (fl oz) of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
3 fl. oz.
Step-by-step explanation:
75% of 12 is the same as multiplying 3 by 4 to get 12. So, you have 3 fl. oz.
Hope it helps!!!!! :))