5 is the difference between the two numbers 12 and 7.
Given,
In the question;
The difference between 3 times a number and 7 is 5.
Write and solve an equation to determine the number.
Now, According to the question:
Let's assume the unknown number to be x,
so three time the number would be 3x.
The difference between 3 times a number (3x) with 7 is 5, so we can write it as:
3x - 7 = 5
Now we can solve this equation to the find x (the unknown number).
3x = 5 + 7
3x = 12
x = 12/3
x = 4
Therefore 3x= 12
So, 5 is the difference between the two numbers 12 and 7.
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Suppose 50% of the registered voters in a country are Republican. If a sample of 629 voters is selected, what is the probability that the sample proportion of Republicans will differ from the population proportion by more than 4%? Round your answer to four decimal places.
The probability that the sample proportion of the Republicans will differ from the population by more than 4% is 95.56%
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of difference a sample, X is from the standard deviation
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
population mean, μ = p = 50% = 0.5
sample size, n = 629
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.50(1 - 0.50)) / 629}
= √{(0.50 * 0.50) / 629}
= 0.0199
Differ by more than 4% is differ by 50% + 4%
X = 50% + 4% = 54% = 0.54
The probability of more than 54% P = P(p > 54%) = P(p > 0.54)
P(p > 0.54) = 1 - P(p < 0.54)
Z score for z < 0.54
z = (X - μ) / σ
= (0.54 - 0.50) / 0.0199
= 2.01
p value for z < 2.01 = 0.0444
P(p > 0.54) = 1 - P(p < 0.54)
= 1 - 0.0444
= 0.9556
= 95.56%
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A painter earns $15 per hour. What is the minimum number of hours he must work to earn at least $200? Write an inequality to represent this situation and solve. Show your work.
Answer:
15h >= 200
>= means greater than or equal to. Just but a horizontal line underneath the >
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
The final solution of the inequality –2(5 – 4x) < 6x – 4 is x < 3.
How to solve inequality?Inequalities are expressions that have the <, >, ≤ and ≥ signs.
Therefore, let's solve the given inequality as follows:
–2(5 – 4x) < 6x – 4
open the brackets on the left side
–2(5 – 4x) < 6x – 4
-10 + 8x < 6x - 4
add 10 to both sides of the inequality
-10 + 8x < 6x - 4
-10 + 10 + 8x < 6x - 4 + 10
8x < 6x + 6
subtract 6x from both sides of the inequality
8x < 6x + 6
8x - 6x < 6x - 6x + 6
2x < 6
divide both sides of the inequality by 2
2x < 6
2x / 2 < 6 / 2
x < 3
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Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.
Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.
How to determine the unknown information?Since the Ms. Morgan found that 30% of her 120 students are athletes, the known and unknown values include the following:
Known value (whole) = 120 students.
Known value (percent) = 30%
Unknown value (part) = ?
Next, we would determine the unknown value as follows:
Number of athletes = 30/100 × 120
Number of athletes = 30 × 1.2
Number of athletes = 36 students.
Unknown value (non-athletes) = 120 students - 36 students
Unknown value (non-athletes) = 84 students.
Since Mr. Gregory found that 27, or 15%, of his student are athletes, the known and unknown values include the following:
Known value (part) = 27 students.
Known value (percent) = 15%
Unknown value (whole) = ?
For the unknown value, we have:
Let the variable T represent the total number of students.
15/100 × T = 27
0.15T = 27
Total number of students, T = 27/0.15
Total number of students, T = 180 students.
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Complete Question:
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.
b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.
Given loga(m) = 10 and loga(n) = 20, find loga(mn2). (Enter an exact number.)
Answer:
log(mn^2) = 50
Step-by-step explanation:
assuming base a for the logs
log(mn^2) = log m + 2log n
2. Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until
she is finished. Write and solve a linear equation to Aind the total number of pages written at 5
months.
Answer:
y = 12x + 35
95 pages
Step-by-step explanation:
Let y represent the total number of pages
Let x represent the total number of months
x = 5 (months)
so..
y = 12(5) + 35
y = 60 + 35
y = 95
Janelys is going to invest in an account paying an interest rate of 5.9% compounded daily. How much would Janelys need to invest, to the nearest ten dollars, for the value of the account to reach $1,890 in 12 years?
The amount that should be invested to the nearest ten dollars is $930.
How much should be invested today?When an amount is compounded daily, it means that the investment increases in value everyday over the investment period.
In order to determine how much should be invested today, the present value of $1890 has to be determined.
The formula for determining the present value is:
PV = FV ÷ (1 + r)^nm
Where:
FV = future value of the investment r = daily interest rate = 5.9% / 365 = 0.01616%n = number of years m = number of compoundingPV = 1890 ÷ (1.00016)^(12 x 365) = 930
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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.
PLEASE HELP!!
F(n)=3n-4
find term 3
The third term of F(n)=3n-4 is 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
F(n)=3n-4
F of n equal to three times of n minus four.
We need to find the third term.
To find third term we need to plug 3 in place of n.
F(3)=3(3)-4
Three times three minus four
F(3)=9-4
Nine minus four gives 5
F(3)=5
Hence, the third term of F(n)=3n-4 is 5.
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The approximate volume in milliliters, m, for a volume of f fluid ounces is equal to
29.57 times the value of f. Which table represents this relationship?
The table that represents this relationship regarding the volume is table D.
How to illustrate the information?From the information, the approximate volume in milliliters, m, for a volume of f fluid ounces is equal to 29.57 times the value of f.
Therefore, when f is 1, the millimeters will be:
= 1 × 29.57
= 29.57
When f is 2, the millimeters will be:
= 2 × 29.57
= 59.14
When f is 3, the millimeters will be:
= 3 ×29.57
= 88.71
When f is 4, the millimeters will be:
= 4 × 29.57
= 118.28
Therefore the correct option is table D.
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Differentiate the function with respect to x.
The differentiation of the given function is 12[tex]x^3[/tex](5[tex]x^2[/tex] +2).
In the given question we have to differentiate the given function with respect to x.
The given function is f(x) = [tex]2x^4(5x^2+3)[/tex]
Before differentiating the function we first simplify the given expression.
To simplify the expression we multiply the 2x^4 to each term under the bracket.
Now the function;
f(x) = [tex]2x^4\cdot5x^2+3\cdot2x^4[/tex]
As we know that if the base is same en power get added.
f(x) = [tex]10x^{4+2}+6x^4[/tex]
f(x) = [tex]10x^{6}+6x^4[/tex]
Now differentiating the function with respect to x.
f'(x) = d/dx([tex]10x^{6}+6x^4[/tex])
f'(x) = 10d/dx([tex]x^6[/tex]) + 6d/dx([tex]x^4[/tex])
As we know that d/dx of x^n =nx^(n-1). So
f'(x) = 10∙6 [tex]x^5[/tex] + 6∙4 [tex]x^3[/tex]
f'(x) = 60[tex]x^5[/tex]+24[tex]x^3[/tex]
Now taking 12x^3 common
f'(x) = 12[tex]x^3[/tex](5[tex]x^2[/tex] +2)
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Solve for value of T
The value of t using straight line angle is 24°.
What is straight line angle ?
A straight angle in geometry is one that has a length of 180 degrees. Because it seems to be a straight line, it is known as a straight angle. In other words, it is an angle whose sides extend in the same straight line in directions opposite to the vertex.
In mathematics, a straight angle is defined as an angle with a degree value of 180. It looks to be a straight line, hence the name "straight." In essence, two rays linked end to end create an angle according to the mathematical concept of angles. As a result, the two rays of the 180-degree angle are subtended in the direction of their endpoints, which are in the opposite direction.
Here we know that sum of angle in straight line at any point is 180° .
Then,
=> (4t-7)°+83°=180°
=> 4t-7+83 = 180
=> 4t+76 = 180
=> 4t = 180-76 = 104
=> t = 104/4 = 26°
Hence the value of t=24°
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No one bothers to help, plsssssssssss!!!!!!!!!!!!!!!!!!!!!!!
slope-related question image pasted below!!!
Answer:
I'm not sure if its right but I got
6/9
Step-by-step explanation:
What I did was:
I took the 2 points:
(-4,4) and (5,-2)
Then did rise over run
Which left me with 6/9
what is the equation of the line in point slope form that contains the point (-2,5) and has a slope of 1/3?
Have an answer I got already, wanting to check and see if its correct :) thank you in advance
An equation of the line in point-slope form that contains the point (-2, 5) and has a slope of 1/3 is y - 5 = 1/3(x + 2).
What is the point-slope form?In Mathematics, the point-slope form can be defined as a type of equation that is typically used when the slope of a straight line and one of the points on this line is given (known).
Mathematically, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Substituting the given parameters into the formula, we have;
y - y₁ = m(x - x₁)
y - 5 = 1/3(x - (-2))
y - 5 = 1/3(x + 2)
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there are 121 boys and 116 girls signed up for a trip to an amusement park the leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students how many groups of 10 students will there be explained and how many groups of nine students will there be explained
By using addition, subtraction, multiplication and division of integers,
it can be calculated that
There are 3 groups of 9 and 21 groups of 10
What is addition, subtraction, multiplication and division of integers?
Addition of integers is used to find the sum total of two or more integers.
Subtraction of integers is used find the difference between two integers.
Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.
Division is the process in which the value of single unit can be calculated from the value of multiple unit
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here, addition, subtraction, multiplication and division of integers will be used
Total number of boys = 121
Total number of girls = 116
Total number of students = 121 + 116 = 237
Now,
The leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students
So the group of 9 is to be made in such a way that on multiplying the number by 9, unit digit of 7 is obtained
So the number is 3 as 9 [tex]\times[/tex] 3 = 27
Remaining number of students = 237 - 21 = 210
They will enter into a group of 10
Number of group of 10 = 210[tex]\div[/tex] 10 = 21
There are 3 groups of 9 and 21 groups of 10
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a body of mass 10.5 kg fell to the ground . calculate the weight of the body.
Answer:
103 N
Step-by-step explanation:
we use the equation: w = mg
where m is mass, W is weight and g is gravitational field strength
w = ?
m= 10.5 kg
g = 9.81 ms‐² (for earth)
so,
w = 10.5 × 9.81
w = 103.005
w ≈ 103 Newtons
Which tool helps you record your transactions?
A.
check leaf
B.
checking account
C.
check register
5. If a marble is randomly chosen from a bag containing exactly 2 red, 2 yellow, 4 green,
3 white, and 1 blue marble, what is the probability that the marble is NOT yellow?
The probability that the marble picked is not yellow is:
10/12
Given:
we have a bag containing exactly 2 red, 2 yellow, 4 green,
3 white, and 1 blue marble.
we are asked to determine the probability that the marble is not yellow = ?
Favorable outcomes for yellow marbles = 2
Total number of outcomes = 12
Probability, P(E) = Number of outcomes favorable to E/Number of all possible outcomes of the experiment.
P(picking an yellow marble) = 2/12
therefore,
P(not picking a yellow marble) = 1 - 2/12
= 12-2/12
= 10/12
Hence the probability that the marble is not yellow is 10/12
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Write and solve a system of equations that represents the scenario below. Be sure to define your variables, and
answer the question.
Ricky Bobby and Betty Sue are super hungry after doing all of these problems, so they ask their uncle Billy Joe Bob to
take them to "Burgers and Dogs" for some tasty mini burgers and mini hot dogs. Ricky Bobby orders 3 mini burgers
and 2 mini dogs for $8. Betty Sue orders 2 mini dogs and 1 mini burger for $6. How much would Uncle Billy Joe Bob spend if he ordered 3 mini dogs and 4 mini burgers?
Can someone help me!
Answer: $11.50
==================================================
Explanation:
x = cost of one burger
y = cost of one hot dog
3 burgers = 3x dollars
2 hot dogs = 2y dollars
3 burgers + 2 hot dogs = 3x+2y = 8 dollars
The first equation to set up is 3x+2y = 8 which is based on the info of what Ricky purchased.
Through similar logic, the other equation is x+2y = 6 based on what Betty ordered.
This is the system of equations
[tex]\begin{cases}3x+2y = 8\\x+2y = 6\end{cases}[/tex]
There are a few approaches we could take. I'll use substitution.
Let's isolate x in the 2nd equation.
x+2y = 6
x = -2y+6
Then plug this into the 1st equation. Solve for x.
3x + 2y = 8
3(-2y+6) + 2y = 8
-6y+18+2y = 8
-4y+18 = 8
-4y = 8-18
-4y = -10
y = -10/(-4)
y = 2.50 dollars is the cost of one hot dog
Then,
x = -2y+6
x = -2*2.50+6
x = -5+6
x = 1 dollar is the cost of one burger
-----------------------
Check:
Ricky: 3x+2y = 3*1+2*2.50 = 3 + 5 = 8 dollars spentBetty: x+2y = 1+2*2.50 = 1+5 = 6 dollars spentThe x and y values are confirmed correct.
------------------------
The last thing to find out is how much is spent if Billy bought 4 burgers and 3 hot dogs
4x+3y = 4*1 + 3*2.50 = 4 + 7.50 = 11.50 dollars is the final answer
This assumes that Billy is paying for himself and the other people pay for themselves as well. If Billy is paying for everyone, then the total comes to 11.50+8+6 = 25.50 dollars.
9.
A.O
B.
1 12
Genevieve's
Function
Gary and Genevieve both plot lines on a coordinate grid. Gary plots the function y=2x-5, and Genevieve plots the function y=-3x + 4. Which of these represents their lines as well as the solution of the system?
The coordinate plane that represents both lines as well as the solution of the system is shown in the diagram below.
What is the Solution of a System of Equations?The solution to a system of equations is the value of x and y that will make the equations of the system true if they are plugged in into either of the two equations in the system.
Thus, when the equations or functions are plotted as a line on a coordinate grid, the system intersect at a point The coordinates of this point is the solution of the system of equations.
The function for Gary, y = 2x - 5, would be a line that has a slope of 2 and cuts the y-axis at -5, while that of Genevieve y = -3x + 4 will have a slope of -3, and will intercepts the y-axis at 4.
The red line in the coordinate grid in the image below is Gary's function y = 2x - 5, while the blue line is that of Genevieve y = -3x + 4. They bot intersect at (1.8, -1.4).
The solution is: (1.8, -1.4).
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Differentiate the function with respect to x.
Using the Quotient Rule, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .
In the given question,
We have to differentiate the given function with respect to x.
The given function is [tex]y=\frac{x^4+1}{3x^4+4}[/tex]
We have differentiate with respect to x.
The given function is in fraction format. So solving the given expression we use Quotient Rule
According to Quotient Rule
"A method for recognizing issues where one function is divided by another is the quotient rule."
The formula of Quotient Rule is
[tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}[/tex]....................(1)
As we see in our function then f(x) = x[tex]^4+[/tex]1 and g(x) = 3x[tex]^4+[/tex]4
Before solving the function we find the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex]
Now solving the f(x) for f'(x) with respect to x.
f(x) = x[tex]^4+[/tex]1
[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(x^4+1)[/tex]
[tex]f'(x)=\frac{d}{dx}x^4+\frac{d}{dx}1[/tex]
We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.
So [tex]f'(x)=4x^{(4-1)}+0[/tex]
[tex]f'(x)=4x^3[/tex]
Now solving the g(x) for g'(x) with respect to x.
g(x) = 3x[tex]^4+[/tex]4
[tex]\frac{d}{dx}g(x)=\frac{d}{dx}(3x^4+4)[/tex]
[tex]g'(x)=3\frac{d}{dx}x^4+\frac{d}{dx}4[/tex]
We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.
[tex]g'(x)=3(4x^{(4-1)})+0[/tex]
[tex]g'(x)=3(4x^{3})[/tex]
[tex]g'(x)=12x^{3}[/tex]
Now finding the value of (g(x))[tex]^2.[/tex]
g(x) = 3x[tex]^4+[/tex]4
[tex](g(x))^4=(3x^4+4)^2[/tex]
Now using the formula of [tex](a+b)^2=a^2+2ab+b^2[/tex].
Now solving
[tex](g(x))^4=(3x^4)^2+2\times(3x^4)\times4+(4)^2[/tex]
Simplifying
[tex](g(x))^4=9x^8+24x^4+16[/tex]
Now putting the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex] in the equation (1)
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4+4)(4x^3)-(12x^3)(x^4+1)}{9x^8+24x^4+16}[/tex]
Simplifying
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4(4x^3)+4(4x^3))-((12x^3)x^4+1(12x^3))}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{(4+3)}+16x^3)-(12x^{(3+4)}+12x^3)}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{7}+16x^3)-(12x^{7}+12x^3)}{9x^8+24x^4+16}[/tex]
Now solving the bracket
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{12x^{7}+16x^3-12x^{7}-12x^3}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{16x^3-12x^3}{9x^8+24x^4+16}[/tex]
[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{4x^3}{9x^8+24x^4+16}[/tex]
Hence, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .
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William plans on buying the new Callaway Rogue Max ST driver for at least $550 He already has $325 saved and earns $20 each time he details his parents car. Write and solve an inequality to determine the number of times he must detail his parents car to have enough money to buy the golf club.
William needs to detail his parents at least 12 times to buy the golf club.
What is Inequality:An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
The symbols we use in Inequality Expressions are
Not equal ' ≠ '
Greater than ' > '
Less than ' < '
Less than or equal ' ≤ '
Greater than or equal ' ≥'
Here we have
William plans to buy the new Callaway Rogue for at least $ 550
The amount that William saved = $ 325
The amount he earns each time he details his parents = $ 20
Here we don't know how many times he detailed his parents,
So represent it with a variable x
After detailing x times the amount he earned will equal $ 20x
The total amount that William will have = $ 325 + $ 20x
William wants at least $550
Therefore,
The inequality that will represent the above situation is
=> 325 + 20x ≥ 550 ------(1)
Now solve the above inequality to get the value of x
=> 65 + 4x ≥ 110
=> 4x ≥ 45
=> x ≥ 11.25
Here we can say 11.25 times so x = 12 times
Therefore,
William needs to detail his parents at least 12 times to buy the golf club.
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Estimate the value of 96.8×9.74
Answer: Estimate : 1000 Exact : 942.83
Step-by-step explanation:
The estimate is 1000 because 96.8 is rounded to 100 and 9.74 is rounded to 10, so 100 times 10 is 1000. If you wanted the exact, then the exact is 942.83200, If you simplify this total, then the final answer is 942.83.
In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 5)3 + 9. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.
The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.
How to find the turning point?
Here we have the temperature function:
T(x) = (x - 5)^3 + 9
The turning point is the point where the curvature of the function changes, by differentiating the function two times and finding the zero, we can get the turning points.
T'(x) = 3*(x - 5)^2
T''(x) = 3*2*(x - 5) = 6*(x - 5)
This is zero when x = 5, then:
T''(5) = 6*(5 - 5) = 0
So the turning point is there.
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5y=15x+10 but in standard form?
Answer:
y=3x+2
Step-by-step explanation:
Divide by 5 on all sides.
3x-y=-2
Step-by-step explanation:
What is the vertex of this problem?
The vertex of the parabola is (-1,-1)
What is vertex of parabola?
The vertex of a parabola is the highest point or the lowest point, also known as the maximum or minimum of the parabola. The vertex is the point of intersection of the parabola and its line of symmetry.
The vertex is the maximum or minimum point of a parabola.
The vertex is the point where the parabola changes direction.
Here, the point where the parabola changes it direction is (-1,-1).
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Given f(x)=3x^2+kx+4 and the remainder when f(x) is divided by x-4 is 68 then What is the value of k?
Answer:
k = 4-----------------------------
GivenFunction f(x) = 3x² + kx + 4,Remainder of f(x) / (x - 4) is 68.According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.
f(x) = 3x² + kx + 4 - 68 = 3x² + kx - 64 = 0When x = 43*4² + k*4 - 64 = 048 + 4k - 64 = 04k - 16 = 04k = 16k = 4To write a linear equation in point-slope form for a given graph:
First, find the
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of the line using riserun or the
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.
Next, substitute the
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and the
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into the point-slope formula.
Finally, remember to
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if possible.
The linear equation in point slope form for the graph given below is y = (4/3)x - 1/3 .
In the question ,
a graph with the line is given
also given that the line passes through the points (1 , 1) and (4 , 5) .
in order to find the linear equation , we first need to find the slope .
slope = (5 - 1)/(4 - 1)
slope = 4/3
So , the linear equation of the line passing through the point (4 , 5) with slope 4/3 , in point slope form is
(y - 5) = (4/3)×(x - 4)
y - 5 = (4/3)x - 16/3
y = (4/3)x - 16/3 + 5
y = (4/3)x -80/15 + 75/15
y = (4/3)x -5/15
y = (4/3)x - 1/3
Therefore , The linear equation in point slope form is y = (4/3)x - 1/3 .
The given question is incomplete , the complete question is
Write a linear equation in point - slope form for the graph given below ?
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How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
Answer: 2.5>9.5
Step-by-step explanation: maybe we should both pay attention to math
The quadratic equation used to model the situation is h(t) = -16t2 + 150t + 4. Graph this equation using the graphing tool. Adjust the axis labels to accurately reflect the variables, and adjust the window to display the entire graph in the first quadrant.
The graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.
The given quadratic equation is h(t) = -16t² + 150t + 4.
What is quadratic equation of graph?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
The graph of a quadratic equation is as follows:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: (75/16,5689/16)
Focus: (75/16,22755/64)
Axis of Symmetry: x=75/16
Directrix: y=22757/64
Plot the points (4, 348), (75/16, 5689/16), (6, 328) on graph
Therefore, the graph of the coordinate points (4, 348), (75/16, 5689/16), (6, 328) is given below.
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