Slope-intercept form is −8x+9. One of the formulas used to get a line's equation is the slope-intercept formula.
What is Slope-intercept form ?Slope-intercept is a specific form of linear equations. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 3 x + 5 , we see that the slope of the line is − 3 .
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is where the slope, or steepness, of the line is located.
-8x + y = -9
move y to right side
-8x = -9-y
Divide both sides by -8
-8x/-8x = -(9/-8) - (y/-8)
Simplify
-8x/-8x = -(9/-8) - (y/-8)
Simplify -8x/-8x : x
Simplify -(9/-8) - (y/-8) : -9 - y / 8
x = -(-9 - y / 8)
y = mx + b.
y = −8x+9
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Which of the following equations has the solution x = all real numbers?
O5(3-x)+7x = 3x + 15 - x
O 5(3-x)+7x = 3x + 10 x
O 5(3-x)+7x = x + 15 - 3x
5(3x) + 6x = 3x + 15 + 2x
The required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct.
Given that,
To determine the equation that has the solution x = all real numbers.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Equation 1
5(3-x)+7x = 3x + 15 - x
15 - 5x + 7x = 3x +15 - x
2x = 2x
Since it implies the variable x solution as all real numbers,
While all other equation has a distinct unique solution,
Thus, the required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct
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solve (-6)(15)(-2)(-1)
The solution to the expression is -180
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
(-6)(15)(-2)(-1)
Remove the brackets in the expression
So, we have the following product expression
(-6)(15)(-2)(-1) = -6 * 15 * -2 * -1
Evaluate the products using a calculator
This gives
(-6)(15)(-2)(-1) = -180
Hence, the solution is -180
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Make a circle graph for each set of data.
Top-Selling U.S. Kids' Magazines as of 2002
Magazine
Issues Sold
(millions)
Seventeen
YM
Teen
Teen People
Boys' Life
Source: Scholastic Kid's Almanac
a.
Boys'
Life
Teen
People
Seventeen
Teen YM
2.352
2.242
1.729
1.625
1.280
G
Teen
People
Boys'
Life
YM
Seventeen
Teen
A circle graph is attached.
A circle graph, also known as a pie chart, is used to visualize information and data. A circle graph is commonly used to show the results of an investigation in a proportional manner. The arcs of a circle graph are proportional to the percentage of the population who answered a specific question.
Given data
Top-selling US kids magazine as of 2002
Seventeen 2.352
Ym 2.242
Teen 1.729
Teen people 1.625
Boys 1.280
First, we have to add up the dataset
Total = 2.352 + 2.242 + 1.729 + 1.625 + 1.280
= 9.228
The proportion of each magazine is then calculated.
This is calculated by dividing each magazine's frequency by the total frequency.
Mathematically, the formula is represented as:
Proportion = issue sold/ Total magazines sold
So we have
Seventeen= 2.352/9.228
= 25.5%
Seventeen= 2.242/9.228
= 24.3%
Seventeen= 1.729/9.228
= 18.7%
Seventeen= 1.625/9.228
= 17.6%
Seventeen= 1.280/9.228
= 13.9%
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help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
isosceles triangle
Step-by-step explanation:
first by using corresponding angle theorem:
<A=<C
<A=50°
then by using exterior angle theorem:
<A+<C=<B(the outer angle)
50°+<C=<B,<B=180°-80°(angle B lies in a staight line)
<B=100°
50°+<C=100°
<C=50°
IXL Last One ! for this assignment! Thank you guys!
Answer:
If not mistaken the point of X is (37 -5) toward the middle because that is where it could be that I can see.
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
59-2x=64-3x
59+x=64
x=5
Hopes this helps please mark brainliest
Help fast I don't know what to do.
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following lists the range and IQR for this data?
The range is 10, and the IQR is 14.
The range is 10, and the IQR is 13.
The range is 14, and the IQR is 13.
The range is 14, and the IQR is 10.
Answer: range 14 IQR 12
Step-by-step explanation:
took the exam got it right
DeShawn buys a bicycle that costs $129.95. The sales-tax rate in his city is 712% . What is the total cost of the bicycle?
As per the given sales tax, the total cost of the bicycle is $1056.194
Sales tax:
Sales tax is defined as the amount of money, calculated as a percentage, that is added to the cost of a product or service when purchased by a consumer at a retail location.
Given,
DeShawn buys a bicycle that costs $129.95. The sales-tax rate in his city is 712%.
Here we need to find the total cost of the bicycle.
Let us consider the 712% is applied as the tax for $129.95.
So, the amount of tax is calculated as,
=> 712% of 129.95
=> 712/100 x 129.95
=> 7.12 x 129.95
=> 926.244
Therefore, the total amount is obtained by adding the tax amount plus the cost of bicycle,
Then,
=> 129.95 + 926.244
=> 1056.194.
Therefore, the total cost of the bicycle is $1056.194.
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16) If m∠10=77⁰, m∠7=47⁰, and m∠16=139⁰, find the measure of each angle.
a. m∠1 =
b. m∠2 =
c. m∠3 =
d. m∠4 =
e. m∠5 =
f. m∠6 =
g. m∠8 =
h. m∠9 =
i. m∠11 =
j. m∠12 =
k. m∠13 =
l. m∠14 =
m. m∠15 =
n. m∠17 =
o. m∠18 =
Using corresponding and alternating angle theorem. The values of the angles in the figure are m∠1 = 47, m∠2 = 133, m∠3 = 139, m∠4 = 41, m∠5 = 139 degrees respectively.
Corresponding and Alternating AnglesThe corresponding angle postulate states that the corresponding angles are congruent if the transversal intersects two parallel lines. In other words, if a transversal intersects two parallel lines, the corresponding angles will be always equal.
Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
a. m∠1 = m∠7
Reason : Corresponding angles are equal
m∠1 = 47°
b. m∠2 = 180 - m∠1
Reason: Angles on a straight line
m∠2 = 180 - 47
m∠2 = 133°
c. m∠3 = m∠16
Reason : alternating angles are equal
m∠ = 139°
d. m∠4 = 180 - m∠3
Reason : Angles on a straight line
m∠4 = 41°
e. m∠5 = 180 - m∠4
Reason: Angles on a straight line
m∠5 = 139°
n. m∠17 = 180 - m∠6
m∠17 = 41°
f. m∠ 6 = m∠15
m∠15 = m∠17
Reason : Opposite angles are equal
m∠ 6 = m∠ 17
Reason : Alternating angles are equal
m∠ 6 = 41°
g. m∠8 = m∠1
m∠ 8 = 47°
h. m∠ 9 = m∠2
m∠9 = 133°
m. m∠15 = m∠ 17
m ∠ 15 = 41°
o. m∠ 18 = 360 - (m∠15 + m∠16 m∠ 17)
m∠18 = 360 - (41 + 139 + 41)
m∠18 = 139°
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Find the perimeter or circumference and area of each figure if each unit on the graph measures
The circumference of the given circle is 17.8 cm and the area of the given circle is 25.1 [tex]cm^2[/tex]
What is area and circumference of circle?
Circumference of circle is the length of the boundary of the circle
If the radius of the circle is r, then the circumference of the circle is [tex]2\pi r[/tex]
Area of the circle is the total space taken by the circle
If the radius of the circle is r, then the area of the circle is [tex]\pi r^2[/tex]
Center of the circle = (2, 3)
Point on a circle = (4, 1 )
Radius of the circle =
[tex]\sqrt{(4-2)^2 + (1 - 3)^2}\\\sqrt{2^2 + (-2)^2}\\\sqrt{4 + 4}\\\sqrt{8}[/tex]
Circumference of circle = [tex]2 \pi \sqrt{8}[/tex]
= [tex]2 \times 3.14 \times 2 \times \sqrt{2}[/tex]
= [tex]2 \times 3.14 \times 2 \times 1.414[/tex]
= 17.8 cm
Area of circle = [tex]\pi \times \sqrt{8} \times \sqrt{8}\\[/tex]
= [tex]3.14 \times 8[/tex]
= 25.1 [tex]cm^2[/tex]
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Complete Question
The figure has been attached here
Find the perimeter or circumference and area of each figure if each unit on the graph measures 1 cm. Round answers to the nearest tenth, if necessary.
how many hours and mins are in 224 minutes.
Answer:
3 hours and 44 minutes
Which set of ordered pairs represents a function?
\{(-1, -1), (-7, -5), (5, -4), (5, -2)\}{(−1,−1),(−7,−5),(5,−4),(5,−2)}
\{(-9, 9), (-8, 1), (2, -4), (-2, 1)\}{(−9,9),(−8,1),(2,−4),(−2,1)}
\{(-6, 3), (-9, 5), (0, -1), (-9, 6)\}{(−6,3),(−9,5),(0,−1),(−9,6)}
\{(5, 8), (-5, 7), (5, 0), (-7, -9)\}{(5,8),(−5,7),(5,0),(−7,−9)}
The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)
How to determine the ordered pair that is a function?The list of options represents the given parameter
All ordered pairs are relations but not all ordered pair are functions
For an ordered pair to be a function, the following must be true:
The y values on the ordered pair must have different x values
Using the above as a guide,
In (a) the y values -2 and -4 have the same x value of 5In (b), all the y values have different x valuesThis means that the ordered pair in option (b) represents a function
Hence, the ordered pair that is a function is (b)
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a8=12, a16=22 Write a rule for the nth term of the arithmetic sequence.
The formula for the arithmetic sequence that contains a(8) = 12 and a(16) = 22 is a(n) = 13 / 4 + (5 / 4) · (n - 1).
How to derive the formula for the arithmetic series
In this problem we must derive the formula behind the arithmetic series. Arithmetic series are sets of numbers generated by expression of the form:
a(n) = a' + r · (n - 1)
Where:
a' - Value of the first element of the series.r - Difference between two consecutive elements.n - Index of the n-th element.If we know that a(8) = 12 and a(16) = 22, then the formula for the arithmetic formula is:
12 = a' + 7 · r
22 = a' + 15 · r
Now we find a system of two linear equations with two variables, whose solution is found by using numerical methods:
(a', r) = (13 / 4, 5 / 4)
Then, the formula for the arithmetic sequence is a(n) = 13 / 4 + (5 / 4) · (n - 1).
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
The correct option for the given function is (D) g(-13) = 20.
Given that:
The function g has domain -20 ≤ x ≤ 5, range -5 ≤ g(x) ≤ 45, g(0) = -2, g(-9) = 6.
Let's analyze each option to see if it fits the given domain.
A. g(7) = -1
At the beginning of the problem, it is said that the domain is restricted to the range [-20, 5]. The input x = 7 here is outside this domain. That is, it cannot be true for function g without being in the domain. So g(7) is not possible.
B. g(-4) = -11
Similarly, it is said that the domain is restricted to the range [-20, 5]. The input x = -4 here is outside this domain. That is, it cannot be true for function g without being in the domain.
C. g(0) = 2
We know in the question that g(0) = -2. So, this is also the wrong option.
D. g(-13) = 20
Unlike the other options, x= -13 is in the range of -20 to 5. g(-13) = 20 is also in the range of -5 to 45. Option D is true for a function g.
x= -13 is in range and 20 is also in range. So this applies to g.
From the statement given,
g(-13) = 20 is true for the value of g.
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f i deposit $100 each month into an account earning 8% interest compounded monthly, how much will i have in the account in 35 years?
The amount of money in the account in 35 years to the nearest cent is $1629.25.
What is the accrued amount in 35 years?The compound interest formula is expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is rate, and t is time.
Given that;
Principal P = $100Interest rate r = 8% = 8/100 = 0.08Compounded monthly n = 12 Time t = 35 yearsAccrued amount A = ?Plug the given values into the compound interest formula and solve for A.
A = P(1 + r/n)^(n*t)
A = $100( 1 + 0.08/12)^( 12 × 35)
A = $100( 1 + 0.08/12)⁴²⁰
A = $1629.25
Therefore, the accrued amount is $1,629.25.
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Question 3
Melissa wants to check the accuracy of the finance charge on her promissory note.
She has a $2,000, two-year loan at a APR of 6%.
What is her monthly payment?
$
What is the total of her monthly payments?
$
What is the finance charge?
6 pts
$
Her monthly payment is $88.64
The total of her monthly payments is $2,127.39
The finance charge is $127.39
Given, Melissa wants to check the accuracy of the finance charge on her promissory note.
She has a $2,000, two-year loan at a APR of 6%.
As, she has a $2,000 loan for two year at a APR of 6%.
Then, the total amount she has to pay is $2,127.39
(a) So, the monthly payments be
$2,127.39/24 = $88.64
(b) Now, she has to pay monthly payments for 24 months
So, the total of her monthly payments is $2,127.39.
(c) the finance charge she has to pay is,
$2,127.39 - $2,000 = $127.39
Hence, her monthly payment is $88.64
the total of her monthly payments is $2,127.39
the finance charge is $127.39
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please help me (10pts)
Answer:
Table B
Step-by-step explanation:
To determine whether or not something is linear, we find the slope between two different coordinates and see if that slope remains consistent throughout the data. To find the slope between two points, use the equation (y2-y1)/(x2-x1)
Table A --> (-1-5)/(3-2) = -6/1 = -6
Now we have to see if the slope remains consistent in "Table A" by finding the slope using two other coordinates:
(6-3)/(5-4) = 3/1 = 3
We see that the slope is not consistent in Table A, so we repeat the same steps with the other Tables to find one with a consistent slope.
Table B --> (0- -3)/(5-3) = 3/2
(6-3)/(9-7) = 3/2
Table B's data creates a consistent slope, so Table B represents a linear function.
The mean per capita income is 21,053 dollars per annum with a standard deviation of 805 dollars per annum. What is the probability that the sample mean would differ from the true mean by less than 162 dollars if a sample of 71 persons is randomly selected? Round your answer to four decimal places.
Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation 805 , the zscore of a measure X is given by:
Z = (X - μ)/σ
s = σ/√n
In this problem, we have that:
μ = 21053, n = 71, σ = 805
s = 805/√71 = 95.53
Eiher it differs by 162 or less dollars, or it differs by more than 162 dollars. The sum of the probabilities of these events is decimal 1. So
Probability it differs by 160 or less dollars.
pvalue of Z when X = 21053 + 162 = 21215 subtracted by the pvalue of Z when X = 21053 - 162 = 20891.
X = 21215
Z = (X-μ)/σ
Z = (21215-21053)/95.53
Z = 1.69
has a pvalue of 0.091
X = 21568
Z = (X-μ)/σ
Z = (21215-21053)/95.53
Z = 1.69
has a pvalue of 0.041
0.091 - 0.041 = 0.05098
p + 0.50 = 1
p = 0.50
Thus, Probability that the sample mean would differ from the true mean by more than 162 dollars if a sample of 71 persons is randomly selected is 50%
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Find the slope of the line passing through the points ( -8,8) and ( 2,8)
The slope of the line passing through the points ( -8,8) and ( 2,8) is 0.
What is slope?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols y and x stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is given by m = change in y/change in x = y/x. where'm' denotes a line's slope
Here the given points are,
[tex](x_1,y_1)=(-8,8)\\(x_2,y_2)=(2,8)[/tex]
Now using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m= [tex]\frac{8-8}{2+8}[/tex]
=> slope m = 0
Hence slope of the given points is 0.
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5² x 6-85 please solve I am in need
Answer:
65 good sir.
Step-by-step explanation:
Expand and simplify (2x + 3) (x + 7)
Answer:
[tex]2x^{2} +17x+21[/tex]
Step-by-step explanation:
multiply the 2x by x and 7 and then multiply 3 by x and 7. you will get 2[tex]x^{2}[/tex]+14x+3x+21. combine like terms so add 14x to 3x and thats the only like trerms in the equation. so 2x^2+17x+21
Calculate the hypotenuse of a right triangle whose legs measure 20 and 18 cm.
Answer: c≈26.91
Step-by-step explanation: c=a2+b2=202+182≈26.90725
Hello..!
We use the Pythagorean formula:
[tex] \sf \red{c {}^{2} } = \blue{ a {}^{2} + b {}^{2} }[/tex]
We know that once we have the formula we extract the Raised data:
[tex] \sf \red{c {}^{2}} = \blue{(20cm) {}^{2} + (18cm) {}^{2} }[/tex]
Having the Raised data, we will add as a power and we know that:
[tex] \sf \red{20 {}^{2} } = \orange{400}[/tex]
[tex] \sf \red{18 {}^{2}} = \orange{324}[/tex]
So, to solve a power we must multiply squared and then get our result, in this case I added and then increased it by 0
[tex] \sf \red{c {}^{2} }= \blue{400cm {}^{2} + 324cm {}^{2} }[/tex]
We have the results, once that is done we will add.
[tex] \sf \red{400 + 324 }= \blue{724}[/tex]
So, we have the result we just have to put it like this:
[tex] \sf\red{c {}^{2} } = \blue{724cm {}^{2} }[/tex]
Once we have our result, we must take the square root, then the (square "²") automatically disappears.
[tex] \sf \red{c =} \green{ \sqrt{724cm} }[/tex]
[tex] \sf \red{c }= \orange{ 26.90cm}[/tex]
So, our result of our problem is: [tex] \orange{ \sf \longmapsto} \sf \blue{ \: 26.90cm}[/tex]
Use the figure to find the integrals
The integrals in this problem are given as follows:
a) 18 units².
b) 18π units².
c) (18π + 4.5) units².
d) (9π + 9) units².
How to obtain the integrals?To obtain the integrals in this problem, we need to have knowledge of the meaning of the integrals, which is that they represent the area of the function over the interval.
For item a, the area is obtained as follows:
Between 0 and 3 -> square of side length 3 -> Area = 3² = 9.Between 3 and 6 -> right triangle of dimensions 3 and 6 -> Area = 0.5 x 3 x 6 = 9.Hence the integral is of 18 units².
For item b, the figure is a semicircle of radius 6, hence the area is given as follows:
A = 0.5πr² = 18π units².
For item c, the area is composed as follows:
Between 6 and 9: Right triangle of dimensions 3 and 3 -> Area = 0.5 x 3 x 3 = 4.5 units².Between 9 and 21 -> 18π units², found in item B.Hence the area is of:
A = (18π + 4.5) units².
For item d, the area is given as follows:
Between 15 and 21: half the area of the semi-circle -> 9π.Between 21 and 24: Right triangle of dimensions 3 and 6 -> 0.5 x 3 x 6 = 9 units ².Hence the area is of:
A = (9π + 9) units².
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ____ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______ feet.
(Simplify your answer.)
The rocket reaches its maximum height at 2.25 second(s) after launch
The maximum height reached by the object is 88 feet.
Time to reach the maximum heightThe function is given as
h(t) = -16t² + 72t + 7
Differentiate the above function
So, we have the following representation
h'(t) = -32t + 72
Set to 0
-32t + 72 = 0
So, we have
32t = 72
Divide by 32
t = 2.25
Hence, the time is 2.25 seconds
The maximum heightIn (a), we have
t = 2.25
Substitute t = 2.25 in h(t) = -16t² + 72t + 7
h(2.25) = -16(2.25)² + 72(2.25) + 7
Evaluate
h(2.25) = 88
Hence, the maximum height is 88 feet
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Method 4: Suppose if, instead of depositing the $600 all at once, you make an initial deposit of $300 into an account that pays 5% APR at the beginning of the year and then you divide up the remaining $300 into 12 envelopes each with $25. Find the balance after one year for the initial deposit of $300, if you also deposit one $25 envelope each month, all year, into the account that pays 5% APR with monthly compounding
The balance after one year if you deposit one $25 envelope each month, all year is $306.97.
Given,
you make an initial deposit of $300 into an account that pays 5% APR at the beginning of the year and then you divide up the remaining $300 into 12 envelopes each with $25.
we are asked to find the balance after one year for the initial deposit of $300, if you also deposit one $25 envelope each month, all year, into the account that pays 5% APR with monthly compounding = ?
The balance after 1 year can be determined using this formula:
Amount deposited monthly x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5% /12 = 0.417%
n = number of years = 1 x 12 = 12
Annuity factor = 1.004167^12 - 1 / 0.00417 = 12.279082
Balance = 12.279082 x 25 = $306.97
Hence we get the required answer.
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Find the x- and y-intercepts of the graph of x +6y= 10. State each answer as an integer or an improper fraction in simplest form.
The x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.
In the given question we have to find the x- and y-intercepts of the graph of x +6y= 10.
The given equation is x +6y= 10.
To find the x intercept we have to put y=o and to find the y intercept we have to put x=0.
Firstly finding the x intercept by putting y=0 in the equation.
x +6×0= 10
x+0=10
x=10
Now finding the y intercept by putting x=0 in the equation.
0 +6y= 10
6y = 10
Divide by 6 on both side
6/6 y =10/6
y=5/3
Hence, the x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.
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7. The amount of water in a tank decreases at a rate of 7% per day. The amount of water in the tank was originally
3,500 cubic inches. Which function models the amount of water in cubic inches left after d days?
A 0.93(3,500)
B 1.07(3,500)
C 3,500 (0.93)
D 3,500(1.07)
C:
3500(0.93)^d
Exponential functions have the form a·b^x, where:
a is the initial amount
b is the percent remaining after each time period
a = 3500, since that's the original volume.
Since 7% is lost each day, 93% remains, so b=0.93.
The graph shows the amount of savings over time in Eliana's account. Lana, meanwhile, puts $45 each week into her savings account. If they both begin with $0, who is saving at the greater rate?
Answer:
first you didn't tell us how much money eliana saves. you just said about Lana's saving.
what is equivalent to (5+i)+(7-4i)
a. 2-3i
b. 2-5i
c. 12-3i
d. 12-5i
What is the remainder when (3x^4+2x^3-x^2+2x-14) divided by (x+2)
Solving x + 2 < -9 for x is: x > -11.
True
False
Answer:
false
Step-by-step explanation:
x+2<-9
x<-9-2
x<-12