Question:
The park district is paying to enlarge the area of a square-shaped dock at a local lake. The area of the dock will increase by 16 square feet. Complete the equation below that can be used to find the area, x, of the original dock if the side length of the new dock is 20 feet.
So, the square root of what (?) equals(=) 20
Answer:
The complete equation is square root of(x + 16) = 20
Solution:
Given that Dock has a shape of square
[tex]\text{ area of square }= (side)^2[/tex]
From question, it is given that side length of new dock is 20 feet
Therefore, area of new dock is given as:
[tex]\text{ area of new dock}= (20)^2[/tex]
Taking square root on both sides,
square root of (new area ) = 20 --- eqn 1
Let "x" be the area of original dock
The area of the dock will increase by 16 square feet
New area = original area + 16
New area = x + 16 ---- eqn 2
From eqn 1,
square root of (new area ) = 20
From eqn 2
square root of(x + 16) = 20
Thus the complete equation is: square root of(x + 16) = 20
Final answer:
To find the area of the original dock, the equation x + 16 = 20^2 can be used, where x is the original area. By solving the equation, we find that x equals 384 square feet.
Explanation:
The area of the original square-shaped dock can be found using the equation for the area of a square, with the area being equal to the side length squared. Given that the new square dock has a side length of 20 feet, and the area is increased by 16 square feet, we can set up an equation to find the original area, x.
The equation is x + 16 = 20^2, where 20^2 is the area of the new, larger dock, and x is the original area of the dock before the enlargement. Therefore, the side length of the original dock is the square root of x. To find x, we can solve the equation:
x + 16 = 400
x = 400 - 16
x = 384
So the area of the original dock is 384 square feet.
$13,957 is invested, part at 7% and the rest at 6%. If the interest earned from the amount invested at 7% exceeds the interest earned from the amount invested at 6% by $833.73, how much is invested at each rate?
Answer:
The Amount invested at 7% interest is $12,855
The Amount invested at 6% interest = $1,102
Step-by-step explanation:
Given as :
The Total money invested = $13,957
Let The money invested at 7% = [tex]p_1[/tex] = $A
And The money invested at 6% = [tex]p_2[/tex] = $13957 - $A
Let The interest earn at 7% = [tex]I_1[/tex]
And The interest earn at 6% = [tex]I_2[/tex]
[tex]I_1[/tex] - [tex]I_2[/tex] = $833.73
Let The time period = 1 year
Now, From Simple Interest method
Simple Interest = [tex]\dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}[/tex]
Or, [tex]I_1[/tex] = [tex]\dfrac{\textrm p_1\times \textrm 7\times \textrm 1}{100}[/tex]
Or, [tex]I_1[/tex] = [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex]
And
[tex]I_2[/tex] = [tex]\dfrac{\textrm p_2\times \textrm 6\times \textrm 1}{100}[/tex]
Or, [tex]I_2[/tex] = [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex]
∵ [tex]I_1[/tex] - [tex]I_2[/tex] = $833.73
So, [tex]\dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}[/tex] - [tex]\dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}[/tex] = $833.73
Or, 7 A - 6 (13,957 - A) = $833.73 × 100
Or, 7 A - $83,742 + 6 A = $83373
Or, 13 A = $83373 + $83742
Or, 13 A = $167,115
∴ A = [tex]\dfrac{167115}{13}[/tex]
i.e A = $12,855
So, The Amount invested at 7% interest = A = $12,855
And The Amount invested at 6% interest = ($13,957 - A) = $13,957 - $12,855
I.e The Amount invested at 6% interest = $1,102
Hence,The Amount invested at 7% interest is $12,855
And The Amount invested at 6% interest = $1,102 . Answer
Final answer:
The total amount invested and the difference in interest earned. Then, using algebraic techniques such as substitution or elimination, we solve for the amounts invested at 7% and at 6%.
Explanation:
To solve the problem of allocating investments at different interest rates, we can set up a system of equations. Let's designate x as the amount invested at 7% and y as the amount invested at 6%. Given the total investment is $13,957, our first equation will be:
x + y = 13,957 (1)
The interest from the amount invested at 7% exceeds the interest from the amount invested at 6% by $833.73. The second equation, reflecting the interest earned, will be:
0.07x - 0.06y = 833.73 (2)
y = 13,957 - x (3)
Now, substitute equation (3) into equation (2) and solve for x:
0.07x - 0.06(13,957 - x) = 833.73
Simplify and solve this equation to find the value of x.
Once we have the value for x, we can use equation (3) to find the corresponding value for y, giving us the amount invested at each interest rate.
Write 48.4% as a decimal and as a simplified fraction
Answer:
121/250
Step-by-step explanation:
Look at the picture
The decimal equivalent of 48.4% is 0.484 and the simplified fraction equivalent is 242/500.
Explanation:To convert 48.4% to a decimal, you simply divide the percentage by 100. Therefore, 48.4% as a decimal would be 0.484.
To write 48.4% as a simplified fraction, we start with the fraction that percentage represents, which is 48.4 / 100. However, both these numbers are divisible by 2 which simplifies it to 242 / 500. That is the simplest form of the fraction represented by 48.4%.
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WORTH 100 SEE PICTURE WHEN YOU CLICK TO ANSWER HERE ARE THE QUESTIONS IF NOT VISIBLE FROM PIC
(answer questions 1-4 with the chart provided)
Answer:
Step-by-step explanation:
Let x represent the number of days , then
(1) The exponential function to represent the spread of Ben's social media spread implies :
f(x) = 2([tex]3^{x}[/tex])
(2) The exponential function that represent carter;s social media spread implies
f(x) = 10([tex]2^{3}[/tex]
(3) the graph of the three functions is attached below
color red graph represents Ben's social media spread , the graph with color blue represents Carter;s social media spread and the graph with green color represents Amber's social media spread
(4) on the 3rd day
Amber will receive 192 shares .
The equation for the spread of his shares is
f(x) = 3([tex]4^{x}[/tex]
where x is the number of days , so we have
3([tex]4^{3}[/tex])
= 3 ( 64)
= 192 shares
Ben's shares on the 3rd day will be
f(x) = 2([tex]3^{x}[/tex] )
= 2([tex]3^{3}[/tex])
= 2 ( 27)
= 54
Therefore , Ben will have 54 shares on the third day
Carter's share on the third day
f(x) = 10 ( [tex]2^{x}[/tex] )
= 10 ([tex]2^{3}[/tex] )
= 10 (8)
= 80
Therefore , Carter will receive 80 shares on the 3rd day
the units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than the original number. What is the original number?
Answer:
36
Step-by-step explanation:
Here is the correct and complete question: The units digit of a two-digit number is twice the tens digit. If the digits are reversed, the new number is 9 less than twice the original number. What is the original number?
Lets assume the original number be"10y+x". (x is unit digit and y is 10th digit)
∴ if number is reversed then resulting number be "10x+y".
As given: x= 2y
and [tex]10x+y= 2(10y+x)-9[/tex]
Now, solving the equation to get original number.
[tex]10x+y= 2(10y+x)-9[/tex]
Distributing 2 to 10y and x, then opening the parenthesis.
⇒ [tex]10x+y= 20y+2x-9[/tex]
subtracting by (2x+y) on both side.
⇒ [tex]8x= 19y-9[/tex]
subtituting the value of "x", which is equal to 2y.
∴ [tex]8\times 2y= 19y-9[/tex]
⇒ [tex]16y=19y-9[/tex]
subtracting both side by (16y-9)
⇒ [tex]3y= 9[/tex]
cross multiplying
We get, [tex]y= 3[/tex]
y=3
∵x= 2y
[tex]x=2\times 3= 6[/tex]
∴ x= 6
Therefore, the original number will be 36 as x is the unit number and y as tenth number.
If r=-4x - 17 find r(5)
Answer:
-37
Step-by-step explanation:
-4(5)-17=-20-17=-37
Answer: r = 3
1st Step: Plug x in for 5
4(5)-17
Second Step: Multiply 4 and 5
20-17
Third Step: 20-17
20-17=3
So, the answer is 3 when r(5)
Hope this helps!
[tex]2 + \frac{5}{6} \sqrt{6} = 2 + \sqrt{6}y [/tex]
Answer:
Therefore,
[tex]y=\dfrac{5}{6}[/tex]
Step-by-step explanation:
Given:
[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]
To Find:
x = ?
Solution:
[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]
Subtract 2 from both the side.
[tex]2-2+\dfrac{5}{6}\sqrt{6}=2-2+\sqrt{6}y[/tex]
Then we have
[tex]\dfrac{5}{6}\sqrt{6}=\sqrt{6}y[/tex]
Divide [tex]\sqrt{6} [/tex]on both the side
[tex]\dfrac{5}{6}\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6}}=y[/tex]
Then we have
[tex]\dfrac{5}{6}=y[/tex]
Therefore,
[tex]y=\dfrac{5}{6}[/tex]
the sum of three numbers is 50 the second number is three times the first number and the third number is twice the second number what are the numbers
Answer:1st is 5 2nd is 15 last is 30
Step-by-step explanation:
1st = 5
2nd = 3 x 5 = 15
3rd = 15 x 2 = 30
5 + 15 + 30 = 50
The three numbers in question are 5, 15, and 30. This has been achieved by setting up and solving algebraic equations based on the given conditions.
Explanation:To solve this problem, we should set up equations based on the information given. Let's define:
First number = x
Second number = 3x (since it is three times the first number)
Third number = 2 * 3x = 6x (since it is twice the second number)
According to the problem, the sum of these three numbers is 50. Therefore, we can write the equation as:
x + 3x + 6x = 50
Solve for x:
10x = 50
x = 50 / 10 = 5
So, the three numbers are:
First number = x = 5
Second number = 3x = 3 * 5 = 15
Third number = 6x = 6 * 5 = 30
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in the triangle abc the side length side are bc=14 and ac=7 whats b
hope this helps you mate
Simplify the rationsl expression 6x(x+3)(x-2)/3(x-2)(x+9)
Answer:
The simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex].
Step-by-step explanation:
Given rational expression is
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
Now to simplify the given rational expression:
[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]
[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]
[tex]=\frac{2x(x+3)}{x+9}[/tex]
Now applying distributive property to the above expression
[tex]=\frac{2x^2+6x}{x+9}[/tex]
Therefore [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]
Therefore the simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]
What is the measure of angle A ?
Answer:25%
It's spit into fourths so yeah
Step-by-step explanation:
Answer: 88 degrees
===========================================
Explanation:
Sides AC and AB are tangents to the circle, so 90 degree angles form at points C and B.
Angle O = 92
Angle B = 90
Angle C = 90
Angle A = unknown
----------
The four interior angles of any convex quadrilateral always add to 360 degrees
(angle O) + (angle A) + (angle B) + (angle C) = 360
92 + A + 90 + 90 = 360
A + 272 = 360
A+272-272 = 360-272
A = 88
-----------
A shortcut is to subtract angle O from 180
angle A = 180 - (angle O) = 180 - 92 = 88
we get the same answer
PLEASE HELP godbless 20 points
Another term for measurement data is
A) quantitative data.
B) categorical data.
C) qualitative data.
D) bivariate data.
Answer:
A) quantitative data.
Step-by-step explanation:
'quantitative' derives from 'quantity', almost synonymous with a measure or measurement.
A freight train made a trip to a repair. On the trip there it travelers 25 mph and on the return trip it went 20 mph. How long did there take if the return trip took 15 hours?
Answer:
Time taken by train in onward journey = 12 hours.
Step-by-step explanation:
Given:
Speed of train making a trip to a repair = 25 mph
Speed of train on return trip = 20 mph
Time taken for return trip = 15 hours
To find the time taken on the on wards trip.
Solution:
The distance traveled by the train on the trip and return trip is the same as the y are of same trips in opposite directions.
Distance can be calculated by using the data for the return trip.
Distance= [tex]Speed\times Time[/tex]
Distance= [tex]20\ mph\times 15\ h=300\ miles[/tex]
Speed of train for on ward trip = 25 mph
Time taken = [tex]\frac{Distance}{Speed}[/tex]
Time taken = [tex]\frac{300\ miles}{25\ mph}= 12\ h[/tex]
Thus, time taken by train in onward journey = 12 hours.
a line intersects the point (13,-4) and (1,12).Find the slope and simplify completely
Answer:
[tex]m=-\frac{4}{3}[/tex]
Step-by-step explanation:
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
the point (13,-4) and (1,12)
substitute the values in the formula
[tex]m=\frac{12+4}{1-13}[/tex]
[tex]m=\frac{16}{-12}[/tex]
[tex]m=-\frac{16}{12}[/tex]
simplify
[tex]m=-\frac{4}{3}[/tex]
Answer:
-4/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(12-(-4))/(1-13)
m=(12+4)/-12
m=16/-12
simplify
m=-4/3
A bicycle wheel with the diameter 70cm is making 25 revolutions while travelling. Find the distance covered by the bicycle
The total distance covered by the bicycle is calculated using the circumference of the wheel and the number of revolutions made. With a wheel diameter of 70 cm, the total distance comes to approximately 55.0 meters after 25 revolutions.
Explanation:The question involves calculating the distance covered by a bicycle wheel making a certain number of revolutions. Given that the diameter of the wheel is 70 cm, we can find the circumference, which is the distance the wheel covers per revolution. The circumference is equal to \\(\pi\cdot d\\), where \\(d\\) is the diameter. Substituting the given diameter:
Circumference = \\(\pi \times 70 \\text{cm}\\)Since the wheel makes 25 revolutions, the total distance covered (\\em{D}}) can be found by multiplying the circumference by the number of revolutions:
Total distance covered = Circumference \\(\times\\) Number of revolutionsTotal distance covered = \\(\pi \times 70 \\text{cm} \times 25\\)Thus, the bicycle covers a distance of \\(25 \times \pi \times 70 \\text{cm}\\), or \\(25 \times \pi \times 0.7 \\text{m}\\), since 100 cm equals 1 meter.
To find the exact value, you would calculate:
Total distance covered = \\(25 \times \pi \times 0.7 \\text{m} \\approx 55.0 \\text{meters}\\)If two angles are complementary and one angle is 10∘greater than the other, then the smaller angle of the two is?
Answer:
the smaller angle = 40
Step-by-step explanation:
Let x be the smaller angle.
Other angle = x + 10
x + x+ 10 = 90
2x = 90 - 10
2x= 80
x = 80/2
x = 40
Answer:
40 degrees. A set of complementary angles make up 90 degrees. 90 - 40 is 50, which is 10 more than forty.
Find the equation of the image of a line y=3x-8 after reflection over the x-axis
Answer:
The required image line is 3x + y = 8
Step-by-step explanation:
We have to find two points on the given straight line then find their reflection points over the x-axis and then finally the straight line passing through those two image points will give the required straight line.
Now, the given straight line is y = 3x - 8.
Now, two any points on this straight line are say (1,-5) and (2,-2).
So, the image of (1,-5) point reflecting over the x-axis will be (1,5) and the image of the point (2,-2) reflecting over the x-axis will be (2,2).
Therefore, the straight line passing through those two image points will have equation
[tex]\frac{y - 5}{5 - 2} = \frac{x - 1}{1 - 2}[/tex]
⇒ y - 5 = 3(1 - x)
⇒ y - 5 = 3 - 3x
⇒ 3x + y = 8
Hence, the required image line is 3x + y = 8 (Answer)
The graph of f(x)= (0.5)^x is replaced by the graph of g(x) = (0.5)^x-k. If g(x) is obtained by shifting f(x) down 2 units, then what is the value of k?
A) k=2
B) k=1/2
C) k= -2
D) k= -1/2
A) k=2 is the right answer
Step-by-step explanation:
The downward funtion transformation is defined as:
f(x) => f(x)-b where b is an integer.
Given
[tex]f(x) = (0.5)^x[/tex]
And
[tex]g(x) = (0.5)^x-k[/tex]
It is also given that g(x) is obtained by shifting function f 2 units downward
We will apply the transformation to function f to find the value of k.
So,
Shifting f(x) 2 units downward
we will get
[tex]g(x) = (0.5)^x-2[/tex]
comparing with [tex]g(x) = (0.5)^x-k[/tex] we get that
k = 2
So,
A) k=2 is the right answer
Keywords: Functions, shifting
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Answer:
ok k does = 2 i got it right on the test
Step-by-step explanation:
:3
A boat rental charges $7.50 for the first hour and $2 for each additional hour. Which rule gives the cost for x hours of renting a boat?
c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat
Solution:Given that a boat rental charges $7.50 for the first hour and $2 for each additional hour.
To find: Rule that gives the cost for x hours of renting a boat
Let "x" be the total hours of renting a boat
[tex]c = f + (v \times x - 1)[/tex]
"c" is the total cost for the boat rent
"f" is the fixed cost for boat rent for first hour
"v" is the cost for each additional hours of rent
"x" is the total hours of renting a boat
In the expression we have used "x - 1" to represent the additional hour of boat rent after first hour
Here f = $ 7.50
v = $ 2
[tex]c = 7.50 + 2 \times x - 1\\\\c = 7.50 + 2(x - 1)[/tex]
Thus c = 7.50 + 2(x - 1) is the rule that gives cost for "x" hours of renting a boat
The cost for renting a boat for x hours can be found using the formula y = 7.50 + 2(x - 1), where y is the total cost and x is the number of hours.
Explanation:Based on the given information, the boat rental company charges $7.50 for the first hour and then an additional $2 for each subsequent hour. Therefore, if x is the number of hours you rent the boat, the total cost would be calculated using the formula y = 7.50 + 2(x - 1). Here, y represents the total cost of renting the boat for x hours. The formula subtracts the one-hour charge included in the initial payment.
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1. Geoff rode his bike along an 8-mile path and lost his cell phone at some random location
somewhere along the way. Geoff searched from mile 4.5 to mile 7. What is the probability
that he found his phone?
I need help!!
Answer:
0.3125
Step-by-step explanation:
Use definition of geometric probability:
[tex]P=\dfrac{\text{Desired Length}}{\text{Total Length}}[/tex]
In your case,
Total Length = 8 miles
Desired Length = 7 - 4.5 = 2.5 miles,
so the probability is
[tex]P=\dfrac{2.5}{8}=\dfrac{25}{80}=\dfrac{5}{16}=0.3125[/tex]
Final answer:
The probability of finding the lost cell phone by searching from mile 4.5 to mile 7 along an 8-mile path is 0.3125 or 31.25%.
Explanation:
The student's question deals with the probability of finding a lost cell phone on an 8-mile path by searching between the 4.5 and 7 mile markers.
To calculate this probability, we consider the length of the path where the phone could potentially be found (the search area) and the total length of the path.
The search area is from mile 4.5 to mile 7, which is 2.5 miles long. Since the phone could be anywhere along the 8-mile path, the probability of finding the phone is the length of the search area divided by the total path length:
Probability = Length of Search Area / Total Path Length = 2.5 miles / 8 miles = 0.3125 or 31.25%.
Choose the word phrase (greater than, less than, or equal to) to make the statements true.
Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips.
Twenty-two paper clips are worth sixty-seven matches.
In the problem, one paper clip equals three matches, one pencil is greater than one paper clip, and twenty-two paper clips are greater than sixty-seven matches.
Explanation:In this scenario, one paper clip is equivalent, or equal to, three matches. This is ascertained from the first sentence which states that each paper clip can be traded for three matches. Similarly, one pencil is greater than a single paper clip as it can be traded for six paper clips. This conclusion is drawn from the second sentence. Lastly, the value of twenty-two paper clips is greater than sixty-seven matches since one paper clip is equal to three matches, hence twenty-two paper clips would be worth sixty-six matches, but since we have sixty-seven matches, twenty-two paper clips are worth more.
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(1.5x 109) (3.5 x 109)
well,I am not sure about the answer.
y-3=3(x+1)
what is the equation in standard form of a perpendicular line that passes through (5,-1)
Answer: x + 3y = 2
Step-by-step explanation:
Given:
y - 3 = 3 ( x + 1 )
y - 3 = 3x + 3
y = 3x + 3 + 3
y = 3x +6
comparing the equation with the formula for finding equation of line in slope - intercept form
y = mx + c , where m is the slope and c is the y - intercept. This means that the slope of the line above is 3
Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if they are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
Considering this rule , this means that the slope of the line we are to find = [tex]\frac{-1}{3}[/tex]
Using the formula : y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) to find the equation of the line , we have
y - (-1 ) = [tex]\frac{-1}{3}[/tex] ( x - 5 )
y + 1 = [tex]\frac{-1}{3}[/tex] ( x - 5 )
multiplying through by 3 , we have
3 ( y + 1 ) = -1 ( x - 5)
Expanding , we have
3y + 3 = -x + 5
writing the equation in standard form , we have
3y + x = 5 - 3
Therefore :
x + 3y = 2
What is the solution set to the inequality 7z+5>47
Answer:
[tex]z>6[/tex]
Step-by-step explanation:7z+5>47
Remove the 5:
[tex]7z+5-5>47-5\\7z>42[/tex]
Divide by 7 to get z by itself:
[tex]\frac{7z}{7} >\frac{42}{7} \\z>6[/tex]
help please ...........
Answer:
D. 120°
Step-by-step explanation:
Interior angles of a rhombus always add up to 360 degrees. Thus we can set up an equation:
g+g+2g+2g=360
Now let's combine all the like terms (g's).
6g=360
Now we divide both sides by six to isolate g.
g=60
We can now substitute g into angle B, to find its value.
2g
2(60)
120
Thus, the measure of angle B is 120, or option D.
CAN SOMEONE PLEASE HELP MEEE
Graph y = –4/3x + 1
Answer:
Step-by-step explanation:
y = -4/3x + 1
in y = mx + b form, the number in the b is the y intercept...so ur y intercept is
(0,1).....this is where ur line crosses the y axis
to find ur x axis, sub in 0 for y and solve for x
y = -4/3x + 1
0 = -4/3x + 1
4/3x = 1
x = 1 / (4/3)
x = 1 * 3/4
x = 3/4........and ur x intercept is (3/4,0)...this is where ur line crosses the x axis.
in y = mx + b form, the letter m represents ur slope....so ur slope is
-4/3.....that negative means ur line is descending.....so when we graph, we will start at the y int.
go ahead and plot ur intercepts.......(0,1) and (3/4,0)....now look at ur slope -4/3.....the numerator (either go up or down)....the denominator (go right)
if the numerator is negative....go down....if it was positive u would go up.
so start at (0,1).....slope is -4/3.....so go down 4 and to the right 3...plot that point......then go down 4 and to the right 3...plot that...ur gonna keep on going down 4 and to the right 3 as far as u need to...connect ur points and u have ur line
if it helps, ur line will be going through points (3,-3), (6,-7),(-3,5), (-6,9).....those are some whole number points.....its kinda hard to graph when ur intercepts dont fall on whole numbers
The graph of the function y = -4/3x + 1 is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -4/3x + 1
The above function is a linear function that has been transformed as follows
Vertically stretched by a factor of -4/3Shifted up by 1 unitNext, we plot the graph using a graphing tool by taking note of the above transformations
The graph of the function is added as an attachment
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y = 5- 2
1-3x + y = -12
What is the value of x and y ?
Answer:
x=5.333
y=3
Step-by-step explanation:
given, y=5-2............(1)
1-3x+y=-12...............(2)
y=5-2=3
put y=3 in equ (2)
1-3x+3=-12
1+3+12=3x
3x=16
x=[tex]\frac{16}{3}[/tex]
x=5.333
hence, x=5.333
y=3 answer
help me??? please????
Answer:
∠2 = 78°
Step-by-step explanation:
Angle of a straight line is 180°.
So, that would mean ∠1 + ∠2 = 180°.
⇒ ∠2 = 180° - ∠1
⇒ ∠2 = 180° - 102°
⇒ ∠2 = 78°
Hence, the answer.
What value of x makes this equation TRUE? 4x + 2 = −14
4x + 2 = -14
4x = -16
x = -4
4(-4) + 2 = -14
-16 + 2 = -14
-14 = -14
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What is the product of any nonzero real number and it's reciprocal?
Answer:
1
Step-by-step explanation:
The product of a nonzero number and its reciprocal is 1
Answer:
Step-by-step explanation:
The product will always equal 1. This is one of the methods we use to solve equations. If our nonzero real number is 3, for example, the reciprocal of 3 is 1/3 and
3 × [tex]\frac{1}{3}[/tex] can be written as
[tex]\frac{3}{1}[/tex] × [tex]\frac{1}{3}[/tex] which is 3/3 which = 1.
Kim drove from Mathtown at (-2, 5) to Geometryville at (3, -1) to Algebra Springs at (-6, -5), and then back to Mathtown. Find the total distance Kim traveled to the nearest hundredth.
Answer:
33.38 km
Step-by-step explanation:
Kim drove from Math Town at (-2, 5) to Geometry Ville at (3, -1) to Algebra Springs at (-6, -5), and then back to Math town.
Now, the distance from (-2,5) point to (3,-1) point will be
[tex]\sqrt{(- 2 - 3)^{2} + (5 - (-1))^{2}} = \sqrt{61}[/tex] km.
Again, the distance from point (3,-1) and (-6,-5) point will be
[tex]\sqrt{(3 - (- 5))^{2} + (- 1 - (- 5))^{2}} = \sqrt{80}[/tex] km.
Therefore, the total distance Kim traveled will be = [tex]2(\sqrt{61} + \sqrt{80}) = 33.38[/tex] Km. (Answer)
The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] on the coordinate plane is given by
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]