Answer:
x=22
Step-by-step explanation:
7x+6=160.
Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.
7x+6-6=160-6
7x=154
Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.
7x/7 = 154/7
x=22
Look Below :
Step-by-step explanation:
160 - 6 = 7x
154 = 7x
Or
7x = 154
x = 22
Please.. Given the image below, DY,EY ,FY are perpendicular bisectors of △ABC. So, 30.11=
a) FY
b) YE
c) EB
d) DY
e) cannot be determined
Answer:
e) cannot be determined
Step-by-step explanation:
hope this helps!!
What is the length of BC?
Answer:
24
Step-by-step explanation:
3x - 15 = x + 33 [sides opposite congruent angles in a triangle are congruent]2x - 15 = 33 [subtract x from both sides]2x = 48 [add 15 to both sides]x = 24 [divide both sides by 2]BC = 24 [BC = x]anyone know how to answer this?
Analyze the graph of the function f(x) to complete the statement.
On a coordinate plane, a curved line, labeled f of x, with a minimum value of (0, negative 3) and a maximum value of (negative 2.4, 17), crosses the x-axis at (negative 3, 0), (negative 1.1, 0), and (0.9, 0), and crosses the y-axis at (0, negative 3).
f(x)<0 over and what other interval?
The function f(x) is less than 0 at x < -1.8
How to analyze the graph?The missing graph is added as an attachment
The interval where f(x) < 0 are the intervals where the y value of the function is less than 0.
This in other words, represent the negative y-axis
From the attached graph, the function f(x) is less than 0 at x < -1.8.
This extends till x = infinity
Hence, the function f(x) is less than 0 at x < -1.8
Read more about function interval at:
https://brainly.com/question/27831985
#SPJ1
GO
What is the value of a in the equation 3 a+b=54, when b = 9?
O 15
O 18
O 21
O27
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the value of a in the equation 3a+b=54, if b=9?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Put in 9 for b.
[tex]\bf{3a+9=54}[/tex] | subtract 9 on both sides
[tex]\bf{3a=45}[/tex] | divide the entire equation by 3
[tex]\bf{a=15}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\bigcirc 15}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]
Answer:
a = 15
Step-by-step explanation:
3a + b = 54 ← substitute b = 9
3a + 9 = 54 ( subtract 9 from both sides )
3a = 45 ( divide both sides by 3 )
a = 15
You invest $5,000 into an account where interest compounds continuously at 3.5%. How long will it take your money to double? Round answer to nearest year.
Answer:
20 years
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
A = $10,000P = $5,000r = 3.5% = 0.035Substitute the given values into the formula and solve for t:
[tex]\sf \implies 10000=5000e^{0.035t}[/tex]
[tex]\sf \implies \dfrac{10000}{5000}=e^{0.035t}[/tex]
[tex]\sf \implies 2=e^{0.035t}[/tex]
[tex]\sf \implies \ln 2=\ln e^{0.035t}[/tex]
[tex]\sf \implies \ln 2=0.035t\ln e[/tex]
[tex]\sf \implies \ln 2=0.035t(1)[/tex]
[tex]\sf \implies \ln 2=0.035t[/tex]
[tex]\sf \implies t=\dfrac{\ln 2}{0.035}[/tex]
[tex]\implies \sf t=19.80420516...[/tex]
Therefore, it will take 20 years (to the nearest year) for the initial investment to double.
P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }
The solution to the division of the given surd is: [tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
Division of Surds.The division of surds follows a systemic approach whereby we divide the whole numbers separately and the root(s) are being divided by each other.
Given that:
[tex]\mathbf{P=(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} ) : \frac{4x}{(x-1)^{2} }}[/tex]
i.e.
[tex]\mathbf{=\dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )}{ \frac{4x}{(x-1)^{2} }} }[/tex]
Using the fraction rule:
[tex]\mathbf{\dfrac{a}{\dfrac{b}{c}}= \dfrac{a\times c}{b}}[/tex]
[tex]\mathbf{\implies \dfrac{(\frac{\sqrt{x} +2}{x-1}+\frac{\sqrt{x}\\ -2}{x-2\sqrt{x} +1} )(x-1)^{2}}{4x}} }[/tex]
By simplification, we have:
[tex]\mathbf{ =\dfrac{\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{2} }{4x} }[/tex]
[tex]\mathbf{P =\dfrac{(6\sqrt{x}-x^2\sqrt{x}-3x\sqrt{x}+2x+2)(x-1) }{8x} }[/tex]
Learn more about evaluating the division of surds here:
https://brainly.in/question/27942899
#SPJ1
In a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event. What is the classical probability of the event
The classical probability of the given event is 1/4 or 0.25 or 25%.
The classical property of an event is the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.
If we suppose an event A.
The total number of favorable outcomes to event A to be n.
The total number of possible outcomes in the experiment to be S.
Then, the classical probability of event A is given as:
P(A) = n/S.
In the question, we are informed that in a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event.
We are asked to find the classical probability of the event.
As we know, the classical probability of an event is the ratio of the number of favorable outcomes to the event to the total number of possible outcomes in the experiment.
Thus, the classical probability = 2/8 = 1/4 or 0.25 or 25%.
Thus, the classical probability of the given event is 1/4 or 0.25 or 25%.
Learn more about the classical probability of an event at
https://brainly.com/question/13850688
#SPJ4
5x + 2 = 8x + 5 Help me before I die quick math is so hardddddd
Answer:
x = -1
Step-by-step explanation:
Note: when you send a number across it can change it sign. If it is positive it will turn negative.
5x + 2 = 8x + 5
Send 8x across
5x + 2 - 8x = 5
send 2 across
5x - 8x = 5 - 2
- 3x = 3
Divide both sides by - 3
- 3x/- 3 = 3/- 3
- 3 cancel out - 3
x = 3/ - 3
3 divided by - 3 is - 1
x = -1
According to the synthetic division below, which of the following statements
are true?
Check all that apply.
3)2 -2 -12
6 12
2 4 0
A. (x+3) is a factor of 2x² - 2x-12.
B. The number -3 is a root of F(x) = 2x² - 2x-12.
c. (2x²-2x-12) + (x-3) = (2x + 4)
D. The number 3 is a root of F(x) = 2x2 - 2x-12.
E. (x-3) is a factor of 2x² - 2x-12.
O (2x2-2x-12) + (x+3) = (2x + 4)
The true statements about the synthetic division are
c. (2x²-2x-12) + (x-3) = (2x + 4)d. The number 3 is a root of F(x) = 2x^2 - 2x-12.e. (x-3) is a factor of 2x² - 2x-12.How to determine the true statements?The synthetic division is given as:
3)2 -2 -12
6 12
2 4 0
In the above representation of the synthetic division, we have:
Quotient = 2x + 4Dividend = 2x^2 - 2x - 12Divisor = x- 3Remainder = 0Because the remainder is 0, then
(2x^2 - 2x - 12) ÷ (x - 3) = (2x + 4) --- option C
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
This means that 3 is a root of 2x^2 - 2x - 12 --- option (D) and x - 3 is a factor of 2x^2 - 2x - 12 --- option (E)
Hence, the true statements are (C), (D) and (E)
Read more about synthetic divisions at:
https://brainly.com/question/12951962
#SPJ1
What is the unit rate in 187pounds of food for 1447.38
The unit rate of 187pounds of food for 1447.38 is 7.74 per pound
Unit rateQuantity of food = 187 poundsTotal cost of food = 1447.38Unit rate = Total cost of food ÷ Quantity of food
= 1447.38 ÷ 187
= 7.74 per pound
Therefore, the unit rate of 187pounds of food for 1447.38 is 7.74 per pound
Learn more about unit rate:
https://brainly.com/question/620388
#SPJ1
What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?
Answer:
108
Step-by-step explanation:
Since 3n is a perfect square, that means that n has to be a multiple of 3. Since 2n is a perfect cube, then n has to be divisible by 2^2=4. Since n is a multiple of 3, then n also has to be divisible by 3^3=27. Therefore, the smallest value for n is 4*27=108.
Given: The
measure of angle B = 27 degrees, measure of angle C
= 82 degrees, and b = 12. Then a =to the
nearest tenth.
Answer:
25
Step-by-step explanation:
We can calculate for a using sine rule.
For angle A,
A + 27° + 82° = 180 ( sum of angles in a triangle).
A + 109 = 180
A = 180 - 109 = 71°
Therefore,
A = 71°
calculating for side a
[tex] \frac{sin \: 27}{12} = \frac{sin71}{a} \\ a = \frac{12 \times sin71}{sin27} \\ a \: = \frac{11.346}{0.454} \\ a = 25[/tex]
Out of 300 students in a class, 60 percent students study physics, 35 percent students study chemistry and 20 percent do not study both of the subjects. how many students study both subjects
22 students study both subjects.
What is Venn diagram in math ?
In a Venn diagram, sets are represented by shapes; usually circles or ovals. The elements of a set are labeled within the circle.N=55,n(M)=23,n(P)=24,n(C)=19,n(M∩P)=12,n(P∩C)=7,n(M∩C)=9,n(M∩P∩C)=4
Now, number of students who studying only Mathematics
n(M∩P)∩C =n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C) (by Venn diagram) diagram=23−9−12+4=6
number of students who studying only Physics
n(P∩M )∩C =n(P)−n(P∩M)−n(P∩C)+n(P∩M∩C) (by Venn diagram)
=24−12−7+4=9
Now, number of students who studying only Chemistry
n(C∩M )∩P =n(C)−n(C∩M)−n(C∩P)+n(M∩P∩C) (by Venn diagram)
=19−9−7+4=7
So, how many students study only one of the three disciplines in detail 6+9+7=22
Learn more about venn diagram
brainly.com/question/14344003
#SPJ4
69. REAL-WORLD APPLICATIONS
A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?
Answer:
Cost of per session the average rate is $45.
Step-by-step explanation:
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
It is required to find what is the cost per session.
Step 1 of 1
It is given that a gym membership with two personal training session cost $125, while gym membership with five personal training sessions cost $260.
To find the cost of per session calculate the average rate.
Now let $f(x)$ be the cost per session use the for the average rate of change, and the input value is the number of personal traings x.
[tex]$m=\frac{f\left(x_{2}\right)-f\left(x_{1}\right)}{x_{2}-x_{1}}$$[/tex]
Now substitute, $125 for [tex]$f\left(x_{2}\right)[/tex], 260 for [tex]$f\left(x_{1}\right), 2$[/tex] for [tex]$x_{1}$[/tex] and 5 for [tex]$x_{2}$[/tex] then,
[tex]$m=\frac{260-125}{5-2}$\$$\begin{aligned}&=\frac{135}{3} \\&=45\end{aligned}$$[/tex]
Cost of per session the average rate is $45.
go 5
U
12 x 9
18
11
17
how do I solve this
Answer:
6/17
Step-by-step explanation:
12/18 * 9/17
use 9 to divide 18 u'll be left with
12/2 * 1/17
use 2 to divide 12 u'll be left with
6/1 * 1/17
now u'll multiply leaving you with
6/17 as the final answer or u can also convert to decimal your answer will be
0.352 by approximation.
Hope this helps please mark me BRAINLIEST
i need help on question 32 for algebra
Answer:
d. 40 feet
Step-by-step explanation:
Perimeter = 140 ft
Width = L + 10
P = 2w + 2L
140 = 2(L + 10) + 2L
140 = 2L + 20 + 2L
120 = 4L
L = 30
w = L + 10
w = 30 + 10
w = 40
Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family. The t-test for two means is appropriate in this situation because Group of answer choices women and men are dependent samples. women and men are independent samples. women and men are matched samples. the observations are paired. None of these.
The t-test for the two means is appropriate in this situation because women and men are independent samples.
What are Independent Samples?Independent samples are those that are chosen at random, ensuring that their results are independent of other observations' values.
The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.
The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population mean values are statistically substantially different. A parametric test is the Independent Samples t-Test.
Learn more about Independent Samples here:
https://brainly.com/question/14099859
#SPJ4
A una excursion van 40 niños acopmañados por 30 adultos.Pasaran la noche en cabañas iguale,pero lod niños y los adultos deben dormir separados.Cuantas menos cabañas ocupen,menos pagaran ¿cuantas cabañas deben ocupar para pagar lo menos posible?¿cuantos dormiran en cada cabaña?
The factor computed illustrates that the number of cabins that should be occupied will be 20 cabins.
How to calculate the cabins?From the information given, there are 40 children and 30 adults. In this case, the common factors are 1, 2, 3, 5, and 10. The highest common factor is 10.
The question depicts that they will have same cabins. Therefore, the total number of cabins will be:
= 10 × 2
= 20 cabins
Learn more about factor on:
brainly.com/question/219464
#SPJ1
HELP ME PLEASE, i will give brainliest
Based on the right angle triangle and the given parameters, cos K = 5/13
Trigonometric ratiossin = opposite / hypotenusecos = adjacent / hypotenuseTan = opposite / adjacentGiven parameters:
Hypotenuse = 13Adjacent = 5Opposite = 12Therefore,
cos K = adjacent / hypotenuse
cos K = 5/13
Learn more about right triangle:
https://brainly.com/question/2217700
#SPJ1
Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
A.
(-7, -1), 36 units
B.
(7, 1), 36 units
C.
(7, 1), 6 units
D.
(-7, -1), 6 units
The coordinates for the center of the circle and the length of the radius are ( -7, -1 ) and 6 respectively.
Option D) is the correct answer.
What are the coordinates for the center of the circle and the length of the radius?Given the equation;
x² + y² + 14x + 2y + 14 = 0
We subtract 14 from both sides
x² + y² + 14x + 2y + 14 - 14 = 0 -14
x² + y² + 14x + 2y = -14
Next, we complete the square for x² + 14
We have, ( x + 7 )² - 49
Next, we complete the square for y² + 2y
We have, ( y + 1)² - 1
We substitute these squares into the given equation
x² + y² + 14x + 2y = -14
( x + 7 )² - 49 + ( y + 1)² - 1 = -14
Collect like terms
( x + 7 )² + ( y + 1)² = -14 + 49 + 1
( x + 7 )² + ( y + 1)² = 36
( x + 7 )² + ( y + 1)² = 6²
Note that, the form of a circle is given as;
( x-h )² + ( y-k)² = r²
Hence, we match the values into the form and determine our center and radius.
( x-(+7) )² + ( y-(+1))² = 6²
( x-7 )² + ( y-1 )² = 6²
Hence Center = ( -7, -1 ) and radius = 6
The coordinates for the center of the circle and the length of the radius are ( -7, -1 ) and 6 respectively.
Option D) is the correct answer.
Learn more about center and radius of circle here: https://brainly.com/question/10618691
#SPJ1
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable. How should Mr. Johns handle this situation
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explaining that one component of math is understanding reasonable answers.
Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable.
Mr. Johns handle this situation to Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers.
Learn more about the reasoning here https://brainly.com/question/25175983
#SPJ4
How much is KM?
Help me please!!!
Answer: 3
Step-by-step explanation:
By the intersecting chords theorem,
[tex](KM)(16)=(4)(12)\\\\KM=3[/tex]
Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's garden measured 45 feet in length and 18 feet in width. This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction. The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced. What is the maximum potential area of this year's resized garden?
The quadratic function is A(x) = 2(405 + 36x – x²). Then the maximum potential area of this year's resized garden will be 1458.
What is the maximum and minimum value of the function?The condition for the maximum will be
f(x)'' < 0
The condition for the minimum will be
f(x)'' > 0
Every summer, Richard plants a garden on a rectangular plot of land.
Last summer, Richard's garden measured 45 feet in length and 18 feet in width.
This summer, Richard decides to resize his garden by decreasing the length of the garden, and increasing the width of the garden by two times the length reduction.
The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the number of feet that the length is reduced.
Length = (45 – x)
Width = (18 + 2x)
Then the maximum potential area of this year's resized garden will be
A(x) = (45 – x)(18 + 2x)
A(x) = 810 + 72x – 2x²
A(x) = 2(405 + 36x – x²)
For maximum potential, A'(x) = 0
A'(x) = 0
36 - 2x = 0
2x = 36
x = 18
Then the maximum potential area will be
A(x) = 2(405 + 36 × 18 – 18²)
A(x) = 1458
More about the maximum and minimum value of the function link is given below.
https://brainly.com/question/13581879
#SPJ1
5284 Ib = _______ tn_______ the answer is 2 tn and 1284 Ib how to convert.
The value of 5284 Ib is expressed as 2000 tons 642 lbs
Conversion of pounds to tonsGiven the following parameters
2000lb = 1 ton
5284 Ib = 5284lb/2000 = 2.642 tons
2.642 tons = 2000 tons 642 lbs
Hence the value of 5284 Ib is expressed as 2000 tons 642 lbs
Learn more on pounds to tons here; https://brainly.com/question/3272440
#SPJ1
Describe a relationship modeled by the function [tex]f(x) = 4x^3 - 72x^2 + 320x[/tex], and explain how the function models the relationship.
Then, identify and interpret the key features of the function in the context of the situation described in part A.
(Describe a relationship that could be modeled by the given function. There is no single correct answer: any scenario that fits the function type is correct.)
The relationship modeled that has the function of f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.
What is the volume of the prism about?For us to know the relationship modeled by the above function, the best way to do it is for one to factor it.
The function is: f(x) = 4x³ - 72x² + 320x
First. we factor it so as to extract the common factor 4x:
Secondly, we factor the quadratic trinomial.
This is often done by writing it as a product of two binomials where the two constant terms are said to be sum up - 18 and its product is said to be 80.
The above terms are known to be -10 and - 8; so the two factors are said to be (x - 10) and (x - 8).
Therefore The relationship modeled that has the function of f(x) = 4x³ - 72x² + 320x is known to be the volume of a right prism that has its dimensions to be : 4 times of its desired length, 10 units lower that its desired length, and 8 units lower than its desired length.
Where it has :
x = the desired length,
4x = 4 times its desired length,
x - 10 = 10 lower than its desired length,
x - 8 = 8 lower than its desired length,
We can therefore say that the volume of the prism is said to be the product of the three factors which are:
V = (4x)(x-10)(x-8)
Learn more about prism from
https://brainly.com/question/23963432
#SPJ1
Please help! Somewhat confused as to how this is done.
Answer:
The second graph
Step-by-step explanation:
Let's start with the top equation, 4y+3x=0
Isolate the y by moving the 3x to the other side. 4y=-3x
Divide both sides by 4 to fully isolate the y which will give you y=-3/4x
There's your first equation.
Then take 4y-x=16 and do the same thing
4y=16+x
y=4+x/4
y=x/4+4
Now you know that one equation is going to go left, or the negative direction, while the other will go right, or positive, meaning there will be a point where they intersect. So just basically look for the one where x/4+4 is rising while going right. Leaving you with either the 1st or 2nd graph.
Then,
Graph both using the rise/run method or just look for an answer choice where one of the equations is positive and intersects at y=4 (since the second equation is x/4+4) which makes it the second graph.
Let me know if you need any extra explanation
Answer:
(-4,3)
Step-by-step explanation:
To solve a system of equations by graphing, we'll need to graph both equations, and find their points of intersection.
Note that both equations are linear (no exponents, no radicals, no variables in a denominator, no variables multiplied to other variables, etc -- just numbers multiplied to a variable and added to other numbers multiplied to a variable).
To graph linear equations, often they are graphed by putting the equation in slope-intercept form. Alternatively, since it is a line, two points can be found on the line, and then the line can be graphed.
Option 1: Convert to slope-intercept formSlope intercept form is [tex]y=mx+b[/tex], where "m" is the slope of the line, and "b" is the y-intercept (the place where the line crosses the y-axis).
To convert to slope intercept form, isolate "y".
First equation:
[tex]4y+3x=0[/tex]
[tex](4y+3x)-3x=(0)-3x[/tex]
[tex]4y=-3x[/tex]
[tex]\dfrac{4y}{4}=\dfrac{-3x}{4}[/tex]
[tex]y=\frac{-3}{4}x[/tex]
Second equation:
[tex]4y-x=16[/tex]
[tex](4y-x)+x=(16)+x[/tex]
[tex]4y=x+16[/tex]
[tex]\frac{1}{4}*(4y)=\frac{1}{4}*(x+16)[/tex]
[tex]y=\frac{1}{4}*x+\frac{1}{4}*16[/tex]
[tex]y=\frac{1}{4}x+4[/tex]
To graph the lines, plot their y-intercepts first, then use their slopes to determine the rest of the line.
Recall that the slope is [tex]\frac{rise}{run}[/tex].
Once the equations are graphed, find the intersection from the diagram, (-4,3).
Option 2: Graphing from implicit formThe equations currently are in an implicit form (a form where the variables aren't isolated, so neither variable is written in terms of the other). To graph any line, find and plot two points, then draw the line between them.
To find points on the line, recall that the equation for a line relates the x-coordinate and y-coordinate through the equation. So, if you want to find the y-coordinate for the line when the x-coordinate is 0, substitute 0 for x, and solve for y. Often zero is used, because multiplying by zero cancel out the term, and makes the calculations easier.
Equation 1 - finding a point where x=0
[tex]4y+3x=0[/tex]
[tex]4y+3(0)=0[/tex]
[tex]4y+0=0[/tex]
[tex]4y=0[/tex]
[tex]\dfrac{4y}{4}=\dfrac{0}{4}[/tex]
[tex]y=0[/tex]
So, if x=0, then y=0. So, the point (0,0) is on line 1.
To find another point, we need to choose another number. As mentioned previously, often zero is used, and we could find a point on the line where the y-coordinate is zero. However, since we just found that the point (0,0) is on the line, x=0 when y=0, and so y=0 when x=0. We'll need a new number.
Another number that it often an easy choice mathematically is to choose the coefficient of the other variable. So, for instance, in equation 1, the coefficient of the y term is "4", so let's choose the x-coordinate to be 4, and find the y-coordinate that goes with it:
Equation 1 - finding a second point, where x=4
[tex]4y+3x=0[/tex]
[tex]4y+3(4)=0[/tex]
[tex]4y+12=0[/tex]
[tex](4y+12)-12=(0)-12[/tex]
[tex]4y=-12[/tex]
[tex]\dfrac{4y}{4}=\dfrac{-12}{4}[/tex]
[tex]y=-3[/tex]
So, if x=4, then y=-3. So, the point (4,-3) is also on line 1.
Those two points can be plotted, and the line drawn.
Equation 2 - finding a point where x=0
[tex]4y-x=16[/tex]
[tex]4y-(0)=16[/tex]
[tex]4y=16[/tex]
[tex]\dfrac{4y}{4}=\dfrac{16}{4}[/tex]
[tex]y=4[/tex]
So, if x=0, then y=4. So, the point (0,4) is on line 2.
To find another point, this time, we can choose the y-coordinate to be zero, because we don't already know the x-coordinate that is associated with it.
Equation 2 - finding a second point, where y=0
[tex]4y-x=16[/tex]
[tex]4(0)-x=16[/tex]
[tex]0-x=16[/tex]
[tex]-x=16[/tex]
[tex]-1*(-x)=-1*(16)[/tex]
[tex]x=-16[/tex]
So, if y = 0, then x = -16. So, the point (-16,0) is also on line 2.
Those two points can be plotted and the line drawn. Once the lines are drawn, the intersection can be found. From the diagram, the intersection is (-4,3).
Jess runs 9/5 of a mile each day. Gigi runs 1 2/3 each day. After a week, who will have a run more than 8 miles.
Answer: They both run more than 8 miles
Step-by-step explanation:
9/5 * 7 = 12 3/5
1 2/3 * 7 = 11 2/3
They both run more than 8 miles
Answer:
Jess and Gigi run more than 8 miles
Step-by-step explanation:
9/5 times 7 = 12.6
1 2/3 times 7 equals 11.6
Jamal simplified the expression startroot 75 x superscript 5 baseline y superscript 8 baseline endroot where x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0. startroot 75 x superscript 5 baseline y superscript 8 baseline endroot = startroot 25 times 3 times x superscript 4 baseline times x times y superscript 8 baseline endroot = 5 x squared y squared startroot 3 x endroot which describes the error jamal made?
The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.
What is the expression about?An expression is often seen as a form of mathematical statement about a thing.
Note that from the expression:
[tex]\sqrt{75x^{5} y^{8} }[/tex]
[tex]\sqrt{25 x 3 x x^{4} x x x y^{8} }[/tex]
= 5x² y² [tex]\sqrt{3x}[/tex]
So, The statement that describes the error that Jamal has made is option A: He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.
See options below
Which describes the error Jamal made?
A. He should have written the square root of y Superscript 8 in the answer as y Superscript 4, not y squared.
B. He should have written the square root of x Superscript 4 in the answer as x, not x squared.
C. He should have written the 5 inside of the radical in the answer.
D. He should have written the 3 outside of the radical in the answer.
Learn more about Superscript from
https://brainly.com/question/14202796
#SPJ1
Answer:
A)
Step-by-step explanation:
Find the equation of a circle whose center is at (-3, 7) and radius is 9 units.
Answer:
(x + 3)² + (y - 7)² = 81
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
here (h, k ) = (- 3, 7 ) and r = 9 , then
(x - (- 3) )² + (y - 7)² = 9² , that is
(x + 3)² + (y - 7)² = 81
Answer:
[tex]x^2+y^2+6x-14y-23=0[/tex]
Step-by-step explanation:
[tex](x-(-3))^2+(y-7)^2=9^2\\x^2+6x+9+y^2-14y+49=81\\x^2+y^2+6x-14y-23=0[/tex]