HELP ASAP- NO LINKS AND NO JOKES
a student solved a system of equations as shown below
3x+2y=7
5x-4y=-3
which step in the solution contains the first error
A. Step 4
B. Step 6
C. step 2
D. Step 1
Answers
Answer:
A
Step-by-step explanation:
step 3 is correct
x = 1
in step 4 the student has substituted x = 1 into y instead of x, that is
3x + 2(1) = 7 ← Incorrect substitution
Should be
3(1) + 2y = 7
3 + 2y = 7 ( subtract 3 from both sides )
2y = 4 ( divide both sides by 2 )
y = 2
Answer:
A. Step 4
Step-by-step explanation:
Identifying the error
In step 4 the value of x is supposed to be substituted into the second equation however the value of x is instead substituted for y which is the first error made
Solving it correctly and explaining each step.
We have the two equations 3x + 2y = 7 and 5x - 4y = -3
It appears that the elimination method is being used as the first step consist of multiplying the first equation by 2 so that we have the two variables -4y and 4y which can cancel out in the next step so we are going to use the elimination method as well to solve it correctly.
What is the elimination method?
The elimination method is a method used to solve a system of equations. When you have two variables that have the same coefficient ( number before variable; x or y ) but different signs ( it works if they have the same too ) you can add the two equations eliminating one of the variables. Using this method will leave you with a singular variable in which you can solve
Solving it using the elimination method
Again we have the two equations 3x + 2y = 7 and 5x - 4y = -3
(step 1) Notice how the first equation has 2y which can be multiplied by 2 resulting in us getting 4y which is opposite of -4y. This sets us up exactly for using the elimination method.
Thus the first step would be too multiply the first equation by 2
3x + 2y = 7
x2
------------------
6x + 4y = 14
Now we have the two equations 6x + 4y = 14 and 5x - 4y = -3
(step 2)Our next step would be to add the two equations so that the variable y is eliminated
6x + 4y = 14
+ 5x - 4y = -3
--------------------
11x 0 = 11
We're left with 11x = 11
(step 3)Our next step would be to solve for x
11x = 11
==> divide both sides by 11
x = 1
(step 4) Now that we have defined one of are variables we plug it in into one of the equations and solve for the other, this is step 4.
5x - 4y = -3
==> plug in x = 1
5(1) - 4y = -3
(step 5)==> simplify
5 - 4y = -3
(step 6) ==> subtract 5 from both sides
-4y = -8
(step 7) ==> divide both sides by -4
y = 2
The real solution would be (1,2)
Related Questions
A right circular cone is intersected by a plane that passes through the cone's
vertex and is perpendicular to its base, as in the picture below. What is
produced from this intersection?
A. A single line
B. A pair of intersecting lines
C. A point
D. A pair of parallel lines
Answers
When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.
How to know what is formed from a line intersecting a cone?The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.
This means the intersecting line forms a right angle with the base of the right circular cone.
Therefore, what is produced from this interaction is a pair of intersecting lines. The intersecting lines also have a point.
learn more on intersection here: https://brainly.com/question/11297403
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The members of the Math Club need to elect a president and a vice president. They determine that there are a total of 272 ways that they can fill the positions with two different members. How many people are in the Math Club
Answers
Answer:
544
Step-by-step explanation:
EASY JUST MULTIPLY!!!
multiply your total of ways to fill the position, by how many members!
so... 272 x 2 = 544 hopes this helps!!
Abag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
a. 9 b. 4/3 c. 1/4 d. 3/4
Answers
Answer:
A: 9
Step-by-step explanation:
if p is red and green
Answer:
--------------------------HeyA-------------------------
GiveN :
Total no.of marbles : 12Total no.of red marbles : 8 Total no.of blue marbles : 3Total no.of green marbles : 1To FinD :
P ( not blue )SolvinG :
- First step is to find out P( blue )
P ( blue ) = 3 / 12 = 1/4- Now , find out P ( not blue )
P ( not blue ) = 1 - 1/4 = 3/4- Option D [ 3/4 ] is the right option.
--------------------HappY LearninG <3 --------------
whats the answer to 3x1/2
Answers
Answer:
1.5
Step-by-step explanation:
3×1/2
3×1/2=
3/1×1/2
3/2= 1.5
The fabric store is having a sale the price of every item in the store has been reduced 30% which equation show the proportional relationship between the regular price of an item at the fabric store and its sale price, s?
Answers
Please hurry!
The diagram shows two squares constructed on the sides of a rectangle. What is the area of C?
Square A=6 ft2
Rectangle B=5 ft2
Don’t mind the writing
Answers
Answer:
25/6
Step-by-step explanation:
a²=6 -> a=✓6 (a must be positive so reject negative solutions)
ab=5 -> b = 5/✓6
thus area of C is b² = 25/6
35 is what percent of 150
Answers
[tex]~~~~~~150\times x\% = 35\\\\\implies 150 \times \dfrac{x}{100} = 35\\\\\implies \dfrac{3x}{2}=35\\\\\implies 3x = 35\cdot 2\\\\\implies 3x = 70\\\\\implies x = \dfrac{70}{3}\\\\\implies x =23.\overline{3}\\\\\text{So, 35 is}~ 23.\overline{3}\%~ \text{of} ~150.[/tex]
Lindsey bought supplies for a class project and brought the receipt to school. The 6 items cost:
$5.00$3.00$8.00$5.00$4.00$5.00
What was the mode of the prices of the items?
Answers
Answer:
$5
Step-by-step explanation:
$5 appeared more in the prices
Answer:
5 dollars
Step-by-step explanation:
cuz I just know
Solve. 3(a – 5) – 6 = –15
Answers
Answer:
a=6
Step-by-step explanation:
distribute:
3a-15-6=-15
combine like terms:
3a-21=-15
add 21 to each side:
3a=6
divide by 3:
a=2
2) Find the surface area of the cube. You should have at least 2 steps shown
Answers
Answer: 294 square millimeters
Step-by-step explanation:
Each side of the cube is 7 mm.
First, find the area of one face. The formula for the area of a square is [tex]s^2[/tex]. 7 mm squared is 49 square millimeters.
A cube has 6 faces, so multiply the area of one face by 6. 49*6 = 294 square millimeters
Time Left:1:32:30
Ryan Harris: Attempt 1
(06.07 MC)
The cost and customer rating of 15 cars is shown on the scatterplot. The cars are
rated on a scale of 0 to 100.
120
100
80
Rating
60
Answers
Based on the relationship between the ratings and cost, the association is a positive correlation. The data point that affects the appropriateness of using linear regression is $4,200 and 15 rating.
A car that is cost effective and rated highly is the data point (3,500,100).
What does the scatterplot show on cost and customer rating?In general, the cost of cars shown is higher when the customer reviews are high as well. This shows a positive correlation between cost and customer ratings.
The car at (4,200, 15) is an outlier because it is expensive and yet has low ratings. It would therefore affect a linear regression model if one is used to fit the data shown.
The car at (3,500, 100) is cost-effective and rated high because it is not as expensive as a lot of other cars, and yet has the highest customer rating of 100.
Find out more on positive correlations at https://brainly.com/question/17104826.
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1 litre is approximately 1.75 pints,
1 gallon = 8 pints
calculate the approximate number of gallons that are equal to 48 000 cm3
Answers
Answer:
10.5 gallons are equal to 48000 cm3
Step-by-step explanation:
What is the slope of the line passing through the points (4, 5) and (0, -7)? Show all your work.
Answers
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 5 ) and (x₂, y₂ ) = (0, - 7 )
m = [tex]\frac{-7-5}{0-4}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
rise over run
you can also use the y2-y1/x2-x1 but these numbers where small enough where graphing can help visually
1) x2 + 5x + 4 = 0
a =
b=
C =
vb2 - 4ac =
-
Answers
Answer:
9
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) then the discriminant is
Δ = b² - 4ac
x² + 5x + 4 = 0 ← is in standard form
with a = 1, b = 5 , c = 4 , then
b² - 4ac = 5² - (4 × 1 × 4) = 25 - 16 = 9
The diameter of the circle above is 86 cm. What is the circumference of the circle? (Use = 3.14.)
A. 135.02 cm
B. 5,805.86 cm
C. 11,611.72 cm
D. 270.04 cm
Answers
Answer:
D
Step-by-step explanation:
Circumference = pi × diameter
what is the slope of the line that contains the points (-2,6) and (2,-2)
Answers
Answer:
[tex]-\frac{8}{4}[/tex]
Step-by-step explanation:
To find slope from 2 points: [tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-2-6}{2-(-2)} =-\frac{8}{4}[/tex]
What is Limit of StartFraction StartRoot x + 1 EndRoot minus 2 Over x minus 3 EndFraction as x approaches 3?
Answers
Answer:
[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \boxed{ \frac{1}{4} }[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \lim_{x \to c} x = c[/tex]
Special Limit Rule [L’Hopital’s Rule]:
[tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]:
[tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Derivative Rule [Basic Power Rule]:
Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify given limit.
[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3}[/tex]
Step 2: Find Limit
Let's start out by directly evaluating the limit:
[Limit] Apply Limit Rule [Variable Direct Substitution]:[tex]\displaystyle \lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} = \frac{\sqrt{3 + 1} - 2}{3 - 3}[/tex]Evaluate:
[tex]\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \frac{\sqrt{3 + 1} - 2}{3 - 3} \\& = \frac{0}{0} \leftarrow \\\end{aligned}[/tex]
When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:
[Limit] Apply Limit Rule [L' Hopital's Rule]:[tex]\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\\end{aligned}[/tex][Limit] Differentiate [Derivative Rules and Properties]:
[tex]\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \leftarrow \\\end{aligned}[/tex][Limit] Apply Limit Rule [Variable Direct Substitution]:
[tex]\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \leftarrow \\\end{aligned}[/tex]Evaluate:
[tex]\displaystyle \begin{aligned}\lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x - 3} & = \lim_{x \to 3} \frac{(\sqrt{x + 1} - 2)'}{(x - 3)'} \\& = \lim_{x \to 3} \frac{1}{2\sqrt{x + 1}} \\& = \frac{1}{2\sqrt{3 + 1}} \\& = \boxed{ \frac{1}{4} } \\\end{aligned}[/tex]
∴ we have evaluated the given limit.
___
Learn more about limits: https://brainly.com/question/27807253
Learn more about Calculus: https://brainly.com/question/27805589
___
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Without using l'Hopitâl's rule, we can instead rationalize the numerator.
[tex]\dfrac{\sqrt{x+1} - 2}{x-3} = \dfrac{\left(\sqrt{x+1}-2\right)\left(\sqrt{x+1}+2\right)}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac{(x+1)-4}{(x-3)\left(\sqrt{x+1}+2\right)} = \dfrac1{\sqrt{x+1}+2}[/tex]
We've removed the discontinuity at [tex]x=3[/tex], so the limand is continuous and
[tex]\displaystyle \lim_{x\to3} \frac{\sqrt{x+1}-2}{x-3} = \lim_{x\to3} \frac1{\sqrt{x+1}+2} = \frac1{\sqrt{3+1}+2} = \boxed{\frac14}[/tex]
urgent help with a geometry assignment!!
Answers
Answer: 480 and 253.2
Step-by-step explanation:
For the first one we want to do (12 x 5 / 2) x 16 which equals 480.
For the next question, the answer is 253.2 because 2πrh is the formula of lateral area. If we just plug in the numbers it's (2 x 3.14 x 4.8 x 8.4) = 253.2cm
Which of the following points on the number line would be the plotted point for √5
Answers
Answer:
Point C
Step-by-step explanation:
The correct answer would be about 2.2 so C is the closest.
pleasee help me! One circle has a circumference of 12 cm. Another circle has a circumference of 32 cm. What is the ratio of the radius of the smaller circle to the radius of the larger circle? 3:8 8:3 1:3 3:1
Answers
Answer:
A: 3;8
Step-by-step explanation:
12/2 = 6
32/2 = 16
6/2 = 3
16/2 = 8
3:8
A microscope shows you an image of an object that is 80 times the object's actual size. So the scale factor of the enlargement is 80. An insect has a body length of 9 millimeters. What is the body length of the insect under the microscope?
Answers
Answer:
80
Step-by-step explanation:
Question 5 (1 point)
(07.07)
Find the product of (x + 3). (1 point)
o a
x2 + 6x + 9
x2 - 6x + 9
Ос
x2-9
d
x2 + 9
Answers
Answer:
a) x² + 6x + 9
Step-by-step explanation:
When we square something, we multiply it by itself:
⇒ (x + 3)² = (x + 3)(x + 3)
Using the FOIL method: (a + b)(c + d) = ac + ad + bc + bd
⇒ (x + 3)(x + 3) = x² + 3x + 3x + 9
= x² + 6x + 9
a.
[tex]\huge{{x}^{2} + 6x + 9}[/tex]
Step-by-step explanation:
Using Binomial Theorem:
[tex]\boxed{{(a+b)} ^n= \sum_{k=0}^{n}\binom{n}{k} a^{n-k}b^{k}}[/tex]
.
.
.
[tex](a+b) ^2 =a^{2} + 2ab +b^{2} [/tex]
The answer seems to be [tex]x^{2} + 6x + 9[/tex]...
3 Najid paid $10 000 income tax in a year. What was his salary that year?
Answers
Answer:
income tax=13% of total salary
Step-by-step explanation:
Here,
let salary be 'x'
Now,
13%of x = $10 000
13/100 × x = $10 000
13x = 1000000
x=10 00000/13
Therefore x =76,923.0769
His salary that year was 76,923.0769
if someone in 2022 is now 89, how old were they in 1971?
Answers
Answer:38
Step-by-step explanation:
they were born in 1933 and 1971 minus 1933 is 38.
does someone mind helping me with this question? Thank you!
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: a = \pi {r}^{2} [/tex]
where, r = d/2 = 6/2 = 3 ft[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: a = 3.14 \times 9[/tex]
[tex]\qquad \sf \dashrightarrow \: a = 13.26 \: \: ft {}^{2} [/tex]
Answer: 28.26
Step-by-step explanation:
D = 6
R = 3
3.14 x 3 x 3 = 28.26
5) Find the x-intercept and the y-intercept of the equation: 8x - y = -24.
Answers
Answer:
First we have to turn it into slope intercept form which is y = mx + b.
we need to isolate y. To do this, we have to subtract 8x from both sides to get
-y = -8x - 24
-25 is the y intercept and -8 is the slope.
Step-by-step explanation:
A circle with some chord, where a diameter of a circle intersects the
midpoint of that chord. Prove: The diameter is perpendicular to the chord.
Answers
Answer:
Step-by-step explanation:
Answer:
This is a theorem that says "if a diameter of a circle bisects a chord, then it is perpendicular."
Step-by-step explanation:
All 6 members of a family work. their hourly wages (in dollars) are the following.
18, 14, 35, 34, 11, 26
assuming that these wages constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.
Answers
The standard deviation of the population dataset is 9.35
How to determine the standard deviation?The dataset is given as:
18, 14, 35, 34, 11, 26
Start by calculating the mean using:
Mean = Sum/Count
This gives:
[tex]\bar x = (18+ 14+ 35+ 34+ 11+ 26)/6[/tex]
Evaluate
[tex]\bar x = 23[/tex]
The standard deviation is then calculated using:
[tex]\sigma = \sqrt{\frac{\sum (x - \bar x)^2}{n}}[/tex]
This gives
[tex]\sigma = \sqrt{\frac{(18 - 23)^2 + (14- 23)^2 + (35- 23)^2 + (34- 23)^2 + (11- 23)^2 + (26- 23)^2}{6}}[/tex]
Evaluate
[tex]\sigma = \sqrt{\frac{524}{6}}[/tex]
This gives
[tex]\sigma = 9.35[/tex]
Hence, the standard deviation of the population is 9.35
Read more about standard deviation at:
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Y-intercept: (0,
y=-2x2 – 16x – 34
What is the y intercept?
Answers
Answer: Solve for Y
y = -16x - 38
And then y intercept is
(0, -38)
Step-by-step explanation:
Help me pls answer pls I’m pls
