Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
Answers
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
How to calculate errors did Parul make?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.
We are given
-5x - 3.5>6.5
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
-5x - 3.5+3.5>6.5+3.5
-5x>10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
-5x/5<-50/-5
we get
x<10
so,
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
The complete question is : Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below. What errors did Parul make? Check all that apply. She added 3.5 to both sides when she should have subtracted. She should have divided both sides by as her first step. She divided one side by -5 while multiplying the other side by -5. She did not change the > symbol to a < symbol. She used a closed circle instead of an open circle on the number line.
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Related Questions
Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points. Write an equation to find the total number of questions (q) on Tim’s math test
Answers
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?
Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
According to the given question:
Let the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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The administrative assistant at a software company often provides breakfast when there is a morning meeting. For last week's sales meeting, she purchased 4 dozen doughnuts and 1 dozen croissants, spending a total of $34. In preparation for yesterday's safety meeting, she spent $52 on 7 dozen doughnuts and 1 dozen croissants. Write a system of equations that could be used in this situation.
Hint: I JUST WANT THE EQUATIONS NOT THE FINAL SOLUTION.
Answers
A dozen of doughnuts cost $6 and a dozen of croissants cost $10.
What is meant by a linear equation?A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero.
Such an equation's solutions are the values that, when used as placeholders for the unknowns, result in the equality being true.
When there are just two variables, it is possible to interpret each solution as the Cartesian coordinates of a particular point on the Euclidean plane. In the Euclidean plane, a linear equation's solutions are represented by lines, and each line can be thought of as the collection of all the solutions to a linear equation with two variables.
Let,
The cost of dozen doughnuts be x
And the cost of dozen croissants be y
Given,
4x+y=34
7x+y=52
By solving both the equations, we get
-3x=-18
x=6
4x+y=34
4(6)+y=34
24+y=34
y=10
Therefore, a dozen of doughnuts cost $6 and a dozen of croissants cost $10.
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(need help asap please this is urgent)
Use the systems of inequalities graphed below to answer the questions.
what is the inequality symbol of the green line?
-y is greater than ax+b -y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
what is the inequality symbol of the green line?
-y is greater than ax+b
-y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
is the point (-3, -5) a solution to the system of inequalities?
-yes -no
is the point (1,6) a solution to the system of inequalities?
-yes -no
Answers
Answer:
Green line: y is greater than or equal to ax+b
Purple line: y is less than ax+b
(-3, -5) : Yes
(1, 6) : No
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Green line
From inspection of the given graph, the green line is a solid line and the shading is above the line.
Therefore, the inequality symbol of the green line is ≥.
"y is greater than or equal to ax+b"
Purple line
From inspection of the given graph, the purple line is a dashed line and the shading is below the line.
Therefore, the inequality symbol of the purple line is <.
"y is less than ax+b"
The solutions to a graphed system of inequalities are found in the overlapping shaded region.
Yes, point (-3, -5) is a solution to the system of inequalities as this point is in the overlapping shaded region.
No, point (1, 6) is not a solution to the system of inequalities as this point is not in the overlapping shaded region.
how manys pounds of mixed nuts that contain 20% peanuts must eugene add to 16 pounds of mixed nuts that contain 70% peanuts to make a mixture with 60% peanuts?
Answers
By resolving equations, we know that we can add 10 pounds of mixed nuts that include 20% peanuts.
What are equations?An equation is a statement that demonstrates the equality of two mathematical expressions, according to mathematics.
For instance, the equation 3x + 5 = 14 is composed of equation 2 3x + 5 and 14, which are separated by the equal sign.
So, we require x pounds of the mixed nuts in total.
This mixture contains 0.70 pounds of peanuts.
The 20% mix, or 0.20*15, is made out of 3 pounds of peanuts.
Equation obtained: 0.70 x + 3 = 0.40(x + 15)
Solve the equation as shown below:
0.70 x + 3 = 0.40(x + 15)
0.70 x + 3 = 0.40(x + 15)
0.70x + 3 = 0.40x + 6
0.70x - 0.40x = 6 - 3
0.30x = 3
x = 10 pounds
Therefore, by resolving equations, we know that we can add 10 pounds of mixed nuts that include 20% peanuts.
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what is the value of b?
Answers
Answer:
b = 44°
Step-by-step explanation:
Opposite angles are congruent.
The school events committee is planning to buy a banner and some helium balloons for graduation night. A store charges them $35 for the banner and $3.50 for each helium balloon. If the committee has at most $125 to spend, how may helium balloons can they buy?
Answers
Answer: About 25
Step-by-step explanation: So, to find how many helium balloons, we need to subtract 35 from 125, then divide it by 3.50. So, 125-35 = 90. So, 90 / 3.50 = 25.714285714285715. So, we are around 25.7 up to 26. But, we can't do this. This is because they can't spend over $91 on balloons. So, we have to round down. If it was 26, they would spend $91, 1 dollar over their budget. So, it would be about 25, which would be 87.50. So, they would have $3.50 left over.
How do I find the value in n of the equation 40+n=50+22
Answers
Ahmad drove 350 miles in 5 hours.
At the same rate, how many miles would he drive in 7 hours?
Answers
Answer:
490 miles
Step-by-step explanation:
Since Ahmad is driving 350 miles in 5 hours, he's averaging 70 miles per hour.
350/5 = 70 mph
Driving 7 miles at 70 mph:
7 x 70 = 490 miles
Answer: 490 miles!
Step-by-step explanation:
350 x 7hrs divided by 5hrs would be = 490miles
multiple 350 and 7 ( 350x7) which will equal 2450 then divide by 5 and you will get 490 milesHow did I get 490? or why didn't you do 350 x 5?
Well because the question asks how many miles would he drive in 7 hours? you will need to multiple the droven miles which is 350miles because that is part of the getting answer, and the question of having to know how many miles would he drive in 7 hours, you wouldn't do 350 x 5 because its not asking " Ahmad drove 350 miles in 5 hours, how many miles would he drive in 5 hours? and which would equal 250 which not correct because it doesn't make sense if he's drove 350 miles in 5 hours and then drove 250miles in 7 hours, back to the explanation, after multiplying 350 into 7 you will end up at 2450, no this isn't the answer you need to divide because it would take more than 7 hours to drive 2450 miles, next you divide by the hours driven in 350 miles which in this in this case would be 5 because your diving 2450 by 5 because sense u cannot get the answer by multiplying 350x5 so this is time where your gonna use the 5 because 350 x 7= 2450 is too large in miles for 7 hours your gonna divide the 2450 to lower it down to 490 miles, doesn't that sound more accurate? the miles increase by 1.4 ( 140 miles ) so another way u could have gotten the answer was by doing 350 + 140 = 490 but however you would need to know how much the miles have increase which u can do by 490 - 350 which equals to 140 miles.
Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Ariana to end up with $233,000?
Answers
The interest rate required for Ariana to end up with $233,000 is approximately 6.6%.
What interest rate is required for Ariana to end up with $233,000?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $62,000Accrued amount A = $233,000Compounded continuously Time t = 20 yearsInterest rate r = ?Using the formula A = P(1 + r/n)^(n*t).
Solve for r when interest is compounded continuously.
r = In( A / p ) / t
Plug the given values into the above equation.
r = In( $233,000 / $62,000 ) / 20
r = In( $233,000 / $62,000 ) / 20
r = 0.0661952
Now, convert r to R as a percentage
R = r × 100%
R = 0.0661952 × 100%
R = 6.6%
Therefore interest rate needed by Ariana to the nearest tenth of a percent is 6.6%.
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Find the surface area of the cylinder in terms of pi
Answers
Answer:[tex]522\pi[/tex] [tex]sq. inches[/tex]
Step-by-step explanation:
formula for surface area of cylinder =[tex]2\pi r^{2} +2\pi rh[/tex] , where r is radius of cylinder given 9 inches and h is height of the cylinder which is 20 inches.putting the values we get,[tex]2\pi (9)^{2} +2\pi (9)(20)\\162\pi +360\pi \\=522\pi sq. inches[/tex]
John's bank account was overdrawn. The status of his account was $-141. He did not realize the problem and wrote another check for $29. The bank charged him a $15 fee for being overdrawn. What was the new status of John's account at this point ?
Answers
Answer:
$-185
Step-by-step explanation:
If Johns bank account is at $-141, and he continues to use money, then the equation would look something like this:
-141 + -29 + -15 =?
It's simple! Just add the numbers together!
141 + 29 = 170
170 + 15 = 185
Johns bank account status is now $-185.
The area of a circle is 113.04 square miles. What is the circle's radius?
Use 3.14 for л.
Submit
miles
Answers
Answer: 6 miles exactly
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
A=πr^2
113.04=3.14×r^2
113.04/3.14=r^2
36=r^2
√36=r
r=6
Identify the null and alternative hypotheses for the following problems.
a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
b. Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar.
c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.
Answers
The null hypothesis is it takes a customer less than or equal to 25 minutes to eat lunch.
The alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.
What is null and alternate hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. The alternative hypothesis is one of the suggested hypotheses in statistical hypothesis testing.
We are given a statement,
The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
According to null hypothesis, There is no difference or change
Hence the null hypothesis is, it takes a customer less than or equal to 25 minutes to eat lunch.
Where as in alternate hypothesis, There should be a difference of change
Hence the alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.
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create three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
Answers
The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.
Quadratic equation:
In math, quadratic equation is the algebraic equation of the second degree in x.
The general form of quadratic equation is
ax² + bx + c = 0,
where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).
Given,
Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,
Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,
=> y = (x-4)² – 1,
=> y = -(x-4)² + 1,
=> y = -3(x-4)² + 3.
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A car starts out at a speed of 50mph. A second car starts out 3 hours later at 65mph to overtake the first one. How many hours will the first car be on the road at the point where it is overtaken?
50 PTS! Please answer quick. you will get brainliest
Answers
Answer:
13 hours----------------------------------
Both cars will make same distance but the first one will be on road for 3 more hours.
Let the number of hours the first car in travel be x.
Then set an equation:
50x = 65(x - 3)50x = 65x - 19565x - 50x = 19515x = 195x = 13determine whether each of these pairs of sets are equal
a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}
Answers
These pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅} are equal, not equal and not equal respectively
How to determine the equality and not equality of set of numbers?The given pairs of sets of numbers are
a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}
To determine the reasons for the answers we have
(a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}
All the number are distinct elements without any repetition is the same in both sets.
This implies that the sets are equal
b) {{1}},{1,{1}}
From the second set of numbers, the number of elements is not the same in both sets. The number of elements in the two sets are 1 and 2.
This therefore means that the pair of numbers are not equal
c) ∅,{∅}
In the third set of numbers, the number of elements is not the same in both sets.
The number of elements in the pairs are 0 and 1 in each of the sets . This implies that the pair of sets of numbers are not equal
In conclusion these pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅} are equal, not equal and not equal respectively
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Find the equation of the line joining the points (2,-8) and (5,6)
Answers
Answer:
y=3/2x-11
x,=2 and x2=5y1= -8 and y2= 6change in y over change in x get x use the formulae[tex]y = mx + c[/tex]thats the formular u got mfind c using one pairwill someone help me with this geometry please
Answers
59/19 = 3.105263157894737
23 x 3.105263157894737 = 71.4 (rounded to nearest tenth)
Answer:
[tex]\huge\boxed{\sf HF=71.4}[/tex]
Step-by-step explanation:
If ΔCDE is similar to ΔFGH, their sides are proportional.
So,
[tex]\displaystyle \frac{23}{HF} =\frac{19}{59} \\\\Cross \ Multiply\\\\23 \times 59 = 19 \times HF\\\\1357 = 29HF\\\\Divide \ 19 \ to \ both \ sides\\\\1357/19 = HF\\\\71.4 = HF\\\\HF=71.4\\\\\rule[225]{225}{2}[/tex]
Which one doesn't belong: 2 PARTS TO 5 PARTS, 2 FOR EACH 5, 2 OUT OF EVERY 5, OR 2 FOR EVERY 5? Explain your reasoning.
Answers
2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
2 parts to 5 parts
2 for each 5
2 out of every 5
2 for every 5
Division has two parts the numerator and denominator.
The numerator represents the part and denominator represents the whole.
2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
Hence, 2 parts to 5 parts does not belong to the given options and 2 for every 5 does not matches.
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g(x) = -2(3x + 4)(x - 1)(x – 3)^2 be a polynomial function.
State the leading term, degree, and if the leading coefficient is positive or negative.
I mostly understand this, but don't know how the square affects things.
Answers
The polynomial is of degree 4, and the leading coefficient is -6.
How to find the degree of the polynomial?A polynomial of degree N with a leading coefficient A and the zeros {x₁, x₂, x₃, ..., xₙ} (notice that we have as many zeros as the degree of the polynomial) is written as:
p(x) = A*(x - x₁)*...*(x - xₙ)
Here we have the polynomial:
g(x) -2*(3x + 4)*(x - 1)*(x - 3)²
We can expand this as:
g(x) = -2*(3x + 4)*(x - 1)*(x - 3)*(x - 3)
Think that as we have "two zeros" at x = 3.
So we have 4 factors, then the degree of the polynomial is 4.
To find the leading coefficient we just need to look at the term that comes by multiplying all the terms with "x", we will get:
-2*(3x)*x*x*X
-6*x⁴
The leading coefficient is negative.
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Annual high temperatures in a certain location have been tracked for several years. Let
X
represent the year and
Y
the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).
x y
2 20.35
3 21.6
4 21.45
5 22.8
6 23.25
7 20.6
8 20.95
9 22.1
10 18.85
11 21.1
12 17.75
13 19.5
14 19.25
15 17.1
Answers
Answer:
haha
Step-by-step explanation:
Write a polynomial function f of least degree that
has rational coefficients, a leading coefficient of 1,
and the given zeros.
5. -4, 1, 2
6. -6, -1, 3
7. 7, 1+ i
8. 2i, 1-i
Answers
The polynomial functions of the given zeroes are:
5) f=x³+x²-10x+8
6) f=x³+4x²-15x-18
7) f=x²-x(1-i-7)+7i+7
8) f=x²-x(1-i)+2i+2
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
5) The given zeroes are -4, 1, 2
(x+4)(x-1)(x-2)=0
x³+x²-10x+8=0
6) (x+6)(x+1)(x-3)=0
x³+4x²-15x-18=0
7) (x-7)(x-(1+i))=0
x²-x(1-i-7)+7i+7=0
8) (x-2i)(x-(1-i))=0
(x-2i)(x-1+i)=0
x²-x(1-i)+2i+2=0
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Solve the following system of equations.
-2x+y = 9
5x+y = -12
Answers
Answer: (x,y) = (-3,3)
Step-by-step explanation:
1. Solve the equation for y
y=9+2x
2. Substitute the given value of y into the equation 5x+y= -12
5x+9+2x= -12
3. Solve x variable
x= -3
4. Substitute the given value of x into the equation y=9+2x
y=9+2x(-3)
5. Solve the equation for y
y=3
Final answer:
x=-3
y=3
You take your car in to get the oil changed. It costs $40 for the oil and $25 an hour for labor.
Write a linear equation that represents the total cost in dollars of the oil change if it requires x hours of labor.
Answers
A linear equation that represents the total cost in dollars of the oil change is Y = 25X + 40
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Linear Equations in Standard Form
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
Given :
Cost of the oil (calculated once) = $40
Cost of labour (calculated per hour) = $25
Thus , a linear equation that represents the total cost in dollars of the oil change if it requires x hours of labor can be expressed as Y = 25X + 40 where X represents no . of working hours of labour and Y represents total cost .
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Angela uses 6.1 pints of white paint and blue paint to paint her bedroom walls.
4
5
of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answers
Blue paint she has used in her bedroom walls is, 1.22 paints.
Fraction definition?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure below the line.
The walls of Angela's bedroom are painted with 6.1 paints each of blue and white paint.
So to find the blue paint ,
she used 4/5 of whole pigments as white paint.
Firstly we multiple it by whole paint that is 6.1 and find white paint and then whole paint subtracted with white paint will give blue paint.
She painted using 4/5 of the whole amount of pigments as white paint
That amount in pints of white paint is equal to
4/5 * 6.1.
= 4.88 paints of white
The number of paints used to paint blue is therefore:
whole paint - white paint.
= 6.1 - 4.88
As a result, 1.22 blue paints she has used.
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State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement
Answers
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.
Now in the given figure, the side YD is similar and equal to the side OD so option C will be the correct answer.
Hence the information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.
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Hey I need help understanding how to solve application problems involving rational equations
Answers
If the figure above is rotated 90° counterclockwise, in which quadrant will it appear?
A. I
B. II
C. III
D. IV
Answers
Answer: Depends on what quadrant it starts in/on.
Step-by-step explanation:
Quadrant 1 is the top-right corner.
Quadrant 2 is the top-left corner.
Quadrant 3 is the bottom-left corner.
Quadrant 4 is the bottom-right corner.
Depending on what quadrant you started on will determine what quadrant you're on after rotating 90 degrees counter-clockwise.
Dilating point A using center C and scale factor 2.5 gives A'. Dilating point B using Center C and scale factor 2.5 gives image B'. What can you say about line AB and A'B'? What is the length of segment A'B'?
Answers
line AB is original figure, line A'B' is transformed figure. the length A'B' is given by √[(2.5x₂-2.5x₁)²+(2.5y₂-2.5y₁)²]
What is dilation?
A process of transformation in which an image or figure changes from the original shape.
What is dilating point?
The point which is acted as the center for all contraction and expansion is termed as dilation point.
let, point A is (x₁,y₂) and point B is (x₂,y₂). By using scale factor 2.5, both A and B transformed to the position A' and B'.
hence, A' = (2.5x₁, 2.5y₁) and B'=(2.5x₂,2.5y₂)
now length of A'B' =√[(2.5x₂-2,5x₁)²+(2.5y₂-2.5y₁)²]
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How can you find value of n in this equation 40+n=55+22
Answers
Answer:
n=37
Step-by-step explanation:
The first thing to do would be to eliminate the 40 from the left side of the equation, leaving n by itself. Then, you subtract the 40 from the 55, then add the result to 22.
hope this helps!!! :3