Question 4c. Want to clarify something I want to ask right why does it become 3y square +6y-y-2
Answers
Answer:
Explanation:
Given the expression:
[tex]3y^2+5y-2[/tex]We want to write the given expression in the form:
[tex](ay-b)(y+c)[/tex]That is, to factorize the expression.
When an expression is to be factorized, follow the steps below:
Step 1: Multiply the coefficient of x² and the constant.
[tex]-2\times3y^2=-6y^2[/tex]Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6
[tex]\begin{gathered} 6y\times-1y=-6y^2 \\ 6y+-y=5y \end{gathered}[/tex]Step 3: Rewrite the middle term, 5y with those numbers.
[tex]\begin{gathered} 3y^{2}+5y-2 \\ =3y^2+6y-y-2 \end{gathered}[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =3y(y+2)-1(y+2) \\ =(3y-1)(y+2) \end{gathered}[/tex]Related Questions
Three-fourths of a box of chocolate is left over. Benjamin eats 2/3 of the leftover chocolate. What fraction of a box does Benjamin eat?
Answers
We will have that he ate the following amount:
So, he ate the following:
[tex]x=(\frac{3}{4})(\frac{3}{4})\Rightarrow x=\frac{1}{2}[/tex]He ate a total of 1/2 of the chocolate.
Which inequality is represented by the number line below?
Answers
An inequality which is represented by the number line above is: x < -7.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
The rules for writing an inequality.In Mathematics, there are four (4) rules that are generally used to write an inequality and these include the following:
The circle/dot on a number line should be filled when the inequality symbol is (≥ or ≤).The circle/dot on a number line should not be filled when the inequality symbol is (> or <).When the arrow points to the left on a number line, the inequality is either (≤ or <).When the arrow points to the right on a number line, the inequality is either (≥ or >).Next, we would apply the aforementioned rules to write the solution to the inequality shown in the number line above:
x < -7
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Determine whether the statement can be assumed from the given figure.
Yes/no
Share/do not share
Answers
Answer:
No
do not share
Step-by-step explanation:
Two rays make up angle 7 and two DIFFERENT rays make up angle 8 (angle 6 is in between them) If they were a linear pair with a shared side, it would look like a loooong line with a ray sticking out that makes two angles. In the image, Angle1 and Angle2 are a linear pair. And Angle1 and Angle4 also.
They do not share at all.
Two students attempted to solve the literal equation[tex]a=1\fra/2(b+c)[/tex]
for c. Who solves it correctly? How do you know?
Answers
Express 4+-4as a complex number ( term of i) 4+-4
Answers
Complex numbers are numbers in the form
[tex]z=a+bi[/tex]where i represents the imaginary number defined as the square root of minus one.
[tex]i=\sqrt{-1}[/tex]We call a as the real part of the complex number and b the imaginary part.
We want to rewrite the number
[tex]\sqrt{4}+\sqrt{-4}[/tex]in terms of the imaginary constant.
Using the following property
[tex]\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}[/tex]We can rewrite the second term of our sum as
[tex]\sqrt{-4}=\sqrt{(-1)(4)}=\sqrt{-1}\sqrt{4}[/tex]Then, our number can be rewritten as
[tex]\sqrt{4}+\sqrt{-4}=\sqrt{4}+\sqrt{-1}\sqrt{4}[/tex]Using the definition of the imaginary unit we can rewrite our number as
[tex]\sqrt{4}+\sqrt{-1}\sqrt{4}=\sqrt{4}+\sqrt{4}i[/tex]Then, we can rewrite the square roots as
[tex]\sqrt{4}=2[/tex]The simplified version of our number is
[tex]\sqrt{4}+\sqrt{-4}=2+2i[/tex]Write a quadratic function for the following characteristics
Answers
Answer:
[tex]y=x^2+6x-16[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given points on the curve:
(-8, 0)(-6, -16)(2, 0)The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.
Therefore, the x-intercepts of the given function are -8 and 2.
Substitute these into the intercept formula:
[tex]\implies y=a(x-(-8))(x-2)[/tex]
[tex]\implies y=a(x+8)(x-2)[/tex]
Substitute the other given point (-6, -16) into the equation and solve for a:
[tex]\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}[/tex]
Therefore, the equation of the function in intercept form is:
[tex]y=(x+8)(x-2)[/tex]
Expand to standard form:
[tex]\implies y=x(x-2)+8(x-2)[/tex]
[tex]\implies y=x^2-2x+8x-16[/tex]
[tex]\implies y=x^2+6x-16[/tex]
Therefore, the quadratic function in standard form is:
[tex]\boxed{ y=x^2+6x-16}[/tex]
Carter budgets
18
% of his salary for food. His salary is $
3
,
900
. How much money does he need to budget for his food?
Answers
Answer:
3900*18%=702
Step-by-step explanation:
If rocks along the furnace creek fault have been offset 30 miles over 10 million years, what is the rate of plate motion in cm/year. (Hint: Rate x Time = Distance, and there are 5280 feet in one mile, and 2.54 cm. in one inch.)
Answers
The rate of plate motion in cm/year is equal to 3.3528 × 10⁻³ cm/year.
What is a conversion factor?A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 mile = 5280 feet
30 miles = X feet
Cross-multiplying, we have:
X = 30 × 5280
X = 158,400 feet.
Next, we would convert the value in feet to inch and then to cm as follows:
Distance = 158,400/12 = 13,200 inches.
In centimeters (cm), we have:
1 inch = 2.54 cm
13,200 inches = Y cm
Cross-multiplying, we have:
Distance, Y = 13,200 × 2.54
Distance, Y = 33,528 cm.
Now, we can determine the rate of plate motion in cm/year:
Rate = Distance/Time
Rate = 33,528/10,000,000
Rate = 3.3528 × 10⁻³ cm/year.
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Find the charge Q that requires 96J of energy to be moved through a potential difference of 16V ?
Answers
6 Coulombs are needed to produce the 96J of energy.
Describe energy.Physics defines energy as the quantity of work or capability that may be applied to a thing to make it functional. Additionally, it refers to the capacity to exert force on an object as well as energy that is neither generated nor destroyed.
96 J of energy and a 16 V potential difference
Using the following formula, the work or energy is:
Work completed equals Charge x Potential Difference.
Charge = thus work completed/potential difference
Charge equals 96/16, or 6 Coulombs.
Therefore, 6 Coulombs of charged are needed to produce 96J of energy.
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(a) It takes 36 pounds of seed to completely plant a 6-acre field. How many pounds of seed are needed per acre?
Answers
Answer:
6
Step-by-step explanation:
The answer would be 6 since it would take 36 pounds of seed to plant a 6 acre field. That means you would need 6 pounds of seed for each acre since 36 ÷ 6 = 6
g(4) please answer asap
Answers
. Length of the rectangular prism is 4 ft. The height and width are both 3 feet. Find the surface area of the prism.
Answers
Ok, so
Here we have a rectangular prism with the following measures:
-Length = 4ft
-Height = 3ft
-Width = 3ft.
Remember that the surface area of a rectangular prism can be found using:
[tex]SA=2lw+2wh+2lh[/tex]Where "l" is the length, "w" is the width, and "h" is the height.
If we replace our values in the equation given, we got that:
[tex]\begin{gathered} SA=2(4)(3)+2(3)(3)+2(4)(3) \\ SA=24+18+24 \\ SA=66 \end{gathered}[/tex]Therefore, the surface area of the prism is 66 ft2.
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x)=0.4x^2 - 104x + 13,586. How many cars must be made to minimize the unit cost? Do not round the answer
Answers
Answer:
130 cars
Step-by-step explanation:
You want the value of x (the number of cars made) that minimizes the unit cost, given by C(x) = 0.4x² -104x +13586.
VertexThe minimum cost will be found at the vertex of this quadratic cost function. For quadratic ax²+bx+c, the vertex is found at x=-b/(2a).
The cost function has a=0.4 and b=-104, so the number of cars that must be made to minimize the unit cost is ...
x = -b/(2a) = -(-104)/(2(0.4)) = 104/0.8
x = 130
130 cars must be made to minimize the unit cost.
__
Additional comment
A graphing calculator can plot the cost function and show you the coordinates of the minimum cost. The attachment shows the minimum cost per car is $6826 when 130 cars are made.
The depth of a rain puddle D(t) is given in inches, and t is given in minutes. If the depth is changing with respect to time, which expression gives the rate of change at which the depth is changing at 1 minute? D″(1)D″(0) − D″(2)D′(1)D(0) − D(2)
Answers
The derivative evaluated at t=1 minute will give us the rate of change (or the slope) of the line equation which approximate the function at that point. In other words, the rate of change is given by
[tex]m=\frac{dD(t)}{dt}|_{t=1}=D^{\prime}(1)[/tex]Therefore, the answer is option 3 from top to bottom.
Simplify the fraction
18
60
as much as possible.
3
10
18
60
12
54
Answers
Answer:
3/10
Hope this helps!
Have a good day :)
HELPPPP!
Does the frequency distribution given appear to be normal?
Score ---Frequency
65-69 4
70-74 5
75-79 6
80-84 4
85-89 6
90-94 4
95-99 5
Yes, the frequencies preceding the maximum are roughly a mirror image of those that follow the maximum
No, there is not a concentration of frequencies in the middle
Yes, there is symmetry in the distribution
No, the frequencies increase, reach a maximum, then decrease
Answers
It should be noted that the frequency distribution given appear to be normal as D. No, the frequencies increase, reach a maximum, then decrease.
How to illustrate the information?It should be noted that the graph that's illustrated shows that there is a concentration of the data points in the middle.
It should be noted that this illustrates that isn't not normal and the bell shaped curve was illustrated.
Therefore, based on the information, the correct option is D.
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Use what you know about domain to select all of the following functions that could be the one graphed.
Answers
Using translation, the functions that could be the one graphed are given as follows:
y = sqrt(x) - 3.y = sqrt(x) - 1.What is a translation?A translation is when a function undergoes a change in it's definition, keeping the same shape and side length, just changing the position.
The possible translations are given as follows:
Translation down.Translation up.Translation left.Translation right.In the context of the graph of this problem, the parent function is the square root of x, defined as follows:
y = sqrt(x)
The domain of this function, as is the domain of the graph, is for non-negative values of x, hence:
x ≥ 0.
From the graph, the function was translated down a units, keeping the domain but changing the range, hence the translation has the following format:
y = sqrt(x) - a.
Hence the first two options can be correct, either with a = 1 or with a = 3.
What is the missing information?The information to solve this problem is given by the image at the end of the answer.
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a class has 30 cups of popcorn. they are filling individual bags with three-fourths cups of popcorn. write a number sentence to show how many bags they can fill with popcorn
Answers
If the clas has 30 cups and fills individual bags with three-fourths cups then the number of bags that can be filled
= 30 / (3/4)
= 30 * 4/3
= 40
Hence 40 bags can be filled with popcorn
Lisa earns $39 for 3 hours of babysitting what does she earn per hour of babysitting?
Answers
Answer:
13$
Step-by-step explanation:
just divide 39 by three.
39 dive by 3=13
13 x 3=39
Are the ratios 5:4 and 18:16 equivalent
Answers
Consider them in the form of fractions: 5/4 is in simplest form, and 18/16 cannot simplify to 5/4. Therefore, the two ratios are not equivalent.
If A(2, 2), B(6, 4), C(4, 4) and D(8, 6) are four points then prove that: AB= CD
Answers
THE ONLY WAY WE CAN PROVE THAT AB IS EQUAL CD IS BY CALCULATING THE DISTANCES AND THEN COMPARING THEM.
FOR AB
[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{(( {6- 2})^{2} + ( ({4 - 2})^{2} } \\ = \sqrt{( {4})^{2} +( {2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
THE DISTANCEAB IS GIVEN ABOVE.
NOW LET US CALCULATE DISTANCE CD
[tex] = \sqrt{ ({8 - 4)}^{2} + ({6 - 4})^{2} } \\ = \sqrt{ {(4})^{2} + ({2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
WE CAN SEE THAT DISTANCE AB AND DISTAMCE CD ARE EQUAL THERE SE CAN NOW SAY
AB=CD
One leg of a right triangle is 8 inches less than the hypotenuse. The other leg is 12 inches. Find the length of hypotenuse.
Answers
Answer:
13 in
Step-by-step explanation:
Let the hypotenuse be x. Then, by the Pythagorean theorem,
[tex](x-8)^2 + 12^2=x^2 \\ \\ x^2-16x+64+144=x^2 \\ \\ 16x=64+144 \\ \\ x=4+9 \\ \\ x=13[/tex]
Zachary has a container of worms for fishing.
When empty, the mass of the container is 225 grams. With the worms in
it, the container has a total mass of 751.4 grams. Each worm has a mass
of 11.2 grams. How many worms are in the container? Write and solve an
equation to model this situation.
Answers
Answer:
there are 47 worms in the container
Step-by-step explanation:
empty container- 225 g.
full container- 751.4 g.
1 worm- 11.2 g.
equation
(751.4-225)/11.2
751.4-225= 526.4
526.4/11.2= 47 worms
PLEASE HELP GEOMETRY 50 POINTS
Answers
Answer:
See below
Step-by-step explanation:
Alternate exterior angles are equal if the lines crossed by the transversal are parallel
15x + 9 = 21x - 27
9 + 27 = 21x - 15 x
x = 6 °
Need help with this question! Need help with showing work.
Answers
Solve each of the following equations using the Extended Square Root Property.
1. 8√x+7=16
x= _____________
2. √7x+4−3=0
x= _____________
3. 8√5x−7=16
x= _____________
Answers
Answer:
1. 81/16, 2. DNE(undefined), 3. 529/64
Step-by-step explanation:
[tex]1. \\8\sqrt{x} +7=16\\\\8\sqrt{x} =16-7-9\\\sqrt{x}=9/8\\x=(9/8)^2=81/64\\\\2.\\1. \\\sqrt{7x} +4-3=0\\\\\sqrt{7x} +1=0\\\sqrt{7x}=-1\\[/tex]
impossible because square root is always positive
[tex]3. \\8\sqrt{5x} -7=16\\8\sqrt{5x} =16+7=23\\\\\sqrt{5x} =23/8\\\\5x=(23/8)^2=529/64[/tex]
You use a juice mix to make orange juice.
You combine 12 ounces of the mix with 36 ounces of water.
Answers
Answer:
48
Step-by-step explanaause tion:
because there are 12 ounces in orange juce and 36 ounces of water combime them together 48
susan says that (-3)(-3)(-3) will be a positive answer. ryan says that the product will be a negative answer. who is correct use words and numbers in your response
Answers
Answer: Ryan is correct
Step-by-step explanation:
-3 multiplied by -3 makes a positive 9. Then you need to multiply that 9 by the other -3 which makes it a negative 27.
(-3) x (-3) x (-3)
9 x -3
-27
In a survey of 100 patients who reported at the hospital one day, it was found out that 70 of them complained fever, 50 complained stomach pains and 30 were injured. All 100 patients had at least all the complaints and 44 had exactly two of the complaints. How many patients had all the complaints?
Answers
Three patients had all the complaints.
What is a Set's Cardinal Number?In a finite set, the number of distinct elements is known as the cardinal number. It is written as n(A) and can be read as "the number of set elements."
Let's assume,
U is the set of patients who reported at the hospital on that day.
F is the set of patients who complained of fever.
S is the set of patients who had stomach troubles.
I is the set of injured patients.
The given data can be written as follows:
n(U) = n(F∪S∪I) = 100
n(F) = 70
n(S) = 50
n(I) = 30
n(F∩S) + n(S∩I) + n(I∩F) - 3×n(F∩S∩I) = 44
Using the cardinal number of the union of three sets formula, we get
n(F∪S∪I) = n(F) + n(S) + n(I) - n(F∩S) - n(S∩I) - n(I∩F) + n(F∩S∩I)
100 = 70 + 50 + 30 - (44 + 3×n(F∩S∩I)) + n(F∩S∩I)
100 = 150 - 44 - 2×n(F∩S∩I)
2×n(F∩S∩I) = 106 - 100 = 6
n(F∩S∩I) = 3
Therefore, 3 patients had all the complaints.
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a seventh-grade student does not believe that -5 is greater than -2. the student argues that a debt of $5 is greater than a debt of $2 how do you respond?
Answers
Answer:
it is greater then -2
Step-by-step explanation:
heres how I was taught, if you have a number say like 8 then its greater the day 5 same for -8 and -5 the long it is away from 0 the greater it is