The quadratic formula states that the solutions x1 and x2 of a quadratic function in the form y = ax^2 + bx + c is equal to:
[tex]\begin{gathered} x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a} \\ x_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]So, using this formula with the values a = 3, b = 4 and c = 2, we have that:
[tex]\begin{gathered} x_1=\frac{-4+\sqrt[]{4^2-4\cdot3\cdot2}}{2\cdot3}=\frac{-4+\sqrt[]{16-24}}{6}=\frac{-4+\sqrt[]{-8}}{6} \\ x_1=\frac{-4+\sqrt[]{2^2\cdot(-2)}}{6}=\frac{-4+2\cdot\sqrt[]{-2}}{6}=\frac{-2+\sqrt[]{-2}}{3}=-\frac{2}{3}+i\cdot\frac{\sqrt[]{2}}{3} \\ x_2=\frac{-4-\sqrt[]{-8}}{6}=\frac{-2-\sqrt[]{-2}}{3}=-\frac{2}{3}-i\cdot\frac{\sqrt[]{2}}{3} \end{gathered}[/tex]Since the zeros have a complex part, the solutions are imaginary.
Is (2,7) a solution to the system of equations: y= x + 5 y= 4x + 1 Part 1 (circle 1) Yes No Part 2 Shows a proof of your answer
Answer
(2, 7) is not a solution to this system of equations.
The ordered pair doesn't fit into the second equation
Explanation
To check if the given ordered pair is a solution to this, we will insert the values into the two equations and if they fit into rach equation, then, the ordered pair is a solution for this.
y = x + 5
y = 4x + 1
(2, 7) means x = 2, y = 7
y = x + 5
7 = 2 + 5
7 = 7
y = 4x + 1
7 = 4(2) + 1
7 = 8 + 1
7 ≠ 9
The ordered pair doesn't fit into the second equation, hence, (2, 7) is not a solution to this system of equations.
Hope this Helps!!!
which statement best describes the association between the energy and light output of these light bulbs?
As we can see from the graph, we can see that we could have two populations of lightbulbs in the graph. If we draw or try to approximate a line to these two different populations of lightbulbs, we end up with the next graph:
Then, we can conclude that, for most cases, as the energy increases, the light output increases too. Of course, there are some exceptions like the point (18, 800), but the tendency is in this way.
Therefore, the statement that best describes the association between the energy and light output is statement F: As the energy increases, the light output increases.
Write the equation of the horizontal line that goes through the point (9, 6).
Given the point:
(x, y) ==. (9, 6)
Let's write the equation of the horizontal line that goes through the given point.
On a horizonal line, every point on the line has the same value of y.
The slope of a horizontal line is 0.
Since every point on a horizontal line has the same value of y, to find the equation of a horizontal line, we are to use the y-coordinate of the point to find the equation of the horizontal line.
We have:
y-coordinate of the point = 6
Hence, the equation of the horizontal line that goes through the point is:
y = 6
ANSWER:
y = 6
which of these is an example of a proportional relationship
A proportional relationship is essentially a function where the output is a direct product of the input and the coefficient. Any relationship that has another constant term is not a proportional relationship because the final product is offset by the constant term.
The final answer where Samuel earns $20 for each lawn he mows can be expressed as 20x. This is a proportional relationship because the total money he earns is a product of the rate and x-value.
Consider a triangle ABC like the one below. Suppose that A = 35°, C = 68°, b = 32. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth.
Solution.
Given the triangle
[tex]\begin{gathered}Using sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex][tex]\begin{gathered} \frac{a}{sin35}=\frac{32}{sin77} \\ a=\frac{32\text{ x sin35}}{sin77} \\ a=18.84 \\ a=18.8(nearest\text{ tenth\rparen} \end{gathered}[/tex][tex]\begin{gathered} \frac{a}{sinA}=\frac{c}{sinC} \\ \frac{18.84}{sin35}=\frac{c}{sin68} \\ \end{gathered}[/tex][tex]\begin{gathered} c=\frac{18.84\text{ x sin68}}{sin35} \\ c=30.45 \\ c=30.5(nearest\text{ tenth\rparen} \end{gathered}[/tex](MP Reason An internet company spends half their yearly profits on advertising for the next year. Of the remaining half, they spend 1/5 on new computers. What fraction of the total profits does the company spend on new computers? Use the number line to show how you can to make his bowl? Write an equati Harcourt Pub 4 find the fraction. 1 o Module 8. Lesson 3
Let the total profit be represented by 1
The internet company spends half their yearly profits on advertising for the next year. The amount of the profit spent on advertising is 1/2 = 0.5
The amount left is 1 - 0.5 = 0.5
Of the remaining half, they spend 1/5 on new computers. It means that the amount spent on new computers is
1/5 * 0.5 = 0.1 = 1/10
Therefore, the fraction of the total profits does the company spend on new computers is
0.1/1 = 0.1 = 1/10
The number line is shown below
At the start of a research study, a colony of penguins had a population of 20,000. One year later, it had a population of 21,200.Assuming the population of the colony has grown exponentially, which expression best models thepopulation? Let t represent the time in years from the start of the research study.1,200(1.015)^t20,000 (1.06)^4t21,200 (1.012)^t20,000 (1.06)^tAssuming the colony continues to grow at the same rate, what will the population of the colony be 4 years after the start of the research study?Round your answer to the nearest whole number.
Solution:
An exponential function is generally expressed as
[tex]\begin{gathered} y=a(b)^t\text{ ----- equation 1} \\ \end{gathered}[/tex]Given that in a research study, a colony of penguins had a population of 20,000.
This implies that
[tex]\begin{gathered} when\text{ t=0,} \\ 20,000=ab^0 \\ \Rightarrow20000=a\times1\text{ \lparen where b}^0=1) \\ thus, \\ a=20000 \end{gathered}[/tex]Substitute the value of a into equation 1.
Thus,
[tex]y=20000(b)^t\text{ ----- equation 2}[/tex]One year later, it had a population of 21,200. This implies that when t equals 1, we substitute the values of 21200 and 1 for y and t respectively into equation 2.
This gives
[tex]\begin{gathered} 21200=20000(b)^1 \\ \Rightarrow21200=20000b \\ divide\text{ both sides by the coefficient of b, which is b.} \\ thus, \\ \frac{21200}{20000}=\frac{20000b}{20000} \\ \Rightarrow b=1.06 \end{gathered}[/tex]Substitute the obtained value of b into equation 2.
Thus, the expression that best models the population is
[tex]20,000(1.06)^t[/tex]Assuming the colony grows at the same rate, the population of the colony after 4 years is evaluated by solving for y when the value of t is 4.
Thus,
[tex]\begin{gathered} y=20,000(1.06)^t \\ when\text{ t=4, we have} \\ y=20,000(1.06)^4 \\ =20000\times(1.06)^4 \\ =20000\times1.26247696 \\ \Rightarrow y=25249.5392 \\ \therefore y=25250\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, after 4 years the population of the colony will be 25250 penguins (nearest whole number).
What is the determinant of H= 0 2 3-1 3 56 3 -2
1) Since this is a Matrix 3x3 we can make use of the Sarrus Rule to find the determinant of this Matrix:
[tex]\begin{bmatrix}0 & 2 & 3 \\ -1 & 3 & 5 \\ 6 & 3 & -2 \\ \end{bmatrix}[/tex]2) We can do that by copying two columns to the right of the Matrix, and multiplying the entries, this way:
Now, let's add algebraically each diagonal and subtract from the other like this:
[tex]\begin{gathered} \det (H)=\lbrack60-9+0\rbrack-\lbrack54+4+0\rbrack \\ \det H)=51-58 \\ \det (H)=-7 \end{gathered}[/tex]GEOMETRY: Express the volume of each cube below as a monomialNeeded fast!
Remember that
The volume of a cube is equal to
[tex]V=b^3[/tex]where b is the long side of the cube
so
Part 19
we have that
[tex]b=7c^6d^2[/tex]substitute in the formula
[tex]V=(7c^6d^2)^3[/tex]Applying property of exponents
[tex]\begin{gathered} V=(7^3)(c^{(6\cdot3)})(d^{(2\cdot3)}) \\ V=342c^{(18)}d^6 \end{gathered}[/tex]Part 20
we have
[tex]b=6r^7s^8[/tex]substitute in the formula
[tex]\begin{gathered} V=(6r^7s^8)^3 \\ V=216r^{(21)}s^{(24)} \end{gathered}[/tex]Jim stocks shelves at a grocery store. He aerns $8.60 per hour for 37.5 hours each week. One week a large shipment arrives late and Jim is asked to work overtime at 1.5 times his regular rate. He works 4.5 hours for overtime. What are his total earnings for the week?
Explanation
Since Jim earns 8.60 per hour for 37.5 hours each week. His normal earnings for a week becomes,
[tex]earnings=8.60\times37.5=322.5\text{ dollars}[/tex]During the late shipment period, Jim had to earned an overtime payment at 1.5 times his regular rate. This means per overtime hour he would earn
[tex]1.5\times8.60=12.9[/tex]Therefore, for 4.5 hours for overtime, we will have;
[tex]12.9\times4.5=58.05\text{ dollars}[/tex]Hence, altogether, he would make;
[tex]322.5dollars+58.05dollars=380.55\text{ dollars}[/tex]Answer: 380.55 dollars
A landscaper's truck is filled with ton of gravel.The gravel is shared equally among 3 projects.3. Write and solve a division equation to find how muchgravel each project will get. Explain your reasoning.
Step 1
Let n represent the weight of tons of gravel.
Step 2
The gravel is shared equally among the 3 projects.
Step 3
Write the division equation
Each project will get
[tex]=\text{ }\frac{n}{3}\text{ tons of gravel}[/tex]Homework: 6.3 HWQuestion 8, 6.3.17ОРAn employee makes $14.41 per hour but is getting a 4% increase. What is his new wage per hour to the nearest cent?His new wage per hour is $(Type an integer or decimal rounded to two decimal places as needed.)
The employee's original wage is $14.41 per hour.
If the wage increases by 4%, the percentage increase will be:
[tex]\Rightarrow\frac{4}{100}\times14.41=0.58[/tex]Therefore, the new wage per hour will be:
[tex]\Rightarrow14.41+0.58=14.99[/tex]The new wage is $14.99.
What is the value of X?
Check the picture below.
Make sure your calculator is in Degree mode.
I have been stuck on this for a while, your help would be most appreciated!
Answer:I Don't Know What She Said
Step-by-step explanation:
The Senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High school A Rented and Filled 6 vans and 7 buses with 471 students. High School B rented and Filled 5 vans and 9 buses with 573 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many Students can a bus carry?
Answer: A van can carry 12 students
A bus can carry 57 students
Explanation:
Let x represent the number of students that a van can carry
Let y represent the number of students that a bus can carry.
The senior class at High school A Rented and Filled 6 vans and 7 buses. This means that
the number of senior class students that the van carried is 6 * x = 6x
the number of senior class students that the bus carried is 7 * y = 7y
If both vehicles were filled with 471 students, it means that
6x + 7y = 471 equation 1
High School B rented and Filled 5 vans and 9 buses. This means that
the number of High School B students that the van carried is 5 * x = 5x
the number of High School B students that the bus carried is 9 * y = 9y
If both vehicles were filled with 573 students, it means that
5x + 9y = 573 equation 2
We would solve both equations by applying the method of elimination. To eliminate x, we would multiply equation 1 by 5 and equation 2 by 6. The new equations are
30x + 35y = 2355 equation 3
30x + 54y = 3438 equation 4
Subtracting equation 3 from equation 4, we have
30x - 30x + 54y - 35y = 3438 - 2355
19y = 1083
y = 1083/19
y = 57
Substituting y = 57 into x equation 1, we have
6x + 7 * 57 = 471
6x + 399 = 471
6x = 471 - 399 = 72
x = 72/6
x = 12
Thus,
A van can carry 12 students
A bus can carry 57 students
What is 3y + 5x = -15 written in slope-intercept form?O y- &x+5O y--gx-5o y- x-5O y--3x+5
The slope-intercept form of a linear equation is:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{where m is the slope} \\ \text{and c is the intercept} \end{gathered}[/tex]Given:
[tex]3y\text{ + 5x = -15}[/tex]Solution
By re-arranging the given expression, we have:
[tex]\begin{gathered} \text{Dividing through by the coefficient of y} \\ \frac{3y}{3}\text{ + }\frac{5x}{3}\text{ = }\frac{-15}{3} \\ y\text{ + }\frac{5}{3}x\text{ = -5} \\ y\text{ = -}\frac{5}{3}x\text{ - 5} \end{gathered}[/tex]A regular hexagon has perimeter 72m. Find the area
A regular hexagon has six equal sides:
If you notice, a regular hexagon has exactly six equilateral triangles inside of it.
So, to find the area we could find the area of a triangle and then multiply this result by 6. This seems to be a little bit complicated to do, so, there's a formula to find the area of a regular hexagon, which is:
[tex]\begin{gathered} A=\frac{3\sqrt{3}s^2}{2} \\ Where: \\ s:Measure\text{ of a side of the regular hexagon} \end{gathered}[/tex]We know that the measure of any side of our regular hexagon equals 12m, so, we could just replace in the equation:
[tex]A=\frac{3\sqrt{3}(12m)^2}{2}\rightarrow A=\frac{3\sqrt{3}(144m^2)}{2}\rightarrow A=216\sqrt{3}m^2[/tex]Simplified, that's about 374.1 m2.
Determine if the conclusion follows logically from the premises.Premise: If you have a maple tree, then you have to rake leaves in autumnPremise: Jon has to rake leaves in autumnConclusion: Jon has a maple treeValid argumentInvalid argument
The conclusion is an invalid argument.
Because if you have any tree you have to rake leaves in autumn. THen Jon could possibly have any tree.
Thus the argument is invalid
Really need help with 11 and 12 just started learning this today and I don't quite understand it would really appreciate it
11.
Given:
[tex]y=x^2[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x[/tex]The given point is (3,9)
Substitute x=3 in the derivative, we get
[tex]\frac{dy}{dx}=2\times\times3=6[/tex]Hence the slope is 3.
12.
Given:
[tex]y=x^2+4[/tex]Differentiate with respect to x, we get
[tex]\frac{dy}{dx}=2x+0[/tex]The given point is (0,4)
Substitute x=0 in the derivative, we get
[tex]\frac{dy}{dx}=2(0)+0=0[/tex]Hence the slope is 0.
Geometry- Need help` brainly logged me out w my other tutor who explained it so if u see this miss tutor my bad
"Reason" means a mathematical justification for the assert on the left. "Given" means something that doesn't need justification; it's an assumption.
The first statement,
[tex]\bar{FG}\cong\bar{FJ},[/tex]is given.
The second reason is Base Angles Theorem. Note the word angles in the middle. Its corresponding statement on the left must involve angles. There is only one option involving angles:
[tex]\measuredangle G\cong\measuredangle J.[/tex]Finally, statement 3 is also in the assumptions made above (tagged by Given:). It's also Given.
AnswerThe reason #1 is Given.
The statement 2 is
[tex]\measuredangle G\cong\measuredangle J.[/tex]The reason #3 is Given.
An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing a queen ? Question content area bottomPart 1The probability of drawing a queen is enter your response here .(Type an integer or a simplified fraction.)
Given:
Total number of cards = 52
Number of cards drawn = 1
Then:
Number of ways of drawing a card from 52 cards
[tex]\begin{gathered} =^{52}C_1 \\ =52 \end{gathered}[/tex]Number of queens in a deck of cards = 4
Number of ways that one card is a queen
[tex]\begin{gathered} =^4C_1 \\ =4 \end{gathered}[/tex]Probability of drawing a queen
[tex]\begin{gathered} =\frac{\text{ Number of favorable cases}}{\text{ Total number of cases}} \\ =\frac{4}{52} \\ =\frac{1}{13} \end{gathered}[/tex]Final answer: 1/13
Three cards are drawn from an ordinary deck and not replaced find the probability of the following P(getting 3 queens)P(getting an ace and king and queen)P(getting club and spade and heart)P(getting 3 diamonds)Answer the following problems using multiplication rule make sure to reduce your fraction
a) P(3 queens) ) = 4/52*3/51*2/50 = 1/5525
b) P(ace,king, queen) = 4/52*4/51*4/50 = 8/16575
c) P( ) = 10/52 * 10/51*10/50 = 5/663
d) P(3 diamonds) = 10/52 * 9/51* 8/50 = 6/1105
True or False? In a two column proof, the right column contains a series of deductions. (Geometry)
In a two column proof the left column contains a series of statements. The reasons why these statements are true are given in the right column. This reasons are deduction made from the data provided by the problem. Then the statement "In a two column proof, the right column contains a series of deductions." is True.
p+3w=-79-5p+w=-5Solve the system using the elimination method if there is no solution put no solution if there is infinite solutions put infinite
p+3w=-79
-5p+w=-5
Multiply the second equation by 3 and then subtract the second equation:
p + 3w = -79
-
-15p + 3w = -15
_____________
16p = -64
p= -64/16
p= -4
Replace p on any equation and solve for w
-4 + 3w = -79
3w = -79 + 4
3w = -75
w= -75/3
w= -25
Solution:
p= -4
w= -25
what is the answer to number 9 and how do i solve?
Given:
[tex]T=\frac{1}{r}\frac{N_{\infty}-N_0}{N_0}[/tex]From question (1)
[tex]r=2[/tex]and given:
[tex]\begin{gathered} N_{\infty}=3.3 \\ N_0=10 \end{gathered}[/tex]we will find the daily cases beak as follows:
[tex]undefined[/tex]Help me please, the one selected is the correct graph
SOLUTION
The table of values is shown below
So the missing values for y are 8 and then 6
The option for the graph is the 3rd graph, the one you selected
1 8. Matt wants to purchase a gasoline motor scooter. The gas mileage is 75 miles for each gallon of gasoline. How many miles will Matt be able drive on 5 gallons of gasoline? 2
Answer:
375 miles
Explanation:
The gas mileage of the scooter = 75 miles for each gallon of gasoline.
Therefore:
If 1 gallon will cover a distance of 75 miles
Then: 5 gallons will cover a distance of:
5 x 75 miles
=375 miles
Matt will be able to drive 375 miles on 5 gallons of gasoline.
How do I know if 6.209 is greater or lesser than 6.29
Since,
[tex]6.29-6.209=0.081[/tex]The difference gives us a positive value.
So, 6.29 is grater than 6.209
Answer: Add a 0 to 6.29 and compare the numbers to see which one is greater
6.29 (or 6.290) is greater than 6.209 since the hundrenth in 6.29 is 9 and the other hundrenth for 6.209 is 0.
in a particular hospital, newborn babies were delivered yesterday. here are their weights (in ounces). 121 ,101 ,97 121,124 ,112 assuming that these weights constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.
The standard population formula is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_{}-\mu)^2}{n}}[/tex]where
x is the data points
μ is the mean of the data
and n is the number of data points
The mean is computed as follows:
[tex]\mu=\frac{\Sigma x}{n}[/tex]In this case, the mean is:
[tex]\mu=\frac{121+101+97+121+124+112}{6}=\frac{676}{6}=112.67[/tex]Then, the standard deviation of the population is:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(121-112.67)^2+(101-112.67)^2+(97-112.67)^2+(121-112.67)^2+(124-112.67)^2+(112-112.67)^2}{6}} \\ \sigma=\sqrt[]{\frac{69.39+136.19+245.55+69.39+128.37+0.045}{6}} \\ \sigma=\sqrt[]{108.22} \\ \sigma=10.4 \end{gathered}[/tex]Angles A and B are supplementary. If m∠A=67°, find m∠B.
Two Angles are Supplementary when they add up to 180 degrees, in this case we have:
[tex]67^o+m\angle B=180^o[/tex][tex]m\angle B=180^o-67^o[/tex][tex]m\angle B=113^o[/tex]