[tex] \sf \: {x}^{2} - 5x - 24 \\ \sf \: {x}^{2} + 3x - 8x - 24 \\ \sf \: x \times (x + 3) - 8(x + 3) \\ \sf \: (x - 8) \times (x + 3)[/tex]
➪Therefore the factors are: (x-8) & (x+3)
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
#2[tex] \tt \: {13x}^{2} - 52 \\ \tt13( {x}^{2} - 4) \\ \tt13(x - 2) \times (x + 2)[/tex]
➪ Therefore the factors are: 13(x-2) & (x+2)
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
#3To find this we will use the standard form of equation i.e. ax+by+c=0We will substitute the given values of x and y and solve the equation for cx = -6y = 3Substitute the values into 3x-9y=14
[tex] \bf 3( - 6) - 9(3) = c[/tex]
[tex] \bf \: - 3 \times 6 - 9 \times 3 = c[/tex]
[tex] \bf \: 3( - 6 - 9) = c[/tex]
[tex] \bf \: 3( - 15) = c[/tex]
[tex] \bf \: - 45 = c[/tex]
[tex] \boxed{ \bf \: c = - 45}[/tex]
➪ So, the equation parallel to 3x-9y=14 is: 3x-9y=-45
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
[tex] \rm \: (5x + 4)(3x - 7) = 0[/tex]
[tex] \rm \: 5x + 4 = 0 \\ \rm \: 3x - 7 = 0[/tex]
[tex] \rm \: 5x = - 4 \\ \rm 3x = 7[/tex]
[tex] \rm \: x_{1} = - \frac{4}{5} , x_{2} = \frac{7}{3} [/tex]
➪ The values of x1 and x2 are: -4/5 & 7/3
Matt reasoned that he can write 9/1000 as 0.9. Is he correct?
I skip counted starting at 70. I never said the number 82 even though I counted beyond it. Which of these numbers could I have been counting by? 2, 5, or 10
Answer:
5 or 10
Step-by-step explanation:
counting by 2's - 70, 72, 74, 76, 78, 80, 82 82 is here, Incorrect
counting by 5's -70, 75, 80, 85, 90 Never said 82, Correct
counting by 10's - 70, 80, 90- Never said 82, Correct
3x+1/5y=7 solve for y.
The range of a set of data is 48. of the lowest value in the data set is 2, what is the highest value
The tubs of yogurt are sold for 75¢ each. Twenty percent of this is profit for the food company. How much profit does the company make on each tub? Show your work
Solve m-3/7 = -5 show your work please :)
Need help figuring out the equation for the linear line on the graph. Rise over run?
Which statement could be proved false using a counterexample?
An acute angle is 89 degrees.
Some acute angles are more than 90 degrees.
All acute angles are 30 degrees.
All acute angles are less than 90 degrees.
The statement 'Some acute angles are more than 90 degrees' can be proven false using a counterexample because by definition, an acute angle cannot be more than 90 degrees. For a statement to be considered true in mathematics, it must cover all possible cases. If a single exception can be found, we can consider the statement false.
Explanation:The statement that could be proved false using a counterexample among the choices would be 'Some acute angles are more than 90 degrees'. In Mathematics, an acute angle is defined as any angle that measures more than 0 degrees but less than 90 degrees. Hence, the idea of acute angles being more than 90 degrees is definitely incorrect.
Let's examine each statement:
An acute angle is 89 degrees. This is true, because 89 degrees is less than 90 degrees, and therefore, it fits the definition of being an acute angle.Some acute angles are more than 90 degrees. This is not true, and also our answer. No acute angled can be more than 90 degrees, because then it would not be an acute angle anymore, it would be termed as an obtuse angle.All acute angles are 30 degrees. This is false, but it is not provided as a choice to select as per the question asked.All acute angles are less than 90 degrees. This is true, as it's the very definition of acute angle, it's always less than 90 degrees.In conclusion, always remember that for a statement to be true in mathematics, it must cover all possible cases. When a single exception can be found, the statement can be considered false.
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In 2010, Washington Township created recreational soccer programs for the spring and fall seasons. The table shows the number of participants who registered for each season during the first four years,
Participation in Town Soccer Programs
Year
Spring league
Fall league
year;2010
spring league;68
fall league;145
year;2011
spring league;79
fall league;148
year;2012
spring league;90
fall league;151
year; 2013
spring league; 101
fall league; 154
Which statement best describes the programs?
A) Participation in the spring league is increasing more than twice as fast as participation in the fall league.
b)Participation in the spring league is increasing at a slightly faster rate than participation in the fall league.
C) Participation in the fall league is increasing more than twice as fast as participation in the spring league.
D) Participation in the fall league is increasing at a slightly faster rate than participation in the spring league.
Answer:
Option A is the answer.
Step-by-step explanation:
Table is given as
Year 2010 2011 2012 2013
Spring league 68 79 90 101
Fall league 145 148 151 154
Now as per given table we will analyze each option given
A). Difference in spring league participation increasing every year = 79-68 = 11
Difference in Fall league increasing every year = 148-145 = 3
Therefore option A is true because [tex]\frac{11}{3}>3[/tex] Spring league is increasing more than twice as fast as fall league.
B). This option is not true because participation in the spring league is increasing nearly 4 times of Fall league.
C) False. Spring league participation is more than fall league.
D) False. Same as option C because spring league participation is more than fall league.
Need help on all of these I don't understand
A university study examined the relationship between amount of sleep and school performance in college-age students. The Venn diagram represents the students who participated in the study. If A represents the students who slept more than 7 hours per night, and B represents the students who improved in school performance, what group of students does region C represent? A. students who slept more than 7 hours per night and did not improve in school B. students who slept more than 7 hours per night and did improve in school C. students who slept for exactly 7 hours and performed at the mean level for school performance D. students that slept for exactly 7 hours and did not improve in school
Region C in the Venn diagram represents students who slept more than 7 hours per night and improved in school performance, as it is the intersection of both sets A and B. The correct option is C.
In the context of the Venn diagram described, where 'A' represents students who slept more than 7 hours per night, and 'B' represents those who improved in school performance, the region 'C' would typically represent the intersection of these two groups.
Therefore, the group of students that region C would represent is option B: students who slept more than 7 hours per night and did improve in school performance. This is because the Venn diagram's intersection area (region C) visually demonstrates where both conditions (sleeping more than 7 hours and improvement in school performance) are met simultaneously.
Find the equation of the hyperbola centered at the origin that has a vertex at (5, 0) and a focus at (9, 0).
What is the measure of DAE
Answer:It's A(45)
Step-by-step explanation:
Got it right on Edge
Write the summation to estimate the area under the curve y = 2x2 + 1 from x = 0 to x = 4 using 4 rectangles and left endpoints.
the summation from i equals 0 to 4 of the quantity 2 times i squared plus 1
the summation from i equals 1 to 3 of the quantity 2 times i squared plus 1
the summation from i equals 0 to 3 of the quantity 2 times i squared plus 1
the summation from i equals 1 to 4 of the quantity 2 times i squared plus 1
Answer:
The correct option is C.
Step-by-step explanation:
The given equation of curve is
[tex]y=2x^2+1[/tex]
We need to find the area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints.
We have 4 rectangles in x = 0 to x = 4. So,
[tex]\Delta x=1[/tex]
Left Riemann sum:
[tex]\sum_{i=0}^{n-1}\Delta xf(x_i)[/tex]
Using Left Riemann sum, we get
[tex]\sum_{i=0}^{4-1}(1)f(i)[/tex]
[tex]\sum_{i=0}^{3}(2i^2+1)[/tex] [tex][\because y=2x^2+1][/tex]
The area under the given curve from x = 0 to x = 4 using 4 rectangles and left endpoints is
[tex]\sum_{i=0}^{3}2i^2+1[/tex]
Therefore the correct option is C.
In the cafeteria 100 milk cartons were put out for breakfast. at the end of breakfast 27 remained what is the number of milk cartons taken to the total number of mil cartons
If Juan drives 50 mph for 1.5 hours and then 70 mph for 0.5 hours, then how far did he drive?
The total distance that he drive is:
110 miles.
Step-by-step explanation:We know that the distance is defined as the product of speed and time.
i.e.
[tex]Distance=Speed\times Time[/tex]
It is given that:
Juan drives 50 mph for 1.5 hours.
This means that at this rate the distance traveled by him is:
[tex]Distance_1=50\times 1.5\\\\i.e.\\\\Distance_1=75\ miles[/tex]
and he travels at the rate of 70 mph for 0.5 hours.
This means that the distance traveled by him at this rate is:
[tex]Distance_1=70\times 0.5\\\\i.e.\\\\Distance_1=35\ miles[/tex]
Hence, the total distance that he drive is:
[tex]Total\ distance=Distance_1+Distance_2\\\\Total\ distance=75+35\\\\i.e.\\\\Total\ distance=110\ miles[/tex]
find the product of: (x+3vs)(2x+3vs)
What is the length of TW
Answer:
32 units.
Step-by-step explanation:
We have been given a graph of a line segment and we are asked to find the length of line segment TW.
Upon looking at our graph we can see that point U divides segment TW in two equal parts (TU and UW), which means that length of TW will be two times the length of TU or UW.
We have been given the length of TU is 16 units. To find the length of segment TW we will multiply 16 by 2.
[tex]\text{Length of TW}=2\times 16=32[/tex]
Therefore, the length of line segment TW will be 32 units.
Teresa is going for a run. she runs for 9.6 miles at a speed of 6 miles per hour. for how many hours does she run?
The required time to run for 9.6 miles is 1.5 hours, as of the given conditions.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
Teresa is going for a run. she runs for 9.6 miles at a speed of 6 miles per hour.
Speed = 6 miles per hour,
Distance = 9.6 miles
As we know,
Time = DIstance/time
Assign the values,
Time = 9.6/6
Time = 1.5 hours
Thus, the required time to run for 9.6 miles is 1.5 hours.
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There are 12 signs of the zodiac. how many people must be in a group before you are guaranteed that at least 6 of them have the same sign
Which of the following statements says that a number is between -3 and 3?
A. |x| < 3
B. |x| > 3
Answer:
A. |x| < 3
Step-by-step explanation:
The absolute value of a number is the value that a number has beyond its sign. This means that the absolute value is the numerical magnitude of the number regardless of whether its sign is positive or negative. Formally, the absolute value of any real number x, is defined by:
[tex]|x|=\left \{ {{x,\hspace{3}if\hspace{3}x\geq0} \atop {-x,\hspace{3}if\hspace{3}x<0}} \right.[/tex]
In this sense, to satisfy the inequality [tex]|x|<3[/tex], the domain of x must be:
[tex]-3<x<3\\\\or\\\\(-3,3)[/tex]
Because for [tex]x<-3[/tex] or [tex]x>3[/tex] the inequality is absurd. For example if x=-4
[tex]|-4|=4<3[/tex] which is not true.
and for x=4
[tex]|4|=4<3[/tex] which is not true.
On the other hand to satisfy the inequality [tex]|x|>3[/tex], the domain of x must be:
[tex]-3>x>3\\\\or\\\\(-\infty,-3)\cup(3,\infty)[/tex]
Because for [tex]x<3[/tex] the inequality is absurd. For example if [tex]x=2[/tex]
[tex]|2|=2>3[/tex] which is not true.
and for x=-1
[tex]|-1|=1>3[/tex] which is not true.
Therefore the correct statement is:
A. |x| < 3
(12, 10) , (-2, r) , m= -4
The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
Given two points,
(12, 10) , (-2, r)
The slope associated with (x₁, y₁) and (x₂, y₂) →
Slope(m) = (y₂ - y₁)/(x₂ - x₁)
So,
m = (r - 10)/(-2-12)
(r - 10)/(-14) = -4
r - 10 = 56
r = 66
Hence "The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66".
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Choose the true statement.
-8 < 8
-8 > 8
-8 = 8
-8 < 8
since a negative number is below 0 and a positive number is above 0 the first statement is true
Multiply.
(21)⋅(−7)
−147
−14
14
147
Answer:
-147
Step-by-step explanation:
∆ABC is plotted on a coordinate plane. If ∆ABC rotates 90° clockwise around point C, what are the coordinates of A'?
here are the answer choices
(0,2)
(4,6)
(7,6)
(8,2)
How is a calculation of net worth different from a day-to-day or month-to-month tallying of expenses?
Net worth is the calculation of an individual's assets minus their liabilities, while tallying of expenses is a regular tracking of personal spending without considering overall assets or debts. An example of this can be seen in the use of credit cards and savings accounts and their respective interest rates.
Explanation:The calculation of net worth and the day-to-day or month-to-month tallying of expenses are two different aspects of personal finance. Net worth is a calculation that is made by subtracting a person's liabilities from their assets. In other words, it is your assets (what you own) minus your liabilities (what you owe). On the other hand, tallying of expenses is a way to track your spending habits on a daily or monthly basis, which does not take into account one's assets or debts.
For instance, let's consider a person who owns a house (an asset), but also owes some amount on the mortgage (a liability). Their net worth would be the value of the house minus what's still owed on the mortgage. This is different from keeping track of daily or monthly expenses, which may include the mortgage payment, grocery bills, car payments, and other outgoings.
A common example of the difference is seen in credit card usage. A person might have a $1,000 credit card debt with a 15% interest rate, and simultaneously, a savings account of $2,000 that pays only 2% interest. They are losing money overall because the credit card debt costs more than the savings account earns. To increase their net worth, the rational decision would be to pay off the debt, but this wouldn't necessarily reduce their monthly expenses since they would still need to meet their day-to-day costs.
Learn more about Net Worth vs ExpensesCalculating net worth is different from day-to-day or month-to-month tallying of expenses. Net worth is a measure of a person's financial wealth, while expense tracking helps monitor spending habits.
Explanation:Calculating net worth is different from day-to-day or month-to-month tallying of expenses. Net worth is a measure of a person's financial wealth and is calculated by subtracting the total liabilities from the total assets. It provides a snapshot of an individual's overall financial health and is not influenced by short-term spending or expenses.
On the other hand, day-to-day or month-to-month tallying of expenses involves tracking and categorizing the money spent on various items or activities over a specific period. It helps individuals manage their budget, track their spending habits, and make informed financial decisions on a regular basis.
While net worth provides a big-picture view of a person's financial situation, day-to-day expense tracking helps monitor and control spending on a more detailed level to achieve financial goals.
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A race car driver won a 900 mile race with a speed of 178.9 miles per hour. find the driver's time.
John made of a pound of fudge and Mary made of a pound of fudge. Ricky takes the sum of the two amounts of fudge and divides it into three equal portions, planning to keep one portion for himself. How much fudge does Ricky keep?
Answer:
Rickey keep 2/3 or 0.7 fudge.
Step-by-step explanation:
Consider the provided information.
John made of a pound of fudge and Mary made of a pound of fudge.
Ricky takes the sum of the two amounts of fudge
The sum of the two amounts of fudge is 2 pound.
He divides it into three equal portions.
[tex]\frac{2}{3}=0.\overline6\approx0.7[/tex]
Hence Rickey keep 2/3 or 0.7 fudge.
What is the solution set for [-x]=10
1/2(2d+6)=p solve for d