Answers
Answer:
Step-by-step explanation:
Let's solve the equation:
3m² + 22m + 7 = 0
Discriminant:
D = b² - 4·a·c = 22² - 4·3·7 = 400
√ D = √ 400 = 20
m₁,₂ = ( - b ± √ D) / (2·a)
m₁ = ( - 22 + 20) / (2·3) = - 2/6 = - 1 / 3
m₂ = ( - 22 - 20) / (2·3) = - 42/6 = - 7
3m² + 22m + 7 = 3·(m - (-1/3))·((m - (-7)) =
= (3m + 1)·(m + 7)
3m² + 22m + 7 = (3m + 1)·(m + 7)
Related Questions
Sketch a graph of the polynomial function f(x) = –x3 + 5x2 – 2x – 8. Use the graph to complete the following:f is __________ on the intervals (–∞, 1/3) and (3, ∞)f is __________ on the interval (1/3, 3)f is __________ on the intervals (–∞, -1) and (2, 4)
Answers
To sketch the graph, we need to find the x-intercepts and y-intercepts.
To find the x-intercepts we solve the equation when y = 0.
That is
[tex]-x^3+5x^2-2x-8=0[/tex][tex]\begin{gathered} f(-1)=-(-1)^3+5(-1)^2-2(-1)-8=1+5+2-8=0 \\ \text{Hence} \\ x=-1\text{ is a zero of f(x)} \\ \Rightarrow\text{ x+1 is a factor of f(x)} \end{gathered}[/tex]Next, we find the result of :
[tex]\frac{f(x)}{x+1}[/tex][tex]\begin{gathered} So \\ \frac{-x^3+5x^2-2x-8}{x+1}=-x^2+6x-8 \end{gathered}[/tex]Now we solve
[tex]\begin{gathered} -x^2+6x-8=0 \\ \Rightarrow-x^2+2x+4x-8=0 \\ \Rightarrow-x(x-2)+4(x-2)=0 \\ \Rightarrow(4-x)(x-2)=0 \\ \Rightarrow x=4\text{ or 2} \end{gathered}[/tex]So the zeros of f(x) are -1, 2, and 4
Next, we find the stationary points.
[tex]\begin{gathered} \frac{df(x)}{dx}=-3x^2+10x-2 \\ \text{When }\frac{df(x)}{dx}=0,\text{ we have} \end{gathered}[/tex][tex]\begin{gathered} -3x^2+10x-2=0 \\ \text{Dividing through by -3 we have} \\ x^2-\frac{10}{3}x+\frac{2}{3}=0 \end{gathered}[/tex][tex]\begin{gathered} (x-\frac{5}{3})^2-(-\frac{5}{3})^2-2=0 \\ \Rightarrow(x-\frac{5}{3})^2=2+\frac{25}{9}=\frac{43}{9} \\ \Rightarrow x=\frac{5\pm\sqrt[]{43}}{3} \\ \Rightarrow x=2.55\text{ or }0.78 \end{gathered}[/tex][tex]\frac{d\frac{df(x)}{dx}}{dx}=-6x+10[/tex]At x = 2.55
[tex]\frac{d\frac{df(x)}{dx}}{dx}=-6(2.55)+10=-5.3<0[/tex]Hence we have a maximum point at x = 2.55
[tex]\frac{d\frac{df(x)}{dx}}{dx}=-6(0.78)+10=5.32>0[/tex]Hence, there is a minimum point at x = 0.78
[tex]\begin{gathered} f(0.78)\text{ = }-6.99 \\ f(2.550=2.83 \end{gathered}[/tex][tex]\begin{gathered} To\text{ check the intervals where the function increasing or decreasing} \\ \text{For x < 0.78 } \\ \frac{df(x)}{dx}=(x-0.78)(x-2.83)\text{ is positive} \\ \text{For 0.78 < x < 2.83 } \\ \frac{df(x)}{dx}=(x-0.78)(x-2.83)\text{ is negative} \\ \text{For x > 2.83} \\ \frac{df(x)}{dx}=(x-0.78)(x-2.83)\text{ is positive} \end{gathered}[/tex]This implies that
f is increasing on the intervals (–∞, 1/3) and (3, ∞)
Make g the subject
X = 3g + 2
Answers
Answer:
g = X - 2/3
Step-by-step explanation:
X = 3g + 2
Try to make g stand alone and collect the terms.
X - 2 = 3g
Divide both sides by the coefficient of g, which is 3
X - 2/3 = 3g/3
g = X - 2/3
This pyramid has the same base as the prism and its height is three times the height of the prism. What is the ratio of the volume of thepyramid to the volume of the prism?1A} volume of Pyramidvolume of priamB} volume of pyramidvolume of priuamC} volume of pyramidvolume of priimD} Volume of pyramidvolume of priem
Answers
This pyramid has the same base as the prism and its height is three times the height of the prism. What is the ratio of the volume of the
pyramid to the volume of the prism?
1
A} volume of Pyramid
volume of priam
B} volume of pyramid
volume of priuam
C} volume of pyramid
volume of priim
D} Volume of pyramid
volume of
prime
____________________________________________
volume of the prism
hi can someone help me here
Answers
Answer:
[tex]\left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]
Given endpoints of the diameter of the circle:
(x₁, y₁) = A (7, -3)(x₂, y₂) = B (0, -4)To find the center of the circle, substitute the given endpoints into the midpoint formula:
[tex]\begin{aligned} \implies \textsf{Midpoint} & =\left(\dfrac{0+7}{2},\dfrac{-4-3}{2}\right)\\& =\left(\dfrac{7}{2},-\dfrac{7}{2}\right)\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and one of the given points (0, -4) into the equation and solve for r²:
[tex]\implies \left(0-\dfrac{7}{2}\right)^2+\left(-4-\left(-\dfrac{7}{2}\right)\right)^2=r^2[/tex]
[tex]\implies \left(-\dfrac{7}{2}\right)^2+\left(-\dfrac{1}{2}\right)^2=r^2[/tex]
[tex]\implies \dfrac{49}{4}+\dfrac{1}{4}=r^2[/tex]
[tex]\implies \dfrac{50}{4}=r^2[/tex]
[tex]\implies r^2=\dfrac{25}{2}[/tex]
Therefore, the equation of the circle is:
[tex]\implies \left(x-\dfrac{7}{2}\right)^2+\left(y+\dfrac{7}{2}\right)^2=\dfrac{25}{2}[/tex]
The graph of the circle is attached.
You are dealt one card from a 52-card deck. Find the probability that you are dealt a six or a red card.
Answers
Answer:
[tex]P(\text{ six or red)=}\frac{7}{13}[/tex]Step-by-step explanation:
The probability of an event is represented by the following equation;
[tex]P(A)=\frac{\text{ Number of favorable outcomes}}{\text{ Number of possible outcomes}}_{}[/tex]Therefore, from a 52-card deck which is better shown with the following image:
There are 4 6's in a 52-card deck and 26 red cards.
*If the events A and B are not mutually exclusive, the probability is:
[tex]P(A\text{ or B)=P}(A)+P(B)-P(A\text{ and B)}[/tex]Then to determine the probability that you dealt a six or a red card:
[tex]\begin{gathered} P(six\text{ or red)=}\frac{4}{52}+\frac{26}{52}-\frac{2}{52} \\ P(\text{ six or red)=}\frac{7}{13} \end{gathered}[/tex]Please help :') ty ty ty ty ty
Answers
Answer:
C
Step-by-step explanation:
The x intercept is 40, which represents the number of month payments needed to repay the loan.
answer:
c) the x-intercept is 40, which represents the number of monthly payments needed to repay the loan.
step-by-step explanation:
the x-intercept is what x equals when y is zero. you can also determine what the x-intercept represents by understanding what the x-axis represents. hope that helps!
find the area of 2 1/2 units * 2 units
Answers
Answer:
5 square units
Explanation:
Emma's Rectangle is:
• 2½ units long.
,• 2 units wide.
[tex]\begin{gathered} \text{Area}=2\frac{1}{2}\times2 \\ =\frac{5}{2}\times2 \\ =5\text{ units}^2 \end{gathered}[/tex]Answer: its 5
Step-by-step explanation:
Use the graph to find the AOS, Vertex, Zeros, Domain, and Range
Answers
In this problem
we have a vertical parabola open downward
so
the vertex is a maximum
Looking at the graph
The vertex is the point (0,4)
The axis of symmetry is x=0 (y-axis)
The zeros are x=-2 and x=2
The domain is all real numbers -----> interval (-infinity, infinity)
The range is all real numbers less than or equal to 4 ----> interval (-infinity,4]
Divide…. Unit 2 test: scientific notation
Answers
Answer:
I do believe the answer for you is B. 2 x 10^14.
Step-by-step explanation:
4 x 10^4
Add four zeros to the original number since the exponent to the 10 is positive.
40,000/ 2 x 10^-10
Since the exponent here is a negative number, make 9 zeros behind the decimal point and the 2 at the end.
40,000/.0000000002
Using a calculator, you will get 2e14 which is equivalent to 2 x 10^14. Hope this helped!
Answer:
The answer is B
Perform the following food service calculation.
Meat served: meat with little bone
Pounds of meat available: 27 lbs.
Number of guests that can be served:
Answers
The number of guests that can be served is 7
How to determine the number of guests?From the question, we have the following parameters that can be used in our computation:
Meat served: 3 lbs meat with little bone
Pounds of meat available: 27 lbs.
The number of guests needed is calculated using the following equation
Number of guests = Pounds of meat available/Meat served
Substitute the known values in the above equation, so, we have the following representation
Number of guests = 27/3
Evaluate the quotient
Number of guests = 9
Hence, 9 guests can be served with the available meat
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Possible question
Perform the following food service calculation.
Meat served: 3 lbs meat with little bone
Pounds of meat available: 27 lbs.
Number of guests that can be served:
Write an inequality that can be solved using the Subtraction Property of Inequality and has a solution of all numbers less than -3.
Answers
Answer:
90183
Step-by-step explanation:
PLS HELP ME ASAP!! I WILL GIVE U BRAINLYEST!! NO LINKS!Frankie worked at the gas station for four months. He earned $4,800.00 andmust pay a total of 12% in income taxes. What is his net pay if there are noadditional deductions? A. 576.00B.5,376.00C.3,600.00D.4,224.00
Answers
Frankie worked at the gas station for four months. He earned $4,800.00 and
must pay a total of 12% in income taxes. What is his net pay if there are no
additional deductions?
A. 576.00
B.5,376.00
C.3,600.00
D.4,224.00
we have that
12%=12/100=0.12
Multiply $4,800.00 by 0.12
$4,800.00*0.12=$576.00
answer is option AYou pick a card at random without putting the 1st card back you pick a second card at random what is the probability of picking a 7 and then picking a 7
Answers
Given:
There are four cards numbered as
[tex]6,\text{ }7,\text{ }8,\text{ and }9.[/tex]Required:
We have to find the probability of picking a 7 and then picking a 7.
Explanation:
When you pick the first card there are four possibilities out of which only one card is numbered as 7.
Therefore, the probability of picking a 7 is
[tex]\frac{1}{4}[/tex]Before picking the second card you have put back the first card. So when you pick the second card there are four possibilities out of which only one card is numbered as 7.
Therefore, the probability of picking a 7 is
[tex]\frac{1}{4}[/tex]Hence the probability of picking a 7 and then picking a 7 is
[tex]\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}[/tex]Final answer:
Hence the final answer is
[tex]\frac{1}{16}[/tex]
Someone please help me. I can't get the right answer
Answers
The required value of x will be 44°.
What is an Isosceles Triangle?An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.
We have been given a triangle in the figure
According to the given figure, we can see that the triangle is an isosceles triangle
As per the property of the isosceles triangle, here two angles are the same.
Now, the sum of angles in a triangle as:
⇒ 68° + 68° + x = 180°
⇒ 136° + x = 180°
⇒ x = 180° - 136°
⇒ x = 44°
Therefore, the required value of x will be 44°.
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When being dealt two cards from a standard deck of fifty-two playing cards, find the probability that both cards are an ace.
Answers
We have:
Total number of cards in a pack = 52
Total number of aces in a pack = 4
The probability of drawing an ace is:
[tex]P(one\text{ }ace)=\frac{4}{52}[/tex]The probability that both are aces is:
[tex]P(both\text{ aces\rparen=}\frac{4}{52}\cdot\frac{3}{51}=\frac{4\cdot3}{52\cdot51}=\frac{12}{2652}=\frac{1}{221}[/tex]Answer: the probability is 1/221
Enter the number in scientific notatlon. 65,978 Hint: Move the decimal left 4 places.
Answers
ANSWER
[tex]6.5978\cdot10^4[/tex]EXPLANATION
We are given the number 65,978.
To put it in scientific notation, we will need to put it in a format such that we have a number between 1 and 10 multiplying a power of ten.
So, to do that, we will move the decimal point from the end of the number (65978.) to just after the first number.
Then the number of times we move it will be the power of 10.
Since we will move it to the left, it will be a positive power.
So, we have that the number becomes:
[tex]6.5978\cdot10^4[/tex]The power is 4 because we moved the decimal four times.
THIS QUESTION IS WHAT I NEED ANSWERED
Answers
Answer: its 1 over 0 which equals B^-1
If Patriciana has 4 more dimes than nickels and they have a combined value of 100 cents, how many of each coin does she have?
Answers
Patriciana has (20/9) nickels and (80/9) dimes of coins .
Evaluation for the number of dimes and nickels.There are 5 cents in a nickel and 10 cents in a dime.
Let the number of number of nickels be represented by the letter x, so that the number of dimes Patriciana has will be 4x.
So, 5x cents + 10 × 4x cents = 100 cents
5x cents + 40 cents = 100 cents
45x cents = 100 cents
divide through by the coefficient of x
x = 100cents/45cents
x = 20/9 by simplification,
and the number of dimes is calculated by putting 20/9 for x in 4x.
Hence, the number of dimes is 4(20/9) = 80/9 and that of nickels is 20/9.
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Jose went to another store that has a sale of 25% off everything. He wants to buy jeans that cost $40. How much money will he save on the jeans?
Answers
Answer:
$30
Step-by-step explanation:
25% of $40 = $10
$10 is the discount price, i.e., $10 is 25% of $40
selling price - discount
= 40 - 10
= $30
Please help meeeeeeeeeee
Answers
Answer:
Okay
Step-by-step explanation:
want me to come over to your place
A basket contains 5 pieces of paper numbered from 1 to 5. A hat contains the letters A, B, C and D. If a blindfolded person picks a number and then a letter, what is the probability that the number is greater than 3 AND the letter is C?
Answers
We have a basket and a hat.
The basket has the numbers 1, 2, 3, 4 and 5.
The hat contains the letters A, B, C and D.
We have to calculate the probabiltiy of drawing a number that is greater than 3 from the basket and drawing the letter C from the hat.
We have two events:
- Drawing a number greater than 3 from the basket
- Drawing a C from the hat
They are independent as the probability of each on does not depend on the outcome of the other event.
Then, we can calculate the probability of the two events happening together as the product of its probabilities:
[tex]P(n>3&l=C)=P(n>3)\cdot P(l=C)[/tex]The probability of drawing a number greater than 3 can be described as 2/5, as we have 2 numbers greater than 3 (4 and 5) out of 5 numbers in the basket.
The probability of drawing a letter C can be described as 1/4, as we have one letter C out of 4 letters available.
Then, we can calculate the probability as:
[tex]\begin{gathered} P(n>3&l=C)=P(n>3)\cdot P(l=C) \\ P(n>3&l=C)=\frac{2}{5}\cdot\frac{1}{4}=\frac{2}{20}=\frac{1}{10} \end{gathered}[/tex]Answer: the probability is 1/10 or 0.1.
-0.125 divided by (-0.5)
Help please
Answers
Answer:
Step-by-step explanation:
Since the numbers, we are given are fractions there is this ultimate rule when we divide fractions
the sign changes from division to multiplciation and the second fraction flips
so lets do this
-0.125 = -1/8
-0.5 = -1/2
Now lets put into into an equation
-1/8 * -2 = 1/4
What is 1/0 and how explain
Answers
Answer:0
Step-by-step explanation:anything divided or multiplied by zero is zero for example how many times does 6 go into 0? ....zero!
Joey invented an electric light device to put on his 26-inch diameter bicycle
wheel. Every time the tire makes a full revolution, a wire touches a battery
contact and a light flashes on the back of the bike seat. How many times will
the light flash if he rides 50 yards?
π = 3.14
F
G
H
J
2 times
7 times
22 times
82 times
Answers
If he rides 50 yards then the light will flash 22 times.
Given,
Diameter of wheel =26 inch
Radius of wheel,r=[tex]\frac{26}{2}=13 inch[/tex]
Distance covered by bicycle =50 yards =50*36=1800 inch
First find the perimeter of wheel,
[tex]Perimeter =2\pi r\\\\Perimeter =2*3.14*13\\\\Perimeter =81.64[/tex]
This perimeter represents the distance covered for 1 revolution
Now, to find number of times of revolution,
[tex]\frac{Total\ distance\ covered }{distance\ covered\ for\ 1\ revolution}\\\\=\frac{1800}{81.64}\\\\=22.04[/tex]
So,it will take 22 revolutions to complete the whole distance.
Hence, the light will flash 22 times if he rides 50 yards.
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HELP PLEASE. WILL GIVE BRAINLIEST.
Partition a segment.
Answers
The coordinate of first stop of bus which is halfway through the route. is (9, -9).
What is coordinate?
Using the horizontal and vertical separations from the two reference axes, a coordinate is a pair of numbers that expresses a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
We have to find the coordinate of first stop of bus which is halfway through the route.
It means, We have to find the coordinates of the midpoint of line segment which has start point and end point coordinates as A(-10, 10) and B(8, -8).
The formula to get the mid point coordinate of a line segment which start point and end point coordinates as A(x₁, y₁) and B(x₂, y₂) is:
[tex]M(a,b) = (\frac{x_2 -x_1}{2} , \frac{y_2-y_1}{2} )[/tex]
putting the value from question:
[tex]M(a,b) = (\frac{8 -(-10)}{2} , \frac{-8-10}{2} )[/tex]
M(a, b) = (9, -9)
Therefore the coordinate of the midpoint is (9, -9)
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer:
10.8 sec
Step-by-step explanation:
Setting [tex]h=10[/tex],
[tex]-16t^2+170t+40=10 \\ \\ 16t^2 -170t-30=0 \\ \\ 8t^2 - 85t-15=0 \\ \\ t=\frac{85 \pm \sqrt{(-85)^2-4(8)(-15)}}{2(8)} \\ \\ t \approx 10.8 (t>0)[/tex]
help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
Which of the fractions is equivalent to 2/5
Answers
Answer:
all the fractions that are equivalent to 2/5 are 4/10, 6/15, 8/20
Step-by-step explanation:
this is all I can rember
Rebekah walks 10 miles in 3 hours. At what unit rate does Rebekahwalk?10/3 miles / 1 hour3 miles / 10 hoursООО10 miles / 3 hours3 hours / 10 miles
Answers
ANSWER
(10/3 miles) / (1 hour)
EXPLANATION
A unit rate is a rate where the denominator is 1. In this problem, the denominator is the time in hours. If Rebekah walks 10 miles in 3 hours, we have to find how many miles will she walk in 1 hour,
[tex]1hour\cdot\frac{10miles}{3hours}=\frac{10}{3}miles[/tex]She will run 10/3 miles in 1 hour. Hence the unit rate is (10/3 miles) / (1 hour).
Albert bought 3 rolls of masking tape that cost the same amount of money and an extension cord that cost $5.50. Albert spent less than $10 altogether.Which inequality can be used to find the cost of each roll of masking tape?A.) 3m+5.50<10B.) 3m-5.50<10C.) 3m+5.50>10D.) 3m-5.50>10
Answers
Data:
m: cost of the masking tape
As the masking cost the same amount of money: 3m
Then, you add to the cost of the masking the 5.50, you get: 3m+5.50
The symbol to less than is <
You get:
[tex]3m+5.50<10[/tex]