Answers
(x+a)(x+3a)= x²+bx+75
x²+4a+3a²=x²+bx+75
by comparing 3a²=75 and b= 4a
a= ±5
possible values of b= ±20
Two possible values of b are 20 and -20.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The mathematical expression as;
(x + a)(x + 3a) = x² + bx + 75
Now,
The mathematical expression is;
(x + a)(x + 3a) = x² + bx + 75
Solve the expression as;
(x + a)(x + 3a) = x² + bx + 75
x² + 3ax + ax + 3a² = x² + bx + 75
x² + 4ax + 3a² = x² + bx + 75
After comparison we get;
4a = b ... (i)
And, 3a² = 75 .. (ii)
Solve the second equation for a as;
3a² = 75
Divide by 3;
a² = 25
Take square root both side, we get;
a = ± 5
So, By equation (i) we get;
b = 4a
Substitute a = 5;
b = 4 x 5
b = 20
And, Substitute b = -5;
b = 4 x -5
b = -20
Thus, Two possible values of b are 20 and -20.
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Related Questions
Here is the graph of a quadratic function f.
Answers
Answer:
B) x² - 8x + 12
E) (x -4)² - 4
F) (x - 2)(x - 6)
Explanation:
As the graph opens upwards. The value of x² will be positive.
The x intercepts are (2, 0), (6, 0) determining (x -2)(x-6)
The (x - 4)² - 4 determines the vertex of x = 4, y = -4
When simplified:
⇒ (x -2)(x-6)
⇒ x² - 2x -6x + 12
⇒ x² - 8x + 12
Does this graph represent a function? Why or why not?
10-
8-
6-
2
--8-
-10-
O A. No, because it fails the vertical line test.
OB. Yes, because it passes the vertical line test.
OC. Yes, because it is a curved line.
OD. No, because it is not a straight line.
-1080
Answers
What is the slope and the y intercept of the line on the graph below?
Answers
The slope and the y intercept of the line on the graph is -1/4 and 1.
What is a Straight Line Function ?A straight line function is what can be written in the form of
y =mx +c
where m is the slope and c is the intercept on y axis.
The intercept on the y axis , c = 1
at x = 4 , y=0
and at x = 0, y =1
The slope can be calculated as
y = mx+1
0 = 4m +1
m = -1/4
Therefore the slope and the y intercept of the line on the graph is -1/4 and 1.
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PLEASE HELP ITS WORTH 20 points and ILL LIKE
Answers
Answer:
es kunno.............................
help me out bro please give me the right answer
Answers
Answer:
Always
Step-by-step explanation:
The alternate interiors are the orange pair and the green pair in between lines a and b. They've got symmetry! Rotating one of those lines 180 degrees won't change the picture or the angles of intersection, but it will flip one onto the other. Anyway, there's you answer above, if that's all you're looking for.
Find the quotient of 1 4/5 and 1 1/5
Give your answer as a fraction in its simplest form
Answers
Answer: 1 1/2
Step-by-step explanation:
1 4/5 = 9/5
1 1/5 = 6/5
[tex]\frac{9}{5} / \frac{6}{5}\\ \\\frac{9}{5} * \frac{5}{6}\\ \\\frac{45}{30} \\ \\1\frac{1}{2}[/tex]
Math
Club
7
6
Debate
Club
15
O
Let p: a student is in the math club and q. a student is
in the debate club.
The verbal translation of p v q is:
A student is in math club
in debate club.
pvq is true for a total of
students.
Answers
The verbal translation of p v q is:
A student is in math club OR debate club
pvq is true for a total of 28 students.
Calculations and Parameters:Given the table:
Math Club Debate Club7 15
6
If p represents a student from the maths club
If a represents a student from the debate club
The verbal translation of p v q is:
A student is in math club OR debate club
Hence, the total number of students based on pvq is 7 + 6 + 15= 28 students.
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Multiply. Write your answer as a fraction or as a whole or mixed number.
4/5 x 3 2/3
Answers
Answer:
1 14/15
Step-by-step explanation:
Change 3 2/3 into an improper fraction, which is 11/3. When multiplying fractions, you can multiply straight across, so 11*4= 44 and 3*5 equals 15. 44/15 as a mixed fraction is 1 14/15
solve for x. x^2+12x<-11
Answers
x²+12x<-11
x²+12x+11<0
x²+12x+11=0
(x+11)(x+1)=0
x+11=0 x+1=0
x= -11 x= -1
Solution: ] -11 , -1 [
please solve the question and give correct answer with explanation so that i can understand it
Answers
Answer:
YesStep-by-step explanation:
Let the speed of the car is c and speed of the plane is p.
We are given:The speed of the plane is 7 times the speed of the car
p = 7cThe distance traveled is
d = 315 kmThe time difference to travel this same distance is 3 hours.
We know that:d = ts, where d- distance, t- time, s - speedFind the time for car and plane and their difference.
Cart = d/s = 315/cPlanet = d/s = 315/p = 315/(7c) = 35/cThe difference315/c - 45/c = 3Solve it for c:
(315 - 45)/c = 3270/c = 3c = 270/3c = 90 km/hNow find the speed of plane:
p = 7c = 7*90 = 630 km/hAs we see, Jenny is right
After surveying students in her homeroom, katie decided to use a number cube to predict the probability that a randomly chosen student in her school planned to stay after school today for extracurricular activities. in katie’s simulation, a roll of 1 represents staying after school, while rolls of 2, 3, 4, 5, or 6 represent leaving school at the end of classes. according to katie’s model, what is the probability that three randomly chosen students will all stay after school for extracurricular activities today? startfraction 1 over 729 endfraction startfraction 1 over 216 endfraction startfraction 1 over 18 endfraction startfraction 1 over 6 endfraction
Answers
Using it's concept, it is found that the probability that three randomly chosen students will all stay after school for extracurricular activities today is of [tex]\frac{1}{216}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, for each student, one out of six rolls represent staying after school, hence there is a [tex]\frac{1}{6}[/tex] probability they stay after school. For the three students, the probability is given by:
[tex]p = \left(\frac{1}{6}\right)^3 = \frac{1}{216}[/tex]
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Which number produces a rational number when multiplied by
O A. 10
( в. я
O C. 144
11
OD. 2.64575131..
Answers
The number that will produce a rational number when multiplied by 1/5 is A. 10.
What is a rational number?A rational number is one that can be written in the form of a fraction where the denominator isn't 0. This number is an integer and does not repeat infinitely.
When 1/5 is multiplied by 10 we get:
= 1/5 x 10
= 2
2 is a rational number so option A is correct.
The full question is:
Which number produces a rational number when multiplied by 1/5?
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atty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and how many quarters did
he have?
Which of the following equations could be used to solve the problem?
n+5n=1,260
25n+100 n=1,260
On+ 5 n=12.60
O5 n+100 n=12.60
Answers
Solve x + 5 = 7.
OA. x = -2 and x = 12
OB. x = 2 and x = -2
C. x = 2 and x = -12
OD. x = -2 and x = -12
Answers
|x+5| = 7 (Spilt into 2 problems)
X+5=7
X+5=-7
Solve for x on both
x=2 and x=-12
You conduct a survey that asks 271 students in your class whether they are attending the class field trip. One hundred twenty-one males respond, 92 of which are attending the field trip. Thirty-one females are not attending the field trip. What percent of females are attending the class field trip?
Answers
Answer:
79% of females are attending the class field trip
Step-by-step explanation:
Question Breakdown:
- Survey 271 students
- 121 males respond, 92 attending field trip
- 31 females not attending field trip
What percent of females are attending the class field trip?
The two-way table or the class whether they are attending the field trip or not is attached below,
The table tells us
• Males who are not attending : 121 - 192 = 29
• Total females who responded : 271 - 121 = 150
• Females who are attending : 250 - 31 = 119
• Total students who are attending : 91 + 119 = 211
• Total students who are not attending : 29 +31 = 60
There are a total of 150 female students and 119 of them are attending the field trip
[tex]\frac{119}{150} = 0.79 x 100 = 79%[/tex]
vFind the mean and median of the data set. 3, 5, 6, 2, 10, 9, 7, 5, 11, 6, 4, 2, 5, 4
Answers
Step-by-step explanation:
2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 9, 10
_
2+2+3+4+5+5+5+6+6+7+9+10 = 64 ÷ 12 = 5.3
_
Mean: 5.3
Median: 5
Is this relation a function? Justify your answer.
Answers
Answer:
Can't see the problem. Send a picture of it.
What is the midpoint of the vertical line segment graphed below?
y
-5
5
(1,4)
-5-(1,-5)
5
Answers
Answer:
see the attachment photo!
Answer:
C. (1, -1/2)
Step-by-step explanation:
The midpoint of a line segment has coordinates that are the average of the end point coordinates.
__
M = (A +B)/2 . . . . . . midpoint of segment between A(1, 4) and B(1, -5)
M = ((1, 4) +(1, -5))/2 = (1 +1, 4 -5)/2 = (2, -1)/2
M = (1, -1/2)
The midpoint of the vertical line segment is (1, -1/2).
_____
Additional comment
The midpoint will always be on the line segment. Since this line segment is vertical with x = 1, the x-coordinate of the midpoint must be 1.
Brandon is analyzing the profits from two of his restaurant locations. the first location showed a profit of $3,000 in the first week of the year but has a showed a steady decrease in profits of 1.5% each week since then. his second location showed a profit of $1,500 in the first week of the year and has showed a steady increase in profits of 1.2% each week since then. which system of equations can brandon use to determine the number of weeks, x, until the profits, y, from the two locations are the same? a. b. c. d.
Answers
The system of exponential functions that can be used to determine the time for the profits to be the same is given by:
[tex]3000(0.985)^x = 1500(1.012)^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]A(t) = A(0)(1 \pm r)^t[/tex]
In which:
A(0) is the initial value.r is the rate of change, as a decimal.For the first restaurant, we have that the parameters are given as follows:
A(0) = 3000, r = -0.015.
Hence the profit after x weeks is given by:
[tex]y_1(x) = 3000(0.985)^x[/tex]
For the second restaurant, we have that:
A(0) = 1500, r = 0.012.
Hence:
[tex]y_2(x) = 1500(1.012)^x[/tex]
Then they will be equal when:
[tex]y_1(x) = y_2(x)[/tex]
[tex]3000(0.985)^x = 1500(1.012)^x[/tex]
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Answer:
Answer:
y=3,000(0.985)^x
y=1,500(1.012)^x
Step-by-step explanation:
plato 2022
Laura worked 8 hours today. She spent
the time in meetings, on the phone,
and the rest of the time on the computer.
Make a circle graph to show how Laura
spent her work day.
Answers
In the function f(x) = a(x + 2)(x-3)^b, a and b are both
integer constants and b is positive. If the end behavior
of the graph of y = f(x) is positive for both very large
negative values of x and very large positive values of x,
what is true about a and b?
A. a is negative, and b is even.
B. a is positive, and b is even.
C. a is negative, and b is odd.
D. a is positive, and b is odd.
Answers
Using limits, considering the end behavior of the function f(x), it is found that the correct statement is given as follows:
D. a is positive, and b is odd.
What is the end behavior of a function?It is given by it's limits as x goes to negative and positive infinity.
In this problem, we have that, considering the end behavior:
[tex]\lim_{x \rightarrow \infty} = \infty \rightarrow ax^{b + 1} = \infty[/tex][tex]\lim_{x \rightarrow -\infty} = \infty \rightarrow ax^{b + 1} = \infty[/tex]This will only be true if a is positive and b is odd, hence option D is correct.
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An elevator can hold a maximum of 1500 pounds. An average child weighs 75 pounds and the average adult weighs 150 pounds. The elevator also can’t fit more than 14 people. How many children and adults can fit in the elevator and stay under the weight limit. Write the inequalities that represent the word problem, and then graph it on DESMOS. What is a solution that represents the amount of children and adults and their combined weight?
Answers
Let's take this problem step-by-step:
Let's first set up some variables:
c: # of childrena: # of adultsLet's examine the information given:
Elevator can hold a maximum of 1500 pounds⇒ average child is 75 pounds
⇒ average adult is 150 pounds
⇒ therefore: [tex]75c + 150a\leq 1500[/tex]
Elevator can fit no more than 14 people⇒ therefore: [tex]c + a \leq 14[/tex]
Let's graph the equations:
[tex]75c+150a\leq 1500\\c+a\leq 14[/tex]
⇒ look at the image attached
The point at which the two graphs intersect:
⇒ is the solution that represents the amount of children and adults and
their combine weight
With the horizontal axis being the # of children and vertical axis being the # of adults:
⇒ the solution is 8 children and 6 adults
Answer: 8 children and 6 adults
Hope that helped!
Simplify the expression given below.
(17^14)^20
A. 289^34
B. 289^280
C. 17^280
D. 17^34
Answers
Answer: Heyaa! ^^
When you simplify (17^14)^20 Your Answer is
C. 17^280Step-by-step explanation:
Multiply the exponents in (17^14)^20And Simplify!!Hopefully this helps you!
In a class there are two girls for every three boys. The ratio 2 : 3 compares the
number of girls to the number of boys.
a) What is the ratio of boys to the whole class? - 3:5
b) If this class has eight girls, determine how many boys there are using the ratio that there are two girls for every three boys
Answers
Answer:
a. I'm not sure if there's more to the question but I can't answer without knowing how many is the whole class
B. 12 boys
A box 10 centimeters high, 5 centimeters long, and 5 centimeters wide.Find the volume of a box with a length of 5 cm, a width of 5 cm, and a height of 10 cm.
Answers
Answer:
250 [tex]cm^{3}[/tex]
Step-by-step explanation:
First, start with the formula for the volume of a rectangular prism (aka a box):
V=length*width*height
Then, plug in your values:
V=5*5*10
V=25*10
V=250
Don't forget your units!
250 [tex]cm^{3}[/tex]
What type of function is represented by the table of values below?
y
4
8
12
16
20
A. exponential
B. cubic
C. linear
D. quadratic
X12345
X
Answers
Answer
The type of function that is represented by the table of values below is C. linear
There are 18 students on the debate club. How many ways can the club send 4 students to the next debate?.
Answers
Let's consider first what equation we must use:
⇒ use Combination Formula ⇒ [tex]._{n} C_{r}=\frac{n!}{r!(n-r)!}[/tex]
⇒ where 'n' is the total number of items and 'r'
is the number of items to choose
Let's look at the problem:
total number of students: 18number of students needed for debate: 4Let's plug it in:
[tex]\frac{18!}{4!*(18-4)!} =\frac{18!}{4!*14!} =\frac{18*17*16*15}{4*3*2*1} =18*17*2*5=3060[/tex]
Thus there are 3060 ways
Answer: 3060 ways
Hope that helps!
HELP ME PLEASE............................................................
Answers
Answer:
2√6
Step-by-step explanation:
find the hypotenuse of the triangle thats 3 and 7
pythagorean
3 squared + 7 squared
16 + 49 = 57
√57 is the hypotenuse
√57 is also the base of the triangle that has side thats 9
pythagorean theorem
x squared + √57 squared = 9 squared
x^2 + 57 = 81
x^2 = 81 - 57
x^2 = 24
x = √24
x = √4 * √6
x = 2√6
Would the answer for c be 21 square root of 3?
Answers
Answer:
c = 14√3 km
Step-by-step explanation:
[tex]x\sqrt{3} =42\Longrightarrow x=\frac{42}{\sqrt{3} } = \frac{42 \times \sqrt{3} }{\sqrt{3}\times \sqrt{3} }=\frac{42 \times \sqrt{3} }{3 }=14 \sqrt{3}[/tex]
Since c = x
Then
c = 14√3
Francesca is growing 1/2 inch each year. How many years will it take for her to grow 6 inches?
Answers
Answer:
12 years
Step-by-step explanation:
1 inch = two years
6x2=12