Answer: a=3 and b=1
Step-by-step explanation:
Let p(x)=x 2 +ax+2b
If x+2 is a factor of p(x)
Then by factor theorem
p(−2)=0
⇒(−2)
2
+a(−2)+2b=0
⇒4−2a+2b=0
⇒a−b=2 ---(i)
Also given that a+b=4 ---(ii)
Adiing (i) and (ii) we get
2a=6
⇒a=3
putting a=3 in (i) we get
a−b=2
⇒3−b=2
⇒b=1
Therefore we get a=3 and b=1
Mrs. Cho has 24 students in her class. Some of her students are also in the play.
Explain why it is not possible for exactly 24% of the students in Mrs. Cho’s class to be in the play.
914 1404 393
Answer:
24% of 24 is not a whole number
Step-by-step explanation:
24% of Mrs. Cho's students is ...
0.24 × 24 = 5.76 . . . students
This is not a whole number. The number of students must be a whole number. There cannot be part of a student in the play.
7) You buy a new car for $25,000 and it begins
to depreciate value as soon as you drive it off
the lot. The car depreciates at an annual rate
of 7%. Write an exponential equation that
shows what is happening to the value of the
car over time.
Answer:
y=25,000(0.07)^t
Step-by-step explanation: t= year/month. not specified, but year is most appropriate for these kind of equations.
Find each value.
7) P(8,3)
a) 512
b) 336
c) 6
d) 24
Answer:
answer is 336
Step-by-step explanation:
I hope you understand what I wrote
How much will you save If you buy an Item listed at $575.50 at a 30 percent discount?
OA. $172.65
OB.
$176.25
O C. $185.63
Reset
Next
Answer:
Answer is A $172.25
Step-by-step explanation:
Step 1: Our output value is 575.50.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$575.50=100\%$.
Step 4: Similarly, $x=30\%$.
Step 5: This results in a pair of simple equations
$575.50=100\%(1)$.
$x=30\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{575.50}{x}=\frac{100\%}{30\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{575.50}=\frac{30}{100}$
$\Rightarrow x=172.65$
Therefore, $30\%$ of $575.50$ is $172.65$
Answer:
The total that will be saved at a 30% discount is $172.65
Explanation:
Since, the marked up price of the item will be $575.50,
and the discount percentage is 30%,
Therefore, $ 172.65 will be saved.
Which of the expressions below is the product of (x+2y) and (2x−3y)?
Answer:
(x +2y ) ( 2x-3y)
= 2x² + 4xy -3xy -6y²
= 2x² +xy -6y²
Step-by-step explanation:
2x^2 +xy-6y is the answer
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm
Calculating the area of the composite figureThe sector area
The area of the sector is calculated as
Area = x/360 * πr²
Where
r² = 8² + 6²
So, we have
r² = 100
This means that
Area = 82/360 * π * 100
Evaluate
Area = 71.55
The triangle area
This is calculated as
Area = 0.5bh
So, we have
Area = 0.5 * 8 * 6
Evaluate
Area = 24
So, the area of the figure is
Figure = 24 + 71.55
Figure = 95.55
Hence, the area is 95.55
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If | 8x -2 | < 4, Which of the following is true of x? Explain as well.
A. -0.75 < x < 0.25
B. -0.25 < x < 0.75
C. 0.25 < x< 0.75
D. x > 0
The true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to determine the true expression of the variable x?The inequality expression is given as
|8x - 2| < 4
Divide through the above equations by 2
So, we have the following inequality expression
|4x - 1| < 2
Remove the absolute value sign from the inequality expression
So, we have
-2 < 4x - 1 < 2
Add 1 to all sides of the above inequality expression
So, we have
-1 < 4x < 3
Divide through the above inequality expression by 4
So, we have
-0.25 < x < 0.75
Hence, the true expression of the variable x in the inequality expression given as |8x - 2| < 4 is -0.25 < x < 0.75
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A genetic experiment with peas resulted in one sample of offspring that consisted of 440 green peas and 155 yellow peas.
a. Construct a 95% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
The 95 percent confidence interval is (0.20, 0.32).
a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:
Let p = proportion of yellow peas = 155/595 = 0.26
Sample size = n = 595
Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03
95% confidence interval = p ± 1.96 × SE
= 0.26 ± 1.96 × 0.03
= 0.26 ± 0.06
So, the 95% confidence interval is (0.20, 0.32).
b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.
Therefore, the 95 percent confidence interval is (0.20, 0.32).
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I have 2 thousands,12 tens,5 hundred and 9 one
Answer:
2 120 500 9. so 2,629 would be the answer
What conclusion can you make about quadrilateral ABCD? Why?
The quadrilateral ABCD is a parallelogram as the opposite sides are equal but not a rectangle because all the interior angles are not right angles.
What is a quadrilateral?A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.
To make any conclusion about the quadrilateral we have to look at the lengths of each side by the distance formula \(D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2\).
AB = \(\sqrt{(4 - 0)^2 + (2 - 8)^2\).
AB = \(\sqrt{16 + 36\).
|AB| = √52.
Similarly, |DC| = √52.
So, AB = DC.
Now, |AD| = √85 and |BC| = √85.
So, AD = BC.
Therefore, The lengths of the opposite sides are equal so it is a parallelogram.
Now, To be a rectangle DC ⊥ CB.
Slope(DC) = 6/- 4 = - 3/2.
Slope(CB) = - 6/ - 7 = 6/7.
So The quadrilateral ABCD is a parallelogram.
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Which expression is equivalent to the following complex fraction?
24
х у
-5 3
ух
+
О
3y+5х
2(у-2х)
2(у-2х)
Зу-5x
О.
у
2(у-2x)(Зу-5x)
х?у?
О
х?у?
2(у-2x)(Зу- 5x)
Answer:
\( \frac{ \frac{2}{x} - \frac{4}{y} }{ \frac{3}{x} - \frac{5}{y} } = \frac{ \frac{2y - 4x}{xy} }{ \frac{3y - 5x}{xy} } = \frac{2y - 4x}{3y - 5x} = \frac{2(y - 2x)}{3y - 5x} \)
Help me solve the equivalent expression (4x+2)-3x+5
Answer:
X+7
Step-by-step explanation:
Remove the parentheses:
4x+2-3x+5
Collect like terms:
4x-3x=x
2+5=7
Solution:
X+7
Hey there!
(4x + 2) - 3x + 5
= 4x + 2 - 3x + 5
COMBINE the LIKE TERMS
= (4x - 3x) + (2 + 5)
= 4x - 3x + 2 + 5
= 1x + 7
= x + 7
Therefore, your answer is: x + 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELP PLEASE! VERY URGENT
Answer:
can i have brainlest pls
Simplify the expression 4x^3 2x^3
Answer:
Step-by-step explanation:
2 3x6
the 3 is an exponet so supost to be smaller
the answer- 2^3 x^6
i think its right
What do 3 sides of an isosceles triangle equal?
An isosceles triangle with all 3 sides equal is called an equilateral triangle.
What is an equilateral triangle?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces.
The isosceles right triangle is yet another unique instance of an isosceles triangle.
Therefore, an isosceles triangle with all 3 sides equal is called an equilateral triangle.
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Complete question:
What do the 3 sides of an isosceles triangle equal is called?
A cylinder has a height of 20 cm and a diameter of
6 cm. What is the volume, in cubic centimeters, of the
cylinder? Use 3.14 for T.
√-25/√9 please solve
Step-by-step explanation:
The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.
Let's break down the expression step by step:
√(-25) / √9
The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.
√(-1) is equal to "i," and the square root of 25 is 5.
So, the expression becomes:
i * 5 / √9
The square root of 9 is 3.
Now, we can simplify further:
i * 5 / 3
Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.
Evaluate this piecewise function at x = -8 and x = 4.
Answer:
option D :
f(-8) = -2 ; f(4) = 3
Step-by-step explanation:
f(-8) = ³√-8 = -2
f(4) = 3 (the constant function)
What is the solution to the equation?
4q + 4 = 20
Question 4 options:
q = 4
q = 6
q = 16
q = 24
Answer:
q = 4
Step-by-step explanation:
4q + 4 = 20
or, 4q = 20 - 4
or, q = 16/4
or, q = 4
Carla has $45. Pineapples cost $5 each and mangos cost $2 each. Let p stand for pineapples and let m stand for mangos. Write an inequality to show how many of each Carla can buy.
Answer
24
Step-by-step explanation:
2:2 = 8
45 / 5 = 168
168 - 45 = 123
123 - 45 = 78
78 take away the 7 is 8 , 8 x 5 = 40 / 8 = 24
Answer:
$5(p)+$2(m) ≤ $45
Step-by-step explanation:
If you have a maximum of 45 dollars you are only able to spend 45 dollars or less so the variables that are filled in with the amount of pineapples and mango´s Carla wants to buy must be less than or equal to 45
The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85
Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Solution:
Step 1: Set up a table with quantity and value.
quantityvaluetotal$3 tickets$2 ticketstogether
Step 2: Fill in the table with information from the question.
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Let x = number of $3 tickets
Let y = number of $2 tickets
Total = quantity × value
quantityvaluetotal$3 ticketsx33x$2 ticketsy22ytogether350950
Step 3: Add down each column to get the equations
x + y = 350 (equation 1)
3x + 2y = 950 (equation 2)
Use Substitution Method
Isolate variable x in equation 1
x = 350 – y (equation 3)
Substitute equation 3 into equation 2
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
Assistance please please please
Answer:
x = 12
Step-by-step explanation:
You can solve this problem by using ratios of corresponding sides.
Assume that when adults with smartphones are randomly selected, 58% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find theprobability that exactly 3 of them use their smartphones in meetings or classesThe probability is a
This is a binomial probability distribution question.
The binomial probability formula is >>>
\(P(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}_{}\)Where
n is the number of trials (number being sampled)
x is the number of success desired
p is the probability of getting a success
q = 1 - p is the probability of failure
From the given problem,
n = 6
x = 3
p = 58% = 0.58
q = 1 - p = 1 - 0.58 = 0.42
Substituting into the formula, we find the probability that exactly 3 of the people use smartphone in meetings or classes:
\(\begin{gathered} P(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}_{} \\ P(x=3)=\frac{6!}{(6-3)!3!}(0.58)^3(0.42)^{6-3}_{} \\ =\frac{6!}{3!3!}(0.58)^3(0.42)^3 \\ =0.2891 \end{gathered}\)100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
In a mosaic, 18 tiles out of 50 are blue. What percent of the tiles are blue?
Answer:
The answer is 36%
Step-by-step explanation:
18/50 x2 = 36/100
.36 = 36%
Hope this helps
Answer:
36%
Step-by-step explanation:
Another question I need help with. Thank you
Answer:
The answer is 5t
Step-by-step explanation:
7th grade help me plzz
Answer: The temperature rose 20 degrees celsius
Step-by-step explanation:
the difference between -10 and 10 is 20.
Answer: 20 degrees Celsius
Step-by-step explanation:
Explanation:it just is do the math
Ravi says,” if 10 years are added to my age, then my age becomes 25.”if Ravi’s present age is x years,
then find the linear equation satisfying the given condition.
Answer:
The linear equation satisfying the given condition is,
\(x=t+15\)
where x is Ravi's age and t is the number of years
(after 10 years (t=10) his age becomes 25)
Step-by-step explanation:
Let x be Ravi's age
Now, his current age is unknown, but if you add 10 to it, then it becomes 25, so
x + 10 =25
so, his current age is x = 25 =10
x = 15
Now, we find the linear equation satisfying the given condition,
Let t be the number of years that have passed since the present time
so, if 0 years have passed, his age will be 15 years
after 1 year, his age will be 16 years
after 10 years, his age will be 25 years and so on
so
\(x = t + 15\)
this satisfies the given condition, since if we add ten years i.e t = 10,
then we get 25
The equation is:
⇨ x + 10 = 25Work/explanation:
Here's the linear equation for Ravi's age.
Ravi's age is x.
If you add 10 to x you get x + 10.
That gives 25.
So the linear equation is x + 10 = 25.
ASAP..... The distance traveled after the driver hit the brakes.....
1: acceleration distance
2: Breaking distance
3: stopping distance
PLEASE HELP ILL GIVE YOU POINTS
Answer:
2. Breaking distance
Step-by-step explanation:
The distance traveled after the driver hit the break is called breaking distance.