(3x-2)(3x+ 2)
Multiply each term in one set of parentheses by the other terms:
3x x 3x =9x^2
3x x 2 = 6x
-2 x 3x = -6x
-2 x 2 = -4
Combine to get:
9x^2 + 6x - 6x -4
Combine like terms:
9x^2 - 4
The value of a would be 9.
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
(3x − 2)(3x + 2) = ax2 − b⠀⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀what is the value of a?⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
At first we have to solve the value of (3x-2)(3x+2)
[tex]\sf{(3x-2)(3x+2) }[/tex] [tex]\sf{3x(3x+2)-2(3x+2) }[/tex] [tex]\sf{9x^{2}+6x-6x-4 }[/tex] [tex]\sf{9x^{2}-4 }[/tex]According to the question,
[tex]\sf{ (3x − 2)(3x + 2) = ax^{2} − b }[/tex] [tex]\sf{9x^{2}-4=ax^{2}-b }[/tex] [tex]\sf{9x^{2}=ax^{2}~and~-4=-b }[/tex] [tex]\sf{a=9~and~b=4 }[/tex]⠀⠀⠀
[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
Hence,
The value of a is 9
PLZ ANSWER ASAP
(look at images below, from khan)
Answer:
D Replace on equation with sum /difference of both equations
The systems are still the same
Step-by-step explanation:
5x + y = 3
4x - 7y = 8
Subtract the second equation from the first
5x + y = 3
-(4x - 7y = 8)
-----------------
x +8y = -5
The second equation in system B is the first equation in system a minus the second equation in system A
We added the same thing to each side of the equation so the the system is still the same
Which of the following is correctly written in Standard Form? −3x + 7y = 12, y = 3/7x + 6 ,5x − 4y = 9 ,3/7x + 2y =9
A study of the effects of color on easing anxiety compared anxiety test scores of participants who completed the test printed on either soft yellow paper or on harsh green paper. The scores for five participants who completed the test printed on the yellow paper were 17, 19, 28, 21, and 1 8. The scores for four participants who completed the test on the green paper were 20, 26, 17, and 24. Using the .05 level, test the researcher's prediction that participants should have lower anxiety scores when taking the test on the yellow paper than when taking the test on the green paper. What is the research hypothesis
Answer:
H0 : μYellow = μGreen
H1 : μYellow < μGreen
Step-by-step explanation:
Let :
Yellow paper = μYellow
Green paper = μGreen
To test the hypothesis :
The null hypothesis is will state that there is no difference in mean of anxiety scores obtained for test taken of yellow and green papers
H0 : μYellow = μGreen.
The alternative hypothesis is the opposite of the null and it is to the left, where we want to test if the anxiety score is lower when take on a yellow paper
H1 : μYellow < μGreen
On a map, the scale shown is 1 inch : 5 miles. If an island is 2.5 squire inches on the map, what is the actual area of the island? The actual island's area is square miles.
Answer:
62.5 square miles
Step-by-step explanation:
if the scale is 1 in. = 5 mi, then 1 square in. = 25 square miles
so if 1 in^2 = 25 mi^2
then you make a proportion
25/1 = x/2.5
(the square inches on the bottom and the square miles on top)
solving for x gives you
x=62.5 square miles
Use the graph to determine the input values that correspond with f(x) = 1.
Answer:
[tex]x = -7[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
Given
See attachment for graph
Required
Find x, for [tex]f(x)= 1[/tex]
From the graph, we have the following readings
[tex]f(x)= 1[/tex] when:
[tex]x = 2[/tex] and [tex]x = -7[/tex]
Hence, (d) is correct
Which of the following methods of sampling is an example of a stratified random sample?
A. Randomly choosing a name from a list of names in the population and then choosing every tenth name thereafter.
B. From 500 names of members of a population in a hat drawing 50 names from the hat without looking.
C. Dividing a target population of students by grade level and choosing the first 25 names from each group.
D. Dividing a population of adults into males and females and randomly choosing a sample proportional to the numbers in each group.
Answer: D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
A painter can paint 36 feet of molding per hour. How many inches of molding can he paint per hour?
Answer:
432 inches
Step-by-step explanation:
We need to convert feet to inches
1 ft = 12 inches
36 ft * 12 inches/ 1 ft = 432 inches
Can someone help me out
Answer:
π×64×4=804.25
Step-by-step explanation:
Formula of cylinder is π×square of radius×height
Answer:
803.8
Step-by-step explanation:
it's 3.14×8×8×4 which would give you 803.84 and then you round which would give you 803.8
strontium-90 is a radioactive material that decays according to the function A(t)=A0e−0.0244t, where A0 is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of 400 grams of strontium-90.
(a) What is the decay rate of strontium-90?
(b) How much strontium-90 is left after 30 years?
(c) When will only 100 grams of strontium-90 be left?
(d) What is the half-life of strontium-90?
(a) The decay rate of strontium-90 is nothing%.
(Type an integer or a decimal. Include the negative sign for the decay rate.)
Answer:
Step-by-step explanation:
The decay rate of strontium-90 is -.0244 as given.
For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.
[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to
A(t) = 400(.4809461353) so
A(t) = 192.4 g
For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:
[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:
[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:
[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:
ln(.25) = -.0244t and divide by -.0244:
61.8 years = t
For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:
[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:
[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:
[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:
ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):
[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:
[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and
H = 28.4 years
.Part D. Analyze the residuals.
Birth weight
(pounds)
Adult weight
(pounds)
Predicted
adult weight
Residual
1.5
10
3
17
1
8
2.5
14
0.75
5
a. Use the linear regression equation from Part C to calculate the predicted adult weight for each birth weight. Round to the nearest hundredth. Enter these in the third column of the table.
b. Find the residual for each birth weight. Round to the nearest hundredth. Enter these in the fourth column of the table.
c. Plot the residuals.
d. Based on the residuals, is your regression line a reasonable model for the data? Why or why not?
Answer:
Hi there! The answers will be in the explanation :D
Step-by-step explanation:
a) I'll attach a doc for the table so it'll basically answer a and b.
c) I'll also attach the graph.
d) I'm not entirely sure for this question, but I'll do my best to answer it correctly for you. I would say no, because we can see that the residuals are all positive, but the graph we're looking is going down which means it's negative. We can also see the table is increasing a bit so it doesn't really make any sense...
Hope this helped you!
the polygons in each pair are similar find the scale factor smaller figure to the larger
Answer:
smaller figure/larger figure = ½
Step-by-step explanation:
The scale factor = any of the side length of the smaller figure / the corresponding side length of the larger figure
Side length of smaller figure = 3
Corresponding sides length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = smaller figure/larger figure = ½
Simplify the algebraic expression by combining like (or similar) terms.
2x−y2+3−3y2+2x+1
Answer:
-4y^2 + 4x +4
Step-by-step explanation:
add -y^2 and -3y^2 = -4y^2
add 2x + 2x = 4x
add 3+1 = 4
and then rearrange
What is the product of these two binomials?
(x2 - 5)(2x - 1)
Select the correct answer.
o 2x3 - x2 + 10x - 5
O 2x3 - x2 - 10x-5
o 2x3 - x2 - 10x + 5
o 2x3 - x2 + 10x + 5
Answer:
2x³ - x² - 10x + 5
Step-by-step explanation:
Use FOIL method.
(x² - 5) (2x - 1) = x²*2x +(x²)*(-1) + (-5)*(2x) + (-5)*(-1)
= 2x³ - x² - 10x + 5
Billy jogs 4/5 kilometer every minute.How many kilometers does he jog after 6 1/8 minutes
5.4 km
0.8×6
0.8×0.75
4.8+0.6 =5.4
4/5 of a kilometer = 800m
6 1/8 minutes = 49/8 min
Now
800×49/8
= 100×49
= 4900m
= 4.9km
Must click thanks and mark brainliest
The probability of winning a raffle is 2/5. What is the probability of not winning the raffle?
0
3/5
2/5
Answer:
3/5
Step-by-step explanation:
um 3/5+2/5 = 1
Example 2.20
Solution
After 7% discount, Faizal get RM1,930 from a bank. He then promised to pay the bank RM2,000
after x days. Determine the value of x.
Kaspersk
Th
The period of days (value of x) for which Faizal promised to pay the bank RM 2,000 after getting 7% discounted present value of RM 1,930 is 180 days.
The value of x is the period of days (number of days) that the loan from the bank will last before Faizal, who received RM 1,930 discounted at 7%, would repay the bank the principal and interest of RM 2,000.
This implies that Faizal is paying an interest of RM 70 (RM 2,000 - RM 1,930), since he borrowed RM 1,930 and will repay RM 2,000.
Data and Calculations:
Present value of loan received = RM 1,930
Discount rate per year = 7%
Future value of the loan to be repaid to the bank = RM 2,000
Interest expense for one year based on 7% = RM 140 (RM 2,000 x 7%)
Interest expense for 180 days or 6 months = RM 70 (RM 2,000 - RM 1,930) or (RM 2,000 x 7%) x 180/360
Interest expense that equals RM 70 will be half of a year or 180 days (RM 140 * 180/360)
Thus, the period of days (x) that will lapse for Faizal to repay the bank is 180 days or half of a year (6 months).
Learn more about time period of a loan here: https://brainly.com/question/19118285
Larry made 14 baskets out of 21 attempts in a recent basketball game. If Scott attempted 24 baskets and made the same proportion of baskets as Larry, how many baskets did Scott make?
Scott made
baskets.
Answer:
16 baskets
Step-by-step explanation:
Create a proportion where x is the number of baskets that Scott made:
[tex]\frac{14}{21}[/tex] = [tex]\frac{x}{24}[/tex]
Cross multiply and solve for x:
21x = 336
x = 16
So, Scott made 16 baskets.
Use the distributive property to simplify
the equation below.
с
8(2a + 4b - c)
[? ]a + [ ]b - [
[ ]
Answer:
16a +32b - 8c
Step-by-step explanation:
8(2a + 4b - c)
Distribute
8*2a + 8*4b+ 8*(-c)
16a +32b - 8c
Answer:
16a + 32b - 8c
Step-by-step explanation:
You bring 8 inside the parenthesis and then multiply it with everything. so for a you put 16, b you put 32 and c you put 8
Factorize p2-15q-5p+2pq
Hope it's help you!!!!!!
16 • (14) =
-9 • (-8) =
- 13 • 7
Answer:
16×14 = -9×(-8) = -13×7
Falso
Step-by-step explanation:
Instructions: Given the vertex of a quadratic function, find the axis
of symmetry.
Vertex: (5,7)
Taking into account the definition of axis of simmetry and vertexn the axis of symmetry is x = 5.
So, first of all, you must know what a quadratic function is. Every quadratic function can be expressed as follows:
f(x) = a*x² + b*x + c
where a, b and c are real numbers.
Axis of symetryThe graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry.
That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are equal of each other.
In other words, the axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves and always passes through the vertex of the parabola.
VertexThe point of intersection of the axis of symmetry with the parabola is called the vertex.
The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
SummaryBeing the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.
Learn more with this examples:
https://brainly.com/question/2799442?referrer=searchResultshttps://brainly.com/question/20862832?referrer=searchResultshttps://brainly.com/question/15266651?referrer=searchResultsPlease help with Question 2b
Answer:
MUST BE IN HLA, NOT FROM C TO ASSEMBLY.
PROGRAM 6: Same
Write an HLA Assembly language program that implements a function which correctly identifies when all four parameters are the same and returns a boolean value in AL (1 when all four values are equal; 0 otherwise). This function should have the following signature:
procedure theSam
What are the values of a, b, and c in the quadratic equation 0 = one-halfx2 – 3x – 2?
a = one-half, b = 3, c = 2
a = one-half, b = –3, c = –2
a = one-half, b = 3, c = –2
a = one-half, b = –3, c = 2
Answer:
b
Step-by-step explanation:
ax^2+bx+c=0
1/2x^2-3x-2=0
Answer:
B
Step-by-step explanation:
Express b+1/3b-2 with “b” as the subject
Answer:
b = [tex]\frac{1+2a}{3a-1}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{b+1}{3b-2}[/tex] ( multiply both sides by 3b - 2 )
a(3b - 2) = b + 1 ← distribute left side
3ab - 2a = b + 1 ( subtract b from both sides )
3ab - b - 2a = 1 ( add 2a to both sides )
3ab - b = 1 + 2a ← factor out b from each term on the left side
b(3a - 1) = 1 + 2a ( divide both sides by 3a - 1 )
b = [tex]\frac{1+2a}{3a-1}[/tex]
Answer:
[tex]→a = \frac{(b + 1)}{(3b - 2)} \\ a(3b - 2) = (b + 1) \\ 3ab - 2a = b + 1 \\ 3ab - b = 2a + 1 \\ b(3a - 1) =( 2a + 1) \\ \boxed{b = \frac{(2a + 1)}{(3a - 1)} }✓[/tex]
b = (2a+1)/(3a-1) is the right answer.in a survey survey of 1200 students who have passed SEE 150 like to admit in science Faculty 600 in humanity first and 240 like to admit either of faculties and the rest were found not to be admitted in both faculties
Step-by-step explanation:
here is your answer it may help you
There are 700 don't like to admit in both faculties.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
In a survey, survey of 1200 students who have passed SEE 150 like to admit in science Faculty 600 in humanity first and 240 like to admit either of faculties and the rest were found not to be admitted in both faculties
Hence, not to be admit in any faculty = N
Science + Humanity - Either + None = 200
=> 150 + 600 - 240 + N = 1200
=> 750 - 240 + N = 1200
=> N = 700
Hence, 700 don't like to admit in both faculties.
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ2
10) Find three numbers whose product is -72. You may use integers from -10 to 10. Give two
examples
Answer:
Step-by-step explanation:
-8 * 9 * 1
If you are going to get - 72, you need to have an odd number of minus signs.
4 * 3 * - 6
You must be careful of the limits. You can't use something like 36 * 2 * 1 because the numbers don't fall within +/- 10
You could use 6*6*-2
URGENT PLS HELP! WILL GIVE BRAINLIEST (PICTURE INCLUDED)
Answer:
1605
Step-by-step explanation:
Hi! I would appreciate if you could solve this for me. The question I need help with is question 41. Thank you. :)
Answer:
Expression: 7+7+9.5+6+9.5
Evaluation: 39 cm
Step-by-step explanation:
Let's write the numerical expression for the figure to the right. The perimeter is the addition of all sides of the figure. Therefore, we write 7+7+9.5+6+9.5 for our expression.
Now, to evaluate the expression, we just add them together. 7+7+9.5+6+9.5=39 cm.
Find the value of x.
A. 4
B. 2
C. 3
D. 6
Answer:
b
Step-by-step explanation:
2x4=8 3x2=6 2x2=4
there all diviseble by 2
therfore ur answer is b
Answer:
the answer is 4
Step-by-step explanation:
A basic cellular package costs $30/month for 60 minutes of calling with an additional charge of $0.40/minute beyond that time. The cost function C (2) for using x minutes would be • If you used 60 minutes or less, i.e. if if x < 60, then C (x) = 30 (the base charge). If you used more than 60 minutes, i.e. (x – 60 minutes more than the plan came with, you would pay an additional $0.40 for each of those (x – 60 minutes. Your total bill would be C (x) = 30 + 0.40 (x – 60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use? minutes. The maximum calling minutes you can use is ? Number
Answer:
The maximum number of minutes to keep the cost at $50 or less is 110 minutes
Step-by-step explanation:
Given
[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]
[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]
Required
[tex]C(x) = 50[/tex] ---- find x
We have:
[tex]C(x) = 30 + 0.40(x - 60)[/tex]
Substitute 50 for C(x)
[tex]50 = 30 + 0.40(x - 60)[/tex]
Subtract 30 from both sides
[tex]20 = 0.40(x - 60)[/tex]
Divide both sides by 0.40
[tex]50 = x - 60[/tex]
Add 60 to both sides
[tex]110 = x[/tex]
[tex]x =110[/tex]
