Find all Values of b that will make the polynomial a perfect square trinomial.
25z^2+bz+36
Please write out how to do this so I can see the steps of what I am doing wrong. thank you!
Answer:
There are two solutions for [tex]b[/tex]: [tex]b = + 30\cdot z[/tex], [tex]b = -30\cdot z[/tex]
Step-by-step explanation:
By Algebra, we know that a polynomial is a perfect square trinomial if it is of the form:
[tex]a^{2} + 2\cdot a \cdot c + c^{2} = (a + c)^{2}[/tex] (1)
By direct comparison, we have the following system:
[tex]a^{2} = 25\cdot z^{2}[/tex], [tex]c^{2} = 36[/tex], [tex]2\cdot a \cdot c = b[/tex].
There are two possible solutions for [tex]b[/tex]:
1) [tex]a = \pm 5\cdot z[/tex], [tex]c = \pm 6[/tex], [tex]b = + 30\cdot z[/tex]
2) [tex]a = \pm 5\cdot z[/tex], [tex]c = \mp 6[/tex], [tex]b = -30\cdot z[/tex]
Can you help me solve this pls?
Answer:
advertising cost would be $2010
Step-by-step explanation:
y = 10000(5) + 10
y = 2000 + 10
y = 2010
Answer:
$2010
Step-by-step explanation:
Let x = 10,000
[tex]y = \frac{10,000}{5}+10\\y=2000+10\\y=2010[/tex]
Therefore, the predicted advertisement costs for selling 10,000 books is $2010.
2logb - 3logb = log8b - log4b
Answer:
b=1/2
Step-by-step explanation:
2logb - 3logb = log8b - log4b
log[tex]b^{2}[/tex] - log[tex]b^{3}[/tex] = log8b - log4b
log([tex]\frac{1}{b}[/tex]) = log(2)
∴1/b = 2
∴b = 1/2
Use the graph to answer the questions.
1) write into vertex form.
2) identify the vertex, focus, and directrix.
Answer:
y = 2( x+5)^2 -4
Vertex (-5,-4)
directrix y = -33/8
focus (-5, -31/8)
Step-by-step explanation:
First identify the vertex, which is the minimum
Vertex = (-5,-4)
The vertex form is y = a( x-h)^2 + k
y = a( x- -5)^2 -4
y = a( x+5)^2 -4
We need to determine a
Substitute a point on the graph
(-3,4) is on the graph
4 = a( -3+5)^2 -4
4 = a( 2)^2 -4
4 = 4a -4
Add 4 to each side
8 = 4a
Divide by 4
8/4 = a
a=2
y = 2( x+5)^2 -4
To find the focus and directrix, write in standard form
4p(y-k)=(x-h)^2
y+4 = 2(x+5)^2
1/2 (y+4) = (x+5)^2
4p = 1/2
p = 1/8
The focal length is 1/8
Subtract this from the y coordinate to get the directrix
y = -4 -1/8
y = -32/8 - 1/8 = -33/8
Add this to the y coordinate to get the coordinate for the focus the x coordinate the same
(-5, -4+1/8)
(-5, -32/4+1/8)
(-5, -31/8)
find the value of x (URGENT/GIVING BRAINLIEST)
Answer:
B) 24
Step-by-step explanation:
Those are alternate interior angle which mean they are congruent or equal to each other
2x=48 divide
48÷2=24
Answer:
B) 24
step by step:
2x = 48 ( two straight lines are parallel forming and the internal stagger angle is equal)
Area of shaded region
Answer:
what are you asking
Step-by-step explanation:
Sigma 18 1 (5n-4) =?
Can anyone solve this?
If square C is 64 in^2, then its dimensions are 8 x 8.
If square D is 81 in^2, then its dimensions are 9 x 9.
Since D is bigger than C and I sits in that extra space, then the dimensions of I are 1 x 1.
Since H is smaller than C, specifically I smaller, than its dimensions are 7 x 7.
Then, H and C make up one side of B, so 7 + 8 = 15. The dimensions of B are 15 x 15.
Since E is bigger than D by I, then the dimensions of E are 10 x 10.
If we find the length of the right side (B + C + D), which is 15 + 8 + 9 = 32, then we know that F + E + D must also add up to 32. F + 10 + 9 = 32 || F = 13. The dimensions of F are 13 x 13.
Then, F is E + G, so 13 = 10 + G. G = 3. The dimensions of G are 3 x 3.
Lastly, since we know the side length of the whole square is 32, then A + F must equal 32. 32 = A + 13. A = 19. The dimensions of A are 19 x 19.
A = 19 x 19 = 361 in^2
B = 15 x 15 = 225 in^2
C = 8 x 8 = 64 in^2
D = 9 x 9 = 81 in^2
E = 10 x 10 = 100 in^2
F = 13 x 13 = 169 in^2
G = 3 x 3 = 9 in^2
H = 7 x 7 = 49 in^2
I = 1 x 1 = 1 in^2
Hope this helps!! :)
The area of a rectangle is represented by 12n2 - 19n - 21. If the width is 3n - 7, which expression represents the perimeter?
A. 7n - 4
B. 7n+4
C. 14n -8
D. 14n +8
Answer:
C 14n - 8
Step-by-step explanation:
rectangle area = length×width = 12n²-19n-21
width = 3n-7
what do we need to multiply with width to get the full area expression ?
think : what do we need to multiply with 3n to get 12n² (4n)?
and what to multiply with -7 to get -21 (3)?
=> length = 4n+3
perimeter is 2×length + 2×width
p = 2(3n-7) + 2(4n+3) = 6n-14+8n+6 = 14n-8
Can someone help me with this pleasee
Answer:
its D
Step-by-step explanation:
good luck
Answer:
5155.07142857
Step-by-step explanation:
diameter/2 = radius
81/2 = radius
40.5 = radius
Area = π r^2
Area = 22/7 *40.5^2
Area = 5155.07142857
The gas tank in Feliz's car is 5/6 full. Each time he drives to or from work, he uses 1/12 of a full tank of gas. Which equation represents the number of times Feliz can drive to or from work with the gas in his tank?
Answer:
5/6 divided by 1/12 (the last box)
Well thats the only box with the right answer and the equation used is how you get the right answer
1.the ratio if the weight of an object on mars to its weight in earth is 9 to 25.If a person weighs 160pouns on earth,how much would the person weigh on mars?
Answer:
57.6 Pounds
Step-by-step explanation:
Weight on Earth = 160 pound
Weight on Mars = (9/25)*160 pound
= 57.6 pounds
Factorise 5x + 10=
ᴘʟᴀʏɪɴɢ: Who Asked (Feat: Nobody did ) ───────────⚪────── ◄◄⠀▐▐⠀►:/:⠀───○
Answer:
5(x+2)
Step-by-step explanation:
5x + 10=
Factor out 5
5(x+2)
Answer:
[tex]5(x + 2)[/tex]
Step-by-step explanation:
Get 5 out
[tex]5x + 10 \\ 5(x + 2)[/tex]
a sum of marbles is shared in the ratio of 4 to 1 the smaller share is 24 marbles what was the total number of marbles shared
Answer:120
Step-by-step explanation: If the smaller number of the ratio is 24 that means the 1 is multiplied by 24 to reach the smaller share of 24. We then multiply 24 with 4 to get the number 96. Lastly you add 96 with 24 to get the total number of marbles
Questlon 18 of 25
Joanne and Betty have a combined age of 41 years. If Joanne is 17 years old,
how old is Betty?
Answer here
SUBMIT
Answer:
24
Step-by-step explanation:
betty age = 41 - 17
= 24
Marcus is rewriting a polynomial by combining like terms. Which terms does he still need to combine to finish rewriting the polynomial?
Help me plz I’m too slow for this
Answer:
160 units²
Step-by-step explanation:
Surface area of the square pyramid = a² + 2al
Where,
a = side length of the square = 8
l = slant height of the triangular face = 6
Plug in the values
Surface area of the square pyramid = 8² + 2*8*6
= 64 + 96
= 160 units²
Alright, everyone. I'm betting in a lot amount of points and I really need someone to help me out here. It would bring lots and lots of weight off my shoulders.
Answer:
See Below.
Step-by-step explanation:
Part 1)
Since the coral structure has an initial volume of 1,200 cubic centimers, a = 1200.
Since it doubles every year, we can let b = 2.
Hence, our equation is:
[tex]y=1200(2)^t[/tex]
Where t is the time in years since the coral was measured.
Part 2)
Evaluate each value:
[tex]y(5)=1200(2)^5=38,400\text{ cm}^3[/tex]
When t = 5, or after five years, the volume of the coral structure is 38,400 cubic centimeters.
[tex]y(1)=1200(2)^1=2,400\text{ cm}^3[/tex]
When t = 1, or after one year, the volume of the coral structure is 2,400 cubic centimeters.
[tex]y(0)=1200(2)^0=1, 200\text{ cm}^3[/tex]
When t = 0, or during the initial year, the volume of the coral structure is 1,200 cubic centimeters.
And:
[tex]\displaystyle y(-1)=1200(2)^{-1}=\frac{1200}{2}=600\text{ cm}^3[/tex]
[tex]\displaystyle y(-2)=1200(2)^{-2}=\frac{1200}{4}=300\text{ cm}^3[/tex]
Part 3)
In this case, since positive values of t indicates the time in years since the coral was starting to be measured, negative values of t indicates the time in years before the coral was starting to be measured.
We acquired that y = 300 when t = -2. So, this means that two years before the coral was starting to be measured, the volume of the coral was 300 cubic centimeters.
Part 4)
We can set y = 37.5 and solve for t. Hence:
[tex]\displaystyle 37.5=1200(2)^t[/tex]
Divide both sides by 1200:
[tex]\displaystyle \frac{37.5}{1200}=\frac{375}{12000}=\frac{1}{32}=2^t[/tex]
Notice that:
[tex]\displaystyle \frac{1}{32}=\frac{1}{2^5}=2^{-5}=2^t[/tex]
Same bases must have the same exponents. Hence:
[tex]t=-5[/tex]
So, five years before the coral was being measured, the volume of the coral was 37.5 cubic centimeters.
Since the initial volume was 1,200 and it grows each year, it can only be 37.5 before the initial year, so our answer makes sense.
You randomly draw a marble from a bag of marbles that contains 888 blue marbles, 555 green marbles, and 888 red marbles.
Answer:
whats the question?
Step-by-step explanation:
Solve for x 11^x/11^3=11^2 PPEASE I HAVE AN F
Find the volume of the rectangular pyramid below.
Answer:
315 yd cubed
Step-by-step explanation:
To find the volume of the pyramid, we first need to consult the equation below. Thebase is for the rectangular portion, then after multiplied by the height it is divided by 3 to get the pyramid.
[tex]\frac{1}{3} (B * H )[/tex]
To get the base, we multiply the length by the width.
21 * 9 = 189
189 * 5 = 945
945 divided by 3 = 315
Answer:
Let's find the base area:
21 x 9 = 189
Now let's multiply the base area by the height:
189 x 5 = 945
Now let's divide by 3( x 1/3 ):
945 divided by 3(x 1/3) = 315 yd^3 is your answer
Step-by-step explanation:
Formula area of a rectangular Pyramid(just like any other pyramid):
BH x 1/3
To find base we multiply length by width just using the basic formula of finding area of a rectangle.
Then we multiply our base area by our height.
One we've done that we now divide by 3(multiplying by 1/3)
Help please. Forthefunction f(x)=x(x+3)(x−1)
Answer:
x-intercepts= (-3,0) , (1,0) and y-intercepts= (0,-3)
For the graph part it would be graphed and shaped like a U.
Step-by-step explanation:
Hope this helps :)
Evaluate the following expression.
2^0
Answer:
1
Step-by-step explanation:
2^0
Any number raised to the zero power is 1
Check all of the correct names for the object pictured below.
Answer:
VU,UV, and probably VU just pick 3 answers cause there is 6 questions in all but i hope these answers help u have a nice day too.
Step-by-step explanation:
The lines shown below are parallel. If the green line has a slope of -3/7, what is
the slope of the red line?
A. -3/7
B. 7/3
C. -7/3
D. 3/7
। Find the H.C. F. of :
x2+ 2xy+y and 3ax+3ay
Answer:
Factorizing 4x2 - 9y2, we get
(2x)2 - (3y)2, by using the identities of a2 - b2.
= (2x + 3y) (2x - 3y)
Step-by-step explanation:
f(x) = 3x + 4 is y =
Which sequences are geometric?
Check all that apply.
Answer:
3, 12, 48, 192, ...
3, 15, 75, 375, ...
2, 10, 50, 250, ...
The manager of a new supermarket wished to estimate the likely expenditure of his customers. A sample of till slips from a similar supermarket describing the weekly amount spent by 500 randomly selected customers was collected and analysed. This expenditure was found to be approximately normally distributed with a mean of $50 and a standard deviation of $15.
Find the probability that any shopper selected at random spends more than $80 per week?
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
Answer:
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
88.54% of shoppers are expected to spend between $30 and 80 per week.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of $50 and a standard deviation of $15.
This means that [tex]\mu = 50, \sigma = 15[/tex]
Find the probability that any shopper selected at random spends more than $80 per week?
This is 1 subtracted by the p-value of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 30.
X = 80
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 30
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 50}{15}[/tex]
[tex]Z = -1.33[/tex]
[tex]Z = -1.33[/tex] has a p-value of 0.0918
0.9772 - 0.0918 = 0.8854
0.8854*100% = 88.54%
88.54% of shoppers are expected to spend between $30 and 80 per week.
Hopefully the photo posted...
The teacher of a statistics class records the heights (in inches) of his students and draws a box-and-whisker plot to look over the data collected. This box-and-whisker plot shows theresult. (a) What is the median height? (b) What is the range of heights?
Answer:
a) Median Height = 66 inches
b) Range of Heights = 18 inches
Step-by-step explanation:
a) The median in a box-and-whisker plot is the second quartile, located between the first and third quartiles indicated by the dashed line. Therefore, the median height is 66 inches.
b) The range in a box-and-whisker plot uses the same process of finding the range of a set of data. You find the difference between the maximum and the minimum values of the data. Therefore, the range of heights is 77 - 59 = 18 inches.
