Answer:
(5+8) (5-8)
Step-by-step explanation:
They are both perfect squares.
Answer:
(5+8x)(5-8x)
Step-by-step explanation:
This is a 'difference of two squares" Difference means subtraction and 25 is a perfect square and 64x^2 is a perfect square.
If you know how to factor quadratic trinomials like
ax^2 + bx + c, you can do the same thing here, using:
64x^2 +0x + 25
BUT, there's a shortcut. It is a pattern that you memorize. Since 25 is 5^2, put 5 first in the parenthesis. And since 64x^2 is 8x squared, put 8x second in the parenthesis like this:
(5 8x)
Make two of them:
(5 8x)(5 8x)
Make one a plus and one a minus.
(5 + 8x)(5 - 8x)
Done!
Well, if the directions say "factor" then you are done. If the directions say "solve" then put each piece equal to zero and solve for x.
Hope this helps!
There is 80% milk in 400 litre misture of milk and water. What will be the percentage of milk in the new mixture when 80 litre more water is added in the mixture?
Step-by-step explanation:
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \error \\ \madeindonesia[/tex]
mean, mode, median, and range for numbers 4, 5, 6, 9, 13, 14, 14, 14, 15
Answer:
mean: 10.4
mode: 14
median: 13
range: 11
Step-by-step explanation:
To find a mean, add up all the numbers of the data set and divide them by the number of numbers.
To find a mode, just search for the number used the most in the data set.
To find a median, search for the number right in the middle of the data set (if there are 2 numbers in the middle, the median is the average of those 2 numbers.)
To find a range, order all the numbers of the data set from lowest to highest. Then subtract the lowest number from the highest number. :)
find the slope intercept form of the line whose slope is 2 and passes through the point (-7,10)
Answer:
y=2x+24
Step-by-step explanation:
Hi there!
We are given that a line has a slope of 2 and passes through (-7, 10)
We want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept
As we are already given the slope, we can immediately substitute it in for m
So replace m with 2 in y=mx+b
y=2x + b
Now we need to find b
As the equation passes through the point (-7, 10), we can use its values to help us find the value of b
Substitute -7 as x and 10 as y
10 = 2(-7) + b
Multiply
10 = -14 + b
Add 14 to both sides
24 = b
Substitute 24 as b into the equation
y = 2x + 24
Hope this helps!
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Find the volume of the shape.
Round to 2 decimal places.
22 cm
14 cm
Answer:
The volume is about 1,128.88 cubic cm.
Step-by-step explanation:
[tex] \frac{1}{3} \pi( {7}^{2} )(22) = 1128.88[/tex]
In a lab experiment, 30 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 4 hours. How many bacteria would there be after 26 hours, to the nearest whole number?
QUICK AND CORRECT PLS!
Answer:
2715 bacteria
Step-by-step explanation:
This is a simple exponential function. We are given that the initial value is 30, that the value doubles every 4 hours.
Thus, we have our function: [tex]y=30*2^{x/4}[/tex]
Plugging in 26 for x, we get 2715.29004 => 2715 bacteria.
find the volume of a cone with a diameter of 18 meters and a height of 20 meters
[tex] \huge \sf \color{pink}{A} \color{green}{N} \color{red}{S} \color{blue}{W} \color{orange}{E} \color{grey}{R}[/tex]
[tex]\large \underline{ \boxed{ \sf{✰ \: Important \: points }}}[/tex]
[tex] \pink{➢}[/tex] Diameter of cone = 18m
[tex] \pink{➢}[/tex]Height of cone = 20m
[tex] \pink{➢}[/tex]A surface of revolution formed by rotating a segment of a line around another line that intersects the first line.
[tex] \pink{➢}[/tex]Cone is basically formed by circular base
[tex]\underline{ \boxed{ \sf{➫\: Volume\:of\:cone = \frac{1}{3} {r}^{2} \pi \: h}}}[/tex]
[tex]\underline{ \boxed{ \sf{ ➪ \: r = radius}}} \\\underline{ \boxed{ \sf{ ➪ \: h = height}}}[/tex]
[tex] \pink{➢}[/tex] We know that radius is half of diameter
[tex] \sf \:➩ r = \frac{18}{2} \\ \sf \: ➩r = \cancel \frac{18}{2} \\ \sf \: ➩r = 9 \: \: \: [/tex]
[tex] \pink{➢}[/tex]Hence radius of cone in data given is 9m
➢ Let's substitute values according to formula
[tex]\sf \: → \frac{1}{3} \times {(9)}^{2}\times 3.14 \times20 \\ \sf→ \frac{1}{3} \times 81 \times 3.14 \times 20 \\ \sf \: → \frac{1}{ \cancel3} \times \cancel{81} \times 3.14 \times 20 \\ \sf→27 \times 3.14 \times 20 \\ \sf \: →1695.6m[/tex]
[tex] \pink{➢}[/tex] Hence volume of cone =1695.6m
Hope it helps !
What is the 35th term in this sequence? 2, 7, 12
Answer:
172
Step-by-step explanation:
Formula to find the nth term =
a+(n-1)d
2+(35-1)*5
= 2+170
= 172
What are the exact solutions of x2 − 3x − 5 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a? x = the quantity of negative 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 29 all over 2 x = the quantity of 3 plus or minus the square root of 11 all over 2 x = the quantity of negative 3 plus or minus the square root of 11 all over 2
Answer:
B. x = the quantity of 3 plus or minus the square root of 29 all over 2Step-by-step explanation:
Given equation
x² - 3x - 5 = 0The roots are
[tex]x=\cfrac{-b+- \sqrt{b^2-4ac} }{2a}[/tex]Substitute values into equation
[tex]x=\cfrac{3+- \sqrt{(-3)^2-4(1)(-5)} }{2(1)} =\cfrac{3+- \sqrt{9+20} }{2} =\cfrac{3+- \sqrt{29} }{2}[/tex]This is matching the option B
Answer:
[tex]x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2-3x-5=0[/tex]
To find the exact solutions of the given equation, use the quadratic formula or complete the square.
Method 1: Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-3, \quad c=-5[/tex]
Substituting these values into the formula:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Method 2: Completing the square
Move the constant to the right side by adding 5 to both sides:
[tex]\implies x^2-3x-5+5=0+5[/tex]
[tex]\implies x^2-3x=5[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2-3x+\left(\dfrac{-3}{2}\right)^2=5+\left(\dfrac{-3}{2}\right)^2[/tex]
[tex]\implies x^2-3x+\dfrac{9}{4}=\dfrac{29}{4}[/tex]
Factor the perfect trinomial on the left side:
[tex]\implies \left(x-\dfrac{3}{2}\right)^2=\dfrac{29}{4}[/tex]
Square root both sides:
[tex]\implies \sqrt{\left(x-\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{29}{4}}[/tex]
[tex]\implies x-\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}[/tex]
Add 3/2 to both sides:
[tex]\implies x-\dfrac{3}{2}+\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}+\dfrac{3}{2}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
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When 3 is added to a certain number the result is multiplied by obtain one less than the number you started with. what is that number
Step-by-step explanation:
coco with a smooth kind of drank that's definitely defeats the purse with a polish sausage you get from home depot
Please help! If you dont know, then dont answer please and thank you
Answer:
327.5
Step-by-step explanation:
URGANT!! Please help
A certain forest covers an area of 1900 km2. Suppose that each year this area decreases by 4.25%. What will the area be after 6 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1464 square kilometers
Step-by-step explanation:
Understanding :
Since it decreases by 4.25%, we can say that each year, the area is 95.75% of the previous yearThe function can be written as 1900(0.9575)ⁿ, where n is the number of yearsYear 6 :
1900(0.9575)⁶1900(0.77060655)1464 square kilometers (nearest square kilometer)What is the volume of this figure?
Enter your answer in the box.
The volume of the figure shown in the image which consist of two rectangular prisms is equal to 3300 cubed feet.
How to find the volume of the composite figures?To find the volume of the composite figures,
Separate the figure.Calculate the volume of the figure by which the composite figure is made of.Add the volume of all the individual figures to get the total volume of composite figuresThe given figure consist of two figures. Both are rectangular prism in which one has 24 ft length (20+4), width of 5 ft and height of 25 ft.
The area of a rectangular prism is the product of length, width and height of it. Thus, the volume of the upper prism is,
V₁=24×5×25
V₁=3000 ft³
Lower prism has 4 ft length, width of 3 ft (8-5) and height of 25 ft. Thus, the volume of this prism is,
V₂=4×3×25
V₂=300 ft³
Thus, the volume of the figure shown in image is,
V=3000+300
V=3300 ft³
Hence, the volume of the figure shown in the image which consist of two rectangular prisms is equal to the 3300 cubed feet.
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What are the dimensions of a rectangle with an area of 72 square centimeters and a perimeter of 36 cenmeter
Answer:
6cm by 12cm
Step-by-step explanation:
To find a list of the possible dimensions we can factor 72, as the dimensions of the rectangle must multiply to the area of 72
1 * 72
2 * 36
3 * 24
4 * 18
6 * 12
8 * 9
Now we can use the perimeter to find which pair is the correct answer, as the dimensions must satisfy the formula 2(Length + Width) = 36 (our perimeter)
We can see that the dimensions 6 and 12 give us our area of 72, and they do make a rectangle with the perimeter 36. This means that the dimensions of the rectangle are 6cm and 12cm.
Which of the following are roots of the polynomial function?
Check all that apply.
F(x) = x3 + 3x2 - 9x+ 5
O A. -5
OB. 1 + 3
O C. 3+2
O D. 1-3
O E. 1
O F. 3 - 2
Answer:
1 and -5
Step-by-step explanation:
[tex]~~~~~x^3+3x^2-9x+5=0\\\\\implies x^3-x^2+4x^2-4x-5x+5=0\\\\\implies x^2(x-1)+4x(x-1)-5(x-1)=0\\\\\implies (x-1)(x^2 +4x -5) = 0\\\\\implies (x-1)(x^2+5x -x -5) = 0\\\\\implies (x-1)[x(x+5) -(x+5)] =0\\\\\implies (x-1)(x-1)(x+5)= 0\\\\\implies (x-1)^2(x+5) = 0\\\\\implies x = 1,~~ x = -5[/tex]
PLEASE HELP EASY ASSIGNMENT!!! ( Kami )
you roll a fair number cube find probability of p(2, then2
You roll a fair number of cube. The Probability of P(2 then 2) would be 1/36.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Here is a complete description You roll a fair number cube to find probability of p(2, then2)
Given the sample space for a die
S = (1, 2,3,4,5,6) = 6
The Probability of 2 then 2 = (1/6) x (1/6)
= 1/36
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A 12-pack of soda costs $6.30 what is the cost per can
Answer:
So our goal is to determine the cost per can which we can find by dividing the amount of cans from the cost of the cans. That would give us the price per can.
[tex]\frac{price}{cans}[/tex]
[tex]\frac{\$6.30}{12\ cans}[/tex]
[tex]\$0.525\ per\ can[/tex]
Hope this helps! Please let me know if you have any questions
which expresion is equivilenet to 3/24
Answer:
1/8
Step-by-step explanation:
divide both sides by 3
WHAT IS 4=34
WHAT IS 4=76
Answer: Both are algebra expressions
Step-by-step explanation:
please help this is my last question
Answer:
Step-by-step explanation:
The area must be 232 in^2
Dylan lives about 27 miles from the mall. If he can drive at an average rate of 36 miles per hour through town, about how long does it take for Dylan to drive to the mall?
Answer:
45 minutes
Step-by-step explanation:
distance / rate = time
27 miles / 36 miles/hr = .75 hr ( 45 minutes )
9!/6!
Evaluate each factorial expression
The value of the given expression will be equal to 441.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The solution will be given as:-
[tex]\dfrac{9!}{6!}=\dfrac{9\times 8\times 7\times 6!}{6!}[/tex]
[tex]\dfrac{9!}{6!}=9\times 8\timex\times 7=441[/tex]
Therefore the value of the given expression will be equal to 441.
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Janet gets paid $24 per hour. She heard that this is 34 of what Adam is paid. How much is Adam paid per hour?
Find the missing factor. Write your answer in
exponential form.
5^-7 = ___ X 5^-9
Answer
5^- 7=X 5^- 9 X = 7 9
Which statements can be used to compare the
characteristics of the functions? Select three options.
f(x) has the greatest maximum.
h(x) has the greatest x-intercept.
g(x) has the smallest minimum value.
All three functions share the same domain..
All three functions share the same y-intercept.
The true statements that can be used to compare the characteristics of the functions are: option B, C, and D.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship that exists between two or more variable of a data set.
How to interpret the functions?From the table of values for this discrete function (see attachment), we can deduce the following characteristics and points:
g(x) has the smallest minimum value of -204.All three functions share the same domain (-1, 0, 3, 8, 15).All three functions share the same y-intercept (2, 3, 2, -3, -10).Read more on function here: https://brainly.com/question/27800214
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Which of the following statements are TRUE? SELECT ALL THAT APPLY.
Answer:
b d e a im not fore sure tho
Step-by-step explanation:
Consider a standard deck of 52 cards (13 cards each in 4 suits, clubs, spades, diamonds and hearts). What is the probability of picking out 5 cards in a row which are all diamonds, without replacing any card to the deck?
Answer: 5/52 or 10.4 I think
Step-by-step explanation: 5/52 = 10.4
The truck left for delivery at 7:15 a.m. and
traveled a total of 45 minutes. It also spent 1/3
hour to drop off the package. How many
minutes in all did the truck take to complete the
delivery?
Answer:
45+1/3 (all 1/3 is 1/3 of an hour, so do 60/3 to get 20) meaning that 45+20 is 65 minutes or an hour and 5 minutes
Step-by-step explanation:
what is the brobability of spinning a b unit 5 exam acellus
Supposing a spinner with 8 regions, 3 of which are B, there is a 0.375 = 37.5% probability of spinning a b.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we suppose a spinner with 8 outcomes, 3 of which are b, hence the probability is given by:
p = 3/8 = 0.375 = 37.5%.
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Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The 200 students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The students in group 1 had a mean score of with a standard deviation of , while the students in group 2 had a mean score of with a standard deviation of . Complete parts (a) and (b) below.
Lower bound is : 2.70 and upper bound is 3.30
a)There is a 90% probability that the difference of the means is in the interval
b) Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
What is Critical Value?Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability if the null hypothesis is true.
Given that:
a) [tex]n_1[/tex]=200, [tex]x_1[/tex]=23.9, [tex]s_1[/tex]=4.7
[tex]n_2[/tex]=200, [tex]x_2[/tex]=18.8, [tex]s_2[/tex]=4.5
The (1-α )% confidence interval for the difference between two mean is:
CI= [tex]x_1-x_2\pm\; t_\frac{\alpha }{2},(n_1+n_2-2\sqrt{\frac{s_1^{2}}{n_1}+\frac{s_2^{2}}{n_2} }[/tex]
the Critical value of 't' will be:
α/2=0.05/2=0.025
Degrees of freedom = [tex]n_1+n_2\\[/tex]-2= 200=200-2=398
[tex]t_{\alpha /2,_(n_1+n_2-2)}= t_{0.025,398}[/tex]=1.96
CI=23.9-18.8±1.96 [tex]\sqrt{\frac{4.7^{2}}{200}+\frac{4.5^{2}}{200} }[/tex]
= 3±0.3089
= (3.3089,2.6911)
≈(3.30, 2.70)
Thus, 90% confidence interval (3.30, 2.70) implies that the true mean difference value is contained in the interval with probability 0.90.
The Lower bound is : 2.70 and upper bound is 3.30
Thus, There is a 90% probability that the difference of the means is in the interval.
b)The difference between means, null value is 0.
As the null value is 0 and not in the interval, which shows that there is a difference between the two means, concluding that priming does have an effect on scores.
Hence, Since the 90% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.
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