Complete the square to solve [tex]2x^2 + 8x - 12 = 0[/tex].
Soooooooo, [tex](4x + 8)^2[/tex] is your answer. :)
The distance between the earth and the sun is approximately 93 million miles. what is this number written in proper scientific notation?
Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.
What is Scientific notation ?
Scientific notation is the way to express the large value in short form. The number in scientific notation have two parts. The digits (decimal point will place after first digit) × 10 ( the power which put the decimal point where it should be).
Here it is given that The distance between the earth and the sun is approximately 93 million miles and 1 million miles equals 1,00,000 miles.
Now, writing 93 millions Scientific notation by writing 1,00,000 in power of 10 and 93 as 9.3 x 10 :
93 million miles = 9.3 x 10 x 1,00,000
= 9.3 x 10^7
Therefore, Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.
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The distance between the Earth and the Sun (93 million miles) in scientific notation is [tex]9.3 *10^7 miles[/tex].
To write the distance between the Earth and the Sun (93 million miles) in scientific notation, follow these steps:
First, write 93 million as a standard numeral: 93,000,000.
Next, identify how many places to move the decimal point to get a number between 1 and 10. For 93,000,000, the decimal point moves 7 places to the left.
After moving the decimal point in 93,000,000.00 by 7 places, you get 9.3, which is between 1 and 10. This is known as mantissa.
Mantissa = 9.3
Write the number as a coefficient multiplied by 10 raised to the number of places the decimal was moved. This is called the exponent term. Exponent term = [tex]10^7[/tex].
Scientific notation of a number = Mantissa*Exponent term
So, 93,000,000 = [tex]9.3 *10^7[/tex].
Therefore, the distance between the Earth and the Sun in proper scientific notation is [tex]9.3 *10^7 miles[/tex].
Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
(Picture one)
A. 126 cm3
B. 907.5 cm3
C. 605 cm3
D. 55 cm3
Find the surface area of the cylinder in terms of pi.
(Picture 2)
A) 396 pi in^2
B) 522 pi in^2
C) 360 pi in^2
D) 1008 pi in^2
The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
we know that,
volume of pyramid is:
V = 1/3 B h
here, we have,
B = 11*11
= 121
h = 15
so, we get,
V = 605 cm^3
again, we have,
surface area of the cylinder :
s = 2πr( r + h)
here, we have,
r = 9
h = 20
so, we get,
s = 522 pi in^2
Hence, The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
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The volume of the square pyramid is A) 126 cm³ and the surface area of the cylinder is B) 522π in².
The volume of a square pyramid is expressed as:
Volume = l² × h/3
The surface area of a cylinder is expressed as:
Surface area = 2πrh + 2πr²
From the diagram:
For the square pyramid:
Length l = cm
Height h = 15cm
Volume =?
Volume = l² × h/3
Plug in the values:
Volume = 11² × 15/3
Volume = 121 × 5
Volume = 605 cm³
Option C) 605 cm³ is the correct answer.
Next, we find the surface area of the cylinder:
Radius r = 9 in
Height h = 20 in
Surface area = 2πrh + 2πr²
Plug in the values:
Surface area = (2π × 9 × 20) + (2π × 9²)
Surface area = 522π in²
Therefore, the surface of the cylinder is 522π in².
Option B) 522π in² is the correct answer.
The party store has a special on greetings cards. It charges $14 for 4 greeting cards and $1.50 for each additional card. Write an equation for the total cost of greeting cards in terms of the number of cards. Define your variables. What is the total cost of 9 greeting cards?
C=14 +1.5(x-4)
c= total cost
x = number of cards
cost for 9 cards:
x=9
c=14+1.5(9-4)
14+1.5(5) = 21.50
total cost = $21.50
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1558.09. What percent of the purchase price was Julio's down payment?
Answer: c
Step-by-step explanation:
(12x 4 + 17x 3 + 8x - 40) ÷ (x + 2)
(6.3 × 1011) ÷ (7 × 105)
Rationalize the denominator. write it in simplest terms.
1
- ------------
√18x
yes it is a negative
In the following triangle, find the values of the angles B and B', which are the best approximations to the solutions of this ambiguous case.
Answer:
Option B. B = 70.05° B' = 109.95°
Step-by-step explanation:
By the sine rule in a given triangle
sin 45°/16.5 = sinB/22
1/(1.414×16.5) = sinB/22
sinB = 22/(1.414×16.5) = 0.94
[tex]B = sin^{-1}(0.94)[/tex]
B = 70.05°
Now we know B' = 180 - Supplementary angle of B'
and B = B' ( opposite angles of equal sides are equal)
B' = 180 - B = 180 - 70.05 = 109.95°
Therefore option B is the answer.
Joe can paint a fence in three hours; mary can paint it in two hours. how long will it take them to paint the fence if they work together?
bacterial colonies can triple in size every 4 days. if you start with 150 bacteria microorganisms, how large would the colony be after 16 days?
Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1.08p. Using this information, which of the following represents the final price of a tablet with the discount and taxes applied based on its original price? (2 points) c[p(t)] = 0.918t c(p) + p(t) = 1.93t c(p) ⋅ p(t) = 0.918pt t[c(p)] = 1.93p
The final price of the tablet is c(t) = 0.918.
What is sale price?
A sale price is the discounted price at which goods or services are being sold.
According to the given question
Tablets are on sale for 15% off the original price(t), which can be expressed with the function:
p(t) = 0.85t
The additional taxes of 8% of the discounted price(p), which can be expressed as a function:
c(p) = 1.08p
Therefore,
The final price of a tablet with the discount and taxes applied based on its original price is given by
c(p(t)) = 1.08 ×p(t)
c(p(t)) = 1.08×(0.85t)
c(p(t)) = 0.918t
⇒ c(t) =0.918t
Hence, the final price of the tablet is c(t) = 0.918.
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Perform the operation(s) and write the answer in simplest form.
( 1/2 + 1/3) / 15/4
A.) 3 1/8
B.) 53/90
C.) 2/9
D.) 8/75
Find all values of $x$ such that $6= \dfrac{35}{x} -\dfrac{49}{x^2}$. If you find more than one value, then list your solutions in increasing order, separated by commas.
Answer:
[tex]x=\frac{7}{3} , \frac{7}{2}[/tex]
Step-by-step explanation:
[tex]6= \frac{35}{x} - \frac{49}{x^2}[/tex]
Now we need to solve for x
To get 'x' alone we make the denominators same
LCD = x^2
WE multiply the whole equation by x^2
[tex]6x^2 = 35x - 49[/tex]
Now we the equation =0, move all the terms to left hand side
[tex]6x^2-35x + 49=0[/tex]
Now we apply quadratic formula to solve for x
a= 6, b= -35 , c= 49
[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x= \frac{-(-35)+-\sqrt{(-35)^2-4(6)(49)}}{2*6}[/tex]
[tex]x= \frac{35+-\sqrt{49}}{12}[/tex]
[tex]x= \frac{35+-7}{12}[/tex]
Now frame two equations , one with + and another with -
[tex]x= \frac{35+7}{12}[/tex] [tex]x= \frac{35-7}{12}[/tex]
[tex]x= \frac{42}{12}[/tex] [tex]x= \frac{28}{12}[/tex]
[tex]x= \frac{7}{2}[/tex] [tex]x= \frac{7}{3}[/tex]
So value of x= {7/3, 7/2}
Which graph represents a reflection of f(x) = 1/10 (10)x across the y-axis?
Answer:
We have to find a graph which represents a reflection of f(x) = 1/10 (10)x across the y-axis.
As we know that on reflecting the graph across the y-axis the x-coordinate of the point changes to opposite sign nut with same magnitude and the y-coordinate remains same.
Hence, the function f(x) is transformed to:
[tex]f(x)=\dfrac{1}{10}\times 10^{-x}[/tex]
The graph of the function passes through the point (0,0.1) and is a strictly decreasing function.
and the end behavior of the graph is that:
when x→∞ f(x)→ 0
when x→ -∞ f(x) → ∞
What is the median of 36, 14, 21, 56, and 10?
Write the sum using summation notation
729 + 1000 + 1331 + 1728 + ... + n^3
The number of significant figures in 0.01500 is
The number of significant figures in 0.01500 is 4.
What are significant figures?Significant figures (or significant digits) are the number of digits in a given value or a measurement, necessary to decide the accuracy and precision of measurement.
The given decimal number is 0.01500.
Certain rules help us determine the number of significant figures. These rules are as follows:
(1) All non-zero digits are significant.
(2) All zeros in between non-zero digits are significant.
(3) Zeros on the right of a decimal point and before (or to the left of) the first non-zero digit are not significant. They only represent the position of the decimal point.
(4) Zeros on the right of a decimal point are significant, provided there is no non-zero digit after them.
(5) Zeros on the right of the last non-zero digit after a decimal point are significant. So, final zeros or trailing zeros in the decimal part are significant.
(6) In a measurement value, zeros that occur on the right of the last non-zero digit are significant.
In the given decimal 0.01500, two non zero digits and two leading zeros are significant
So, number of significant figures are 4
Therefore, the number of significant figures in 0.01500 is 4.
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Which is relatively better: a score of 79on a psychology test or a score of 48on an economics test? scores on the psychology test have a mean of 85and a standard deviation of 5.scores on the economics test have a mean of 52and a standard deviation of 3?
The correct option is that a score of 79 on a psychology test is relatively better than a score of 48 on an economics test.
To determine which score is relatively better, we can calculate the z-scores for each test score. The z-score tells us how many standard deviations away from the mean a particular score is.
For the psychology test, the mean is 85 and the standard deviation is 5. The score is 79. The z-score can be calculated using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where [tex]\( X \)[/tex] is the score,[tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
For the psychology test:
[tex]\[ z_{psychology} = \frac{79 - 85}{5} = \frac{-6}{5} = -1.2 \][/tex]
For the economics test, the mean is 52 and the standard deviation is 3. The score is 48. Using the same formula:
[tex]\[ z_{economics} = \frac{48 - 52}{3} = \frac{-4}{3} \approx -1.33 \][/tex]
Now, comparing the z-scores:
- The z-score for the psychology test is -1.2, which means the score is 1.2 standard deviations below the mean.
- The z-score for the economics test is approximately -1.33, which means the score is about 1.33 standard deviations below the mean.
Since a lower (more negative) z-score indicates a worse relative performance, the score of 79 on the psychology test is relatively better than the score of 48 on the economics test, because -1.2 is greater than -1.33. This means that the psychology test score is closer to its mean relative to its standard deviation than the economics test score is to its mean relative to its standard deviation.
1. Which of the following statements is true? A. 15 ÷ 0 = 0 B. 15 − 0 = 0 C. 0 ÷ 15 = 0 D. 15 + 0 = 0
type the slope-intercept equation of the line that passes through the points (0,2) and (2,0) y={?]x+{ }
GEOMETRY- What is the area of the figure, show your work please!
Which point satisfies both f(x)=2^x and g(x)=3^x (0,1) (0,-1) (1,0) (-1,0)
A cold front moved in last weekend. In 8 hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour?
I need the answer as quick as I can and I put it at max points!
Answer:
Step-by-step explanation:
The difference between 14 and 0 is 14, and the difference between 0 and -10 is 10. 14+10=24 for total change. For the average over 8 hours, we have 24/8=3 degrees
Five students visiting the student health center for a free dental examination during national dental hygiene month were asked how many months had passed since their last visit to a dentist. their responses were as follows. 5 18 12 24 28 assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (give the answer to two decimal places.)
To find for the value of the confidence interval, let us first calculate for the values of x and s, the mean and standard deviation respectively.
x = (5 + 18 + 12 + 24 + 28) / 5
x = 17.4 months
s = sqrt{[(5 – 17.4)^2 + (18 – 17.4)^2 + (12 – 17.4)^2 + (24 – 17.4)^2 + (28 – 17.4)^2]/(5-1)}
s = 9.21
The formula for the confidence interval is given as:
Confidence Interval = x ± t s / sqrt(n)
Where t can be taken from standard distribution tables at 95% level at degrees of freedom = n – 1 = 4, t = 2.132. Therefore:
Confidence Interval = 17.4 ± 2.132 * 9.21 / sqrt(5)
Confidence Interval = 17.4 ± 8.78
Confidence Interval = 8.62 months, 26.18 months
Final answer:
To construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, use the sample mean and sample standard deviation. Calculate the confidence interval using the formula and given data.
Explanation:
In order to construct a confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program, we can use the sample mean and sample standard deviation. The formula for constructing a confidence interval for the mean is:
Confidence Interval = sample mean ± (critical value) × (sample standard deviation / √sample size)
Using the given data, the sample mean is 17.4 months and the sample standard deviation is 9.18 months. With a confidence level of 95%, the critical value is 2.776. Plugging these values into the formula, we get:
Confidence Interval = 17.4 ± (2.776) × (9.18 / √5)
Calculating this, we find that the 95% confidence interval for the mean number of months elapsed since the last visit to a dentist is approximately 4.81 to 29.99 months.
a bell tolls every 10 minutes. another bell tolls every 15 minutes. both bells toll at 6:00pm. they will toll together at what time
Both the bells will ring after 30 minutes at 6:30 pm.
What is the lowest common multiple?The smallest common positive number that is a multiple of two or more numbers.
Given that, a bell tolls every 10 minutes. another bell tolls every 15 minutes. both bells toll at 6:00pm.
To find the time for which both will ring together, we will find LCM of 10and 15
10 = 5x2
15 = 5x3
LCM = 5x2x3 = 30
The LCM of 15 and 10 is 30
So, both will ring after 30 minutes.
Right now the time is 6:00 pm, so after 30 minutes it will be 6:30 pm
Hence, Both the bells will ring after 30 minutes at 6:30 pm.
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Monica gets on an elevator in a skyscraper. The elevator starts to move at a rate of -20ft/s. After 6 seconds on the elevator, Monica is 350 ft from the ground floor building.
1) The rate of the elevator is negative. What does this mean in the situation? What value in the slope-intercept form of an equation does the rate represent?
2) How many feet was Monica above the ground when she got on the elevator? Show work
3) What value in the slope-intercept form does your answer to part a represent?
Show all work
In this scenario involving an elevator's movement, the negative velocity indicates downward motion and corresponds to the slope in the equation of a line. By applying the slope and initial conditions, we calculated that Monica was initially 470 feet above the ground, which is the y-intercept in the slope-intercept form.
Explanation:The student's question involves understanding the implications of negative velocity in a real-world situation involving an elevator, calculating an initial position based on this velocity and elapsed time, and tying these concepts to algebraic representations in slope-intercept form.
A negative rate of -20ft/s indicates that the elevator is moving downward. This rate represents the slope in the slope-intercept form of an equation, y = mx + b, where m is the rate of change or slope.To find how many feet Monica was above the ground when she got on the elevator, we use the formula y = mx + b, where y is the final position (350 ft), m is the rate of change (-20 ft/s), and x is the elapsed time (6 s). Replacing the values and solving for b (initial position), we get 350 = -20(6) + b, leading to b = 470 ft. Therefore, Monica was 470 feet above the ground when she got on the elevator.The answer to part a, -20ft/s, represents the slope, and the answer to part b, 470 feet, represents the y-intercept (b) in the slope-intercept form.Use ABC to find the value of sin A. See picture below. Thanks!
Find the product of (x − 2i)^2.
The product of (x-2i)²=x²-4+i4x
What is the process of multiplication of complex numbers?The product or multiplication of two complex numbers is also a complex number. The formula for multiplying complex numbers is: (a + ib) (c + id) = (ac - bd) + i(ad + bc).
Given here (x-2i)² =(x-2i) (x-2i)
=x²-4+i4x
Hence, the product is x²-4+i4x
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Mr. calloway is an algebra teacher. every class period he draws a piece of paper out of a hat without looking to determine the number of homework problems he will assign. each different color of paper represents a different number of homework problems. the hat contains 2 blue, 6 red, 10 yellow, and 7 purple pieces of paper.what is the probability that mr. calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period if he replaces all pieces of paper before each drawing?
The probability that Mr. Calloway will draw a purple piece of paper during the first class period and a blue piece during the second class period with replacement is [tex]\frac{14}{25}[/tex].
The question involves calculating the probability of drawing a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement. To find this probability, we first calculate the probability of each event separately since the events are independent. Mr. Calloway's hat contains a total of 25 pieces of paper (2 blue, 6 red, 10 yellow, and 7 purple).
The probability of drawing a purple piece of paper in the first class period is the number of purple papers divided by the total number of papers:
P(purple) = Number of purple pieces / Total pieces = [tex]\frac{7}{25}[/tex]
Since the pieces are replaced, the probabilities in the second class period are the same as in the first. Thus, the probability of drawing a blue piece of paper in the second class is:
P(blue) = Number of blue pieces / Total pieces = [tex]\frac{2}{25}[/tex]
Because these events are independent, we multiply the probabilities of each event happening:
Total probability = P(purple) times P(blue) = ([tex]\frac{7}{25}[/tex]) times ([tex]\frac{2}{25}[/tex]) = [tex]\frac{14}{25}[/tex].
Therefore, the probability that Mr. Calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement is [tex]\frac{14}{25}[/tex].
What is the point of symmetry for the circle (x – 5)2 + (y + 4)2 = 25?
In a circle, the point of symmetry is the centerpoint; any straight line that passes through this point is a line of symmetry. The standard form of equation of a circle is given as:
(x – h)^2 + (y – k )^2 = r^2
Where,
h = x coordinate of the center
k = y coordinate of the center
In the problem statement, we are given that the equation of the circle is:
(x – 5)^2 + (y + 4)^2 = 25
So identifying the variables from the standard form of equation of a circle:
h = 5
k = - 4
Therefore the point of symmetry is (5, -4).