Rewrite the equation by completing the square.
4x2 + 28x + 49 = 0
(x+) =
Answer: x = - 3.5
Step-by-step explanation:
Rewrite the equation by completing the square.
4x2 + 28x + 49 = 0
Completing the square method :
Divide through by the Coefficient of x^2
x^2 + 7x + (49/4) = 0
a = 1, b = 7, c = 49/4
Move c to the right side of the equation
x^2 + 7x = - 49/4
Complete the square on the left hand side by squaring its half of the x term
(7/2)^2 = (49/4)
Add the output to both sides of the equation
x^2 + 7x + (49/4) = - (49/4) + (49/4)
(x + 7/2)^2 = 0
Square root of both sides
x + 7/2 = 0
x = - 7/2
x = - 3.5
Answer:
x = - 3.5
Step-by-step explanation:
Which formula(s) can be used to find the nth partial sum of a geometric sequence or the sum of the first n terms of a geometric series?
Step-by-step explanation:
An=A1. R raised to the power n-1
Martin charges $10 for every 5 bags of leaves he rakes. Last weekend, he raked 27 bags of leaves. How much money did he earn?
Answer:
$54 : 27 bags
Step-by-step explanation:
its to much to explain
i got my math wrong
Write the explicit formula for the sequence.
2, 4, 6, 8, 10, ...
Answer:
a(n) = 2 + 2(n - 1)
Step-by-step explanation:
Since each new term is derived from the previous term by adding 2, this is an arithmetic sequence, and the "common difference" is 2.
Then a(n) = 2 + 2(n - 1)
Circle M is shown below. AB is tangent to the circle at point A. The radius of a circle M is 15. JB = 10. DF = 18. AC = 10.
Answer:
e
Step-by-step explanation:
can someone please help me with this question "when trying to find my heart rate, i counted 25 beats in 20 seconds. How many beats would that be per minute? please explain."
Answer:
75
Step-by-step explanation:
because if you multiply 20 and 25 by 3 you get 60 and 75, 60 being the amount of seconds are in a second and 75 being your heartrate per minute.
Some Insight: This is a Unit Rate question. Please Answer soon as possible.
Answer: C
Step-by-step explanation:
Because it only shows a single price and we don’t know what that price is for.
What is the volume of the prism below?
O A. 144 units 3
B. 56 units
C. 288 units 3
D. 180 units 3
Answer:
A. 144 units³
Step-by-step explanation:
Volume of prism= 1/2×height× base × length
Height= 3
Base= 8
Length= 12
Lets put all of these together
1/2×3 × 8 × 12
1/2×3 = 3/2 × 8 = 12 × 12 = 144 units³
Determine the measure of the named angle below.
mZK
K
40°
Step-by-step explanation:
Bro this problem cannot be solved. No solutions. I need at least one more angle or the type of triangle it is. Like iscoceles or scalene, or equilateral. Pls give me that info and then I can solve it for u
Pedro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0.50 EndRoot. Pedro A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.2 and 0.3. Lena A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5. Harriet A number line going from 0 to 0.9 in increments of 0.1. A point is at 0.5. Yermin A number line going from 0 to 0.9 in increments of 0.1. A point is just to the right of 0.7. Whose point is the best approximation of StartRoot 0.50 EndRoot?
Answer:
Yermin. √0.5 will be at Yermin's point
Step-by-step explanation:
Say Pedro line point is 0.25
Lena is 0.45
Harriet is 0.5
and Yermin is 0.7
The √0.5 = 0.707
≈ 0.7
Therefore it is at Yermin's point
Answer
DDDDDDDDDDDDDDD
Step-by-step explanation:
One of the first things we notice in this dream is an
amazing universalism. It does not say some men, but it
says all men. It does not say all white men, but it says all
men, which includes black men. It does not say all
Gentiles, but it says all men, which includes Jews. It does
not say all Protestants, but it says all men, which includes
Catholics.
- "The American Dream,"
Dr. Martin Luther King, Jr., 1964
How does this passage make use of an appeal to
logos?
It explains what "all men" means and what it
includes.
It relies on the use of the word "amazing."
It focuses on the use of negative words.
It points out differences in religion.
Intro
Done
When talking about logos, we look for strong words and phrases, as well as repitition.
1. Elimination
The answer is surely not "It relies on the use of the word 'amazing.'" This is because it is not important, and not repeated. If we were to remove this word, this secton of the speech would still be powerful.
The answer is not likely to be "It focuses on the use of negative words." This is because negative words are not included in this, so there isn't a focus on them.
The answer is not "It points out differences in religion" because mentioning religion was a small detail. It doesn't point out the differences in religion, but rather points out there are different religion. Nonetheless, this is just an example to prove MLK's point and wouldn't be right anyway,
2. Conclusion
Because we have eliminated all answers but one, we skip a few steps. We now must justify why the answer is the remaining choice.
The answer is most likely "It explains what 'all men' means and what it includes." This is because not only is this statement the evident main idea, it also includes the powerful repitition that is utilized to display a message.
If we were to apply this to another section of a Martin Luther King Jr. speech, "I Have a Dream", we would find the answer includes thw words "I Have a Dream". This line could be considered the most quotable and well-known quotes related to social justice. The line is repeated many times, with elaborations, just as "all men" is.
Please let me know if this helped, or if you have any questions! If you wouldn't mind, I'd be very grateful for a rating! Thank you!
Answer:
A. It explains what “all men” means and what it includes.
Step-by-step explanation: It told me once I got it wrong because the answer on here was useless. Good luck on your assignment!
There are 2 violet balls and 4 pink balls in a bag.if two balls are drawn one after the other , then what is the probability of getting violet first and pink next, if the first ball drawn is replaced?
Answer:
c
Step-by-step explanation:
The probability of getting violet first and pink next is [tex]\dfrac{2}{9}[/tex].
Given:
The number of violet balls is 2.
The number of pink balls is 4.
To find:
The probability of getting violet first and pink next, if the first ball drawn is replaced.
Explanation:
We know that,
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Total number of balls is:
[tex]2+4=6[/tex]
The probability of getting violet a ball is [tex]\dfrac{2}{6}[/tex].
The first ball drawn is replaced, then the total number of balls remains the same. Then the probability of getting a pink ball is [tex]\dfrac{4}{6}[/tex].
The probability of getting violet first and pink next, if the first ball drawn is replaced is:
[tex]P=\dfrac{2}{6}\times \dfrac{4}{6}[/tex]
[tex]P=\dfrac{1}{3}\times \dfrac{2}{3}[/tex]
[tex]P=\dfrac{2}{9}[/tex]
Therefore, the probability of getting violet first and pink next is [tex]\dfrac{2}{9}[/tex].
Learn more:
https://brainly.com/question/15620045
Given segment CE and point D that lies on CE, find CD if CE= 11, CD= -16-3x, and ED= -13-2x
Answer:Assuming all three, we shall find that each of the relations in 3:14 leads to a ... Then by 3:15 the relations AD//BC and AB||DE imply AD//CE, which excludes ... From 2:72, 3:11, 3:14, and 3:16 we deduce 3:19 If A, B, C are three distinct ... a point D lies between X and Y in AB/C if it belongs to XY/C, that is, if XY||CD
Step-by-step explanation:
Bobby is making a cake. The recipe calls for 1( 3)/(4) cups of flour for every( 1)/(8) cups of sugar. How many cups of flour is needed for 1 cup of sugar?
If you want I will give BRAINLIEST >_
Answer:
5 cups
Step-by-step explanation:
To get 1 cup of sugar, u must add 1/8 by 8. now you have one cup of sugar. But to find out how much flour u need, u also need to multiply 1 3/4 by 8, which gives u 5 cups
Answer:
14 cups of flour are needed for 1 cup of sugar.
Step-by-step explanation:
Use a ratio.
cups of flour : cups of sugar
1 3/4 : 1/8
? : 1
We know that you must multiply by 8 to get from 1/8 to 1. Now we have to do the same to the other side. So, multiply 1 3/4 by 8.
1 3/4 * 8 = 14
Therefore, 14 cups of flour are needed for 1 cup of sugar.
Tell me if this was helpful:)
Denzel wants to walk to the store from his house but he is not sure how far away it is. Find the distance between his house
(-8, -9) and the store (-4, -10). Each unit is equal to one mile. Round your answer to the nearest mile.
22 miles
4 miles
31 miles
17 miles
Answer:
4 miles
Step-by-step explanation:
Suppose we have two points:
[tex]A = (x_{1}, y_{1})[/tex]
[tex]B = (x_{2}, y_{2})[/tex]
The distance between these points is:
[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
In this question:
Points (-8, -9) and (-4, -10).
So the distance is:
[tex]D = \sqrt{(-8 - (-4))^{2} + (-9 - (-10))^{2}} = \sqrt{17} = 4.12[/tex]
The distance is 4.12 miles.
Rounding to the nearest mile, 4 miles.
Find two numbers, if their sum is 49 and their difference is 1/2 .
Answer:
[tex]x=24\frac{3}{4}\\ y=24\frac{1}{4}[/tex]
Step-by-step explanation:
Let the two numbers be x and y
So we have:
[tex]x +y = 49\\x-y=\frac{1}{2}[/tex]
using the elimination method, add the two equations together:
[tex]2x=49\frac{1}{2} \\2x=\frac{99}{2}[/tex]
solve for x:
[tex]x=\frac{99}{4}\\x=24\frac{3}{4}[/tex]
substitute our value for x back into the first equation we made:
[tex]x+y=49\\(\frac{99}{4}) + y=49\\y=49-\frac{99}{4}\\y=\frac{97}{4} \\ y=24\frac{1}{4}[/tex]
therefore,
[tex]x=24\frac{3}{4}\\ y=24\frac{1}{4}[/tex]
A coin weighs about 14 to the negative second pounds. Find the weight of 1000 of the coins. Round your answer to the nearest tenth.
Answer:
i think its about 5 pounds idk please tell me if im wrong..
Step-by-step explanation:
The answer is: 250/49 because 14^-2 is equal to 1/196 and if you multiply that by 1000 it equals 250/49 or 5.1
Based on the data given in the picture, calculate the area of the car track...
Please, I need help, i will mark the answer with a brainliest mark...
Refer to the diagram below. We need to find the areas of the green and blue regions, then subtract to get the area of the orange track only.
The larger green region is composed of a rectangle of dimensions 200 meters by 4+42+4 = 50 meters, along with two semicircles that combine to make a full circle. This circle has radius 25 meters.
The green rectangle has area 200*50 = 10000 square meters. The green semicircles combine to form an area of pi*r^2 = pi*25^2 = 625pi square meters. In total, the full green area is 10000+625pi square meters. I'm leaving things in terms of pi for now. The approximation will come later.
The blue area is the same story, but smaller dimensions. The blue rectangle has dimensions 200 meters by 42 meters, so its area is 200*42 = 8400 square meters. The blue semicircular pieces combine to a circle with area pi*r^2 = pi*21^2 = 441pi square meters. In total, the blue region has area 8400+441pi square meters.
After we figure out the green and blue areas, we subtract to get the orange region's area, which is the area of the track only.
orange area = (green) - (blue)
track area = (10000+625pi) - (8400+441pi)
track area = 10000+625pi - 8400-441pi
track area = (10000-8400) + (625pi - 441pi)
track area = 184pi + 1600 is the exact area in terms of pi
track area = 2178.05304826052 is the approximate area when you use the pi constant built into your calculator. If you use pi = 3.14 instead, then you'll get 2177.76 as the approximate answer. I think its better to use the more accurate version of pi. Of course, be sure to listen/follow your teachers instructions.
Simplify the radicals in the given expression:
8^3√a^4b^3c^2-14ab^3√ac^2
8ab√ac^2-14ab^3ac^2
8a^2ba^3√b-14abc^3a
8ab^3ac^2-14ab^3√ac^2
8a^2bc√b-14abc√a
i've gotten the answer it is "8ab^3ac^2-14ab^3√ac^2"
Answer: it’s option c
Step-by-step explanation:
Simplified form of radical 8∛(a⁴b³c²)-14b∛(ac^(2)) is -6ab∛ac².
What is radical?
The symbol '√' that expresses a root of a number is known as radical and is read as x radical n or nth root of x. The horizontal line covering the number is called the vinculum and the number under it is called the radicand. The number n written before the radical is called the index or degree.
Given radical
8∛(a⁴b³c²)-14b∛(ac^(2))
Rewriting a⁴b³c² as (ab)³ ac²
8∛((ab)³ac²)-14b∛(ac²)
8ab∛ac² - 14b∛ac²
-6ab∛ac².
Hence, -6ab∛ac² is the simplified form of 8∛(a⁴b³c²)-14b∛(ac^(2)).
Learn more about radical here:
https://brainly.com/question/1369233
#SPJ2
Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:
Opinion A: Improving the healthcare system is more important than improving the education system.
Opinion B: Improving the education system is more important than improving the healthcare system.
Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."
The outcomes were as follows:
39% chose Opinion A, 54% chose Opinion B, and 7% chose "Neutral."
Part A: Create and interpret a 98% confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B. (5 points)
Part B: The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met? (5 points)
Answer:
A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B
= (0.51, 0.57)
This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)
B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.
Critical value = 2.33
Standard error = σₓ = √[p(1-p)/n]
p = sample proportion = 0.54
n = sample size = 1500
σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287
98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.54 ± (2.33 × 0.01287)
CI = 0.54 ± 0.02998)
98% CI = (0.51, 0.57)
98% Confidence interval = (0.51, 0.57)
B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?
For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;
- The sample data must have been obtained using a random sampling technique.
- The sampling distribution must be normal or approximately normal.
- The variables of the sample data must be independent of each other.
On the second point, the condition for a binomial distribution to approximate a normal distribution is that
np ≥ 10
and n(1-p) ≥ 10
The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.
For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.
Hope this Helps!!!
Neil goes to the pet shop and selects a treat for his dog. He chooses one, then chooses another. What is the probability Neil selects a bone and then a ball? There are 3 collars, 4 bones, and 5 balls.
Answer:
15.15% probability that Neil selects a bone and then a ball
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Initially, there are 3+4+5 = 12 treats. 4 of those are bones. So the probability of selecting a bone is 4/12 = 1/3.
Now suppose a bone has been selected. Now there are 11 treats, 5 of which are balls. So the probability of selecting a ball in this situation is 5/11.
What is the probability Neil selects a bone and then a ball?
[tex]p = \frac{1}{3}*\frac{5}{11} = \frac{5}{33} = 0.1515[/tex]
15.15% probability that Neil selects a bone and then a ball
help plssssssssssssssssss
Answer:
80
Step-by-step explanation:
BECAUSE ON THE BOX PLOT ON HOW IT IS LOOK AT THAT LAST LINE AND LOOK HOW FAR IT GOES THATS HOW MUCH IT WOULD BE
BRAINLEST PLEASEWhat is central tendency??
Answer:
central tendency is the tendency for the values of a random variable 2 cluster round it's mean,mode amdedian
Step-by-step explanation:
it's also called center/location of the distribution
What is the y-intercept of line 12?
Answer:
y int. of line 1 = 0
y int. of line 2 = 4
Step-by-step explanation:
hope this helps! moo!
Answer:
Answers are below
Step-by-step explanation:
The y-intercept of line 1 is 0 because it crosses the y-axis at 0.
The y-intercept of line 2 is 4 because it crosses the y-axis at 4.
What is the rate of change
Answer:
Slope = 0
Step-by-step explanation:
Let's use the equation [tex]\frac{y2 - y1}{x2 - x1}[/tex] for this problem.
We have two points: (2,0) and (-2, 0)
Let's plug them both into the equation shown above.
[tex]\frac{0 - 0}{-2 - 2}[/tex]
Solve.
0 - 0 = 0
-2 - 2 = -4
[tex]\frac{0}{-4}[/tex] = [tex]-\frac{0}{4}[/tex] = 0
A zero in the numerator means this equation has a slope of 0.
Any line with a slope of 0 is a horizontal line.
Slope (rate of change) = 0
A bag contains 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the theoretical probability of drawing a brown marble?
20/53 chance or 0.38 probability.
Evaluate 3x^3 - 5y^2 x=5 y=2
Could use some quick help I don't really know what i'm doing wrong.
Answer:
355
Step-by-step explanation:
3[tex]x^{3}[/tex]-5[tex]y^{2}[/tex]=3*5³-5*2²
3*5³-5*2²=3*125-5*4
3*125-5*4=375-20
375-20=355
Answer:
355
Step-by-step explanation:
3-5=3*5³-5*2²
3*5³-5*2²=3*125-5*4
3*125-5*4=375-20
375-20=355
Question 2 Please help. Find the arc length for the following:
Answer:
The answer is 9.4 units.
A basketball has a volume of 23047 cm
What is the diameter of this basketball?
4 of 5 QUESTIONS
24 cm
16.6 cm
27.7 cm
12 cm
SUBMIT
Answer:
17.65693585 = r
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
23047 = 4/3 (3.14) r^3
23047 = 4.1866666666 r^3
Divide by 4.186666 on each side
23047/4.18666666 = 4.1866666666/4.18666666 *r^3
5504.856688 = r^3
Take the cubed root on each side
(5504.856688)^1/3 = r^3^(1/3)
17.65693585 = r
The value of the expression 16 -2/4 is ______.
Answer:
8
Step-by-step explanation:
2/4 is equal to a half,so half of 16 is 8 so,you would do
16-8=8
