This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Given:
Equations: r = 1 + cos θ ...(1)
r = 1 − sin θ ...(2)
Where, r ≥ 0, 0 ≤ θ < 2π
We need to determined the point of intersection of the graphs of the equations.
To obtain the points of intersection, Equate the two equations above as follows;
r = 1 + cos θ = 1 - sin θ
=> 1 + cos θ = 1 - sin θ
Solve further for θ. We get,
1 + cos θ = 1 - sinθ
cos θ = - sinθ
Now dividing both sides by - cos θ and solve it further,
[tex]\dfrac{cos\;\theta}{-cos\;\theta} =\dfrac{-sin\;\theta}{-cos\;\theta}\\\\tan\;\theta=-1\\\\\theta=tan^{-1}(1)\\\\\theta=45^{0}=\dfrac{-\pi }{4}[/tex]
To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +\pi =\dfrac{3\pi }{4} \\[/tex]
Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e
[tex]\dfrac{-\pi }{4} +2\pi =\dfrac{7\pi }{4} \\[/tex]
Therefore, the values of θ are 3π / 4 and 7π / 4.
Now substitute these values into equations (i) and (ii) as follows;
[tex]When \;\theta=\dfrac{3\pi }{4},[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{3\pi }{4} =1+\dfrac{-\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{3\pi }{4} =1-\dfrac{\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]
[tex]When\; \theta=\dfrac{7\pi }{4}[/tex]
[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{7\pi }{4} =1+\dfrac{\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{7\pi }{4} =1-\dfrac{-\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]
Represent the results above in polar coordinates of the form (r, θ). i.e
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
Therefore, at the pole where r = 0, is also one of the points of intersection.
Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]
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If it’s 11:50 amwhat timewillitbetwohoursfromnow
Answer:
It will be 1:50
Step-by-step explanation:
Answer:
11:50 + 2 hr. = 1:50 or 13:50 Military/European time
Step-by-step explanation:
Given: 2x + 3y= 6.
What is the y-intercept?
(0,3)
(2,0)
(0,2)
no intercept
Determine if the two triangles shown are similar. If so, write the similarity statement. options:
A) ΔWUV ∼ ΔFGH
B) ΔUVW ∼ ΔFGH
C) Impossible to determine.
D) The triangles are not similar.
Answer:
B
Step-by-step explanation:
∠ U = ∠ F = 76° thus are congruent
Consider the ratios of corresponding sides
[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]
[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]
Thus Δ UVW ~ Δ FGH by the SAS postulate
Yes the given two triangles are similar.
The similarity statement is B) ΔUVW ∼ ΔFGH
What do we mean by similar triangles ?
The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.
Are the given triangles similar or not ?Here, in the given triangles,
∠U = ∠F = 76°
Therefore they are congruent.
The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]
Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]
Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.
Learn more about Similarity of triangle here :
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Was it evaluated correct?
explain your reasoning
Answer:
Yes
Step-by-step explanation:
Yes. They did exponents and grouping symbols first, then multiplication and division left to right. Addition came before multiplication and division because it was inside a grouping symbol.
In which of the following scenarios will conducting a two-sample t-test for means be appropriate? Check all that apply.
A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.
B. To test if the mean annual income of Ontarians is higher than that of British Columbians.
C. To test if there is a difference between the mean annual income of husbands and that of wives in Canada.
D. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
F. To test if there is a difference between the mean annual income of British Columbians and a known national mean.
G. None of the above
Answer:
B. To test if the mean annual income of Ontarians is higher than that of British Columbians
E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
Explanation:
The options chosen have two populations that are independent. For example in option B, the annual income of Ontarians is a different population from annual income of British Columbians and they are also independent. The two sample t test can only be used when the populations are independent, it can also be used when computing difference between the means of two populations
The scenarios where conducting a two-sample t-test for means be appropriate include:
A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.It should be noted that the two sample t-test is used when the populations are independent band the sample size is small.
Therefore, it will be appropriate to test if there is a difference between the proportion of low-income families in British Columbia and a known national and the difference between the mean annual income of male British Columbians and that of female British Columbians.
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m∠C= step by step thank you so much
Answer:
please mark my answer brainliest
Step-by-step explanation:
in tri ABD and bcd...
AD =DC ...given
AB =BC.....given
BD =BD.....common
therefore...both tri are congruent...by SSS CRITERION
therefore angle adb...and angle bdc are equal...cpct...
therefore angle bdc =32°
angle dbc =90°
therefore angle bcd =angle C=180- (90 +32) =58°
angle C=58°....answer
Which of the following represents a closer relationship between two variables?a) r =.00.b) r = .50.c) r = -30. d) r = -65.
Answer:
d) r = -65.
Step-by-step explanation:
The absolute value of r represents the relationship strength and the sign represents the relationship direction
Also if the relationship is nearest to 1 then it would be termed as positive correlated and if the relationship is nearest to -1 then it would be termed as negative correlated
Therefore based on the given options, the last option is correct
In the healthy handwashing survey conducted by Bradley Corporation, a study was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n=20 adult Americans is obtained, and the number x who flush public toilets with their feet is recorded.
A) Explain why this is a binomial experiment.
B) Find and interpret the probability that exactly 12 flush public toilets with their foot.
C) Find and interpret the probability that at least 16 flush public toilets with their foot.
D) Would it be unusual to find more than 17 who flush public toilets with their foot? Why?
Answer:
A) It fulfills the condition of binomial experiment
B) P (x=12) =0.1678
C)P ( x ≥16)= 0.1011
d) P (x>17) =0.0096 < 0.5
Step-by-step explanation:
A. The binomial probability distribution has the following four properties
1. the outcomes of each trial maybe classified into success and failure.
2) the probability of success p remains constant for all trials.
3) the successive trials are all independent.
4) the experiment is repeated a fixed number of times ,n.
These all conditions are fulfilled by the given question so it is a binomial experiment.
B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678
C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)
where
P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645
P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270
P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080
P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015
P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001
so
P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011
d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)
=0.0270 +0.0080+ 0.0015+0.0001
=0.0096
From this we see that the probability of more than 17 people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.
an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec. Find the rate of change of the water depth when the water depth is 10 ft.
Answer:
the rate of change of the water depth when the water depth is 10 ft is; [tex]\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
[tex]\dfrac{h}{r}= \dfrac{20}{8}[/tex] ( similar triangle property)
[tex]\dfrac{h}{r}= \dfrac{5}{2}[/tex]
[tex]\dfrac{h}{r}= 2.5[/tex]
h = 2.5r
[tex]r = \dfrac{h}{2.5}[/tex]
The volume of the water in the tank is represented by the equation:
[tex]V = \dfrac{1}{3} \pi r^2 h[/tex]
[tex]V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h[/tex]
[tex]V = \dfrac{1}{18.75} \pi \ h^3[/tex]
The rate of change of the water depth is :
[tex]\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
[tex]\dfrac{dv}{dt}= - 4 \ ft^3/sec[/tex]
Therefore,
[tex]-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]
the rate of change of the water at depth h = 10 ft is:
[tex]-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}[/tex]
[tex]100 \pi \dfrac{dh}{dt} = -4 \times 6.25[/tex]
[tex]100 \pi \dfrac{dh}{dt} = -25[/tex]
[tex]\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}[/tex]
Thus, the rate of change of the water depth when the water depth is 10 ft is; [tex]\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]
Answer:
the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
h = 2.5r
The volume of the water in the tank is represented by the equation:
The rate of change of the water depth is :
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
Therefore,
the rate of change of the water at depth h = 10 ft is:
Thus, the rate of change of the water depth when the water depth is 10 ft is;
Step-by-step explanation:
Find the equation of the line that contains the points (4,2) and (6,10). Write the equation in the form y=mx+b and identify m and b.
An online retailer is offering a 30% savings on your total order. You decide to purchase a pair of pants for $82, two shirts for $53 each, and a pair of shoes for $120. A sales tax of 8.25% will be added to your order. What is the final price including all discounts and taxes for the clothing? Round your answer to the nearest cent
Answer:
$233.39
Step-by-step explanation:
Pants = $82, 2 Shirts = $53 * 2, Shoes = $120
Add all these values up to find the total cost of your order excluding tax.
82 + 53(2) + 120 = 308
Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.
308 * 0.0825 = 25.41
Now you add the tax to the total value.
308 + 25.41 = 333.41
The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).
333.41 * 0.30 = 100.023
Now you subtract the discount from the total price.
333.41 - 100.023 = 233.38700
The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.
The final price of the clothing including all discounts and taxes is $233.39.
Solve m +9 = 2.
Please and thank you.
Answer:
the answer is -7
Step-by-step explanation:
m+9=2-9
-9
m=. -7
(90) points ill give brainly immideatly but gotta be right -------- Maria and her parents are hiking in the mountains. During one hike, Maria monitored their changing elevation and displayed it in the graph below. Which of the following BEST describes a functional relationship shown in the graph? A Maria's elevation remained constant for two hours. B Maria's elevation decreased between 1:00 and 3:00. C Maria's elevation increased between 9:00 and 12:00. D Maria spent more time decreasing her elevation than increasing her elevation.
Answer:
(C) Maria's elevation increased between 9:00 and 12:00
Step-by-step explanation:
Looking at the graph, we can test each statement.
For A, it says Maria's elevation remained constant for 2 hours. Looking at the graph, we can see that it remained constant for just one hour, so this is eliminated.
For B, Maria's elevation decreased between 1:00 and 3:00, we can see that while x is between 1:00 and 3:00, the y is decreasing, meaning this statement is false - this is eliminated.
For C, Maria's elevation increased between 9:00 and 12:00, we can see that while x is between 9:00 and 12:00, the graph is increasing - which means this is correct.
For D, Maria spent more time decreasing her elevation than increasing, we can count how many hours were spent doing each. Comparing the x-axis, we can see that Maria spent 5 hours increasing and 3 hours decreasing, meaning that Maria spent more time INCREASING than decreasing, making this statement false.
Hope this helped!
Answer: C A B C D
Step-by-step explanation: I HAVE NONE IM JUST SMART
I THINK?
PLEASE HELP!!!! I will award brainliest!! Look at the figure shown below. A student made the table shown below to prove that PQ is equal to RQ. 1. Provide the missing statement and justification in the proof. 2. Using complete sentences, explain why the proof would not work without the missing step.
Answer:
See below.
Step-by-step explanation:
1.
Statement 8. triangle SQR is congruent to triangle TQP
Reason 8. ASA
2.
The only way to prove those two sides are congruent is to first prove that the triangles that contain those sides are congruent. Then you can use CPCTC to prove those sides congruent.
A chef orders carrots and celery in bulk. The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb
combined.
What is the weight of the carrots?
Answer:
Y= 7.9 lb
X= 10.1 lb
Step-by-step explanation:
The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.
Let carrot= x
Let celery= y
X+y = 18...... equation one
X= 2.2 +y.... equation two
Substituting the value of x into equation one
2.2 +y +y =18
2y= 18-2.2
2y= 15.8
Y= 7.9 lb
Substituting the value of yinto equation 2
X= 2.2 +y
X= 2.2 + 7.9
X= 10.1 lb
As the sample size for a t-distribution increases, the differences between the t-distribution and the standard normal distribution ______.
Answer:
The differences become smaller
Step-by-step explanation:
Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.
Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.
This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.
For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.
Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.
Darren picked 25 flowers that he plans to divide evenly into 3 vases. He will use as many flowers per vase as he can, but may have flowers left
Answer:
He will use flowers per vasebut will have one leftStep-by-step explanation:
In this problem we are required to place flowers evenly across 3 flower vases.
Given that we have 25 flower to collect from and distribute evenly.
we are going to divide 25 by 3
We have
[tex]= \frac{25}{3}\\\\ =8\frac{1}{3}[/tex]
From the result in the improper fraction we can see the Darren can place 8 flowers evenly of the 25 flowers and there will be just one left over
what complex number has an absolute value of 5 ?
Answer:
the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}
please give me heart
Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.
Answer:
Step-by-step explanation:
H₀ : The distribution of the sample agrees with the population distribution.
H₁ : the distribution of the does not agree with the population distribution.
Using the Chi-square test statistics
we will compute the expected frequencies
Now expected frequency for Washington will be
Fe = Npi = 1000×51% = 5100
expected frequency for Oregon
Fe = Npi = 1000×30% = 300
expected frequency for Idaho
Fe = Npi = 1000×11% = 110
expected frequency for Montana
Fe = Npi = 1000×8% = 80
The Chi=square test statistics is;
x² = ∑ [ (Fo - Fe)² / Fe )
now we substitute
Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question
x² = (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80
x²= 31.9376
so the chi-square test statistics is 31.9376
Now the chi-square critical value
first we compute for degree of freedom
d.f = k -1 = 4 - 1 = 3
So from the critical value table, degree of freedom 3 and significance level 0.05,
the chi-square critical value is 7.8147
Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.
There is sufficient evidence to warrant rejection of the claim that the distribution of the sample agrees with the distribution of the state populations.
The answers listed below are characteristics of a Type I error EXCEPT for one. Select the characteristic that is not for Type I errora) upsetting status quo for falsehoodb) reject null hypothesis when null is truec) a "missed opportunity"
Answer:
c
Step-by-step explanation:
:)
Multiply the place value of 6 in 37651 by 11
Answer: Hi!
The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.
All we need to do is multiply 600 by 11:
600 * 11 = 6600
Hope this helps!
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).
6 in the hundreds place is 600.
600 times 11 equals 6600.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
♡ Hope this helps! ♡
❀ 0ranges ❀
Laura orders 50 m² of concrete paving slabs. The slabs cost £16.75 per m². How much do the slabs cost in total
Answer:
£837.5
Step-by-step explanation:
Cost of slabs = £16.75 / m²
Ordered amount = 50 m²
Total cost:
£16.75*50 = £837.5Total cost of slabs is £837.5
Which fraction is equal to k in the equation below?
1\3 / 2= k
Answer:
0_10 =0_2
Step-by-step explanation:
Convert the following to base 2:
0_10
Hint: | Starting with zero, raise 2 to increasingly larger integer powers until the result exceeds 0.
Determine the powers of 2 that will be used as the places of the digits in the base-2 representation of 0:
Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value
0 | 2^0 | 1
Hint: | The powers of 2 (in ascending order) are associated with the places from right to left.
Label each place of the base-2 representation of 0 with the appropriate power of 2:
Place | | | 2^0 |
| | | ↓ |
0_10 | = | ( | __ | )_(_2)
Hint: | Divide 0 by 2 and find the remainder. The remainder is the first digit.
Determine the value of 0 in base 2:
0/2=0 with remainder 0
Place | | | 2^0 |
| | | ↓ |
0_10 | = | ( | 0 | )_(_2)
Hint: | Express 0_10 in base 2.
The number 0_10 is equivalent to 0_2 in base 2.
Answer: 0_10 =0_2
If it took 4 hours to clean 8 houses, how many houses could be cleaned in 7 hours
Answer:
14
Step-by-step explanation:
you clean 2 a hour so 7*2=14
Answer:
14 houses
Step-by-step explanation:
This is the question.
Answer:
B
Step-by-step explanation:
Hello!
A function is a equation that every input has one output
To find if an equation is a function we put in a number for one variable and solve
I'll use 0
y^2 = 0^2 + 5(0) + 4
Simplify
y^2 = 0 + 0 + 4
Combine like terms
y^2 = 4
To remove the square from y you put 4 in the square root in both negative and positive
[tex]y=\sqrt{4}[/tex] [tex]y=-\sqrt{4}[/tex]
Simplify
y = 2, y = -2
For one input (0) we get two outputs (2 and -2) this means it is not a function. So the answer is B
Hope this Helps!
t takes one person 2 hours to grade 1 exam and it takes another 4 hours to grade 1 exam. If both work together, how many exams they can grades in 8 hours
Answer:
4
Step-by-step explanation:
2×4 equals 8 4 papers in 8 hours
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(
Answer Choice 1
Take it step by step!
First find what sqrt(x-7) is like. Compare it to sqrt(x).
You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.
Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.
Hope that helped,
-sirswagger21
50 Points! PLEASE ANSWER ASAP
Answer:
a. 1120 is the area b. max # of ppl is 80
Step-by-step explanation:
a. Area= Length* width = 28 * 40 = 1120
(8,10) and (8,38) have 28 units between them
(8,10) and (48,10) have 40 units between them
b. Since the area is 1120 and they say that only one person is allowed per 14 square feet, you would divide 1120 by 14 to get 80 people
If each coordinate equals 1 foot then:
(8,10) to (48,10) is 40 feet (48-8)
(8,10) to (8,38) is 28 feet (38-10)
so now you got length 40 and width 28
40 x 28 = 1120
a. 1120ft^2
b. 1120 / 14 = 80
What is the remainder when f(x) = x^2 + 14x − 8 is divided by (x − 5)? 103 88 87 72
Answer:
The remainder is 87.
Step-by-step explanation:
By definition of remainder theorem, whenever a polynomial f(x) is divided by (x-b) the remainder will be: f(b)
Following the Remainder Theorem, in this question the remainder will be f(5).
In this case we were given f(x) as
f(x) = x^2 + 14x − 8
We're are to find the remainder when it is divided by (x-5)
Then(x-5)= 0
X=5
If we substitute x=5 into equation of f(x), we will have the remainder of
f(x) = x^2 + 14x − 8
f(4)= (5)^2 +14(5)-8
f(4)=25+70-8
f(4)=87
Hence, The remainder is 87.
Answer:
87
Step-by-step explanation:
Plz HELP ASAP (algebra)
Answer:16
Step-by-step explanation:
Given: 15% of 60 is 9.
so 9 kids are 15 year old.
and 1 other kid is 16 year old.
Thus, there are total of (15+1) kids that are either 15 or 16 year old. you can also draw venn diagram to find that.