Answer:
x ≈ 48.3177
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] ⇔ n log x
Given
[tex](1.1)^{x}[/tex] = 100 ( take the log of both sides )
log[tex]1.1)^{x}[/tex] = log100 , then
x log1.1 = log100 ( divide both sides by log1.1 )
x = [tex]\frac{log100}{log1.1}[/tex] ≈ 48.3177 ( to 4 dec. places )
Find a tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 7 cos(t)j t = π/6
The tangent vector to r(t) at any t in the domain is
[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]
At t = π/6, the tanget vector is
[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]
To get the unit tangent, normalize this vector by dividing it by its magnitude:
[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]
So the unit tangent at the given point is
[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]
Applying derivatives, the tangent vector of unit length at the point given is:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
The vector function is:
[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]
The tangent vector is it's derivative, which is given by:
[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]
At point [tex]t = \frac{\pi}{6}[/tex], we have that:
[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]
[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]
The norm of the vector is:
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]
[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]
The unit vector is given by each component divided by the norm, thus:
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]
[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]
A similar problem is given at https://brainly.com/question/20733439
URGENT!! The diagram shown below represents the height of a blimp flying over a football stadium. Find the height of the blimp if the angle of elevation at the southern end zone, point A, is 70∘, the angle of elevation from the northern end zone, point B, is 62∘, and the distance between the viewing points of the two end zones is 145 yards. Round your answer to the nearest tenth and do not include units.
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
The height of the blimp over the football stadium = 161.9 yards
Hope this helepd you. Brainliest would be nice!
help pleaseeeeeeeeee
It's Class B:
[tex]32\% \text{ of } 50 = 32\%\cdot50=\dfrac{32}{100}\cdot50 = \dfrac{32}{2}=16[/tex]
Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars).
Weekly Usage
(hours) Annual Maintenance
Expense ($100s)
13 17.0
10 22.0
20 30.0
28 37.0
32 47.0
17 30.5
24 32.5
31 39.0
40 51.5
38
40.0
(a) Use the data to develop an estimated regression equation that could be used to predict the annual maintenance expense for a given number of hours of weekly usage. What is the estimated regression model?
Let x represent the number of hours of weekly usage.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
(b) Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
(c) How much of the variation in the sample values of annual maintenance cost does the model you estimated in part (b) explain?
If required, round your answer to two decimal places.
(d) If the maintenance contract costs $3000 per year, would you recommend purchasing it? Explain.
Answer:
Step-by-step explanation:
Hello!
The given data corresponds to the variables
Y: Annual Maintenance Expense ($100s)
X: Weekly Usage (hours)
n= 10
∑X= 253; ∑X²= 7347; [tex]\frac{}{X}[/tex]= ∑X/n= 253/10= 25.3 Hours
∑Y= 346.50; ∑Y²= 13010.75; [tex]\frac{}{Y}[/tex]= ∑Y/n= 346.50/10= 34.65 $100s
∑XY= 9668.5
a)
To estimate the slope and y-intercept you have to apply the following formulas:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95[/tex]
[tex]a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53[/tex]
^Y= a + bX
^Y= 10.53 + 0.95X
b)
H₀: β = 0
H₁: β ≠ 0
α:0.05
[tex]F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}[/tex]
F= 47.62
p-value: 0.0001
To decide using the p-value you have to compare it against the level of significance:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.
c)
The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:
[tex]R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86[/tex]
This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X
d)
Without usage, you'd expect the annual maintenance expense to be $1053
If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553
If used 1000 hours weekly the expected maintenance expense will be $96053
It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.
Given rectangles ABCD and A'B'C'D, describe the transformation that takes place from ABCD to A'B'C'D'
Answer:
A 90° clockwise rotation about the origin and a translation of 7 units down.Step-by-step explanation:
First of all, we need to define the image and pre-image.
The pre-image is the rectangle ABCD, before the transformation. The image is the rectangle A'B'C'D', after the transformation.Second, let's write down the coordinates of each rectangle.
ABCD coordinates:
A(-6,5)
B(-1,5)
C(-1,1)
D(-6,1)
A'B'C'D' coordinates:
A'(5,-1)
B'(5,-6)
C'(1,-6)
D'(1,-1)
The first rule we need to apply is the 90° clockwise rotation which is
[tex](x,y) \implies (y,-x)[/tex]
Which gives us (5,6), (5,1), (1,1), (1,6).
Then, we use the 7 units-down rule
[tex](x,y) \implies (x,y-7)[/tex]
Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).
Therefore, the right answer is the third choice.
Answer:
A 90° clockwise rotation about the origin and a translation of 7 units down.
Find the largest of three consecutive whole numbers such that twice the sum of the two smallest numbers is 13 more than three times the largest number.
Answer:
17, 18, 19
Step-by-step explanation:
Let's say that the three consecutive numbers are
x-1,x,x+1.
Twice the sum of the two smallest numbers:
2(x -1 +x)
13 more than three times the largest number
13+3(x+1).
2(2x-1)=13+3x+3
4x-2=3x+16
4x-3x=16+2
x=18. So the numbers are:
17, 18, 19
A spring has natural length 24 cm. Compare the work W1 done in stretching the spring from 24 cm to 34 cm with the work W2 done in stretching it from 34 to 44 cm. (Use k for the spring constant) So:W1= ? W2:=? These answers must be written in terms of k. How are W2 and W1 related? W2 = ? W1
Answer:
From the analysis W1=W2.
they are directly related
Step-by-step explanation:
the work-done in stretching a spring can be expressed as
[tex]W=\frac{1}{2}kx^2[/tex]
where k= spring constant
x= change on length of spring
Hence for W1
Given data
x= 34-24= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k[/tex]
Hence for W2
Given data
x= 44-34= 10 cm
solving in terms of k we have
[tex]W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k[/tex]
Evauluate 37/100+3/10
Answer:
67/100
Step-by-step explanation:
Find common denominators, note that what you do to the denominator, you must do to the numerator.
The common denominator is 100:
(3/10)(10/10) = (3 * 10)/(10 * 10) = 30/100
Add:
37/100 + 30/100 = 67/100
67/100 is your answer.
~
Answer:
67/100
Step-by-step explanation:
37/100+3/10
Get a common denominator
37/100 + 3/10 *10/10
37/100+30/100
67/100
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc) estimate Create a t-chart to graph the coordinates Find the 0's of the function Solve for y and use the slope-intercept form
Answer:
creat a t-chart to graph the coordinates.
pat and tim work together at a pizzeria, Pat can fold 30 pizza boxes per minute and tim can fold 20 pizza boxes per minute. Working together, how many SECONDS will it take them to fold 200 boxes? plz help will give everything
Step-by-step explanation:
1 min = 60 sec
Boxes both can fold per min = 30 + 20 = 50
No of boxes to fold = 200
Time taken in sec = 200 ÷ 50 = 4 min = 60 x 4 = 240 sec
which of the following describes an irrational number?
A. a repeating and non-terminating decimal.
B. a fraction
C. a terminating decimal
D. a non-terminating and non-repeating decimal
Answer:
A.
Step-by-step explanation:
B is wrong because irrational numbers can include pie.
C and D are wrong because irrational numbers don't get a whole number, and instead gives a decimal numbers.
Licence plates in Costa Rica are made up of 6 one-digit number. How many license plates can be made if the numbers can be repeated? (Probability unit grade 12 data management)
Answer:
There are 10 digits and 6 numbers so the answer is 10 * 10 * 10 * 10 * 10 * 10 = 10⁶ = 1,000,000.
3. A strip of wood 78 inches long is to be cut into pieces 3 3la inches long. How many pieces can be cut?
A. 21
B. 12
C. 26
D.20
Answer:
Option D (20) is the right answer.
Step-by-step explanation:
The given values are:
Length of wood,
= 78 inches
Wood pieces,
= [tex]3\frac{3}{4} \ inches[/tex]
On converting this in proper fraction, we get
= [tex]3\frac{3}{4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3.75 \ inches[/tex]
Now,
On dividing "78" from "3.78", we get
= [tex]\frac{78}{3.75}[/tex]
= [tex]20.8 \ pieces[/tex]
So we got "20 pieces".
What is the simple interest earned on
$300 over 6 years at 4% interest?
Answer:
$72
Step-by-step explanation:
I = Prt
I = ($300)(0.04)(6)
I = $72
Round your answer to the nearest hundredth.
2
25
Ab=
Answer:
sin(25 degrees)/2 = 0.21
Step-by-step explanation:
Since the sine of an angle is the opposite side divided by the hypotenuse, the sine of 25 degrees equals the opposite, or 2, divided by the hypotenuse, or what you are trying to find. So sin(25 degrees) = 2/x, or x = sin(25 degrees)/2, and using your calculator and rounding, the final answer is 0.21
Answer:The answer is actually 4.73
Step-by-step explanation:
Solve the system by using the inverse of the coefficient matrix. -3x + 9y = 9 3x + 2y = 13 Group of answer choices
Answer:
x= 3
y=2
Step-by-step explanation:
-3x + 9y = 9 ----------- equation 1
3x + 2y = 13--------------- equation 2
In Matrix Form
[tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right][/tex]
Let A = [tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right][/tex] X = [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] and B = [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Then Mathematically AX= B
or X= A⁻¹ B
Where A⁻¹ = Adjacent A/ mod of A
Adjacent A = [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex]
Mod Of A= -6 - (27) = -33 which is not equal to zero
so Putting These values in the given formula
X= 1/-33 [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex] [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Now Multiplying Rows and Columns
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right][/tex]
Solving the Matrix we get
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}-99\\-66\end{array}\right][/tex]
From Here we find x= 99/33 or 3
and y = 66/33= 2
Find the measure of angle d when angle a is 128 angle b is 126 and angle c is 54
Step-by-step explanation:
sum of four angles=360°
a=128
b=126
c=54
d=?,let d=x
128+126+54+x=360°
308+x=360
find like terms
x=360-308
x=52°
The sum of an irrational number and a rational number is irrational. Sometimes True Always True Never True
Answer:
Always true
Step-by-step explanation:
Trust me
Answer:
true
Step-by-step explanation:
rename the mixed number as an improper fraction
Answer:
Convert [tex]\frac{2}{3}[/tex] to an improper fraction.
So your answer is [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Hope this helped you!!
━━━━━━━☆☆━━━━━━━
▹ Answer
[tex]\frac{11}{3}[/tex]
▹ Step-by-Step Explanation
3 * 3 = 9
9 + 2 = 11
Therefore, the answer is 11/3.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
A copy machine makes 104 copies in 3 minutes and 15 seconds. how many copies does it make per minute
Answer:
32 copiesStep-by-step explanation:
First convert 3 minutes and 15 seconds into minutes by converting 15 sec to min and add it to 3min
60 sec = 1min
15 sec = 15 / 60 × 1 min
= 0.25min
Add it to 3min
3min + 0.25min = 3.25 min
We use ratio and proportion
3.25min = 104 copies
1 min = 104× 1/ 3.25
= 104 / 3.25
= 32
The final answer is 32 copies
Hope this helps you.
Answer:
Step-by-step explanation:
3 min 15 sec = 3*60 + 15 = 180 + 15 = 195 seconds
In 195 seconds 104 copies are made
In one second, the number of copies made = [tex]\frac{104}{195}\\[/tex]
In 60 seconds, the number of copies made = [tex]\frac{104}{195}*60[/tex]
= 32 copies
An item has a listed price of $30 if the sales tax rate is 7% how much is the sales tax in dollars
Answer:
The sales tax is 2.10
Step-by-step explanation:
Take the price of the item and multiply by the sales tax rate to determine the tax
30 * 7%
30 * .07
2.10
The sales tax is 2.10
Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 7 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Sloth CW Ratios
1.5
1.09
0.98
1.42
1.49
1.25
1.18
Fill in the blank for a with the estimate of the standard deviation of this measurement in three-toed sloths to two decimals, and include the leading zero
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero)
Does this interval include the value obtained from other species? (answer yes or no in blank d)
Answer:
Step-by-step explanation:
Hello!
Given the variable
X: Ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloth.
The researcher's claim is that the ratio of the SC of the sloths is more variable than in other animal species that are more active.
For more active species the standard deviation of the ratio is σ= 0.09
1)
To calculate the sample standard deviation you have to calculate the sample variance first:
[tex]S^2= \frac{1}{n-1} [sumX^2-\frac{(sumX)^2}{n} ][/tex]
n=7; ∑X= 8.91; ∑X²= 11.8599
[tex]S^2= \frac{1}{6} [11.5899-\frac{(8.91)^2}{7} ]= 0.0287= 0.029[/tex]
S= √S²= √0.029= 0.169≅ 0.17
The sample standard deviation of the ratio is 0.17
2)
The parameter of interest is the population standard deviation. To calculate a confidence interval for the standard deviation of a population you have to estimate the population variance first. Then calculate the square root of both limits of the interval for the variance to obtain the interval for the standard deviation.
The statistic to use is the Chi-Square and the formula for the interval is:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{6; 0.025}= 1.2373[/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{6; 0.975}= 14.449[/tex]
[tex][\frac{6*0.029}{14.449} ;\frac{6*0.029}{1.2373} ]\\[/tex]
[0.0120; 0.1406]
Using a 95% confidence level you'd expect the interval [0.0120; 0.1406] to include the true value of the population variance of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
Now you have to calculate the square root of each limit:
[√0.0120; √0.1406]
[0.1097; 0.3750]
Using a 95% confidence level you'd expect the interval [0.1097; 0.3750] to include the true value of the population standard deviation of the ratio of the length to width of the anterior semicircular canals (SC) of the three-toed sloths.
3)
As you can see the calculated interval doesn't include the value obtained for the other species.
I hope this helps!
The polynomial 24x3 − 54x2 + 44x − 99 is factored by grouping. 24x3 − 54x2 + 44x − 99 24x3 + 44x − 54x2 − 99 4x(____) − 9(____) What is the common factor that is missing from both sets of parentheses? 6x + 11 6x − 11 6x2 + 11 6x2 − 11
Answer: 6x² + 11
Step-by-step explanation:
24x³ - 54x² + 44x - 99
= 6x²(4x - 9) + 11(4x - 9)
= (6x² + 11) (4x - 9)
This can be rewritten as: 4x(6x² + 11) - 9(6x² + 11)
This is the answer to your problem.
select the option for "?" that continues the pattern in each question
3,-6, 12, 4, 20
13
14
6
16
Answer:
The next number in the sequence is: 13
Step-by-step explanation:
So we start with 3, then the pattern is:
subtract 9, add 18, subtract 8, add 16, subtract 7, add 14...
If we apply this to the pattern we can see that it works. You should be able to continue the pattern if needed.
In a poll of 745 randomly selected adults, 591 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.
Answer:
The calculated value Z = 2.734 > 2.576 at 0.01 level of significance
Null hypothesis is rejected
The claim that 75% of adults say that it is morally wrong to report all income on tax returns.
Step-by-step explanation:
Step(i):-
Given random sample size 'n' = 745
Given In a poll of 745 randomly selected adults, 591 said that it is morally wrong to not report all income on tax returns
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{591}{745} = 0.7932[/tex]
Given Population proportion P = 0.75
Q = 1-P
Q = 1 - 0.75 = 0.25
Null Hypothesis :H₀: P=0.75
Alternative Hypothesis :H₁:P≠ 0.75
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.7932-0.75 }{\sqrt{\frac{0.75 X 0.25}{745} } }[/tex]
Z = 2.734
Level of significance ∝ = 0.01
The critical value Z =2.576
The calculated value Z = 2.734 > 2.576 at 0.01 level of significance
Null hypothesis is rejected
The claim that 75% of adults say that it is morally wrong to report all income on tax returns.
A survey of 481 of your customers shows that 79% of them like the recent changes to the product. Is this percentage a parameter or a statistic and why
Answer:
Statistic, because it is a property of a sample and not the population.
Step-by-step explanation:
The difference between a parameter and an statistic is that the parameter is a property of a population distribution and an statistics is referred to a sample property.
For example, a sample mean is a statistic while a population mean is a parameter.
In t his case, the proportion is referring to the sample of 481 customers, so it is not a property of the population (altough we can use it to infere about the population), so this proportion (79%) is an statistic.
Triangle ABC is a right triangle. The sides measure AB = 3 and BC = 4. Use the Pythagorean theorem to find CA. A. CA = 25 B. CA = 2.5 C. CA = 20 D. CA = 5
Answer:
CA = 5
Step-by-step explanation:
Since the sides are 3 and 4, we recognize this as a 3:4:5 right triangle, with CA = 5. Using the Pythagorean theorem confirms this:
CA² = AB² +BC²
CA² = 3² +4² = 9 +16 = 25
CA = √25
CA = 5
Answer:
D. CA = 5
Step-by-step explanation:
The Pythagorean Theorem states that given a right triangle with legs a and b and hypotenuse (longest side) c:
a² + b² = c²
Here, the legs are 3 and 4, so a = 3 and b = 4. Plug these in to find c:
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25 = 5
The answer is thus D.
~ an aesthetics lover
Joel is fertilizing an irregularly shaped garden. the grid has squares with side lengths of 2 m. Estimate the area of the garden. Given that the price of the fertilizer is $2.99 per square meter, find the cost of the fertilizer
Answer:
34.99
Step-by-step explanation:
P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?
Answer: Q(x) = x² - 4x + 2
Step-by-step explanation:
P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)
R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2
I will use synthetic division (but you can also use long division).
-2 | 1 -2 -6 4
| ↓ -2 8 -4
1 -4 2 0 ← remainder
The reduced polynomial is: x² - 4x + 2
Subtract -1/2n - (-1/2n)