Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
The dotplot below displays the difference in scores for 18 games between a high school soccer team and its opponent.
A dotplot titled difference in Score. A number line going from negative 2 to 4 is labeled Team score minus opponent score. Negative 2, 1; negative 1, 2; 0, 2; 1, 3; 2, 6; 3, 3; 4, 1.
Which of the following is the best explanation for the dots at –1?
In one game, the team beat the opponent by 1 goal.
In two games, the team beat the opponent by 1 goal.
In one game, the team lost to the opponent by 1 goal.
In two games, the team lost to the opponent by 1 goal.
Answer: Choice D
In two games, the team lost to the opponent by 1 goal.
========================================================
Explanation:
Negative scores indicate the team lost, and the absolute value of those values represent how much of a loss.
So a difference of -1 means the team lost by 1 point.
We have 2 dots over this value, so there are 2 occasions where the team lost to the opponent by 1 goal.
An example would be that say the team scored 3 goals and the opponent scored 4 goals. So we have a differential of 3-4 = -1. The order is important because we would not say 4-3 = 1.
Answer:
d
Step-by-step explanation:
took the test
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
Answer:
[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]
Step-by-step explanation:
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.
Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?
Answer:
The answer is "0.6368 and 0.773".
Step-by-step explanation:
The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]
For point a:
Therefore the Probability =0.6368
For point b:
[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]
hawkville's population is 2500 people. next year the town clerk expects the population to grow by 1.2%, how many new residents will hawkville have next year?
Answer:
30 new residents
Step-by-step explanation:
Find how many new residents they will have by finding 1.2% of the current population.
2500(0.012)
= 30
So, Hawkville will have 30 new residents
(-5/2) divide 13/7 x 9/7
Help :(
Answer:
-45/26
Step-by-step explanation:
(-5/2)÷(13/7)×(9/7)
(-5/2)×(7/13)×(9/7)
-45/26
Answered by Gauthmath must click thanks and mark brainliest
LET R equal the rental fee for one locker write an equation that represents the situation
Answer:
R x 1= price of 1 locker
Step-by-step explanation:
it would continue the same way. Just multiply R and the number of lockers.
Is there a certain situation it was asking about?
What is the correct way to read 43.106
Step-by-step explanation:
Forty three thousand one hundred and six
Answer:
Forty three AND one hundred six thousandths
Step-by-step explanation:
If there is a comma ( , ) between the two numbers, you are correct.
If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals. Those are the "th" numbers. 1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.
If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six" or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".
What is the largest value of x for which the following equation has a real solution (x,y)?
Answer:
x = 9/2
Step-by-step explanation:
x^2+7x+y^2+4y=191/4
Complete the square: (x+7/2)^2-(49/4)+(y+2)^2-4 = 191/4
Simplify: (x+7/2)^2+(y+2)^2=191/4+49/4+4
(x+7/2)^2 + (y+2)^2 = 64
(x+7/2)^2 + (y+2)^2 = (8)^2
Center of circle -> (-7/2, -2)
Radius -> 8
-7/2 + 8 = 9/2
x = 9/2
Multiply:
2 × (–21) × 7
A)
294
B)
–273
C)
–7
D)
–294
Answer:
[tex]2\times \left(-21\right)\times \:7[/tex]
PEMDAS order of operations:
[tex]2\times \left(-21\right)=-2\times \:21=-42[/tex]
[tex]=-42\times \:7[/tex]
[tex]=-294[/tex]
D) -294 is your answer
OAmalOHopeO
The least-squares regression equation
y = 3 + 1.16x can be used to predict the height of a plant (in centimeters) after x weeks. Suppose the height of a plant was 9.2 centimeters after 5 weeks.
Calculate and interpret the residual for this plant after 5 weeks.
The residual is
✔ 0.4
, which means that the predicted height of the plant is
✔ 0.4 centimeters less
than the actual height of the plant of
✔ 9.2
centimeters.
Answer:
✔ 0.4
✔ 0.4 centimeters less
✔ 9.2
1.16(5) + 3 = 8.8
9.2 - 8.8 = .4
ED2021
The residual is 0.4
What is regression?
'Regression takes a group of random variables, thought to be predicting Y, and tries to find a mathematical relationship between them. This relationship is typically in the form of a straight line (linear regression) that best approximates all the individual data points.'
According to the given problem,
y = 3 + 1.16x
After 5 weeks, x = 5,
⇒ y = 3 + 1.16(5)
⇒ y = 3 + 5.8
⇒ y = 8.8
Now subtracting y from actual height of plant,
⇒ 9.2 - 8.8
= 0.4
Hence, we can conclude the residual to be 0.4.
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#SPJ2
ty
This graph shows a portion of an even function.
Use the graph to complete the table of values.
6
f(x)
-1
4
-3
-5
-6
2
DONE
2
4.
6
Answers:
first box = 1second box = 1third box = 3fourth box = 3Refer to the graph below.
==========================================================
Explanation:
If f(x) is an even function, then f(-x) = f(x) for all x in the domain.
What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.
The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.
Use the rule [tex](x,y) \to (-x,y)[/tex] to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.
---------------
We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.
1 goes in the second box
---------------
The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.
It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3
3 goes in the third box
----------------
Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.
3 goes in the fourth box.
See the graph below.
Find the sum of the arithmetic series given ai = 45, an = 85, and n = 5.
Answer:
C. 325.
Step-by-step explanation:
The last term a5 = 85
a1 = 45
Sum of n terms = n/2 (a1 + l)
So here we have n = 5, a1 = 45 and the last term l = 85
= (5/2)(45 + 85)
= 5/2 * 130
= 325.
The required sum of the arithmetic series is 325.
Arithmetic series is defined as a sequence of numbers arranged in a particular pattern.
The sum of the nth term of an arithmetic sequence is expressed as:
[tex]S_n = \frac{n}{2}[a+l]\\[/tex] where:
n is the number of terms
a is the first term
l is the last term
Given the following
a = 45
n = 5
an = l = 85
Substitute the given values in the formula above:
[tex]S_5= \frac{5}{2}(45+85)\\ S_5=\frac{5}{2}(130)\\ S_5=5 \times 65\\S_5=325[/tex]
Hence the sum of the arithmetic series is 325
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Translations _______ side lengths of the figure.
A. change
B. alter
C. preserve
D. all of these
Answer:
C. preserve
Step-by-step explanation:
When you translate something in geometry, you're simply moving it around. You don't distort it in any way. If you translate a segment, it remains a segment, and its length doesn't change. Similarly, if you translate an angle, the measure of the angle doesn't change.
write the first 10 multiplies of 6 and 8 pairs of numbers and find this LCM
↪[tex] \huge\rm{answer: } \: \boxed{ \purple{24 }}[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
M(6)= {0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ...}
M(8) = {0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...}
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
I hope you understood!✏
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
[tex] \huge\boxed{ \boxed{ \rm{Hope \: this \: helps }}}[/tex]
Answer:
6=0,6,12,18,24,30,36,42,48,54,60
8=0,8,16,24,32,40,48,56,64,72,80
HCF=24,48
LCM=0,6,12,18,,30,36,42,48,54,60,8,16,24,32,40,,56,64,72,80
rút gọn :
(x+2)^2+(3-x)^2= ?
Step-by-step explanation:
=x^2+2x+4+9-6x+x^2
=2x^2-4x+13
The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?
Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively
The reason the above values of the points of the complex conjugate are correct is as follows:
Definition:
The complex conjugate of a complex number is a complex number that
having equal magnitude in the real and imaginary part as the complex
number to which it is a conjugate, but the imaginary part of the complex
conjugate has an opposite sign to the original complex number
Graphically, the complex conjugate is a reflection of the
original complex number across the x-axis because the transformation for
a reflection of the point (x, y) across the x-axis is given as follows;
Preimage (x, y) reflected across the x-axis give the image (x, -y)
In a complex number, x + y·i. we have;
x = The real part
y = The imaginary part
The reflection of z₁(1, -2) across the x-axis gives the point A(1, 2), while the
reflection of z₂(6, -7) across the x-axis gives the point L(6, 7)
To summarize;
Point A(1, 2) is the reflection and therefore represents the complex
conjugate of z₁(1, -2) and point L(6, 7) is the reflection and therefore
represents the complex conjugate of z₂(6, -7)
Learn more about complex numbers here;
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Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
perpendicular to
7y = x − 4
and passes through the point
(−2, 1)
Answer:
[tex]y = -7x -13[/tex]
Step-by-step explanation:
Given
Perpendicular to
[tex]7y = x -4[/tex]
Passes through
[tex](-2,1)[/tex]
Required
The equation
First, we calculate the slope of:
[tex]7y = x -4[/tex]
Divide through by 7
[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]
A linear function is:
[tex]y=mx + c[/tex]
Where;
[tex]m \to slope[/tex]
So:
[tex]m = \frac{1}{7}[/tex]
For the perpendicular line; the slope is:
[tex]m_2 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_2 = -\frac{1}{1/7}[/tex]
[tex]m_2 = -7[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = -7(x - -2) + 1[/tex]
[tex]y = -7(x +2) + 1[/tex]
Open bracket
[tex]y = -7x -14 + 1[/tex]
[tex]y = -7x -13[/tex]
Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)
Answer:
$240,300
Step-by-step explanation:
Given :
Overhead cost :
Computer support = $267000
legal support = $133500
Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)
+
(number of legal hours used by Audit services * activity rate per legal hour)
The overhead applied to audit is thus :
40,000 * (267,000 / (40,000 + 10,000)) +
200 * (133500 / (200 + 800)
(40000 * 5.34) + (200 * 133.5)
= $240,300
Express 80 inches in standard notation using feet and inches.
80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
The solution to the given problem is to use some standard conversion units that are:
1 foot = 12 inches1 inch = 0.8333 feetSolution:
As mentioned above that one inch is equal to 0.8333 foot therefore
1 foot = 12 inches
then,
80 inches would be equal to
= [tex]\frac{80}{12}[/tex] ft
= [tex]\frac{20}{3}[/tex] ft
= 6ft 8 inches
= 6' 8"
Thus, 80 inches in standard notation using feet and inches would be expressed as 6 ft 8 inches by converting inches into feet and inches.
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7,25 x (y+5,6)=58 vậy y =
Answer:
y=2,4
Step-by-step explanation:
7,25x( y+5,6)=58
7,25y+ 40,6=58
7,25y=58-40,6
y=17,4:7,25
y=2,4
x
A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.
Lower endpoint______ Upper endpoint__
Answer:
it simple as look
Step-by-step explanation:
He y I a m r a v I t ha n k S
Wowowowowowowowowk
1.2 Write the ratio 1:2 in the simplest form.
Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings?
FINAL ANSWER: D
Given : Molly and Lynn both set aside money weekly for their savings.
Molly already has $650 set aside and adds $35 each week.
Lynn already has $825 set aside but adds only $15 each week.
To Find : inequality to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings
Solution:
Molly already has $650
adds $35 each week.
=> added in w weeks = 35w
After w weeks = 650 + 35w
Lynn already has $825
adds $15 each week.
added in w weeks = 15w
After w weeks = 825 + 15w
Molly’s savings to exceed Lynn’s savings
⇒ 650 + 35w > 825 + 15w
⇒ 20w > 175
⇒ 4w > 35
⇒ w > 35 /4
At least 9 weeks
Answer:
D
Step-by-step explanation:
First, to eliminate some answers you can figure out which way the sign should go. The question wants to know when Molly's savings will be larger so the sign should open towards her side of the equation. Since her savings are represented on the left the sign should be a greater than, >.
Then, figure out where the variables belong. The variable represents the number of weeks that have passed, so they should be multiplied by the number that is affected by the passing of weeks. This is the amount each person saves, aka the independent variable. So the "w" variable should be next to the 35 and 15.
This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?
write an absolute value equations to satsify the given solution set shown on a number line -1/2 1/2 and a
Plz help fast
9514 1404 393
Answer:
|x| = 1/2
Step-by-step explanation:
Perhaps the simplest equation is ...
|x| = 1/2
__
You could get more elaborate:
|2x| = 1
3 -|6x| = 0
What is the domain of the function Y = In
-X+3
2
0x62
O x32
O X<3
O
X> 3
ASAP
Answer:
i think 1/58 is correct
i hope its help you
necesito la respuesta, entre a b c o d
Answer:
a)a^4 + 19a^2 -12ab - 3b^4 +6b...
the mubrer
2. The first term in a sequence is 3.
The rule for the sequence is to multiply by 3 then add 2
Write the next 3 terms in the sequence
Answer:
3, 11, 35.
Step-by-step explanation:
The first 3 terms of the sequence can de written as:
n, 3n + 2, 3(3n + 2) + 2
So when n = 3 the first 3 terms are
3, 3(3) + 2, 3(3(3) + 2)) + 2
= 3 , 9 + 2, 33 + 2
= 3, 11, 35.
Question 2
<
>
B 0.67/1
The measure of one angle of a right triangle is 0° more than the measure of the smallest angle.
Find the measures of all three angles, and separate your answers with commas.
9514 1404 393
Answer:
45°, 45°, 90°
Step-by-step explanation:
If the difference of two angles is 0°, then they are congruent, and the triangle is isosceles.
The angle measures of the isosceles right triangle are 45°, 45°, 90°.
In how many distinct ways can the letters of the word MAMAS be arranged?
Answer:
120 ways
Step-by-step explanation:
There are 5 letters.
5! = 5*4*3*2*1
= 20*6
= 120
Answer:
The answer is 30. You cant repeat letters. Ther are 5 letters, the M and A are repeat letters so 5-2=3 5!/3! = 30
Step-by-step explanation:
