Which is the graph of the function f(x) = x3 + x2 + x + 1?
Answer:
Step-by-step explanation:
the answer is on the graph
Which pair of complex numbers has a real-number product? (1 2i)(8i) (1 2i)(2 – 5i) (1 2i)(1 – 2i) (1 2i)(4i)
The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
According to the statement
we have given Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
So, For this purpose
we have to multiply these pairs with each other.
So,
(1+2i)(8i) = 8i +16(i)^2
And
(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2
And
(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5
And
(1+2i)(4i) = 4i + 6(i)^2
From these multiplication we found that the third pair have a real number product.
So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.
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Find the seventh term of the sequence which has a first term of 1/2 and has a common ratio of three
The seventh term of the sequence is 364.5
Geometric progressionFrom the question, we are to determine the seventh term of the sequence
Using the formula,
[tex]a_{n} = ar^{n-1}[/tex]
Where [tex]a_{n}[/tex] is the nth term
a is the first term
and r is the common ratio
From the given information,
a = 1/2
r = 3
Thus,
[tex]a_{7} = (\frac{1}{2}) 3^{7-1}[/tex]
[tex]a_{7} = (\frac{1}{2}) 3^{6}[/tex]
[tex]a_{7} = \frac{1}{2} \times 729[/tex]
[tex]a_{7} = 364\frac{1}{2} \ OR \ 364.5[/tex]
Hence, the seventh term of the sequence is 364.5
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WILL MAKE BRAINLIEST!!
Complete the congruence statement for the figure below.
One pen is chosen without looking from a bag that has 3 blue pens, 6 red pens, and 3 green pens.
Find the probability of choosing a green pen.
The probability of choosing. a green pen is 0.25
What is probability?Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected/Total outcome
If a bag has 3 blue pens, 6 red pens, and 3 green pens, then;
Total pen = 3+6+3
Total pen = 12
If a green pen is chosen, then
Pr(choosing a green pen) = 3/12
Pr(choosing a green pen) = 0.25
Hence the probability of choosing. a green pen is 0.25
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If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
(–h, –k)
(h, k)
(–h, k)
(h, –k)
The vertex of the transformed parabola with the equation [tex]y=a(x-h)^2+k[/tex] is (h, k).
What are the transformation rules for horizontal and vertical shifts?The transformation rules are:
Translation: (x, y) → (x + a, y) or (x, y) → (x - a, y) (Horizontal shift)
Translation: (x, y) → (x , y + b) or (x, y) → (x , y - b) (Vertical shift)
Calculation:It is given that, the transformed parabola is [tex]y=a(x-h)^2+k[/tex]
This parabola has vertex at (h, k).
Since this equation is obtained by shifting h units horizontally and k units vertically.
So, the original vertex is at (h - h, k - k) = (0, 0)
Thus, the equation of the actual parabola is [tex]y=ax^2[/tex]
Therefore, the given transformed equation of parabola has vertex (h, k).
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Answer:
B] (h,k)
The next answer is Vertex (-5, -4)
☆
EDGE2022; Good luck :3!!!!
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = 3/4x
O h(x) = 1/4x
Answer:
last answer:
h(x) = 1/4 x
Step-by-step explanation:
First, change f(x) to y.
f(x) = 4x
y = 4x
Then switch the x and y.
y = 4x
x = 4y
Last, solve for y.
x = 4y
x/4 = 4y/4
x/4 = y
y = x/4
This is the same as:
y = 1/4 x
h(x) = 1/4 x
2. Which of the following expressions is equivalent to 322?
01
08.1/1
032.2
08-2
Answer:
C. (32/4)*2
Step-by-step explanation:
C is the correct answer because when we divide 4/2 it equals 2.
Hope this helps!
Answer:
D
Step-by-step explanation:
Given expression:
[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]
Evaluation of the given expression:
[tex] = 8 \times 2 \times 2 [/tex]
[tex] = 32 [/tex]
A. [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]
B. [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]
C. [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]
D. [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]
Only expression D evaluates to the same value as the given expression.
Answer: D
Freddie had saved 231 pennies.
Which statement best describes
the number of pennies he had?
he has 231 pennies..............
10. A drawer contains only green marbles. After
5 red marbles are added to the drawer, the
probability of picking a red marble is
How many marbles were there in the drawer
originally?
(A) 5
(B) 7
(C) 12
(D) 30
(8)
Answer:
(D) 30
Step-by-step explanation:
number of green marbles = x
number of red marbles = 5
total number of marbles = x + 5
p(red) = (number of red marbles)/(total number of marbles)
p(red) = 5/(x + 5)
p(red) = 1/7
5/(x + 5) = 1/7
(x + 5) × 1 = 5 × 7
x + 5 = 35
x = 30
Answer: (D) 30
What do these values indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?
Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.
Reason Behind a Biased Estimator
The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a biased estimator.
Brief Description of Sample Mean Absolute Deviation
The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.
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1. What is the approximate area of circle A?
2. What is the approximate area of circle B?
3. What is the approximate area of the shaded region 1 (between the square and circle A)?
4. What is the approximate area of shaded region 2 (between circles A & B)?
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
How to estimate geometric areas
In this situation we have a square whose side length is known and two circles whose radii have to be estimated. By direct inspection we find that the diameter of circle A is two thirds of the length of the square side (l), in inches and the diameter of circle B is the half of the diameter of the former. Now we proceed to find the key dimensions of the figure:
Circle A
Diameter: 16 inches
Radius: 8 inches
Circle B
Diameter: 8 inches
Radius: 4 inches
The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.
The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.
The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.
The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.
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Consider the function f(x)=x2 bx c. if the minimum of this function is located at point (2,0), then what are the values of b and c?
The values of b and c are -4 and 4 respectively
How to determine the values of b and c?The function is given as:
f(x) = x^2 + bx + c
Differentiate f(x)
f'(x) = 2x + b
Set to 0
2x + b = 0
Solve for b
b = -2x
The minimum is (2, 0).
So, we have:
b = -2 * 2
b = -4
Substitute b = -4 in f(x) = x^2 + bx + c
f(x) = x^2 - 4x + c
Substitute (2, 0)
0 = (2)^2 - 4(2) + c
This gives
0 = 4 - 8 + c
Evaluate
c = 4
Hence, the values of b and c are -4 and 4 respectively
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8 more than 3 times a number is the same as -5 times the number.
a. x = -1
b. x = 1
c. x = -2
Answer:
3x +8 = -5x
3x + 5x = -8
8x = -8x
x = -8 /8
x = -1
Hope it helps...
Please contact me for further explanation....
The line plot (shown in the attached image) shows the prices of sunglasses at a department store.
a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.
Please help!!
a. The mean, median and mode for this plot are 70.8, 70 and 60 respectively.
b. Mean best represents the data for this plot.
c. When there are outliers, the mean might be a deceptive center tendency measure.
Mean, Median, and Mode
Mean = Sum of prices / Total number of sunglasses
Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25
Mean = 70.8
Median is equal to (n/2 + 1) when n is an odd number.
Here, the number of sunglasses is represented by n.
⇒ (25/2 + 1)th term is the median
Median = 13th term
Median = 70
Mode is the most frequent data from the plot.
⇒ Mode = 70
Mean Being the Best Central Measure
The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.
Misleading Measure
When there are outliers, the data mean is significantly impacted. As a result, it may be inaccurate when examining the data's average price.
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Use the distributive property to write an
addition sentence equivalent to:
8(5+2)
Answer:
8(5) + 8(2)
Step-by-step explanation:
8 (5 + 2) is 8 (7) or 56
If I distribute the 8 through the problem, I will get the same answer
8(5) + 8(2)
40 + 16
56
During a snowstorm, Madeline tracked the amount of snow on the ground. When the storm began, there were 3 inches of snow on the ground. Snow fell at a constant rate of 1 inch per hour until another 2 inches had fallen. The storm then stopped for 3 hours and then started again at a constant rate of 2 inches every 3 hours for the next 9 hours. When the storm stopped again, the sun came out and melted the snow for the next 2 hours at a constant rate of 3 inches per hour. Make a graph showing the inches of snow on the ground over time using the data that Madeline collected.
The graph depicts that at the end of the snowstorm, there was 5 inches of snow left. See the attached graph.
How many hours did the snow fall?It is not be noted that the total amount of hours which the snow fell is:
2 + 9 = 11 hours.
Although the graph depicts a peak of 14 hours, recall that there were three hours when the snow didn't fall.
While the maximum depth of the snow was 11 inches.
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Find the other endpoint of the line segment with the given endpoint -5, 2 and midpoint 2, -5
Answer:
( 9, -12 )
Step-by-step explanation:
Mario's Math Tutoring
you have the midpoint
2, -5
use the midpoint formula
(x1+x2)/2 , (y1+y2)/2
to get the endpoint
x :
(-5+x2)/2 = 2
(-5+x2) = 4
-5+x2 = 4
x2 = 9
y:
(2+y2)/2 = -5
(2+y2) = -10
2+y2 = -10
y2 = -12
Thank you Mario!
What is the area of a square with a perimeter of 44 mm?
Answer:
The area of the square is 121mm
Step-by-step explanation:
To solve this we need two basic formulas:
P = 4s
A = [tex]s^{2}[/tex]
P = perimeter
s = the length of the side
Since the shape is a square all the sides are the same length. To get the value of 's' we need to isolate:
P = 4s
44 = 4s
44 / 4 = 4s / 4
11 = s
Now plug in the answer for 's' to get the area:
A = [tex]s^{2}[/tex]
A = [tex]11^{2}[/tex]
A = 121
Hope this helps.
Identify the function with a period of 4 and an amplitude of 2.
Answer:
it's only 2pi/B because the period of sin and cos is 2pi. If we were dealing with tan it'd be pi/B, since the period of tan is just pi.
Can someone help me please
Answer: B. [tex]12log(x)-4log(y)[/tex]
Step-by-step explanation:
Properties of logs:
[tex]log_{a} (\frac{B}{C} )=log_{A}B-log_{A} C[/tex]
[tex]logA^B = BlogA[/tex]
So, [tex]log\frac{x^{12} }{y^4} =logx^{12} -logy^4 =12log(x)-4log(y)[/tex]
It would be 12 log x - 4 log y (B)
find the slope of a line parallel to the line through the given points. E(5, 7), F(3, 1) •-3
•-1/3
•1/3
Answer:
3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (1 - 7)/(3 - 5)
slope = -6/(-2)
slope = 3
Parallel lines have equal slopes.
Answer: 3
Help me pleaseeeeeeeeeeeeeeeeeeeee
Answer:
a = 16.52 cmb = 23.85 cm=========================
Given AB = 22 cmm∠A = 42°m∠B = 75°To findSide length of a and bSolutionThe law of sines is:
a/sin A = b/sin B = c/sin CStep 1Find the value of ∠C using the angle sum theorem:
m∠A + m∠B + m∠C = 180°42° + 75° + C = 180°117° + C = 180°C = 180° - 117°C = 63°Step 2Find side a:
Note, the sides of a triangle are marked as:
a = BC, b = AC, c = AB (opposite to respective angle).Use two pairs with one unknown:
a/sin A = c/sin CSubstitute values and solve for a:
a/ sin 42° = 22/sin 63°a = 22*sin 42°/sin 63°a = 16.52 cm (rounded)Step 3Find side b, similar to finding side a:
b/ sin 75° = 22/sin 63°b = 22*sin 75°/sin 63°b = 23.85 cm (rounded)Answer:
a = 16.5 cm (nearest tenth)
b = 23.8 cm (nearest tenth)
Step-by-step explanation:
Definition
A, B and C are the angles and a, b and c are the sides opposite the angles.
From inspection of the triangle:
A = 42°B = 75°c = 22 cmInterior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42° + 75° + C = 180°
⇒ C = 180° - 117°
⇒ C = 63°
To find the missing side lengths a and b, use the Sine Rule:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Substitute the given values into the Sine Rule formula:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
Finding side a:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=16.52162239...[/tex]
Therefore, side a is 16.5 cm (nearest tenth).
Finding side b:
[tex]\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=23.84984577...[/tex]
Therefore, side b is 23.8 cm (nearest tenth).
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In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
Answer:
PRQ = 65 degrees
Step-by-step explanation:
Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).
SPR + QPR = 180
135 + QPR = 180
QPR = 45
TQP + RQP = 180
110 + RQP = 180
RQP = 70
Since interior angles of a triangle add up to 180 ...
QPR + RQP + PRQ = 180
45 + 70 + PRQ = 180
PRQ = 65
What is the y-intercept of the function f(x)=-2/9x + 1/3?
Answer:
y-intercept = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
the coefficient is the slope (slope = -2/9x)
the constant is the y-intercept (y-intercept=1/3)
this is true for all functions like this
Answer:
The y-intercept is
c) 1/3
Step-by-step explanation:
The length of a rectangle is 6 inches more than its width. Its area is 91 square inches. The length is .
Answer:
13 in
Step-by-step explanation:
let w be width then length is w + 6
the area (A) of a rectangle is calculated as
A = length × width , then
A = w(w + 6) = 91 , that is
w² + 6w = 91 ( subtract 91 from both sides )
w² + 6w - 91 = 0 ← in standard quadratic form
(w + 13)(w - 7) = 0 ← in factored form
equate each factor to zero and solve for w
w + 13 = 0 ⇒ w = - 13
w - 7 = 0 ⇒ w = 7
however, w > 0 then w = 7
and length = w + 6 = 7 + 6 = 13 in
1/5n+3/5n=7/9
Can you help?
The value of n in 1/5n+3/5n=7/9 is 35/36
How to solve the equation?The equation is given as:
1/5n+3/5n=7/9
Multiply through by 5
n + 3n = 35/9
Evaluate the sum
4n = 35/9
Divide both sides by 4
n = 35/36
Hence, the value of n in 1/5n+3/5n=7/9 is 35/36
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Find the area of this circle
Answer:
[tex] {75ft}^{2} [/tex]
Step-by-step explanation:
[tex]a = \pi{r}^{2} = 3 {r}^{2} \\ a =3 ({ \frac{10}{2} })^{2} = 3 \times {5}^{2} \\ a = 3 \times 25 = 75[/tex]
First, we replace π with 3, since we were told to.We know 10 is the diameter and the radius is half of the diameter, so we divide 10 by 2.We get 5. 5 squared is the same as (5×5). Finally, we multiply 3 by 25.To start solving this exercise, we obtain as data:
π = 3r = 10 ft²a = ?To find the area of the circle. We apply the following formula: A =π r², where
a = areaπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation:
[tex]\boldsymbol{\sf{A=3*(10 \ ft)^{2} }}[/tex]Taking the square root:
[tex]\boldsymbol{\sf{A=3*100 \ ft^{2} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{A=300 \ ft^{2} }}}[/tex]Therefore, the area of the circle is 300 ft².
A company designs microphones for use in conference rooms. a new microphone needs to focus on the person speaking and not the voices of other people in the room. which polar equation would best match the desired audible range of the microphone?
r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.
How do you know if an equation is polar?Determine the kind of polar equation. The polar equation has the shape of a limaçon, and is written as r = a - b cos. We just need to assess the equation throughout the range [0, 1] and then reflect the graph about the polar axis because the equation passes the condition for symmetry to the polar axis.What is a polar in math?The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.What is the meaning of polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.Learn more about polar form here:
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Answer:
D
Step-by-step explanation:
Bd=16 and ac is the perpendicular bisector of bd. 2x-14 37-x d 2y-2 3 y=[?] enter
The value of y from the given expression is 5
Perpendicular Bisector
Given:
BD = 16
BC = 2y - 2
CD = y + 3
Since AC is a perpendicular bisector of BD:
BC = CD
2y - 2 = y + 3
2y - y = 3 + 2
y = 5
Hence, the value of y from the given expression is 5
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