Answer:
The x-coordinate of Q is 5
Step-by-step explanation:
* Lets revise the division of the line segment
- If point (x , y) divides a line segment internally whose endpoints are
(x1 , y1) and (x2 , y2) at the ratio m1 : m2 from (x1 , y1), then:
# [tex]x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}[/tex]
# [tex]y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}[/tex]
* Lets solve the problem
∵ Point R divides PQ in the ratio 1 : 3
∴ R is (x , y)
∴ P is (x1 , y1) and Q is (x2 , y2)
∴ m1 = 1 and m2 = 3
∵ x-coordinate of R is -1 and the x-coordinate of P is -3
∴ x = -1
∴ x1 = -3
- Use the rule above
∵ [tex]-1=\frac{(3)(-3)+(1)(x_{2})}{1+3}=\frac{-9+x_{2}}{4}[/tex]
- By cross multiplication
∴ (-1) (4) = -9 + x2
∴ -4 = -9 + x2 ⇒ add 9 to both sides
∴ 5 = x2
* The x-coordinate of Q is 5
the x-coordinate of point O is -2.5.
The question deals with dividing a line segment in a given ratio and finding the coordinates of a point. We are told that point R divides line segment PO in the ratio 1:3, the x-coordinate of R is -1, and the x-coordinate of P is -3. We are asked to find the x-coordinate of point Q, presumably typo for O.
Using the section formula, which states that the coordinates of a point dividing a line segment in the ratio m:n can be calculated using the formula (mx2 + nx1) / (m + n) for x-coordinate, here we have m = 1, n = 3, x1 (P's x-coordinate) = -3, and R's x-coordinate = -1. So, we can calculate the x-coordinate of point O (Q seems to be a typo in the question) as follows:
(1×(-1) + 3×(-3)) / (1 + 3) = (-1 - 9) / 4 = -10 / 4 = -2.5
Therefore, the x-coordinate of point O is -2.5.
Which inequality represents all values of x for which the product below is defined?
√5x * √x+3
A. x>0
B. x≤-3
C. x≥-3
D. x≥0
Answer:
D
Step-by-step explanation:
you cannot take the root of a negative number so that eliminates B and C. you can take the root of 0 to be 0 so D is valid.
The correct inequality will be x≥0
What are inequalities?Inequality a statement of an order relationship which are greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to know which inequality represents all values of x ?We know that a negative value under square root is not defined.So, here the values of x will be all the numbers greater or equal to 0
So the correct inequality will be x≥0
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The table shows the height in feet of several students in Miss Patel’s class
Answer:
a. 21/4, 11/2, 49/10, 5/1
b. James 5.5, Olivia 5 1/4, Feng 5, Carmela 4.9
Step-by-step explanation:
Answer with Step-by-step explanation:
Olivia: [tex]5\dfrac{1}{4}[/tex]
= [tex]\frac{21}{4}[/tex] (21/4=5.25)
James: 5.5
= [tex]\dfrac{55}{10}[/tex]
= [tex]\dfrac{11}{2}[/tex]
Carmela: 4.9
= [tex]\dfrac{49}{10}[/tex]
Feng: 5
= [tex]\dfrac{5}{1}[/tex]
b. Heights from greatest to least is:
James 5.5
Olivia 5.25
Feng 5
Carmela 4.9
What are the solutions of x2 - 2x + 26 = 0 ?
O
A. x = 5; or x = -5;
B. x = 1+5i or x = 1-5i
C. x = 2 +10; or x = 2 -10;
O
D. * = 2+5; or x = 2-5;
SUBMIT
Answer:
B
Step-by-step explanation:
Given
x² - 2x + 26 = 0 ← in standard form : ax² + bx + c = 0 : a ≠ 0
with a = 1, b = - 2, c = 26
Use the quadratic formula to solve for x
x = ( - (- 2) ± [tex]\sqrt{(-2)^2-(4(1)(26)}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{4-104}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{-100}[/tex] ) / 2
= ( 2 ± 10i ) / 2
= 1 ± 5i
Solutions are x = 1 + 5i or x = 1 - 5i → B
The equation x² - 2x + 26 = 0 has no real solutions. Thus, none of the given options are correct.
Explanation:To solve the equation x² - 2x + 26 = 0, we can use the quadratic formula.
For an equation of the form ax² + bx + c = 0, the quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
By substituting the values a = 1, b = -2, and c = 26 into the formula, we get:
x = (-(-2) ± √((-2)² - 4(1)(26))) / (2(1))
Simplifying further:
x = (2 ± √(-92)) / 2
Since taking the square root of a negative number results in a complex solution, we can conclude that there are no real solutions to the equation x² - 2x + 26 = 0.
Each exterior angle of a regular decagon has a measure of (3x+6) what is the value of x
Answer: 10
Step-by-step explanation:
We know that a regular decagon has 10 sides.
The sum of all exterior angles of any regular polygon is [tex]360^{\circ}[/tex].
Given: Each exterior angle of a regular decagon has a measure of [tex](3x+6)[/tex].
Then the sum of all the exterior angle will be :-
[tex]10\times(3x+6)=360\\\\\Rightarrow\ 30x+60=360\\\\\Rightarrow 30x=300\\\\\Rightarrow x=\dfrac{300}{30}=10[/tex]
Hence, the value of x = 10
What are the solutions to x^2 + 4x - 12 = 0?
Answer:
That can be factored:
(x +6) * (x -2)
Therefore, x = -6 and x =2
Step-by-step explanation:
For this case we have the following quadratic equation:
[tex]x ^ 2 + 4x-12 = 0[/tex]
We can factor the equation, for it, we must find two numbers that when multiplied give as result -12 and when summed give as result +4. These numbers are: +6 and -2.
Then, the factorization is given by:
[tex](x + 6) (x-2) = 0[/tex]
Thus, the solutions are:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
Answer:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
What is the approximate distance between the points (-3,-4)(-8,1) on a coordinate grid?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{25+25}\implies d=\sqrt{50}\implies d\approx 7.071[/tex]
What does mean, median, mode, and range means in mathematics?
Mean is dividing the sum of all the numbers by how many numbers there are
Median is the middle of the set of number ordered from least to greatest
Mode is the number that appears the most often in the data set
Range is subtracting the biggest number in the data set by the smallest number
Hope this helped!
~Just a girl in love with Shawn Mendes
Final answer:
The mean is the average of a data set, the median is the middle value, the mode is the most frequent value, and the range is the difference between the highest and lowest values. The median is preferred in skewed distributions.
Explanation:
Mean, Median, Mode, and Range in Mathematics
The mean is the average of a data set, calculated by adding up all the values and dividing the total by the number of values. The median is the middle value when the data set is ordered from least to greatest, or the average of two middle values if there is an even number of values in the data set. The mode is the value that appears most frequently in a data set. The range is the difference between the highest and lowest values in the data set. Each of these measures provides different information about the distribution of the data and can be affected by outliers or the overall shape of the data distribution.
For example, consider the data set: 4, 5, 6, 6, 7, 8, 9. The mean is (4+5+6+6+7+8+9)/7 = 6.43, the median is 6, and the mode is 6 (since it appears the most). The range is 9-4 = 5.
In cases where data sets include outliers or are skewed, the mean may not be representative of the data's center. For instance, if a data set is 4, 5, 6, 6, 7, 8, 100, the mean is significantly influenced by the outlier (100), while the median remains a better indicator of the center. In such distributions, the median is often preferred over the mean.
What is the surface area of the cone? (Use 3.14 for pi .)
794.42 in.2
483.56 in.2
822.68 in.2
414.48 in.2
Answer:
794.42 in² (since I used the pi = 3.14159 , the result is slightly different,
Step-by-step explanation:
Formula: Given radius and slant height calculate the height, volume, lateral surface area and total surface area.
Given r, s find h, V, L, A
h = √(s² - r²)
r = 11 in
h = 4.796 in
s = 12 in
V = 607.7 in³
L = 414.7 in²
B = 380.1 in²
A = 794.8 in
Agenda: r = radius
h = height
s = slant height
V = volume
L = lateral surface area
B = base surface area
A = total surface area
π = pi = 3.14159
√ = square root
Answer: the correct option is
(A) 794.42 in.²
Step-by-step explanation: We are given to find the surface area of the cone shown in the figure.
We know that
the SURFACE AREA of a cone with height h units and radius r units is given by
[tex]S=\pi r(r+\sqrt{h^2+r^2}).[/tex]
For the given cone, we have
r = 11 in. and
[tex]h=\sqrt{12^2-11^2}=\sqrt{144-121}=\sqrt{23}=4.8.[/tex]
Therefore, the surface area of the given cone is
[tex]S\\\\=\pi r(r+\sqrt{h^2+r^2})\\\\=3.14\times11(11+\sqrt{4.8^2+11^2})\\\\=34.54(11+12)\\\\=34.54\times23\\\\=794.42.[/tex]
Thus, the required surface area of the given cone is 794.42 in.²
Option (A) is CORRECT.
find three different ways to write the number 437,000 using powers of 10.
Answer:
4370*10^2
437*10^3
43.7*10^4
Step-by-step explanation:
The given number is
437000
Scientific notation can be used to write the number in different ways. We can use the powers of 10 to write the given number.
First way:
The first way is:
4370*10^2
Separating the hundred from the given number
The second way:
437*10^3
Separating the 1000 from the number in the form of power of 10
The third way:
43.7*10^4
Hence scientific notation can be used for writing the number in different ways..
the PE clasd has 12 boys and 8 girls what is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls the greatest common factor of the numbers of girls and boys
Answer:
4
Step-by-step explanation:
We are given that a PE class has 12 boys and 8 girls. The teacher needs to divide in maximum number of teams so that each team has an equal number of boys and girls.
For this, we will factors of 12 and 8 and their greatest common factor.
12 = 4 × 3 = 2 × 2 × 3
8 = 4 × 2 = 2 × 2 × 2
The greatest common factor is 4, therefore the maximum number of teams with equal number of boys and girls is 4.
Please help...........
Answer:
THE ANSWER IS D
Step-by-step explanation:
if you have multiple choice answers like these you can plug in all the numbers for each equation and the only one that works is d
becuase it ends up equaling 2=2
The diameter of a bicycle wheel is 29 in. How many revolutions
does the wheel make when the bicycle travels 200 ft?
Round your answer to the nearest whole number
The number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.
What is the distance?Distance is a numerical representation of the distance between two objects or locations.
The circumference of the bicycle wheel is;
C= π × diameter
C=π × 29 in
C= 91.11 in
Distance traveled by bicycle wheel in 1 revolution is 91.11 in
Unit conversion;
1 feet = 12 inches
1 inch=1/12 feet
91.11 in=7.592 ft
In one revolution, a bicycle wheel travels 7.592 feet. For a distance of 200 feet, the number of revolutions done by a bicycle wheel is:
[tex]\rm n= \frac{200}{7.5 } \\\\ n= 26.34 \\\\ n= 26 \ rev[/tex]
Hence, the number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.
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4+m/8=3/4 can anybody help?
Answer:
C. -26
Step-by-step explanation:
First, subtract by 4 both sides of equation.
4+m/8-4=3/4-4
Then, simplify.
4+m/8-4=m/8
3/4-4=-13/4
m/8=-13/4
Multiply by 8 both sides of equation.
8m/8=8(-13/4)
Simplify to find the answer.
8(-13/4)
-8*13/4
13*8/4=-104/4
104/4=-26
X=-26 is the correct answer.
C. -26 is the correct answer.
For this case we must solve the following equation:
[tex]4+ \frac {m} {8} = \frac {3} {4}[/tex]
We subtract 4 on both sides of the equation:
[tex]\frac {m} {8} = \frac {3} {4} -4\\\frac {m} {8} = \frac {3-16} {4}\\\frac {m} {8} = \frac {-13} {4}[/tex]
We multiply by 8 on both sides of the equation:
[tex]m = \frac {-13 * 8} {4}[/tex]
[tex]m = -26[/tex]
Answer:
Option C
Blake brought 2 magazines for $4.95 each. If the sales tax was 6.75%, what was the total amount that he paid for the magazines?
Answer:
$10.57
Step-by-step explanation:
Blake brought 2 magazines for = $4.95 each
Cost of 2 magazines = 4.95 × 2 = $9.90
Sales tax rate = 6.75%
Total amount that he paid for the magazines = 9.90 + (6.75% × 9.90)
= 9.90 + (0.0675 × 9.90)
= 9.90 + 0.66825
= $10.56825 ≈ $10.57
He paid $10.57 for the magazines.
if city A is 32% less than city b what is city A population
Answer:
there is definitely missing context in this question but if we are going off of per say 100% then A is 68%
Step-by-step explanation:
ASAP GUYS!!!! (I NEED TO FINISH THIS QUICK) Graph Complete the sequence of transformations that produces △X'Y'Z' from △XYZ. A clockwise rotation °______ about the origin followed by a translation ______ units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
Answer:
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
Step-by-step explanation:
* Lets revise the rotation and translation
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 180° anti-clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° anti-clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180° clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° clock wise
∴ Its image is (-y , x)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is = (x , y - k)
* Now lets solve the problem
- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)
∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)
∴ The image of X is (3 , 5)
∴ The image of Y is (3 , 2)
∴ The image of Z is (1 , 2)
- From the graph
∵ X' = (5 , -1)
∵ Y' = (5 , -4)
∵ Z' = (3 , -4)
- Every x-coordinate add by 2
∴ There is a translation 2 units to the right
- Every y-coordinate subtracted by 6
∴ There is a translation 6 units down
- From all above
* A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ
Answer:
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
Step-by-step explanation:
“the sum of -52 and 18 times a number is 2.” The number is
Answer:
50 is the answer
Step-by-step explanation:
If the probability of an event happening is 3/8 . What is the probability that the event will not happen ?
a. 0
b. 3/8
c. 5/8
d. 3/4
e. 1
Answer: C is the answer.
Step-by-step explanation:
It is 5/8 because, there is 3 out of 8 chances of the event happening. The rest of the chances, that is 5 out of eight chances, that are not going to happen.
Choose the correct classification of 3x4 − 9x3 − 3x2 + 6.
5th degree polynomial
4th degree polynomial
9th degree polynomial
24th degree polynomial
Answer:
The correct option is 2.
Step-by-step explanation:
The given polynomial is
[tex]3x^4-9x^3-3x^2+6[/tex]
In a polynomial, the highest degrees of its individual terms with non-zero coefficients is called degree of a polynomial.
The degrees of [tex]3x^4,-9x^3, -3x^2,6[/tex] are 4, 3, 2, 0 respectively.
In the given polynomial, the highest degree of its monomial is 4.
We can say that the given polynomial is 4th degree polynomial.
Therefore the correct option is 2.
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the come to the volume of the prism?
base area=B
base area =B
volume of cone
volume of prism
1
2
volume of cone
volume of prism
1
3
volume of cone
volume of prism
2
3
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Answer:
[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]
[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]
The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
The cone in the diagram has the same height and base area as the prism.
now, we know that,
The formula of volume of a cone:
if 'B' is the base of the cone,
and 'h' is the height of the cone,
its volume is V = (1/3) (Bh) cubic units.
The formula of volume of a prism:
if 'B' is the base of the prism,
and 'h' is the height of the prism,
its volume is V = (Bh) cubic units.
The cone in the diagram has the same height and base area as the prism.
so, the ratio of the volume of the come to the volume of the prism:
The formula of volume of a cone: The formula of volume of a prism
= 1/3 *BH : BH
=1/3
=1:3
Hence, The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
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Which function can be used to model the monthly profit for x trinkets produced?
f(x) = –4(x – 50)(x – 250)
f(x) = (x – 50)(x – 250)
f(x) = 28(x + 50)(x + 250)
f(x) = (x + 50)(x + 250)
The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).
Explanation:The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).
To model the monthly profit, we need to consider the profit made for each trinket produced. The function f(x) = (x + 50)(x + 250) represents the profit made for x trinkets produced, where x is the number of trinkets produced. This function is a quadratic function with two factors that represent the difference between the production cost and the selling price of the trinkets.
For example, if we produce 100 trinkets, we can substitute x = 100 into the function to find the monthly profit. f(100) = (100 + 50)(100 + 250) = 150 * 350 = 52,500. So, the monthly profit for producing 100 trinkets would be $52,500.
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The quadratic function f(x) = –4(x – 50)(x – 250) accurately models the monthly profit for x trinkets produced, displaying a concave-downward parabola as expected in this context.
To determine the appropriate quadratic function to model the monthly profit for x trinkets produced, let's analyze the given options.
A quadratic function is generally represented as f(x) = ax^2 + bx + c. The given options are all factored forms of quadratic expressions. The correct form should represent a concave-downward parabola since the profit typically decreases as production increases.
Comparing the given options:
f(x) = –4(x – 50)(x – 250): This expression has a negative leading coefficient, indicating a concave-downward parabola.
f(x) = (x – 50)(x – 250): This expression also has a positive leading coefficient, which would create a concave-upward parabola. It does not match the expected behavior for profit in this context.
f(x) = 28(x + 50)(x + 250): This expression has a positive leading coefficient, indicating a concave-upward parabola. It does not align with the expected downward trend of profit.
f(x) = (x + 50)(x + 250): This expression has a positive leading coefficient, suggesting a concave-upward parabola. Similar to option 3, it does not represent the expected profit behavior.
Therefore, the correct quadratic function to model the monthly profit for x trinkets produced is f(x) = –4(x – 50)(x – 250).
The question probable may be:
All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.
Which function can be used to model the monthly profit for x trinkets produced?
f(x) = –4(x – 50)(x – 250)
f(x) = (x – 50)(x – 250)
f(x) = 28(x + 50)(x + 250)
f(x) = (x + 50)(x + 250)
a 12 ft ladder leans against the side of a house. The bottom of the ladder is 6 ft from the side of the house. how high is the top of the ladder from the ground?
Answer:
Approximately 10.39 ft.
Step-by-step explanation:
First, draw a short diagram to understand the sides of the right triangle.
The 12 foot ladder leaning against the building would be the hypotenuse and because the bottom of the ladder is 6 feet from the house, that would be the bottom leg. We are trying to figure out the leg to the left (the top of the ladder from the ground.
To solve this, we must use the converse of the Pythagorean Theorem. To do this, we can set up the following equation.
12^2 - 6^2
144 - 36 = 108
Then we must find the square root of 108, which is approximately 10.39 feet.
Dylan and Dusty plan to take weekly surfing lessons together. If the 2-hour lessons are $20 per person and they plan to spend $100 each on new surfboards, what is the maximum number of lessons the two can take if the total amount spent for lessons and surfboards is at most $480?
Answer:
they can both take 7 lessons each
Answer:
Each one can take 7 lessons.
Step-by-step explanation:
Dylan and Dusty plan to take weekly surfing lessons together.
They want to spend $100 each on new surfboards = $100 × 2
= $200
They want to spent total amount for lessons and surfboards is at most $480.
After spending on two new surfboards the money left with
= 480 - 200
= $280
The charges for 2-hours classes for surfing lessons = $20 per person
The charges for 1 hour classes for them = $20.00
With $280 they will be able to take maximum number of lessons
= [tex]\frac{280}{20}[/tex]
= 14 lessons
Each one can take 14/2 = 7 lessons.
Solve the equation.
—10x + 1 + 7х = 37
Answer:
X=- 12
Step-by-step explanation:
Answer:
x = -12
Step-by-step explanation:
—10x + 1 + 7х = 37
Combine like terms
-3x +1 = 37
Subtract 1 from each side
-3x+1-1 = 37-1
-3x = 36
Divide each side by -3
-3x/-3 = 36/-3
x = -12
Please help right now
Solve log x = 5.
Answer:
100000
Step-by-step explanation:
Since we have the natural base of the log, the base is 10.
Now think of it this way, since we are solving for the value that is being "logged" we can say 10 to the power of 5 equals what?
And since 10^5 is 100000, x is 100000.
The value of x is 100000.
A logarithm helps us know by what power a number must be raised to get the desired number.
A natural log is a log with base 10.
For example,
We want to know by what power must 10 be raised so we get 1000 as an output,
therefore, we can write it as,
[tex]\bold{log_{10} 1000 = 3}[/tex]
[tex]\bold{10^3 = 1000}[/tex]
where, 10 is the base meaning number to which power is to be raised,
1000 is the desired number,
And 3 is the answer.
Now, looking at our question,
[tex]\bold{log\ x= 5}[/tex]
can be written as
[tex]\bold{log_{10} x= 5}[/tex]
[tex]\bold{10^5 = x}[/tex]
[tex]\bold{10^5 = 100000}[/tex]
Therefore, 10 is been raised to the power of 5 giving the desired result which is 100,000.
Hence, the value of x is 100000.
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Which of the following is a 3rd degree polynomial with roots i and 2?
Answer:
D
Step-by-step explanation:
Given the roots of a polynomial, say x = a, x = b, x = c, then
(x - a), (x - b) and (x - c) are the factors and the polynomial is the product of the factors.
Note complex roots occur in conjugate pairs, thus
x = i is a root ⇒ x = - i is also a root
given roots x = 2, x = i, x = - i are roots, then
(x - 2), (x - i) and (x + i) are the factors and
f(x) = (x - 2)(x - i)(x + i)
= (x - 2)(x² - i²)
= (x - 2)(x² + 1)
= x³ + x - 2x² - 2
= x³ - 2x² + x - 2 → D
The 3rd degree polynomial with roots i and 2 is P(x) = x^3 - 2x^2 + x - 2, which is found by multiplying the factors (x - i), (x + i), and (x - 2).
Explanation:A 3rd degree polynomial with roots i and 2 must also have the complex conjugate of i, which is -i, as a root because the coefficients of the polynomial are real numbers. Thus, the polynomial will have three roots: i, -i, and 2. To find the polynomial, we can use the fact that a polynomial equation is the product of its factors. Therefore, we start by writing down the factors that correspond to each root:
(x - i)(x + i)(x - 2)Multiplying these factors together will give us the desired 3rd degree polynomial:
Multiply the factors (x - i) and (x + i), which are conjugates, to get x^2 + 1 because (i)(-i) = -i^2 = 1.Now, multiply the quadratic polynomial x^2 + 1 by (x - 2) to get the 3rd degree polynomial.The full expansion gives us the polynomial P(x) = x^3 - 2x^2 + x - 2.
Learn more about 3rd Degree Polynomial here:https://brainly.com/question/30765847
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Point M lies between points L and N on .
If LN = 12x + 16, what is the length of in units?
16 units
40 units
48 units
64 units
Answer:
LN=64 units
Step-by-step explanation:
step 1
Find the value of x
we know that
LN=LM+MN -----> equation A
see the attached figure to better understand the problem
we have
LN=12x+16
LM=10x+8
MN=5x-4
substitute the values in the equation A
12x+16=(10x+8)+(5x-4)
Solve for x
12x+16=15x+4
15x-12x=16-4
3x=12
x=4
step 2
Find the value of LN
LN=12x+16
LN=12(4)+16=64 units
What is the volume of this solid?
Paula’s paycheck varies directly with the number of hours she works. If she earns $52.50 for 6h of work, how much will she earn for 11 h of work? Round your answer to the nearest cent
Answer:
$96.25
Step-by-step explanation:
Find the unit rate of pay:
$52.50
------------- = $8.75/hr
6 hours
Now multiply this rate by 11 hours:
($8.75/hr)(11 hrs) = $96.25
Answer: $ 96. 25
Step-by-step explanation:
It is said that two variables x and z vary directly if they meet the following relationship:
[tex]z = kx[/tex]
Where k is the constant of variation.
In this case z represents the gains and x represents the hours of work.
Now we must find the value of the constant k.
We know that for 6 hours of work the earnings are $ 52.50
So
[tex]x = 6[/tex]
[tex]z = \$\ 52.50[/tex]
[tex]52.50 = 6k[/tex]
[tex]k= \frac{52.50}{6}[/tex]
[tex]k= 8.75[/tex]
Then the equation is:
[tex]z = 8.75x[/tex]
Finally when x = 11, then:
[tex]z = 8.75*11\\\\z =\$\ 96.25[/tex]
Given f(x)=2x+3 find x=9 show your work
Answer:
f(9) =21
Step-by-step explanation:
I will assume you want to find f(9) when x=9
Let x=9
f(9) = 2(9) +3
= 18+3
=21
f(9) =21