Answer:
21
Step-by-step explanation:
Rule of logs:
[tex] b^{\log_b x} = x [/tex]
Your problem:
[tex] 10^{\log_{10} 21} = 21 [/tex]
The value of the given logarithm expression will be 21.
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
The expression is given below.
[tex]\rightarrow 10^{\log 21}[/tex]
We know that
[tex]\rm a ^{\log_ab} = b[/tex]
Then the expression will be
⇒ 21
More about the logarithm link is given below.
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The first 5 terms of a number pattern are shown below.
4, 9, 14, 19, 24
Which expression is equivalent to the value of the nth term in the pattern?
[tex]\bf 4~~,~~\stackrel{4+5}{9}~~,~~\stackrel{9+5}{14}~~,~~\stackrel{14+5}{19}~~,~~\stackrel{19+5}{24}\qquad \impliedby \stackrel{\textit{common difference}}{d=5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=4\\ d=5 \end{cases} \\\\\\ a_n=4+(n-1)5\implies a_n=4+5n-5\implies a_n=5n-1[/tex]
Find the solution of the system of equations shown on the graph
Answer:
(7, 9)
Step-by-step explanation:
The lines cross at point (7, 9). This is the solution.
__
If we assume the variables being graphed are x and y, then the solution is ...
x = 7y = 9HELP ASAP!! Identify the reflection of the figure with vertices P(−11,−13), Q(−17,19), and R(23,−27) across the x-axis.
P (−11, 13), Q (−17, −19), R (23, 27)
P (11, 13), Q (17, −19), R (−23, 27)
P (11, −13), Q (17, 19), R (−23, −27)
P (−13, −11), Q (19, −17), R (−27, 23)
Answer:
P' (−11, 13), Q' (−17, −19), R' (23, 27)
Step-by-step explanation:
When we reflect a point across the x-axis, we negate the y-coordinates to obtain the image points.
The mapping for the reflection across the x-axis is
[tex](x,y)\to (x,-y)[/tex]
The vertices of the given figure are;
P(−11,−13), Q(−17,19), and R(23,−27)
We apply the rule to obtain:
[tex]P(-11,-13)\to P'(-11,13)[/tex]
[tex]Q(-17,19)\to Q'(-17,-19)[/tex]
[tex]R(23,-27)\to R'(23,27)[/tex]
The correct option is P' (−11, 13), Q' (−17, −19), R' (23, 27)
Graph the function y=|x+1-4
Answer: see graph
Step-by-step explanation:
I am assuming the question should read: y = |x + 1| - 4
You can graph this using transformations or by creating a table.
Transformations:
The parent function is y = |x|
The transformation is moving the graph 1 unit to the left and 4 units down - the vertex is moved from the origin to (-1, -4)
Table:
Choose x-values and solve for y
[tex]\begin{array}{c|c||c}\underline{\quad x\quad }&\underline{\quad y=|x+1|-4\quad }&\underline{Coordinate}\\-1&y=|-1+1|-4&(-1,-4)\\0&y=|0+1|-4&(0,-3)\\1&y=|1+1|-4&(1,-2)\end{array}[/tex]
In 1980 the population of detroit michigan was approximately 1,200,000.If the population decreased at an annual rate of 14.6% over the next vacate , what was the population of detriot in 1990, 10 years later
Answer:
247,605
Step-by-step explanation:
Each year, the population is multiplied by a factor of (1 -14.6%) = 0.854. Multiplying by that factor for 10 years gives the value ...
1,200,000×0.854^10 ≈ 247,605
The population in 1990 is predicted to be 247,605.
Among 100 students who enrolled in both Math 101 and English 101, 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both Math 101 and English 101. What percentage of the students scored an A in neither Math 101 nor English 101?
Answer:
The percentage of the students scored an A in neither Math 101 nor English 101 is 55%
Step-by-step explanation:
* Lets study the meaning of or , and on probability
- The use of the word or means that you are calculating the probability
that either event A or event B happened
- Both events do not have to happen
- The use the word and, means that both event A and B have to happen
* The addition rules are:
# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
- The union is written as A∪B or “A or B”.
- The Both is written as A∩B or “A and B”
* Lets solve the question
- There are 100 student enrolled in both math and English Exams
- 30% of them scored an A in Math
- 35% of them scored an A in English
- 20% of them scored an A in both
- To find the neither lets find either and then subtracted from the total
∵ P(A or B) = P(A) + P(B) - P(A and B)
∵ P(Math) = 30%
∵ P(English) = 35%
∵ P(Math ∩ English) = 20%
∴ P(Math ∪ English) = 30% + 35% - 20% = 45%
- To find the neither subtract either from the total
∵ The total of students who enrolled is 100
∴ The percentage of the students who enrolled is 100%
∴ The percentage of the students scored an A in neither Math nor
English = 100% - 45% = 55%
* The percentage of the students scored an A in neither Math 101 nor
English 101 is 55%
To find the percentage of students who scored an A in neither Math 101 nor English 101, subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either subject.
Explanation:To find the percentage of students who scored an A in neither Math 101 nor English 101, we need to subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either Math 101 or English 101.
Given that 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both subjects, we can calculate the percentage of students who scored an A in neither subject as follows:
Percentage of students who scored an A in neither subject = 100% - (Percentage of students who scored an A in Math 101 + Percentage of students who scored an A in English 101 - Percentage of students who scored an A in both subjects)
= 100% - (30% + 35% - 20%)
= 100% - 45%
= 55%
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Summations with Algebraic Expressions
Image Shown
[tex]\displaystyle\\\sum_{n=3}^5(-2x-4n)=-2x-4\cdot3+(-2x)-4\cdot4+(-2x)-4\cdot5\\\sum_{n=3}^5(-2x-4n)=-6x-12-16-20\\\sum_{n=3}^5(-2x-4n)=-6x-48[/tex]
Amy was thinking of a number then divides by 2 then adds 11 and the answer was 12 what was the original number?
Answer:
2
Step-by-step explanation:
Let x be the original number.
x/2 +11=12
Now solve for x
x=2
Answer:
The number was 2
Step-by-step explanation:
To solve this you would just have to work backwards using the inverses of operations previously used
First you would subtract 11 from 12:
12-11=1
Then you would multiply by 2:
1 x 2=2
Parallelogram ABCD is a rectangle
A (4,3)
B(-2,1)
D(5,0)
6 8
1
C(-1,-2)
What are the slopes of the sides that make this quadrilateral a rectangle?
-2 and 12
-12 and 2
-13 and 3
-3 and 13
Answer:
I think it's -13 and 3.i hope this answer helps
If angle EAC is congruent to angle ECA, name the congruent segments.
A. AE, EC
B. EC, CA
C. AE, AC
D. AE, EC, AC
Answer:
A. AE, EC
Step-by-step explanation:
Because you know that the bottom two angles are congruent, you can conclude that this is an isosceles triangle. This means that the sides are congruent.
Use the x-intercept method to find all real solutions of the equation. -9x^3-7x^2-96x+36=3x^3+x^2-3x+8
Answer:
x ≈ 0.290640965127
Step-by-step explanation:
By subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.
___
The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.
A girl scout sells 3 boxes of cookies during week 1. She has a goal to sell twice as many cookies each week as she did the week before. If she succeeds in doing this during weeks 2, 3, 4, and 5, how many boxes will she sell all together? a0
Answer
93 boxes
Step-by-step explanation:
Week one= 3 boxes
Week two= 2×3=6 boxes
Week three= 2×6=12 boxes
Week four= 2×12=24 boxes
Week five= 2×24=48 boxes
Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5
[tex]T=3+6+12+24+48=93[/tex]
Answer:
Step-by-step explanation:
Week one= 3 boxes
Week two= 2×3=6 boxes
Week three= 2×6=12 boxes
Week four= 2×12=24 boxes
Week five= 2×24=48 boxes
Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5
T=3+6+12+24+48=93
Need help with a math question PLEASE HELP NEED ANSWER SOON
Answer:
720
Step-by-step explanation:
So there are 6 slots and 6 commercials so.
There are 6 outcomes which means.
we can use this formula
(p-1)(p-2)(p-3)..etc.
So
We have (6-1)(6-2)(6-3)(6-4)(6-5)(6-6)
6,5,4,3,2,1,0 and zero is 0!=1
So now we multiply
6*5*4*3*2*1*1=720
Hopefully this helps!
HELP ASAP!! A truck starts from a warehouse, which is 8 miles south and 3 miles west of the town center. The truck travels 3 miles north, makes a right turn, and then travels for 4 miles. What is the truck’s final position? What single translation vector moves the truck from its starting position to its final position?
The answer, I think, is (1, -5);(4,3).
Answer:
1, −5); (4, 3)
Step-by-step explanation:
The starting point coordinates and the changes in x or y of each movement are given.
Draw the given information in the coordinate plane to better visualize it. The truck starting coordinates are (−3, −8).
To find the vector that gives the translation (−3, −8)→(1, −5), subtract the x and y coordinates of the starting point from the x and y coordinates of the end point. The vector is: ⟨1 − (−3), −5 − (−8)⟩ = ⟨4,3⟩.
Therefore, the truck’s final position is (1, −5) and ⟨4, 3⟩ is the single translation vector that moves the truck from its starting position to its final position.
Which points lie on the graph of f(x) = - Square root -X ? (–9, 3) (–4, –2) (–1, 1) (0, 0) (1, 1) (2, –4) (9, 3)
Answer:
(0, 0) and (-4, -2)
Step-by-step explanation:
See the graph. Only two of the listed points are on the curve.
Rob is a geologist. He is surveying a conical crater that was created by a meteor impact. From one end to another, the crater forms a V shape. The deepest part of the crater is 400 feet deep. The depth of the crater varies at a rate of 0.25 foot with the horizontal distance from the west end of the crater. The equation that models the depth of the crater, d, in feet, with respect to the horizontal distance in feet from the west end of the crater, h, is d = . The depth of the crater is 250 feet at horizontal distances of and feet from the west end.
Answer:
equation: d(h) = 0.25|h -1600| -400depth is 250 ft at 1000 ft and 2200 ft from the west edgeStep-by-step explanation:
The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.
d(h) = 0.25×|h -1600| -400
We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.
__
At a depth of 250 ft, the distance from the west edge can be found from ...
-250 = 0.25|h -1600| -400
150 = 0.25|h -1600| . . . . . . . . add 400
600 = |h -1600| . . . . . . . . . . . multiply by 4
This resolves to two equations:
-600 = h -1600 ⇒ h = 1000600 = h -1600 ⇒ h = 2200The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.
_____
Comment on the equation
We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:
d = 400 -0.25×|h -1600|
Answer:
0.25|x-1,600|-400 / 1,000 / 2,200
Step-by-step explanation:
A store is having a 20% off sale. If the reduced price of an item is $114.40 what was the original price?
Answer:
143
Step-by-step explanation:
Let x = original price
20% of the original price is .2x
We get 20 % off so we subtract it from the original price
x- .2 x
That is equal to 114.40
x-.2x = 114.40
Simplify
.8x = 114.40
Divide each side by .8
.8x/.8 = 114.40/.8
x = 143
The original price is 143
Answer:
143
Step-by-step explanation:
i got it right
SAFF (Students against Fatty Food) is a group of students who are protesting the food in high school cafeterias. At a recent rally, the students covered the first 40 yards by 40 yards of the football field. There were 24 students in each 8 feet by 8 feet square. What steps would you take to determine how many students were present at the rally?
Convert yards to feet, then divide by feet square and multiply by the number of students.
Multiply the feet by the number of students.
Multiply yards by feet and divide by the number of students
Multiply the number of students by the yards of the football field.
Answer:
The total area covered by students is 40 yd x 40 yd = 1600 yd^2
24 students covered 8 ft x 8ft or (8 ft x 1 yd/3 ft)^2 = [(8/3) yard]^2 = (64/9) yd^2
Therefore, you need the amount of students per yard or 24 students/(64/9) yd^2
and multiply (students/yd^2) x (area covered by students) = number of total students present
Therefore: number of students present = 24 students/(64/9) yd^2 x 1600 yd^2 = 5400 students
Step-by-step explanation:
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Identify the reflection of the figure with vertices E(8,4), F(-16,-8), and G(24,-16) across the y-axis.
E (2, 1), F (−4, −2), G (6, −4)
E (−8, 4), F (16, −8), G (−24, −16)
E (−8, −4), F (16, 8), G (−24, 16)
E (4, 8), F (−8, 16), G (16, −24)
Answer:
[tex]\boxed{\text{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]
Step-by-step explanation:
When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,
E (8,4) ⟶ E' (-8,4)
F (-16,-8) ⟶ F' (16,-8)
G (24,-16) ⟶ G' (-24,-16)
[tex]\text{The reflected figure has coordinates } \boxed{\textbf{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]
The figure EFG and its reflection E'F'G' are shown in the diagram below.
The graph of y=-0.2x² is ? the graph of y=x².
There are options to answer this question.
Choose one of the best answers.
A. Narrower than and opens in the same direction as
B. Wider than and opens in the same direction as.
C. Narrower than and opens in the opposite direction of
D. Wider than and opens in the opposite direction of
Could you explain your answer?
If your answer is wrong and it's going mark your answer report and it's called improper answer.
Please don't plagiarism your answer from other websites, if you copy and paste your answers from other sites and it's going to be mark your answer report.
No need to spam answers, if you spam your answers and it's going be mark your answer report.
Thank you!
-Charlie
Answer:
D
Step-by-step explanation:
y = -0.2 x²
This has a negative sign, as opposed to y = x², so it will point in the opposite direction.
The leading coefficient (0.2) is less than 1. This means the parabola is shrunk vertically, or stretched horizontally. So the parabola is wider than y = x².
Final answer:
The graph of y = -0.2x² is wider than and opens in the opposite direction of the graph of y = x² due to the negative and smaller in absolute value coefficient.
Explanation:
The comparison of the graphs of y = -0.2x² and y = x² is affected by the coefficients of the x² term. In the case of y = x², the coefficient is positive (1), implying the graph is a parabola that opens upwards. On the other hand, the negative coefficient (-0.2) in y = -0.2x² indicates the graph is also a parabola but opens downwards.
Furthermore, the absolute value of the coefficient affects the width of the parabola. A coefficient smaller in absolute value than 1, such as -0.2, makes the parabola wider than the parabola of y = x², which is the standard case. Therefore, the graph of y = -0.2x² is wider than and opens in the opposite direction of the graph of y = x².
In triangle ABC, the length of side AB is 12 cm, the length of side BC is 5 cm, and the length of side CA is 9 cm. Find the measure of angle A using the law of cosines.
Answer:
22.20 is the correct answer! Hope I helped.
The measure of angle A is 22.19°.
What is a Triangle?A triangle is a polygon with three sides, vertices, and angles.
The length of the sides of a triangle ABC is
AB = 12 cm
BC = 5 cm
CA = 9 cm
The angle of the law of cosines has to be used to determine the value of angle A
b² = a²+c² - 2 ac cos A
Substituting the values
5² = 12² + 9² -2 * 12 *9 cos A
cos A = 0.9259
A = 22.19°
Therefore, the measure of angle A is 22.19°.
To know more about Triangle
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A rock is tossed at an initial velocity of 60 m/s at an angle of 10° with the ground. After 0.9 second, how far has the rock traveled horizontally and vertically?
Step-by-step explanation:
In the x direction:
x = x₀ + v₀ₓ t + ½ at²
x = (0 m) + (60 m/s cos 10°) (0.9 s) + ½ (0 m/s²) (0.9 s)²
x ≈ 53 m
In the y direction:
y = y₀ + v₀ᵧ t + ½ gt²
y = (0 m) + (60 m/s sin 10°) (0.9 s) + ½ (-9.8 m/s²) (0.9 s)²
y ≈ 5.4 m
Answer:
53.2 m horizontally and 5.4 m vertically
Step-by-step explanation:
Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.
A. y2 = 2x
B .y = one divided by twox2
C .y2 = 8x
D. y = one divided by eightx2
Answer:
D. y = one divided by eightx2
Step-by-step explanation:
The standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is y = one divided by eightx2.
Avery and Caden have saved $27,000 towards a down payment on a house. They want to keep some of the money in a bank account that pays 2.4% annual interest and the rest in a stock fund that pays 7.2% annual interest. How much should they put into each account so that they earn 6% interest per year
Answer:
They should put $6750 in the bank account and $20,250 in the stock fund.
Step-by-step explanation:
Consider the provided information that Avery and Caden have saved $27000.
Let x is the money deposit in the bank and y is the money deposit in stock fund.
Therefore,
x + y = 27000
x = 27000 - y
The bank account will pay 2.4% annual interest.
[tex]\frac{2.4}{100}x+x=1.024x[/tex]
Stock fund pays 7.2% annual interest.
[tex]\frac{7.2}{100}y+y=1.072y[/tex]
Therefore,
1.024 x + 1.072 y = 1.06 × 27000
Substitute the x = 27000 - y in above equation.
1.024 (27000 − y) + 1.072 y = 1.06 × 27000
27648 − 1.024 y + 1.072 y = 28620
0.048 y = 28620-27648
0.048 y = 972
y = 20250
Now, substitute the y = 20250 in x = 27000 - y.
x = 27000 − 20250
x = 6750
Hence, they should put $6750 in the bank account and $20,250 in the stock fund.
NEED HELP WITH A MATH QUESTION
Answer:
Step-by-step explanation:
The total number of orders for large is 27
the probability of ordering something hot is 22/27=0.8148
to convert to percentage, multiply by 100: 0.8148*100=81.48%. rounded = 81%
There are 27 people total who are buying large drinks. 22 of those large drinks are hot drinks.
To figure out what percentage 22 is of 27, divide 22 by 27.
22/27= .814... or 81% or 80%.
81% of large drinks bought are hot.
Hope this helps!
Peaches are being sold for $2 per pound. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches , which best describes the values of x and y
Answer:
X would be the unit of measure (weight) and Y would be the ammount. In a equation that would be, 2x = y.
Answer:
The values of both x and y will be greater than or equal to zero.
Step-by-step explanation:
We are given that
Cost of 1 pound of peaches=$2
If x represents the number of pounds of peaches bought.
Total cost of the peaches represented by y.
We have to find the the values of x and y which describes the best.
To find the total cost of peaches we will multiply the cost of one pound with total number of pounds of peaches.
If cost of 1 pound of peaches=$2
Cost of x pounds of peaches=[tex]2\times x=2x[/tex]
Therefore, the total cost of x pounds of peaches, [tex]y=2x[/tex]
Weight of a thing is always greater than 0 or equal to .
The total cost of a thing is always greater than or equal to zero.
Therefore,the values of both x and y will be greater than or equal to zero.
What would a monthly payment be on a purchase of a $11,000 car at 5.9% for 4 years?
A) $257.83
B) $252.50
C) -$257.83
D) $250.00
Answer:
A) $257.83
Step-by-step explanation:
A spreadsheet or financial calculator will tell you the monthly payment on $11,000 at 5.9% annual rate for 4 years is ...
$257.83
Julie has $80 in her savings account and plans to save $x each month for 8 months. The expression $8x + $80 represents the total amount in the account after 8 months. Factor this expression.
Answer:
8(x+10)
Step-by-step explanation:
8x + $80
We can factor out an 8 from each term
8(x+10)
Suppose you increase your walking speed from 6 m/s to 12 m/s in a period of 1 s. What is your acceleration ?
a = acceleration = dv/dt ~ delta v/ delta t.
a = ( 12 m/s - 6 m/s ) / ( 1 s ) = 6 m/s^2
Done.
Please help, question above
Answer:
4^ (r-s)
Step-by-step explanation:
When the bases are the same, and we are dividing, we subtract the exponents
x^a ÷ x^b = x^ (a-b)
4^r ÷ 4^s = 4^ (r-s)