[tex]a^{\log_a b}=b\\\\12^{\log_{12}24}=24[/tex]
Answer:
The correct answer option is A) 24.
Step-by-step explanation:
We are given the following log expression and we are to simplify it:
[tex] 1 2 ^ { log _ { 1 2 } } ^ { 2 4 } [/tex]
Here, we are going to apply the rule for solving a log problem:
[tex]a^{log_a^{(b)}[/tex] [tex] = b[/tex]
So if [tex] 1 2 ^ { log _ { 1 2 } } ^ { 2 4 } [/tex], then it would be equal to 24.
Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.
Answer:
1.25.
Step-by-step explanation:
The common ratio r is 1/5 and the first term a1 = (1/5)^(1-1) = 1.
Sum to infinity = a1 / (1 - r)
= 1 / (1 - 1/5)
= 1 / 4/5
= 5/4
= 1.25 (answer)
Answer:
Step-by-step explanation:
1.25
On the first day of camp, 5 10 of the skaters were beginners. Of the beginners, 2 6 were girls. What fraction of the skaters were girls and beginners? Complete the explanation. of the skaters were girls and beginners
Answer:
1/6
Step-by-step explanation:
5/10(3/3)=15/30
2/6(5/5)=10/30
15/30 - 10/30= 5/30 = 1/6
Answer: 1/6
Step-by-step explanation:
What are the next three numbers in this pattern
Hello There!
Divide by 3 each time
so
#1 is 9, because 27/3 = 9
#2 is 3, because 9/3 = 3
#3 is 1, because 3/3 = 1
So your answer is 9, 3, 1
Enter the values for a and b that complete
the sum:
3/x + 5/x^{2} =ax+b/x^{2}
ANSWER
a=3, b=5
EXPLANATION
The given equation is
[tex] \frac{3}{x} + \frac{5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]
We simplify the left hand side.
We collect LCD to obtain:
[tex] \frac{3x + 5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]
Both sides of the equation are now the same.
By comparing the coefficients of x, we have
[tex]a = 3[/tex]
By comparing the constant terms
[tex]b = 5[/tex]
Answer:
For the first part
A=3
B=5
For the second part
M=3
N=14
P=2
Step-by-step explanation:
Right on edge 2020
Which is TRUE about ALL expressions?
contain variables
contain only numbers
are the same as equations
do not include an equal sign
Expressions do not have an equal sign (although they can have operators such as plus or minus).
[tex]2x+1[/tex] is an expression.
[tex]2x+1=1[/tex] is an equation since it has an equal sign.
What intervals would you use to determine where
the function is positive and negative?
Answer:
B.
Step-by-step explanation:
The function is positive when it is above the x-axis
The following x values are where the function has positive y coordinates:
(-2,0)
(4,inf)
The function is negative when it is below the x-axis
The following x values are where the function has negative y coordinates:
(-inf,-2)
(0,4)
So you should see all of these intervals listed in choice B
Answer:
B
Step-by-step explanation:
A sports team came to town. The stadium filled all 10,000 seats at two-level pricing. Level 1 tickets are $50 each, and level 2 tickets are $150 each. The stadium made $75,000 in ticket sales. The system of equations that models this scenario is:
x + y = 10,000
50x + 150y = 75,000
What do the x and y represent in the system?
A.x represents the number of level 2 tickets; y represents the number of level 1 tickets
B.x represents the cost of level 1 tickets; y represents the cost of level 2 tickets
C.x represents the cost of level 2 tickets; y represents the cost of level 1 tickets
D.x represents the number of level 1 tickets; y represents the number of level 2 tickets
Answer: D
Step-by-step explanation:
Answer: The correct option is
(D) x represents the number of level 1 tickets; y represents the number of level 2 tickets
Step-by-step explanation: Given that a sports team came to town. The stadium filled all 10,000 seats at two-level pricing. Level 1 tickets are $50 each, and level 2 tickets are $150 each. The stadium made $75,000 in ticket sales.
The system of equations that models this scenario is:
x + y = 10,000
50x + 150y = 75,000
We are to find the terms that x and y represents.
Since the total number of seats is 10000 and it is given that x + y = 10000, so x and y represents the number of tickets.
Also, since the price of one level 1 tickets is $50 and that of one level 2 ticket is $150 and 50x + 150y = 75000, so
x represents the number of level 1 tickets; y represents the number of level 2 tickets.
Thus, (D) is the correct option.
Which ordered pair makes both inequalities true? y < –x + 1 y > x Which ordered pair makes both inequalities true? y < –x + 1 y > x (–3, 5) (–2, 2) (–1, –3) (0, –1) (–3, 5) (–2, 2) (–1, –3) (0, –1) Mark this and return
Answer:
(-2, 2)
Step-by-step explanation:
You can graph the equations and points and see which points fall into the doubly-shaded area. The only one that does is (-2, 2).
___
You can also evaluate the inequalities at the given points to see which might work. The inequality y > x is the simplest to evaluate, and it immediately eliminates the last two choices:
-3 > -1 . . . not true
-1 > 0 . . . not true
So, we can check the first two choices in the first inequality:
-(-3) +1 > 5 . . . not true
-(-2) +1 > 2 . . . TRUE
The ordered pair (-2, 2) makes both inequalities true.
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Inequalities are,
y < x + 1 .....................(1)
y > x .....................(2)
To find: Ordered pair which makes he inequalities true.
Pair 1:
x = -3 , y = 5
Inequality (1),
LHS = 5
RHS = -(-3) + 1 = 4
⇒ LHS > RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 2:
x = -2 , y = 2
Inequality (1),
LHS = 2
RHS = -(-2) + 1 = 3
⇒ LHS < RHS
Inequality (2),
LHS = 2
RHS = -2
⇒ LHS > RHS
Thus, this pair satisfies the pair of inequalities.
Pair 3:
x = -1 , y = -3
Inequality (1),
LHS = -3
RHS = -(-1) + 1 = 0
⇒ LHS < RHS
Inequality (2),
LHS = -3
RHS = -1
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Pair 4:
x = 0 , y = -1
Inequality (1),
LHS = -1
RHS = -(0) + 1 = 1
⇒ LHS < RHS
Inequality (2),
LHS = -1
RHS = 0
⇒ LHS < RHS
Thus, this pair does not satisfy the pair of inequalities.
Therefore, 2nd Option is correct.
The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r , a, and ar to represent the first three terms, respectively.] The three numbers are _____, _____, and _____.
Answer:
-1/10, -1/5 , -2/5 or -2/5, -1/5 , -1/10
Step-by-step explanation:
let a/r, a, ar be the first 3 terms of the geometric series
their product would be equal to a^3
a^3=-1/125
a=-1/5
Substitute a=-1/5 into the first 3 terms
-1/5r + -1/5+-r/5=-7/10
Multiply the terms such that they have a common denominator:
-1/5r +-r/5r + -r^2/5r = -3.5r/5r
Multiply both sides by 5r
-r^2-r-1=-3.5r
Add 3.5r to both sides and multiply the equation by 2
-2r^2 + 5r -2=0
Factorize the equation
(2r-1)(r-2)=0
r=0.5 or r-2
For the first three terms where r=0.5
-2/5, -1/5 , -1/10
For the first three terms where r=2
-1/10, -1/5 , -2/5
Susan Williams purchased $80,000 of whole life. What will the cash value of her policy be at the following anniversary dates?
Anniversary date Cash Value
5 year _________
20 year _________
Answer:
5 year = $2,400
20 year = $18,560
Step-by-step explanation:
Firstly,
You have to identify the cash value per unit. so It 'll be 5 years = 30 dollars per unit.
Secondly,
Now, take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. so It'll be 80 times 30 is $2,400
Answer: $2,400
Now,
Just like the previous one identify the cash value per unit. so It'll be 20 years= 232 dollars per unit.
Next,
take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. 80 times 232 is $18,560
Answer: $18,560
What is the value of log625^5
Answer:
Value of log625^5 is 13.95
Step-by-step explanation:
We need to find the value of log625^5
Using log rule log a^n = nloga
log625^5
= 5log625
=5(2.79)
=13.95
So, value of log625^5 is 13.95
Answer with explanation:
We have to find the value of :
[tex]\rightarrow\log 625^5\\\\\rightarrow 5 \log625\\\\\rightarrow 5 \log 5^4\\\\\rightarrow 4 \times 5 \log 5\\\\ \rightarrow 20 \log 5\\\\\rightarrow 20 \times 0.69897\\\\ \rightarrow 13.9794\\\\=13.98\\\\ \text{Used following properties of log}\\\\ \log a^b=b \log a[/tex]
if ABCD is an isosceles trapezoid, what is the value of x
Answer:
Since we know that ABCD is an isosceles trapezoid, we can also asume that its diagonals have the same length, which means:
AC = BD
=> 7x - 21 = 5x + 13
=> 7x - 5x = 21 + 13
=> 2x = 34
=> x = 34/2 = 17
So the answer is C.
Since we know that ABCD is an isosceles trapezoid, the value of Option C. x= 17
we can also assume that its diagonals have the same length, which means:
AC = BD
=> 7x - 21 = 5x + 13
=> 7x - 5x = 21 + 13
=> 2x = 34
=> x = 34/2 = 17
So the answer is C.
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals
Properties of Isosceles TrapezoidIt has an axis of symmetry. It has no rotational symmetry and one line of symmetry joining the midpoint of the parallel sides.One pair of sides is parallel and they are the base sides. (AB II DC in the given image)The remaining sides other than the base are non-parallel and are equal in length. (c = d in the given image)The diagonals are the same in length. (AC = BD)The base angles are the same. (∠D = ∠C, ∠A=∠B)The sum of opposite angles is 180° or supplementary. (∠A + ∠C = 180° and ∠B + ∠D = 180°)The line segment joining the midpoints of the parallel sides is perpendicular to the bases. (PQ ⊥ DC)Learn more about Isosceles Trapezoid, refer
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(URGENT) Can someone help me find x, I’ve gotten it wrong twice.
Answer:
x = 24.10
Step-by-step explanation:
The given sides of the triangle are the hypotenuse (x) and a side of length 20 that is adjacent to the 34° angle and opposite the 56° angle.
The mnemonic SOH CAH TOA reminds you of relationships between the hypotenuse and adjacent or opposite sides:
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If we want to use the "adjacent" side, we would choose ...
cos(34°) = 20/x
x = 20/cos(34°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
__
If we want to use the "opposite" side, we would choose ...
sin(56°) = 20/x
x = 20/sin(56°) ≈ 20/0.83 ≈ 24.10 . . . . . rounding according to instructions
_____
Comment on rounding
If you round correctly (only at the last step), the proper answer is 24.12.
Find the area 6m, 3m
Check the picture below.
What is the probability of drawing three black cards, one at a time with replacement, from a standard deck of 52 cards?
A.'3/52
Its not b
C.1/8
d.75/676
Answer: I think it is A.
Step-by-step explanation:
I can't tell the difference!! :(
Answer:
the first one is 350 inches (350 in) and the second on is 350 square inches (350 in2)
Step-by-step explanation:
The difference between two numbers is 10. The greater number is b. Write an expression that represents the lesser number.
Answer:
B-10=N
Step-by-step explanation:
N is the lesser number. So if B is the greater number & there is a difference of 10 this would be your expression
If the given sequence is a geometric sequence, find the common ratio.
3/3, 3/12, 3/48, 3/192, 3/768
a. 4
b. 1/30
c. 30
d. 1/4
Answer:
d. 1/4
Step-by-step explanation:
The common ratio will be the ratio of any two adjacent terms:
(3/12)/(3/3) = (1/4)/1 = 1/4
Answer:
d
Step-by-step explanation:
If the sequence is geometric then a common ratio r will exist between consecutive terms.
[tex]\frac{3}{12}[/tex] ÷ 1 = [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{48}[/tex] ÷ [tex]\frac{3}{12}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{192}[/tex] ÷ [tex]\frac{3}{48}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{3}{768}[/tex] ÷ [tex]\frac{3}{192}[/tex] = [tex]\frac{1}{4}[/tex]
A common ratio of r = [tex]\frac{1}{4}[/tex]
Hence sequence is geometric
The length and width of a rectangle are consecutive even integers. The perimeter is 68 meters. Find the length
and width
The length is
meters long while the width is
meters
Answer:
The dimensions are 16 meters by 18 meters
Step-by-step explanation:
P = 2(l+w)
is the formula for the perimeter of a rectangle.
We know the length is 2 more than the width ( consecutive even integers)
l = w+2
P = 2 (w+2+w)
P = 2(2w+2)
68 = 2 (2w+2)
Divide each side by 2
34 = 2w+2
Subtract 2
34-2 = 2w+2-2
32 = 2w
Divide by 2
32/2 = 2w/2
16 =w
l = w+2
l =16+2
l = 18
The dimensions are 16 meters by 18 meters
the width of the rectangle is 16 meters and the length is 18 meters.
To find the length and width of a rectangle when given that the length and width are consecutive even integers and the perimeter is 68 meters, we first need to express the length and width in algebraic terms. Let's call the width 'w' and since the length is the next consecutive even integer, it can be expressed as 'w + 2'. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where 'l' is the length and 'w' is the width. In this case, since width is 'w' and length is 'w + 2', the perimeter formula becomes P = 2(w+2) + 2w.
Let's solve for 'w':
68 = 2(w + 2) + 2w
68 = 2w + 4 + 2w
68 = 4w + 4
64 = 4w
w = 16
Now that we have the width, we can easily find the length:
l = w + 2
l = 16 + 2
l = 18
Therefore, the width of the rectangle is 16 meters and the length is 18 meters.
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.
Answer: [tex]15.57\°[/tex]
In order to understand better this problem, we can use the figure attached, in which we have a right triangle (with a 90 degree angle), where [tex]c[/tex] is its hypotenuse, [tex]a[/tex] is the adjacent side to the angle of elevation [tex]\theta[/tex] from the boat to the top of the lighthouse and [tex]b[/tex] is the opposite side to [tex]\theta[/tex].
Knowing this, we will use the tangent trigonometric function to find [tex]\theta[/tex]:
[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}[/tex] (1)
[tex]tan\theta=\frac{34m}{122m}[/tex] (2)
[tex]tan\theta=0.278[/tex] (3)
[tex]\theta={tan}^{-1} (0.278)[/tex] (4)
Finally:
[tex]\theta=15.572\°[/tex]
Answer:
16
Step-by-step explanation:
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.
The factorization of x2 + 3x – 4 is modeled with algebra tiles. What are the factors of x2 + 3x – 4? A) (x + 4) and (x – 4) B) (x + 3) and (x – 4) C) ( x + 4) and (x – 1) D) (x + 3) and (x – 1)
Answer:
C: (x + 4)(x - 1)
Step-by-step explanation:
Please use " ^ " to indicate exponentiation. Thanks.
x2 + 3x – 4 → x^2 + 3x - 4 = (x + 4)(x - 1) This matches Answer C.
Ryan is riding his bike. He biked a distance of 12 miles at a rate of 4 miles per hour. Rearrange the distance formula, d = rt, to solve for Ryan's time in minutes.
480 minutes
180 minutes
8 minutes
3 minutes
Answer:
180 minutes
Step-by-step explanation:
Starting with the distance formula ...
d = rt
dividing by the coefficient of t will give an equation for t:
t = d/r
Ryan's rate of 4 miles per hour can be expressed in minutes as 4 miles per 60 minutes. The Ryan's time is ...
t = (12 mi)/(4 mi/60 min) = 12·60/4 min = 180 min
Ryan's time is 180 minutes.
Answer:
180 MINUTES
Step-by-step explanation:
I TOOKTHE TEST ON FLVS
Which of the following transformations appears to be a dilation? HELP ASAP!
Answer:
The answer is the 2nd one
Step-by-step explanation:
A dilation is a transformation in which the lines connecting every point P with its image P' all intersect at a point C.
C is called the center of dilation, and CP'/CP is the same for every point P.
The only picture where the objects are similar and the image has not been rotated or reflected is
It is also seen from the picture that all the faces of the first figure appears to be parallel to all the faces of the second figure. Thus, CP'/CP is the same for every point P.
Therefore, the transformation in the picture above appears to be a dilation.
The transformation in the picture above appears to be a dilation is option 2nd.
How does dilation works?Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.
Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.
Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).
C is called the center of dilation, and CP'/CP is the same for every point P.
It is also seen from the picture that all the faces of the first figure appear to be parallel to all the faces of the second figure.
Thus, CP'/CP is the same for every point P.
Therefore, the transformation in the picture above appears to be a dilation is option 2nd.
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URGENT! thanks!
Bonnie makes the frame of a cube out of 12 pieces of wire that are each six inches long. Meanwhile Roark uses 1-inch-long pieces of wire to make a collection of unit cube frames that are not connected to each other. The total volume of Roark's cubes is the same as the volume of Bonnie's cube. What is the ratio of the total length of Bonnie's wire to the total length of Roark's wire? Express your answer as a common fraction.
Answer:
1/36
Step-by-step explanation:
Bonnie uses 12×6" = 72" of wire to make her cube.
Roark uses 12×1" = 12" of wire to make each of his cubes. He must make 6³ = 216 cubes to match the volume of Bonnie's cube.
The ratio of wire lengths is then ...
72/(12×216) = 6/6³ = 1/6² = 1/36
Find the area of the shaded sector. Round your answer to the nearest tenth. Use 3.14 for π.
A. 141.3 m2
B. 22.5 m2
C. 3.8 m2
D. 70.7 m2
Answer:
B
Step-by-step explanation:
The area of the shaded sector Rounded to the nearest tenth, is 22.5
How to find the area of a sector of a circle?Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.
If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.
Too solve this problem is to multiply the entire area of the circle by (81/360)
Area of the sector = (81/360) x π x r^2
π = 3.14
r = cm
Area of the sector = (81/360) x 3.14 x 8.91^2
Area of the sector = 22.5
The area is 22.5 m2
Learn more about the area;
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What are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 −
5x3 − x2 − 8x + 4?
Select one:
a. Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
b. Positive: 1; negative: 3 or 1; complex: 2 or 0
c. Positive: 3 or 1; negative: 1; complex: 2 or 0
d. Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
Answer:
b.
Step-by-step explanation:
We have to look at sign changes in f(x) to determine the possible positive real roots.
[tex]f(x)=-3x^4-5x^3-x^2-8x+4[/tex]
There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.
Now we have to look at sign changes in f(-x) to determine the possible negative real roots.
[tex]f(-x)=-3x^4+5x^3-x^2+8x+4[/tex]
There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:
1 positive
3 or 1 negative
We need to pair them up now with all the possible combinations.
If we have 1 positive and 1 negative, we have to have 2 imaginary
If we have 1 positive and 3 negative, we have to have 0 imaginary
Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.
Which equation and solution can be used to solve this problem?
Thirteen less than a number is sixteen.
13-n=16: Add 13 to both sides. The answer is 29.
n+13=16: Subtract 13 from both sides. The answer is 3.
n+16=13 Subtract 13 from both sides. The answer is 3.
n-13=16: Add 13 to both sides. The answer is 29.
Answer:
n = 29
Step-by-step explanation:
We need to find an equation that represents the following statement: "Thirteen less than a number is sixteen" which is the same as: "A number minus thirteen equals sixteen"
In that sense, the equation that represents that statement is: n - 13 = 16
Now, the solution is: n - 13 = 16 → n = 29
Answer:
n = 29
Step-by-step explanation:
Factor this expression:
mn - 4m - 5n + 20
Answer:
(m-5) (n-4)
Step-by-step explanation:
mn - 4m - 5n + 20
We will factor by grouping
mn -5n -4m +20
Factor an n out of the first 2 terms and a -4 out of the last 2 terms
n (m-5) -4(m-5)
Now factor out a m-5
(m-5) (n-4)
25 Points!!! This should be quick and easy for anyone who knows math well!
Answer:
Output = 8- input
Step-by-step explanation:
The first point is (1,7)
The input is 1 and the output is 7
The lines goes down, so we know that this is subtraction
Output = 8- input
7 = 8-1
Lets check another point
(5,3)
3 = 8-5
This checks
Please help me! Will mark brainliest!
Answer:
x = 8
Step-by-step explanation:
The 12 on the right is 1/3 the number 36 on the segment above. The value of x will have the same proportion to the segment above it, so will be 1/3 of 24, or 8.
x = 8