A logarithm is a power that requires a number to be raised to another power.
The logarithmic equation given in the question can be written as
log2(16) =x
We will rewrite this equation in the exponential form by considering the definition of logarithm.
The definition states that,
If x and b are two positive real numbers and the value of b is not equal to 1, then the log of
log b (x)=y is equivalent to by=x
We will convert the given equation according to the above definition,
2x=16
The bases of all the values involved must be identical. So, we will create equivalent expressions in the equation that all have equal bases.
2x=24
Now we have the same bases; the two expressions can only be said equal if the exponents are also equal.
x=4
The variable x is equal to 4.
4
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Mr Tan gave $2000 to his wife and two children altogether. His wife received twice as much as his son. His daughter received $300 less than his wife. How much did Mr Tan's daughter receive?
Answer:
Mr Tan's daughter received $620
Step-by-step explanation:
the son received $460
$460 × 2 = $920
the wife received $920
$920 - $300 = $620
$460 + $920 + $620 = $2000
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
C = 35x cm, d=?, r=?
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle is 35x cm. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
35x cm = 2 × π × (Radius of the circle)
(Radius of the circle) = 35x/ (2 × π)
The radius of the circle = 5.57x cm
Diameter of circle = 2 × (Radius of the circle)
= 2 × 5.57x cm
= 11.14x cm
Hence, the radius and the diameter of the circle are 5.57x cm and 11.14x cm, respectively.
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Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -5,15,-45,135,-405,. . . .
The sequence -5,15,-45,135,-405,. . . . is a geometric sequence and its 10th term is a(10) = 98,415
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-5,15,-45,135,-405,....
In this sequence:
a(1) = -5
a(2) = 15
a(3) = -45
and so on.
Notice that:
15 = -5 . (-3) ⇒ a(2) = a(1) . (-3)
-45 = 15 . (-3) ⇒ a(3) = a(2) . (-3)
Since the n-th term is obtained by multiplying the (n-1)-th term by a constant, r = -3, hence, the given sequence is a geometric sequence.
The formula for the nth term in a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = -3, and a(1) = -5
a(10) = (-5) . (-3)¹⁰⁻¹
a(10) = (-5) . (-3)⁹
= 98,415
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Please help on geometry step by step im trying to learn
Answer:
m∠FQR = 23°
Step-by-step explanation:
Since m∠KQF = 90°, it's a complementary angle and is equal to 90°
Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°
(3x - 23)° + (2/3x + 3)° = 90
3x - 23 + (2/3)x + 3 = 90
Combine like terms
multiply the denominator by 3. (3 × 3) = 9 + 2 = 11
(11/3)x - 20 = 90
+ 20 +20
(11/3)x = 110
÷(11/3) ÷(11/3)
x = 30°
Step 2: Find m∠FQR
m∠FQR = ((2/3)x + 3))
(2/3)(30) + 3
20 + 3 = 23
m∠FQR = 23°
I hope this helps!
Answer:
Step-by-step explanation:
(2/3x+3) + (3x-23)=90
(2/3+3)x -20 =90
11/3x =90 + 20
x= 110 * 3/11 =30
FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23
Translation of (x-1)²+(y+3)²=36,2 units left and 4 units down
Identify the centers and radii of the two circles. To find the transformation rule, we need to find how many units horizontally and vertically to move the center of one circle to the center of the other circle.
The equation for the shifted circle is
(x+2) ^2+(y+4) ^2=36.
Description: The standard shape of a circle is
(x−h)2+(y−k)2=r2,
where r is the circle's radius and (h,k) is the circle's center.x2+y2=36 centered at (0,0). If the circle is shifted two units to the left, it means that the new center is h = -2. If we move the circle down four units, the new center is k = −4. So, the shifted circle has the equation (x+2)2+(y+4)2=36.
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Find the geometric mean between pair of numbers.
1/5 and 60
The geometric mean of 1/5 and 60 is 2√3.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Solving for the geometric mean between 1/5 and 60 using the formula:
GM = n√x1 x2 . . . xn
where n = 2, x1 = 1/5, and x2 = 60
GM = √(1/5)(60)
GM = √12
GM = 2√3
Hence, the geometric mean of 1/5 and 60 is 2√3.
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Elon works in New York City and makes $45 per hour. He works in an office and must get his suit dry cleaned everyday for $75. If he wants to make at least $260 a day, how many hours must he work?
Write the inequality that represent the situation above. (Use the variable h)
How many hours will the Elon need to work each day? (Round your answer to the nearest tenth)
If Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.
Given that Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day.
We are required to write the inequality that represent the situation of Elon.
Inequality is just like an equation that shows the relationship between two variables but in greater than, less than,greater than or equal to,less than or equal to signs.
Suppose the number of hours that Elon works be x hours each day.
The earning of Elon will be 45x.
Since the expenditure is $75,the saving will be 45x-75 and if he wants to make $260 a day, the inequality will be 45x-75≥260.
45x≥260+75
45x≥335
x≥335/45
x≥7.55
Hence if Elon earns $45 per hour, spend $75 on dry cleaning everyday and wants to make at least $260 a day then the inequality that shows the situation is 45x-75≥260 and he atleast work for 7 and half hour each day.
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PLEASE HELP! The value of x is 6 numbers away from –1 on a number line. Which numbers could be the value of x?
On a number line, the value of x is six places away from zero. Any of the following numbers, from 1 to 5, could serve as the x.
When X is 6 numbers away from -1, it has a value of 5.
The values from -1 after 6 is -1,0,1,2,3,4,5 so 5 is the 6th number from -1
A number line is a straight line with numbers spaced at equal segments or intervals in mathematics.
A number line is often shown horizontally and can be extended indefinitely in any direction.
Moving from left to right causes the numbers on the number line to climb, whilst moving from right to left causes them to fall.
On a number line, both positive and negative integers can be shown.
Comparing numbers is made simpler by writing them on a number line. The number line's leftmost numerals are smaller than its right most digits.
A number line can be used to do addition, subtraction, and multiplication. We always move to the right, to the left, or by skipping a count while adding, subtracting, or multiplying.
Hence, x could be any one of the following Numbers: 5, 4, 3, 2, or 1.
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Write these propositions using p and q and logical connectives (including negations). (a) you do not drive over 65 miles per hour. (b) you drive over 65 miles per hour, but you do not get a speeding ticket. (c) you will get a speeding ticket if you drive over 65 miles per hour
Writing the propositions using p and q with logical connectives, including negations, in each of the statement will give;
(a) you do not drive over 65 miles per hour-
¬ p
(b) you drive over 65 miles per hour, but you do not get a speeding ticket
p ∨ ¬ q
(c) you will get a speeding ticket if you drive over 65 miles per hour-
p → q
We are to represent each statement using letters; p and q
The letters p and q are then connected with the logical connectives symbols; example negation, conjunction, disjunction and implication symbols.
Thus, each statement given in the question is logically written as;
(a) ¬ p
(b) p ∨ ¬ q
(c) p → q
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Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
What is the interest that Carla will earn at the end of 6 months?Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.
It is expressed as;
I = prt
Given the data in the question;
Principal P = $625Annual interest r = 2.5% = 2.5/100 = 0.025Time period t = 6 months = 6/12 = 0.5 yearsInterest I = ?Plug the given values into the formula above and solve for I.
I = p × r × t
I = $625 × 0.025 × 0.5
I = $7.81
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
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Add or Subtract.
5/19 + 7/38
Answer:17/38
Step-by-step explanation:
5/19+7/38
\frac{5}{19}+\frac{7}{38}
Answer:
[tex]\frac{17}{38}[/tex]
Step-by-step explanation:
[tex]\frac{5 * 2}{19 * 2} +\frac{7}{38}[/tex]
[tex]\frac{10+ 7 }{38}[/tex] 10 +7 =17
[tex]\frac{17}{38}[/tex]
Which number line model shows the subtraction −3−6?
Answer:
C.
-3-6=-9
Step-by-step explanation:
-3-6=-9
C. The blue arrow goes to negative 3. Then the red arrow goes from negative 3 to negative 9.
Hope this helps!
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Have a great day!
Which of the following are reasonable answers for the product of two negative numbers and a positive number? Select all that apply. A. 20 B. 10 C. negative 20 D. negative 15
Every item in the Just a Dollar store is priced
$
1.00
. When Jack opens the store, there is
$
125.00
in the cash register. When he counts the money in the cash register at the end of the day, the total is
$
935.00
. If the sales tax rate is
8
%
, how many items were sold that day?
750 items were sold that day
How to calculate the number of items sold ?The first step is to calculate the total revenue
Total revenue= 935 - 125
= 810
Therefore the number of items sold can be calculated as follows
810= 1x + 8/100
810= 1x + 0.08x
810= 1.08x
x= 810/1.08
x= 750
Hence 750 items were sold that day
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How can I solve this?
Answer:
Mean: 160
Median: 150
Mode: none
Range: 105
Standard deviation: 35.3
Step-by-step explanation:
Given:
Mean = 320Median = 300Mode = noneRange = 210Standard deviation = 70.6If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.
Therefore, if each value in the data set is multiplied by 0.5:
Mean: 320 × 0.5 = 160Median: 300 × 0.5 = 150Mode: none × 0.5 = noneRange: 210 × 0.5 = 105Standard deviation: 70.6 × 0.5 = 35.3Proof
Data set: {1, 2, 3, 4, 5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3[/tex]
[tex]\sf Median = 3[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 5-1=4[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}[/tex]
If we multiply each value by 0.5, the new data set is:
{0.5, 1, 1.5, 2, 2.5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5[/tex]
[tex]\sf Median = 1.5[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 2.5-0.5=2[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}[/tex]
Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.
PLEASE ANSWER FAST Estimate 4001 + 283 + 97 =
Answer:
4400
Step-by-step explanation:
4001→4000 (you need to round the number to the nearest thousand)
283→300 (you need to round the number to the nearest hundred)
97→100 (you need to round the number to the nearest ten, in this case 100)
4000+300+100= 4400
Hope this helps! :)
in the figure below, G is between E and H, and F is the midpoint of EG. if EH = 14 and FG = 3, find GH
The length of GH is 8 units.
The image is not given. Attached a sample image below.
Given,
We can assume that the figure may be a line.
G is between points E and H
F is the midpoint of EG
The length of EH = 14 units
The length of FG = 3 units
We have to find the length of GH.
Here,
EH = EG + GH
Length of EG = FG + EF
F is the mid point of E and G. So, EF = FG ⇒ 3 units
Now,
EG = FG + EF
EG = 3 + 3
EG = 6 units
Now, we can find GH.
GH = EH - EG
EG = 6 units
EH = 14 units
Therefore,
GH = 14 - 6
GH = 8 units.
The length of GH is 8 units.
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2. 8 × - 11 - 3× + 8
please solve this thankyou!!
Answer:
-54.8 ( in fraction -274/5)Step-by-step explanation:
2.8 × (-11) - 3 × 8 =
-30.8 - 24 =
-54.8 ( in fraction -274/5)
How do i solve this?[tex]2(-15)-\sqrt[3]{18(-15)-1061}[/tex]
- 40.18 is the solution of this function .
What does a math cube root mean?
The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The opposite of cubing an integer is to get its cube root.Finding a number that, when multiplied twice by itself, equals the original number is necessary in order to compute the square root of any number. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to find the cube root of any number.[tex]2( -15) - \sqrt[3]{18( -15 ) - 1061}[/tex]
= [tex]2 ( -15 ) - \sqrt[3]{3 - 1061}[/tex]
= [tex]-30 - \sqrt[3]{ - 1058}[/tex]
= - 30 - 10.18
= - 40.18
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PLEASE HELP!!! Given the function defined by f(x)=6x-3, find f(-4.6). Simplify.
2 (-8 - 7) ÷ 3(5)
explain please
Answer:
-50
Step-by-step explanation:
2(−8−7)
3
(5)
=
(2)(−15)
3
(5)
=
−30
3
(5)
=(−10)(5)
=−50
The sum of the measures of the angles in △ABC is 180°. The sum of the measures of angle B and angle C is twice the measure of angle A. The measure of angle B is 32° less than the measure of angle C.
Answer:
< A = 60 degrees.
< B = 44 degrees
<C = 76 degrees.
Step-by-step explanation:
A + B + C = 180 --------(1)
2A = B + C -------(2)
B = C - 32 -------(3)
We see from equation 2 that B + C = 2A so we
replace The A + B in equation (1) by 2A:
A + 2A = 180
3A = 180
A = 60.
Substitute A = 60 in equation (2):
120 = B + C
Rearranging equation (3):
32 = -B + C
Adding theses last 2 equations:
152 = 2C
C = 152/2 = 76.
Substituting for A and C in equation (1):
60 + 76 + B = 180
B = 180 - 60 - 76 = 44 degrees.
(3x^5+8x^3-10x^2)-(-12x^5+4x^3+14x^2)
Answer:x
2
(
15
x
3
+
4
x
−
24
)
Step-by-step explanation:
If a tourist paid Rs. 5610 for a carved window made of wood with a discount of 15% including 10% value added tax, how much does he get back while leaving Nepal? Find it.
Answer:
3/2
Step-by-step explanation:
15% × 10( use p%)
15/100 × 10 (simplify the expression)
15/10 (reduce the expression)
3/2(Solution)
Your friend gave you a free parking pass to a baseball game. Unfortunately, the parking spot number was smudged on the ticket. You know the parking spot was 7 spaces away from your friend's spot. If your friend's parking spot is number 19 in the same row, write and solve and absolute value equation to determine your possible parking spot number(s)? (use \displaystyle xx as the variable to represent the parking spot)
The possible parking spot numbers can be either 12th spot or 26th spot.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that the parking spot was smudged on the ticket.
Let's assume the possible parking spot numbers can be given by x which is represented by an inequality.
Your parking spot is 7 spaces away from your friend's spot which is number 19 in the same row. So , the possible parking spot numbers can be given by ;
19 - 7 ≤ x ≤ 19 + 7
12 ≤ x ≤ 26
Therefore , the possible parking spot numbers can be either 12th spot or 26th spot.
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Zachary purchased a computer for $1,100 on a payment plan. Two months after he purchased the computer, his balance was $870. Six months after he purchased the computer, his balance was $410. What is an equation that models the balance y after x months?
Answer:
y = 1100 - 115x
Step-by-step explanation:
Let the monthly payment be $p
In two months Zach would have paid 2p dollars
Balance would be 1100 - 2p = y
We know after 2 months, balance y was actually 870
Substituting y = 870 we get
1100 - 2p = 870
Subtract 1100 on both sides
1100 - 1100 - 2p = 870 -1100
==> -2p = - 230
Divide by -2 on both sides
-2p/-2 = -230/-2
p = 115 which represents the monthly payment .
So the balance y after m months is given by the equation
y = 1100 - 115x
We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent
6. Savannah is making pots and plates to sell at a local art fair. Each pot weighs 2 pounds and each plate weighs 1 pound. Savannah cannot carry more than 50 pounds to the fair. She only has enough clay to make 40 plates. In addition, she only has enough clay to make 24 pots. She will make $12 profit on every plate and $25 for every pot that she sells. How many pots and how many plates should Savannah make to maximize her profit?
Answer
She should make 24 pots and 2 plates
Expand each binomial. (x-y)³
The binomial expansion of the given expression is:
x³ - y³ - 3x²y + 3y²x
What is a polynomial?
A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
monomialbinomialtrinomialWe solve first by perfect square trinomial, then we apply the distributive property.
(x- y)³ = (x - y)²(x - y)
(x - y)² = x² - 2xy + y²
(x - y)( x² - 2xy + y²)
x³ - 2x²y + y²x - x²y + 2y²x - y³
x³ - y³ - 3x²y + 3y²x
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1. For the right triangle RST shown below, what is the tan R?
A. r/s
B. r/t
C. t/r
D. t/s
E.s/t
R
S
T
Reason:
Angle R is the reference angle since we're computing tan(R)
Side r is opposite angle R. This is the opposite side because it's furthest away from angle R.
Side t is opposite angle T. This is the adjacent side because it's nearest to reference angle R.
The tangent involves the ratio of opposite over adjacent
tan(angle) = opposite/adjacent
tan(R) = r/t
Do the following side lengths form a right triangle?
95, 76, 57
Answer:
Yes
Step-by-step explanation:
A right triangle is a triangle that has one angle whose measure is 90°. A right triangle CANNOT have two 90º angles. This is because the angles of a triangle must add up to 180°. With one angle measuring 90°, the other two angles in the right triangle must add up to 90°
