The logarithmic form is 2log₁₀6
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
loga where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logabc where a is the base is given as logab+logc
loga b/c where a is the base is given as logab-logac
Now it is given to us to find the logarithmic form of 36=6^2
Let us consider the base of the logarithm to be 10
thus log₁₀36=log₁₀[tex]6^{2}[/tex]
log₁₀36=2 log 6
Hence the expression becomes 2log6
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Evaluate ^3 √216. Use pencil and paper. Explain how you can check that your result is correct. Show your work.
The evaluation of the expression given in surd form is 6.
What is the evaluation of the surd form?Surds are expressions that use a root symbol, such as a square root, or another root symbol. Since the decimals of irrational numbers do not finish or recur, they cannot be expressed accurately in decimal form, hence surds are used instead.
Surds, in mathematics, are square root values that cannot be factored into a whole number or an integer. Numbers that are surds are irrational numbers.
From the given expression, the cube root of 216 can be computed as:
[tex]\sqrt[3]{216}[/tex]
Factor the number 216 as:
= [tex]\sqrt[3]{6^3}[/tex]
= 6
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Which expression is equal to 7(1+3)?
Answer: 7+21
Step-by-step explanation:
A school is studying Math for Data and Financial Literacy standardized test scores. Which of the following displays could be used to represent the data, and why?
Bar chart, because test scores are numerical
Box plot, because test scores are categorical
Circle graph, because test scores are categorical
Stem-and-leaf-plot, because test scores are numerical
ik its not A bar charts
A school is studying Math for Data and Financial Literacy standardized test scores. A bar chart could be used to represent the data because test scores are numerical
This is further explained below.
What is a bar chart?Generally, A bar chart or bar graph is a kind of chart or graph that displays categorical data using bars of varying lengths and heights that are proportionate to the values that they represent. It is possible to lay out the bars either vertically or horizontally.
Column charts are occasionally used interchangeably with vertical bar charts.
In conclusion,Standardized exam results in Math for Data and Financial Literacy are now being analyzed at a school.
Due to the numerical nature of the test results, a bar chart could be an appropriate representation of the data.
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A box of chocolates has 3 milk chocolates for every 2 white chocolate. There are 60 chocolates in a box. How many white chocolates are in the box?
Answer: so the answer will be 90 white chocolates that are in the box
Step-by-step explanation:
so first you have a box of chocolates has 3 milk chocolates for every 2 white chocolate. so first you need to divide 3 divided by 2 which is 1.5
and after you need to multiply 1.5 x 60= 90
The grocery store sells beans in bulk the grocers sign above the beans says at this store you can buy any number of pounds of beans at the same rate and all prices include tax
I need help.. but we are only doing question 34 please answer quickly
Answer: 33. r=13.6 34. m=12
Step-by-step explanation:
33.
-0.8+r=12.8
-0.8+r+0.8=12.8+0.8
r=13.6
34.
[tex]\displaystyle\\-\frac{m}{3}=-4\\\\\frac{m}{-3}=-4[/tex]
Multiply both parts of the equation by -3:
[tex]\displaystyle\\\frac{m}{-3}(-3)=(-4)(-3)\\\\ \frac{m(-3)}{-3} =12\\\\m=12[/tex]
What number has the prime decomposition of 5 (power of 2) x 61?
The prime decomposition is [tex]5^{2}[/tex]×61.
Prime factor decomposition of a number means writing it as a product of prime factors. To factorize a number, divide it by the first possible prime number. Take a resulting quotient below the number.
Therefore the prime decomposition is
[tex]5^{2}[/tex] × 61
Here 5 and 61 is a prime number .
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Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. How many cans of paint did Tim buy?
If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.
Number of can of paints boughtLet x represent the number of can
Quantity of addictive mixed in each liter=3/8
Total addictive mixed=3/4
Hence,
x(3/8)=3/4
Cross multiply
x=8(3/4)
x=6 cans of paint
Therefore If Tim bought some cans of paint and 3/4 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 3/8 of a liter of additive in each can. The number of cans of paint that Tim buy is: 6 cans.
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hhhhhhhhhhheeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllllllpppppppppppppp please
Answer:
The correct answer is B
Step-by-step explanation:
It is A because all angles must be congruent to there opposing sides.
Hope that helps! Have an amazing rest of your day! :)
A triangle has sides with lengths of 57 yards, 74 yards, and 95 yards. Is it a right triangle?
The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Pythagoras theorem shows the relationship between sides of a right triangle. It states that for a right angled triangle:
Hypotenuse² = Leg1² + Leg2²
To prove that a triangle with side lengths of 57 yards, 74 yards, and 95 yards is a right triangle:
95² = 74² + 57²
9025 = 5476 + 3249
9025 ≠ 8725
The triangle with side lengths of 57 yards, 74 yards, and 95 yards is not a right triangle because it does not obey Pythagoras theorem.
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I WILL MARK BRAINLY ASAP! Please Help its A Math Question (geometry) .
thank you alot!
Answer:
25 degrees
Step-by-step explanation:
A gardener can care for the greens property in 5 hours. if his helper assists him, they will be done in 4 hours. how many hours does it take for the helper to do it alone
If a gardener can care for the greens property in 5 hours and if his helper assists him, they will be done in 4 hours, then the number of hours it takes for the helper to do it alone is equal to 20.
The number of hours it takes for the helper to do it alone can be found as follows;
Time taken by both the gardener and the helper to complete the job=4
Work done by both the gardener and the helper in one hour = 1/4
Similarly,
Time taken by the gardener to complete the job = 5
Work done by the gardener in one hour = 1/5
The number of hours it takes for the helper alone can be calculated by subtraction. Subtracting the fraction done by the gardener in 1 hour from the fraction done by both the gardener and the helper in 1 hour;
1/4 - 1/5
As the common denominator is 20, we multiply 1/4 by 5 and 1/5 by 4.
5/20 - 4/20 = 1/20
The number of hours it takes for the helper to do it alone can be found by finding the reciprocal of 1/20 which is equal to 20/1
20/1 = 20
Hence, the helper takes 20 hours to do it alone.
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can someone please answer this
The linear equation of the table is y = 5x + 2.
when x = 20, y = 102
when y = 42, x = 8
How to find the linear equation that generates the table?Linear equation can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 17 - 12 / 3 - 2
m = 5 / 1
m = 5
Therefore, let's find the y-intercept using (2, 12)
y = 5x + b
12 = 5(2) + b
12 = 10 + b
b = 12 - 10
b = 2
Therefore, the linear equation is y = 5x + 2.
when x = 20
y = 5(20) + 2 = 100 + 2
y = 102
when y = 42
42 = 5x + 2
42 - 2 = 5x
5x = 40
x = 40 / 5
x = 8
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Brian goes to the arcade with $20. The arcade charges $2.00 a game and a $1.50 entrance fee.
Write and solve an equation to find the number of games Brian can play. SHOW ALL WORK!
Brian can play only 9 games
How to calculate the number of games played ?Brian goes to the arcade with $20
The arcade charges $2 per game and $1.50 entrance fee
The equation can be represented as follows
20-1.50= 2x
18.5 = 2x
divide by the coefficient of x which is 2
x= 18.5/2
x= 9.25
Hence Brian will be able to plat only 9 games
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There are 6 bananas 4 apples and 3 oranges for every 1 orange there are how many bananas
Answer:
There are 18 bananas
Step-by-step explanation:
6 x 3 = 18
18 bananas.
If m∠ADB=( 3a + 10)° and m∠BDC= 13a°, find a, m∠ADB, and m∠BDC.
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
What is the numerical value of a, ∠ADB and ∠BDC?When two angles have measures adding to up to 90 degrees, they are called complementary .
Given that;
m∠ADB = ( 3a + 10 )m∠BDC = 13aNumerical value of a = ?For complimentary angles;
m∠ADB + m∠BDC = 90°
Plug in the given values and solve for a.
( 3a + 10 ) + 13a = 90
3a + 10 + 13a = 90
10 + 16a = 90
16a = 90 - 10
16a = 80
a = 80/16
a = 5
Now, find the measure of ∠ADB and ∠BDC.
m∠ADB = ( 3a + 10 ) = 3(5) + 10 = 15 + 10 = 25°
m∠BDC = 13a = 13( 5 ) = 65°
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
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There are 3 points on a line A, B and C.
If B is between A and C what is the length of BC.
AB= x²-6x
BC= x²+20x
AC= 60-12x
Given :
B is between A and C
AB= x²-6x
BC= x²+20x
AC= 60-12x
B divide into 2 equal parts
AB and AC are equal
AC = AB +BC
60-12x = x²-6x + x²+20x
[tex]60= 2x^{2} -6x +20x +12x[/tex]
[tex]60 = 2x^{2} -6x +32x\\[/tex]
[tex]60= 2x^{2} +26x[/tex]
[tex]30 = x^{2} +13x\\\\[/tex]
[tex]x^{2} +13x -30 = 0\\x^{2} +15x-2x-30 =0[/tex]
[tex]x(x+15) -2 (x+15) =0[/tex]
[tex](x-2) (x+15) =0\\[/tex]
x=2 , x=-15
x never be negative the x is 2
BC = x²+20x
BC = 2*2 +20*2
BC = 4 +40
BC = 44
length of BC =44
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The figure shown is composed of a triangle within
a trapezoid. Determine the area of the
shaded region.
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
What is the Area of a Trapezoid?Area of ay trapezoid is determined using the formula:
Area = 1/2 × (a + b) × h, where a and b are the lengths of the bases of the trapezoid that are parallel, and h is the height or distance between the bases of the trapezoid.
What is the Area of a Triangle?
To find the area of a triangle, use:
Area = 1/2 × base × height of the triangle.
The area of the shaded region = area of the trapezoid - area of the triangle
Area of the trapezoid:
a = 5 m
b = 9 m
h = 6m
Substitute
Area of the trapezoid = 1/2 × (5 + 9) × 6
Area of the trapezoid = 1/2 × (14) × 6
Area of the trapezoid = 7 × 6
Area of the trapezoid = 42 m²
Area of the triangle:
Base = 7 m
Height = 6 - 4 1/2 = 1.5 m
Substitute
Area of triangle = 1/2 × 7 × 1.5
Area of triangle = 5.25 m².
The area of the shaded region = area of the trapezoid - area of the = 42 - 5.25 = 36.75 m²
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F=GmM/r^2 solve for G
Solution of the equation for G is given as G = Fr²/Mm
According to the question we have been given the formula for evaluating the value of F which is given as :
F = GmM/r²
Now we need to solve the equation for evaluating G. Which is given step by step as :
F = GmM/r²
Multiplying both the sides by r² we get
Fr² = GmM*r²/r²
Fr² = GmM
dividing both the sides by Mm we get
Fr²/Mm = GmM/Mm
Fr²/Mm = G
or, G = Fr²/Mm
Hence the solution for G is given as G = Fr²/Mm
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need help brainleist to first person who gets it right
Answer:
Step-by-step explanation:
Answer: I believe A is 52 degrees.
Solution: Find angle c (D + C adds up to 180 degrees cuz its a line)
So do 180-116=64 degrees
Assuming this is an isosceles triangle because the sides on d and c look equal, we know that those 2 angles add up to 128 degrees(64 + 64).
Therefore, since the shape is a triangle(adds up to 180 degrees) you just do 180 minus 128 to get angle A which is 52 degrees.
savannah is working two summer jobs, making $10 per hour washing cars and making $22 per hour tutoring. In a given week she can work at most 8 total hours and must earn no less that $110. Of x represents the number of hours washing cars and y represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities are 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively.
What is inequality?In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
Total amount by washing cars = 10x
Total amount by tutoring = 22y
Total hours should be no less than 8
So,
x + y ≥ 8
And,
Total amount ≥ 10
10x + 22y ≥ 10
By substitution,
10(8 - y) + 22y ≥ 10
y ≥ 2.5
And x ≥ 5.5
Hence "The system of inequalities is 10x + 22y ≥ 110 and x + y ≥ 8 and values of x and y are 5.5 and 2.5 respectively".
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Write the slope-intercept equation for a line that passes through the points (-2, 4) and (3, -5)
The slope intercept equation for a line that passes through the points (-2,4) and (3,-5) is y = -9/5x ₊ 2/5.
Given the points are:
P₁ = (-2,4) = (x₁ , y₁)
P₂ = (3,-5) = (x₂ , y₂)
Therefore, the equation of the line that passes through the above points is:
y = mx ₊ b , Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
= ( -5 - 4 ) / ( 3 - ( -2) ) = -9 / 5
∴ m = - 9/5
Using either P₁ or P₂, plug in one of their respective x- and y-values into:
y = -9/5 x + b
substitute (3,-5)
₋5 = (₋9/5)(3) ₊ b
₋5 = ₋27/5 ₊ b
₋5₊27/5 = b
₋ 25 ₊ 27/5 = b
b = 2/5
slope intercept equation:
y = mx ₊ b
y = -9/5x ₊ 2/5
Therefore, y = -9/5x ₊ 2/5 is the equation of the line that passes through both points (-2, 4) and (3, -5).
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Find the value of f(5) for each function
1. f(x) = -2(x+1)
2. f(a) = 3(a +2)-1
3. f(h) =- h/10
4. f(m) = 1 - 4 (m/2)
5. f(m) = 2(m-3)
Answer:
1. -12
2. 20
3.-1/2
4. -9
5. 4
Step-by-step explanation:
1. -2(5+1) = -12
2. 3(5+2)-1 = 21-1 = 20
3. -5/10 = -1/2
4. 1-4(5/2) = 1-20/2 = 1-10 = 9
5. 2(5-3) = 4
|14c+5|>7
How can I graph this?
Answer:
Step-by-step explanation:
step 1: Absolute value inequality entered
|14c+5| > 7
step 2: Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is |14c+5|
For the Negative case we'll use -(14c+5)
For the Positive case we'll use (14c+5)
step 3: -(14c+5) > 7
Multiply
-14c-5 > 7
Rearrange and Add up
-14c > 12
Divide both sides by 14
-c > (6/7)
Multiply both sides by (-1)
Remember to flip the inequality sign
c < -(6/7)
Which is the solution for the Negative Case
step 4:
(14c+5) > 7
Rearrange and Add up
14c > 2
Divide both sides by 14
c > (1/7)
Which is the solution for the Positive Case
c < -6/7
c > 1/7
A full bag of dog food weighs 51/2 pounds
How much dog food do you have if there are 334
bags in the cupboard
Step-by-step explanation:
I guess the question really is how much weight of dog food do you have.
1 bag = 51/2 pounds
334 bags = 334 × 1 bag = 334×51/2 = 167×51 =
= 8,517 pounds
2. In a triangle, the measure of the first angle is six times a number. The measure of the second angle is nine less than the first angle. The measure of the third angle is three times the number more than the measure of the first angle. Determine the measure of each angle in degrees.
The measure of the angle 1, 2, and 3 will be 54°, 45°, and 81°, respectively.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The initial angle of a triangle is measured by multiplying a value by six. The second angle's measurement is nine less than the first angle's. The third angle's measure is three times greater than the first angle's measurement. Let x be the number. Then the measure of the angle 1, 2, and 3 will be
∠1 = 6x
∠2 = 6x - 9
∠3 = 3x + 6x
The sum of all angles will be 180°, then the equation will be
∠1 + ∠2 + ∠3 = 180°
6x + 6x - 9 + 3x + 6x = 180°
21x = 189°
x = 9°
Then the measure of the angles will be
∠1 = 6x = 6 × 9 = 54°
∠2 = 6x - 9 = 6 × 9 - 9 = 45°
∠3 = 3x + 6x = 9x = 9 × 9 = 81°
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A logging company is funding a study to determine the best practice for reforesting a cut section of forest. the previous best practice has been to plant the same type of tree with equally spaced intervals. the proposed method of reforestry is to plant a variety of trees at differing intervals. in the study, some tracts of land are reforested using the previous best practice. what are these tracts of land in the study?
The tracts of land in the study is the Control group.
The tracts of land in the study are reforested using the previous best practice whose results are already known. Now, it is not known, how the proposed method of reforestrey to plant a variety of trees at different intervals would grow. So, the tracts of land of previous plant can serve as a standard to which comparisons can made as to whether the newly proposed method is performing better than the previous or not.
This study was conducted at the Agua Salud Project site located in the Panama Canal Watershed (9° 13 N′, 79° 47′ W, 33 m amsl) with an average rainfall of 2700 mm annually, 80% of which falls between May and mid-December. Mean daily maximum and minimum temperatures are 32 °C and 23 °C . The topography is characterized by short and steep slopes. Soils are silt clay to clay with pH values of 4.4 to 5.8 and have very low levels of both plant available and total phosphorus. The data were collected from the Agua Salud native species and T. grandis plantation, both established in 2008 and planted in the same 3 m by 3 m spacing configuration.
Despite this information, changing landowners’ perceptions and transitioning from one species to a lesser known one, is a risk for the landowner and may require financial incentives.
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Solve each equation. 7x²+8 x=-6 .
7(-6)^2+8
-42^2
-1,764+8
-1,772
Triangle G is a scaled copy of triangle F
What scale factor takes triangle F to Trangle G?
timmy is downloading movies from the internet. He can download 6 movies every 15 minutes. jonathan, who is also downloading movies, can download at a rate of 12 movies every 20 minutes
The unit rate of downloading per movie for each person is for Timmy it will take 2.5 minutes and for Jonathan it will take 1.66 minutes.
In question it is not given that what to do, so we will find the rate of downloading per movie for each person.
With the help of following steps as given below :
Timmy takes 15 minutes to download 6 movie.
6 Movies = 15 Minutes
1 Movie = 15/6
1 Movie = 2.5 Minutes
Jonathan takes 20 minutes to download 12 movies.
12 Movies = 20 Minutes
1 Movie = 20/12
1 Movie = 1.66 Minutes
Therefore, Timmy and Jonathan will take 2.5 and 1.66 minutes, respectively, to download one movie.
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