If the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
Given that the expression is log₄ 5x+log₄3x.
We have to express the expression in single logarithm.
Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents which we have to multiply like bases, we can add the exponents.
The expression is log₄ 5x+log₄3x.
log₄ 5x+log₄3x=[tex]log_{4} 15x^{2}[/tex] (We are not required to change the base)
Hence if the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
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En 1999 la ciudad tenía 300 gatos callejeros y se ha demostrado que la cantidad de gatos crece un 10% año con año, ¿Cuántos gatos callejeros hay en la actualidad?
Number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.
As per the question statement, a certain city had 300 stray cats in 1999, and the number of cats are growing by 10% every year since then.
We are required to calculate the total number of stray cats in the city today.
To do so, we will need to know the formula of compound interest which goes as [tex]A=[P*(1+\frac{R}{100})^n][/tex]
Where, A = Final Amount i.e., (Principle + Interest).
P = Principle on which Interest in compounded
R = Rate of Compound Interest per annum
n = Time period of interest.
Here, (P = 300), (R = 10) and [n = (2022-1999) = 23]
Using these values of P, R and n in the above-mentioned formula to calculate the amount in the case of compound interest, we get,
Total number of stray cats in the city today (T) = [tex][300*(1+\frac{10}{100})^{23} ][/tex]
[tex]or, T=[300*(\frac{100+10}{100})^{23} ]\\or, T=[300*(\frac{110}{100})^{23}]\\or, T=[300*(\frac{11}{10})^{23}]\\or, T=2686.29[/tex]
Since, number of cats cannot be a decimal value, therefore, Total number of stray cats in the city today are 2686, rounded off from 2686.29.
Compound Interest: Compound interest means that the interest increases exponentially, rather than increasing linearly over time, or in simpler words, it is a continuous interest on principal plus interest.
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hola ayuda pls, con esta division
9624 dividido 8 pls ayuda XD
Answer:
Step-by-step explanation:
un confesionario tiene 120 coches el 35% son blancos y el 5% rojos. ¿cuántos coches de cada color hay?
Question
You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Answer:
19.08-6%=12.25+x
18.00=12.25+x
18.00-12.25=5.75
x=5.75
cat food is $5.75
Step-by-step explanation:
rapunzel bought 9.54 pounds of grapes and 4.51 pounds of bananas. what is the total amount of the fruit
Answer:
14.05 lb
Step-by-step explanation:
9.54 + 4.51 = 14.05 lb
Find the domain and range !!!! HELP ASAP PLS
Step-by-step explanation:
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4. If m/3 = 54°, find the measure of each missing angle.
540
4
2. 3
7
10
6/5
58
9
11
12 13.
14
a. m/1 =
36
b. m/2 = 40
c. m/4 =
36
d. m25 =
40
e. m26 = 54
f. m27 = 126
9. m28=
54
h. m29 = 126
i. m210 = 54
j. m/11=
54
k. m/12 = 126
1. m/13 = 54
m. m/14 = 120
Gina Wilson (All Things Algebra),2014
Using multiple line and angle theorems, the values of each of the 14 angles are given.
Using the geometry theorems :
1.)
∠2 is a right angle = 90°
2.)
∠1 + ∠2 + ∠3 = 180° (sum of angle on a straight line)
90 + ∠1 + 54° = 180°
∠1 = (180 - 144) = 36°
(∠2 and ∠5) ; (∠3 and ∠6) ; (∠1 and ∠4) are vertically opposite ;
Hence,
∠4 = 36°
∠5 = 90°
∠6 = 54°
∠3 = ∠8 = 54° (corresponding angles)
∠9 + ∠8 = 180° (sum of angle on a straight line)
∠9 = (180 - 54) =126°
∠7 = ∠9 = 126° (vertically opposite angles)
∠8 = ∠10 = 54° (vertically opposite angles)
∠4 = ∠13 = 36° (corresponding angles )
∠12 + ∠13 = 180° (sum of angle on a straight line)
∠12 = (180 - 36) =126°
∠11 = ∠13 = 36° (vertically opposite angles)
∠12 = ∠14 = 126° (vertically opposite angles)
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Dan's car depreciates at a rate of 15% per year.
By what percentage has Dan's car depreciated after 3 years?
Give your answer to the nearest percent.
Answer:
45%
Step-by-step explanation:
15 x 3 = 45
There are 20 cubic feet of sand left over from a project. Mr. Wilson wants to build a sand box to hold the left-over sand. He built a rectangular box. The box is 5 feet long by 2 feet wide. How deep will the sand be once it is poured into the sandbox
The depth of the box once the sand is poured into it is 2 feet
Volume of a boxVolume of the sand left = 20 cubic feetLength of the box = 5 feetWidth of the box = 2 feetHeight of the box = x feetVolume of the box = length × height × width
20 = 5 × 2 × x
20 = 10x
divide both sides by 10x = 20/10
x = 2 feet
Therefore, the depth of the box once the sand is poured into it is 2 feet
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would you classify 156 as a perfect square perfect cube both or neither
what are the area and perimeter of 7in 16in
The Area and Perimeter of the rectangle is 112 Inches² and 46 Inches respectively.
Suppose in question they are talking about rectangle.
So, let
Length (l) of rectangle = 16 Inches
Width (w) of rectangle = 7 Inches
As we have both sides of rectangle now we will determine the value of area and perimeter of rectangle.
Area of rectangle = l × w
= 16 × 7
= 112 Inches²
Perimeter of rectangle = 2( l + w )
= 2( 16 + 7 )
= 2 × 23
= 46 Inches
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QUICK!!
solve the tables pls
A function that represents the meters Jackie can run in any given minutes is b = 150m.
The meters she would run after 12 minutes is 1,800 meters.
How many meters can she run in 12 minutes?The independent variable is the variable that cannot be altered in the process of an experiment. The independent variable is the minutes ran by Jackie.
The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable. The dependent variable is the total distance that Jackie runs.
The function that represents the distance run is:
Total distance = distance run per minute x number of minutes
b = 150 x m
b = 150m
Distance run in 12 minutes = 150 x 12 = 1800 meters
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find the product of the integers 2(-4)
Answer:
-8
Step-by-step explanation:
2(4)=8, and a negative number times a positive number results in a negative number.
Need Help Asap! Will give Brainliest.
A rental car agency charges a flat fee of $131.00 plus $49.00 per day to rent a certain car. Another agency charges a fee of $77.00 plus $58.00 per day to rent the same car.
Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole number of days.6
11
3
12
The number of days for which the costs are the same is 6 days.
How to illustrate the information?Let the number of days be represented by d.
A rental car agency charges a flat fee of $131.00 plus $49.00 per day to rent a certain car. This will be
131 + 49d
Another agency charges a fee of $77.00 plus $58.00 per day to rent the same car. This will be
77 + 58d
Equate both equations
131 + 49d = 77 + 58d
Collect like terms
58d - 49d = 131 - 77
9d = 54
Divide
d = 54 / 9
d = 6 days.
Therefore, the number of days for which the costs are the same is 6 days.
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37. Ten people ordered calculators. The least expensive was
$19.95 and the most expensive was $39.95. Half ordered a
$29.95 calculator. Select the best estimate of the amount
spent on calculators.
a. $240
b. $310
c. $345
SECTION
d. $355
An G
spelle
per I
Exer.
The amount spent on calculators is $310 which is option (b) .
The class upper bound is the largest data value that the class can contain. The class lower bound of a class is the smallest data value that the class can contain. The average is the average of the given numbers, calculated by dividing the sum of the given numbers by the total number of numbers.It is given that half people ordered $29.95 calculator which means that 5 people have ordered $29.95 per calculator then , amount is given by
(number of people ) × cost per calculator = total amount spent
[tex]5\times29.95=\$149.75[/tex]
It is given that least expensive calculator was $19.95 and the most expensive calculator was $39.95.
Mean will be [tex]=\frac{least\ + \ most}{2}[/tex]
[tex]=\frac{19.95+39.95}{2} \\\\=\frac{59.9}{2} \\\\=29.95[/tex]
so the other 5 people have spent an average of amount [tex]=5\times29.95[/tex]
[tex]=\$149.75[/tex]
Total amount spent on calculators will be [tex]=149.75+149.75=\$299.5[/tex]
which is approximately equal to $310 which is option (b) .
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Let f(x)=x-2 and g(x)=x²-3 x+2 . Perform each function operation and then find the domain. -2 g(x)+f(x)
The outcome of -2 g(x) + f(x) is 4 x -2 x ² and the domain is [ 0 , 2 ] .
Given,
f (x) = x - 2 and g (x) = x² - 3 x + 2
The question states to find the summation of the function f, that is, f (x) = x - 2, and function g, that is, g (x) = x² - 3 x + 2
Performing the addition operation on these functions is just like simple addition.
This means that when we add the two functions f (x) and g (x), we get
f (x) + g (x) = x - 2 + x² - 3 x + 2
=> f (x) + g (x) = x ² - 2 x
This implies that the summation or addition of the two functions f (x) and g (x) gives x ² - 2 x
needed result = -2 g(x) + f(x) = -2 ( x² - 2 x ) = -2 x ² + 4x = 4 x -2 x ²
To find domain,
y = 4 x -2 x²
=> 4x -2 x² ≥ 0
=> 2 x * ( 2 - x ) ≥ 0
=> 2 x ≥ 0 and 2 - x ≥ 0
=>x ≤ 2 and x ≥ 0
=> the final Domain = [ 0 , 2 ]
Therefore, we get the result of -2 g(x) + f(x) as 4x -2 x ² and the domain as [ 0 , 2 ] .
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Estimate the value of √13 by plotting it on a
number line.
Answer:
√ Using Pythagoras Theorem OB2 = OA2 + AB2 OB2 = 32 + 22 OB2 = 9 + 4 OB = √13
Step-by-step explanation:
Which length of time is between 5.50 am and 8.35 am ?
Answer:
3 hours and 25 minutes
Step-by-step explanation:
Since these times are both AM, you can just change the form to 8.35 and 5.50 and subtract.
8.35- 5.50 = 2.85
And since there are max of 60 minutes in an hour, you take the 60 minutes from the 85 minutes, and you're left with 3 hours and 25 minutes.
Hope this helped :D
Answer:
i think 165 minutes which would be 2.75 converted in hours
Step-by-step explanation:
Please answer the problems step by step. (More than one question)
1. (2-3)(-8+2)+|-3+5|=?
2. -|-2-5+3|(5-2)=?
3. use two unit multipliers to convert 80ft into centimeters
4. use two unit multipliers to convert 12 square feet into square inches.
Answer:
1) 8
2) -12
3) 80ft = 2438.4 centimetres
4) 12 square feet = 1728 square inches
Step-by-step explanation:
1) ➟ (2−3)(−8+2)+|−3+5|
➟ (-1)(-6)+(2)
➟ 8
2) (−|−2−5+3|)(5−2)
=(−|−7+3|)(5−2)
=(−|−4|)(5−2)
=−4(5−2)
=(−4)(3)
=−12
3) 80ft = 2438.4 centimetres
4) 12 square feet = 1728 square inches
Please help me solve for x.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{9 + x}{15}=\cfrac{15}{9}\implies \cfrac{9 + x}{15}=\cfrac{5}{3}\implies 27+3x=75 \\\\\\ 3x=48\implies x=\cfrac{48}{3}\implies \boxed{x=16}[/tex]
Factor each expression.
3 x²+10 x+8
After solving, the factors of equation 3x²+10x+8 are:
(x+2) and (3x+4)What exactly is an equation?An equation is a mathematical statement made up of two representations joined by an equal sign.An equation is 3x - 5 = 16.After solving this equation, we get the value for the variable x as x = 7.So,
Given the equation: 3x²+10x+8
Then,
3x²+10x+8 3x²+x( + )+8 3x²+x(6+4)+8 3x²+6x+4x+83x(x+2)+4(x+2)Factors are: (x+2) and (3x+4)
Therefore, after solving, the factors of equation 3x²+10x+8 are:
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the angle is 11/12 on a circle
Here we will show you how to calculate the angle in degrees made by the hour hand and minute hand on a 12-hour clock at 11:12.
Before we continue, note that a clock is shaped like a circle and is composed of 360 degrees.
There are 60 minutes in an hour, and 360 degrees divided by 60 minutes is 6. Therefore, the minute hand moves 6 degrees per minute.
As you can see, the hour hand and minute hand showing 11:12 on the clock make an angle. We used the hands to make the pie chart below so it is easier to visualize what we are calculating.
The hour hand and minute hand on a clock showing 11:12 actually make two angles: The hour hand to the minute hand is outlined in blue, and the minute hand to the hour hand is outlined in red.
360 - (336 - 72) = 96 degrees
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While working for a contracting company, you are preparing for a job tiling a floor. The customer says that the
rectangular laundry room is 15 feet by 8 feet, 8 inches. To place the order for the floor covering, you must calculate the
area.
What is the area of the laundry room, in square feet, to the nearest square foot?
65
130
132
9,360
18,720
Answer:
(2)
15x8.66666667=130.00000005
Step-by-step explanation:
to get the are in square feet you have to Length (in feet) x width (in feet) = area in sq. ft.
Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:
Length: 13x - 9 units
Width: 4.5x + 8 units
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.. The inequality that represents the given situation is 13x - 9 > 4.5x + 8
What is Inequality?Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
From the question, we are to determine the inequality that represents the given situation
From the given information, we have that
The length of the laptop is given by 13x - 9 units
and The width of the laptop is given by 4.5x + 8 units
If the length is greater than the width, then we can write that
13x -9 > 4.5x + 8
Hence, the inequality that represents the given situation is 13x - 9 > 4.5x + 8
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Where is the point (-3,1) located when it is translated four units left and two units up 
Answer:
-5,3. You crawl before you can walk.
Step-by-step explanation:
Answer:
(-7, 3)
Step-by-step explanation:
Original point: (-3, 1)
So original x = -3
4 units left means x coordinate is decreased by 4
So, new x-coordinate = -3 - 4 = -7
Original y coordinate = 1
2 units up means y coordinate increases by 1
So new y-coordinate = 1 + 2 = 3
Translated point = (-7, 3)
See graph for visual explanation
pleaseee explain
round to the nearest decimal point
Given the following relation:
[tex] \frac{1}{A } = \frac{55}{26} \\ [/tex]
We can solve for A, by taking the reciprocal on both sides, meaning we flip the fractions. This operation does not change our original relation.
[tex] \frac{A}{1} = \frac{26}{55} \\ or \: A = \frac{26}{55} [/tex]
Approximation to the nearest tenth place:
[tex]A = \frac{26}{55} \approx0.4[/tex]
skills check mathematics help needed please
Answer:
1. 600000+90000+ 6000
2. 6000+ 300
3. 6x+ 33x
4.
5.
6.
7. 75
8. 21
9. -5x
10. 3x
11. 10 km
12. 4.6
13.
14.
15. $3.5
16.$1.5
17. 4x-1=3x-5
+1 +1
4x= 3x-4
-3x -3x
x=-4
18. 3x-3=27-2x
+3 +3
3x= 30-2x
+2x +2z
5x= 30
/5 /5
x= 6
19. 0.5
20. 1
James has factorised an expression correctly.
His answer is 2(7y - 3).
What was the expression that he factorised?
Answer:
14y - 6
Step-by-step explanation:
given factored expression
2(7y - 3) ← multiply each term in the parenthesis by 2 to give original
= 14y - 6 ← expression before being factorised
Word problem to find the translation
Answer:
3 units left and 2 units down
Step-by-step explanation:
The ordered pair is written (x,y) The x tells us the location right or left from the origin (0,0) and the y tells us the up or down from the origin (0,0).
We are translating the point from (6,4) to (3,2) Look at the x values. We start at 6 and move to 3. That means that we moved 3 units to the left.
Now look at the y values. We start at 4 and move to 2. That means that we moved down 2 spaces.
i need help with this math and i don’t really understand
Answer:
Point G
Step-by-step explanation:
It is point G because since you mirrored it and flipped it, you need to flip figure one and if you move it to where figure two is, in the same place, the new point R is where point G is, so G corresponds to R
P.S. someone else aske the same question