Answer:
[tex]\sf x =15.5[/tex]
Step-by-step explanation:
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]
[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]
[tex]\sf 2x+1 =32[/tex]
[tex]\sf 2x+1 -1=32-1[/tex]
[tex]\sf 2x =31[/tex]
[tex]\sf x =15.5[/tex]
Answer:
Step-by-step explanation:
[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]
[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x
~~~~~~~~~~~~~~
[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5
[tex]log_{2} \frac{10x+5}{5}[/tex] = 5
[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]
10x + 5 = 32 × 5
2x + 1 = 32
x = 15.5
Change the following decimals to fractions give your answers in their simplest form a) 0.3 b) 0.46 c) 0.075
Answer:
[tex]0.3 = \frac{3}{10}\\\\ 0.46 = \frac{23}{50} \\\\0.075 = \frac{3}{40}[/tex]
Step-by-step explanation:
To convert decimals to fractions, you look at the place of the last digit of the fraction (i.e. the digit that the farthest right from the decimal)
For 0.3, 3 is in the tenths place, so we end up with the fraction [tex]\frac{3}{10}[/tex]
For 0.46, 6 is in the hundreths place, so before simplifying we have [tex]\frac{46}{100}[/tex]
The GCF of 46 and 100 is 2 so we divide the fraction by [tex]\frac{2}{2}[/tex] to get [tex]\frac{46}{100}[/tex] ÷[tex]\frac{2}{2}[/tex] = [tex]\frac{23}{50}[/tex]
For 0.075, the 5 is in the thousandths place, so before simplifying we have [tex]\frac{75}{1000}[/tex]
The GCF of 75 and 1000 is 25 so we decide the fraction by [tex]\frac{25}{25}[/tex] to get [tex]\frac{75}{1000}[/tex] ÷[tex]\frac{25}{25}[/tex] = [tex]\frac{3}{40}[/tex]
enrollment is a business seminar increased from 50 people to 62 people. what was the percent increase?
well, it went up from 50 to 62, so it really went up by 12 folks.
if we take 50 to be the 100%, what is 12 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 50 & 100\\ 12& x \end{array} \implies \cfrac{50}{12}=\cfrac{100}{x}\implies \cfrac{25}{6}=\cfrac{100}{x} \\\\\\ 25x=600\implies x=\cfrac{600}{25}\implies x=24[/tex]
An equation is shown below:
4(2x - 5) + 15 = 11
Write the steps you will use to solve the equation and explain each step.
Answer:
Step-by-step explanation:
The carson family pays $3,252 a year for their cell phones is $3,252 a reasonable answer?
Answer:
Here we will show you how to calculate how much you will make in a year if you make $3252 an hour. Our calculations are based on the following information, but you can change the numbers further down on this page to make it better reflect your situation.
Hourly Pay: $3252
Work hours per week: 40
Work weeks per year: 52
Income Tax Rate: 12%
To calculate how much $3252 an hour is per year, we first calculate weekly pay by multiplying $3252 by 40 hours per week, and then we multiply the product by 52 weeks, like this:
$3252 × 40 hours
= $130,080.00 per week
$130,080.00 × 52 weeks
= $6,764,160.00 per yearNow you know that your gross income per year (income before tax) is $6,764,160.00 if you make $3252 per hour. However, you have to deduct taxes to find your net yearly income (income after tax).
Everyone has to pay 6.2% Social Security Tax and 1.45% Medicare Tax. Furthermore, we assume you will pay about 12% in Federal, State, and Local income taxes. Here is how to calculate your net income (the actual amount you will receive per year):
Social Security Tax
($6,764,160.00 × 6.2)/100
= $419,377.92
Medicare Tax
($6,764,160.00 × 1.45)/100
= $98,080.32
Income Taxes
($6,764,160.00 × 12)/100
= $811,699.20
+ $6,764,160.00 Gross Income
- $419,377.92 Social Security Tax
- $98,080.32 Medicare Tax
- $811,699.20 Federal/State/Local Taxes
= $5,435,002.56 Net IncomeThere you have it. Now you have the answer to "$3252 an hour is how much a year?" If you make $3252 per hour, then your yearly income before taxes is $6,764,160.00 and your yearly income after taxes is $5,435,002.56
We made some assumptions about how much you work and how much taxes you have to pay. You can adjust these assumptions below to match your situation to get the exact amount for your situation.
Step-by-step explanation:
n expression is shown below. -x + 1 + 4x - 3
Answer:
3x - 2
Step-by-step explanation:
Collect like timers. -x + 4x = 3x and -3 + 1 = -2, 3x - 2
Hey there!
-x + 1 + 4x - 3
= -1x + 1 + 4x - 3
COMBINE the LIKE TERMS
= (-1x + 4x) + (1 - 3)
= -1x + 4x + 1 - 3
= 3x - 2
Therefore, your answer is: 3x - 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Swimming Pool On a certain hot summer's day, 163 people used
the public swimming pool. The daily prices are $1.25 for children
and $2.00 for adults. The receipts for admission totaled $257.00.
How many children and how many adults swam at the public pool
that day?
There were
children at the public pool.
If $1209 is deposited in an account that pays 8. 2% interest compounded monthly, what is the balance after 26 years? Use: A=P(1+r)t
Round to the nearest cent
Answer:
Step-by-step explanation:
We can use the interest equation (mind you it is the same thing as said in the problem) to solve this:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the resulting amount, r is the interest rate, n is the number of times compounded per year and t is the time.
[tex]A=1209(1+\frac{.082}{12} )^{12*26}[/tex]
A = $10,120.29
pls help ASAP first correct answer gets brainleist
Answer:
4.58257569 meters (Could probably get away with rounding it to 4.6 meters)
Step-by-step explanation:
Pythag theorem
a^2 +b^2 =c^2
Insert your numbers
10^2+b^2=11^2
Simplify squares
100+b^2=121
subtract 100 from both sides
b^2=21
sqrt both sides
sqrt(b^2)=sqrt(21)
simplify sqrts to get b
b= 4.58257569
A. where will vertex A be located after a rotation of -90°
B. where will vertex B be located after a rotation of 90°
C. where will vertex C be located after a -180° rotation
D. where will vertex D be located after a 270° rotation?
Answer:
this image should help a lot:
vertex b: (-5,3)
vertex a: (0,-1)
vertex c: (-6,-7)
vertex d: (-4,-1)
Step-by-step explanation:
What is the sum of the two amounts of money shown?
Enter your answer in the box.
$
first amount:
$10 + $5 + 25 cents + 25 cents + 25 cents + 5 cents + 5 cents $10 + $5 + $0.25 + $0.25 + $0.25 + $0.05 + $0.05$15.85second amount:
$5 + 25 cents + 25 cents + 1 cents + 1 cents + 1 cents + 1 cents$5 + $0.25 + $0.25 + $0.01 + $0.01 + $0.01 + $0.01$5.54total amount:
$5.54 + $15.85 $21.39Hey there!
Guide:
• Penny = 0.01¢ (1 cent)
• Nickel = 0.05¢ (5 cents)
• Dime = 0.10¢ (10 cents)
• Quarter = 0.25¢ (25 cents)
• Half dollar = 0.50¢ (50 cents)
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
EQUATION #1.
$10.00 + $5.00
= $15.00
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.25¢ + 0.25¢ + 0.25¢ + 0.05¢ + 0.05¢
= 0.75¢ + 0.10¢
= 0.85¢
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
$15.00 + 0.85¢
= $15.85
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Total/Answer: $15.85
______________________________
EQUATION #2.
$5.00 + 0.00
= $5.00
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.25¢ + 0.25¢ + 0.01¢ + 0.01¢ + 0.01¢ + 0.01¢
= 0.50¢ + 0.04¢
= 0.54¢
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
$5.00 + 0.54¢
= $5.54
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Total/Answer: $5.54
______________________________
NOW ADD THEM TOGETHER!
$15.85 + $5.54
= $21.39
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
1/6 of a birthday cake is left over from a party. The next day, it is shared among 7 people. How big A piece of the original cake did each person get?
Answer:
j
Step-by-step explanation:
Explanation:
Draw 6 identical rectangles side by side as shown in figure 1 in the diagram below. Shade one of the rectangles to represent 1/6 of the cake left over.
Now draw in horizontal lines (see figure 2) to split the leftover amount into 7 equal portions. Notice that we have a 7 by 6 grid of tiny rectangles. There are 7*6 = 42 tiny rectangles in total.
Each person will therefore get 1/42 of the original cake when splitting up this last leftover slice.
this is due today! please help and i will give 50 points
Answer:
D) 154 ft²
Step-by-step explanation:
Formula
Area of a rectangle = width x length
We only need to calculate the area of the walls.
There are two pairs of walls with the following dimensions:
5 ft x 7 ft6 ft x 7 ftTherefore, area to paint = 2(5 x 7) + 2(6 x 7)
= 70 + 84
= 154 ft²
Bottom cube 's LSA need to be counted
H=7ftL=6B=5LSA:
2H(L+B)2(7)(5+6)14(11)154ft²Using the Linear equation 4x-3y=12, express each of the following.
y in terms of x. y=
Using the Linear equation 4x-3y=12, express each of the following.
x in terms of y. x=
Using the given linear function, it is found that the expressions are given by:
[tex]y = \frac{4x}{3} - 4[/tex].[tex]x = \frac{3y}{4} + 3[/tex].What is the given linear function?It is:
4x - 3y = 12.
To find y in terms of x, we isolate y, hence the expression is given by:
[tex]3y = 4x - 12[/tex]
[tex]y = \frac{4x}{3} - 4[/tex]
To find x in terms of y, we isolate x, hence the expression is given by:
[tex]4x = 12 + 3y[/tex]
[tex]x = \frac{3y}{4} + 3[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
what is a solution in 6th-grade math?
Answer:
A solution means any variable that makes the equation true
what numbers are missing from the pattern 1,14,21,28,?,?,?,?,28,21,14,7 ?
Answer:
ANSWER1,14,21,28,35,42,42,35,28,21,14,7
x=15 in the form of |x-b|=c
(where b is a number and c can be either number or an expression)
Step-by-step explanation:
don't mind with my hand writting
The MOST precise measurements this ruler can give are to the nearest A) inch. B) half inch. C) eighth inch. D) quarter inch.
pls can I get some help this is compound interest (10) will give brainliest
Answer:
2.7
Step-by-step explanation:
The length of a rectangular frame is represented by the expression 2x 10, and the width of the rectangular frame is represented by the expression 2x 6. Write an equation to solve for the width of a rectangular frame that has a total area of 140 square inches. 4x2 32x − 80 = 0 4x2 32x 60 = 0 2x2 32x − 80 = 0 x2 16x 60 = 0.
The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
What is the area of the rectangle?The area of the rectangle is the product of its length and its breadth.
As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².
Now we know the area is the product of length and breadth, therefore,
[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]
[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]
Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.
Learn more about the Area of Rectangle:
https://brainly.com/question/14383947
Answer:
A.) 4x2 + 32x − 80 = 0
Step-by-step explanation:
Just took the test
A scale model of a ramp is a right triangular prism as given in this figure. in the actual ramp, the triangular base has a height of 0.5 yards. what is the surface area of the actual ramp, including the underside? enter your answer as a decimal in the box.
The surface area of the actual ramp including the underside is 16.8 ft²
The height of the actual ramp = 1.2 feet
The height of the model = 6 cm
What is the surface area of a right triangular prism?A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm
Actual base = 16 cm × 0.2 ft/cm = 3.2 ft
convert the units
9 cm = 9 cm × 0.2 ft/cm = 1.8 ft
10 cm = 10 cm × 0.2 ft/cm = 2 ft
The surface area of a right triangular prism
= (Perimeter of the base × Length of the prism) + (2 × Base Area)
Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)
= 16.8 ft²
Hence, the surface area of the actual ramp including the underside is 16.8 ft²
Learn more about the area here:
brainly.com/question/25292087
Answer:
7.2 yd² for K12
surface area of prisms: find it and. fix it
Answer:
Step-by-step explanation:
i can't solve without seeing the prism
A rectangular bathroom mirror is 4
feet tall and 7 feet wide. What is its
area?
square feet
Given -
A rectangular bathroom mirror is 4 feet tall and 7 feet wide.ie, length of the mirror, L = 4 feet and breadth of the mirror, B = 7 feet .
To find -
the area of the mirrorSolution -
As we know to find the area of rectangle we use the formula, Area = L × B
Hence, we will be doing the same.
Area = 4 × 7
Area = 28 square feet
Answer:
28 sq. feet
Step-by-step explanation:
Given:-
The length of bathroom mirror :- 4 feetWidth :- 7 feetTo find:-
The area of the rectangular bathroom mirrorSolution:-
Area of rectangular bathroom mirror:- L × B
putting the values ,
Area :- 4 × 7 sq. feet
Area:- 28 sq. feet
=
Find the area of a circle with a radius of 15 cm. (Use a = 3.14)
The area of the circle is_cm2. Round your solution to the
nearest hundredth, if applicable.
Step-by-step explanation:
Area of a circle = pi x r(squared)
= 3.14 x (15)2
= 3.14 x 225
=706.5cm2
Brainliest if correct
Answer:
The answer is D
Step-by-step explanation:
Mark brainliest
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Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify 972-317 + V8 - 28
011/2-5/7
0 1184 – 5/14
065
be
C 6/9
Question 5 Multiple Choice Worth 1 points)
(03.01 LC
Answer:
The choice A.
Step-by-step explanation:
[tex]9 \sqrt{2} - 3 \sqrt{7} + \sqrt{8} - \sqrt{28} \\ \\ 9 \sqrt{2} - 3 \sqrt{7} + ( \sqrt{2} \sqrt{4} ) - ( \sqrt{4} \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + (2 \sqrt{2} ) - (2 \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + 2 \sqrt{2} - 2 \sqrt{7} \\ (9 \sqrt{2} + 2 \sqrt{2} ) + ( - 3 \sqrt{7} - 2 \sqrt{7} ) \\ 11 \sqrt{2} - 5 \sqrt{7} [/tex]
The simplified value of in radical form is 11√2 - 5√7.
What is Radical?In mathematics, a radical is the inverse of an exponent, which is represented by the symbol '√' , also known as root. It can be a square root or a cube root, and the number preceding the symbol or radical is known as an index number or degree. This is a whole integer with an exponent that cancels out the radical.
We have 9√2 - 3√7 + √8 - √28
First, solve the radical as possible
√8= 2√2
and, √28= 2√7
So, 9√2 - 3√7 + √8 - √28
= 9√2 - 3√7 + 2√2- 2√7
= 9√2 + 2√2- 3√7- 2√7
= 11√2 - 5√7
Learn more about Radical here:
https://brainly.com/question/1369233
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Which ordered pair is a solution to the system of inequalities {y <3x-1
y>|x-2|
Answer:
(4, 4)
Explanation:
I have solved it using graph.(4, 4) is the only point which lies inside both of the inequalities.
Which of the following is NOT a unit fraction? 7/11 1/16 1/50 1/2
Answer:
7/11
Step-by-step explanation:
This is the only fraction without a 1 in its numerator.
Answer:7/11
Step-by-step explanation: unit fractions have 1 unit like 1/2 1/3 1/100 but 7/11 is not have 1 numerator
Suppose $500 is divided into two bank accounts. One account pays 15% simple interest per year and the other pays 10%. After three years there is a total of $200 in interest between the two accounts. How much was invested into the bank account that pays 15% simple interest (rounded to the nearest cent)?
Answer:
x = amount invested in the 15% account
x*.15*3 + (500-x)*.1*3 = 200
x = 333.33
so, 500-333.33 = 166.67 at 10%
Step-by-step explanation:
Answer:
x = amount invested in the 15% account
x*.15*3 + (500-x)*.1*3 = 200
x = 333.33
so, 500-333.33 = 166.67 at 10%
Step-by-step explanation:
sorry if i did it wrong
The numbers in any column row or diagonal in the gird below multiply to give an answer of 1 complete the grid
Step-by-step explanation:
Let’s just start with rows. I’m going to use a, b, and c for the missing numbers (a in the first row, b in the second, c in the third).
Row 1 — 5 × 4 × a = 1
20 × a = 1 → a = 1/20
Row 2 — b × 1 × 100 = 1
b × 100 = 1 → b = 1/100
Row 3 — 20 × 1/4 × c = 1
5 × c = 1 → c = 1/5
—
Check Columns:
5×1/100×20 = 5(20)/100 = 100/100 = 1 ✓
4 × 1 × 1/4 = 1 ✓
1/20×100×1/5 = 100/(20*5) = 100/100 = 1 ✓
Check Diagonals:
5 × 1 × 1/5 = 5/5 = 1 ✓
20 × 1 × 1/20 = 20/20 = 1 ✓
Is 1,-9 a solution to y=-9
Answer:
yes
Step-by-step explanation:
(x,y) -> (1,-9) y=-9