Given the expression 6(5+3)
The expression shows that 6 was factored out from the bracket
evaluate the expression in parenthesis
= 6(5+3)
= 6(8)
This shows that the factors of the expression are 6 and 8
A scientist begins with 100 milligrams of a radioactive substance, which decays exponentially.after 9 hours 55mg of the substance remains How many milligrams will remain after 21 hours? Round the answer to the nearest whole number and include units
We have that the general expression for a function with exponential growth or decay is:
[tex]f(t)=ab^t[/tex]where 'a' represents the initial value, 'b' represents the growth or decay and t represents the time.
In this case, we have that a = 100, since that is the initial population (100 mg of radioactive substance). Also, since we have that after 9 hours, 55 mg of the substance remains, we have the following equation:
[tex]f(9)=55[/tex]now, given the exponential function, with a = 100, we have:
[tex]f(t)=100b^t[/tex]then, combining both expressions, we get:
[tex]f(9)=100b^9=55[/tex]solving for b, we have:
[tex]\begin{gathered} 100b^9=55 \\ \Rightarrow b^9=\frac{55}{100} \\ \Rightarrow b=\sqrt[9]{\frac{55}{100}}=0.935 \\ b=.935 \end{gathered}[/tex]then, the function is defined as follows:
[tex]f(t)=100\cdot(0.935)^t[/tex]finally, to find out how many milligrams will remain after 21 hours, we can make t = 21 and evaluate the function:
[tex]\begin{gathered} t=21 \\ \Rightarrow f(21)=100(0.935)^{21}=24.38 \\ f(21)=24.38mg \end{gathered}[/tex]therefore, there will be 24.38mg after 21 hours
2f = -12f=??[tex]2f = - 12 \\ \\ f = [/tex]
Given:
2f = -12
We are required to find the value of f.
To find f, divide both sides of the equation by 2.
We have:
[tex]\begin{gathered} \frac{2f}{2}=-\frac{12}{2} \\ \\ f\text{ = -6} \end{gathered}[/tex]ANSWER:
f = -6
Find the quotient.0.56/−0.7
ANSWER
-0.8
EXPLANATION
The division between a positive number and a negative number gives as a result a negative number. With this in mind, we can do the division as if the numbers were both positive and then add the minus sign to the result:
Adding the minus sign, the result is -0.8
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation The slope is passes through the point (1 The unit rate is $ Vmin. If the graph ofa proportional relationship r), then r equals the slope and unit rate.
Let:
(x1,y1)=(0,0)
(x2,y2)=(1,3.40)
The slope is:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{3.40-0}{1-0}=\frac{3.40}{1}=3.40[/tex]The unit rate is:
[tex]\frac{3.40}{\min }[/tex]Hi can someone please explain this?
Image is attached
Answer:
B
Step-by-step explanation:
Since triangles BCD and PQR are similar, we can find BD through the three proportional sides. Line BD is to PR and option B is the only answer where BD and PR are both numerators/denominators in this case the denominators of the two fractions. Hope this helps!
As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?5x + 6y = 182x – 3y = 12factor:
Given the equations
[tex]\begin{cases}5x+6y=18 \\ 2x-3y=12\end{cases}[/tex]First, she multiplied the second equation by 6:
[tex]\begin{gathered} 6\cdot(2x-3y)=6\cdot12 \\ 6\cdot2x-6\cdot3y=6\cdot12 \\ 12x-18y=72 \end{gathered}[/tex]You have to determine the factor to multiply the equation 5x+6y=18 to be able to add both equations and eliminate one of the variables.
To do so, compare the coefficients of the like terms:
5x and 12x, "12" is not a multiple of 5, so there is no factor that when multiplied by 5x will give 12x as a product.
6y and 18y, 18 is a multiple of 6, if you multiply 6y by 3 the product will be 18y.
So, the factor you have to use to multiply the equation and eliminate one variable is 3.
Make the following conversions. Round your answers to 2 decimal places, where necessary.5 hours 10 minutes toa. Minutes: ? minb. Hours: ? hr
Let's do the math for this question.
The area of the scale model of a playground is 6 square yards. The scale model is enlarged by a scale factor of 3 to create the actual playground. What is the area of the actual playground?
The actual area of the playground is 54 square yards
How to determine the area?The given parameters are
Area of the scale model = 6 square yardsScale factor of dilation = 3The actual area of the playground is calculated as
Actual area = Area of the scale model * Scale factor of dilation^2
Substitute the known values in the above equation
So, we have
Actual area = 6 * 3^2
Evaluate the exponent
Actual area = 6 * 9
Evaluate the product
Actual area = 54
Hence, the value of the area is 54
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In the expression 5^2, the 2 represents the _________________.
A: product
B: sum
C: base
D: exponent
The number, 2, in the given expression represents the exponent. The correct option is D: exponent
The exponent in a mathematical expressionFrom the question, we are to determine what the number, 2, represents in the given expression
The given expression is
5^2
That is,
5²
An exponent is a number or letter written above and to the right of a mathematical expression called the base
In the given expression, the number 2 is written above and to the right of 5. The number 5 is the base in the expression.
Thus,
The 2 represents the exponent
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HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
(3.11), (310/100),(1/3),(3/10),(2/-3) Hope I helped
Step-by-step explanation:
310/100 when divided gives us 3 10/100 or in simple form 3.1
1/3 is the smallest rational number but in simple form it is equal to 0.3(3) never ending multiplication of 3
3.11 is displayed in simple form so there is no need to change the number
3/10 can be displayed in simple form as 0.3( remember when dividing by a multiplication of 10 move the decimal point to the left of the lumber by the amount of zeros)
2/-3 since we are dividing the number by a negative number the result will end up in the negatives so lets think of it as 2/3 and later add the negative sign. 2/3 is equal to 0.6(6) and since we are dividing by a negative the result will be -0.6(6)
If a car will go 108 miles on a 6 gallon of gasoline in city driving. What is the rate in miles per gallon.
To find the rate in miles per gallon, divide the number of miles by the number of gallons of gasoline:
[tex]\frac{108\; \text{miles}}{6\; \text{gallons}}[/tex]Reduce the fraction by 6:
[tex]\frac{108}{6}=18\text{ miles per gallon}[/tex]The rate in miles per gallon is 18.
given the function. calculate the following values.
Answer:
[tex]5, \sqrt{2}, 10[/tex]
Step-by-step explanation:
[tex]x=-7 \implies x<0 \implies f(-7)=5 \\ \\ x=0 \implies x \geq 0 \implies f(0)=\sqrt{2(0)^2+2}=\sqrt{2} \\ \\ x=7 \implies x \geq 0 \implies f(7)=\sqrt{2(7)^2+2}=10[/tex]
what percent of 51 is 127.5?20.67 is 42.5% of what?
a) We have to find what percent of 51 is 127.5.
As 127.5 is larger than 51, we expect a percentage larger than 100%.
We can find the percentage by dividing the part, 127.5, by the total, 51, and multiplying by 100%:
[tex]\frac{127.5}{51}\cdot100\%=2.5\cdot100\%=250\%[/tex]b) We have to find the value x of which 42.5% is equal to 20.67.
We can write this as:
[tex]\begin{gathered} x\cdot\frac{42.5}{100}=20.67 \\ x\cdot0.425=20.67 \\ x=\frac{20.67}{0.425} \\ x\approx48.63 \end{gathered}[/tex]Answer:
a) 127.5 is 250% of 51.
b) 20.67 is 42.5% of 48.63.
A brick has dimensions of110. cm x 655 cm x 1330 cm.What is the volume of the brick in cubic meters?
Answer: We have to find the volume of the brick, the formula for the volume is as follows:
[tex]V=l\times w\times h\Rightarrow(1)[/tex]Identifying the known variables and plugging in the equation (1) gives the following answer:
[tex]\begin{gathered} l=110cm \\ w=655cm \\ h=1330cm \end{gathered}[/tex]The volume therefore is:
[tex]\begin{gathered} V=(110cm)\times(655cm)\times(1330cm) \\ V=95,826,500cm^3 \end{gathered}[/tex]Angela purchase a shirt for $14.65 a pair of jeans for $21.99 and she was charged $2.93 tax how much change should she receive if she paid with a $50 bill
The cost of the shirt = $14.65
The cost of the pair of jeans = $21.99
Tax = $2.93
Amount paid = $50
Change = Amount paid - (Cost of shirt + Cost of jeans + tax)
Change = 50 - (14.65 + 21.99 + 2.93)
Change = 50 - 39.57
Change = $10.43
a hotel manager has 12 diferent promotional events,plans to run 4 weeks, how many events can she run
Answer: 3 per week.
Step-by-step explanation: 3 x 4 = 12.
Which picture shows a properreflection across the red dashed line?АB
When you reflect a point across the red dashed line y = x, the x-coordinate and y-coordinate change places;
If you reflect over the red dashed line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
Thus, the picture that shows a proper reflection across the red dashed line is B
Is this the right answer to the question. Not 100% sure.
Answer:
Yes, you are correct. Lines l and m are parallel, so corresponding angles are congruent. It does follow that x = 60.
Determine all solutions to the equation radical 2 times cosine 2 times x equals sine squared x plus cosine squared x on the interval [0, 2π).
Given
The equation,
[tex]\sqrt{2}\cos2x=\sin^2x+\cos^2x[/tex]To determine all the solutions in the interval [0, 2π).
Explanation:
It is given that,
[tex]\sqrt{2}\cos2x=\sin^2x+\cos^2x[/tex]Since
[tex]\sin^2x+\cos^2x=1[/tex]Then,
[tex]\begin{gathered} \sqrt{2}\cos2x=\sin^2x+\cos^2x \\ \Rightarrow\cos2x=\frac{1}{\sqrt{2}} \\ \Rightarrow2x=\cos^{-1}(\frac{1}{\sqrt{2}}) \\ \Rightarrow2x=\frac{\pi}{4} \\ \Rightarrow x=\frac{\pi}{8} \end{gathered}[/tex]Hence, the solutions of the given equation in [0, 2π) is,
[tex]a)\text{ }x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}[/tex]
elenas bed measures 3‘ x 6‘ on the scale drawing what are the actual measurements of her bed
Using proportions, supposing a scale of 1 inch = 3 feet, the actual measurements of her bed are given by: 9 ft x 18 ft.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division, from the relations built in the problem.
One example of application of proportions is for scale problems, as the actual scale and the drawing length are compared to find the actual length of the object drawn.
In the context of this problem, the scale is given by:
1 inch = 3 feet.
The drawn length of the bed is given by:
3 inches x 6 inches.
Hence the actual length is given by:
9 feet x 18 feet.
As:
3 x 3 = 9.6 x 3 = 18.What is the missing information?The scale of the drawing is missing, hence we are going to suppose that it is 1 inch = 3 feet.
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what is the answer too 14:10=:55
Answer: Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The height of the object based on the information is 1963 feet.
How to calculate the height?It should be noted that a function is important to show the relationship between the variables given in the data.
In this case, the function given for the height of the object is given as:
h = 16t² + 1899
where t = time
When the time is 2 seconds, the height will be:
h = 16t² + 1899
h = 16(2)² + 1899
h = 64 + 1899
h = 1963
The height is 1963 feet.
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The function g is defined as follows.
g(x)=x² +1
If the graph of g is translated vertically upward by 4 units, it becomes the graph of a function h.
Find the expression for h (x).
Answer:
Use that steps to find your answer
Answer:
h(x) = g(x) + 5 = x² + 5
Step-by-step explanation:
Since the graph is translated vertically upward by 4 units, there is no change in the x values; for the same x value the new y value is +4 times the old y value
3 The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Large Car Large Truck Average Mass (kilograms) 1,354 1,985 2,460 Parta
The average mass of the large truck is 2460 kg and the average mass of the small car is 1354 kg.
Based on the given data, the mass of the large truck is 1106 kg.
Now, rounding off to the nearest hundred, the average mass of the larger truck is 2500 kg and the average mass of the small car is 1400 kg.
So, the larger truck is 1100 kg heavier than than the smaller car.
Alyssa paints 3 walls blue. Each of the walls is 8.3 feet tall and 7.5 feet wide. Round the length and width to the nearest whole number. Then estimate the area that Alyssa will paint. Write equations to show your work. Once, you have done everything find the exact area. Write equations to show your work. Then, compare your estimate to the exact answer. Why is your answer reasonable?
The equation to show the area Allysa will paint is Area = 3(Height x Width) = 3( 8.3ft * 7.5ft) and the area is 186.75 ft²
How to solve Algebraic Word Problems?We are given the dimensions of wall as 8.3ft by 7.5ft.
Thus;Height of wall = 8.3 ft
Width of wall = 7.5 ft
Now, there are total 3 walls in the bedroom to be painted blue.
The formula to calculate the area of one wall is;
A = Height x WidthFormula to calculate the area of four walls will be;
Area = 3(Height x Width) = 3( 8.3ft * 7.5ft)
= 3 (62.25 ft²)= 186.75 ft²
Thus, an area that Alyssa will paint = 186.75 ft²
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Solve for x using the "Quadratic Formula". You MUST show every level of work (like you saw in the lesson) in order to receive full credit.
3x^2-5x+1
The solution to the quadratic equation 3x² - 5x + 1 using quadratic formula is; x = (5 + √13)/6 or (5 - √13)/6
How to use the quadratic formula?
The general form of a quadratic equation is given as;
ax² + bx + c = 0
The quadratic formula that is used to solve this is given by;
x = [-b ± √(b² - 4ac)]/(2a)
Now, we are given the quadratic equation as;
3x² - 5x + 1
Thus, using quadratic formula we have;
x = [-(-5) ± √((-5)² - (4 * 3 * 1))]/(2 * 3)
x = [5 ± √(25 - 12)]/6
x = (5 ± √13)/6
x = (5 + √13)/6 or (5 - √13)/6
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Simplify the expression
10 - 2(-10x + 7)
Answer: 20x - 4
Step-by-step explanation:
10 - 2(-10x+7)
Distribute the -2:
10 + 20x -14
Combine Like Terms:
20x - 4
Find the 29th term of an arithmetic sequence with a1 = 2 and d =5
Arithmetic Sequence is a sequence of numbers such that the difference between each number is constant. The formula for the arithmetic sequence is given by;
[tex]a_n=a_1+(n-1)d[/tex]where An is the last term
A₁ is the first term
n is the number of terms (or number in the sequence)
d is the common difference
In our problem we are given the first term (a₁) = 2, a common difference of 5 (d = 5), and the number of terms which is 29 (n = 29).
Now in order to find the 29th term of the sequence (a₂₉), we just need to follow the formula;
[tex]\begin{gathered} a_{29}=a_1+(n-1)d_{} \\ a_{29}=2_{}+(29-1)5 \\ a_{29}=2_{}+(28)5 \\ a_{29}=2_{}+140 \\ a_{29}=142 \end{gathered}[/tex]Therefore the 29th term of the arithmetic sequence is 142.
Formula: an=a1 + (n-1) x d
a1=2
d=5
n=29
plug in the values: an= 2 + (29-1) x 5 = 142
SO THE ANSWER IS : 142
Translate "the sum of m and 2.33 multiplied by s is 52.25" into an algebraic equation. Do not solve the equation.
Answer:
[tex](m + 2.33) \times s = 52.25[/tex]
:)
y=5x+50 in standard form
Answer:
-5x + y = 50
Step-by-step explanation:
to formula for standard form is Ax + By = C
the formula (y=5x+50) is in slope-intercept form, which is y=mx+b
to write (y=5x+50) in standard form, move the 'mx' (which in this case is 5x) to the other side of the '=' or also known as the equation:
y = 5x + 50
y - 5x = 5x - 5x + 50
y - 5x = 50
(here, we subtracted 5x on both sides of the equation to 'move it')
Ax = -5x
By = 1y = y
C = 50
so, to write it in the standard form:
-5x + y = 50
