Explanation
Step 1
set the equation
a) let x represents the number
[tex]number=x[/tex]b) now , translate
[tex]i)Mary\text{ multiplied a number by 3}\Rightarrow x*3=3x[/tex]then
[tex]\begin{gathered} ii)shed\text{ added the result to 6} \\ 3x+6 \end{gathered}[/tex]finally
[tex]\begin{gathered} iii)\text{ she got 12, hence} \\ 3x+6=12 \end{gathered}[/tex]therefore, the equation is
3x+6=12
Step 2
now, solve the equation
[tex]3x+6=12[/tex]The subtraction property of equality states that if the same number is subtracted from both sides of an equation, then the equality still holds, so we can subtract 6 in both sides in order to isolate the term where x is, hence
[tex]\begin{gathered} 3x+6=12 \\ 3x+6-6=12-6 \\ 3x=6 \end{gathered}[/tex]finally, apply the division property of equality and divide both sides by 3
[tex]\begin{gathered} 3x=6 \\ \frac{3x}{3}=\frac{6}{3} \\ x=2 \end{gathered}[/tex]so, the number is 2
I hope this helps you
You are multiplying as many 5s and 2s as you want but you must have at least one of each. What could the last digit of the product be?
The last digits of multiplying 5s and 2s with at least one of each will be zero (0)
Multiplication of numbersFrom the question, we are to determine what the last digit of the product could be
From the given information,
We are multiplying as many 5s and 2s as we want but we must have at least one of each
Since we must have at least one of each of 5 and 2, we will always have a 5 × 2
But, 5 × 2 = 10
NOTE: 10 multiplied by any number will always result in a number with a last digit of zero (0)
Example
2 × 5 × 2 × 2 × 2 × 2 = 160
5 × 2 × 5 × 5 × 5 × 5 = 6250
Thus, the last the digit of the product will be 0
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Which function is shown in the graph? A. f(x) = x2 – 3x – 10 B. f(x) = x2 + 3x – 10 C. f(x) = x2 + x - 12 D. f(x) = x2 – 5x – 8
The graph shown have roots of x = -2 and x = 5
We could solve for x in each of the quadratic equations or we could plot the graphs of each of the quadratic equation.Then we pick the one with the roots of -2 and 5.
Plotting the graphs:
The roots of quadratic functionis the value of x when y is equal to zero.
From the graph attached above, f(x) = x² + 3x – 10 representing the blue parabola has roots of (-5, 0) and (2, 0).
This means the roots are -5 and 2.
Hence, the function in the graph is f(x) = x² + 3x – 10
Four students, Naomi, Nathan, Jonathan, and Carson, line up one behind the otherHow many different ways can they stand in line?
This is a Permutations of 4 people in a line
The answer is 24
[tex]4!=4\cdot3\cdot2\cdot1=4\cdot3\cdot2=12\cdot2=24[/tex]Carter is jogging with a velocity of 3.8 m/s when he accelerates at 3.7 m/s² for 3 s. How
fast is Carter running now?
Uniformly Varied Rectilinear Motion.
When we start to solve a physics exercise, we get the exercise data:
Initial Speed = 3.8m/s
Acceleration (a)= 3.7 m/s²
Time (t) = 3 sec.
He tells us that Carter treats at a speed of 3.8 m/s, this is the speed, since he asks us, at what speed does he treat now. Then we must calculate the final speed.
The formula to calculate the final velocity is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=V_{o}+a*t} \end{gathered}$} }[/tex]
We substitute the data in the formula used and solve:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+3.7 \ \frac{m}{\not{s^{2}} }*3 \ s } \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=3.8 \ \frac{m}{s}+11.1 \ \frac{m}{s} } \end{gathered}$} }[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_{f}=14.9 \ m/s} \end{gathered}$} }}[/tex]
Carter now runs a new speed of 14.9 m/s.What is the answer to this
Answer:
b
Step-by-step explanation:
the square root of 9 is 3 because 3*3=9
3+6=9
Your local library holds a penny drive in which people in the community are asked to donate their spare pennies to the library. When you stop by to donate some pennies, you hear someone announce that she plans to donate pennies for one month in the following manner: she will donate 1 penny today, 2 pennies tomorrow, 4 pennies the next day, and will continue to double the number of pennies that she donates each day thereafter.
The amount donated by the person follows a geometric progression, which is given by an exponential function.
First part:
The relationship between the amount donated and the day of the month is not a constant rate relationshipSecond part;
Please find attached the graph of the Amount Donated to the Days which is shaped as the graph of an exponential equationWhat is an exponential function?An exponential function is one in which the input variable is an index of a constant
A constant rate relationship is one in which at all points of the function, the ratio of the output to input stays the same or is a constant.
The given parameters are;
The Pennies a person plans to donate to the library on each day of the month, is given by the following table;
Day. Amount Donated
1. 1
2 2
3 4
4 8
First part
Required;
If the relationship between the day and the amount donated is a constant rate relationship
Solution;
Given that we have;
1/1 = 2/2 ≠ 4/3 ≠ 8/4, the relationship between the day of the month and the amount donated is not a constant rate relationship
Second part;
The shape of the graph of Day to the Amount Donated
Solution;
The sequence of the day has a constant difference of one day, which is given by the equation;
U = 1 × n
Where;
U = The day of the month
n = The number of days
The sequence for the amount donated is given by the exponential function;
S = a•r^n
Where;
a = The first term = 1
r = The common ratio = 2
U = The number of days
The graph of Amount Donated to the Days is therefore the graph of an exponential function, please see the attached graph of Amount Donated to the Day of the month
The possible questions obtained from a similar question are;
First part; If the amount donated and the days have a constant rate relationship
Second part; The shape of the graph of the Amount Donated to the Day of the month
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2. Based on the diagram, what property can we use to prove ABCD is aparallelogram?
there are 4 properties we can use to prove if it is a parallelogram, in which 3 of them involve seeing if the sides are parallel or congruent, however for those we must know the value for the angles or sides, the other property is to prove that the diagonals bisect each other.
To prove the diagonals bisect each other is to see if the point of crossing divides into equal parts.
in this case since the division of the points gives the same values for both diagonals we can say that ABCD because the diagonals bisect each other.
There are 4 triangles and 2 circles. What is the simplest ratio of circles to total shapes?
Answer:
1:3
Step-by-step explanation:
circles:total
2:4+2
=2:6
=1:3
Reason
There are 2 circles and 4+2 = 6 shapes total.
The ratio of circles to total shapes is 2:6 which reduces to 1:3
The order is important since 3:1 is different from 1:3.
a high school has 1446 students enrolled. a middle school 1/6 as many enrolled as the high school. how many ( m) are enrolled in the middle school? is this a adidtive or multiplicative question?
High school = 1446 students
Middle school = 1/6 as many as Highschool
Multiply 1/6 by the number of students enrolled at the high school.
m = 1/6 (1446) = 241
It is a multiplicative question
ZA and ZB are supplementary angles. If m/A= (7x - 20)° and
m/B = (2x - 7)°, then find the measure of ZB.
Answer:
Measure of angle B = 39
Step-by-step explanation:
(7x-20) + (2x-7) = 180 (combime like terms)
9x - 27 = 180 (move 27 to the other side)
9x = 207 (divide both sides by 9)
x = 23
2x - 7 (subsititute x with 23)
2 (23) - 7
46 - 7
39
measure of angle b = 39
What is the slope of the line that passes through the points (9,1) and (10,−1)? Write your answer in simplest form.
The slope of the linear equation that passes through the points (9,1) and (10,−1) is -2.
How to get the slope of the line?For a linear equation that goes through two points (x₁, y₁) and (x₂, y₂), the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that our line goes through the points (9,1) and (10, −1), so we can use these two values in the equation for the line, we will get:
slope = (-1 - 1)/(10 - 9) = -2/1 = -2
So the slope of the linear equation is -2.
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A basketball team played six games. In those games, the team won by 8 points, lost by 6, won by 9, won by 10, lost by 4, and won by 7. What was the mean difference in game scores over the six games?
The mean difference in game scores over the six games is 4.
What is mean?The ratio of the overall sum of data to the total number of data sets is known as the mean. Mean is often computed by adding up all the data and dividing it by the total number of data.
Given that a basketball team played six games. In those games, the team won by 8 points, lost by 6, won by 9, won by 10, lost by 4, and won by 7.
The data's mean difference will be determined as follows:
Mean = ( 8 - 6 + 9 + 10 - 4 + 7 ) / 6
Mean = 4
Therefore, the mean difference in game scores over the six games is 4.
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Write an equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex.
An equation of the parabola that has the same shape as the graph of f(x) = 4x², but with the point (10,4) as the vertex is y = 4x² - 80x + 404.
What is the vertex form of the parabola?The standard vertex form of the parabola is given by,y = a(x - h)² + k where (h, k) is the vertex.
Real numbers, a, h, and k are included here, where a ≠ 0. A point on the parabola is represented by the variables x and y, respectively.Given:
f(x) = 4x²
Vertex = (10,4)
a = 4
The value of a in the vertex form of the equation is taken to be 4 since the coefficients of x² must match for the parabola to have the same shape as the given parabola.
The equation can be written as,
y = a(x - h)² + k where (h, k) is the vertex.
Replacing the value of the vertex, we get
y = 4(x - 10)² + 4
y = 4(x² - 20x + 100) + 4
y = 4x² - 80x + 400 + 4
y = 4x² - 80x + 404
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How to do this problem
From the graph, the y-intercept is the point (0,40). We can calculate the slope of the line, given two points, using the following formula
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2)_{} \\ \Rightarrow m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} (x_1,y_1)=(0,40),(x_2,y_2)=(2,0) \\ \Rightarrow m=\frac{0-40}{2-0}=-20 \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line is
[tex]\begin{gathered} y=mx+b \\ \Rightarrow y=-20x+40 \end{gathered}[/tex]The answer is y=-20x+40
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go?
The probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go is 0.3240
Probability:
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes.
Given,
Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita reports that 48% of its customers order their food to go.
Here we need to find the probability that, in a random sample of 50 customers at Anita's, exactly 3 order their food to go.
Let us consider this as,
Binomial Problem with
n = 5 and
By converting the percentage into decimal value,
=> 48/100 = 0.48
p(to go) = 0.48
Then the value is,
P(x=3) = 5C3(0.52)^3*(0.48)2
P(x=3) = 0.3240
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What is the missing angle
Answer:
45 degrees
Step-by-step explanation:
The triangle is a 45, 45, 90 meaning that both angles other than the 90 are the same.
Another way to solve is you know that a triangle's angles = 180
Take the 180 and subtract 90 for the right angle
and then subtract 45 for the labeled angle and your answer is 45
Please help me find the horizontal asymptote.
Answer:
[tex]y=3/2[/tex]
Step-by-step explanation:
[tex]f(t)=\frac{3t^{1/3}}{(64t^2 +4)^{1/6}} \\ \\ =\frac{3}{(64+4t^{-2})^{1/6}} \\ \\ \\ \lim_{t \to \infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \\ \lim_{t \to -\infty} f(t)=\frac{3}{64^{1/6}}=3/2 \\ \\ \therefore y=3/2[/tex]
Solve for x and simplify the answer
2x^2+2x=-3
8x^2 - 9 when x = -4
Answer:
119
Step-by-step explanation:
substitute x = - 4 into the expression
8x² - 9
= 8(- 4)² - 9
= 8(16) - 9
= 128 - 9
= 119
The following sequence is a geometric sequence
17
,
51
,
153
,
459
,
1377
,
...
Find the sum of the first 13 terms of this sequence.
What is the common ratio for this sequence?
r
=
What is the index of the final term of this sum?
last index =
What is the sum?
Sum =
Answer:
13,551,737
Step-by-step explanation:
You want the sum of the first 13 terms of the geometric sequence with first term 17, and successive terms 51, 153, ....
Common ratioThe common ratio is found by dividing a sequence term by the one before it:
r = 51/17 = 3
The common ratio is 3.
IndexThe index of the 13th term of the sequence is n = 13.
SumThe sum of n terms of a geometric sequence with first term a1 and common ratio r is ...
Sn = a1·(r^n -1)/(r -1)
For a1 = 17, r = 3, and n = 13, the sum is ...
[tex]S_{13}=17\cdot\dfrac{3^{13}-1}{3-1}=17\cdot\dfrac{1594322}{2}=\boxed{13,\!551,\!737}[/tex]
Dina goes to a carnival. Some rides at the carnival have a height requirement, but others do not. Dina is tall enough to go on all rides.
What is a mathematical question you can ask about this situation? What information would you need to know to answer your question?
The mathematical question that can be asked in a situation when Dina goes to a carnival and some rides have a height requirement is how many extra centimeters of height Diana has? The information required to solve this question is the required height for the ride and the height of Diana.
According to the question,
We need to ask a mathematical question. Let's solve a mathematical question in the given situation by taking one example.
If the required height to ride is 150 cm and the height of Diana is 165 cm, how many extra centimeters of height Diana has than the required height?
Solution:
Required height = 150 cm
Dian's height = 165 cm
Extra height = Diana's height - required height of the ride
Extra height = 165 cm - 150 cm
Extra height = 15 cm
Hence, in this supposed situation, Diana's height is 15 cm extra than the required height of the ride.
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Please help I’ll mark you as brainliest if correct!!
Answer:
x (y + 1)
Step-by-step explanation:
Simplify the following:
x y + x
Factor x out of x y + x:
Answer: x (y + 1)
What is the area of this face?
4 in.
4 in.
4 in.
1 in.
1 in.
16 in²
15 in²
17 in²
12 in²
The area is the entire amount of space occupied by a flat (2-D) surface or shape of an object.
The area of the face is 17 in²/17 inches2.
How to find the area of the face?The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area.
Draw a square on a piece of paper using a pencil. A 2-D figure, that is.
The term "Area" refers to the area that a shape occupies on paper.
By squaring the side's length, the area of each face may be calculated.
To determine the overall surface area of the cube, multiply the area of each face by the number of faces.
For big square,
a = 4 in
a*a = 4 * 4 inches
[tex]a^{2}[/tex] = 16 in²
For another small square,
a = 1 in
[tex]a^{2}[/tex] = 1*1 = 1 in²
In total,
[tex]a^{2}[/tex] = 16 + 1 = 17 in²
Therefore, the area of the face is 17 in²
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What different types of funding sources are available to businesses? Explain why a business should use a particular type of fund. Most companies use a mix of these funds, however. Provide examples that justify this business decision.
The types of funding sources that are available to businesses include:
Family and FriendsEquity ProvidersDebt Providers Institutional Investors.A business can use a particular type of fund that meets its goals.
A reason why companies van use a mix of different funding is to improve a company's financial strength.
What is funding about?Providing resources to finance a need, a program, or a project is the act of funding. While usually in monetary form, this can also refer to an organization or company's time or effort.
Having adequate funding enables your firm to seize any possibilities that present themselves, such as investing in new goods and services that can advance your company. Working capital can act as a safety net when your company requires additional funding.
Although there are many diverse reasons why businesses want financing, there are certain frequent ones. Business grants and loans may be used for working capital, equipment purchases, staff expansion, or even the refinancing of existing debt to lower monthly payments.
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Solve for x: (round your decimal to 4 places)
In(x + 2) = 4
The value of x is 52.5981
The given equation is:
In(x + 2) = 4
Taking log on the right hand side of the equation, we get
x + 2 = [tex]e^{4}[/tex]
The value of [tex]e^{4}[/tex] is 54.59815
⇒ x + 2 = 54.59815
Subtract 2 on both the sides of the equation
⇒ x = 54.59815 - 2
⇒ x = 52.59815
Rounding 52.59815 to 4 places, we get
⇒ x = 52.5981
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Rectangle ABCD is congruent to rectangle EFGH. If side EF is 8 feet and side BC is 9 feet, what is area of rectangle EFGH?
Answer:
64 is the area!
- love bri <3
|x - 3|= 2x - 15
8 - 2|6 - x|= 20
By solving both equations we get x =:
1. x = 12
2. x = 28/3
solution1. |x - 3| = 2x - 15
|x - 3| - 2x = 2x - 15 - 2x
by simplifying,
- 2x + |x - 3| = -15
- 2x + x -3 = -15 and -2x - (x - 3) = -15
by solving equation ,
= -x -3 = - 15
= -x = -12
x = 12
2. 8 - 2|6 - x|= 20
6 |6 - x| = 20
6 |-x + 6| = 20
dividing both side with 6,
(6 |-x + 6|)/6 = 20/6
| -x + 6| = 10/3
add 6 on both sides,
x - 6 + 6 = 10/3 +6
x = 28/3
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In a class of 50 students, on average, 10 will be left-handed. If a class includes 25 "lefties", estimate how many students are in the class.
The total number of lefties present in the class are 125.
What is meant by the term percentage?Percentage is an assessment of a portion in relation to a whole, frequently expressed as how many of some there are per 100.A group with half girls as well as half boys is an instance of a situation in which the percentage of boys with in group is equal to 50%.For the given question;
The total students in the class are 50.
There are 10 out of 50 on an average students be left-handed.
Let the percentage of left handed be 'x'.
Then, x% of 50 = 10
x = 10×100 / 50
x = 20%.
Now the average number of left-handed students are 25.
The total students will be.
Let 'y' be the total number of students.
Then, 25 is the 20% of y.
20% of y = 25.
y = 25 ×100 / 20
y = 125
Thus, the total number of lefties present in the class are 125.
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make f the subject when d= 2(1-f) / f-4
[tex]d(f-4)=2(1-f)\\\\frac{d(f-4)}{d} =\frac{2(1-f)}{d} \\f-4=\frac{2(1-f)}{d} \\f=\frac{2(1-f)}{d} +4[/tex]
Attached is the solution
Answer:
Step-by-step explanation:
d= 2(1-f) / f-4
d = 2 - 2f / f-4
d = 1/2 - 2f - f
d = 1/2 - f
0=1/2-f-d
f = 1/2 - d
When solving the following system of equations, which variable would be the easiest to solve for? 5x+3y=22 4x-2y=16
Variable x would be easier to solve for.
Step - by - Step Explanation
What to find?
• The value of x.
,• The value of y.
,• The variable that was easier to solve.
Given:
5x+3y=22
4x-2y=16
Using elimination method,
First solve for x.
To solve for x, multiply through the first equation by 2 and then multiply through the second equation by 3.
10x + 6y = 44 _____________(3)
12x - 6y = 48 ______________(4)
Add (3) and (4)
22x = 92
Divide both-side of the equation by 22
x = 92/22
Reduce the fraction by 2.
x =46 / 11
To solve for y,
Multiply through the first equation by 4 and through the second equation by 5.
20x + 12y = 88 _________________ (5)
20x - 10y = 80 __________________(6)
Subtract equation 6 from 5.
22y= 8
Divide both-side of the equation by 22.
y = 8/22
We can reduce the fraction by 2.
y = 4 / 11
Judging from the steps above, we can deduce that the variable that was easier to solve is x.
Answer: x of first equation
Step-by-step explanation: