Explanation
the origins mean the center of the cartessian plane, it is the point with coordinate
[tex](0,0)[/tex]Answer:
the origin is located at the intersection of the vertical and horizontal axes and the distance to all can be measured from this point..(0,0)
3. Select all expressions that are equivalent to (2n + 6)(n + 3)a. 2(n? + 6n +9)b. 2n? + 6n + 18c. 2n2 + 12n + 18d. 12n + 18e. 2(n + 3)(n + 3)f. 2(n + 3)?
Select all expressions that are equivalent to (2n + 6)(n + 3)
we have
(2n + 6)(n + 3)
apply distributive property
2n^2+6n+6n+18
2n^2+12n+18
Verify each option
option A
2(n^2 + 6n +9)=2n^2+12n+18 -------> is ok
option B
is not correct
option C
is correct
option D
is not correct
option E
2(n + 3)(n + 3)= (2n + 6)(n + 3) ------> is correct
option F
2(n + 3)^2=2(n^2+6n+9)=2n^2+12n+18 -----> is ok
therefore
answers areA, C, E, Fthe sum of the interior angles of an octagon is 1080 degrees. each angle is six degrees larger than the angle just smaller than it. what is the measure of the fourth angle?
The measure of the fourth angle that is x and the value is 133°
What is an octagon?A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.
Let the 8 interior angles of the octagon be:
x-12, x-8, x-4, x, x+4, x+8, x+12, x+16.
Their sum = 8x+16 = 1080, or
this implies 8x = 1080–16 = 1064
thus on further solving we get x = 133
Hence the sixth angle = x+8 =141 degrees.
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b. Express the mass of 21,000 molecules of oxygen in scientific notation.
grams
(Type your answer using the appropriate number of significant digits. Type you
The mass of 21,000 molecules of oxygen in scientific notation is expressed as 1.1151 x [tex]10^{-28}[/tex] grams in the proper significant digits.
What are Significant Digits?The number that is provided as digits is tried and established using significant figures. A meaningful representation of numbers is carried by these digits.
The crucial or important digits that can accurately represent the exact meaning of a certain number are known as the significant figures of that number.
Frequently, significant digits are employed in place of figures. By counting out each of the values beginning with the first non-zero digit on the left, we can use it to determine the number of significant digits.
The molecular mass of Oxygen is seen as 32 grams.
So, 6.023 x [tex]10^{23}[/tex] molecules of oxygen have mass as 32 grams
So, one molecule of oxygen has mass = [tex]\frac{32}{6.023 * 10^{23}}[/tex] grams
= 5.31 x [tex]10^{-23}\\[/tex] grams
So, 21,000 molecules will have mass = 21,000 x 5.31 x [tex]10^{-23}\\[/tex] grams
= 111510 x [tex]10^{-23}\\[/tex] grams
= 1.1151 x [tex]10^{-28}[/tex] grams
Thus 21000 molecules of oxygen have a mass of 1.1151 x [tex]10^{-28}[/tex] grams.
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Determine if it has a minimum of maximum and what that value is whilst also Identifying the domain and range
Hello!
First, let's rewrite the expression here:
[tex]f\mleft(x\mright)=-2x^2+12x-15[/tex]We will have to find the coefficients a, b and c:
• a ,= -2;
,• b ,= 12;
,• c ,= -15;
As we can see, coefficient a is negative. It means that the parabola will face downwards and have a maximum value.
We can obtain this point by using the two formulas below to calculate the coordinates (x, y) of this point, look:
[tex]\begin{gathered} X_V=\text{ }-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \end{gathered}[/tex]As we know the coefficients, let's replace the values in the formulas:
Xv:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{12}{2\cdot(-2)}=-\frac{12}{-4}=-(-3)=+3 \\ \\ X_V=3 \end{gathered}[/tex]Now let's find Yv:
[tex]\begin{gathered} Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{12^2-4\cdot(-2)\cdot(-15)}{4\cdot(-2)}=-\frac{144-120}{-8}=-\frac{24}{-8}=-(-3)=+3 \\ \\ Y_V=3 \end{gathered}[/tex]Doing this, we obtained the coordinate of the maximum point (x, y) = (3, 3).
As it doesn't have any restrictions, the domain will be: [-∞, +∞].
[tex]-\infty\: We have one restriction in the range, do you remember which?The maximum value will be when y = 3, so the range is [-∞, 3].
Look at the graph of this function below:
The table represents an absolute value function f(x).
x f(x)
−2 4
−1 3
0 2
1 1
2 0
3 1
4 2
5 3
6 4
What are the vertex and range of the function?
Vertex (0, 2), Range: {y | 0 ≤ y < ∞}
Vertex (0, 2), Range: {y | 2 ≤ y < ∞}
Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
Vertex (2, 0), Range: {y | 2 ≤ y < ∞}
From the table of the absolute value function the vertex and the range of the function is Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
What is vertex of a function?the vertex represents the point where the graph crosses the axis of symmetry. This point usually occurs mid way the graph.
Examining the table shows that the coordinates of the vertex is
2 for the x coordinate0 for the y coordinateTherefore vertex ( 2, 0)
What is range ?The range is the point covered by the y coordinate. Since the ertex has the y coordinate as zero, this means that o is part of the values of the y making the third option the best choice
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Answer: Option 1
Step-by-step explanation:
just took the test
There are 100 centimeters (cm) in 1 meter (m) Choose the correct answers from the drop-downs lists to complete the sentence. To convert 4 m to centimeters Choose 4 by C
given: 100 cm = 1 meters
We need to convert 4 m to cm
so,
[tex]4m=4\cdot100\operatorname{cm}=400\operatorname{cm}[/tex]Which is the area of the figure, in square units
The area of the given figure ABCDEFG is 28 units².
What do we mean by area?The area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.So, the area of the given figure:
First, let's mark all the points and name the figure ABCDEFG.We can clearly see that side CE = CB = BD = EC = 4 units making ECBD a square.And, rest 3 triangles are divided from the figure of different dimensions.Now, calculate areas separately and as as follows:
Area of square ECBD:
a²4²16The area of square ECBD is 16 units².
Area of triangle ACB:
1/2 × b × h1/2 × 4 × 31/2 × 126The area of triangle ACB is 6 units².
Area of triangle CEG:
1/2 × b × h1/2 × 2 × 41/2 × 84The area of triangle CEG is 4 units².
Area of triangle BDF:
1/2 × b × h1/2 × 1 × 41/2 × 42The area of triangle BDF is 2 units².
Area of the given figure: 16 + 6 + 4 + 2 = 28 units²
Therefore, the area of the given figure ABCDEFG is 28 units².
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How do I use the graphs to evaluate the expressions
Given the graph, we cam find f(-3)+g(-2) below.
Explanation
[tex]\begin{gathered} f(-3)=-2 \\ g(-2)=0 \\ f(-3)+g(-2)=-2+0=-2 \end{gathered}[/tex]Answer: -2
function c gives the cost,in dollars, of buying n apples. what does each expression or equation represent in this stiuation1.C(5)=4.502C(2)
1)
From the function given, the cost of 5 apples is $4.50
5 apples cost $4.50
Convert. 260 milliliters to centiliters.
Answer:
26 centilitres.
Explanation:
First, we start by recalling the standard conversion between millilitres and centilitres.
[tex]10\text{ milliliter = 1 centileter}[/tex]Let 260 milliliters = x centiliters
We express it as a ratio:
[tex]\frac{10\text{ }milliliters}{1\text{ centiliter}}=\frac{260milliliters}{x\text{ centiliters}}[/tex]Cross multiply to solve for x:
[tex]\begin{gathered} 10x=260\times1 \\ x=\frac{260}{10} \\ x=26\text{ centiliters} \end{gathered}[/tex]Therefore, 260 millilitres is 26 centiliters.
which best describes your ability determine best method for solving a system of linear equations
The best method for solving a system of linear equations is the substitution method.
What is a system of equations?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
We have been given the system of the equations as;
y = -2x + 2
y = 4x + -4
Thus, y = -2 x + 2 ........ equation number 1
y = 4 x - 4.............. equation number 2
Then substitute equation number 2 in equation number 1
4 x - 4 = -2 x + 2
4 x + 2 x = 2 +4
6 x = 6
so, x = 1
Now substitute x= 1 in equation number 2;
Therefore y =( 4 × 1) - 4
y = 4 - 4 = 0
For x = 1 and y = 0
Hence, the best method for solving a system of linear equations is the substitution method.
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The complete question is;
which best describes your ability to determine the best method for solving a system of linear equations. Then solve the system.
y = -2x + 2
y = 4x + -4
Tonya spends 55% of her savings on a new dress. If she saved $120, how much was the dress? mathematical representation.
a50/23 = b
b.0.55 x 120 = d
c.190x = 45; change the decimal to a %
d.x/45 = 190; change the decimal to a %
e.55d = 120
f.23 x 50 = b
g.23/50 = b
h.2.50/45 = p
i.2.50p = 45
j..23 x 50 = b
k..45 x 190 = x
l..55d = 120
The coat of the dress based on the percentage is $66.
How to calculate the value?From the information, it was stated that Tonya spends 55% of her savings on a new dress and that she saved $120.
Let the cost of the dress be represented as x
Therefore, the appropriate information given I'll be expressed as:
= 55% × 120 = x
0.55 × 120 = x
Multiply
x = 66
The amount spent is $66.
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MTR Apply Mathematics During a drought, the water level of a lake
decreases 3 inches every week. What will be the change in the water level
of the lake if the drought lasts for 7 weeks?
The level of water decreases would be 21 inches in 6 weeks if the water level of a lake decreases by 3 inches every week.
What are Arithmetic operations?The addition, subtraction, division, and multiplication of built-in functions can also be used to specify arithmetic operations. The term "arithmetic operator" refers to the operator that executes the calculation.
We have been given that a lake's water level decreases 3 inches every week when there is a drought.
We have to determine the lake's water level looks like after a seven-week drought.
As per the given condition,
Level of water decreases a week = 3 inches.
Level of water decreases in 6 weeks = 7 × 3 = 21 inches
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find the final amount of money in an account if $3,100 is deposited at 2.5% interest compounded quarterly and the money is left for 5 years
Given -
Money deposited in an account = $3,100
Interest rate = 2.5% compounded quarterly
Time = 5 years
To Find -
The final amount of money =?
Step-by-Step Explanation -
As we know there are 4 quarters in a year.
So,
In five years, there are 20 quarters.
On applying the formula:
Final Amount =
[tex]\begin{gathered} =\text{ }P\times(1+i)^n \\ \\ =\text{ 3100 }\times(1+\text{ 0.025/4})^{20} \\ \\ =\text{ 3100}\times(1\text{ + 0.00625})^{20} \\ \\ =\text{ 3100}\times(1.00625)^{20} \\ \\ =\text{ 3100}\times1.1327 \\ \\ =\text{ 3511.3939} \end{gathered}[/tex]Final Answer -
The final amount of money = $3511.4
What is the degree of the power function represented in the table f(x)
-3, -2, -1, 0, 1, 2, 3
The degree of the power function represented in the table f(x) is 2.
How to illustrate the information?In order to find the degree of the power function represented in the given table, you must find the difference of the y-values.
The second difference is illustrated as:
2 - 6 = -4.
-2 - 2 = -4
-6 - (-2) = -4
This illustrates that the second differences are constant.
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What is the degree of the power function represented in the table?
1
2
3
4
x h(x)
−2 −8
−1 −2
0 0
1 −2
2 −8
graph the line with the slope -3/2 and y intercept -1
Answer: y = -3/2x - 1
Step-by-step explanation:
y = mx + b
1. m is the slope so substitute -3/2 for m. ( y = -3/2x + b)
2. b is the y intercept so substitute -1 in for b. ( y = -3/2x - 1)
The side lengths in yards of a triangle and a square are shown in the diagram. (4x - 2) yd 2x yd 2(x + 7) yd 2.5x yd The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?
(4x -2) yd, 2x yd, 2(x + 7) yd, 2.5x yd. The triangle's perimeter is the same as the square's perimeter. The value of x=6
Given that,
The graphic displays the yards-long sides of a triangle and a square. The triangle's perimeter is the same as the square's perimeter.
We have to find the value of x in the given side.
In the picture we can see the triangle and square.
The perimeter of the triangle is sum of the three sides of the triangle.
The perimeter of the square is 4 times the side of the square.
4x-2+2x+2(x+7)=4×2.5x
4x-2+2x+2x+14=10x
8x+12=10x
10x-8x=12
2x=12
x=12/2
x=6
Therefore, the value of x=6
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First person to solve gets Brainliest!!!!
Below is the graph of y=3x".Translate it to make it the graph of y=3(x-4)3 +1.
There are two shiftments, 1 to the side along the x-axis and 1 vertical along the y-axis
Horizontal shifts:
[tex]y=(x\pm a)^n[/tex]Vertical shifts
[tex]y=x^n\pm a[/tex]Since the x is substracted 4 units, it means that the graph is translated 4 units to the right.
Since the function is completely added 1 unit its means that all the graph is shifted 1 unit up.
At the bakery cupcakes are displayed in 12 rows with 6 cupcakes per row. If a
customer buys 24 cupcakes, how many cupcakes are left?
How many gallons of water does the full tank hold?
Given:
a.) After 2 minutes, the tank contains 400 gallons.
b.) After 5 minutes, the tank is full.
For us to be able to determine how many gallons of water does the full tank hold, let's first determine the discharge rate of the water filling in the tank.
We get,
[tex]\text{ Rate of discharge = }\frac{\text{ Volume}}{\text{ Time}}\text{ = }\frac{400\text{ Gallons}}{2\text{ Minutes}}[/tex][tex]\text{ Rate of discharge = 200 Gallons/Minute}[/tex]Since the tank is after 5 minutes of pumping water at a constant rate, we will just multiply the rate of discharge by the time it took for the tank to be full.
We get,
[tex]\text{Volume of the Tank = Time x Rate of Discharge = 5 (Minutes) x 200 Gallons/(Minute)}[/tex][tex]\text{ Volume of the Tank = 1000 Gallons}[/tex]Therefore the volume of the tank is 1000 Gallons
Malcolm's Bakery Shop sells gourment cupcakes. The shop's cost for making 3 cupcakes is $6.75, and the cost of making 5 cupcakes is $9.75 . What is the shop's cost per minute?
A. $1.50
B. $1.95
C. $2.25
D. $3.00
The average cost per minute which the shop runs is $1.50
Shop's Cost per MinuteTo find the shop's cost per minute, we can write down equations and proceed to solve.
In the given question, 3 cupcakes cost $6.75 and 5 cupcakes cost $9.75.
But we were not given the average cost per cupcake.
To do that, let's write an equation for this.
[tex]y = mx + c[/tex]
Let's find the slope to this equation which determines the average cost per minute.
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\m = \frac{9.75 - 6.75}{5 - 3} \\m = 1.50[/tex]
The shop's cost per minute was calculated to be $1.50.
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find the equatuon of the line y=_x+_
Answer: y = -2x + 5
Step-by-step explanation:
y = _x + 5
(5,0) (3,4)
(y2 - y1) / (x2 - x1)
(4 - 0 ) / (3 -5)
4 / -2
-2
y = -2x + 5
I need help with this practice problem from my ACT prep guideIt is trigonometry It asks to graph the function yourself, on paper, or on desmos
If we start with the parent function f(x) = cot(x), the transformation needed to go from this function to cot(x + π/6) is expressed as:
[tex]f(x)\to f(x+\frac{\pi}{6})[/tex]That is, we need to make a shift of π/6 units to the left, beginning with the cot(x) graph. The graph of cot(x + π/6) is:
(10) Use the following freauency bar graph to answer the following questions.Chart of MTH 150 GradescountGradesa) How many students received a C for the course?b) How many students passed the course (with a C or higher)?c) How many students received no credit for the course (i.e. got an F)?d) How many total students took the course?e) Which letter grade represents the mode?
From the frequency bar graph, we can read the following information.
15 students got an A
6 students got a B
5 students got a C
10 students got a D
14 students got an F
a) As described above, 5 students got a C
b) Adding up the frequencies of the students who got C or higher:
5 + 6 + 15 = 26
26 students passed the course
c) Assuming the students who did not pass got any credits, then we add up the students with D and F: 10 + 14 = 24
24 students received no credit for the course
d) Total students in the course: 15 + 6 + 5 + 10 + 14 = 50
e) The mode is the letter grade that got the highest frequency:
Mode = A
A got 15
The current in a resistor is inversely proportional to the resistance. By what factor will the current change if the resistance increases 10%.
The factor by which the current changes if the resistance increases 10% is; 90.9% reduction
How to Interpret Ohms' Law?
Ohm's law states that the electrical current (I) flowing in a circuit is directly proportional to the voltage (V) and inversely proportional to the resistance(R). Therefore, if the voltage is increased, the current will increase provided the resistance of the circuit does not change. Thus;
I = V/R
Now, we are told that the resistance increases by 10%.
Thus, New value of resistance = 1.1R
Thus, new current/old current = 1/1.1 = 0.909 = 90.9%
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determine each quotient 5 divided by 1/105 divided by 3/105 divided by 9/10
Solution
- To divide by a fraction, you simply invert the fraction and instead multiply by the inverted fraction.
- Thus, we have:
[tex]\begin{gathered} \text{ 5 divided by }\frac{1}{10}: \\ \\ 5\div\frac{1}{10}=5\times\frac{10}{1}=50 \\ \\ \text{ } \\ \text{ 5 divided by }\frac{3}{10}: \\ \\ 5\div\frac{3}{10}=5\times\frac{10}{3}=\frac{50}{3} \\ \\ \\ \\ \text{ 5 divided by }\frac{9}{10}: \\ \\ 5\div\frac{9}{10}=5\times\frac{10}{9}=\frac{50}{9} \end{gathered}[/tex]Mina got a story book of 56 pages from her school library for 7 days. She did not want to complete the book immediately.. She planned to read the book in such a way that all her other activities were not disturbed and wanted to spend equal amount of time in reading. She did it successfully and returned the book on the specific day. How she must have planned her reading?
Please with explanation...
Mina must have planned to read 8 pages everyday.
To accomodate reading in her everyday life, without spending extra time and not disturbing other activities, Mina should read particular number of pages everyday. These pages should be enough to be completed in 7 days.
So, relating the number of pages and days -
Number of pages to be read each day = total number of pages ÷ number of days
Keep the values in relation -
Number of pages to be read each day = 56 ÷ 7
Performing division
Number of pages to be read each day = 8
Thus, to return the book on time Mina should have planned to read 8 pages everyday.
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Suppose a basketball player has made 359 out of 449 free throws. If the player makes the next 3 free throws, I will pay you $39. Otherwise you pay me $43.
Step 1 of 2 : Find the expected value of the proposition
The expected value of the proposition is $22.6
How to determine the expected value?The given parameters are
Proportions of free throws = 359 out of 449Amount paid for making a throw = $39Amount collected for losing a throw = $43Represent the proportion as a fraction
So, we have
p = 359/449
The expected value is then calculated as
E(x) = p * Amount paid for making a throw - (1 - p) * Amount collected for losing a throw
Where p represents the proportion defined above
So, we have
E(x) = 359/449 * 39 - (1 - 359/449) * 43
Evaluate the difference
E(x) = 359/449 * 39 - 90/449 * 43
So, we have
E(x) = 22.6
Hence, the proposition has an expected value of $22.6
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Answer:
-1.09
The problem requires one to calculate the win payoff and win probability as well as the lose payoff and probability. You would then do a calculation like this:
[(Win Payoff) x (Win Probability)] + [(Lose Payoff) x (Lose Probability)]
Circumference of 2 circles =220m and 286m find area!
Helppp!!!!
Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The areas are 123.83 [tex]m^{2}[/tex] and[tex]209.07m^{2}[/tex]
What is a circle?The form having the greatest surface area for a given perimeter is a circle.
Every line through the center of a circle forms a line of reflection symmetry, and every angle has rotational symmetry around the center. The orthogonal group O is the symmetry group of it (2,R). Circle group T is the collection of rotations alone.
Every circle is comparable.The radius and circumference of a circle are proportionate.The ratio between the enclosed area and the square of its radius is one.2 and, respectively, serve as the proportionality constants.The unit circle is the circle with radius 1 and an origin center.It becomes the Riemannian circle when viewed as a large unit sphere circle.A distinct circle can be found through any three locations that are not all on the same line. It is feasible to express explicitly equations for the coordinates of the circle's center and radius in terms of the coordinates of the three specified points in Cartesian coordinates.
Circumference= [tex]2\pi r[/tex]= 220 and 286
[tex]2\pi r[/tex]= 220
2*3.14*r=220
r= 220/35.03= 6.28
area=[tex]\pi r^{2}[/tex]
= 3.14*6.28*6.28
= 123.83[tex]m^{2}[/tex]
[tex]2\pi r[/tex]= 286
2*3.14*r= 286
r= 286/35.03 = 8.16
area= [tex]\pi r^{2}[/tex]
= 209.07[tex]m^{2}[/tex]
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