Answer:
The value of n is 29/5
Explanation:
Given that (2n + 18) and (7n - 11) are two vertical angles, by definition, they are congruent.
so
2n + 18 = 7n - 11
Subtract 2n from both sides of the equation
2n + 18 - 2n = 7n - 11 - 2n
18 = 5n - 11
Add 11 from both sides of the equation
18 + 11 = 5n - 11 + 11
29 = 5n
Divide both sides by 5
n = 29/5
Answer:
n = 29/5 or 5 4/5
Transform 3 tons to pounds
To transform a ton to pounds we need to remember that each ton is 2000 pounds, then:
[tex]3\text{ T=3(2000) lb=6000 lb}[/tex]Therefore we have 6000 lb
Kyle has 20 gallons of gasoline to use for his snow plowing business. He uses gasoline in his snow plow at a constant rate. Let a represent the
number of driveways plowed and y represent the amount of gas remaining. Look at the graph of the function. Construct a function for this
scenario. Assume he must complete a driveway once he starts it.
20
10
0
Part A
10
20
30
What is the equation of the line?
The required equation of the line is y = -(1/2)x + 20 which represents the given function in the shown graph.
Let a represent the number of driveways plowed and y represent the amount of gas remaining.
The graph of the function is given in the question
As per the given function, we take two points (0,20), and (40,0)
The required equation of the line will be as:
y - 20 = [(0 -20)/40-0)](a-0)
y - 20 = -(20/40)a
y - 20 = -(1/2)a
y = -(1/2)a + 20
Therefore, the required equation of the line is y = -(1/2)x + 20.
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Use the long division method to find the result when 2x^3-7x^2+17x-7 is divided by 2x-1.
Given the expression below
[tex]\frac{2x^3-7x^2+17x-7}{2x-1}[/tex]To divide the above expression using long division, we will follow the steps below:
Step 1: Arrange the indices of the polynomial in descending order. Replace the missing term(s) with 0.
Looking at the expression given, polynomials is already arranged in descending order, from degree 3 to 0, and there are no missing terms of x.
Step 2: Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient.
Looking at the expression given, it can be seen that
[tex]\begin{gathered} \text{dividend}=2x^3-7x^2+17x-7 \\ \text{divisor}=2x-1 \end{gathered}[/tex][tex]\frac{2x^3}{2x}=x^2[/tex]Step 3: Multiply the divisor by the first term of the quotient.
[tex]x^2(2x-1)=2x^3-x^2[/tex]Step 4: Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend. Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".
Step 5: Repeat step 2 – 4 to find the second term of the quotient.
[tex]\frac{-6x^2}{2x^2}=-3x[/tex][tex]-3x(2x-1)=-6x^2+3x[/tex]Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.
[tex]\frac{14x}{2x}=7[/tex][tex]7(2x-1)=14x-7[/tex]The quotients from the divisions gives
[tex]x^2-3x+7[/tex]Hence, the result of the division is as written below x² - 3x +7
5x+4=x+44 solve for x
5x + 4 = x + 44
x is adding on the right, then it will subtract on the left
4 is adding on the left, then it will subtract on the right
5x - x = 44 - 4
4x = 40
4 is multiplying on the left, then it will divide on the right
x = 40/4
x = 10
3) Mary made 1/5 of a batch of cookies in 1/10 of an hour. How many batches of cookies can she make in one hour?
Given in the scenario:
a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.
Let's determine how many batches of cookies can she make in one hour.
Step 1: Let's convert the given into a ratio and proportion.
Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10
At x = number of batches of cookies in one hour, we get = x : 1
Step 2: Let's determine the value of x.
[tex]\frac{\frac{1}{5}}{\frac{1}{10}}\text{ = }\frac{x}{1}[/tex][tex](1)(\frac{1}{5})\text{ = (x)(}\frac{1}{10})[/tex][tex]\frac{1}{5}\text{ = }\frac{1}{10}x[/tex][tex](1)(10)\text{ = (1)(5)(x) }\rightarrow\text{ 10 = 5x}[/tex][tex]\frac{5}{5}x\text{ = }\frac{10}{5}[/tex][tex]\text{ x = 2}[/tex]Therefore, Mary can make 2 batches of cookies in one hour.
write an equation for a parabola opening upward, shifted 6 units right, and three units down
y = (x-6)²-3
1) Let's write a transformation described as it is, algebraically speaking.
• opening upward, (a >0)
,• shifted 6 units right, (-6)
,• and three units down -3
2) Starting from the parent function y=x², then we can write:
y = (x-6)²-3
Notice that the horizontal shift is within the parentheses with a swapped sign. And outside that -3 indicating the vertical shift.
How do you graph y= -1/2x
Step-by-step explanation: move down 1 and right 2 because it has to be a negative slope.
Answer: See attached, or read below.
Step-by-step explanation:
First, we see there is no b value, so there is no y-intercept. The line will intercept the graph at (0, 0), also known as the origin.
Next, we see a negative slope of -1/2. This means, starting at the origin, we will move down one unit and right two. Then repeat. Lastly, draw a straight line through all three points for our graph.
Which system type is a linear system with infinitely many solutions?InconsistentConsistent dependentInconsistent dependentConsistent independent
We are asked which system type is a linear system with infinitely many solutions.
Inconsistent = No solution
Consistent independent = One solution
Consistent dependent = infinitely many solutions.
In a consistent dependent system, the lines are merged and they basically become the same line. Hence, every coordinate pair on the line is a solution to both lines.
Therefore, the correct answer is Consistent dependent.
A consistent dependent system is a linear system with infinitely many solutions.
Can anyone help me this please this is my last question to pass
Lets take 2 pair of points from the table:
[tex]\begin{gathered} (x_1,y_1)=(0,4) \\ (x_2,y_2)=(2,10) \end{gathered}[/tex]The equation of line is y = mx + b
Where
m is slope
b is y-intercept
Let's find the slope (m):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{10-4}{2-0} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]So, the equation becomes:
[tex]y=3x+b[/tex]Let's plug in the first point (x, y) = (0,4) to find b:
[tex]\begin{gathered} y=3x+b \\ 4=3(0)+b \\ 4=0+b \\ b=4 \end{gathered}[/tex]Final Equation of the line:
[tex]y=3x+4[/tex]Solve for x in the equation x2+2x+ 1 = 17.X=-1+ /15X=-1+ /17X=-2+2.15X=-1+ /13
First, write the quadratic equation in standard form. Then, use the quadratic formula to find the solutions for the quadratic equation.
Remember that if a quadratic equation is written in standard form:
[tex]ax^2+bx+c=0[/tex]Where a, b and c are constants, then the solutions for x are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Starting with the given equation:
[tex]x^2+2x+1=17[/tex]Substract 17 from both members to write the equation in standard form:
[tex]\begin{gathered} \Rightarrow x^2+2x+1-17=17-17 \\ \Rightarrow x^2+2x-16=0 \end{gathered}[/tex]Use the quadratic formula, setting a=1, b=2 and c=-16:
[tex]\begin{gathered} x=\frac{-(2)\pm\sqrt[]{(2)^2-4(1)(-16)}}{2(1)} \\ =\frac{-2\pm\sqrt[]{4+64}}{2} \\ =\frac{-2\pm\sqrt[]{68}}{2} \end{gathered}[/tex]Simplify the expression using the properties of radicals. Since 68 is equal to 4 times 17, then:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{68}}{2} \\ =\frac{-2\pm\sqrt[]{4\cdot17}}{2} \\ =\frac{-2\pm\sqrt[]{4}\cdot\sqrt[]{17}}{2} \\ =\frac{-2\pm2\cdot\sqrt[]{17}}{2} \\ =\frac{2(-1\pm\sqrt[]{17})}{2} \\ =-1\pm\sqrt[]{17} \end{gathered}[/tex]Therefore, the solutions for x in the given equation are:
[tex]\begin{gathered} x_1=-1+\sqrt[]{17} \\ x_2=-1-\sqrt[]{17} \end{gathered}[/tex]write an equation for the n th term of the arithmetic sequence 23, 16, 9, 2, ... .Then find a25?
Given the sequence:
23, 16, 9, 2
Use the arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]Where
an = nth term
a1 = first term
n = number of terms
d = common difference
d = a2 - a1 = 16-23 = -7
Since d = -7, let's find the equation for the nth term.
[tex]\begin{gathered} a_n=23+(n-1)-7 \\ a_n=23+n(-7)-1(-7) \\ a_n=23-7n+7 \\ \text{Combine like terms} \\ a_n=-7n\text{ +23}+7 \\ \\ a_n=-7n+30 \end{gathered}[/tex]The equation for the nth term is:
[tex]a_n=-7n+30[/tex]Let's find the 25th term, a25:
Substitute n for 25 and evaluate
[tex]\begin{gathered} a_{25}=-7(25)+20 \\ \\ a_{25}=-175+30 \\ \\ a_{25}=-145 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} a_n=-7n+30 \\ \\ \\ a_{25}=-145 \end{gathered}[/tex]Consider the following functions.f(x) = x + 4 and g(x) = x - 7=Step 2 of 4: Find (f - 3)(x). Simplify your answer.Answerf-8)(x) =
Solution
[tex]\begin{gathered} f(x)=x+4 \\ g(x)=x-7 \end{gathered}[/tex]Now
[tex]\begin{gathered} (f-g)(x)=x+4-(x-7) \\ (f-g)(x)=x+4-x+7 \\ (f-g)(x)=11 \\ \end{gathered}[/tex]The final answer
[tex]11[/tex]Which of the following functions shows the quadratic parent function,
Given the function f(x);
[tex]f(x)=x[/tex]When the function is flipped across the x-axis, we'll have the sign reversed.
So, the new function formed is;
[tex]undefined[/tex]Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.
We have the equation
[tex]20y=x^2-10-15[/tex]Let's complete the square, to do it let's add and subtract 25 on the right side
[tex]\begin{gathered} 20y=x^2-10-15+25-25 \\ \\ 20y=(x-5)^2-15-25_{} \\ \\ 20y=(x-5)^2-40 \\ \\ \end{gathered}[/tex]Now we can have y in function of x
[tex]\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\ \\ \end{gathered}[/tex]Now we can already identify the vertex because it's in the vertex form:
[tex]y=a(x-h)+k[/tex]Where the vertex is
[tex](h,k)[/tex]As we can see, h = 5 and k = -2, then the vertex is
[tex](5,-2)[/tex]Now we can continue and find the focus, the focus is
[tex]\mleft(h,k+\frac{1}{4a}\mright)[/tex]We have a = 1/20, therefore
[tex]\begin{gathered} \mleft(5,-2+5\mright) \\ \\ (5,3) \end{gathered}[/tex]The focus is
[tex](5,3)[/tex]And the last one, the directrix, it's
[tex]y=k-\frac{1}{4a}[/tex]Then
[tex]\begin{gathered} y=-2-5 \\ \\ y=-7 \end{gathered}[/tex]Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7
Two lines are graphed on the coordinate plane below(INSERT PHOTO)What is the solution to the system represented by the lines?A- (4,6)B- (4, -6)C- (-4,-6)D- (-4, 6)
Take into account that a system of equations represented by two lines, has a solution that is given by the point where the lines cross each other.
Then, based in the previous explanation and the given graph, you can notice that at the point (4,6) the lines cross each other.
Hence, the point (4,6) is the solution to the system of equations.
Lloyd is working a problem on the board in his math class. He needs to simplifythe expression below.(2x-3) + (2x*- 3x) – (3x*- 5).What should he write as his answer?
Answer:
-x² - x + 2
Step-by-step explanation:
We are given the following expression:
(2x-3) + (2x²- 3x) – (3x²- 5).
To simplify, we first need to remove the parenthesis. If there is a negative sign before the parenthesis, we change the signal of everything that is inside(+ goes to -, - goes to +). So
(2x-3) + (2x²- 3x) – (3x²- 5) = 2x - 3 + 2x² - 3x - 3x² + 5
Now we need to combine the like terms:
With x²: 2x² - 3x² = -x²
With x: 2x - 3x = -x
Independent: -3 + 5 = 2
Now adding these terms, we get the simplified expression, which is:
-x² - x + 2
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 7.5 km. 9 km. 9 km. km² Surface Area:
We can split this prism into 5 planar figures: 1 square and 4 equal triangles. The area of the square is given by
[tex]\begin{gathered} A_{\text{square}}=L^2 \\ A_{\text{square}}=9^2 \\ A_{\text{square}}=81km^2 \end{gathered}[/tex]On the other hand, the area of one triangle is given by
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\text{base}\times height \\ A_{\text{triangle}}=\frac{1}{2}9\times7.5 \\ A_{\text{triangle}}=33.75km^2 \end{gathered}[/tex]Then, the surface area S is given by
[tex]S=A_{\text{square}}+4\cdot A_{\text{triangle}}[/tex]By substituting our last results, we have
[tex]\begin{gathered} S=81+4\times33.75 \\ S=216km^2 \end{gathered}[/tex]then, the answer is 216 square kilometers
Three time a number is two times the difference of that number and one
Please help. Write an algebriac expression
Answer:
[tex]3x = 2(x - 1)[/tex]
Suppose you invested $4,500 and it grew by 4% every year for 30 years. How much would this investment be worth after 30 years?
Answer:
a) 14,595.29
Explanation:
We'll use the below compound interest formula to solve the given problem;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A = future amount
P = initial amount = $4500
r = interest rate in decimal = 4/100 = 0.04
n = number of compounding periods = 1
t = time period = 30 years
Let's go ahead and substitute the above values into our formula and solve for A;
[tex]\begin{gathered} A=4500(1+\frac{0.04}{1})^{1\times30} \\ A=4500(3.24339751003) \\ A=14,595.29 \end{gathered}[/tex]We can see from the above that the investment would be worth $14,595.29 after 30 years.
What is the slope of the line shown below?10(-6,3)5(12,5)5101610OAA.6B. -6C. -D. 6
Consider that the slope (m) of a line passing through two given points is calculated using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]It is evident from the graph that points (-6,3) and (12,6) lie on the line,
[tex]\begin{gathered} (x_1,y_1)=(-6,3) \\ (x_2,y_2)=(12,6) \end{gathered}[/tex]Then, substitute the values in the formula to obtain the slope of the given line,
[tex]\begin{gathered} m=\frac{6-3}{12-(-6)} \\ m=\frac{3}{12+6} \\ m=\frac{3}{18} \\ m=\frac{3}{6\cdot3} \\ m=\frac{1}{6} \end{gathered}[/tex]Thus, the slope of the given line is,
[tex]\frac{1}{6}[/tex]Therefore, option A is the correct choice.
which choice represents the best rational approximation for 15 ?es)A)2B)2.2C)2.5D)2.7
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Sebastian used difference of squares to factor the expression x^4– 16. His work is shown below. His teacher says that he did not "factor completely."How would you explain to Sebastianwhat he needs to do to completely factorthis expression?
To factor properly this expression, we need to use the next expression for the product of the difference of two squares as follows:
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]Since the squares are:
[tex](x^2)^2-(4)^2=(x^2+4)(x^2-4)[/tex]We can also see that we have another difference of two squares in the last part of the expression:
[tex]undefined[/tex]A rectangle has a perimeter of 14 cm what’s the dimensions of the rectangle
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(lengthe + width)
Given that the perimeter = 14, it means that
2(lenght + width) must be equal to 14
Looking at the options,
2(1 + 6) = 14
2(2 + 5) = 14
2(3 + 4) = 14
2(4 + 3) = 14
2(5 + 2) = 14
2(6 + 1) = 14
Thus, the correct options are A, B, C, D, E, F
The recommended daily allowance of niacin for adults is 20 mg. One serving of a certain breakfast cereal provides 8 mg of niacin, What percent of the recommendeddaily allowance of niacin does one serving of this cereal provide?
Given:
Total allowance = 20mg.
Used = 8 mg
Percentage of daily allowance is:
[tex]\begin{gathered} =\frac{8}{20}\times100 \\ =\frac{8}{2}\times10 \\ =8\times5 \\ =40 \end{gathered}[/tex]So 40% daily allowance .
Hi, can you help me answer this question please, thank you!
Given information:
[tex]\begin{gathered} H_0\colon\mu_1=\mu_2 \\ H_a\colon\mu_1<\mu_2 \end{gathered}[/tex]n1=12
Mean x1=75.4
SD1=9.7
n2=19
Mean x2=83.3
SD2=17.8
significance level alfa=0.02
To find the test statistic let's use the formula:
[tex]undefined[/tex]How would I solve Question 1 & 2 to find g(x)-f(x)
We will have the following:
1)
[tex]g(x)-f(x)=5^x-12-3x[/tex]2)
[tex]\begin{gathered} f(x)-g(x)=log_3(5x-5)-log_3(x-1) \\ \\ \Rightarrow f(x)-g(x)=log_3(\frac{5x-5}{x-1}) \\ \\ \Rightarrow f(x)-g(x)=log_3(5) \end{gathered}[/tex]Perimeter of a plecewise rectangular figureFind the perimeter of the figure below. Notice that one side length is not givenAssume that all intersecting sides meet right angles,Be sure to include the correct unit in your answer.6 yd8 ydydyd13 yd9 ydx515 yd
The perimeter is the sum of all sides.
You can observe in the figure that one side length is missing, but we can find it by subtraction.
[tex]13yd-8yd=5yd[/tex]Once we have all side lengths, we can sum them.
[tex]\begin{gathered} P=13yd+6yd+8yd+9yd+5yd+15yd \\ P=56yd \end{gathered}[/tex]Therefore, the perimeter of the figure is 56 yards.Find the image of the given point
under the given translation.
P(-8, 2)
T(x, y) = (x - 5, y + 4)
P' = ([?], [])
The image of the given point under the given translation is P' = (-13,6).
Given:
P(-8, 2)
Translation T(x, y) = (x - 5, y + 4).
Translation:
In translation notation, the first number represents how many units in the x direction, the second number, how many in the y direction. Both numbers tell us about how far and in what direction we are going to slide the point.
P'(x,y) = (x - 5 , y + 4)
= (-8-5 , 2+4)
= (-13,2+4)
= (-13,6)
Therefore The image of the given point under the given translation is P' = (-13,6).
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Sket the right triangle and find the length of decide not given it necessari approximate the length to the nearest thousand
Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below
[tex]\begin{gathered} H^2=L^2_1+L^2_2 \\ H\to\text{ hypotenuse} \\ L_1,L_2\to\text{ legs} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} H=15,L_1=3 \\ \Rightarrow L^2_2=15^2-3^2=216 \\ \Rightarrow L_2=\sqrt[]{216}=14.6969\ldots\approx14.697 \\ \Rightarrow L_2=14.697 \end{gathered}[/tex]The answer is 14.697
The five‐number summary of a distribution consists of(a) mean, median, standard deviation, and two quartiles.(b) minimum, maximum, mean, median, and standard deviation. (c) minimum, maximum, median, and two quartiles(d) mean, standard deviation, correlation, and two quartiles
The five-number summary of a distribution consists of
1)The minimum(smallest observation)
2)The maximum ( Largest observation)
3)median
4)Two quartiles( The first quartile and the third quartile)
That is option C