Answers
Answer:
The answer is 7
Step-by-step explanation:
You are absolutely right. The angles of a triangle need to add up to 180 so from the picture we can create the following equation:
90 + 30 + 8x + 4 = 180 (adding together numbers)
124 + 8x = 180 (subtracting 124 from both sides to maintain equality)
124 - 124 + 8x = 180 - 124
8x = 56 (dividing by 8 both sides to isolate x)
(8*x)/8 = 56/8
x = 7
Related Questions
the average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. what would the standard deviation have to be in order for a 6% probability that a gallon of gas costs less than $1.80? round z-value calculations to two decimal places and final answer to the nearest cent.
Answers
σ =171.1 is z-value calculations to two decimal places .
What does "z-score" mean?
The Z-score provides information on how far a given value deviates from the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations above or below the mean a specific data point falls. In essence, standard deviation represents the degree of variability present in a given data collection.Given that,
mean = μ = 212.2
x=1.80
Using standard normal table,
P(Z < z) = 11%
= P(Z < z) = 0.11
= P(Z < -1.23) = 0.11
z = 1.23 Using standard normal table,
using z-score formula
σ = X - μ /Z
σ =1.80 - 212.2 / 1.23
σ =171.1
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A 150-pound person uses 5.7 calories per minute when walking at a speed of mph. How long must a person walk at this speed to use at least 240 calories ? (Round up to the nearest minute )
Answers
Since 5.7 calories are burned in one minute, we have that:
[tex]\frac{240}{5.7}=42.10526\ldots\approx42[/tex]Then, if a person walks for 42 minutes, then they would burn exactly 239.4 calories.
So, a 150-pound person must walk for at least 43 minutes in order to use at least 240 calories (The answer is actually 42.105... but if we round down it to 42, that person would burn less than 240 calories. That's why it is better to round up).
Write an equation for each line.(1). y-intercept -2.1, x-intercept of 3.5(2). through (1.2, 5.1), x-intercept of 3.7
Answers
hello
since we're given y and x intercept, we can use it to find the slope of the equation
y-intercept = 2.1
x-intercept = 3.5
what this implies that in a given graph, y-axis is (0, 2.1) and x-axis (3.5, 0)
now we can use this co-ordinate to find our slope
so our odered pair are (3.5, 0) and (0, 2.1)
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]y2 = 2.1
y1 = 0
x2 = 0
x 1 = 3.5
[tex]\begin{gathered} \text{slope}=\frac{2.1-0}{3.5-0} \\ \text{slope}=\frac{2.1}{3.5} \\ \text{slope}=0.6=\frac{3}{5} \end{gathered}[/tex]now we know our slope as 3/5
we can use this slope to find the equation of the line
remember our y-intercept = 2.1
equation of staright line is given as y = mx + c
m = slope
c = y-intercept
now, the equation of this line is
y = 3/5x + 2.1
[tex]y=\frac{3}{5}x+2.1[/tex]b.
we have one point (1.2, 5.1) and an x-intercept of 3.7
let the first point (1.2, 5.1) be A and the second point as B
A = (1.2, 5.1)
B = (3.7, 0)
y2 = 0
x2 = 3.7
y1 = 5.1
x1 = 1.2
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_{\square}} \\ \text{slope}=\frac{0-5.1}{3.7-1.2} \\ \text{slope}=-\frac{5.1}{2.5} \\ \text{slope}=-2.04 \end{gathered}[/tex]y = mx + c
m = slope
c = y-intercept
let's use co-ordinate B to find our y-intercept
[tex]\begin{gathered} y=mx+c \\ 0=-2.04(3.7)+c \\ \text{solve for c} \\ 0=-7.548+c \\ c=7.548 \end{gathered}[/tex]we can now re-write our equation with the standard form of y = mx + c
y = -2.04x + 7.548
Can you please tell me the answer for this and it’s steps
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]y=|x-a|[/tex]Each absolute value graph will have a “V” shape. It consists of two parts: one with a negative slope and one with a positive slope. The point of intersection is called the vertex. An absolute value graph is symmetric, meaning that it can be folded in half along its line of symmetry.
Therefore, the sketch of the function would be:
Instructions: For the following sequence, state the common ratio, identify which is the explicit form and which is the recursive form of the rule, and find the term listed.
Answers
Solution:
Given the sequence;
[tex]-3,6,-12,24[/tex]The common ratio is the ratio between two consecutive numbers in a geometric sequence.
Thus;
[tex]\begin{gathered} r=\frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \\ r=\frac{6}{-3} \\ \\ r=-2 \end{gathered}[/tex]Common Ratio:
[tex]r=-2[/tex]Also, given the formula;
[tex]a_n=-3\cdot(-2)^{n-1}[/tex]The formula is an explicit formula of the geometric sequence.
The recursive formula is;
[tex]\begin{gathered} a_n=r(a_{n-1}) \\ \\ a_n=-2(a_{n-1}) \end{gathered}[/tex]Then, the ninth term is;
[tex]\begin{gathered} n=9 \\ \\ a_9=-3\cdot(-2)^{9-1} \\ \\ a_9=-3\cdot(-2)^8 \\ \\ a_9=-3(256) \\ \\ a_9=-768 \end{gathered}[/tex]The ninth term is;
[tex]a_9=-768[/tex]The function h defined by h() = (37 + 5)(15 − ) models the height, in meters, of an object seconds after it is dropped from a helicopter.Find or approximate the time when the object hits the ground. Explain or show your reasoning.
Answers
The object hits the ground in 15 seconds
Explanation:The objec hits the ground when h = 0
so
(37 +5t)(15 - t) = 0
37 + 5t = 0
OR
15 - t = 0
5t = -37
t = -37/5
This cannot be the time, because it is negative. Time can only be zero or positive.
Therefore,
15 - t = 0
t = 15
The object hits the ground in 15 seconds
Find the indicated expression, where n = 16, r = 14. (Simplify the answer as much as possible.)(n text(!)) / (\(n - r\) text(!) )
Answers
Given that n=16 and r=14;
[tex]\frac{n!}{(n-r)!}[/tex]Recall that;
[tex]a!=a(a-1)(a-2)(a-3)\ldots[/tex][tex]\frac{16!}{(16-14)!}[/tex]Thus, we have;
[tex]\frac{16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{2\times1}[/tex][tex]=10,461,394,944,000[/tex]Consider the following function.f(x) = (x2 + 9)(6x + 2), (2, 18)==(a) Find the value of the derivative of the function at the given point.f'(2) =(b) Choose which differentiation rule(s) you used to find the derivative. (Select all that apply.)power rulequotient ruleproduct rule
Answers
For this problem, we are given a function and we need to determine the derivative on the given point.
The function is:
[tex]f(x)=(x^2+9)(6x+2)[/tex]The derivative is:
[tex]\begin{gathered} f^{\prime}(x)=(x^2+9)^{\prime}(6x+2)+(x^2+9)(6x+2)^{\prime}\\ \\ f^{\prime}(x)=2x(6x+2)+(x^2+9)(6)\\ \\ f^{\prime}(x)=12x^2+4x+6x^2+54\\ \\ f^{\prime}(x)=18x^2+4x+54 \end{gathered}[/tex]Now we need to apply the given point, which means replacing "x" with 2 and evaluating the expression.
[tex]\begin{gathered} f^{\prime}(2)=18(2)^2+4(2)+54\\ \\ f^{\prime}(2)=18\cdot4+8+54\\ \\ f^{\prime}(2)=72+62=134 \\ \end{gathered}[/tex]For this problem we used the following differentiation rules: power rule and product rule.
Juan broke a cell sample into 1111 batches, each weighing 1. 8\times 10^{-8}1. 8×10 −8
grams. How much did the original sample weigh? Use scientific notation to express your answer
Answers
The original cell sample weigh broken by Juan was 1.98 x 10^{-7}grams.
What is the definition of scientific notation?Scientific notation is a handy way to shorten extremely large numbers with positive exponential values and also very small numbers with negative exponential values. To shorten long numbers in scientific notation, be using positive exponents and decimals. This is the standard way to write a number in scientific notation. Remember that a scientific notation number must be authored in the format m×10^n.For the given question;
The sample of the cell was broken in 11 pieces by Juan.
The weight of the each cell sample is 1. 8 x 10^{-8}grams.
Thus, the original sample weigh will be-
= 1. 8 x 10^{-8}grams x 11
= 1. 8 x 11 x 10^{-8}grams
= 19.8 x 10^{-8}grams
In the scientific notation.
= 1.98 x 10^{-7}grams
Thus, the original cell sample weigh broken by Juan was 1.98 x 10^{-7}grams.
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The correct question is-
Juan broke a cell sample into 11 batches, each weighing 1. 8 x 10^{-8}grams. How much did the original sample weigh? Use scientific notation to express your answer.
hi hi hi ill show u a pic of it
Answers
1 2x² + 7x+6=0
3 m²-7m + 2 = 0
5 3x² + 2x = 8
74a² +9a + 1 = 0
9 81² + 6t = 35
11 29² = 14 - q
25b²11b- 12 = 0
4 2h²-5h-11 = 0
6n² + 8 = 15n
8 5K² = 2k +18
10 3y² + 7 = 2y
12 0.5x2-3x - 9.4 = 0
Answers
Answer:
Step-by-step explanation:
Using pythagorean therund i was alud to find the answer 3.14 also known more comonly new york piza or pi
Using the graph of f(x)=x^2 as a guide describe the transformations and then sketch a graph of each function g(x)=(x+1)^2+3
Answers
According to the Transformation rules for functions:
1) When a function f(x) is shifted left "k" units:
[tex]f\mleft(x+k\mright)\text{ }[/tex]2) When it is shifted right "k" units:
[tex]f\mleft(x-k\mright)[/tex]3) When it is shifted up "k" units:
[tex]f(x)+k[/tex]4) When it is shifted down "k" units:
[tex]f(x)-k[/tex]Observe in the graph attached that the vertex of the following parent function is located at the origin:
[tex]f(x)=x^2[/tex]Knowing that the function g(x) is:
[tex]g\mleft(x\mright)=\mleft(x+1\mright)^2+3[/tex]You can determine that the function g(x) is the function f(x) but shifted left 1 unit and shifted up 3 units.
Find the rate of change of each linear function 1. y = 7x - 12
Answers
Given the function :
[tex]y=7x-12[/tex]The general form of the linear function is : y = m * x + b
Where m is the slope
The rate of the change of the linear function = slope of the function
So, the rate of the change = m = 7
Answer: the rate of change or "slope" is 7
Step-by-step explanation:
MATH
Or
Hunter has 2
1
2
hours to spend at Wally's Game World. He spends
1
4
of an hour playing arcade games, and he spends the rest of the time playing miniature golf with his friends. If each round of golf takes
3
4
of an hour, how many rounds does Hunter play?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions
Answers
In linear equation, 3 rounds does Hunter play .
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable.It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.A linear equation in one variable would be 9x + 78 = 18, for instance.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.= [tex]2\frac{1}{2} - \frac{1}{4}[/tex]
= 9/4
= [tex]\frac{9/4}{3/4}[/tex]
= 3
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To solve the equation 8d = 2d, Lin divides each side by 2d, and Elena subtracts 2d from each side. Will both moves lead to the solution? Explain your reasoning. Question 5 Solve the equation 8d = 2d that Lin and Elena were working on in Question 4. d=
Answers
Lin working
[tex]\begin{gathered} 8d=2d \\ \text{divide both sides 2d} \\ \frac{8d}{2d}=\frac{2d}{2d} \\ 4=1 \end{gathered}[/tex]Elena working
[tex]\begin{gathered} 8d=2d \\ \text{subtract 2d from both sides} \\ 8d-2d=2d-2d \\ 6d=0 \\ d=0 \end{gathered}[/tex]Elena moves will lead to a solution of d which will be equals to zero . Lin working will definitely cancel d on both sides and lead to no solution .
help me with this question please!
Answers
Answer: sales tax rate
Step-by-step explanation: p being the price and you mutiply 0.0635 by price to get the total
Pamela, Jody, Dawn, Ross, and Carmen each wrote their name on a slip of paper, folded it, and dropped it into a bowl for a gift exchange. Ross drew out a name first. What is the probability that he will not draw his own name? A. 2/5B. 1/4C. 1/5 D. 4/5
Answers
Given data:
The given number of names are n=5.
TEhe expression for the probability that Ross doesn't drew his
name is,
P(R')=4/5
Thus, the option (D) is correct.
9. a three-digit number, xyz, is formed of three different non-zero digits x , y , and z. a new number is formed by rearranging the same three digits. what is the greatest possible difference between the two numbers? (for ex- ample, 345 could be rearranged into 435, for a difference of 435 - 345
Answers
In linear equation, 792, which is the highest possible difference.
What are a definition and an example of a linear equation?
An equation in which there is only one variable is known as a linear equation in one variable.It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.One such linear equation in one variable is 9x + 78 = 18.Let m be the digit from 2 to 8.
The larger three digit number will look like 9m1, while the smaller three digit number will look like 1m9.
Assume a three digits number lets say 189.
Then the largest possible three digit number after rearranging above number is 981.
981 - 189 = 792
Again assume a three digits number lets say 149.
Then the largest possible three digit number after rearranging above number is 941.
941 - 149 = 792
for m their difference is constant i.e:792, which is the highest possible difference.
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Simplify the following expression using the distributive property -6(2x+4)Answer choices:-12x+4-4x-2-12x+24-12x-24
Answers
The given expression is,
[tex]-6(2x+4)[/tex]distributive property is,
[tex]A\times(B+C)=AB+AC[/tex]thus,
[tex]\begin{gathered} -6(2x+4) \\ -12x-24 \end{gathered}[/tex]the answer is -12x-24.
I need help with a question
Answers
---------------------------------
[tex]\begin{gathered} 6=1-2n+5 \\ 2n=1+5-6 \\ 2n=0 \\ n=\frac{0}{2} \\ n=0 \end{gathered}[/tex]solve the following inequalities for the variable x13<_-2x+5
Answers
Subtracting 5 at both sides:
[tex]\begin{gathered} 13-5\le-2x+5-5 \\ 8\le-2x \end{gathered}[/tex]Dividing by -2 (notice that dividing by a negative number changes the sign):
[tex]\begin{gathered} \frac{8}{-2}\ge\frac{-2x}{-2} \\ -4\ge x \end{gathered}[/tex]Angie is working on solving the exponential equation 23^x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.Hint: Use the change of base formula: log base b of y equals log y over log b.
Answers
x= 0.5714
Explanation
[tex]23^x=6[/tex]
Step1
[tex]\begin{gathered} 23^x=6 \\ \operatorname{mean}s \\ x=\log _{23}6 \\ as \\ \log _ba=\frac{\log _a}{\log _b} \end{gathered}[/tex]
therefore, replace
[tex]\begin{gathered} x=\frac{\log 6}{\log \text{ 23}} \\ x=\frac{0.778151}{1.361728} \\ x=0.5714 \end{gathered}[/tex]so, the answeris
x= 0.5714
I hope this helps you
If ABC measures 90°, what is the measure of AC?A. 180°90⁰B. 270°AC. 90°D. 45°8DO
Answers
Given:
Angle ABC measures 90°.
Required:
To measure AC.
Explanation:
Here
[tex]\angle ABC=90\degree[/tex]Therefore
[tex]\hat{AC}=90\degree[/tex]Final Answer:
The option C is correct.
90 degree.
A building has three elevators. Each elevator is out of order 20% of the time.The following set of random numbers represents 20 simulations of theelevators, with 0 and 1 representing a broken elevator and 2, 3, 4, 5, 6, 7, 8,and 9 representing a working elevator. In how many of the simulations wereall three elevators working?931 188 763 841 559 144 652 277 653 673404 396 011843599 797 414 761 273 844uA. 11B. 100C. 8oD. 12
Answers
The total stimulations in which all three elevators are working is 12(option d) by the concept of data representation.
What is data representation?Data Representation: A method for analyzing numerical data is data representation. Data representation is used to create a diagram that shows the connections between facts, ideas, information, and concepts. It is a fundamental learning technique that is clear-cut and uncomplicated. The data type in a particular domain is always what determines it. There are many various styles and sizes of graphical representations.
According to the given data:
A building has 3 elevators.
The following set of random numbers represents 20 stimulations of the elevators, with 0, 1 representing the broken elevator and 2,3,4,5,6,7,8and 9 representing a working elevator.
Stimulation data:
931 188 763 841 559 144 652 277 653 673 404 396 011 843 599 797 414 761 273 844
Now, as we observe from the given data, the stimulation in which all three elevators are working are-
763,559,652,277,653,673,396,843,599,797,273,844a total of 12 stimulations.
Thus, the total stimulations in which all three elevators are working is 12
Hence, option d is correct.
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Use The Following Function f(x)=-2(x-3)^2 +2, to find:a. vertexb.the directions of the parabola. c. the width of the parabola.d.the axis of symmetrye.the x-interceptsf.the y-interceptsg.the number of solutions.h.the standard form of the equation
Answers
Required:
a. vertex
b.the directions of the parabola.
c. the width of the parabola.
d.the axis of symmetry
e.the x-intercepts
f.the y-intercepts
g.the number of solutions.
h.the standard form of the equation
Solution:
The vertex form of the equation of a parabola is
[tex](y-k)=4p(x-h)^2[/tex]where h and k are the coordinates of the vertex.
a) Manipulating this function to the vertex form:
[tex]\begin{gathered} y=-2(x-3)^2+2 \\ (y-2)=-2(x-3)^2 \end{gathered}[/tex]Here, h = 3 and k = 2 . Thus the vertex is at V ( 3, 2 )
b) If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If a is negative, it opens down or to the left.
In this function x is squared and a is equal to -2 . Therefore, the parabola opens downward.
c) The focal width of the parabola is equivalent to 4p. From the vertex form of the equation, we can tell that 4p is 2. Thus, the width of the parabola is 2 units
[tex](y-2)=-2(x-3)^2[/tex]h) THE STANDARD FORM OF THE EQUATION
[tex]\begin{gathered} y=-2(x-3)^2+2 \\ y=-2(x^2-6x+9)+2 \\ y=-2x^2+12x-18+2 \\ y=-2x^2+12x-16 \\ \end{gathered}[/tex]d) The axis of symmetry is given by x = -b / 2a
In the above equation of the parabola, a = -2 and b = 12. Thus x = -b / 2a = - (12) / 2 ( -2 ) = -12 / - 4 = 3
The axis of symmetry is x = 3
THE INTERCEPT FORM y = a(x - r)(x - s), where r and s are the x-intercepts on the graph. It tell us if there are two x-intercepts, one x-intercept or no x-intercepts.
[tex]\begin{gathered} y=-2x^2+12x-16 \\ y=-2(x^2-6x+8) \\ y=-2\lbrack(x-4)(x-2)\rbrack \end{gathered}[/tex]e) From the intercept form of the equation of the parabola, we can tell that r = + 4 and s = + 2. Therefore , the x - intercepts of the parabola are at x = 4 and x = 2
f) The y -intercept is the point at which the parabola crosses the y -axis where x is zero. In the given funxction , if we let x be equal to zero then y is :
[tex]\begin{gathered} y=-2x^2+12x-16 \\ y=-2(0)^2+12(0)-16 \\ y=-16 \end{gathered}[/tex]The y -intercept of the parabola is y = -16 .
g) A parabola can have one, two, or no solutions. The solution of a parabola refers to the points where the graph does intersect with the x-axis. In the given function , there are two points where the parabola intersects the x-axis ( refer to e ) at x = 4 and x = 2. Therefore, the given parabola has two solution.
h) The standard equation of a parabola is
[tex]y=ax^2+bx+c[/tex]The standard form of the given function is : ( refer to the deriviation above, after c )
[tex]y=-2x^2+12x-16[/tex]Answers:
a) V ( 3, 2 )
b) The parabola opens downward
c) The width of the parabola is 2 units
d) The axis of symmetry is x = 3
e) The x - intercepts of the parabola are at x = 4 and x = 2
f) The y -intercept of the parabola is y = -16
g) The given parabola has two solutions.
h) The standard form of the given function is
[tex]y=-2x^2+12x-16[/tex]Use the graph that shows the solution to f(x)=g(x).f(x)=x2g(x)=(12)x−1 What is the solution to f(x)=g(x)?
Answers
Given the following question:
[tex]f(x)=g(x)[/tex]x = point of intersection
Given the following graph there is only one point of intersection.
[tex]x=2[/tex]Your answer is option D.
Answer: x=1
Step-by-step explanation: I took the test
(x - 1)(x + 3) ≤ 0
how tol solve this algebric inequalities and how to show them in the number line ?
Answers
Answer:
refer to the attachment
Please help me find the linear equation of question 9
Answers
Equation of a line in slope-intercept form
y = mx + b
where m is the slope and b is the y-intercept
From the graph, we can see that the line intercepts the y-axis at the point (0,-3), then b = -3.
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the line passes through the points (0, -3) and (2, -2), then its slope is:
[tex]m=\frac{-2-(-3)}{2-0}=\frac{-2+3}{2}=\frac{1}{2}[/tex]Substituting with m = 1/2 and b = -3 into the equation, we get:
[tex]\begin{gathered} y=\frac{1}{2}x+(-3) \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]
divisible by 2 and 9
3 digit number
first number is 5 and last number is 4 what’s the middle number
Answers
After using Trial and error - The number 504 is divisible by 2 and 9.
What is meant by trial and error method in math's?
The fundamental approach to problem-solving is trial and error. It is characterized by numerous, different attempts that are made repeatedly until success or the agent gives up. The issue is repeated through several steps until the correct solution is obtained. The trial and error approach to issue solving is used in this situation.
Using this approach,
we are given that
first digit of the three digit number is 5
last or the third number of the three digit number is 4
the possible outcomes for the middle or second number are- 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
we also know that no matter what number we put in the middle it'll be divisible by 2 since the last digit of the three digit number is ever (4 is even).
Hence we only need to take into consideration that the whole number should be divisible by 9.
using the trial and error method i put the middle digit to be 0, hence the number becomes 504.
now checking,
504 ÷ 2 = 252
and
504 ÷ 9 = 56
hence 504 is divisible by both 2 and 9.
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Express x in terms of y. Then find the value of x when y= 53 (x + 2y) = 2x + 5yX in terms of y:X=
Answers
Solve the equation for x, it means express x in terms of y
[tex]\begin{gathered} 3(x+2y)=2x+5y \\ 3x+6y=2x+5y \\ 3x-2x=5y-6y \\ x=-y \end{gathered}[/tex]Once found the expression of x in terms of y, replace for the given value of y to find x
[tex]\begin{gathered} y=5 \\ x=-y \\ x=-5 \end{gathered}[/tex]