The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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Which function describes this graph?
The graph in the question is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.
Given a graph which is downward sloping and we are required to find the function whose the graph is.
Function is like a relationship between two or more variables expressed in equal to form. It may be a linear function,exponential function, logarithmic function or quadratic function.
In the given graph the values of y becomes negative when the curve crosses then x axis. For all x>1 the value of log x is greater than 0. So the value of [tex]log_{2}x,log_{4}x,log_{20}x[/tex] should be greater than 0 for x greater than 1. But in graph it is negative. That's why the graph will be of y=[tex]log_{0.2}x[/tex].
Hence the given graph is of the function f(x)=[tex]log _{0.2}x[/tex] which is option a.
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a green grocer had 623 oranges. He packed them in cartons, which could only take 11 oranges or 12 oranges respectively, and no oranges remained. How many cartons had 12 oranges only?
Answer:51 crates could have 12 oranges and one crate could hold 11 oranges.
Step-by-step explanation: 623 / 12 is 51.9... 51 x 12 is 612. 612 + 11 is 623 math checks out.
35 POINTS!!! PLEASE HELP !!!!!!!!!!!!!!
( I already know the answer isn't -2, -1 so D is out of the question
A function is shown in the table.
x g(x)
−2 2
−1 0
0 2
1 8
Which of the following is a true statement for this function? (5 points)
Group of answer choices
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = −1 to x = 0.
The function is increasing from x = 0 to x = 1.
The function is increasing from x = −2 to x = −1.
Answer:
The function is increasing from x = 0 to x = 1.
Step-by-step explanation:
A function is increasing when the y-value increases as the x-value increases.
A function is decreasing when the y-value decreases as the x-value increases.
From x = -2 to x = -1 the function is decreasing as the y-value decreases as the x-value increases:
x-value -2 to -1 → increasey-value 2 to 0 → decreaseFrom x = -1 to x = 0 the function is increasing as the y-value increases as the x-value increase:
x-value -1 to 0 → increasey-value 0 to 2 → increaseFrom x = 0 to x = 1 the function is increasing as the y-value increases as the x-value increase:
x-value 0 to 1 → increasey-value 2 to 8 → increaseIf a rectangle is not a square, what is the greatest number of lines of symmetry that can be drawn?
Answer: B
Step-by-step explanation: what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry
Simplify[tex](\frac{16}{81}x^{16}\right))^{\frac{1}{2}}[/tex]
Answer:
[tex]\sf \dfrac{4}{9}x^8[/tex]
Step-by-step explanation:
Law of exponents:[tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]
16 = 4 *4 = 4²
81 = 9 *9 = 9²
[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]
[tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]
And that the terms of this series may be arranged without changing the value of the series, determine the sum of the reciprocals of the squares of the odd positive integers
The terms of this series may be arranged without changing the value of the series. The sum of the reciprocals of the squares of the odd positive integers is [tex]\pi ^{2} /8[/tex].
In mathematics, a sequence is the cumulative sum of a given collection of terms. Usually, those phrases are actual or complicated numbers, but plenty of extra generalities are feasible.
A series is described as an arrangement of numbers in a specific order. then again, a chain is described as the sum of the factors of a sequence.
In mathematics, a series is, more or less speaking, a description of the operation of including infinitely many quantities, one after the alternative, to a given beginning quantity. The look at of series is a primary part of calculus and its generalization, mathematical analysis.
k=1
1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.
up to ∞ terms = 2/6
[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+
..∞0] = T²/6
→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+
1/4(3)²+....0] =²/6
[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+
1/(3)²+....x] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6
⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6
=
↑
[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8
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Solve for x. You must show all your work to receive credit.
Step-by-step explanation:
since the 2 arc angles cover the full circle, we know their sum must be 360°.
so,
23x - 5 + 37x + 5 = 360
60x = 360
x = 6
and so the angle at V = 5×6 + 17 = 30+17 = 47°
A group of friends wants to go to the amusement park. They have $284.25 to spend on parking and admission. Parking is $9.25, and tickets cost $27.50 per person, including tax. How many people can go to the amusement park?
Answer:
7
Step-by-step explanation:
The start this question by looking at two important things, how much money we have and how much money it costs per person. The friends have a total of $284.25 and we don't know how much it costs per person. To find this we must set up an equation and solve it!
Because each person must pay for parking and a ticket, we can find the cost for one person by adding the parking and ticket cost together.
$9.25 + $27.50 = $36.75
Now that we have solved this equation, we know that it costs $36.75 for one person. To find how many total people can go we dived the total amount of money we have by how much it costs per person. Let's call the number of people that can go 'p'.
p = [tex]\frac{284.25}{36.75}[/tex]
Once we simplify/solve this equation we get 7 [tex]\frac{36}{49}[/tex] so essentially, we get the whole number 7 and a long decimal, but the only important part is the 7. We take the whole number from our answer which is 7.
We now know the answer: 7.
Let's check our work!
7 * 36.75 = 257.75
284.25 - 257.75 = 26.5
26.5 < 36.75 so we are correct!
The final answer is 7!
Have an amazing day!
If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?
Answer:
I am not 100% confident, but I think that she is 11.
Step-by-step explanation:
Answer:
14 years old
Step-by-step explanation:
Define the variable
Let x be the actual age of Zeba (in years).
Create an equation using the give information and the variable x:
[tex](x - 5)^2=5x+11[/tex]
To find Zeba's age now, solve the equation for x.
Expand the brackets:
[tex]\implies x^2-10x+25=5x+11[/tex]
Subtract 5x from both sides:
[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]
[tex]\implies x^2-15x+25=11[/tex]
Subtract 11 from both sides:
[tex]\implies x^2-15x+25-11=11-11[/tex]
[tex]\implies x^2-15x+14=0[/tex]
Factor the found quadratic
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-14x-x+14=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-14)-1(x-14)=0[/tex]
Factor out the common term (x - 14):
[tex]\implies (x-1)(x-14)=0[/tex]
Apply the zero product property:
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-14)=0 \implies x=14[/tex]
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
Check
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her actual age is 14 years old.
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1. General term for -2, -5, -8, -11
2. General term for 22, 20, 18, 16
The general terms for the given arithmetic sequences are given as follows:
1. [tex]a_n = -2 -3(n - 1)[/tex]
2. [tex]a_n = 22 - 2(n - 1)[/tex]
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The general term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
For sequence 1, given by -2, -5, -8, -11, the first term and the common ratio are given as follows:
[tex]a_1 = -2, d = -3[/tex]
Hence the general term that defines sequence 1 is presented below:
[tex]a_n = -2 -3(n - 1)[/tex]
For sequence 2, represented by 22, 20, 18, 16, the first term and the common ratio are given as follows:
[tex]a_1 = 22, d = -2[/tex]
Hence the general term that defines sequence 2 is presented below:
[tex]a_n = 22 - 2(n - 1)[/tex]
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In a certain exam of grade ten, 75% students got high score in mathematics, 65%
students got high score in English. If 6% of them did not get high score in both
mathematics and English, then calculate:
i. the percent of students who got high score in both the subjects.
ii. the total number of students who got high score either in mathematics or
in English if 300 students had attended the exam.
Mathematics, grade 10
(i) The percentage of students who got high scores in both the subjects English and Mathematics is 46%.
(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.
What is probability?The probability exists in the analysis of the possibilities of happening of an outcome, which exists acquired by the ratio between favorable cases and possible cases.
The number of students who got high scores in Mathematics was 75%.
The number of students who got high scores in English was 65%.
(i) The percentage of students who got high scores in both the subjects
100% - 6% = 94%
(75% + 65%) - 94%
= 140% - 94%
= 46%
Therefore, the percentage of students who got high scores in both the subjects English and Mathematics is 46%.
(ii) The total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam
= 300 [tex]*[/tex] 46%
= 300 [tex]*[/tex] (46 / 100)
= 300 [tex]*[/tex] 0.46
= 138.
Therefore, the total number of students who got high scores either in Mathematics or in English if 300 students had attended the exam exists 138.
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Given u=(-12,-5) and v=(3,9) what is proj v u?
[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]
So, the correct answer is Option 1.
The limits of the class intervals are
The lower and the upper class limit are as follows
interval lower limit upper limit
10-14 10 14
15-19 15 19
20-24 20 24
25-29 25 29
This is further explained below.
What is the class limit?Generally, The lower class limit and the upper-class limits are just the minima and maximum values that are allowed in each class, respectively: The gap that exists between the upper-class limit and the lower class limit is referred to as the class interval.
In conclusion, The lower and the upper class limit are as follows
interval lower limit upper limit
10-14 10 14
15-19 15 19
20-24 20 24
25-29 25 29
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I’m gonna ask this question again can someone help me solve this and leave in terms of pi
The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].
The circumference for a circle with diameter 10 is [tex]10\pi[/tex].
The circumference for a circle with diameter 19 is [tex]19\pi[/tex].
The circumference for a circle with diameter 30 is [tex]30\pi[/tex].
The circumference for a circle with diameter 16 is [tex]16\pi[/tex].
Relatively easy, right?
The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].
The area of a circle with radius 5 is [tex]25\pi[/tex].
The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].
The area of a circle with radius 15 is [tex]225\pi[/tex].
The area of a circle with radius 8 is [tex]64\pi[/tex].
Hope this helped!
(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)
Answer:
Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]
Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]
Step-by-step explanation:
For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
radius = 5
diameter = 10
circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]
for the second row
radius = 9.5
diameter = 19
circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]
for the third row
radius = 15
diameter = 30
circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]
for the fourth row
radius = 8
diameter = 16
circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]
Which solution finds the value of x in the triangle below?
A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction = StartFraction 8 Over x EndFraction. x times 2 StartRoot 3 EndRoot = 24. x = StartFraction 24 Over 2 StartRoot 3 EndRoot EndFraction. x = StartFraction 12 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 12 StartRoot 3 EndRoot Over 3 EndFraction. x = 4 StartRoot 3 EndRoot.
Secant 60 degrees = StartFraction 8 Over x EndFraction. One-half = StartFraction 8 Over x Endfraction. x = 16
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction StartRoot 3 EndRoot Over 2 EndFraction = StartFraction 8 Over x EndFraction. x times StartRoot 3 EndRoot = 16. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 StartRoot 3 EndRoot Over 3 EndFraction.
The value of x in the triangle is 4
How to determine the solutions?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = 8
Adjacent = x
Angle = 60
The cosine of the angle is then calculated as:
cos(angle) = Adjacent/Hypotenuse
Substitute the known values in the above equation
cos(60) = x/8
Multiply both sides by 8
x = 8 * cos(60)
Evaluate the product
x = 4
Hence, the value of x in the triangle is 4
So, the complete parameters are:
Hypotenuse = 8
Adjacent = x
Angle = 60
x = 4
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Answer:
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Step-by-step explanation:
The answer above is correct.
Select the correct answer. daniel has a list of numbers that are not in any order. he wants to find the order of the numbers with the help of a spreadsheet. which statistical function will help him do so? a. mode b. rank c. median d. average
The correct option is B.
Rank
What is Rank function?The RANK function in a Microsoft Excel spreadsheet enables users to order the various pieces of data by their numerical values. By entering an absolute value for the range of cells the user wants to rank, they can also use the rank function. If an absolute value is not specified, the program's auto-formula may cause the rank of the various cells to alter.
What is Spreadsheet?A spreadsheet is a computer program used for organizing, organizing, analyzing, and storing tabular data. Spreadsheets were created as electronic alternatives to paper accounting worksheets. Data typed into table cells serves as the program's input.
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16. On your own paper, graph the following system of equations. Describe the graphs (perhaps give a few points on each line) and give the solution to the system of equations.
-2x - 5y = 20
y=4/5x+2
Answer:
(-5, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]
Both equations are linear equations.
Equation 1Rearrange Equation 1 to make y the subject:
[tex]\implies -2x-5y=20[/tex]
[tex]\implies -5y=2x+20[/tex]
[tex]\implies y=-\dfrac{2}{5}x-4[/tex]
Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]
[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]
Plot the found points and draw a straight line through them.
Equation 2The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]
[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]
Plot the found points and draw a straight line through them.
SolutionThe solution(s) to a system of equations is the point(s) of intersection.
From inspection of the graph, the point of intersection is (-5, -2).
To verify the solution, substitute the second equation into the first and solve for x:
[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]
[tex]\implies \dfrac{6}{5}x=-6[/tex]
[tex]\implies 6x=-30[/tex]
[tex]\implies x=-5[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]
Hence verifying that (-5, -2) is the solution to the given system of equations.
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First simplify first one
-2x-5y=205y=-2x-20y=-2/5x-4Another one is
y=4/5x+2On first line
at x=0
y=-4At x=5
y=-2-4=-6On second line
At x=0
y=2At x=5
y=20+2=22Graph attached
Solution is (-5,-2)
Out of total 47 observation arranged in ascending order, the 12th and 13th observation are 25 and 30 respectively. What is the value of Quartile 1
Answer: i believe the answer is 26
Step by step explanation
Total no. of observation = (12+13) = 25
Median = Average of 18/2 observation + (18/2+1)
=1/2 (12th observation + 13 observation)
1/2 × (25 +27) = 1/2 × 52
=26
What number should go in the space? Multiplying by 1.36 is the same as increasing by _________%.
The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.
How to calculate the percentage increase of a number?The formula for calculating the percentage increase of a number is
%increase = 100 × (Final - initial)/initial
Calculation:Consider the number as 'x'
The result when the number is multiplied by 1.36 is 1.36x
So, the percentage increase is calculated as follows:
%increase = 100 × (Final - initial)/initial
Where Initial = x and Final - 1.36x
⇒ %increase = 100 × (1.36x - x)/x
⇒ %increase = 100 × x(1.36 - 1)/x
⇒ %increase = 100 × 0.36
⇒ %increase = 100 × 36/100
∴ %increase = 36
Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.
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The angle measurements in the diagram are represented by the following expressions. \qquad \blueD{\angle A=7x + 40^\circ}∠A=7x+40 ∘ start color #11accd, angle, A, equals, 7, x, plus, 40, degrees, end color #11accd \qquad\greenD{\angle B=3x + 112^\circ}∠B=3x+112 ∘ start color #1fab54, angle, B, equals, 3, x, plus, 112, degrees, end color #1fab54 Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd: \blueD{\angle A} =∠A=start color #11accd, angle, A, end color #11accd, equals ^\circ ∘
⟨A = 7•x + 40° and ⟨B = 3•x + 112°
From a possible diagram of the question, ⟨A = ⟨B, which gives;
x = 18°⟨A = 166°How can the value of x and the measure of ⟨A be found?Given;
⟨A = 7•x + 40°
⟨B = 3•x + 112°
In the diagram from a similar question posted online, we have;
⟨A and ⟨B are corresponding anglesCorresponding angles formed by parallel lines having a common transversal are congruent, therefore;
⟨A and ⟨B are congruentWhich gives;
⟨A = ⟨B7•x + 40° = 3•x + 112°
7•x - 3•x = 112° - 40° = 72°
7•x - 3•x = 4•x = 72°
x = 72° ÷ 4 = 18°
Therefore;
x = 18°Which gives;
⟨A = 7•x + 40°
⟨A = 7 × 18 + 40° = 166°
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Answer:d
Step-by-step explanation:
khan
Simplify.
2[(8 ÷ 4)-(-5)] + 6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]
[tex]\mathsf{= 2(7) + 6}[/tex]
[tex]\mathsf{= 2 \times 7 + 6}[/tex]
[tex]\mathsf{= 14 + 6}[/tex]
[tex]\mathsf{= 20}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]
First, we will start with the division:
[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]
Now we will resolve what is inside the bracket:
[tex]\longrightarrow \sf{2[2+5] +6}[/tex]
[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]
Now we will solve the multiplication:
[tex]\longrightarrow \sf{14 +6= 20}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]
how do i get the method on how to solve this x+5(-2)-1
Answer:
I forgot the name but I can show you how to do it lol
Step-by-step explanation:
x+5(-2)-1
x-10-1 we multiplied 5 and -2
x-11
x=11
how I did the last one is there is a non-existent 0 with an equal sign like my teacher says so we added 11 to both sides.
If (a2b−3c)34a−1b4c5=apbqcr What is the value of p+2q?
Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.
Then substitute the values of p and q into p+2q to get -10
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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2. Solve for x.
9
6
8
X
Answer:
I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side
An airplane travels 6111 kilometers against the wind in 9 hours and 7911 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind
Answer:
Speed of the plane in still air: [tex]779\; {\rm km \cdot h^{-1}}[/tex].
Windspeed: [tex]100\; {\rm km \cdot h^{-1}}[/tex].
Step-by-step explanation:
Assume that [tex]x\; {\rm km \cdot h^{-1}}[/tex] is the speed of the plane in still air, and that [tex]y\; {\rm km \cdot h^{-1}}[/tex] is the speed of the wind.
When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be [tex](x - y)\; {\rm km \cdot h^{-1}}[/tex]. When this plane is travelling in the same direction as the wind, the ground speed of this plane would be [tex](x + y)\; {\rm km \cdot h^{-1}}[/tex].The question states that when going against the wind ([tex]v = (x - y)\; {\rm km \cdot h^{-1}}[/tex],) the plane travels [tex]6111\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex]. Hence, [tex]9\, (x - y) = 6111[/tex].
Similarly, since the plane travels [tex]7911\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex] when travelling in the same direction as the wind ([tex]v = (x + y)\; {\rm km \cdot h^{-1}}[/tex],) [tex]9\, (x + y) = 7911[/tex].
Add the two equations to eliminate [tex]y[/tex]. Subtract the second equation from the first to eliminate [tex]x[/tex]. Solve this system of equations for [tex]x[/tex] and [tex]y[/tex]: [tex]x = 779[/tex] and [tex]y = 100[/tex].
Hence, the speed of this plane in still air would be [tex]779\; {\rm km \cdot h^{-1}}[/tex], whereas the speed of the wind would be [tex]100\; {\rm km \cdot h^{-1}}[/tex].
Geometry: complete this proof, ASAP!!!!!!!!!!!!!!!! It’s urgent
Answer:
1. AC is perpendicular to BD
1. Given
2. ACB is a right angle
2. Definition of perpendicular lines
3. Triangle ACB is a right triangle
3. Definition of right triangles
4. Angles 1 and 3 are complementary
4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.
Find the values of the unknown angles marked with letters.
a=
b=
c=
Answer:
a = 97° , b = c = 146°
Step-by-step explanation:
a and 83° are same- side interior angles and sum to 180°
a + 83° = 180° ( subtract 83° from both sides )
a = 97°
34° and b are same- side interior angles and sum to 180°
b + 34° = 180° ( subtract 34° from both sides )
b = 146°
b and c are corresponding angles and are congruent , so
c = b = 146°
Answer:
< a = 97 degrees.
< b = 146 degrees.
< c = 146 degrees.
Step-by-step explanation:
We have 2 lines crossing 2 parallel lines.
Internal angles between the 2 parallel lines add up to 180 degrees, so
34 + <b = 180
<b = 180 - 34 = 146 degrees
Also
<a + 83 = 180 degrees (also internal angles)
---> <a = 97 degrees
< c and < b are corresponding angles so are congruent, therefore
<c = < b = 146 degrees.
Marika is training for a track race. She start sprinting by 100 yards. She gradually increases her distance, adding 4 yards a day for 21 days. the explicit formula that models this situation is an=100+(n-1)4. how far does seh sprint on day 21
Answer:
180 yards
Step-by-step explanation:
The number of yards she sprints on day 21 can be found by evaluating the formula with n=21.
Solutiona21 = 100 +(21 -1)4 = 100 +(20)(4) = 100 +80 . . . . . use 21 in place of n
a21 = 180
Marika sprints 180 yards on day 21.
If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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