Sandra, this is the solution:
6/7 * 1/2 = 6/14
And we can simplify, as follows:
6/14 = 3/7
The answer is 3/7
If the slope of one line is 7/8, what is the slope of the line that is perpendicular to it?88/71/7-1/8-8/7
Given:
Slope of the line 7/8
Slope of the perpendicular line is:
The multiplication of both line should be equal to -1
that mean:
[tex]m_1m_2=-1[/tex]Where m1 and m2 slopes of perpendicular line:
that mean:
[tex]m_1=\frac{7}{8}[/tex]Then slope of perpendicular line is:
[tex]\begin{gathered} m_1m_2=-1 \\ m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{\frac{7}{8}} \\ m_2=-\frac{8}{7} \end{gathered}[/tex]So slope of perpendicular line is -8/7
The following chart shows the number of months a savings account has been open and the balance of the account. Find the slope of the line through these points. Number of Balance Months (dollars) 1 $400 5 $800 7 $1,000 10 $1,300 D 80 D. 100 UD 100 80
SOLUTION
To find the slope, let us take two y-values and two x-values. This becomes
[tex]\begin{gathered} y-\text{values 800 and 400} \\ x-\text{values 5 and 1} \end{gathered}[/tex]The slope becomes
[tex]\begin{gathered} m=\frac{change\text{ in y}}{\text{change in x}} \\ m=\frac{800-400}{5-1} \\ m=\frac{400}{4} \\ m=100 \end{gathered}[/tex]Hence the answer is 100, the third option.
Use the given right triangle to find ratios, inreduced form, for sin A, cos A, and tan A.
In the given right triangle,
BC=5
AC=12.
Hypotenuse of the triangle, AB=13.
Now, the ratio of sin A can be expressed as,
[tex]\sin A=\frac{opposite\text{ side}}{hypotenuse}[/tex]The opposite side to angle A is BC.
Hence,
[tex]\begin{gathered} \sin A=\frac{BC}{AB} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]The ratio of cos A can be expresssed as,
[tex]\cos \text{ A=}\frac{\text{adjacent side}}{hypotenuse}[/tex]The side adjacent to angle A is AC.
Hence,
[tex]\begin{gathered} \cos \text{ A=}\frac{AC}{AB} \\ \cos \text{ A=}\frac{12}{13} \end{gathered}[/tex]The ratio tan A can be expressed as,
[tex]\begin{gathered} \tan \text{ A=}\frac{\text{opposite side}}{adjacent\text{ side}} \\ \tan \text{ A=}\frac{BC}{AC} \\ \tan \text{ A=}\frac{5}{12} \end{gathered}[/tex]Therefore, sin A=5/13, cos A=12/13 and tan A=5/12.
n^2+7n+15=5 factoring
let's rewrite:
[tex]n^2+7n+15=5[/tex]as:
[tex]n^2+7n+10=0[/tex]The factors of 10 that sum to 7 are 2 and 5, therefore:
[tex]n^2+7n+10=(n+2)(n+5)[/tex]a) complete the table in the answer space for the equation y=21/2x when x=2 and x=5b) using a scale of 2cm to 1 unit on the x-axis and 2cm to 2 unit on the y-axis, draw the graph of y= 21/2x for 0.5 ≤ x ≤ 7c) from the graph in (b) ,find:i. the value of y when x=4.5ii. the value of x when y= 7.6d) draw a suitable straight line on the graph in (b) to find the value of x which satisfy the equation 21/2x=15-2x for 0.5 ≤ x ≤ 7.State the values of x
For a)
x=2
[tex]y=\frac{21}{2(2)}=5.25[/tex]x=5
[tex]y=\frac{21}{2(5)}=2.1[/tex]b)
c)
We locate for each case the points
d)
First we need to solve the equation given
[tex]\frac{21}{2x}=15-2x[/tex]We isolate the x
[tex]21=2x(15-2x)[/tex]we simplify
[tex]21=30x-4x^2[/tex]Then we make zero the equation
[tex]4x^2-30x+21=0[/tex]Then we solve the second-degree equation.
The solutions are
[tex]\begin{gathered} x=0.781 \\ x=6.719 \end{gathered}[/tex]Both solutions are inside the given interval
Therefore the lines are
Answer the questions below.(a) Here are the prices in thousands) for 9 houses for sale in a local neighborhood:$163, $285, $286, $ 287, $ 292, $304, $308, $310, $314.Which measure should be used to summarize the data?MeanMedianMode(b) A data set shows the age of each resident at Lakeview Retirement Home.Which measure gives the age shared by the most residents?MeanMedianMode(c) In a survey, 9 people gave the following ratings for a local politician (on a scale of 0 to 100);42, 44, 45, 46, 47, 49, 50, 53, 54.Which measure should be used to summarize the data?MeanMedianModeX
a.
In the first question we need to summarize a set of the prices of houses in a local neighborhood, the best metric to summarize this data is the Median, since the set is assymetrical.
b.
The metric that shows the age shared by most residents is the Mode.
c.
The metric that best represents the ratins is the Mean, as the set is symmetrical and there are not clear outliers.
what is the total cost of a $716 tablet computer that is on sale at 15% off if the local sales tax rate is 7%, the cost of the tablet is how much money round to two decimal places as needed
Since the cost of the tablet is $716
Since the discount on it is 15%
Then let us find the cost after the discount
Multiply 15% by 716 to find the amount of the discount, then subtract it from the cost
[tex]\begin{gathered} d=\frac{15}{100}\times716 \\ d=107.4 \end{gathered}[/tex]Now, find the cost after the discount
[tex]\begin{gathered} C=716-107.4 \\ C=608.6 \end{gathered}[/tex]Let us find the cost after adding 7% for tax
The cost after the tax will be 100% + 7% = 107%
Then multiply 107% by $608.6 to find the final cost
[tex]\begin{gathered} FC=\frac{107}{100}\times608.6 \\ FC=651.202 \end{gathered}[/tex]Round it to 2 decimal places, then
FC = $651.20
The final cost of the tablet is $651.20
The expression -2(u-v)2 evaluated for.u = -3 and v =2
Answer:
-50
Step-by-step explanation:
We are given the following expression:
-2(u - v)²
To evaluate for u = -3 and v = 2, we replace u by -3 and v by 2.
So
-2(-3 - 2)² = -2(-5)² = -2(25) = -50
Find the answer for given questions? Slope- intercept? Point slope standard form?
Answer:
The equation in slope-intercept form will be;
[tex]y=-\frac{1}{2}x+1[/tex]The function in point-slope form is;
[tex]y-2=-\frac{1}{2}(x+2)_{}[/tex]The standard form of the equation is;
[tex]x+2y=2[/tex]Explanation:
Given the function f(x);
[tex]\begin{gathered} f(-2)=2 \\ f(8)=-3 \end{gathered}[/tex]Firstly, let us find the slope;
[tex]\begin{gathered} m=\frac{f(8)-f(-2)}{8-(-2)}=\frac{-3-2}{8+2}=\frac{-5}{10} \\ m=-\frac{1}{2} \end{gathered}[/tex]we can then solve for the constant term;
[tex]\begin{gathered} y=mx+b \\ at\text{ f(-2)=2;} \\ 2=-\frac{1}{2}(-2)+b \\ 2=1+b \\ b=2-1 \\ b=1 \end{gathered}[/tex]The equation in slope-intercept form will be;
[tex]y=-\frac{1}{2}x+1[/tex]Applying the point-slope form of equation;
[tex]y-y_2=m(x-x_2)[/tex]Substituting the second point;
[tex]\begin{gathered} y-2=-\frac{1}{2}(x-(-2)) \\ y-2=-\frac{1}{2}(x+2)_{} \end{gathered}[/tex]The function in point-slope form is;
[tex]y-2=-\frac{1}{2}(x+2)_{}[/tex]The standard form of the equation can be written as;
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1 \\ \text{multiply through by 2} \\ x+2y=2 \end{gathered}[/tex]The standard form of the equation is;
[tex]x+2y=2[/tex]elimination Strategy
-2x -4y = 38
5x - 4y = 3
To eliminate, since the coefficient of y is the same, we need to eliminate y by subtracting
So the correct option is A
Look at this graph: 9 5 1 2 3 4 5 6 7 8 9 10 What is the slope?
To find the slope, pick the points and determine the coordinates.
Let's take the points:
(x1, y1) ==> (0, 7)
(x2, y2) ==> (3, 8)
Use the slope formula below to find the slope:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Substitute the values into the slope formula above:
[tex]m=\frac{8-7}{3-0}=\frac{1}{3}[/tex]Therefore, the slope is = ⅓
ANSWER:
[tex]\frac{1}{3}[/tex]Jim Goodman, an employee at Walgreens earned 35,000 an increase of 17.6% over the previous year. What were Jim’s earnings the previous year? ( round to the nearest cent)
Last year earnings = X
Present Year earnings = $35,000
Increase = 17.6% = 0.176
[tex]X\cdot(1+0.176)=35000[/tex]This means, that last year earnings multiply by 1.176 equals the present earnings
If we solve for x:
[tex]x=\frac{35000}{1.176}=29761.90[/tex]We found that last year Jim used to earn $29,761.90
the exponential function f(x) =5^x after a vertical stretch by a factor of 3 and a reflection across the y axis
after a vertical stretch by a factor of 3:
[tex]f(x)=5^{3x}[/tex]And after a reflection across the y-axis:
[tex]f(x)=5^{-3x}[/tex]I need help with my mathCheck whether (0, 0) is a solution(1) x > -4
ANSWER
Yes, (0,0) is a solution.
EXPLANATION
To check if (0,0) is a solution of this inequality we simply have to replace x by 0 and y by 0. If the inequality is true after replacing, then the point is a solution.
In this inequality we only have x,
[tex]0>-4[/tex]0 is indeed greater than -4, thus this inequality is true and therefore (0, 0) is a solution
8 Divided by 9/12 Answer
Answer:
10.6667
Step-by-step explanation:
8 x 12/9 X 96/9
you take 96/9 and simply it which gives you 10.6667
f(x) = x +3, g(x) = x - 3. Find(f-g)(x)
Steph, let's recall that composite function is a function that depends on another function. A composite function is created when one function is substituted into another function.
Given f(x) = x +3, g(x) = x - 3
• f (g(x)) = f (x - 3)
,• (x - 3) + 3
,• x - 3 + 3
,• x
• g (f(x)) = g (x + 3)
,• (x + 3) - 3
,• x + 3 - 3
,• x
For the given functions, f (g(x)) = g (f(x))
Student became unresponsive, no final interaction
I’d very much appreciate some help!I was tested on this question and didn’t know how to solve it much, this is new material for me. I need a step by step tutorial with reasons! Thank you!
Answer:
The value of x is;
[tex]x=4[/tex]Explanation:
From the question, it was stated that line BD bisects(divide into two equal halves) angle ABC.
So, angle ABD will be the same as angle CBD.
[tex]\measuredangle ABD=\measuredangle CBD[/tex]Given;
[tex]\begin{gathered} m\measuredangle ABD=7x-10 \\ m\measuredangle CBD=4x+2 \end{gathered}[/tex]substituting the given values we have;
[tex]\begin{gathered} \measuredangle ABD=\measuredangle CBD \\ 7x-10=4x+2 \end{gathered}[/tex]Solving the resulting equation for x, we have;
[tex]\begin{gathered} 7x-10=4x+2 \\ \text{add 10 to both sides;} \\ 7x-10+10=4x+2+10 \\ 7x=4x+12 \\ \text{subtract 4x from both sides} \\ 7x-4x=4x-4x+12 \\ 3x=12 \\ \text{divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=4[/tex]The shaded area in the circle below represents a damaged section of a 6-foot diameter tabletop.What value is closest to the area of the damaged section?A. 4.0 square feetB. 8.1 square feetC. 7.7 square feetD. 6.0 square feet
The rule of the area of the sector is
[tex]A=\frac{\emptyset}{360}\times\pi\text{ }\times r^2[/tex]The angle is 77 degrees
The diameter is 6 feet
The radius is half the diameter, then
The radius = 6/2 = 3 feet
Substitute the values of the angle and the radius in the rule above
[tex]A=\frac{77}{360}\times\pi\times(3)^2=6.0475658=6.0\text{ square f}eet[/tex]So the answer is D
The area of the damaged section is 6.0 square feet
The table below gives the distribution of milk chocolate M&M’s. If a candy is drawn at random, what is the probability that it is not orange or red?
To find the probability of the drawn candy to not be red or orange we first need to calculate the probability of it being red or orange. This is done by using the formula below:
[tex]\begin{gathered} P(\text{red or orange) = P(red) + P(orange)} \\ P(\text{red or orange) = 0.13 + 0.2 = 0.33} \end{gathered}[/tex]We now need to find the probability of that not happening. To do that we will subtract that value of 1.
[tex]\begin{gathered} \text{\textasciitilde }P(\text{red or orange) = 1 - P(red or orange)} \\ \text{\textasciitilde }P(\text{red or orange) = 1 - 0.33 = 0.67} \end{gathered}[/tex]The probability of it not being red or orange is 0.67
The Editor-in-Chief of the student newspaper was doing a final review of the articles submitted for the upcoming edition. Of the 12 total articles submitted, 5 were editorials. If he liked all the articles equally, and randomly selected 1 article to go on the front cover, what is the probability that the chosen article is an editorial? Write your answer as a decimal rounded to four decimal places.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
total articles = 12
editorials = 5
P (editorial) = ?
Step 02:
articles selected = 1
P (event) = favorable outcomes / total outcomes
P (editorial) = 5 / 12 = 0.4167
The answer is:
P (editorial) = 0.4167
Fill in the blanks below.Find the slope of the line passing through the points (3,7) and (3,-4).slope: 0Find the slope of the line passing through the points (-2,5) and (9,5).slope: 0
Part a
we have the points (3,7) and (3,-4)
Note that the x-coordinates are equal
that means
Is a vertical line (parallel to the y-axis)
that means
the slope is undefinedVerify
m=(-4-7)/(3-3)
m=-11/0 ----> undefined
Part b
we have the points (-2,5) and (9,5)
Note that the y-coordinates are equal
That means
Is a horizontal line (parallel to the x-axis)
The slope is zeroVerify
m=(5-5)/(9+2)
m=0/11
m=0
The diagram shows a tin can in the shape of a cylinder and its dimensions. What is the volume of the can in cubic inches in terms of tt? А 1087 in. B 3241 in. 9 in. 3 © 817 in. D 541 in. 6 in. -
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
r is the radius
h is the height
You have the diameter on the base, you use the diameter to find the radius, as the diameter is:
[tex]d=2r[/tex]Then, the radius is:
[tex]r=\frac{d}{2}[/tex]d=6in
[tex]r=\frac{6in}{2}=3in[/tex]Then, the volumen of the given cylinder is: 81pi cubic inches[tex]V=\pi(3in)^2\cdot9in[/tex][tex]V=\pi\cdot9in^2\cdot9in[/tex][tex]V=81\pi in^3[/tex]The range is (- infinity, infinity) and the turning points are (-1.73 , -10.39) and (1.73 , 10.39). What intervals is the function increasing on and decreasing on?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Show the increasing and decreasing points of the given graphs
STEP 2: Get the intervals of increment and decrement
For intervals where the function is increasing on, we have:
[tex](-1.73,1.73)[/tex]For the intervals where the function is decreasing on, we have two intervals which will be combined using the union sign and will be gotten as:
[tex](-\infty,-1.73)\cup(1.73,\infty)[/tex]Hi I need help please :). Directions: For each real world situation write and solve a system of equations give the solution as either an ordered pair or list what each variable is worth then explain what the solution means in terms of the situation
From the information in the statement, we know that
• 3 tickets and 2 combos cost $44
,• 6 tickets and 5 combos cost $97.25
Then, let be
• x: the cost of a ticket
,• y: the cost of a combo
And we can write the following system of linear equations
[tex]\begin{cases}3x+2y=44\Rightarrow\text{ Equation 1} \\ 6x+5y=97.25\Rightarrow\text{ Equation 2}\end{cases}[/tex]To solve the system of linear equations, we can use the elimination or reduction method.
First, we multiply Equation 1 by -2
[tex]\begin{gathered} (3x+2y)\cdot-2=44\cdot-2 \\ \text{ Apply the distributive property to the left side of the equation} \\ 3x\cdot-2+2y\cdot-2=-88 \\ -6x-4y=-88 \end{gathered}[/tex]Second, we add Equations 1 and 2
[tex]\begin{gathered} -6x-4y=-88 \\ 6x+5y=97.25\text{ +} \\ ------------ \\ 0x+y=9.3 \\ \mathbf{y=9.3} \end{gathered}[/tex]Third, since we already have the value of y, then we replace its value with any of the initial equations and solve for x. For example in Equation 1
[tex]\begin{gathered} 3x+2y=44 \\ 3x+2(9.3)=44 \\ 3x+18.6=44 \\ \text{ Subtract 18.6 from both sides of the equation} \\ 3x+18.6-18.6=44-18.6 \\ 3x=25.4 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{25.4}{3} \\ \mathbf{x=8.5} \end{gathered}[/tex]Then, the solution of the system of linear equations that describes the situation mentioned in the statement is
[tex]\begin{cases}x=8.5 \\ y=9.3\end{cases}[/tex]Finally, now we know that the cost of a ticket is $8.5 and that the cost of a popcorn/drink combo is $9.3.
How do you solve letter b using a subtraction equation with one variable that has a solution of 2/3
Let x be the variable. Then, a subtraction equation which involves the variable x and 2/3 as a result could be:
[tex]x-\frac{1}{3}=\frac{1}{3}[/tex]because, x wil be given as
[tex]\begin{gathered} x=\frac{1}{3}+\frac{1}{3} \\ x=\frac{2}{3} \end{gathered}[/tex]Trigonometry For the triangle below, find the exact value of cos A
Given
To find the exact value of cos A.
Explanation:
It is given that,
[tex]\begin{gathered} opp.side=8 \\ adj.side=8 \\ hypotnuse=\sqrt{8^2+8^2} \\ =\sqrt{64+64} \\ =\sqrt{128} \\ =8\sqrt{2} \end{gathered}[/tex]That implies,
[tex]\begin{gathered} cosA=\frac{8}{8\sqrt{2}} \\ cosA=\frac{1}{\sqrt{2}} \end{gathered}[/tex]Hence, the exact value of cos A is,
[tex]\frac{1}{\sqrt{2}}[/tex]If Jake makes 5 out of every 7 shots he makes at the free throw line. What is the ratio of shots made to total shots?a7 to 5b5 to 2C5 to 7d7 to 2
Given:
5 shots made every 7 total shots
Shots made = 5
Total shots = 7
In this question, we are asked to find the ratio of shots made to total shots.
Given that there are a 5 shots made
A panel for a political forum is made up of 11 people from three parties, all seated in a row. The panel consists of 5 Republicans, 5 libertarians, and I GreenParty member. In how many distinct orders can they be seated if two people of the same party are considered identical (not distinaX?
So,
Here we have the following table:
We want to find the probability to choose a man. So, there are 7+21 = 28 men in total.
The total number of people is 70, so this probability is:
[tex]P(\text{male)}=\frac{28}{70}=0.4[/tex]b) The probability that the person is a man who doesn't practice sport.
If we look at the table, there are 7 men who doesn't practice sport, so:
[tex]P(no\text{ sport and male)=7/70}[/tex]7/70 = 0.1, so this probability is 0.1
c) Finally, remember that:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]We want the to find the probability that the person doesn't practice sport given that it is a man.
If we replace:
[tex]P(\text{No sport | male )=}\frac{P(No\text{ sport and male)}}{P(male)}=\frac{0.1}{0.4}=0.25[/tex]6. 5. Convert each function to slope-intercept form, and then determine in which quadrant the solution falls by graphing the following system of equations. 3x + y = 5 slope-intercept = -9x-3y = 12 slope- intercept = In Ou
The slope intercept form of a line is:
[tex]y=mx+b[/tex]Then we can write each of the equations as:
[tex]\begin{gathered} 3x+y=5 \\ y=5-3x \\ y=-3x+5 \end{gathered}[/tex][tex]\begin{gathered} -9x-3y=12 \\ -3y=12+9x \\ y=\frac{12}{-3}+\frac{9x}{-3} \\ y=-4-3x \\ y=-3x-4 \end{gathered}[/tex]We have parallel lines, as they both have the same slope (m=-3).
If we graph the lines, we get:
The lines don't intersect, so we have no solution.
We can demonstrate this as:
[tex]\begin{gathered} 3x+y=5 \\ -9x-3y=12\longrightarrow3x+y=\frac{12}{-3}=-4 \\ \longrightarrow3x+y=5\ne-4\longrightarrow\text{ no solution (they are not equal)} \end{gathered}[/tex]A Distance Run (km) B Distance Run (km) 0889 1 1/2 2 4 5 4 55 5 1 8 2 1 1/367 0 1 1 1 24 77 1 2 3 3 6 8 9 3 5 5 6 7 8 9 3 10 034 4 5 310 What is the DIFFERENCE in the MEANS of the 2 sets of data? Type your answer without a label.
To find the mean, we have to add all the numbers to then divide that sum by the total number of elements.
Chart A.Let's sum each row.
8 + 8 + 9 = 25
1 + 2 + 2 + 4 + 5 + 5 + 8 = 27
1 + 1 + 3 + 6 + 7 = 18
0 + 3 + 4 + 4 + 5 = 16
[tex]\bar{x}=\frac{25+27+18+16}{4}=\frac{86}{4}=21.5[/tex]The mean of chart A is 21.5.
Chart B.1 + 1 + 2 + 4 + 7 + 7 = 22
2 + 3 + 3 + 6 + 8 + 9 = 31
3 + 5 + 5 + 6 + 7 + 8 + 9 = 43
[tex]\bar{x}=\frac{22+31+43+0}{4}=\frac{96}{4}=24[/tex]Then, we subtract
[tex]24-21.5=2.5[/tex]Hence, the difference between the means is 2.5.