By definition, let m be the slope a line, then m can be calculated by the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}^{}[/tex]Given that (x1, y1) and (x2, y2) are known points of the line. By reflecting all the points of the line across the line y = x
For the rectangle shown below, which can be used to find the value of x?A. 3^2 + x^2 = 15^2B. (x + 3)^2 = 15^2C. 3^2 + 15^2 = x^2D. 3 + 15 = x^2
Since the rectangle is composed of 2 right triangles, we can apply the Pythagorean theorem to one of the triangles:
c^2 = a^2 +b^2
Where:
c= hypotenuse (longest side) = 15
a & b = the other two legs of the triangle ( x , 3 )
Replacing:
15^2 = 3^2 + x ^2
Solve for x
225 = 9 + x^2
225-9 = x^2
216 = x^2
√216 = x
x= 14.69
So, to find the value of x, we can use:
A. 3^2 + x^2 = 15^2
X-4-3-2-1012f(x)-6-4-1-2-5-8-16Which is a possible turning point for the continuousfunction f(x)?O(-3,-4)O (-2,-1)O (0,-5)O (1,-8)
Solution
[tex](-2,-1)[/tex]The final answer
Option B
I would like to know the answer for this question it’s very confusing
As the first step, let us say that the velocity of the boat in relation to a fixed point in the map of this travel is equal to its velocity in relation to the water PLUS the water velocity in relation to the fixed point WHEN it is in the same direction (travel downstream), and MINUS when traveling in the opposite direction (upstream).
From this, we will remember the definition of velocity by:
[tex]V=\frac{\Delta S}{\Delta t}[/tex]The ΔS is the distance ran by the boat, which is 60 miles. Δt is 4h for the upstream case, and 3h for the downstream case.
From this, we say that the value of V is for the boat in relation to the water (which is what we need here) and v for the water. Now, we have the following system of equations.
[tex]\begin{gathered} V-v=\frac{60}{4}=15 \\ V+v=\frac{60}{3}=20 \\ \\ V-v=15 \\ V+v=20 \end{gathered}[/tex]Now, to proceed with the solution, we will sum up the equations, which will result in the following:
[tex]\begin{gathered} V-v+(V+v)=15+20 \\ 2V=35 \\ V=\frac{35}{2} \\ \\ V=17.5mph \end{gathered}[/tex]From the solution developed above, we are able to conclude that the rate of the boat in still water, what is the velocity the boat reaches in relation to the water, is equal to 17.5 miles per hour.Are The Ratios 2:4 and 1:3 equivalent?Yes or No
The ratio 2:4 is equivalent to and 1:3 if both numbers are obtained by the same multiplication:
Since
1 x 2 = 2 and
3 x 2 = 6 (instead of 4)
then they are NOT equivalent
A committee has seven men and four women. If four people are selected to go to a conference, what is the chance that the group is two men and two women?
Given:
A committee has seven men and four women.
four people are selected to go to a conference
We will use the combinations as follows
the number of ways to choose the four people are:
[tex]7C4+7C3+7C2+7C1+7C0[/tex]The rule of combinations is:
[tex]\text{nCr}=\frac{n!}{(n-r)!\cdot r!}[/tex]so, the number of ways will be:
[tex]35+35+21+7+1=99[/tex]The number of ways to make a group of two men and two women will be:
[tex]7C2=21[/tex]So, the chance that the group is two men and two women =
[tex]\frac{21}{99}=\frac{7}{33}[/tex]so, the answer will be 7/33
A new model of shirt at the clothing store comes in 4 colors: black, white, red, and blue
The data provided of the 16 sold shirts can be used to count the frequency of each color.
The results are shown below:
White = 5
Black = 2
Blue = 4
Red = 5
We can check the total is 5 + 2 + 4 + 5 = 16
Now we are ready to draw the bar graph, where each color must have a height that equals its frequency.
Target is having a sale on bath towels usually bath towels cost $15 today I paid only $12 what percent of the original price did I pay for the bath towels
80%
1) Since the prices on Target dropped from $15 to $12 to find the equivalent percentage of $12 in comparison to $15 we need to write down the following ratio:
[tex]\begin{gathered} 15----100\% \\ 12----x\% \\ \frac{15}{12}=\frac{100}{x} \\ 15x=12\cdot100 \\ \frac{15x}{15}=\frac{1200}{15} \\ x=80\% \end{gathered}[/tex]Note that we cross multiplied that ratio and then on the second step we have divided both sides by 15.
2) Hence, I paid 80% of the original price that day
I have this question and I can’t figure it out
Hello!
First, let's remember about the integers numbers.
These numbers can be positive or negative (and include the number 0). The main characteristic is that these numbers don't have a decimal part.
Knowing it, we can say that are integers:
• -1,
,• 0,
,• 2,
,• -2.
In the number line, we'll have:
If f(5)=2 and g(5)=9, what is (f+g)(5)
Answer:
11
Step-by-step explanation:
You have an equation [tex]f(x)[/tex] and you set [tex]x=5[/tex], and the result is 2.
You have another equation [tex]g(x)[/tex] and you set [tex]x=5[/tex], and the result is 9.
Therefore, if you add both equations, represented by [tex](f+g)(x)[/tex], and you set [tex]x=5[/tex], the result is simply 2 + 9 = 11.
In JKL, LJ K L and mZK = 26Find mZJ.
From the information given, we can draw a triangle.
A rough drawing of the triangle is shown below:
7. Find the value of x in the figure below. Justify your answer. 4 pts 20° (x - 15)° X = Reason:
Answer
x = 85°
Explanation
The image of this question shows that the two angles 20° and (x - 15)° both sum up to give a right angle (90°). So,
20° + (x - 15)° = 90°
20° + x - 15° = 90°
x° + 20° - 15° = 90°
x + 5° = 90°
x = 90° - 5°
x = 85°
Hope this Helps!!!
[tex] {a}^{12} {b}^{ - 9} \ \: {c}^{ - 6} [/tex]what is the answer ?
We have the following expression:
[tex](a^{12}b^{-9})\frac{c^{-6}}{\square}[/tex]Now let's recall two properties of the exponents that will help to solve this exercise:
[tex]x^{-1}=\text{ }\frac{1}{x}\Rightarrow4^{-3\text{ }}=\text{ }\frac{1}{4^3}[/tex]Then we have:
[tex]a^{12}c^6/b^9[/tex]Now, we have all the exponents with positive sign
The base of the exponents is different (a,b and c), therefore there is no additional step we can take
Student became unresponsive. Closing the session
✓ 2 ✓ 3 ✓4 Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer. 16 A 9 A 13 A Check PLUS EGEE E Com. Tune here to
the given diagram:
We have to find the value of DE
Since all the lines intersect at right angle
[tex]\begin{gathered} \text{Here, AC + DE = BF} \\ 5\text{ + DE =13} \\ DE=13-5 \\ DE=8\text{ ft} \end{gathered}[/tex]Answer : DE = 8ft
How many weeks are in 259 days
SOLUTION
We want to find the number of weeks in 259 days
Now, 7 days make a week. So to get the number of weeks in 259 days, we divide the 259 by 7, we get
[tex]\frac{259}{7}=37[/tex]So the answer is 37 weeks
Select all of the ordered pairs that are solutions to the equation y= -6x + 7
We must substitute each pair into our equation:
A. If we substitute point (1,1), we have
[tex]\begin{gathered} 1=-6(1)+7 \\ 1=-6+7 \\ 1=1 \end{gathered}[/tex]then, this point is a solution.
B. If we substitute point (-1,1), we have
[tex]\begin{gathered} 1=-6(-1)+7 \\ 1=6+7 \\ 1=13\text{ !!!} \end{gathered}[/tex]this means that this point is not a solution.
C. If we substitute point (-6,7), we have
[tex]\begin{gathered} 7=-6(-6)+7 \\ 7=36+7 \\ 7=43\text{ !!!} \end{gathered}[/tex]this means that this point is not a solution.
D. If we substitute point (3,-11), we have
[tex]\begin{gathered} -11=-6(3)+7 \\ -11=-18+7 \\ -11=-11 \end{gathered}[/tex]then, this point is a solution.
Therefore, the solutions are option A and D
Find the zeros of each function by using a graph and a table. f(x)=x^2+2x–24.
Explanation
Step 1
[tex]f(x)=x^2+2x-24[/tex]Zeros
A(-6,0) B(4,0)
because
[tex]\begin{gathered} f(x)=x^2+2x-24 \\ f(-6)=(-6)^2+2(-6)-24=36-12-24=0 \\ f(4)=4^2+2\cdot4-24=16+8-24=0 \end{gathered}[/tex]Step 2
table
[tex]\begin{gathered} (-6,0) \\ (4,0) \\ f(-1)=-1^2+2\cdot-1-24=1-2-24=-25 \\ (1,-25) \\ \end{gathered}[/tex]I hope this helps you
Can you pls help me with this question thank you
The expression we have is:
[tex]2x+5[/tex]In this expression, we have two terms: 2x and 5.
The elements in these terms are variables, coefficients, and constants.
A variable is a letter that can take different values, a coefficient is a number that accompanies the variable, and a constant is a number that does not have any variable next to it (its value will not change).
In this case:
2 is the coefficient,
x is the variable,
and 5 is the constant.
Answer: a) 5
Paxton did the following multiplication problem. Where should he put the decimal point in his product? 9.18 % 73 2754 64260 67014 6.701.4 67.014 6.7014 670.14
We have the multiplication of 9.18 * 7.3 and want to know where the decimal point has to be.
In the multiplication we have to sum the decimal position of the numbers and taht is the position of the decimal point of the result.
In this case, the decimal point of 9.18 is 2 places and for 7.3 is one place, so the final result will have 2+1=3 places. The decimal point has to be 3 places.
The number is 67014 and the decimal point is three places from rigth, 67.014
Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4.20.Write and solve an equation to find the original price of the charging cord
The total discount in Arlene's purchase was 4.20, this includes the discount applied over both, the case and the charging cord. We already know the original price of the phone case, the discount applied and the value of the discount, use it to find the original price of the chargind cord:
[tex]\begin{gathered} 0.15(18+x)=4.20 \\ 18+x=\frac{4.20}{0.15} \\ 18+x=28 \\ x=28-18 \\ x=10 \end{gathered}[/tex]The original price of the charging cord is $10
simplify: 9x^4-27x^6/3x^3
simplify: 9x^4-27x^6/3x^3
we have the expression
[tex]\begin{gathered} 9x^4-\frac{27x^6}{3x^3} \\ \\ 9x^4-9x^{(6-3)} \\ 9x^4-9x^3 \end{gathered}[/tex]we have the expression
[tex]\begin{gathered} \frac{9x^4-27x^6}{3x^3} \\ \frac{9x^4}{3x^3}-\frac{27x^6}{3x^3} \\ 3x-9x^3 \end{gathered}[/tex]this is the answer
Write a polynomial function of least degree with the given zeros: -2, 1,4
Since we want a polynomial p(x) with zeros -2,1 and 4, we have the following expression:
[tex]p(x)=(x-(-2))(x-1)(x-4)[/tex]If we multiply these factors we get:
[tex]\begin{gathered} p(x)=(x+2)(x-1)(x-4) \\ \Rightarrow p(x)=(x^2+x-2)(x-4) \\ \Rightarrow p(x)=x^3-4x^2+x^2-4x-2x+8 \\ p(x)=x^3-3x^2-6x+8 \end{gathered}[/tex]Therefore, the polynomial function with the given zeros is p(x)=x^3-3x^2-6x+8
Rewrite barrel as a unit rate. hour O A. barrel/hour B. 10 barrels/hour O C. To barrel/hour OD. 1 barrels/hour
Then the correct answer is A. 5/8 barrel/hour
Volume of the box with the cone shape cut out of it. What are the side lengths of the box and what is the volume of the box/cube only?
Answer:
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³
Explanation:
The sides of a cube are all equal, so in this case, the side length of the box is 6 cm.
Then, the volume can be calculated as
Volume = side x side x side
Volume = 6 cm x 6 cm x 6 cm
Volume = 216 cm³
To know the volume of the box with the cone shape cut of it, we need to calculate the volume of the cone with the following equation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Where π = 3.14, r is the radius and h is the height. The diameter of the cone is 4 cm, so the radius is
r = 4 cm/2 = 2 cm
Then, replacing r = 2 cm and h = 6 cm, we get
[tex]\begin{gathered} Volume=\frac{1}{3}(3.14)(2\text{ cm\rparen}^2(6\text{ cm\rparen} \\ Volume=\frac{1}{3}(3.14)(4\text{ cm}^2)(6\text{ cm\rparen} \\ Volume=25.12\text{ cm}^3 \end{gathered}[/tex]Now, the volume of the box without the cone shape is
V = 216 cm³ - 25.12 cm³
V = 190.88 cm³
So, the answers are
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³
RIn this figure, sin ZQOP = cos 2and cos ZROQ = sin 2
So, Sin QOP = QP/OQ = OPPOSITE/ Hyp
Then, cos PQO = QP/OQ = Adjacent/ Hyp
Using the same logic, Cos ROQ = RO/OQ = Adj/Hyp
Then, sin QPO = RO/OQ = Opp/Hyp
What is the slope of LaTeX: f\left(x\right)=3x-1
To find the slope of the expression:
[tex]f(x)=y=3x-1[/tex]We need to remember that this is the Slope-intercept Form of the line equation:
[tex]y=mx+b[/tex]Where
m = slope
b is the y-intercept.
Therefore, the slope of the line equation above is m = 3.
Photo attached. Total cost as function of x = Domain of total cost function =
1. Identify the given from the statements.
• Let the side of the square base= s
• Height of the rectangular box be= h
,• Given that :
s^2h = 20ft^3
solving for sh: s^2h = 20
s^2=20/h
s*s/s = 20/h /s
s = 20/hs
• Therefore sh = 20/s
Expandingthe given statements , we learn that :
• Material cost for base per square foot = 20 cents
,• Material cost for sides per square foot = 18 cents
,• Material cost for the top per square foot = 14 cents
2. Calculate Total cost
Total cost = {(s^2*20) + 4(sh)*18 +s^2*14}cents
= 20s^2 + 72*20/s + 14s^2
=34s^2 + 1440/s
• Expressing Total cost in terms of x , let s = x .
• Then Total cost (x) = 34x^2 +1440/x
2. Calculating the domain of TC(x) =34x^2 +1440/x
x <0 or x> 0
Domain (-∞;0) U(0;∞)
1/4+3/8 in simplest term
Kinsley measured a city park and made a scale drawing the scale of the drawing was 13 millimeters and 5 meters if the actual width of the soccer field is 65 meters how wide is the field in millimeters
Kinsley measured a city park
Scale of drawing : 13 milimeter and 5 meter
Actual width is 65 meter
Let the field in Milimeter is x
So,
[tex]\begin{gathered} 13\text{ milimeters and 5 meters=x milimeters and 65 meters} \\ \frac{13}{5}=\frac{x}{65} \\ \text{Apply cross multiplication} \\ x=\frac{13\times65}{5} \\ x=\frac{13\times13}{1} \\ x=169 \\ Park\text{in milimeters = 169} \\ So, \\ 13\text{ milimeters and 5 meters=169 milimeters and 65 meters} \end{gathered}[/tex]Answer: 13 milimeters and 5 meters = 169 milimeters and 65 meters
How many quarts of pure antifreeze must be added to 3 quarts of a 50% antifreeze solution to obtain a 60% antifreeze solution?quart(s) of pure antifreeze must be added(Round to the nearest tenth as needed.)
Initially we have 3 quarts of a 50% antifreeze solution
We want to obtain a 60% antifreeze solution by adding x quarts of pure antifreeze
Therefore we can set the following equation,
[tex]1x+0.5*3=0.6*(x+3)[/tex]where x are the quarts of pure antifreeze added
let's solve for x
[tex]\begin{gathered} x+1.5=0.6x+1.8 \\ x-0.6x=1.8-1.5 \\ 0.4x=0.3 \\ x=\frac{0.3}{0.4} \\ x=0.75 \end{gathered}[/tex]rounding to the nearest tenth, 0.8 quarts of pure antifreeze must be added
A biologist records the number and types of fish caught in a local lake during a 2-yearperiod. The biologist reports that 796 of the fish caught during this period were trout,whereas 43% of the fish caught were bass. These reports of the number of trout andbass at this lake are examples ofcumulative frequencies.percentile ranks.relative frequencies.smooth curves.
Record for the number and types of fish caught in a local lake during a 2-year
period
Fish caught during this period were trout = 796
Fish caught during this period were bass = 43%
Total percentile = 100%
Fish caught during this period were trout = 100 - percentage of fish caught during this period were bass
fish caught during this period were trout = 100 - 43 = 57%
Hence the reports of the number of trout and
bass at this lake are examples of percentile ranks