In order to solve the given expression follow these steps:
1. Take the square roots on both sides in order to get rid of the power on the left side:
√(x-5)² = ±√3
x - 5 = ±√3
2. add 5 on both sides:
x-5 + 5 = 5 ±√3
x = 5 ±√3
Then, the solution is x = 5 ±√3
The wholesale price for a pair of shoes is $7.50. A certain department store marks up the wholesale price by 60%. Find the price of the pair of shoes in the department store. Round your answer to the nearest cent, as necessary.
Given:
Wholesale price for a pair of shoes is $7.50
[tex]\text{The price of pair of shoes in the departmental store=7.50}+(7.50\times\frac{60}{100})[/tex][tex]\text{The price of pair of shoes in the departmental store=7.50}+4.50[/tex][tex]\text{The price of pair of shoes in the departmental store= \$12}[/tex]What is the equation of the line that is perpendicular to the line 5x – 3y = 2 and passes through the point (-1,3)?
Answer:
3x+5y=12.
Explanation:
Given the line: 5x-3y=2
First, we determine the slope by making y the subject of the equation.
[tex]\begin{gathered} 3y=5x-2 \\ y=\frac{5}{3}x-\frac{2}{3} \end{gathered}[/tex]Comparing with the slope-intercept form: y=mx+b
• Slope = 5/3
Let the slope of the perpendicular line = n
By definition. two lines are perpendicular if the product of their slopes is -1.
Therefore:
[tex]\begin{gathered} \frac{5}{3}\times n=-1 \\ n=-\frac{3}{5} \end{gathered}[/tex]Next, we use the point-slope form to find the perpendicular to the given line that is passing through (-1, 3).
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{3}{5}(x-(-1)) \\ y-3=-\frac{3}{5}(x+1)\text{ Multiply both sides by 5} \\ 5(y-3)=-3(x+1) \\ 5y-15=-3x-3 \\ 5y+3x=-3+15 \\ 3x+5y=12 \end{gathered}[/tex]The required equation is 3x+5y=12.
The following data represents the weight of goods in a truck in tons. Find the lower limit of the outlier.1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
0.5
Explanations:The given dataset is:
1.5, 1.4, 1.7, 1.2, 2, 1.8, 2.5
Step 1: Rearrange the dataset in ascending order
1.2, 1.4, 1.5, 1.7, 1.8, 2, 2.5
Step 2: Find the lower quartile, Q₁
The lower quartile is the median of the first half of the data set
That is Q₁ is the median of 1.2, 1.4, 1.5
Q₁ = 1.4
Step 3: Find the upper quartile, Q₃
The upper quartile is the median of the second half of the data set
That is Q₃ is the median of 1.8, 2, 2.5
Q₃ = 2
Step 4: Find the interquartile range (IQR)
IQR = Q₃ - Q₁
IQR = 2 - 1.4
IQR = 0.6
Step 5: Find the lower limit of the outlier using the formula below
Lower limit = Q₁ - 1.5(IQR)
Lower limit = 1.4 - 1.5(0.6)
Lower limit = 1.4 - 0.9
Lower limit = 0.5
Rewrite in simplest terms: -0.3(8b – 2c)+7c - 0.9(9c – 2b)
The given expression is
-0.3(8b – 2c) +7c - 0.9(9c – 2b)
We would apply the distributive property as shown below
a(b + c) = a * b + a * c
The term outside the bracket is used to multiply the terms inside the bracket. Thus, we have
- 0.3 * 8b + - 0.3 * - 2c + 7c - 0.9 * 9c + - 0.9 * - 2b
= - 2.4b + 0.6c + 7c - 8.1c + 1.8b
The next step is to collect like terms. Thus, we have
- 2.4b + 1.8b + 0.6c + 7c - 8.1c
= - 0.6b - 0.5c
The simplified expression is
- 0.6b - 0.5c
А
B
The scale factor that takes A onto B is
The scale factor that takes B onto A is
Let,
x₁, y₁ = 2, 2
x₂, y₂ = 6, 10
a.) The slope of the line.
[tex]\text{ Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{\text{ 10 - 2}}{\text{ 6 - 2}}\text{ = }\frac{\text{ 8}}{\text{ 4}}[/tex][tex]\text{ Slope = 2}[/tex]Therefore, the slope of the line is 2.
b.) The y-intercept of the line.
Substitute slope = m = 2 and x, y = 2, 2 in y = mx + b
[tex]\text{ y = mx + b}[/tex][tex]\text{ 2 = 2(2) + b}[/tex][tex]\text{ 2 = 4 + b }\rightarrow\text{ b = 2 - 4}[/tex][tex]\text{ b = y-intercept = -2}[/tex]Therefore, the y-intercept is -2.
For us to answer the other 2 questions, let's first complete the equation of the graph.
Substitute slope = 2 and y-intercept = -2 in the y = mx + b
y = mx + b
y = (2)x + (-2)
y = 2x - 2
The equation of the line is y = 2x - 2
c.) Finding the value of a.
x = a
y = 8
We get,
[tex]\text{ y = 2x - 2}[/tex][tex]\text{8 = 2a - 2}[/tex][tex]\text{ 2a = 8 + 2 = 10}[/tex][tex]\text{ }\frac{\text{2a}}{\text{ 2}}\text{ = }\frac{\text{10}}{\text{ 2}}[/tex][tex]\text{ a = 5}[/tex]Therefore a = 5
d.) Finding the value of b.
x = 4
y = b
[tex]\text{ y = 2x - 2}[/tex][tex]\text{ b = 2(4) - 2}[/tex][tex]\text{ b = 8 - 2 = 6}[/tex]Therefore, b = 6
A 7m long ladder leans against a wall such that the foot of the ladder is 4.5m away from the wall. What is the angle of elevation of the ladder?
Given:
• Height of ladder = 7 m
,• DIstance of foot of ladder to the wall = 4.5 m
Let's find the angle of elevation of the ladder.
First sketch the figure representing this situation.
Where x is the angle of elevation of the ladder.
Let's solve for x.
To solve for x, apply the Trigonometric ratio formula for cosine.
[tex]\cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]Where:
• Adjacent side is the side adjacent to the angle x = 4.5
,• Hypotenuse is the longest side = 7
,• θ is the angle = x
Hence, we have:
[tex]\cos x=\frac{4.5}{7}[/tex]Take the cos inverse of both sides:
[tex]\begin{gathered} x=\cos ^{-1}(\frac{4.5}{7}) \\ \\ x=49.9\approx50^o \end{gathered}[/tex]Therefore, the angle of elevation of the ladder is 50 degrees.
ANSWER:
c. 50 degrees
7 in.Rounded to the nearest tenth, find:Surface Area =square inchesVolume =cubic inchesBlank 1:Blank 2:
The Solution.
By formula, the surface area of the given figure is
[tex]S.A=4\pi r^2[/tex][tex]\begin{gathered} SA=\text{surface area}=\text{?} \\ r=7\text{ inches} \\ \pi=3.14 \end{gathered}[/tex][tex]S\mathrm{}A=4\times3.14\times7^2=4\times3.14\times49=615.44\approx615.4inches^2[/tex]b. By formula, the volume of the given figure is
[tex]V=\frac{4\pi r^3}{3}[/tex]Where,
[tex]r=7\text{ inches,}\pi=3.14,V=volume=?[/tex]Substituting the values in the formula, we have
[tex]V=\frac{4\times3.14\times7^3}{3}=\frac{4\times3.14\times343}{3}=\frac{4308.08}{3}[/tex][tex]V=1436.0267\approx1436.0inches^3[/tex]Hence, the correct answers are:
a. Surface area = 615.4 square inches
b. Volume = 1436.0 cubic squ
The rectangle has side length r and s for each expression determine whether it gives the perimeter of the rectangle the area of the rectangle or neither select the correct choice in each row r+s r times s 2r+2a r2+s2
we have the following:
[tex]\begin{gathered} P=2r+2s \\ A=r\cdot s \end{gathered}[/tex]there P is perimeter and A is area
therefore, r + s and r^2 + s^2 are neither
I need help with 1.76 only. Thanks.1-75Your seam will be given a bag containing a set of coloredblocks or counters, Bach seam will receive a bag that isidentical to yours2. Taka the blocks in your buy. If you were toreach into the bag and select one block withoutkuking, what is the likelihood that it would beRed?ii. Green?fil, Blue?iv. Orange?b. Do your answers for pant (a) represent theoretical or experimentalprobabilities? Judify your response1.76If you were to select one back from the bag 12 times, replacing the block youdrew baween each selection, how many of those times would you expect tohave selected a blue block? What if you drew 24 times? Discuss bothsituations with your team and explain your answers,
The number of possiblities is given by the combinations of 5 blue block taken at 1
[tex]5C1[/tex]where 5C1 denotes the combinations of 5 blue block taken at 1 time. Then, we have
[tex]5C1=5[/tex]then, we will expect 5 times form the total of 12.
Similarly, for the other case (number of times = 24), we will get
[tex]2\times5C1=2\times5=10\text{ times}[/tex]that is, we will double the number of times.
Alice traveled 30 miles in 3 hours. What graph shows the relationship between time traveled in hours and total miles traveled?The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Given that Alice traveled 30 miles in 3 hours. Initially, the distance traveled is 0 miles.
Take distance on the x-axis and time on the y-axis.
From the given information, the two points on the graph are (0,0) and (30,3).
Mark the points on the graph.
The distance-time graph of a body is a straight line. Join the points by a straight line to get the required graph.
For the function, f(x) = 38 • 0.24%, what is the decay factor? A) 38 B) 0.24 C) 0.14 D) 0.76
The decay factor is equal to 24%. In decimal form its equal to 0.24. Hence, the answer is B) 0.24
Hello, I'm confused on this one. Writing English expression into algebraic language.
STEP-BY-STEP EXPLANATION:
Firstly, you need to understand that are many operations symbols that are used in algebra. The operations are listed below
[tex]+\text{ , - , }\times,\text{ }\frac{\square}{\square}[/tex]When translating a word statement into an algebraic equation, the following points are very important
0. Read the problem carefully and figure out what you are asked to find
,1. Assign a variable to what you are looking for
,2. Write down the variables
,3. Write down the expression or equation
As you can see from the first question given,
A number multiplied by 24
Firstly, we need to assign a variable.
Let the variable be m
The next step is to identify the operation is the statement
The mathematical operation is multiplication
Hence, the expression is written below as
A number multiplied by 24 = m x 24
PART 4
A number multiplied by 2 and then take away 21
Firstly, assign a variable
Let the variable be m
Secondly, multiply the variable by 2
m x 2 = 2m
Take away mean minus
The next thing is to take away 21
Therefore, we have
2m - 21
Rewrite 3^x = 243 as a logarithmic equation. log3(243) = x logx(243) = 3 log3(x) = 243 log243(x) = 3
In general, the logarithmic function definition states that
[tex]y=log_b(x)\Leftrightarrow x=b^y[/tex]Therefore, in our case,
[tex]3^x=243\Leftrightarrow x=log_3(243)[/tex]Thus, the answer is log3(243)=x, the first option.when Nolan left his house this morning, his cell phone was 30% charged and it then started to lose 5% charge for each hour thereafter. Write an equation for B, in terms of t, representing the charge remaining in Nolan's battery, as a percentage, t hour after Nolan left his
b= 30 -5t
1) Gathering the data
30%=0.3
5% = 0.05
Setting a table
charge hour
30% 0
25% 1
20% 2
15% 3
The first part 30-5b is the charge in %, t is the instant
30-5t =b
I’m not sure if I’m suppose to include “x=___” in my answer or just put the answer in alone without including the variable. Please let me know which way is correct. I’m not sure if I’m writing out the problem wrong.
SOLUTION
Given the question in the inage on the question tab;
[tex](x-9)^2=2[/tex][tex]\begin{gathered} \sqrt{(x-9)^2}=\pm\sqrt{2} \\ x-9=\pm\sqrt{2} \\ x=\pm\sqrt{2}+9 \\ \therefore x=\sqrt{2}+9,\text{ -}\sqrt{2}+9 \\ \end{gathered}[/tex]Final answer:
[tex]x=\sqrt{2}+9,\text{ -}\sqrt{2}+9[/tex]D In the diagram, ABDE, ZA ZD, andCAFD What theorem can be used to prove the triangles are congruent? E HL SSA AAS SAS
there are two triangles and
it is given that two sides of both the triangle is equal or congruent
and there is also given that so by side - angle - side the given triangles are congruent
so the answer is SAS.
Which statements are best supported by the graph K?I. The X-intercept is located at (-3,0)II. The coordinates of the y-intercept are(0,9)III. The axis of symmetry is x=-3
Answer
All of the statements (I, II and III) given are supported by the graph K.
Step-by-step Explanation
The question asks us to check which statements are best supported by the graph K? The statements include
I. The X-intercept is located at (-3,0)
II. The coordinates of the y-intercept are (0,9)
III. The axis of symmetry is x=-3
We will take each of the statements one at a time.
I. The X-intercept is located at (-3,0)
Note that the x intercept is the point where the graph meets the x-axis, that is, the value of x on the graph when y=0.
From the graph, we can see the point where the graph meets the x-axis is x = -3, hence, the x-intercept is truly located at (-3, 0).
II. The coordinates of the y-intercept are (0,9)
The y intercept is the point where the graph meets the y-axis, that is, the value of y on the graph when x=0.
From the graph, we can see that the point where the graph meets the y-axis is y = 9, hence, the coordinates of the y-intercept is (0, 9)
III. The axis of symmetry is x = -3
The axis of symmetry is the central axis of the graph, which signifies the middle point of the graph. It is evident that this graph is centered on x = -3.
Hence, this statement too, is correct.
Hope this Helps!!!
Notebook cost $2.50 and pens cost $0.75. The cost of n notebooks and p pens is 2.50n+0.75p.Find the cost2 notebooks and 4 pens3 notebooks and 5 pens
Cost =2.50n + 0.75 p
n= number of notebooks
p = number of pens
2 notebooks and 4 pens
Replace n =2 , p=4 and solve:
C = 2.50(2) + 0.75 (4) = 5 +3 = $8
3 notebooks and 5 pens
Same process
C = 2.50 (3) + 0.75 (5) = 7.5 + 3.75 = $11.25
In which quadrant is the coordinate pair (-11, 1) located?a IVb Ic IId III
Step 1: Using the cartesian plane, let's locate the coordinate par (-11, 1)
Michael recently started a new hourly wage job. The equation y=18.75x + 2500 models his total pay, y, in dollars as it relates to the number of hours, x, that he has worked.A. What is Miguel's hourly rate of pay?B. Does it appear the Miguel received a signing bonus? If so, how much was the bonus?How many hours must Miguel worked to receive $10,000 in total pay?
Given
y = 18.75x + 2500
Part A:
Based on the given equation where x is the number of hours worked. Since the coefficient of this term is 18.75, then we can conclude that Miguel's hourly rate is $18.75.
Part B:
The given equation has a constant of 2500, at x = 0, where the number of hours worked is zero, then the value of the equation is 2500. This appears that Miguel has a signing bonus, and the amount of bonus is $2500.
Part C:
Substitute y = 10000, to the equation and solve for x
[tex]\begin{gathered} y=18.75x+2500 \\ 10000=18.75x+2500 \\ 10000-2500=18.75x \\ 7500=18.75x \\ 18.75x=7500 \\ \frac{18.75x}{18.75}=\frac{7500}{18.75} \\ x=400 \end{gathered}[/tex]Therefore, Miguel must work 400 hours to receive $10,000 in total.
Eric is exploring the formula for the circumference of a circle. He computed the circumferences of several circles with different radii. He then plotted the results and connected them with a line, as shown below. The graph shows the circumference (in m) versus the radius (in m). Find the domain and the range of the function shown.
Answer:
Domain of a function
The domain of a function is the set of all possible inputs for the function.
Hence,
From the graph below, the domain of the function will be
Hence,
The domain will be
[tex]\Rightarrow0\leq x<\infty[/tex]Step 2:
Range of the function
The range of a function is the set of its possible output values.
From the graph below, the range of the function will be
Hence,
The range of the graph is
[tex]0\leq y<\infty[/tex]only need help finding the length please and thank you
Solution:
Let the length of the chocolate bar is L and the width be W.
The area of the chocolate bar is expressed as
[tex]\begin{gathered} \text{Area = length}\times width \\ =L\times W \end{gathered}[/tex]Given that the area of the chocolate bar is 47.94 square feet, we have
[tex]\begin{gathered} A=L\times W \\ \Rightarrow47.94=LW\text{ ---- equation 1} \end{gathered}[/tex]Item 26Which relation is a function?{(1, 2), (2, 3), (3, 2), (2, 1)}{(1, −1), (−2, 2), (−1, 2), (1, −2)} {(4, 2), (3, 3), (2, 4), (3, 2)}{(1, 4), (2, 3), (3, 2), (4, 1)}
Using the given relations, let's determine the relation which represents a function.
A relation represents a function if for each value of x there is only one possible y-value.
This means that in the relation no value of the x-coordinate must appear twice or be repeated.
Using the relations given, the relation which is a function is:
{(1, 4), (2, 3), (3, 2), (4, 1)}
This is because, in this relation, there is only one value y for each value of x.
In this relation, no x value appears more than once.
Therefore, the relation which is a function is:
{(1, 4), (2, 3), (3, 2), (4, 1)}
ANSWER:
{(1, 4), (2, 3), (3, 2), (4, 1)}
solve the system of equations and choose the correct ordered pair. 2x - 6y = 85x - 4y = 31
We have
[tex]\begin{gathered} 2x-6y=8\text{ (1)} \\ 5x-4y=31\text{ (2)} \end{gathered}[/tex]we must solve the system of equations
First, we will solve for x the first equation
[tex]\begin{gathered} 2x-6y=8 \\ 2x=8+6y \\ x=\frac{8}{2}+\frac{6}{2}y \\ x=4+3y \end{gathered}[/tex]Then, we must replace the value of x in the second equation
[tex]\begin{gathered} 5(4+3y)-4y=31 \\ 20+15y-4y=31 \\ 11y=11 \\ y=\frac{11}{11} \\ y=1 \end{gathered}[/tex]Finally, we replace the value of y in the equation that we solved for x
[tex]\begin{gathered} x=4+3(1) \\ x=4+3 \\ x=7 \end{gathered}[/tex]So, the correct ordered pair is (7, 1)
Ost< and cost is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find sin t.18) cos i =316I need help with #18
sin^2t + cos^2t = 1
sint = 1/4
(1/4)^2 + cos^2 t = 1
1/16 + cos^2 t = 1
cos^2 t = 1 - 1/16
cos^2 t = (16 - 1)/16
cos^2 t = 15/16
take root both side,
[tex]\begin{gathered} cost=\sqrt[]{\frac{15}{16}} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]so the answer is option D
In the figure, segment RS bisects segment DE at S. Given that DS=4x+12 andSE=8x-8, find the value of x.
Step 1: Let's recall that a segment bisector is a ray or segment which cuts another line segment into two equal parts.
Step 2: Upon saying that, we have:
DS = SE
Step 3: Replacing with the equation we have to solve for x:
4x + 12 = 8x - 8
4x - 8x = - 8 - 12
-4x = -20
Dividing by - 4
-4x/-4 = -20/-4
x = 5
Step 4: If x = 5, let's find the length of DS and SE:
4 * 5 + 12 = 8 * 5 - 8
20 + 12 = 40 - 8
32 = 32
Step 5: x = 5 and DS/SE = 32
What is the common ratio of the sequence 18,24,32…
Answer:
4/3
Explanation:
The given sequence is 18, 24, 32, ...
Then, the common ratio can be calculated as
24/18 = 4/3
32/24 = 4/3
Because 24 and 18 are consecutive numbers and 32 and 24 are consecutive numbers.
Therefore, the common ratio is 4/3
Watts are units that measure the rate at which energy is used. A kilowatt is equal to 10 to the 3rd power watts. A gigawatt is equivalent to 10 to the 9th power watts. How many kilowatts are in a gigawatt?
can you tell me which one is the answer just that I don't need anything else.
Thus the answer is Option (D) 7/15.
The graph of a periodic function f is shown below.What is the period of this function? What is the amplitude of this function? Write a function formula for f. (Enter "theta" for θ.)f(θ)=
The period of the function is 3.14, amplitude is 3 and the
Function: ,f(θ) = 3*cos(2*θ) + 1
To know the period of this function
The period is the distance between two maximums or two minimums, because that's the part that repeats after. In the graph I've marked two maximums in red: one is at θ = 0 and the other one is at θ = 3.14. Therefore the period is 3.14
The amplitude is the distance between the maximum or minimum to the midline. In other words it's half the distance between the maximum and minimum: 3
Finally, the function is a cosine - because it starts at the higher value while the sine starts at zero - with an amplitude of 3, shifted 1 unit up (because the midline is 1 and not 0) and since the period is 3.14 it is also dilated horizontally by a factor of 2: f(θ) = 3cos(2θ) + 1
Therefore, the period of the function is 3.14, amplitude is 3 and the Function: ,f(θ) = 3*cos(2*θ) + 1
To learn more about periodic function refer her
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