Given:
[tex]|\frac{x}{8}|=3[/tex]Applying absolute value property
[tex]\frac{x}{8}=-3\text{ and }\frac{x}{8}=3[/tex]Multiply both-side by 8.
That is;
[tex]\begin{gathered} \frac{x}{8}\times8=-3\times8 \\ \\ \text{and } \\ \\ \frac{x}{8}\times8=3\times8 \end{gathered}[/tex][tex]x=-24\text{ and x=24}[/tex]Hence, x=-24 and x=24
Write a compound inequality for the graph shown below.Use x for your variable.++><++-10-9-8-7-65 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x0Dand<>D400 050 020XC
STEP - BY - STEP EXPLANATION
What to do?
Write the compound inequality of the given graph.
Given:
Step 1
Determine the two inequality separately.
[tex]x\ge4[/tex][tex]x<6[/tex]Step 2
Combine the two inequalities
[tex]4\leq x<6[/tex]ANSWER
The compound inequality is
4≤x < 6
Statistics approximating the mean of a data set given a frequency distribution
Solution
- The mean formula is given as:
[tex]\begin{gathered} \bar{x}=\sum_{i=1}^n\frac{fix_i}{f_i} \\ \\ where, \\ x_i=\text{ The ith data point} \\ f_i=\text{ The frequency of the ith data point} \end{gathered}[/tex]- Thus, we can find the mean as follows:
[tex]\begin{gathered} \text{ We have been told to use the midpoint of the classes. Thus, we can say:} \\ x_i=\lbrace3,8,13,18,23,28\rbrace \\ fi=\lbrace22,21,15,9,4,3\rbrace \\ \\ \text{ Thus, the mean commute distance for students is:} \\ \bar{x}=\frac{3(22)+8(21)+13(15)+18(9)+23(4)+28(3)}{22+21+15+9+4+3} \\ \\ \bar{x}=\frac{767}{74} \\ \\ \bar{x}=10.36486486...\approx10.4\text{ \lparen To 1 decimal place\rparen} \end{gathered}[/tex]Final Answer
The mean distance is 10.4 miles
Anthony is a waiter at a restaurant. Each day he works, Anthony will make a
guaranteed wage of $35, however the additional amount that Anthony earns from
tips depends on the number of tables he waits on that day. From past experience,
Anthony noticed that he will get about $7 in tips for each table he waits on. How
much would Anthony expect to earn in a day on which he waits on 20 tables? How
much would Anthony expect to make in a day when waiting on t tables?
Total earnings with 20 tables:
Total Earnings with t tables:
Answer:
His guaranteed wage is 35$, and he makes 7$per each table, so 7$*table.
1) if he waits on t (tables)= 20 --> 35$+7*20
so he makes 35$+140$= 175$
2) t tables: 35$+7*t
Can you show the steps in how to solve it
To break even, the equations must satisfy that
[tex]C(x)=R(x)\text{.}[/tex]Substituting the explicit form of the equations, we get:
[tex]50x+1600=66x\text{.}[/tex]Subtracting 50x, we get:
[tex]\begin{gathered} 50x+1600-50x=66x-50x, \\ 1600=16x\text{.} \end{gathered}[/tex]Dividing by 16, we get:
[tex]\begin{gathered} x=\frac{1600}{16}, \\ x=100. \end{gathered}[/tex]Answer:
[tex]100\text{ units.}[/tex]f(x) = x^2 - 8x + 7Find the vertexaxis of symmetrygraph itfind the domainfind the range
Answers:
Vertex: (4, -9)
axis of symmetry: x = 4
Domain: (-∞, ∞)
Range: [-9, ∞)
Explanation:
If we have a quadratic function with the form y = ax² + bx + c, the x-coordinate of the vertex will be at x = -b/2a
So, for f(x) = x² - 8x + 7, we get a = 1, b = -8 and c = 7, then the x-coordinate of the vertex will be:
[tex]x=\frac{-(-8)}{2(1)}=\frac{8}{2}=4[/tex]Then, the y-coordinate will be the value of f(x) when x = 4
[tex]\begin{gathered} f(x)=x^2-8x+7 \\ f(4)=4^2-8(4)+7 \\ f(4)=16-32+7 \\ f(4)=-9 \end{gathered}[/tex]Therefore, the vertex of the equation is the point (x, y) = (4, -9).
The axis of symmetry is located in the vertex, since the parabola opens up, the axis of symmetry is the vertical line x = 4.
To graph the function, we need to find some points before and after the vertex. So, we will give values to x as 2, 3, 5, and 6. Then, we can calculate f(x) as:
[tex]\begin{gathered} f(2)=2^2-8(2)+7=4-16+7=-5 \\ f(3)=3^2-8(3)+7=9-24+7=-8 \\ f(5)=5^2-8(5)+7=25-40+7=-8 \\ f(6)=6^2-8(6)+7=36-48+7=-5 \end{gathered}[/tex]So, to graph the function, we will use the points (2, -5), (3, -8), (5, -8), (6, -5) and the vertex (4, -9). Therefore, the graph is:
Finally, the domain is the set of values that the variable x can take. In this case, x can be any number, so the domain is the set of all real numbers or written as an interval
(-∞, ∞)
And the range is the set of all values that f(x) can take. In this case, f(x) is always greater than -9, so the range is the set [-9, ∞)
Dean is on top of a 300 m high cliff. He sees Emily in her new sailboat. If dean calculates the angle of depression to the boat to be 25° how far from the base of the cliff is Emily’s boat
To answer this question we will use the following diagram as reference:
Let d be the distance from the base of the cliff to Emily's boat, then, from the above diagram we can set the following equation:
[tex]\tan 25º=\frac{300m}{d}\text{.}[/tex]Then:
[tex]d=\frac{300m}{\tan 25º}\text{.}[/tex]Simplifying the above result we get:
[tex]d\approx643.35m[/tex]Answer:
[tex]643.35m[/tex]The figure below is a net for a right rectangular prism. Its surface area is 384 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.Yes
Solution
For this case we know the total surface area given by:
384 cm^2
And we have the following: 108+48 +108+48 = 312 cm^2
the ramianing area is:
384 -312= 72 cm^2
And we can do the following:
2*9*? = 72
Solving for ? we got:
? = 72/18 = 4 cm
the final answer is:
The area of each missing face is: 36 cm^2
The lenght of each missing edge is: 4 cm
Two times x, minus the quantity 7 times y, equals 20
In order to determine the associated algebraic equation of the given statement, you consider part by part.
Two times x: 2x
minus the quantity 7 times y: - 7y
equals 20: = 20
Which is equivalent to:
2x - 7y = 20
Name the ordered pair for a fourth point. Q. so that points P.Q.R. and S will be the vertices of a Given: Points P6.-1), R(0.-1) and S(4.-5) rectangle Response
to find Q we need to make 2 distance measure
that they fulfill these conditions
PS=RQ and RS=QP
the formula of distances between 2 points is
[tex]\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Distance PS
[tex]\begin{gathered} \sqrt[]{(6-4)^2+(-1-(-5))^2} \\ \\ PS=\sqrt[]{20} \end{gathered}[/tex]Distance RQ
[tex]\begin{gathered} \sqrt[]{(0-x)^2+(-1-y)^2} \\ \\ RQ=\sqrt[]{x^2+(1+y)^2} \end{gathered}[/tex]where x and y are de coordinates of Q
Distance RS
[tex]\begin{gathered} \sqrt[]{(0-4)^2+(-1-(-5))^2} \\ \\ RS=\sqrt[]{32} \end{gathered}[/tex]Distance QP
[tex]\begin{gathered} \sqrt[]{(x-6)^2+(y-(-1))^2} \\ \\ QP=\sqrt[]{(x-6)^2+(y+1)^2} \end{gathered}[/tex]now solve the equals
PS=RQ
[tex]\begin{gathered} \sqrt[]{20}=\sqrt[]{x^2+(1+y)^2} \\ 20=x^2+(1+y)^2 \end{gathered}[/tex]RS=QP
[tex]\begin{gathered} \sqrt[]{32}=\sqrt[]{(x-6)^2+(y+1)^2} \\ 32=(x-6)^2+(y+1)^2 \end{gathered}[/tex]if I subtract the two equations I will get
[tex]32-20=(x-6)^2-x^2[/tex]and i will solve to find x
[tex]\begin{gathered} 12=-12x+36 \\ 12x=36-12 \\ x=\frac{24}{12} \\ \\ x=2 \end{gathered}[/tex]the value of x is 2, then I can replace x on any equation to find y
so replacing
[tex]\begin{gathered} 20=x^2+(1+y)^2 \\ 20=(2)^2+y^2+2y+1 \\ y^2+2y+1-20+4=0 \\ y^2+2y-15=0 \end{gathered}[/tex]use factor to solve y
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \\ y=\frac{-2\pm\sqrt[]{4+60}}{2} \\ \\ y=\frac{-2\pm8}{2} \\ \\ y=-1\pm4 \end{gathered}[/tex]then y will have two values
[tex]\begin{gathered} y_1=-1+4=3 \\ y_2=-1-4=-5 \end{gathered}[/tex]the real coordinate is y=3 because if is y=-5 the point dont form a rectangle
if x=2 and y=3 the point Q is (2,3)
Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number.
We know that:
[tex]\tan\theta=1.19[/tex]where theta is the angle we are trying to find; to get the angle we take the inverse tangent at both sides of the equation. Then:
[tex]\begin{gathered} \tan^{-1}(\tan\theta)=\tan^{-1}1.19 \\ \theta=50 \end{gathered}[/tex]Therefore, the angle we are looking for is 50°
Identify an angle That's congruent to < PQR in the given figure.
You need to rotate the figure to see the new orientation
3. When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.Let f(x) refer to the amount of drug left in the body after I hours.(a) Write down an exponential function to model this situation. Write your answer using functionnotation(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.
Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.
Let f(x) refer to the amount of drug left in the body after I hours.
(a) Write down an exponential function to model this situation. Write your answer using function
notation
(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.
(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
Part a)
Let
t -----> number of hours
f(x)=a(1+r)^t
where
a=549 mg
r=12%=0.12
substitute
f(x)=549(1+0.12)^t
f(x)=549(1.12)^tPart b)
For t=12 hours
substitute in the function
f(12)=549(1.12)^12
f(12)=2,139 mgPart c)
For t=180 minutes
Remember that
1 h=60 minutes
so
180 minutes=180/60=3 hours
For t=3 hours
substitute
f(3)=549(1.12)^3
f(3)=771 mgSolve the system by substitution.y =10xY=4x+22
Given the system:
[tex]\begin{cases}y=10x \\ y=4x+22\end{cases}[/tex]Let's clear x from equation 1:
[tex]\begin{gathered} y=10x\rightarrow\frac{y}{10}=x \\ \rightarrow x=\frac{y}{10}\text{ (A)} \end{gathered}[/tex]And substitute (A) in equation 2:
[tex]\begin{gathered} y=4x+22 \\ \rightarrow y=4(\frac{y}{10})+22 \\ \rightarrow y=\frac{4}{10}y+22 \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} y=\frac{4}{10}y+22 \\ \rightarrow y-\frac{4}{10}y=22 \\ \rightarrow\frac{3}{5}y=22\rightarrow3y=110\rightarrow y=\frac{110}{3} \end{gathered}[/tex]Now, let's use (A) to calculate x:
[tex]\begin{gathered} x=\frac{y}{10} \\ \rightarrow x=\frac{\frac{110}{3}}{\frac{10}{1}}\rightarrow x=\frac{110}{30}\rightarrow x=\frac{11}{3} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{11}{3} \\ \\ y=\frac{110}{3} \end{gathered}[/tex]Find the greatest number that divides 30 and 60 without leaving a remainder.
The greatest number that divides 30 and 60 without leaving a remainder is its GCF.
Find the GCF of 30 and 60 by listing their factors. We get the following:
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Since the greatest common factor of the two numbers is 30, then the greatest number that divides 30 and 60 without remainder is 30.
Complete the conversion. 1 12, gal = qt Click the icon to view the customary units. 1 12 gal = 2 qt (Type an integer, fraction, or mixed number.)
1 gal = 4 qt
Multiply by 4
12 1/2 (4) = 50 qt
Translate thefollowing phaseinto an inequality-3 times r is at least 33A) inequality B) Solve the equality for r.C) express the solution in interval notation.
Given the phrase:
-3 times r is at least 33
Let's translate the given phrase into an inequality.
• Part A.
Let's figure out the inequality in steps.
-3 times r is written as:
-3r
-3 times s is at least 33 means that -3r is greater than or equal to 33.
Hence, we have the inequality:
[tex]-3r\ge33[/tex]• Part B.
Let's solve the inequality for r.
To solve for r, divide both sides of the inequality by -3:
[tex]\begin{gathered} \frac{-3r}{-3}\ge\frac{33}{-3} \\ \\ r\le-11 \end{gathered}[/tex]• Part C.
Let's express the solution in interval notation.
Here, the solution is:
[tex]r\le-11[/tex]It means s must be less than or equal to 11.
Therefore, the solution in interval notation is:
[tex](-\infty,-11\rbrack[/tex]ANSWER:
• A) -3r ≥ 33
• B) r ≤ -11
• C) (-∞, -11]
2.write the equation of a circle with the following parameters Center at (0,-1)Passing through (-35,0)
Solution:
Given:
[tex]\begin{gathered} center\text{ }=(0,-1) \\ Through\text{ p}oint\text{ }(-35,0) \end{gathered}[/tex]The equation of a circle is gotten by;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ x=-35 \\ y=0 \\ h=0 \\ k=-1 \\ \end{gathered}[/tex]Substituting these values into the equation to get the value of r;
[tex]\begin{gathered} (-35-0)^2+(0-(-1))^2=r^2 \\ (-35)^2+(1)^2=r^2 \\ 1225+1=r^2 \\ r^2=1226 \end{gathered}[/tex]Thus, the equation of the circle is;
[tex]\begin{gathered} (x-0)^2+(y-(-1))^2=1226 \\ x^2+(y+1)^2=1226 \end{gathered}[/tex]In a textbook, 900 digits are used for the page numbers. How many pagesare in the textbook, starting with page 1? (Hint: First find how many digitsare used for pages 1-9 and 10-99.)
Given:
900 digits are used for the page numbers. How many pages are in the textbook, starting with page 1
We will find the number of the pages of the book as follows
The number of digits from 1 to 9 = 9
The number of digits from 10 to 99:
There are 90 numbers, each number has 2 digits
So, the number of digits from 10 to 99 = 90 x 2 = 180
The number of digits from 100 to 999:
There are 900 numbers, and each number has 3 digits
so, the number of digits from 100 to 999 = 900 x 3 = 2700
The overall digits are given = 900
So, number of digits from 1 to 99 = 9 + 180 = 189
Subtract 189 from 900 = 900 - 189 = 711
Divide 711 by 3 = 237
So, the number of pages that have 3 digits = 237
So, the number of pages of the book = 237 + 99 = 336
So, the answer will be 336 pages
Use any method to add or subtract (1 point)
5/7 - (3/14 + 3/14)
Answer:
5/7 - (3/14 + 3/14) = 2/7See the steps of solution:
5/7 - (3/14 + 3/14) = Solve parenthesis first5/7 - (3 + 3)/14 = Add fractions with same denominator5/7 - 6/14 = Simplify5/7 - 3/7 = Subtract fractions with same denominator(5 - 3)/7 = Simplify2/7 AnswerAnswer:
2/7 (or) 0.285
Step-by-step explanation:
Given problem,
→ 5/7 - (3/14 + 3/14)
Let's solve the given problem,
→ 5/7 - (3/14 + 3/14)
→ (5/7) - (6/14)
→ ((5 × 2)/(7 × 2)) - (6/14)
→ (10/14) - (6/14)
→ (10 - 6)/14
→ 4/14 = 2/7
Hence, required answer is 2/7.
What percentage is 1 m longer than 1 yard? Round to one tenth percent. 1 yard = 91.4 cm
An eighth-grade student estimated that she needs $8,800 for tuition and fees for each year of college. She already has $5,000 in a savings account. The table shows the projected future value of the account in five years based on different monthly deposits.future value of a savings account. initial balance, dollars, $5000, $5000, $5000, $5000. Monthly deposit, dollars. $100, $200, $300, $400. Account value in five years, dollars. $12,273; $18,737; $25,202; $31,667.The student wants to have enough money saved in five years to pay the tuition and fees for her first two years of college. Based on the table, what is the minimum amount she should deposit in the savings account every month?AnswerF$200G$300H$100J$400
Since each year cost $8,800 for two years tuition he will need $17,600 then if he want to save at least this much in five years according to the table he needs to save $200 monthly
Solve equations x-27=56
Answer:
x = 83
Step-by-step explanation:
Add 27 to both sides
x - 27 +27 = 56 + 27
x = 83
Here is a pattern of squares. S represents the number of small squares in the pattern as a function on n, the step number. Hint: create a table and use your graphing calculator. Step 1 Step 2 Step 3 Step 4 Which expression could define S? n²+3 n +3 n²+2 3n
In the given figure :
Step 1 has 3 square, step 2 has 6 number of square
step 3 has 11 number of squares
step 4 has 18 number of squares
So, the sequence is 3, 6, 11, 18
As we can see that the figure makes a complete square and two more squares
So the expression will be :
[tex]n^2+2[/tex]Answer : C)
[tex]n^2+2[/tex]i need help asap with this (Its ACD and not AGD just incase that confuses you)
4)
In the case of a square, its diagonals are equal and bisect each other, meeting at 90°.
In our case, using a diagram,
Therefore,
[tex]\begin{gathered} a+2b=90 \\ and \\ 2a-b=90 \end{gathered}[/tex]Solving the system of equations for a and b,
[tex]\begin{gathered} \Rightarrow a=90-2b \\ \Rightarrow2(90-2b)-b=90 \\ \Rightarrow5b=90 \\ \Rightarrow b=18 \end{gathered}[/tex]Finding a,
[tex]\begin{gathered} b=18 \\ \Rightarrow a=90-2*18=90-36=54 \end{gathered}[/tex]The answers are a=54, b=18[tex]4a ^{2} - 12a - 16[/tex]I need help factoring
4(a-4)(a+1)
1) Factorizing 4a²-12a -16
4a²-12a -16 Note that the GCD (4,12,16) is 4, Rewrite them
4a²- 4*3a - 4* 4
2) 4(a² -3a -4) Rewrite a² -3a -4 answering the question, What are the numbers whose sum is 3 and product is 4?
Answer:
1 -4 = -3
1 x -4 = -4
3) Hence, the answer is:
4a²-12a -16= 4(a-4)(a+1)
What is the average rate of change of f(x) from x1=-10 to x2=-3? Please write your answer rounded to the nearest hundredth. f(x)= the square root of -9x+5
We have the following information
[tex]\begin{gathered} x_1=-10 \\ x_2=-3 \end{gathered}[/tex]and the function
[tex]f(x)=\sqrt[]{-9x+5}[/tex]In order to find the average rate, we need to find y1 and y2. Then, by substituting x1 into the function, we have
[tex]\begin{gathered} f(-10)=\sqrt[]{-9(-10)+5} \\ f(-10)=\sqrt[]{90+5} \\ f(-10)=\sqrt[]{95} \end{gathered}[/tex]Similarly, by substituting x2, we get
[tex]\begin{gathered} f(-3)=\sqrt[]{-9(-3)+5} \\ f(-3)=\sqrt[]{27+5} \\ f(-3)=\sqrt[]{32} \end{gathered}[/tex]Therefore, the average rate is given by
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{-3-(-10)}[/tex]which gives
[tex]\begin{gathered} \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{5.6568-9.7467}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=-\frac{4.0899}{7} \end{gathered}[/tex]Therefore, the average rate is
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=-0.58[/tex]it says (6^2)^2 then it says select one Add, Subtract, Multiply
Multiply
Here, we want to select the arithmetic operation that could be used to evaluate the given indices expression
The key to solving this is to use an important indices relationship
That is;
[tex](a^x)^y=a^{xy}[/tex]Hence, we have to multiply the powers
So the correct option here is multiply
Please help solve the following questions using the exponential equation
SOLUTION
We want to solve
[tex]7^{2x+4}=2^{x-5}[/tex]Taking logarithm of both sides, we have
[tex]\begin{gathered} \log 7^{2x+4}=\log 2^{x-5} \\ (2x+4)\log 7=(x-5)\log 2 \\ \text{expanding we have } \\ (2x)\log 7+(4)\log 7=(x)\log 2-(5)\log 2 \end{gathered}[/tex]Collecting like terms we have
[tex]\begin{gathered} (2x)\log 7-(x)\log 2=-(4)\log 7-(5)\log 2 \\ x(2\log 7-\log 2)=-4\log 7-5\log 2 \\ \text{dividing both sides by }(2\log 7-\log 2),\text{ we have } \\ x=\frac{-4\log 7-5\log 2}{2\log 7-\log 2} \end{gathered}[/tex]Hence the solution set expressed in terms of logarithm is
[tex]x=\frac{-4\log7-5\log2}{2\log7-\log2}[/tex]Using a calculator to obtain a decimal approximation, we have
[tex]\begin{gathered} x=\frac{-4\log7-5\log2}{2\log7-\log2} \\ x=\frac{-3.3804-1.5051}{1.6902-0.3010} \\ x=\frac{-4.8855}{1.3892} \\ x=-3.51677 \\ x=-3.52 \end{gathered}[/tex]Hence the answer is -3.52 to 2 decimal places
blake needed at least 225 votes to become president of his seventh-grade class. if three-fourths of the seventh-grade students voted for him and he won. how many seventh-grade students could there be?im looking for the inequality and answer. thank you.
Given :
The number of votes to win is at least 225 votes
three-fourths of the seventh-grade students voted for him and he won.
Let the number of students = x
So, the inequality will be:
[tex]\frac{3}{4}x\ge225[/tex]Solve the inequality :
Multiply both sides by 4/3
[tex]undefined[/tex]1 Find the area of the triangle given below and type your result in the empty box. 19 cm 15 cm 12 cm
We have a right triangle with sides 12 cm, 15 cm and 19 cm.
The area of the triangle is half the product of the legs, as they represent the base and height of the triangle:
[tex]A=\frac{b\cdot h}{2}=\frac{12\cdot15}{2}=6\cdot15=90\operatorname{cm}^2[/tex]NOTE: The legs are the shortest sides that form the right angle of the triangle.
Answer: the area of the triangle is 90 cm^2