We have the inequality:
[tex]3x\text{ - 4 }>5[/tex]Let's find out 3 solutions, as follows:
3x - 4 > 5
Adding 4 at both sides of the inequality:
3x - 4 + 4 > 5 + 4
3x > 9
Dividing by 3 at both sides, we have:
3x/3 > 9/3
x > 3
Now, we can find 3 solutions that fulfill the condition of the inequality:
x = 4, x = 5, x = 6
These three solutions are > 3
19. Translate the following statement into an algebraic statement: "Two more than seven times a number is fifteen" I
2+7x=15
Explanation
Step 1
Let
x represents the number
seven times a number = 7x
two more = +2 or 2+, you need to add 2
is = "="
Step 2
replace,
"Two more than seven times a number is fifteen"
[tex]2+7x=15[/tex]I hope this helps you
State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
Solve the compound inequality. Graph the solution-7 *x+3<4-The solutions are(Type an inequality or a compound inequality. Sim
Answer:
[tex]-10\leqslant x<1[/tex]Explanation:
To solve compound inequalities, we do the same as in an equation or inequality: we need to do the same operation in all places.
We want to solve for x:
[tex]-7\leqslant x+3<4[/tex][tex]-7-3\leqslant x+3-3<4-3[/tex][tex]-10\leqslant x<1[/tex]And that's the answer
Jane is attending physical therapy after knee surgery. She walked 9 3/4 miles over 3 days. How many miles is this per day? (Simplify the answer and write it as a mixed number.)
She walked 3 1/4 miles per day.
Given,
Jane walked 9 3/4 miles in the course of 3 days.
If we calculate this mixed number into a fraction,
We get:
9 3/4 miles = {(9×4)+3} / 4 miles
=39/4 miles.
So, Jane walks 39/4 miles in 3 days.
Therefore, in one day she walked:
(39/4 ÷ 3) miles
= 13/4 miles per day
Let's now convert this fraction into a mixed number:
when 13 is divided by 4 we get the remainder as 1 and the quotient as 3.
So, a mixed number is given by:
quotient remainder/divisor
Hence 13/4 = 3 1/4.
So, Jane walked 3 1/4 miles per day.
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The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
The solution that we have that would have to do with the measurement of the unknown side would be 12.
How to solve for the unknown
The Pythagoras theorem says that the length of the suym of the square of a triangle is the same as the sum of the square of the other two sides.
From the definition that we have above.
We have the shortest side as 5.
The longest side as 13
Then we would have
13² - 5² = 25 - 169
= 144
Next we would have to take the square root of 144
= √144
= 12
Hence we would say that the length of the unknown is given as 12
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How do I identify the horizontal and vertical asymptotes, find several points, and graph each function?Y=4/x+3 -2
Given:
[tex]y=\frac{4}{x+3}-2[/tex]Required:
To identify the horizontal and vertical asymptotes, and to point the graph.
Explanation:
Now the graph of the given function is
To find the horizontal asymptotes apply the limit
This chart shows the cost per pound of different fruits.
From the given data, the cost per pound of apple, CP=$1.89≈$2.
We have to estimate the cost of n=3.2≈3 pounds(lb) of apple.
The cost of n=3 lb of apple can be calculated as,
[tex]\begin{gathered} T=CP\times n \\ =2\times3\text{ lb} \\ =6 \end{gathered}[/tex]Therefore, the cost of 3. pounds of apples is about $6.048.
HELP ME PLEASE!!! Question 1Jim is planning his spring garden. He will construct a rectangular gardensurrounded by a chain link fence. The length of Jim's garden will be 8 feet morethan 3 times its width (w).(Drawing and labeling a diagram may be helpful)Part A: Write an expression in terms of w to represent the amount of chain linkfencing (the perimeter) Teeded to enclose Jim's garden.
We have a rectangular garden.
The length L is 8 feet more than 3 times its width.
3 times the width is 3w, so we will add 8 to it and equal it to the length L:
[tex]L=8+3w[/tex]The perimeter will be 2 times the length plus 2 times the width. We can write it and transform it to an expression in terms only of w:
[tex]\begin{gathered} P=2L+2w \\ P=2(8+3w)+2w \\ P=16+6w+2w \\ P=16+8w \end{gathered}[/tex]The perimeter has a value of P=16+8w.
We can draw the diagram as:
Part B: If the perimeter of Jims garden is 88 feet, what would be the width of the garden?
We will use the equation we derived in Part A, and we have to replace P=88, in order to find w.
[tex]\begin{gathered} P=16+8w \\ 88=16+8w \\ 88-16=8w \\ 72=8w \\ w=\frac{72}{8} \\ w=9.75 \end{gathered}[/tex]The width is 9.75 feet.
Which of the following is the explicit formula for a compound interestgeometric sequence?
INFORMATION:
We have the following options
And we must select the one that represents the explicit formula for a compound interest geometric sequence
STEP BY STEP EXPLANATION:
To select the correct one, we need to know that:
[tex]P_n=P_1(1+i)^{(n-1)}[/tex]Finally, the correct one would be option A
ANSWER:
[tex]A.\text{ }P_n=P_1\cdot(1+i)^{n-1}[/tex]Evaluate 2(x - 4) + 3x - x^2 for x = 2.O A. -6O B. -2O C. 6O D. 2
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
In a circle with radius 8, an angle measuring radians intercepts an arc. Find thelength of the arc in simplest form.
s = 28π/3
Explanation:The radius, r = 8
The angle, θ = 7π/6 radian
The length of the arc, s = rθ
s = 8 x 7π/6
s = 28π/3
Find the vertical and horizontal lines that passes through the point (3,6).
We have to find the vertical and horizontal lines that passes through the point (3,6).
A vertical line will be defined as x = constant. If it passes trough a point (x,1,y1), the line will be defined as a x=x1, so the point (x1,y1) belongs to the line.
The same goes for horizontal lines, but in this case the line is defined as y = constant.
For a point (x1,y1), the horizontal line that pass through the point will be y = y1.
Then, for point (x,y)=(3,6), the vertical and horizontal lines as:
x=3 and y=6.
Answer:
Vertical line: x = 3
Horizontal line: y = 6.
-12 -24 4bI need help can someone help .
To eliminate the coefficient divide each side by 3
Now solve the two step equation
3g - 5 = 17
3g = 17 + 5 = 22
then g= 22/3
Now solve 9 = 4a + 13
9 -13 = 4a
-4 = 4a then -1= a
a= -1
The problem is below, we know the man weighs 60, the cat weighs 10 but we’re having a hard time explaining how
Given data:
The weight of man and daughter = 90
The weight of man and cat is = 70
The weight of cat and daughter = 40 .
The man weights 60 kg.
then daughter weight = 90-60 = 30.
Thus the daughter weight is 30kg.
therefore the cat weight iwith daughter, 40-30 = 10 .
also with father, 70-60 = 10 .
Thus, the father weight is 60 kg.
The daughter weight is 30 kg and
The cat weight is 10 kg.
I’m trying to make a study guide and need step by step explanation on how to solve this question please
Given:
The dimension of square shape floor is 200 feet by 200 feet.
The area of the square is calculated as,
[tex]\begin{gathered} A=side^2 \\ A=200^2=40000 \end{gathered}[/tex]Now, given that the 1/2 bottle will cover approximately 2000 quare feet.
It gives,
[tex]\begin{gathered} \frac{1}{2}\text{ bottle=2000 square f}ee\text{t} \\ 1\text{ bottle=4000 square fe}et \end{gathered}[/tex]So, the number of bottles required are,
[tex]\frac{A}{4000}=\frac{40000}{4000}=10\text{ bottles}[/tex]Answer: option B)
For the function f(x) = x² + 2x - 24 solve the following.
f(x) = 0
For the function, f(x) =0, we have x = -6 and x =4
The given function is f(x) = x² + 2x - 24
For f(x) = 0
f(x) = x² + 2x - 24 =0
x² + 2x - 24 =0
Middle Term Splitting is a method to solve quadratic equations of the form ax² + bx +c, In middle-term splitting, we split the middle term into the factors of the constant terms, then we take common multiples from the terms and then convert the equation into factors, we equate each factor to zero and we get the desired results.
By splitting the middle term, we have:
x² + 6x -4x - 24 =0
x( x + 6) -4(x+6) =0
( x + 6 ) ( x - 4 ) = 0
( x + 6 ) = 0 and ( x - 4 ) = 0
x = -6 and x = 4
Hence, for f(x) =0, we have x = -6 and x =4
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The endpoints of the line are (0, 5) and (6, 4). Find the slope of the line.
Solution:
Given the endpoints of the line;
[tex](0,5),(6,4)[/tex]The slope, m of the line is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ Where }x_1=0,y_1=5,x_2=6,y_2=4 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} m=\frac{4-5}{6-6} \\ \\ m=-\frac{1}{6} \end{gathered}[/tex]CORRECT ANSWER:
[tex]-\frac{1}{6}[/tex]Quadratic Factoring: Demonstrate solving some quadraticequations using the following methods: factoring, taking theroot, and completing the square.
The Solution:
Let's solve with the Factoring Method:
[tex]x^2-x-6=0[/tex][tex]\begin{gathered} x^2-3x+2x-6=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \end{gathered}[/tex][tex]\begin{gathered} x+2=0\text{ or }x-3=0 \\ x=-2\text{ or }x=3 \end{gathered}[/tex]Solving by the Completing the Square:
[tex]\begin{gathered} x^2-x=6 \\ x^2-x+(\frac{1}{2})^2=6+\frac{1}{4} \\ \\ (x-\frac{1}{2})^2=\frac{25}{4} \end{gathered}[/tex]Take the square root of both sides.
[tex]\begin{gathered} x-\frac{1}{2}=\sqrt{(\frac{25}{4})} \\ \\ x=\frac{1}{2}\pm\frac{5}{2}=\frac{1\pm5}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ \\ x=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]Therefore, the answers is:
[tex]x=-2\text{ or }x=3[/tex]Select the expressions that are equivalent to 7(7f)1. 49f2. 7(f+6f)3. f+144. f+49
ANSWER :
49f and 7(f + 6f)
EXPLANATION :
From the problem, we have :
[tex]7(7f)[/tex]When multiplied, it will be 49f
When breaking it down, 7f is equal to f + 6f. Then it will be 7(f + 6f)
The next options f + 14 and f + 49 has two terms, so it will not be equivalent to the given expression with one term.
So the only expressions that are equivalent to the given expression are 1 and 2
The numbers of trading cards owned by 9 middle- school students are given below. ( note that these are already ordered from least to greatest.
Given the numbers:
355, 382, 383, 427, 500, 572, 601, 638, 669
Total numbers = 9
a) We find the mean:
[tex]\begin{gathered} mean=\frac{355+382+383+427+500+572+601+638+669}{9} \\ mean=\frac{4527}{9}=503 \end{gathered}[/tex]Change 669 to 606:
[tex]\begin{gathered} mean=\frac{355+382+382+427+500+572+601+638+606}{9} \\ mean=\frac{4464}{9}=496 \end{gathered}[/tex]Then:
[tex]\begin{gathered} mean=changed\text{ mean}-original\text{ mean} \\ mean=496-503=-7 \end{gathered}[/tex]Answer: It decreases by 7
b) We find median
Median: 355, 382, 383, 427, 500, 572, 601, 638, 669
Median = 500
669 changed to 606
Median: 355, 382, 383, 427, 500, 572, 601, 606, 638
Median = 500
Answer: It stays the same
Lin is paid $90 for 5 hours of work. She used the following table to calculate how much she would be paid at this rate for 8 Hours of work. 1. What is the meaning of the 18 that appears in the table? 2. Explain how Lin used this table to solve the problem. 3. At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work. AMOUNTS EARNED ($) | TIME WORKED(hours)
Let
y ------> the amount earned
x ----> the number of hours worked
In this problem we have a direct variation
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
k=y/x
In this problem the value of k is hourly rate
so
we have
For y=$90 -------> x=5 hours
substitute
k=90/5
k=$18 per hour
substitute in the linear equation
y=18x
so
Part 1) What is the meaning of the 18 that appears in the table?
18 is the hourly rate ( amount earned by a one hour of work)
Part 2) Explain how Lin used this table to solve the problem.
using the table
For x=8 hours
the value of y=$144
Verify with the equation
y=18x
y=18(8)=144 -----> is ok
Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.
For x=3 hours
substitute in the equation
y=18x
substitute the value of x
y=18(3)=$54
For x=2.1 hours
y=18(2.1)=$37.8
Im just needing a little bit more help with these type of problems ;/
Answer:
Expected value = 2.21
Explanation:
The formula to obtain the expected value is given by:
[tex]E\mleft(X\mright)=\mu=∑xP\mleft(x\mright)[/tex]We will proceed to calculate the given scenario as given below:
[tex]\begin{gathered} E\mleft(X\mright)=\mu=∑xP\mleft(x\mright) \\ E(X)=(1\times0.31)+(2\times0.41)+(3\times0.07)+(4\times0.18)+(5\times0.03) \\ E(X)=0.31+0.82+0.21+0.72+0.15 \\ E(X)=2.21 \\ \\ \therefore E(X)=2.21 \end{gathered}[/tex]Therefore, the expected value of this scenario is 2.21
...........................
Solution
We have the following:
5!= 5*4*3*2= 20*3*2= 60*2= 120
What is the scale factor for AXYZ to AUVW?O A1/1O B. 1/1/20OC. 2OD. 4371620A A837-105353X 6 Z12
SOLUTION:
We want to know the scale factor of the transformation from;
[tex]\Delta XYZ\rightarrow\Delta UVW[/tex]We do this by taking ratios of corresponding sides, they should be the same in either case;
Thus , the scale factor is;
[tex]\frac{20}{10}=\frac{12}{6}=\frac{16}{8}=2[/tex]Thus, the scale factor is 2.
Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
State the domain and range for each graph and then tell if the graph is a function(write yes or no)
For the point 1)
- The domain will be: (note that this is not an interval, it is a set of two points)
[tex]\mleft\lbrace-3,2\mright\rbrace[/tex]-The range is the set R of all real numbers (since the line extends to infinite)
-The first graph is NOT a function
For the point 2)
-The domain will be the interval
[tex](-5,5\rbrack[/tex]-The range is the interval:
[tex]\lbrack-2,2\rbrack[/tex]-The second graph is a function.
If you borrow $100 for 3 years at anannual interest rate of 9%, howmuch will you pay altogether?
We are to determine the amount that you have pay back after borrowing a principal amount ( P ) for ( t ) number of years which is compounded annualy at rate ( R ).
You borrowed a principal amount of:
[tex]P\text{ = \$100}[/tex]The time duration for which we have borrowed the money for is:
[tex]t\text{ = 3 years}[/tex]The annual interest rate coumpounded each year is:
[tex]R\text{ = 9\% / year}[/tex]Step 1: Determine the simple interest that accumulated at the end of ( t ) years.
The folllowing formula is used to determine the simple interest that the borrower has to pay once the period of borrowing/lending is over i.e ( t ) years.
The simple interest is the proportional rate of interest ( R ) and the initial borrowed/loaned amount called principal amount ( P ).
[tex]\text{Simple Interest ( I ) = }\frac{P\cdot R\cdot t}{100}[/tex]Use the above simple interest formula ( I ) by plugging in the respective values as follows:
[tex]\text{Simple Interest ( I ) = }\frac{100\cdot9\cdot3}{100}\text{ = \$27}[/tex]Therefore, the total amount of interest that the borrower must pay as an extra ( over the borrowed amount ) is $27.
Step 2: Determine the total amount that is to be returned/paid to the lender
The total amoun that is to be paid by the borrower ( you ) to the lender is the principal amount borrowed ( P ) and the amount of interest accumulated for the contractual time period i.e ( I ).
[tex]\begin{gathered} \text{Total amount to be paid = P + I} \\ \text{Total amount to be paid = \$100 + \$27} \\ \text{Total amount to be paid = }127 \end{gathered}[/tex]Therefore, the amount that you need to pay altogether is:
[tex]\textcolor{#FF7968}{127}\text{\textcolor{#FF7968}{ dollars}}[/tex]The graph represents a quadratic function. Write an equation of the function in standard form.
A quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
Given that, the graph is passing through (2, 0), (10, 0) and (6, -4).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (2, 0)
y = ax² + bx + c
0 = 4a + 2b + c ----------------(1)
The equation passes through (6, -4)
y = ax² + bx + c
-4= 36a + 6b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = 1/4, b = -3, and c = 5
The quadratic equation will be:
y = ax² + bx + c
y = (1/4) x² - 3x + 5
Therefore, a quadratic function in standard form with the given characteristics is (1/4) x² - 3x + 5.
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A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 3 hrs, 14 hrs, and 10.5 hrs, respectively. Find how long it takes to fill the daily quota if all three machines are running.
Answer
It will take 2 hours to fill the daily quota if all the machines are running.
Explanation
To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:
Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines
[tex]\begin{gathered} \Rightarrow\frac{1}{3}+\frac{1}{14}+\frac{1}{10.5}=\frac{1}{x} \\ \text{Where x is the }time\text{ it takes to fill the daily quota} \\ \frac{1}{3}+\frac{1}{14}+\frac{2}{21}=\frac{1}{x} \\ \text{Multiply all through by 42x} \\ 42x(\frac{1}{3})+42x(\frac{1}{14})+42x(\frac{2}{21})=42x(\frac{1}{x}) \\ 14x+3x+4x=42 \\ 21x=42 \\ x=\frac{42}{21} \\ x=2 \\ \text{Therefore it will take 2 hours to fill the daily quota} \end{gathered}[/tex]15. Find the volume of a rectangular prism with the following dimensions.a length of 11 cm, a width of 4.2 cm, and a height of 7.1 cm.3308.24 cm3328.02 cm322.3 cm346.2 cm
For this problem, we are given the dimensions of a rectangular prism and are asked to determine its volume.
The volume of a rectangular prism is given by the product of the three dimensions, therefore we have:
[tex]\begin{gathered} V=\text{ height}\cdot\text{ length}\cdot\text{ width}\\ \\ V=11\cdot4.2\cdot7.1=328.02\text{ cubic cm} \\ \end{gathered}[/tex]The correct answer is 328.02 cubic centimeters.