We want to find a fraction a/b such that
[tex]\dfrac{9}{11}\leq\dfrac{a}{b}\leq\dfrac{11}{13}[/tex]
This is true if and only if
[tex]\dfrac{9b}{11}\leq a \leq\dfrac{11b}{13}[/tex]
We can choose a value for a only if the two extremes include at least one integer, i.e. if
[tex]\dfrac{11b}{13}-\dfrac{9b}{11}\geq 1[/tex]
Solving for b, we have [tex]b>35[/tex]
So, the smallest fraction is given for [tex]b=36[/tex]. We have
[tex]\dfrac{9}{11}\leq \dfrac{a}{36} \leq \dfrac{11}{13}[/tex]
Solving for a, we have a=30.
The fraction 30/36 can be simplified to 5/6. So, we have
[tex]\dfrac{9}{11}\leq \dfrac{5}{6} \leq \dfrac{11}{13}[/tex]
and this is the smallest possible denominator.
We want to find a fraction a/b such that
\dfrac{9}{11}\leq\dfrac{a}{b}\leq\dfrac{11}{13}
11
9
≤
b
a
≤
13
11
This is true if and only if
\dfrac{9b}{11}\leq a \leq\dfrac{11b}{13}
11
9b
≤a≤
13
11b
We can choose a value for a only if the two extremes include at least one integer, i.e. if
\dfrac{11b}{13}-\dfrac{9b}{11}\geq 1
13
11b
−
11
9b
≥1
Solving for b, we have b>35b>35
So, the smallest fraction is given for b=36b=36 . We have
\dfrac{9}{11}\leq \dfrac{a}{36} \leq \dfrac{11}{13}
11
9
≤
36
a
≤
13
11
Solving for a, we have a=30.
The fraction 30/36 can be simplified to 5/6. So, we have
\dfrac{9}{11}\leq \dfrac{5}{6} \leq \dfrac{11}{13}
11
9
≤
6
5
≤
13
11
and this is the smallest possible denominator.
Line AB contains (0,4) and (1,6). Line CD contains points (2,10) and (-1,4). Lines AB and CD are
A) parallel, because the slopes are the same
B) perpendicular, because the slopes are the same
C) parallel, because the product of the slopes is -1
D) perpendicular, because the product of the slopes is -1
Answer: parallel because the slopes are the same
Step-by-step explanation:
A birdhouse has a shadow that is 12 feet long.
Jin is 5 feet tall, and he is standing next to the birdhouse.
Jin has a shadow that is 3 feet long.
Use this information to complete the statement about the birdhouse.
Math item stem image
CLEAR CHECK
The height of the birdhouse is
feet.
Answer:
20
Step-by-step explanation:
Set up ratios
for the shadows- 12:3, or 4:1
then height=4*5, or 20
Answer:20 feet
Step-by-step explanation:
5/3 = x/12
Use butterfly method.
3x = 60
x = 20
Given z1 = -3
[tex] \sqrt{3} [/tex]
+ 3i and z2 = 6cos150° + 6isin150°, use complete sentences to explain why z1 = z2. Explain the steps of your work for full credit.
Answer:
See explanation
Step-by-step explanation:
The given complex number are:
[tex]z_1=-3\sqrt{3}+3i[/tex]
and
[tex]z_2=6\cos 150\degree+6i\sin 150\degree[/tex]
When we rewrite [tex]z_1=-3\sqrt{3}+3i[/tex] in complex form, we obtain;
[tex]z_1=r(\cos \theta+i\sin \theta)[/tex]
where
[tex]r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6[/tex]
and
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]
[tex]\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree[/tex]
Hence,
[tex]z_1=6(\cos 150\degree+i\sin 150\degree)[/tex]
[tex]z_1=6\cos 150\degree+6i\sin 150\degree[/tex]
Hence
[tex]z_1=z_2[/tex]
Eric sells shirts. It costs him $100 to buy all the shirts and $10, total, to print designs on them. Eric sells each shirt for $4. So far he has sold 20 shirts. He uses the equation y = 4x − 110 to calculate his profit. In the equation y = 4x − 110, which is the constant term?
A) y
B) 4
C) x
D) −110
Answer:
D) -110
Step-by-step explanation:
x and y are variables, and any number that is in front of a variable (multiplication) is called a coefficient. 4 is the coefficient. x can be substituted. A constant is a number that does not change. -110 is the constant.
The range of the graphed function is
Answer:
C
Step-by-step explanation:
plato gang
Answer:
B
Step-by-step explanation:
The range of the function are the corresponding values of y for the given points
x = 1,3 → y = 5
x = 4 → y = 2
x = 6 → y = - 2
The range of the graphed function is { - 2, 2, 5 } → B
Find the median of the set of data.
23 18 67 32 54 41 70 11 56 33 41 58
35
56
42
41
41 there are 12 numbers take middle
Hi
The answer is 41
11 18 23 32 33 =41= 54 56 58 67 70
Answer:
42
Step-by-step explanation:
23+18+67+32+54+41+70+11+56+33+41+58=504
(There's 12 sets of numbers)
504/12=42
what is the volume of the sphere? round to the nearest cubic unit.
diameter: 16cm
a)268cm
b)2145cm
c)17, 157cm
d)536cm
Volume of a sphere:
(4/3)(pi)r^3
.
radius (r) is half the diameter or 8 inches.
(4/3)(3.14)8^3
2144 cubic inches
The volume of the sphere would be 2144 cubic inches
What is the Volume of a sphere?A sphere is a three-dimensional shape analouge of a circle.
The Volume of a sphere = 4/3πr^3
We are given that the diameter of the sphere as 16 cm.
Since radius (r) is half the diameter or 8 inches.
Volume of a sphere:
= 4/3πr^3
= (4/3)(3.14)8^3
2144 cubic inches
Learn more about sphere;
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Find the solution to the system of equations. You can use the interactive graph below to find the solution.
{21x + 7y = 42
{-5x + 5y = 10
X =
Y =
X=1 and
Y=3
Look at the image attached to see what I did
X = 1
Y = 3
Hope this helps!
HELP ME WITH THIS MATH PROBLEM FOR 17 POINTS!!
Maureen deposited $19,000 at 11 percent interest compounded annually. What was the total interest earned at n = 8 years?
Answer:
%88 i believe
Step-by-step explanation:
hope this helps!
Answer: $43786.22 (Round)
Step-by-step explanation: Use this formula: A= P(1+r/n)^nt
We are trying to find A in this problem.
Plug it in:
A= 19,000(1+0.11/1)^(1)(8)
What is the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR?
There are 720 different 6-letter arrangements that can be formed using the letters in the word QUASAR, calculated by 6 factorial (6!).
Explanation:The question asks for the total number of different 6-letter arrangements that can be formed using the letters in the word QUASAR. This is a problem of permutations where all the letters are distinct. To find the number of different permutations of the letters in QUASAR, we multiply the number of choices available at each position. There are 6 choices for the first letter, 5 for the second, and so on, until 1 choice for the last letter.
Therefore, the permutations are calculated as 6 × 5 × 4 × 3 × 2 × 1, which is equal to 6! (6 factorial).
The calculation of 6! is as follows:
6 × 5 × 4 × 3 × 2 × 1 = 720.So, there are 720 different 6-letter arrangements that can be formed from the word QUASAR.
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10. Marcia drew a scatter plot comparing the number of people who bought tickets to the school play and
the amount of money raised by the event. She graphed the ordered pairs (number of tickets, money
raised) for each date of the play. Which of the three scatter plots below most likely represents the data?
Answer:
C- graph III
Step-by-step explanation:
The only graph showing a positive trend. If your selling tickets, you'll have an increased profit.
VARIABLE ON BOTH SIDES. PLEASE HELP! 40 PTS
2x + 4 = 3 (x-2) + 2 show your work
2x+4= 3x-6+2
2x+4=3x-4
2x-3x+4=3x-3x-4
-x+4=-4
-x+4-4= -4-4
-x=-8
Need to multiply by -1 for x to be positive and also for -8
-1(-x)= -1(-8)
x=8
Answer:
Step-by-step explanation:
2x+4=3(x-2)
2x+4=3x-6
+6 -2x
10 = 1x
1 = 1x
10= x
Explain what type of function is the best model for the data set and justify your choice. Help???????
Answer:
The function is linear
Step-by-step explanation:
* Lets check from the table the type of the function
- At first check if it is linear or not
- The points are:
(165 , 198) , (168 , 201.6) , (170 , 204) , (172 , 206.4) , (175 , 210)
* Find the slope for each two points if the value of the slop is
constant, then the function will be linear
∵ The slop = (y2 - y1)/(x2 - x1)
∴ m1 = (201.6 - 198)/(168 - 165) = 1.2
∴ m2 = (204 - 201.6)/(170 - 168) = 1.2
∴ m3 = (206.4 - 204)/(172 - 170) = 1.2
∴ m4 = (210 - 206.4)/(175 - 172) = 1.2
∵ m1 = m2 = m3 = m4
# Note: You can use any to points to find the slope you will
have the same value
∴ The graph of the points is a line with slope 1.2
* The function is linear
Answer:
A linear function is the best model.
The ratio of y to x for the ordered pairs is constant, so the relationship is a direct variation. A direct variation is a type of linear function.
When the data set is plotted, it forms a line.
Step-by-step explanation:
prime factorization of 52
Answer:
The first prime factor we test is 2:
52 / 2 = 26
26 / 2 = 13
13 is a prime number so the prime factorization is
2 * 2 * 13 = 52
Step-by-step explanation:
52 is a composite number. 52 = 1 x 52, 2 x 26, or 4 x 13. Factors of 52: 1, 2, 4, 13, 26, 52.
Solve for x. (X+10)(x+10)=0
Answer:
use foil method-first inside outside last
Step-by-step explanation:
Answer:
X = -10
Step-by-step explanation:
Adding negative ten and ten results in zero, and zero multiplied by anything is, of course, still zero.
(-10 + 10) * (-10 + 10) = 0
0 * 0 = 0
X=-10
Because (x+10)(x+10)=0
So it becomes (x+10)^2=0
And therefore x=-10
What is the value of x?
A.30 B.45 C.85 D.90
Answer:
45°
Step-by-step explanation:
This is the inscribed angle, in which the angle is 1/2 of the opposite arc. The opposite arc for this question measures at 90°. Divide by 2.
90/2 = 45
45, or B)45° is your answer.
~
What are the solutions to the equation? x^2−12x+36=4
x1=
x2=
(not multiple choice)
Answer:
x1=4
x2=8
Step-by-step explanation:
1- Factor the equation.
2- solve a Single Variable Equation
3- Parabola, Finding the Vertex
You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a system with the same solution? 3x + 3y = 4 18x − 9y = 12 A) multiply the first equation by 6 and subtract the second equation B) multiply the first equation by −6 and add the second equation C) multiply 3x by 6 in the first equation and subtract the second equation D) add 2 times the first equation and −1/3 times the second equation Eliminate
C would be the correct answer. You caanot multiply just one part of an equation, you must multiply the whole thing. All of the other steps follow this rule, so C is an incorrect step, and is therefore the correct choice.
Hope this helps!
Answer:
C) Multiply 3x by 6 in the first equation and subtract the second equation.
Step-by-step explanation:
We have been given a system of equations.[tex]3x+3y = 4[/tex] and [tex]18x-9y = 12[/tex]. We are asked to choose the "incorrect" step that will make "not" produce a system with the same solution.
Let us see our give choices one by one.
A) multiply the first equation by 6 and subtract the second equation.
When we will multiply 1st equation by 6, the coefficient of x would be 18. When we will subtract 2nd equation the both x's will cancel out. Therefore, option A is correct.
B) multiply the first equation by −6 and add the second equation.
When we will multiply 1st equation by -6, the coefficient of x would be -18. When we will add 1st equation to 2nd equation the both x's will cancel out. Therefore, option B is correct as well.
C) Multiply 3x by 6 in the first equation and subtract the second equation.
We need to remember that we cannot multiply only one term of equation by some quantity as it will make the whole equation false, therefore, option C is incorrect.
Which shows the numbers $5.25, $0.69, $123.46 rounded to the nearest dollar? A) $5.25, $.70, $124 B) $5.00, $1.00, $123 C) $5.00, $1.00, $124 D) $6.00, $.1.00, $123
Answer:
B) $5.00,$1.00,$123
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
One half the difference of the cube of a number, x, and three
Answer:
(1/2)(x³ - 3)
Step-by-step explanation:
That would be (1/2)(x³ - 3).
The expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].
Let the number be [tex]x[/tex].
The cube of the number is [tex]x^3[/tex].
Difference of the cube of the number with [tex]1[/tex] is [tex]x^3 - 1[/tex].
Now, one-half difference of a number cubed and one is represent as,
[tex]\frac{1}{2} (x^3 - 1)[/tex].
So, the expression ' one-half difference of a number cubed and one' is written as [tex]\frac{1}{2} (x^3 - 1)[/tex].
Learn more about expressions here:https:
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a group of musicians wants to sell a total of 1,000 tickets for 20 concerts suppose they sell the same number of tickets for each concert how many tickets with they sell for each concert?
Answer:
50 tickts
Step-by-step explanation:
We want to spread 1,000 tickets equally over 20 concerts. This calls for division
1000/20=50
50 tickets are sold each concert
The high school field hockey team needs to buy new practice uniforms. The company the team is ordering from charges $250.00 for a one time print layout fee and then $28.00 for each uniform. What is the maximum number of uniforms the team can buy and stay within its budget of $550.00?
Answer:
10 uniforms
Step-by-step explanation:
You will start by subtracting 250 from 550 to get 300. You will then divide 300 by 28 to get the total number of uniforms. You will get the answer 10.7, but because we are dealing with uniforms, we will remove the decimal and just use 10.
What percent is represented by the shaded area
Answer:
the answer is 25%
Step-by-step explanation:
100% : 4 =25
Helllllppppppp!! Can i have an explanation of this?
Okay so if the regular price of the shirt is 100% as $25 and you have a 30% discount you are still paying 70% (100-30=70) so 70% as a decimal is .70 and $25 x .70 is $17.50. Therefore the shirt is $17.50 after the discount.
Alright so, what it’s basically asking for is 70% of 25. This is the price of the shirt after you’ve accounted for the 30% discount
Then you would multiply 25 by .70, giving you $17.50
Hope this helps!
3n-7/6=2n+5/3 n=what
[tex]\frac{3n-7}{6}=\frac{2n+5}{3}[/tex] Multiply 3 and 6 on both sides to get rid of the fraction (or cross multiply)
[tex]\frac{3n-7}{6}(3)=\frac{2n+5}{3} (3)[/tex]
[tex]\frac{3n-7}{6}(3)(6)=(2n+5)(6)[/tex]
3(3n - 7) = 6(2n + 5) Distribute/multiply 3 into 3n-7, and 6 into 2n+5
(3)3n - (3)7 = (6)2n + (6)5
9n - 21 = 12n + 30 Subtract 9n on both sides
-21 = 3n + 30 Subtract 30 on both sides
-51 = 3n Divide 3 on both sides
-17 = n
Answer:
n = 17/6 = 2.833
Step-by-step explanation:
Step by step solution :
Step 1 :
5
Simplify —
3
Equation at the end of step 1 :
7 5
(3n - —) - (2n + —) = 0
6 3
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
2n 2n • 3
2n = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2n • 3 + 5 6n + 5
—————————— = ——————
3 3
Equation at the end of step 2 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 3 :
7
Simplify —
6
Equation at the end of step 3 :
7 (6n + 5)
(3n - —) - ———————— = 0
6 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 6 as the denominator :
3n 3n • 6
3n = —— = ——————
1 6
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
3n • 6 - (7) 18n - 7
———————————— = ———————
6 6
Equation at the end of step 4 :
(18n - 7) (6n + 5)
————————— - ———————— = 0
6 3
Step 5 :
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 6
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 1 0 1
3 1 1 1
Product of all
Prime Factors 6 3 6
Least Common Multiple:
6
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (18n-7)
—————————————————— = ———————
L.C.M 6
R. Mult. • R. Num. (6n+5) • 2
—————————————————— = ——————————
L.C.M 6
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(18n-7) - ((6n+5) • 2) 6n - 17
—————————————————————— = ———————
6 6
Equation at the end of step 5 :
6n - 17
——————— = 0
6
Step 6 :
When a fraction equals zero :
6.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
6n-17
————— • 6 = 0 • 6
6
Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
6n-17 = 0
Solving a Single Variable Equation :
6.2 Solve : 6n-17 = 0
Add 17 to both sides of the equation :
6n = 17
Divide both sides of the equation by 6:
n = 17/6 = 2.833
One solution was found :
n = 17/6 = 2.833
Choose the TRUE statements.
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 49 units to the left of zero on a number line is −49.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.
Answer:
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.by-step explanation:
Correct:
The absolute value of a number 35 units to the left of zero on a number line is 35.
The absolute value of a number 12 units to the left of zero on a number line is 12.
The absolute value of a number 125 units to the right of zero on a number line is 125.
Wrong:
The absolute value of 49 units to the left of zero on a number line is -49.
This answer is wrong because when u use absolute value, ur final number is always going to be positive, but i this case it’s negative so it wrong.
Have a good day! Hope this helped!!❤️❤️
Solve three and four and nothing more ok
Answer:
4=2/3 . 7/9=14/21
4/5. /5/6=20/30=2/5
Step-by-step explanation:
what are the next three terms in the sequence -1, 9, 19, 29
39. each term is ten more than the term before it :)
Answer:
39, 49, 59
Step-by-step explanation:
Note the difference between consecutive terms
9 - (- 1) = 9 + 1 = 10
19 - 9 = 10
29 - 9 = 10
The difference is a constant + 10
To obtain the next term in the sequence add 10 to the previous term
29 + 10 = 39
39 + 10 = 49
49 + 10 = 59
The next 3 terms are 39, 49, 59
Find the slope and y-intercept of the line. y=-x+7
Answer:
slope = - 1, y- intercept = 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x + 7 ← is in slope- intercept form
with slope m = - 1 and y- intercept c = 7
The slope of the line y = -x + 7 is -1, and the y-intercept is 7.
To determine the slope and y-intercept of the line given by the equation y = -x + 7, we first recognize that it is in slope-intercept form, which is y = mx + b.
Identify the slope (m): In the equation y = -x + 7, the coefficient of x is -1. Thus, the slope of the line is -1.
Identify the y-intercept (b): The constant term in the equation is 7. Thus, the y-intercept is 7, meaning the line intersects the y-axis at the point (0, 7).
The slope of the line y = -x + 7 is -1, and the y-intercept is 7.
What is the solution to the system of equations?
Answer:
There are infinitely many solutions. It is the same line.
Step-by-step explanation:
If you start by multiplying the first equation by 2 to get rid of the fractions, you get -x + y = -2. If you solve it for y, you get y = x - 2. The second equation can be solved for y also, giving you y = x - 2. That means they are the same line and the solution to this situation is infinitely many solutions because all the points on one line are identical to the points on the other line because they are the same line.