Answer:
4x remainder 1.
Step-by-step explanation:
We add up to get 4x^2+4x+1
We just factor from there.
The model represents an inequality. What is the solution set for the inequality?
Given:
The figure of an algebraic tiles model of an inequality.
To find:
The inequality for the given model.
Solution:
On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,
[tex]LHS=8(x)+12(1)[/tex]
[tex]LHS=8x+12[/tex]
On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,
[tex]RHS=12(-1)[/tex]
[tex]RHS=-12[/tex]
Now, the inequality for the given model is:
[tex]8x+12\geq -12[/tex]
Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].
Plot the numbers
and
on the number line below.
In this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.
To plot the numbers -1 1/6 and 4/3 on a number line, we need to find their relative positions and mark them accordingly.
Let's start with -1 1/6:
-1 1/6 can be written as a mixed number or an improper fraction. To simplify the plotting process, let's convert it to an improper fraction.
-1 1/6 = -(6/6 + 1/6) = -7/6
On the number line, we start from zero and move to the left because it is a negative number. Since -7/6 is less than -1, we will place it closer to zero but to the left of -1.
Next, let's plot 4/3:
4/3 is already in the form of an improper fraction. To plot it, we start from zero and move to the right since it is a positive number. 4/3 is greater than 1, so we will place it to the right of 1.
On this number line, we marked -7/6 to the left of -1, and 4/3 to the right of 1.
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8, 9, 3, 9, 3, 8, 4,4
1)
Mean
Median
Mode
Range
Answer:
8,
4 and 8
3,4,8,9
6
Step-by-step explanation:
What are the fourth roots of −3+33√i ?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
Answer:
In order of increasing angle measure, the fourth roots of -3 + 3√3·i are presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]
[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]
Step-by-step explanation:
The root of a complex number a + b·i is given as follows;
r = √(a² + b²)
θ = arctan(b/a)
The roots are;
[tex]\sqrt[n]{r}[/tex]·[cos((θ + 2·k·π)/n) + i·sin((θ + 2·k·π)/n)]
Where;
k = 0, 1, 2,..., n -2, n - 1
For z = -3 + 3√3·i, we have;
r = √((-3)² + (3·√3)²) = 6
θ = arctan((3·√3)/(-3)) = -π/3 (-60°)
Therefore, we have;
[tex]\sqrt[4]{-3 + 3 \cdot \sqrt{3} \cdot i \right)} = \sqrt[4]{6} \cdot \left[cos\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) \right][/tex]
When k = 0, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]
When k = 1 the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]
When k = 2, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]
When k = 3, the fourth root is presented as follows;
[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]
Answer:
Step-by-step explanation:
Just took the test.
1) 4sqrt6 cis(pie/6)
2) 4sqrt6 cis (2pie/3)
3) 4sqrt6 cis(7pie/6)
4) 4sqrt6 cis (5pie/3)
20 is what percent of 52? Solve with an Equation
Answer:
38.46
Step-by-step explanation:
Percentage Calculator: 20 is what percent of 52? = 38.46.
The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters
Answer:
It's B
Step-by-step explanation:
I took the test
Answer:
B= (√30 - 2√5)
Step-by-step explanation:
10. Fill in the blanks so as to make the statement true:
(i) A number which can be expressed in the form m/n, where m and n are
integers and n is not equal to zero, is called a ________.
(ii) If the integers m and n have no common divisor other than 1 and n is
positive, then the rational number m/n is said to be in the ________.
(iii) Two rational numbers are said to be equal, if they have the same
________ form.
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/______
(v) lf p and q are positive integers , then m/n is a ________ rational
number and m/-n is a ________ rational number.
(vi) The standard form of -1 is ________.
(vii) If m/n is a rational number, then n cannot be ________
(viii) Two rational numbers with different numerators are equal, if their
numerators are in the same ________ as their denominators.
Step-by-step explanation:
(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .
(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .
(iii) Two rational numbers are said to be equal, if they have the same Simplest form .
(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .
(v) The standard form of -1 is -1/1
(vi) If m/n is a rational number, then n cannot be 0
(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.
The equation for the line of best fit is y=–0.7x+39. In this equation, what does the y-intercept of 39 tell you?
Expand (p - q)(p+q).
Answer:
p^2 - q^2
Step-by-step explanation:
This is an example of "the product and difference of two squares."
The relevant formula is (a - b)(a + b) = a^2 - b^2 (no middle term).
Here,the desired product is (p - q)(p + q) = p^2 - q^2.
Answer:
(p - q)(p+q). :p²-q²....
What polynomial must be added to 3x2 + 4x + 7 to obtain the sum of 0?
Answer:
do (3x2+4x+7)+y=0
y=-3x^2-4x-7
On January 1, Mario had a savings account balance of $2742 and by April 1, his balance had increased to $3597. Find Mario's average savings rate in dollars per month for that period.
Answer: $285
Step-by-step explanation:
First and foremost, we should note that from January 1 to April 1 is 3 months. Since Mario had a savings account balance of $2742 on January 1 and by April 1, his balance had increased to $3597. The increase in balance will be:
= $3597 - $2742
= $855
Then the average savings rate will be:
= Total amount saved / Number of months
= $855/3
= $285
He had an average savings of $285 per month.
Help.
I have killed three children, the other six are locked in my basement and the cops are at my door. Do I invite them inside and poison their tea,, or do I just stab them??
P.S
Best way to get rid of bodies??
TYY!!! ^^
Answer:
Eat them. )llllllllllllllllllllllllll)
HELLPP ASAP!!!!
1. Find the unknown side lengths in these right triangles.
Answer:
10
Step-by-step explanation:
5x2
Can someone please explain the Pythagorean theorem to me?
Answer:
Pythagoras theorem is is a mathematical law that states that the sum of squares of the lengths of the two short sides of the right triangle is equal to the square of the length of the hypotenuse.
Step-by-step explanation:
The hypotenuse is the side opposite to the right angle and so the equation for finding the hypotenuse would be:
a^2+^b^2=c^2
Evaluate the expression 8a+11−3b for a = 4 and b = 2.
Answer: 37
8(4)+11-3(2)
32+11-6
43-6
37
How can you tell from the equation of a rational function if the function has a hole in the graph ( a removable discontinuity) at x, rather than a vertical asymptote? Give an example
Consider that,
x^2+4x+4 = (x+2)(x+2)
x^2+7x+10 = (x+2)(x+5)
Dividing those expressions leads to
(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)
The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.
On a test. I can't find answers anywhere else.
i think this is correct
For every 2 gallons of vanilla ice cream a shop sells, they sell 11 gallons of chocolate ice cream. If they sell 16 gallons of vanilla ice cream, how many gallons of chocolate ice cream is sold?
Answer: 88 gallons
Step-by-step explanation:
Every 2 vanillas = 11 chocolates
so 16 vanillas = 88 chocolates
i did this by multiplying both numbers by 8
sorry if this is wrong
Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.
Answer:
(a) 1, 2, 3, 6, 8
Step-by-step explanation:
Given
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
Required
The sequence of hours worked each day
See attachment for options
From the question, we understand that:
[tex]Median = 3[/tex]
This means that, the middle number is 3 (when sorted)
So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively
Next, is to determine the mean of (a) and (d)
The mean of a data is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
(a)
[tex]\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}[/tex]
[tex]\bar x = \frac{20}{5}[/tex]
[tex]\bar x = 4[/tex]
(d)
[tex]\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}[/tex]
[tex]\bar x = \frac{15}{5}[/tex]
[tex]\bar x = 3[/tex]
Option (a) is true, because it has:
[tex]Median = 3[/tex]
[tex]Mean = 4[/tex]
The surface areas of to somewhere figures are 36 inches squared and 49 inches squared. If the volume of the similar figure is 640 inches cubed, what is the volume of the larger figure?
A) 1029in^3
B) 746in^3
C) 408in^3
D) 882in^3
Answer:
345
Step-by-step explanation:
5 1/2 ÷ 3 2/3 + 1 4/5 , giving answer as a fraction in lowest terms
Answer:
6761/320
Step-by-step explanation:
[(51/2)÷32/3]+14/5
=6761/320
Help me please
Point K(–5, 2) is the midpoint of line segment Y Z , with endpoint Y(1, –3). What are the coordinates of Z?
Find the exact value of cot 330° in simplest form with a rational denominator.
Answer:
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
Step-by-step explanation:
The cotangent function can be rewritten by trigonometric relations, that is:
[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)
By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:
[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)
[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)
By (2) and (3) in (1), we have following expression:
[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]
If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:
[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]
[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]
The exact value of cot 330° with a rational denominator is √3.
To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.
Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.
Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.
(3/√3) x (√3/√3) = 3√3/3
Simplifying further, we can cancel out the common factor of 3:
(3√3/3) = √3
Therefore, the exact value of cot 330° with a rational denominator is √3.
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The diameter of the U.S. Capitol Building’s dome is 96 feet at its widest point. Find its circumference. Use 3.14 for π.
Answer:
301.44 ft
Step-by-step explanation:
The sum of the ages of Noah and Billy is 25; the sum of the ages of Noah and Ty is 20; and the sum of the ages of Billy and Ty is 31. Who is the oldest of the three and how old is he?
Answer:
the oldest is Ty and his age is 24
Step-by-step explanation:
Let us assume the billy age be x
Noah age be y
And, Ty age be z
Now according to the question
y + x = 25 ..........(1)
y + z = 20..........(2)
x + z = 31..............(3)
z = 31 - x
since
y + z = 20
y + 31 - x = 20
y - x = -11 .............(4)
Now solve (1) and (4) equation
So,
y + x = 25
y - x = -11
2y = 36
y = 18
x = 25 - 18
= 7
z = 31-7
= 24
Hence, the oldest is Ty and his age is 24
4. A car is travelling 75 kilometers per hour. How many meters does the car travel in one
minute?
Answer:
1250 Meters
Step-by-step explanation:
75 kilometers divided by 60 minutes is 1.25 kilometers per minute.
1 kilometer = 1000 meters
Answer:
75km/hr =75000
60 sec =1min,60 min=1hr
75000÷60=1250m
Help me it says use the figure for 1 and 2
HELPPP ME PLEASEEEEEE
Answer:
Step-by-step explanation:
[tex]y^2 = 100 + 196 = 296\\\\y = \sqrt{296} \\\\y = 17.20[/tex]
what is 2/4 divided by 3
Answer:
0.166
Step-by-step explanation:
Kay found four frogs on Monday and nine frogs on Tuesday in the pond by her house. Each frog has 5 warts. How many more warts are on the frogs from Tuesday than from Monday?
Answer: 25
Step-by-step explanation:
Given
Kay found 4 frogs on Monday
and 9 frogs on Tuesday by her house
each frog has 5 warts
So, total warts on Monday and Tuesday
[tex]\Rightarrow \text{Monday=}4\times 5\\\Rightarrow 20\\\\\Rightarrow \text{Tuesday =}9\times 5\\\Rightarrow 45[/tex]
The difference of warts is
[tex]\Rightarrow 45-20\\\Rightarrow 25[/tex]
Thus, there are25 more warts on frogs from Tuesday than from Monday
Frogs On Monday:
4 frogs x 5 = 20 warts
Frogs On Tuesday:
9 frogs x 5 warts = 45
Last Step:
45 (9 frogs each with 5 warts) - 20 (4 frogs each with 5 warts) =
Answer: 25
~Hope this helps!
~Hocus Pocus