Step-by-step explanation:
8.5 I believe is the answer
12 + 4y < 32 y < 5 y > 5 y < −8 y > −8
The solution of the inequality expression given as 12 + 4y < 32 is y < 5
What is an inequality expression?An inequality expression is an expression where both sides of the expression have unequal values and they make use of any of the symbols <, >, <=, >= and !=
How to determine the solution to the inequality expression?The inequality expression is given as
12 + 4y < 32
Subtract 12 from both sides of the inequality
So, we have the following expression
12 - 12 + 4y < 32 - 12
Evaluate the like terms in the above inequality
So, we have the following expression
4y < 20
Divide both sides of the inequality by 4
So, we have the following expression
4y/4 < 20/4
Evaluate the quotient
y < 5
Hence, the solution is y < 5
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Write all classifications that apply to the real number 10
10 is a natural number, whole number and an integer.
Natural numbers may be defined as the numbers which include all the positive integers that is non-negative integers, and the numbers will be from 1 to infinity. 10 is a natural number as it lies in the range from 1 to infinity. Whole numbers may be defined as the numbers which include all the positive integers as well as zero. So, the range of whole numbers is from zero to infinity and 10 is a whole number as it lies in this range. Integers may be defined as the collection of positive and negative numbers along with zero but no fractions. 10 lies in this range so 10 is an integer.
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Given a point, P, that exists on a great circle on the surface of a sphere, explain why no line
can be drawn on the sphere that is parallel to the great circle containing P.
If a given point, P, exists on a great circle on the surface of a sphere, no line can be drawn on the sphere that is parallel to the great circle because each pair of great circles(parallel lines) will always intersect, regardless of how they are drawn.
Why are there no parallel lines in spherical geometry?Lines are described as the large circles that round the sphere. A great circle is a circle with its center in the center of the sphere. Any two great circles will meet at two opposed places. Hence "parallel lines" do not exist (great circles) on a sphere. Because a line is defined as a great circle, we can deduce that each line passes through two antipodal points, dividing the sphere in half. If two lines (great circles) are drawn, they will always cross paths as they travel over to the opposite hemisphere.To learn more about Spherical Geometry visit:
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find the value of the arc shown in red leave ir answer in terms pi
The arc marked in red is a quarter of the circle's circumference.
Hence the arc marked red subtends an angle of 90degrees.
[tex]\begin{gathered} \text{Given an arc that subtends }\theta\text{ at the center of with radius r} \\ \end{gathered}[/tex][tex]\text{arc length, l = }\frac{\theta}{360}\times2\pi r[/tex]In our case
[tex]\theta=90^o,\text{ r = 6m}[/tex][tex]l=\frac{90}{360}\times2\pi(6)=\frac{1}{4}\times2\pi(6)=3\pi m[/tex]You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y = -0.000475x² + 0.851x, where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?
The bridge is 895.79 feet above the river.
The length of the section of the bridge above the arch is 179.58 feet.
The underside of the bridge is in the shape of an arc.
The height of the bridge is represented by the function,
y = - 0.000475x² + 0.851x
Now, when the height will be maximum, dy/dx = 0
Therefore,
dy/dx = (d/dx)( - 0.000475x² + 0.851x )
dy/dx = - 0.00095x + 0.851 = 0
- 0.00095x + 0.851 = 0
Subtracting 0.851 from each side,
- 0.00095x = - 0.851
Dividing each side of the equation by 0.00095
x = 895.7895 feet ≈ 895.79 feet
Therefore, the maximum height of the bridge is h = 895.79 feet.
The length of the section is represented by x,
y = - 0.000475x² + 0.851x
To obtain the x-intercept, we put y = 0:
- 0.000475x² + 0.851x = 0
x ( - 0.000475x + 0.851) = 0
Therefore,
x = 0 and,
- 0.000475x + 0.851 = 0
- 0.000475x = - 0.851
x = 1791.58 feet
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What is the complete factorization of the polynomial below? x3 - 2x2 + x - 2
A.(x + 2)(x + i)(x - i)
B.(x - 2)(x - i)(x - i)
C.(x - 2)(x + i)(x - i)
D.(x + 2)(x - i)(x - i)
The polynomial factors are (x -2)(x+ i)(x - i)
What is Factorization of PolynomialsIn mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
To find the factors of the given polynomial, we can proceed as
[tex]x^3 -2x^2 + x - 2[/tex]
Let's factor out a common term
[tex]x^3 - 2x^2 + x - 2 = x^2(x-2) + (x-2)\\x^2(x-2)+(x-2)\\(x-2)(x^2+1) = (x-2)(x+i)(x-i)[/tex]
The factors of the given polynomial is (x-2)(x+ i)(x- i)
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what is the product of the HCF and LCM of 12 ,18,30
The product of the HCF and LCM of 12 ,18,30 can be written as 1080.
What is HCF and LCM?The H.C.F. can be described as the greatest factor that can be found when expressing given two or more numbers, on the other hand the LCM can be described as the least factor that exist between a two given number.
factors of 12 are: 3, 4, 2, 6, 12.
factors of 18 are: 2, 3 , 6 9 , 18
factors of 30 are ; 2, 3, 6, 5, 10
HCF; The factor that is greatest among the factors of the numbers = 6
To calculate the LCM, we need to find to find the prime factor of the three numbers as:
Prime factor of 12 are ; 2*2*3
Prime factor of 18 are ; 2*3*3
Prime factor of 12 are ; 2*3*5
LCM is now the multiplication of the prime factors which is the highest occurrence of them in either numbers as ; 2*2*3*3*5 =180
From the given numbers we can see that the HCF = 6 and LCM = 180, then if we find the product as (6*180)=1080 which is the number of the product of the lowest common factor as well as the highest common factor.
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Can someone pls help
Answer:
6/4
Step-by-step explanation:
For a RIGHT triangle, Tan = opposite leg / adjacent leg = 6/4 for angle F in this example
find the area of a circle
The area is 28.26 in²
The reading rug in Mrs. Shaw s room has a perimeter
of 28 meters. The table gives the length and width of
the rug. If the equation 4(x + 3.3) = 28 can be used to
find the perimeter of the rug, what is the value of x?
What expression is equivalent to y^2/5 if y=0
IN THE PLACE OF Y PLUG IN 0
[tex] = \frac{( {0})^{2}}{5} \\ = \frac{0}{5} \\ = 0[/tex]
The answer is 0
what is 15^ 1/3 in radical form? 15√3. b. 1/3√15 c. 3√15
The radical form ∛ is 1/3.
The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Example: 3 + x, 3x, √4, ∛27 are all expressions.
We have,
[tex]15^{\frac{1}{3} }[/tex]
We need to write it in radical form.
This means we must remove the power 1/3 in the given expression.
Some of the expressions in the radical form are:
∛ = 1/3
√ = 1/2
We know that,
∛ = [tex]\frac{1}{3}[/tex]
So,
Since ∛ is 1/3 we can write the expression as ∛15.
[tex]15^{\frac{1}{3} }[/tex] = ∛15.
Thus,
The radical form of the expression [tex]15^{\frac{1}{3}[/tex] is ∛15.
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Callan goes for a hike every Saturday. Callan hikes at a rate of 6 kilometers per hour.
Complete the table for the given ratio.
Hours, a
1
3
4
Kilometers, y
6
Plot the ordered pairs (x, y) from the table on the following graph.
Kilometers (y)
The table can be given as for 3 hours we have 18 km and for 4 hours we have 24km, founded by using average.
What is average and how to calculate it?Average is the ratio of the sum of all elements of the dataset to the number of elements in the dataset. To calculate the average we first find the sum of all elements of the dataset and divide it by the number of elements.So, we are given that Callan hikes at a rate of 6 km an hour.
In this way, he will hike 18 km in 3 hours.
And 24 km in 4 hours.We can plot this using graphs.(Refer to the graph attached below)
Hence, using averages, we know that the table can be given as for 3 hours we have 18 km and for 4 hours we have 24km.
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in each of the following describe the rate of change between the first and the second, assuming that the first coordinate is measured in minutes and the second coordinate is measured in feet. what are the units of your answer
Answer: no clue sonny boi but good luck
Trigonometry Lesson #7: More Problem Solving... 111
5. From the top of a cliff 110 m high, an observer sees two boats, one directly behind the
other, heading for shore. The angle of depression from the observer to the boat furthest
from the observer is 48° and the angle of depression to the nearest boat is 57°.
Calculate the distance between the boats, to the nearest metre.
The distance between the two boats is found as 21.60 m.
What is termed as the angle of depression?The angle of depression is defined as "an angle made between the horizontal line and also the line of sight whenever an observer looks downwards at an object." When we look down, it determines the shift in angle of our vision.For the given question,
Let the distance of ship c from the bottom of the cliff is 'a'.
Let the distance between both ships is 'b' m.
The height of the cliff is 110 m.
The angle of depression by both the ship with the top of the cliff is 48° and 57°.
Data from the figure shown,
Consider right triangle ABD,
tan 48° = AB/BD
tan 48° = 110/(a+b)
a + b = 110/tan 48°
a + b = 99.04 .......eq 1
Now in right triangle ACD,
tan 57° = 110/a
a = 110/tan 57°
a = 71.43 m
Put the value of in eq 1.
a + b = 99.04
b = 99.04 - 71.43
b = 21.60 m
Thus, the distance between the two boats is found as 21.60 m.
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View the image to answer.
The value of the [tex]\lim_{x\to \ 0} h(x)[/tex] cannot be determined based on the given information.
Squeeze Theorem :
When standard algebraic techniques like factorization, conjugation, algebraic manipulation, etc. fail to solve a limit problem, the squeeze principle is utilized. It does, however, demand that you can "squeeze" your issue between two other, "simpler" functions whose bounds are quickly computed and equal.
It states that if [tex]g(x),f(x) and h(x)[/tex] are three functions such that,
[tex]g(x)\leq h(x)\leq f(x)[/tex]
and [tex]\lim_{x\to \ 0} f(x) = \lim_{x \to \ 0} g(x) =L[/tex] , Then
[tex]\lim_{x\to \ 0} h(x) = L[/tex]
Given Data :
[tex]g(x)=\frac{x^{2} }{3} +\frac{2}{5}[/tex]
Now, [tex]\lim_{x\to \ 0} g(x) =\frac{2}{5}[/tex]
and [tex]f(x) = x^{2} -2x+4\\[/tex]
and [tex]\lim_{x \to \ 0} f(x)=4[/tex]
Since,[tex]\lim_{x \to0} f(x) \neq \lim_{x\to \ 0} g(x)[/tex]
Thus, we cannot employ the Squeeze Theorem, Hence the data is insufficient to calculate the limit of h(x).
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a + a what's the answer
Answer:
2a
Step-by-step explanation:
when you have two of the same variable you can combine them. We know that all variables that do not have a coefficient by default have the constant 1 so 1a+1a equals 2a
Lexi bought a new car. She drove 5⁴ miles in the first month that she owned the car and 4⁵ miles in the second month that she owned the car. How many miles did Lexi drive in all during the first two months that she owned the car?
Answer:
Your answer is 1649 miles.
Step-by-step explanation:
[tex]5^{4} + 4^{5} = 1649[/tex]
answer 22746 X 76828636467 and will be brainliest have to put name! and add me as friend
Answer:2.10971436E14
Step-by-step explanation:
Answer:
Step-by-step explanation:
1,747,544,165,078,382 is the answer.
A shot-putter throws a shot and its height is noted every 20 feet, the data is in the table below:
Feet Traveled Feet Above Ground
20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64
Please find the quadratic function of best fit for these data and, to the hundredths place, say what height, in feet, the shot started its flight.
The quadratic function of best fit for the data is given as follows:
h(t) = -0.004t² +1.032t + 5.667.
Using this function, the initial height of the shot is of 5.67 feet.
Why a quadratic function of best fit is used, and how to find it?The input and the output of the data are given as follows:
Input: feet traveled.Output: feet above the ground.As the input increases, the output increases and then it decreases. Since this behavior of increase/decrease is not uniform over the entire domain of the relation, a quadratic function best models this data.
To find the quadratic function of best fit, we insert the points (input,output) into a calculator, from point (20, 25) to point (200,64).
Inserting the points into the calculator, the function is defined as follows:
h(t) = -0.004t² +1.032t + 5.667
The height in which the shot started its flight is given by the height when t = 0, hence:
h(0) = -0.004(0)² + 1.032(0) + 5.667 = 5.667 feet = 5.67 feet (rounded to the hundredths place).
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6. Encuentra las áreas de los rectángulos con las siguientes longitudes de lado. a. 5 pulgadas y pulgadas b. 5 pulgadas y pulgadas a. pulgadas y pulgadas b. 7 pulgadas y pulgadas
Area of Rectangles of the given values are 5/3inches², 20/3inches², 10/3inches² and 1 inches²
What is Area of Rectangle?
The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle called its area.
Since we know that,
Area of Rectangle = length x width
So, by the given values we can find the area of the following:
a) 5inch and 1/3inch
Let,
Length = 5inch
Width = 1/3inch
Since,
Area of Rectangle = length x width
= 5 x 1/3
= 5/3inches²
b) 5inch and 4/3 inch
Let,
Length = 5inch
Width = 4/3inch
Since,
Area of Rectangle = length x width
= 5 x 4/3
= 20/3inches²
c) 5/2inch and 4/3 inch
Let,
Length = 5/2inch
Width = 4/3inch
Since,
Area of Rectangle = length x width
= 5/2 x 4/3
= 5 x 2/3
= 10/3inches²
d) 7/6 inch and 6/7inch
Let,
Length = 7/6inch
Width = 6/7inch
Since,
Area of Rectangle = length x width
= 7/6 x 6/7
= 1 inches²
Hence, The following area of rectangles are 5/3inches², 20/3inches², 10/3inches² and 1 inches²
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AcDNecT
2. A caterer needs to buy 21 pounds of pasta
to cater a wedding. At a local store, 8 pounds
of pasta cost $12. How much will the caterer pay for the pasta there?
a.
Write a ratio for the given information about the cost of pasta.
If a caterer needs 21 pounds of pasta and a local store sells 8 pounds of pasta for $12, then the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta, calculated using the unitary method.
As per the question statement, a caterer needs 21 pounds of pasta to cater a wedding, while a local store sells 8 pounds of pasta for $12.
We are required to calculate the total amount which the caterer will have to pay at the store for their 21 pounds of pasta.
To solve this question, first we will need to calculate the price of 1 pound of pasta at the local store, from their rate provided in the question statement, and then multiply the cost of unit pound of pasta with the number of pounds the caterer needs, to obtain our desired answer, that is,
Using the unitary method, we get,
The local store sells 8 pounds of pasta for $12,
Or, it then sells 1 pound of pasta for $(12/8)
Or, the cost of 21 pounds of pasta at this store will $[(12/8) * 21] = $31.5
Hence, the caterer has to pay a total amount of $31.5 at the store for their 21 pounds of pasta.
Unitary Method: In Mathematics, the unitary method is a process of finding the value of a single unit, and then calculating the value of multiple units of the same, but multiplying the value of the single unit with the total number of units.To learn more about Unitary Method and total amounts, click on the link below.
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use the quadratic formula to solve the equation 2x^2-11x=1
we have the equation
2x^2-11x=1
2x^2-11x-1=0
where
a=2
b=-11
c=-1
substitute in the quadratic formula
[tex]x=\frac{-(-11)\pm\sqrt[]{(-11)^2-4(2)(-1)}}{2(2)}[/tex][tex]x=\frac{11\pm\sqrt[]{129}}{4}[/tex]the solutions are
[tex]x=\frac{11+\sqrt[]{129}}{4}\text{ and }x=\frac{11-\sqrt[]{129}}{4}[/tex]- (-1) ²- 2(-1) + 8
4 |5-8| what is the answer
Answer: 12 is the answer. Hope this helps Have a good day mark me brainlist
Step-by-step explanation:
4•(5-8)
Calculate the difference
4•(-3)
The absolute value of any number is always positive is always positive.
4•3
Multiply the numbers
=12
If G(x)=-3x+5 find: G(0)
Answer:
G(0) = 5
Step-by-step explanation:
substitute x = 0 into G(x) , then
G(0) = - 3(0) + 5 = 0 + 5 = 5
Divide.
(6x³+13x²-12x-6)÷(3x+2)
Your answer should give the quotient and the remainder.
19x/3+2/9 is the quotient and 50 is the remainder for the given equation (6x³+13x²-12x-6)÷(3x+2).
What is Quotient?The result of dividing two numbers is known as the quotient. Six divided by two results in the number three. Latin's "how many times" is the meaning of the word "quotient." That makes perfect sense: by dividing two numbers, you can determine "how many times" the second number enters the first.
What is Remainder?The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remainder is the name for this amount.
On dividing the equation,
The quotient will be 19x/3+2/9 and the remainder will be 50.
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how much more does it cost to buy 2 large pool that is 3,126 equipment sets than 2small pool that is 2,721 equipment sets
Answer:h
Step-by-step explanation:
Can someone please help me soon
Because we have a closed dot at (4, 17), we conclude that when x = 4 the value of the function is 17, so the correct option is the third one.
What is the value of the function when x = 4?
Here we have the graph of a piecewise function, and we want to see which value the function takes when x = 4.
To do so, we need to find x = 4 on the horizontal axis, and then move until we hit the graph.
For x = 4 we can see two points on the graph.
One open point at y = 7, where the open dot means that this value does not belong to the function.
A closed point at y = 17, where the closed dot means that this value belongs to the function.
From this, we conclude that when x = 4, the value of the function is 17.
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Is the graph of [tex]4x+5y=\frac{3}{7}[/tex] a line? Explain.
We can say that the graph of 4x+5y = 3/7 is a line because it can be represented by the straight line equation.
What exactly is a line equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
How do you graph an equation using the slope and y-intercept?Calculate the y-intercept of the equation y = mx + b.Calculate the y-intercept. The main point will be (0, b).Calculate the slope=m of the equation y = mx + b.Use the rise and run from the slope to make a single step.Make a line connecting those two points.Given equation : 4x+5y = 3/7
The given equation can be written as
5y = -4x + 3/7
y = (-4/5)x + 3/35
This is a form of y = mx + c
It is a the equation of the straight line.
Therefore, we can say that the graph of 4x+5y = 3/7 is a line as it can be represented as the equation of the straight line.
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