Given the two points:
C (-5, 4) and Q (2, 0)
To find the distance, use the distance formula below:
[tex]d\text{ =}\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Where,
(x1, y1) = (-5, 4)
(x2, y2) = (2, 0)
Therefore, we have:
[tex]\begin{gathered} d=\sqrt[]{(2-(-5))^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{(2+5)^2+(0-4)^2} \\ \\ \text{ =}\sqrt[]{7^2+(-4)^2} \\ \\ \text{ =}\sqrt[]{49+16} \\ \\ \text{ =}\sqrt[]{65} \end{gathered}[/tex][tex]undefined[/tex]NEED HELP WITH THIS MATH QUESTION QUICK!
Answer:
[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]
[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]
Step-by-step explanation:
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the dividend is divided.
Quotient: The result of the division.
Remainder: The part left over.
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
[tex]\textsf{Dividend}: \quad 10x^4-14x^3-10x^2+6x-10[/tex]
[tex]\textsf{Divisor}: \quad x^3-3x^2+x-2[/tex]
Therefore:
[tex]\large \begin{array}{r}10x+16\phantom{)}\\x^3-3x^2+x-2{\overline{\smash{\big)}\,10x^4-14x^3-10x^2+6x-10\phantom{)}}}\\{-~\phantom{(}\underline{(10x^4-30x^3+10x^2-20x)\phantom{-b)}}\\16x^3-20x^2+26x-10\phantom{)}\\-~\phantom{()}\underline{(16x^3-48x^2+16x-32)\phantom{}}\\28x^2+10x+22\phantom{)}\\\end{array}[/tex]
Solution:
[tex]10x+16+\dfrac{28x^2+10x+22}{x^3-3x^2+x-2}[/tex]
[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]
[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]
QUIK ANSWER PLEASE!!! Solve the equationy^3 - 27 = 9y^2 - 27y
The first step is to simplify both sides of the equation. The equation can be written as
y^3 - 3^3 = 9y(y - 3)
For the left hand side, we would apply the difference of two cubes formula. it is expressed as
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
By comparing with the left hand side of the equation,
x = y and y = 3. It becomes
(y - 3)(y^2 + 3y + 3^2)
= (y - 3)(y^2 + 3y + 9)
The equation becomes
(y - 3)(y^2 + 3y + 9) = 9y(y - 3)
If we divide both sides of the equation by (y - 3), it becomes
(y - 3)(y^2 + 3y + 9)/(y - 3 = 9y(y - 3)/(y - 3)
y^2 + 3y + 9 = 9y
y^2 + 3y - 9y + 9 = 0
y^2 - 6y + 9 = 0
We would solve the quadratic equation by applying the method of factorisation. We would find two terms such that their sum or difference is - 6y and their product is 9y^2. The terms are - 3y and - 3y. The equation becomes
y^2 - 3y - 3y + 9
y(y - 3) - 3( y - 3) = 0
(y - 3)(y - 3) = 0
y - 3 = 0 twice
y = 3 twice
Write the equation of a line in the form y=Mx+b that passes through the point (3,6) and has a slope of -2/3. Sketch this line
Find an equation for the perpendicular bisector of the line segment whose endpoints are (3, -8) and (7,2).
ANSWER
[tex]y=-\frac{2}{5}x-1[/tex]EXPLANATION
We want to find the equation of the perpendicular bisector of the line segment with the given endpoints.
To do this, we first have to find the slope of the given line, since the slope of a line perpendicular to a given line is the negative inverse of the slope of the line.
Then, we have to find the midpoint of the given line since the line is a bisector, it passes through the midpoint of the given line segment.
To find the slope of the line, apply the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the two endpoints of the line segment
Hence, the slope of the line is:
[tex]\begin{gathered} m=\frac{2-(-8)}{7-3}=\frac{2+8}{7-3} \\ m=\frac{10}{4} \\ m=\frac{5}{2} \end{gathered}[/tex]The negative inverse of this is:
[tex]\begin{gathered} -(\frac{1}{\frac{5}{2}}) \\ \Rightarrow-\frac{2}{5} \end{gathered}[/tex]To find the midpoint of the endpoints, apply the formula for midpoint:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Hence, the midpoint of the given endpoints are:
[tex]\begin{gathered} (\frac{3+7}{2},\frac{-8+2}{2}) \\ \Rightarrow(\frac{10}{2},\frac{-6}{2}) \\ \Rightarrow(5,-3) \end{gathered}[/tex]Now, we have the slope and an endpoint of the perpendicular bisector.
To find the equation of the line, we have to apply the point-slope method:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, the equation of the perpendicular bisector of the line segment is:
[tex]\begin{gathered} y-(-3)=-\frac{2}{5}(x-5) \\ y+3=-\frac{2}{5}x+2 \\ y=-\frac{2}{5}x+2-3 \\ y=-\frac{2}{5}x-1 \end{gathered}[/tex]A 25 ft ladder is leaning against a building.The base of the ladder is 6 ft away from the building.How high up is the ladder?
Applying the Pythagorean Theorem, the ladder's height from the ground is: 24.3 ft.
How to Apply the Pythagorean Theorem?If we know any two sides of a right triangle, the Pythagorean Theorem can be used to find the length of the third side, c, if c is the longest side, and a and b are the shorter sides of the right triangle, we ill have the equation:
c² = a² + b².
The ladder forms a right triangle with the wall of the building. Therefore:
c = length of the ladder = 25 fta = distance of base of the ladder from the building = 6 ftb = how high the ladder is up on the wall of the buildingSubstitute
25² = 6² + b²
b = √(25² - 6²)
b = 24.3 ft.
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write the equation of the line that passes through the given points.
(4, 0) and (0, 2)
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First find the gradient. Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Gradient = (2-0)÷(0-4) = -1/2
Equation of line is y = -1/2x + c
Substitute either one of the points into the equation to find c.
0 = -1/2(4) + c
c = 2
Hence, the equation of the line is y = -1/2x + 2.
Which one is the option to describe a piece wise function ?
.
A piece-wise function is a function that changes its value, based on the input
That is a function its range depends on the domain.
The correct answer is the third option
A carton of 12 eggs costs $3.00. A carton of 18 eggs costs $4.32. Suppose a supermarket wants to sell the eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different-sized cartons? Explain
The price the supermarket can charge per egg that is between the prices of per egg for the two different-sized cartons is $0.245 per egg.
According to the question,
We have the following information:
Cost of 12 eggs in a carton = $3.00
Cost of 18 eggs in another carton = $4.32
Now, to find the charge per egg that is between the prices of per egg for these different-sized cartons, we will first find the charge per egg of both of them.
We know that to find the cost of 1 product we divide the given cost by the number of products.
Cost of 12 eggs in a carton = $3.00
Cost of 1 egg = $ (3.00/12)
Cost of 1 egg = $0.25
Cost of 18 eggs in another carton = $4.32
Cost of 1 egg = $(4.32/18)
Cost of 1 egg = $0.24
Now, we have to find the price of egg between 0.24 and 0.25.
Note the difference between these two charges is 0.01.
We will divide it by 2 to find the exact middle charge:
0.01/2 = 0.005
We can add this in $0.24 or subtract it from$ 0.25.
$0.24 + $0.005 = $0.245
Hence, price the supermarket can charge per egg is $0.245.
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We have to find two partial products to add 513×46
Answer
Explanations:
The product of two integers using the partial product is expressed using the distributive law as shown:
[tex]513\times46=(500+13)\times(40+6)[/tex]Expanding the result using the distributive law as shown;
[tex]undefined[/tex]Choose the best answer. The diagonals of a rhombus:A. bisect each other and intersect at different anglesB. are the same length and intersect at a right angleC. are the same length and intersect at different anglesD. bisect each other at right angles
The property of a rhombus regarding the two diagonals states that they bisect each other at right angles.
Hence, option D is the correct answer.
Write an equation that says that the length of the green line is equal to the length of theblack line. Combine like terms
Explanation:
Length of green line = length of black line
Length of green line = 26
Total length of black line = h + h + *
Total length of black line = 2h + 8
Equate the two expressions
26 = 2h + 8
Collect the like terms
26 - 8 = 2h
18 = 2h
Isolate h by dividing both sides by 2
18/2 = 2h/2
h = 18/2
h = 9
The equation is 26 = 2h + 8
Determine wether y varies directly with x. If so find the constant of variation k and write the equation
The given data is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
What is defined as the direct variation?A simple connection between two variables is described by direct variation. If y=kx, we say it varies significantly with x (or even as x in some textbooks) for some constant k, known as the constant of variation or the constant of proportionality.Because y varies directly with x, it would fit a equation y=kx for each and every point with in set.We may have 11=7k for the initial point, implying that k=11/7.
Again for second point, we'd have 13=8k, which means k=13/8.
Using proportions, we can see that 11/7 doesn't really equal 13/8: cross multiply and you get 11*8=7*13, or 88=91.
Thus, this is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
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The complete question is-
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x y
7 11
8 13
9 15
10 17
Under which transformation is size not preserved?A. reflectionB. dilationC. rotationD. translation
The philosophy of dilation is to resize uniformly the figure in question. Under this intuitive idea, dilation is the answer. Now, what does uniformly mean here?
It means that, as can be seen in the figure, the length of every side of the right triangle can be calculated by multiplying its corresponding side in the left ("small") triangle by a constant. However, this can be done from the right triangle to the left triangle; that's why I put a bidirectional arrow.
Finally, I want to give you some motivation for this concept: Every time you are resizing an image on your phone or in your computer, you're applying this concept.
Find the equation of a parabola with a focus of (0, 9) and directrix y = –9.
Answer:
Step-by-step explanation:
Given that,
To find the standard form of the equation of the parabola with a focus at (0, 9) and a directrix y = -9.
What is a parabola?
A parabola is a cross-section cut out of the cone and represented by an equation
Focus of the prabola = (h , k + F ) = (0, 9)
Since the directrix, y = -9
F = -9
k + F = 9
k = 0
Vertex of the parabola = (h, k )
= (0, 0)
Standard equation of the parabola
( y - k ) = 4a (x - h)²
( y - 0 ) = 4a (x - 0)²
y = 4 * 9 x²
y = 36 x²
Thus, the required expression for the parabola with focus at (0, -9) and a directrix y = 9 is y = 36x².
What is the average rate of change please write your answer as an integer or simplify fraction
Given:
f(x)=6x+3
Required:
To calculate the average rate
Explanation:
[tex]\begin{gathered} Average\text{ rate of change} \\ \\ y=6x+3\text{ at \lparen x=5\rparen} \\ \\ y=6(5)+3=33 \end{gathered}[/tex][tex]\begin{gathered} y=6x+3\text{ at\lparen x=10\rparen} \\ \\ y=6(10)+3 \\ \\ y=63 \end{gathered}[/tex][tex]\begin{gathered} average\text{ }rate\text{ }of\text{ }change \\ \\ y=63-33 \\ \\ y=30 \end{gathered}[/tex]Required answer:
30
Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
1. The decrease in dollars, based on a 7.5 percent decrease, is $615.
2. The balance in the account at the end of last year was $7,585.
What is a percentage?A percentage is a ratio or proportion of a variable in another.
For instance, the percentage decrease in the investment account was 7.5%, which in dollar terms amounts to $615.
The percentage reference gives an idea of the investment status and the fractional effect that the decrease had on it.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, Tammy's investment account decreased to $7,585 by $615, representing a 7.5% decrease.
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What is the LCM of 9 and 15?
What is the LCM of 9 and 15?
we know that
9=(3^2)
15=(3)(5)
so
the LCM=(3^2)(5)=45
the answer is
LCM=453^2=3*3=9I'll give brainliest!
The scientific notation is [tex]5.72 * 10^{6}[/tex]
Factor out 1 of the powers of 10
[tex]= (5.5 * 10^{6}/10^{6} + 2.2 * 10^{5}/10^{6}) * 10^{6}[/tex]
Perform division of exponents:
[tex](5.5 * 10^{0} + 2.2 * 10^{-1}) * 10^{6}[/tex]
Convert Scientific notations to real numbers:
[tex]= (5.5 + 0.22) * 10^{6}[/tex]
Combine real numbers:
[tex]= (5.72) * (10^{6})[/tex]
Convert to proper Scientific notations:
[tex]= 5.72 * 10^{6}[/tex]
Manually check answer
= (5.5 x 1000000) + (2.2 x 100000)
= 5500000 + 220000
= 5720000
[tex]= 5.72 * 10^{6}[/tex]
What are Scientific notations?
Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place following the decimal. This makes it challenging to express a small number of integers in their enlarged form. We thus employ scientific notations. Learn general forms for numbers as well.
Rules for Scientific Notation
We must adhere to the following rule in order to calculate the power or exponent of 10:
The base must always be 10.
Exponents that are non-zero integers must be either positive or negative in order to be used.
The coefficient's absolute value is more than or equal to 1, but it must be less than 10.
Positive and negative numbers, including whole and decimal values, can be coefficients.
The remaining significant digits of the number are represented by the mantissa.
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What is the slope of a line perpendicylar to the line whose equation is 5x - 6y = 30 Fully simplify your answer.
Answer:
-6/5
Step-by-step explanation:
[tex]5x-6y=30 \\ \\ 6y-5x=-30 \\ \\ 6y=5x-30 \\ \\ y=\frac{5}{6}x-5[/tex]
Perpendicular lines have negative reciprocal slopes, so the answer is -6/5.
Find the values of x and y in the following right triangle. Enter square roots not decimals.
Recall the following trigonometric identities. If the legs of the right triangle have lengths a and b, the hypotenuse has length c, and the side a is adjacent to an angle θ, then:
[tex]\begin{gathered} \sin \theta=\frac{b}{c} \\ \cos \theta=\frac{a}{c} \end{gathered}[/tex]Then, for the given right triangle:
[tex]\begin{gathered} \sin (30º)=\frac{x}{8} \\ \cos (30º)=\frac{y}{8} \end{gathered}[/tex]Then, x and y are given by the expressions:
[tex]\begin{gathered} x=8\cdot\sin (30º)=8\cdot\frac{1}{2}=4 \\ y=8\cdot\cos (30º)=8\cdot\frac{\sqrt[]{3}}{2}=4\cdot\sqrt[]{3} \end{gathered}[/tex]Therefore, the answers are:
[tex]\begin{gathered} x=4\cdot\sqrt[]{3} \\ y=4 \end{gathered}[/tex]What are the coordinates of the foci of the conic section shown below?(y + 2)² /16 - (x − 3)² /9 = 1A. (3, -2±5)B.(-2+5,3)C. (-2,3±5)D.(-2+√7,3)
SOLUTION
Given the question on the question tab;
Explanation:
[tex]\frac{(y+2)^2}{16}-\frac{(x-3)^2}{9}=1[/tex][tex]h=3,k=-2,a=3,b=4[/tex][tex]The\text{ }standardform\text{ }is\frac{\text{ }\left(y+2\right)^2}{4^2}-\frac{\left(x - 3\right)^{2}}{3^{2}}=1.[/tex][tex]The\text{ }linear\text{ }eccentricity\text{ }is\text{ }c=\sqrt{b^{2} + a^{2}}=5.[/tex][tex]\begin{gathered} The\text{ first focus is:} \\ \left(h,k−c\right)=\left(3,−7\right). \\ The\text{ second focus is:} \\ \left(h,k+c\right)=\left(3,3\right) \end{gathered}[/tex]Final answer:
QuestionWhich of the following expressions is equivalent to the verbal expression 'the quotient of 23x and 15t'?Select the correct answer below:23x · 15115123x0 23x + 151
Explanation
The quotient is the number obtained by dividing one number by another
for example:
the quotient of a and b is
[tex]a\text{ divided by b=}\frac{a}{b}[/tex]so
Step 1
Let
number 1=23x
number 2=15 t
so, the quotient would be
[tex]\frac{23x}{15t}[/tex]therefore, the answer is C:
[tex]\frac{23x}{15t}[/tex]I hope this helps you
To determine the value of tangent of 7 times pi over 8, which identity could be used?
Given:
[tex]\tan \frac{7\pi}{8}[/tex]To Determine: The identity that is equivalent to the given tangent
Note that, the identity rule below would be applied
[tex]\tan \frac{\alpha}{2}=\sqrt[]{\frac{1-\cos \alpha}{1+\cos \alpha}}[/tex]Also,
[tex]\tan \frac{\alpha}{2}=\frac{\sin \alpha}{1+\cos \alpha}[/tex]And also,
[tex]\tan \frac{\alpha}{2}=\frac{1-\cos \alpha}{\sin \alpha}[/tex]From the given tangent, we can re-write it as below:
[tex]\begin{gathered} \tan \frac{7\pi}{8}\cong\tan \frac{\frac{7\pi}{4}}{2} \\ \text{Note} \\ \frac{7\pi}{8}=\frac{\frac{7\pi}{4}}{2} \end{gathered}[/tex]Therefore:
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\sqrt[]{\frac{1-\cos\frac{7\pi}{4}}{1+\cos\frac{7\pi}{4}}}[/tex]Also:
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\frac{\sin \frac{7\pi}{4}}{1+\cos \frac{7\pi}{4}}[/tex]And also,
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\frac{1-\cos \frac{7\pi}{4}}{\sin \frac{7\pi}{4}}[/tex]It can be observed from the option provided, the correct options is
I and III only
Fill in the blank to make equivalent rational expressions.
2/y^2=_/3y^5
The expression that can complete the blank is 6y^3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to complete the blanks?The expression is given as
2/y^2=_/3y^5
Replace the blank with x
So, we have
2/y^2 = x/3y^5
Multiply both sides of the equation by 3y^5
So, we have
x = 3y^5 * 2/y^2
Evaluate the products
x = 6y^3
This means that the blank is 6y^3
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Look at the table. Is F(x) an exponential function? If so, Identify the base. if not, Why not?
ANSWER
YES, the base is 4 ......option B
Find each indicated value or measure assume that all segments that appear to be tangent are tangent.
Answer:
6
Step-by-step explanation:
Using the intersecting chords theorem,
[tex]x^2=36 \\ \\ x=6 (x>0)[/tex]
Which statement correctly compares the function shown on this graph with the function y = 3x - 6?
The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + c
where -
[m] is slope of line
[c] is y - intercept
Given is a equation of a straight line and a graph of a straight line.
We have the following equation -
y = 3x - 6
For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.
Now, the equation of the line plotted on graph -
m = (4 - 0)/(0 + 1.3)
m = 3.07
m = 3 (approx.)
Its y - intercept [c] = 4
Therefore, the equation of the plotted line -
y = 3x + 4
Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.
Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
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[The complete question needs the plotted graph. It is attached at the end of the answer]
The expression 81 √ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base? Answers are 19 30 80 and 810.
The distance between home plate and first base is -1 feet
what is distance ?
Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.
How to determine the number
From the information given, we have that;
The expression for the number of feet between home plate and first base is given as;
√81-√100
Where;
√81 is the number of feet at home plate
√100 is the number of feet at the first base
To determine the distance, we take find the square root of the numbers and substitute, we have;
9 - 10 Find the difference
-1 feet
Thus, the distance between home plate and first base is -1 feet
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A cylindrical candle is to be made from 18 in 3 of wax. If the candle’s height is twice its
diameter, what radius and height should it have, to the nearest tenth?
The radius is 1.13 inches and the height of the cylinder is 4.52 inches.
How to calculate the value?From the information, it's important to use the volume of a cylinder to illustrate the information.
Use the volume of a cylinder.
V = πr²h
V = volume.
r = radius
h = height
where:
V = 18
h = 2(2r) = 4r
Plug in the values into the equation and solve for r.
18 = πr²(4r)
18 = 4πr³
Divide both sides of the equation by 4π.
9 / (2π) = r³
r³ = 1.43
r = 1.13 inches.
Finally, multiply the radius by 4 to get the height. This will be:
= 4 × 1.13
= 4.52 inches.
In conclusion, the height is 4.52 inches.
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could you please help me out with a question
of the circumference is 21.2, we get that the diameter is
[tex]d=\frac{21.2}{\pi}\approx6.75[/tex]and therefore the radius is
[tex]r=3.37[/tex]