Answers
Solution
Secant is a line that touches a circle at two distinct points
See figure below
Chord is a straight line that touches two points on the the circumference of the circle
A
Related Questions
Find the values of x and y in the following right triangle. Enter square roots not decimals.
Answers
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]1. It costs $9.81 for 9 pounds of grapefruit. How much would it cost for 1 pound of grapefruit?
Answers
9.81 / 9 = 1.09
$1.09
Answer:
the anser is 1.09
Step-by-step explanation:
9.81 divided by 9 = 1.09
find the remainder for the given division. (z^2+3z+1)/(z-2)
Answers
Explanation
Given the expression
[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.
According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.
Therefore, we will have;
[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]
QUIK ANSWER PLEASE!!! Solve the equationy^3 - 27 = 9y^2 - 27y
Answers
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
Consider the graph of the function f. a) Find the domain, range, and zeros of the function. b) write an equation for the function f. (In vertex form, standard form, or intercept form)c) compare the graph of f to the graph of g(x) = x^2.
Answers
Solution:
Given the graph;
(a) The domain of a function is the set of values for which the function is real and defined. Thus, the domain D is;
[tex]\begin{gathered} (-\infty,\infty) \\ D:All\text{ }real\text{ }numbers \end{gathered}[/tex]The range is;
[tex]y\leq8[/tex]The zeros of the function are the points y=0;
[tex]x=1,x=5[/tex](b) The equation of a parabola in vertex form is;
[tex]\begin{gathered} y=a(x-h)^2+k \\ Where\text{ }(h,k)\text{ is }the\text{ }vertex; \\ and\text{ }given\text{ }(1,0) \\ \\ 0=a(1-3)^2+8 \\ \\ -8=4a \\ \\ a=-2 \\ \\ \end{gathered}[/tex]Thus, the equation is;
[tex]y=-2(x-3)^2+8[/tex](c) Using the graph below;
The graph of g(x) has its intercept at (0,0).
The transformation goes as;
Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units
Using (5,0);
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 0=a(5-3)^2+8 \\ 4a=-8 \\ \\ a=-2 \end{gathered}[/tex]write the equation of the line that passes through the given points.
(4, 0) and (0, 2)
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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.
is this triangle possible?
Answers
Answer: The triangle is not possible.
Step-by-step explanation:
1) Find the missing angle
62+59+x=180
x=59
2) Use the Law of Sine to check if the triangle sides are the same.
The Law of sine means that Sine the angle and divide with the side across it will equal to same.
[tex]\frac{sin(x)}{x} =\frac{sin(y)}{y}[/tex]
Substitute the numbers.
[tex]\frac{sin(59)}{10} =\frac{sin(62)}{10}[/tex]
0.0636 = -0.0739
3) Solve
Since the decimals aren't the same, the triangle is not possible.
Look at the table. Is F(x) an exponential function? If so, Identify the base. if not, Why not?
Answers
ANSWER
YES, the base is 4 ......option B
Write the equation of the line that passes through the points (4, -1)
and (3,-2).
Ox+y = -5
O y = x-5
O y = -x +3
Oy - 3x + 13
Answers
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Given points:
(x₁, y₁) = (4, -1)(x₂, y₂) = (3, -2)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{-2-(-1)}{3-4}=\dfrac{-1}{-1}=1[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and the point (4, -1) into the point-slope formula to create the equation of the line:
[tex]\implies y-(-1)=1(x-4)[/tex]
[tex]\implies y+1=x-4[/tex]
[tex]\implies y+1-1=x-4-1[/tex]
[tex]\implies y=x-5[/tex]
Which one is the option to describe a piece wise function ?
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.
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
could you please help me out with a question
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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]I'll give brainliest!
Answers
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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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
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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?
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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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The first term of an Ap is 5 and the common difference is-3/2 Find the term whose value is 201/2
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The term in the AP whose value is 201 / 2 is 71.3.
How to find the term in an arithmetic progression?The first term of an arithmetic progression is 5 and the common difference is - 3/2.
The formula of the arithmetic progression can be described as follows:
nth term = a + (n - 1)d
where
a = first termn = number of termsd = common differenceTherefore, using the arithmetic progression formula,
a = 5
d = 3 / 2
nth term = 201 / 2
let's find the term(n)
Therefore,
- 201 / 2 = 5 + (n - 1) - 3 / 2
- 201 / 2 = 5 - 3 / 2 n + 3 / 2
- 201 / 2 - 3 / 2 - 5 = - 3 / 2 n
- 107 = -3 / 2 n
-3n = - 214
n = 214 / 3
n = 71.3
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Determine wether y varies directly with x. If so find the constant of variation k and write the equation
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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
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
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The equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
What exactly are equations?A mathematical formula known as an equation is one in which two expressions with the same value are separated by the "equal to" sign. For instance, 3x plus 5 equals 15.There are numerous kinds of equations, including linear, quadratic, cubic, and others. The slope-intercept form, standard form, and point-slope form are the three main types of linear equations.So, the equation for P will be:
Let, P be the total money earned when Madeline sells the 'x' number of computers.Let, 80 be the constant as that is the basic pay.Let, 'x' be the number of computers Madeline sells.Now, the equation can be:
P = 20x + 80(Refer the table attached below)
Therefore, the equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
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What is the LCM of 9 and 15?
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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=9three fifths of thr tshirts in a tshirt shop are on sale. five eighths of those tshirts are on sale. one third of those blue tshirts that are on sale are size medium. what fraction of the shops tshirts are blue tshirts that are on sale and are size medium? explain
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3/5 of the T-shirts of the shop are on sale
5/8 of those on sale are blue
1/3 of the blue shirts on sale are medium size.
First calculate how many of the shirts on sale are blue:
[tex]\frac{5}{8}\frac{\div3}{5}=\frac{5}{8}\cdot\frac{5}{3}=\frac{25}{24}[/tex]25/24 of the shirts on sale are blue
Then divide that number by three to know how many are medium size:
[tex]\frac{25}{24}\div3=\frac{25}{72}[/tex]25/72 are blue and medium size
We have to find two partial products to add 513×46
Answers
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]Under which transformation is size not preserved?A. reflectionB. dilationC. rotationD. translation
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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 Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.
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Answer:
[tex]\begin{gathered} \sin A=\frac{\sqrt[]{6}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Explanation:
Let x represent unknown side length
We can go ahead and find x using the Pythagorean Theorem as seen below;
[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;
[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;
[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;
[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Samantha borrowed money to buy lawn equipment to start her new lawn service business. She borrowed $800 for 9 months and paid $70.50 in interest. What was the rate of interest.
Answers
Using simple interest, the rate of interest on the amount that Samantha borrowed to buy the law equipment is 11.75%.
What is the simple interest?A simple interest system does not accumulate (compound) interest on both the principal and interest, unlike compound interest.
The simple interest uses the following formula, Interest = Principal x Rate x Period.
This simple interest formula can be reversed to find either the principal, rate, or period, as the case may be.
The loan amount = $800
Period of loan = 9 months
Total interest paid = $70.50
Rate of interest = (Interest × 100)/(Principal × Time)
= 11.75% ($70.50 x 100)/($800 x 9/12)
Check:
Interest = $70.50 ($800 x 11.75% x 9/12)
Thus, Samantha's interest rate on the loan is 11.75%.
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Carly has twice as many sisters as Connor.
Connor has twice as many sisters as Alicia.
Alicia has 3 sisters.
How many sisters does Carly have?
Answers
Answer:
12
Step-by-step explanation:
Alicia has 3 sisters.
Connor has twice as many sisters.
Twice means "two times".
Connor has 2×3, that is 6 sisters.
Carly has twice (two times) as many sisters as Connor.
Carly has 2×6, or 12 sisters.
Fill in the blank to make equivalent rational expressions.
2/y^2=_/3y^5
Answers
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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In a jar there are 65 red, 154 yellow and 70 green beads. You extract 54 beads at random.
Estimate the number of red beads obtained.
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The number of red beads obtained from the jar is 12 beads.
How many red beads obtained?The number of red beads that can be obtained from the jar is the ratio of red beads to the total number of beads multiplied by the total number of beads picked at random.
Number of red beads obtained = (number of red beads / total number of beads) x number of beads picked
Total number of beads = 65 + 154 + 70 = 289
Number of red beads obtained = (65 / 289) x 54 = 12.14 ≈ 12 beads
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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.
Answers
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.
The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form?answers:•x+y1=0•y-1=0•x-y+1 = 0
Answers
We will have the following:
First, we find the slope:
[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]So, the equation that represents the line is:
[tex]y=1[/tex]So:
[tex]y-1=0[/tex]***Explanation***
We are given the points (-2, 1) & (2. 1).
From this we cans see that the line passes both times through y = 1.
We also know that the slope (m) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So the slope for this line will be:
[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]Now, we also know that the equation of the line in general form is given by:
[tex]y-y_1=m(x-x_1)[/tex]So, the equation of the line will be given by:
[tex]y-1=(0)(x+2)\Rightarrow y-1=0[/tex]So the function is a constant value, thus a horizontal line.
***Explanation for the general form of a line***
The general form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]Here "x" & "y" are two variables; "x1" & "y1" are the component of a point that belongs to that lline and "m" is the slope of that line. We remember that (x1, y1) can be any point that belongs to the line.
So, we simply replace the values, in our case I willl solve for (-2, 1), but we could also use (2, 1), the solution at the end will be the same.
So:
[tex]y-(1)=(0)(x-(-2))\Rightarrow y-1=0\cdot x+0\cdot2[/tex][tex]\Rightarrow y-1=0[/tex]Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO
Answers
Solution:
Given:
When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;
[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;
[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;
[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;
[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]Therefore, the dimensions of the original piece of cardboard are 26 in by 22in
Write an equation that says that the length of the green line is equal to the length of theblack line. Combine like terms
Answers
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