Which one of these points lies on the given circle
O (-2.5, -2.5)
O (1, 3)
O (2, - √5)
O (-√3, -√7)
Answers
Step-by-step explanation:
every point on the circle has the same distance from the center : r (radius).
we can see that radius right there on the x-axis : the distance of (3, 0) to (0, 0) is simply 3. that is our radius.
the distance formula is applied Pythagoras
distance² = (difference in x coordinates)² +
+ (difference in y coordinates)²
distance = sqrt( ... )
so,
(-2.5, - 2.5)
(-2.5 - 0)² + (-2.5 - 0)² = 6.25 + 6.25 = 12.5
that is not 3² = 9, so the point is NOT on the circle.
(1, 3)
(1 - 0)² + (3 - 0)² = 1 + 9 = 10
that is not 3² = 9, so the point is NOT on the circle.
(2, -sqrt(5))
(2 - 0)² + (-sqrt(5) - 0)² = 4 + 5 = 9
that IS 3² = 9, so, the point IS on the circle.
(-sqrt(3), -sqrt(7))
(-sqrt(3) - 0)² + (-sqrt(7) - 0)² = 3 + 7 = 10
that is not 3² = 9, so the point is NOT on the circle.
Related Questions
a man invested $6000 at 8% per annum simple interest for 5 years.
a).calculate the simple interest.
b).the total amount of money collected at the end of the 5 year period.
Answers
Answer:
*r = R/100 = 8%/100 = 0.08 per year, A = P(1 + rt)
a) A = 6000[1 + (0.08 × 5)] = 8400
b) A = $8,400.00
Answer:
a) $2400
b) $8400
Step-by-step explanation:
The simple interest formula can be used to find the amount of interest. The amount collected at the end of the period is the total of principal and interest.
__
a)The simple interest is given by the formula ...
I = Prt . . . . . . P is the principal amount, r is the annual rate, and t is the number of years
For this investment, the interest is ...
I = $6000·0.08·5 = $2400
The simple interest amounts to $2400.
__
b)The amount collected at the end of 5 years is the principal plus interest:
P +I = $6000 +2400 = $8400
The total collected is $8400.
Write a rule to describe the transformation
Answers
what is the slope of the line graphed below?
Answers
Answer:
5
Step-by-step explanation:
the gradient is 5
change in Y over change in X
What is the domain of the given function?
{(3,-2), (6, 1), (-1, 4), (5, 9), (-4, 0)}
{x|x = -4,-1, 3, 5, 6}
Oyly=-2, 0, 1, 4, 9}
O {x|x = -4, -2, -1, 0, 1, 3, 4, 5, 6, 9)
Oyly=-4, -2, -1, 0, 1, 3, 4, 5, 6, 9)
h
Answers
Answer:
A
Step-by-step explanation:
the domain are the value on the x coordinate
i.e 3, 6, -1, 5, -4 = {-4,-1,3,5,6}
LL
F
C
9
5
D
2x+3
E
What is the value of x and the length of segment DE?
1 5
9
9
2x + 3
2. 10x+15=9(9)
Length of DE=
units
Answers
Answer:
[tex]x=\boxed{6.6}[/tex]
[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]
Step-by-step explanation:
Geometric Mean Theorem - Altitude Rule
The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:
[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]
From inspection of the given diagram:
altitude = FD = 9segment 1 = CD = 5segment 2 = DE = [tex]2x+3[/tex][tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]
Substitute the found value of x into the expression for DE:
[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]
What is the area of the triangle below?
On a coordinate plane, a triangle has a base of 6 units and a height of 9 units.
27 square units
45 square units
54 square units
90 square units
Answers
Answer:
27 units
Step-by-step explanation:
6 (base) × 9 (height) = 54
54 × 1/2 = 27
State the various transformations applied to the base function f(x)=|x| to obtain a graph of the function g(x) = |x| − 2.
Horizontal shift of 1 unit to the right and a vertical shift upward of 2 units.
Horizontal shift of 1 unit to the right and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Horizontal shift of 1 unit to the left and a vertical shift upward of 2 units.
Answers
Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
Transformation of functionTransformation technique is a way of changing the position of an object on an xy-plane.
Given the parent function of a modulus function f(x) = |x|, the graph of the function g(x) = |x| - 2 shows a vertical translation of the parent function down by 2 units.
The resulting graph of the translated function is as shown below
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a pie shop offers 20% off the price of a large pie every Monday night. If the regular price is $22, what is the discounted price?
brainliest to answrer
Answers
Answer:
$17.60
Step-by-step explanation:
20% of $22 is $4.4 - Subtract $4.40 from $22 to calculate the discounted price: $17.60
Hope this helped! :)
Translate the shape A four squares right and two squares down.What are the coordinates of the vertices of the image?.
Answers
The translated vertices are:
A' = (5, 2)B' = (5. -1)C' = (7. -1)What are the coordinates of the vertices of the image?.The vertices of the original figure are:
A = (1, 4)B = (1, 1)C = (3, 1).Now we want to apply a translation of four units to the right and 2 units down, then each point (x, y) becomes (x + 4, y - 2).
This means that the translated vertices are:
A' = (1 + 4, 4 - 2) = (5, 2)B' = (1 + 4, 1 - 2) = (5. -1)C' = (3 + 4, 1 - 2) = (7. -1)If you want to learn more about translations:
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how do u convert a percentages into fractions ??
Answers
Answer:
Step-by-step explanation:
To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100
ex: 11% = 11/100
write the slope-intercept form of the equation of a line passing through the following two points: (-3, 7) & (6, -5)
Answers
In order to find equation, first find slope:
[tex]\sf slope : \dfrac{y_2 - y_1}{x_2 - x_1} \quad where \ (x_1, y_1) , \ (x_2, y_2) \ are \ points[/tex]
Given points: (-3, 7) and (6, -5)
[tex]\rightarrow \sf slope : \dfrac{-5-7}{6-(-3)} =-\dfrac{4}{3}[/tex]
Equation:
[tex]\sf y- y_1 = m(x - x_1)[/tex]
insert values
[tex]\rightarrow \sf y - 7 = -\dfrac{4}{3} (x -(-3))[/tex]
[tex]\rightarrow \sf y = -\dfrac{4}{3} x - 4 +7[/tex]
[tex]\rightarrow \sf y = -\dfrac{4}{3} x +3[/tex]
anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board. two students will be selected, and they will alternate attending the school board meetings. all five students are equally well qualified, so the school superintendent decides to draw names at random. what is the probability he will choose debbie and esther as the two representatives? enter your answer as a fraction in simplest terms.
Answers
Probability that he will choose debbie and esther as the two representatives is 1/20 .
What is the meaning of Probability ?Probability is the stream in mathematics in which likeliness of an event to happen is studied.
The range of probability lies between 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.
It is given that anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board.
two students will be selected, and they will alternate attending the school board meetings.
all five students are equally well qualified, so the school superintendent decides to draw names at random.
probability he will choose debbie and esther as the two representatives = ?
Probability of chosing debbie is 1/5
Probability of choosing Esther is also 1/5
Either of them if chosen first the probability is 1/5
and the either of them chosen second the probability is 1/4
Probability that he will choose debbie and esther as the two representatives = (1/5)*(1/4) = 1/20 .
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a letter is chosen from the nine letters in the word "bumblebee." what is the probability the letter is a b or an e?
statistics and probability
Answers
Answer:
2/3
Step-by-step explanation:
Probability (b or e) :
⇒ There are 3 b's and 3 e's in the word "bumblebee"
⇒ P (b or e) = No. of b's and e's / Total letters
⇒ P (b or e) = 3 + 3 / 9
⇒ P (b or e) = 6/9
⇒ P (b or e) = 2/3
Simplify the expression: 4+(11-3)²
Answers
Answer:
68
Step-by-step explanation:
[tex]4+\left(11-3\right)^2\\(11-3)=8\\=4+8^2\\=4+64\\=68[/tex]
In an oblique drawing, which surface is shown in its true size and shape and is parallel to the horizon?
top
side
bottom
front
Answers
In an oblique drawing, the surface that is shown in its true size and shape and is parallel to the horizon is the front.
What is the drawing about?The Position of an object in a drawing is known to be parallel to the plane of projection and the circular shape is true in front plane of the oblique view.
The measurements on the front and oblique faces are known to have all its lengths to be true.
Note also that A pictorial drawing that has the front view of an object parallel to the projection plane and shown its true size and shape is known to be Oblique Drawing.
Therefore, In an oblique drawing, the surface that is shown in its true size and shape and is parallel to the horizon is the front and as such, option d is correct.
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If f(x) and f¹(x) are inverse functions of each other and f(x) = 2x+ 5, what is ƒ˜¹ (8) ?
Answers
If f(x) and f¹(x) are inverse functions of each other then value of ƒ˜¹ (8) = 3/2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have,
f(x) = 2x + 5
Let us consider f(x) as y
So, y= 2x + 5
Now replace x to y and y to x
x= 2y+ 5
Solving for y we get
2y = x - 5
y = (x - 5)/2
[tex]f^{-1[/tex](x) = (x - 5)/2
Now, [tex]f^{-1[/tex](8) = (8 - 5)/2
[tex]f^{-1[/tex](x) = 3/2
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Isabel says that 0.02 can be expressed as 20%. Is she correct? Explain why or why not.
Answers
[tex]\text{She is not correct because}\\\\20\% = \dfrac{20}{100} = \dfrac 2{10} = 0.2 \neq 0.02[/tex]
Is LMN = OPQ? If so, name the congruence postulate that applies. N Given: LM = OP PQ = MN P M = 00 O A. Congruent - SAS O B. Congruent - SSS O C. Might not be congruent O D. Congruent - ASA
Answers
Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.
When is the SSS rule used?It is used when the two triangles given have three equal corresponding sides which also have equal angles.
All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.
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please simplify and keep the answer with exponents.
(6^7 * 6^12)/ 6^8
Answers
Answer:
6¹¹
Step-by-step explanation:
Simplifying the numerator :
When two terms with the same base are multiplied, the powers are added6⁷ x 6¹²6¹⁹Solving the expression :
When two terms with the same base are divided, the powers are subtracted6¹⁹ / 6⁸6¹¹At the local pet store, zebrafish cost $2.10 each, and neon tetras cost $1.95 each. if ernesto bought 13 fish for a total cost of $26.70 not including tax, how many of each type of fish did he buy?
Answers
Answer:
zebrafish: 9neon tetras: 4Step-by-step explanation:
The numbers of zebrafish and neon tetras can be found by writing an equation relating the numbers of each to their total cost.
__
setupLet z represent the number of zebrafish Ernesto bought. Then the number of neon tetras is (13 -z), and the total cost of the purchase was ...
2.10z +1.95(13 -z) = 26.70
solution0.15z +25.35 = 26.70 . . . . . . simplify
0.15z = 1.35 . . . . . . . . . . . . subtract 25.35
z = 9 . . . . . . . . . . . . . . . divide by 0.15
Ernesto bought 9 zebrafish and 4 neon tetras.
what is the mean of, 50, 30, 40, 10, 20, 80, 60, 90, 10, 30, 110, 70?
Answers
Answer:
50
Step-by-step explanation:
Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.
600 / 12 = 50.
Look at the photo and answer the question.
Please don’t just put the answer at the top of the text and don’t make it hard to find.
Answers
Answer:
second option
Step-by-step explanation:
5 newton pushing it to the right
while a mere 4 newton pushing it to the left
more force pushing towards right
This would be the answer because there are 5 newtons forcing the given object to the right while there are 4 newtons forcing the object to the left. Because 5 is greater than 4, the object would accelerate to the right in this model with 1 newton more of force than it would to the left.
The length of a reclangle can be represented by the expression 2x - 1. The width of the same rectangle can be represented by the expression x^2 - x + 3. Which of the following expressions can represent the area of the rectangle?
Answers
Answer:
2x^3 - 3x^2 + 7x - 3
Step-by-step explanation:
Area = length * width
= (2x - 1)(x^2 - x + 3)
= 2x(x^2 - x + 3) - 1(x^2 - x + 3)
= 2x^3 - 2x^2 + 6x - x^2 + x - 3
= 2x^3 - 3x^2 + 7x - 3
Which of the expressions are equivalent to the one below? (5x1)-7
Answers
Answer:
-2
Step-by-step explanation:
[tex](5 \times 1) - 7 \\ 5 - 7 \\ - 2[/tex]
Triangle DEF, with vertices D(9,-8), E(8,-3), and F(2,-5), is drawn inside a rectangle,
as shown below.
What is the area, in square units, of triangle DEF?
[
Answer: A=?
units²
Answers
The area of the triangle DEF is 2 square units
How to determine the area?The given parameters are:
D(9,-8), E(8,-3), and F(2,-5),
The area of the triangle is calculated using:
Area = 0.5|x1 * (y2 -y3) + x2 * (y1 -y3) + x3 * (y2 -y1) |
This gives
Area = 0.5|9 * (-3 + 5) + 8 * (-8 + 5) + 2 * (-3 + 8) |
Evaluate
Area = 0.5|4|
Expand
Area = 2
Hence, the area of the triangle DEF is 2 square units
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The diagonals of a trapezoid are 15 cm and 13 cm. The height is 12 cm. Find the area of the trapezoid.
Answers
Answer:
168cmsqured
Step-by-step explanation:
as for me,15 acts as the lower part of the trapezium while 13 acts as the upper part of the trapezium .so since I know the measurements of the both sides I can easily calculate the area use using the formula indicated in the image.hope it helps
A wire goes from the top of a 55 ft pole to the ground. It makes a 70
o angle with the ground. How long is the wire? NEEDN ASAP!!! ill give 20 points for this
Answers
Answer:
58.5 ft
Step-by-step explanation:
sin 70=55/length
length=58.5 ft
Which ordered pair is a solution to the following system of inequalities?
y < –x2 + x
y > x2 – 4
(0, –1)
(1, 1)
(2, –3)
(3, –6)
Answers
Answer: (0,-1)
Step-by-step explanation:
Let's start with the first inequality, [tex]y < -x^{2}+x[/tex]. To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.
A) [tex]-1 < -0^{2}+0 \longrightarrow -1 < 0 \longrightarrow \text{ True}[/tex]B) [tex]1 < -1^{2}+1 \longrightarrow 1 < 0 \longrightarrow \text{ False}[/tex]C) [tex]-3 < -2^{2}+2 \longrightarrow -3 < -2 \longrightarrow \text{ True}[/tex]D) [tex]-6 < -3^{2}+3 \longrightarrow -6 < -6 \longrightarrow \text{ False}[/tex]Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).
A) [tex]-1 > 0^{2}-4 \longrightarrow -1 > -4 \longrightarrow \text{ True}[/tex]C) [tex]-3 > 2^{2}-4 \longrightarrow -3 > 0 \longrightarrow \text{ False}[/tex]Therefore, the answer is (A) (0, -1).
Part A: Solve for the "h." Show all work
Answers
Answer:
2.7 m
Step-by-step explanation:
Corresponding sides of similar triangles are proportional. This figure shows similar triangles ∆ABC ~ ∆ADE.
__
The proportion that can be used to find h = DE is ...
DE/BC = DA/BA
h/(0.9 m) = (12 m+6 m)/(6 m) . . . . . filling in the values given
h = (0.9 m)(18/6) . . . . . multiply by 0.9 m
h = 2.7 m
The value of "h" is 2.7 m.
Which is the completely factored form of 12x3 – 60x2 + 4x – 20?
Answers
Answer:
[tex]4(x-5)(3{x}^{2}+1)[/tex]
Step-by-step explanation:
1) Find the Greatest Common Factor (GCF).
1 - What is the largest number that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is [tex]4.[/tex]
2 - What is the highest degree of [tex]x[/tex] that divides evenly into [tex]12x^3,-60x^2,4x,[/tex] and [tex]-20[/tex] ?
It is 1, since [tex]x[/tex] is not in every term.
3 - Multiplying the results above,
The GCF is 4.
2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
[tex]4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})[/tex]
3) Simplify each term in parentheses.
[tex]4(3{x}^{3}-15{x}^{2}+x-5)[/tex]
4) Factor out common terms in the first two terms, then in the last two terms.
[tex]4(3{x}^{2}(x-5)+(x-5))[/tex]
5) Factor out the common term [tex]x-5[/tex].
[tex]4(x-5)(3{x}^{2}+1)[/tex]