Answer:
radius = 6.5
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius )
x² + y² = 42.25 ← is in this form
with r² = 42.25 ( take the square root of both sides )
r = [tex]\sqrt{42.25}[/tex] = 6.5
It takes 20 men 60 days to complete a building work.How many days longer will It take 15 men, assuming they work all work at the same rate?
Answer:
80days
Step-by-step explanation:
20m=60days
15m(will take more days)
20÷15×60 = 80 days
vertex of y=-2(x-3)^2+2
Answer:
vertex = (3, 2 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 2(x - 3)² + 2 ← is in vertex form
with vertex = (3, 2 )
A top view of two walls of a room is represented by the x and y-axis, with units in meters. A ball is rolled from the point (0,15). It hits the adjacent wall at (20,0). Find the absolute value function that models the path of the ball. Determine when the ball passes within 3 meters of the wall represented by the x-axis.
Answer:
The absolute value function that models the path of the ball is
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The coordinates when the ball passes within 3 meters of the wall is [tex]\left (3, 12\tfrac{3}{4} \right )[/tex]
Step-by-step explanation:
Given that the ball rolls without other external influences, we have;
(y - 0) = (x - 15)
The slope, m is give by the relation;
m = (y₂ - y₁)/(x₂ - x₁)
m = (15 - 0)/(0-20) = -3/4
The equation of the path of the ball in slope and intercept form is presented as follows;
y = m·x + c
15 = -3/4 ×0 + c = 15
c = 15
The absolute value function that models the path of the ball is then;
[tex]f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |[/tex]
The vale of the function when x = 3 is given by the relation
[tex]f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}[/tex]
Therefore, we have the coordinates as [tex]\left (3, 12\tfrac{3}{4} \right )[/tex].
Write the expression in simplest form. (-11/2x+3)-2(11/4x-5/2)
Answer:
-11x+8 or 8-11x
Step-by-step explanation:
Bill wants to be a marine biologist when he grows up. His entire room is ocean-themed, so he is painting his bed frame blue to match. He estimates that he will need 5 cups of paint, but the hardware store only sells paint in quarts. If Bill buys 2 quarts of paint, how many cups will he have left?
Answer:
3 cups
Step-by-step explanation:
Bill needs 5 cups of paint for his bed frame.
The store only sells in quarts and so he buys 2 quarts of paint.
Let us convert to cups to see how many he bought:
1 quart = 4 cups
2 quarts = 2 * 4 = 8 cups
Bill bought 8 cups of paint. Therefore, the number of cups he has left is:
8 - 5 = 3 cups
He will have 3 cups left.
Which best explains why the equation 3x + 8 = 3x - 5 has no solutions?
O A. The equation is not true for any value of x.
B. The equation has a variable on both sides.
O C. The equation is true for any value of x.
SUE
Answer:A is the ans
Step-by-step explanation:
Feel pleasure to help u
in the following APs,find the missing terms in the boxes
1). 5_,_,9/2
2).-4,_,_,_,_,6
3)._,38,_,_,_,-22
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
(1)
Given a₁ = 5 and a₄ = [tex]\frac{9}{2}[/tex] , then
5 + 3d = [tex]\frac{9}{2}[/tex] ( subtract 5 from both sides )
3d = - [tex]\frac{1}{2}[/tex] ( divide both sides by 3 )
d = - [tex]\frac{1}{6}[/tex]
add - [tex]\frac{1}{6}[/tex] to each term
5, [tex]\frac{29}{6}[/tex], [tex]\frac{14}{3}[/tex], [tex]\frac{9}{2}[/tex]
(2)
Given a₁ = - 4 and a₆ = 6, then
- 4 + 5d = 6 ( add 4 to both sides )
5d = 10 ( divide both sides by 5 )
d = 2
Add 2 to each term
- 4, -2, 0, 2, 4, 6
(3)
Given a₂ = 38 and a₆ = - 22, then
a₁ + d = 38 → (1)
a₁ + 5d = - 22 → (2)
Subtract (1) from (2) term by term
4d = - 60 ( divide both sides by 4 )
d = - 15
Substitute d = - 15 into (1)
a₁ - 15 = 38 ( add 15 to both sides )
a₁ = 53
Thus
53, 38, 8, - 7, - 22
Which preferred pairs shoes an equivalent ratio of pounds to dollars?
Answer: 40, 36
Step-by-step explanation:
the first dot is 5/4
the second dot is 10/8
the second 15/12
the fourth dot is 20/16
They all are equivalent to 40,36
Answer:
25,20
Step-by-step explanation:
It’s right
If c+1/d=5 , what is the value of 30d/2c+2
Answer:
3
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Step-by-step explanation:
You can solve for any variable. From the first equation, let's solve for c :
[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]
Now, replace the value of c into the other equation:
[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]
Using distributive property
[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]
However, keep in mind that this is true for:
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Consider the function f(x) = x2 + 12x + 11. x-intercepts: 0 = x2 + 12x + 11 0 = (x + 1)(x+ 11) y-intercept: f(0) = (0)2 + 12(0) + 11 What are the intercepts of the function? The x-intercepts are . The y-intercept is
Answer:
The coordinates of the x-intercepts are;
(-1, 0) and (-11, 0)
The coordinate of the y-intercept is;
(0, 11)
Step-by-step explanation:
The given function is f(x) = x² + 12·x + 11
The x-intercept is at f(x) = 0 which gives;
0 = x² + 12·x + 11 which has been factored as (x + 1)(x+11) such that we have;
(x + 1)(x+11) = 0
x = -1, or x = -11
The y-intercept occurs at x = 0, we therefore have;
f(0) = (0)² + 12·(0) + 11 = 11
Therefore, we have f(0) = 11 = Y
Given that at the x-intercept, y = 0, then the coordinates of the x-intercepts are;
(-1, 0) and (-11, 0)
Given that at the y-intercept, x = 0, then the coordinate of the y-intercept is;
(0, 11).
Answer:
man up there is right
Step-by-step explanation:
what is the coordinates of A and Q
Answer:
Coordinate of A: -9
Coordinate of Q: 9
Step-by-step explanation:
1 - 10 = -9
1 + 8 = 9
Clinical literature reports that the duration of a typical cold is roughly 18 days. Researchers wanted to know if people tend to underestimate the duration of a typical cold, on average. They surveyed a random sample of 352 healthy adults in Georgia and asked them how long they think that a typical cold lasts. The researchers reported a 95% confidence interval of 6.9 to 8.2 days for the mean expected duration of typical cold. The researchers reported that the answers to this question were strongly right-skewed. The 95% confidence interval (6.9, 8.2) they obtained is
Answer:
The 95% confidence interval (6.9, 8.2) they obtained means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Option B from the complete Question.
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution if there is no information provided for the population standard deviation and it is obtained from the z-tables if the population standard deviation is known or the sample size is large enough that the sample properties can be approximated to be the same as the population properties.
Standard error of the mean = σₓ = (σ/√n)
σ = standard deviation of the sample
n = sample size
Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
So, the confidence interval (6.9, 8.2) obtained in the question means that "We are 95% confident that the population mean duration is between 6.9 and 8.2 days".
Hope this Helps!!!
What does it mean if P(A or B) equals 1?
[tex]P_(_A_o_r_B_)[/tex] = 1
This means that the probability of event A or event B of happening is 1 or certainly would happen.
Helppp!!!! please!!!
Answer:
18Step-by-step explanation:
8 faces and 12 vertices means hexagon as its base
That means 6+6 edges of its bases and 6 side edges.
6+6+6=18
HELP ME ASAP I BEG PLEASE
Answer:
Step-by-step explanation:
#2: Amber is correct. The distribution is skewed to the left.
PLEASE HELP ME!! Whoever answers best is the brainlest! And, please show your work. Thank you! What is the value of the expression 9 − (1/2) ^4 ⋅ 48? (A)1 (B)3 (C)6 (D)9
Answer:
C. 6
Step-by-step explanation:
Use Order of Operations BPEMDAS to help you solve:
9 - 1/16(48)
9 - 3
6
Expand the following using the Binomial Theorem and Pascal's Triangle. Please show work.
(2x+3)^5
6.247 * 10 to the twelfth power in standard form
Answer: 6,247,000,000,000
Step-by-step explanation:
Here we have the number:
6.247x10^12 and we want to write this in standard form.
You can see that we have a 10^12, this means that we need to move the decimal dot 12 places to the right, if there is not a decimal to the right, we add a zero.
6.247x10^12 = 62.47x10^11 = 624.7x10^10 = 6,247x10^9 = 62,470x10^8 and so on.
eventually, the standard form is:
6.247x10^12 = 6,247,000,000,000
So we end with 12 digits after the six.
58. 122. 61. None of the choices are correct
Answer:
C. 61
Step-by-step explanation:
Two sides are equal, so the triangle is an isosceles triangle.
Both base angles are equal.
Angles in a triangle add up to 180 degrees.
58 + x + x = 180
58 + 2x = 180
2x = 122
x = 61
Find the common difference of the sequence shown. 1/6, 1/3, 1/2 , 2
Answer:
1/6
Step-by-step explanation:
sequence should be 1/6,1/3,1/2,2/3
common difference=1/3-1/6=2/6-1/6=1/6
or 1/2-1/3=(3-2)/6=1/6
or c.d.=2/3-1/2=(4-3)/6=1/6
Answer:
The answer is 1/6.
Step-by-step explanation:
I got it right when I did it.
match each pair of angle measures of a triangle with the remaining angle measure
Answer:
6 and 102 = 62
119 and 23 = 38
96 and 51 = 33
28 and 87 = 65
Step-by-step explanation:
just did mine :D
Rectangle A,B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), D(-8, -4). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
AB= 5 units
Image of coordinates is shown in the attachment.
What is the value of Y?
Answer: 57 = y
Step-by-step explanation: To find the value of y in this problem, we use the exterior angle theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
So in the diagram shown, the exterior angle, 114,
is equal to the sum of the remote interior angles, y + y.
So we have 114 = y + y.
Solving from here, first combine like terms on the right side.
So we have 114 = 2y.
Now divide both sides by 2 to get 57 = y.
Can someone please help
Answer:
(6, -4)
Step-by-step explanation:
If ABCD is dilated by a factor of 2, you multiply the coordinates by 2. For the coordinate D', you would multiply 3 by 2 to get 6 and you would multiply -2 by 2 to get -4. Answer: (6, -4)
1. The perimeter of the given triangle PQR is
cm
P
7cm
3cm
R
4cm
O 16
28
26
65
Answer:
No, it is not possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm because here we see that sum of the lengths of two sides is equal to third side i.e., 4+3 = 7. As we know that, the sum of any two sides of a triangle is greater than its third side, so given statement is not correct.
Step-by-step explanation:
Find the equation of the line through point (−2,−2) and parallel to 3x+4y=12. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.
Answer:
3x + 4y = - 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + 4y = 12 ( subtract 3x from both sides )
4y = - 3x + 12 ( divide all terms by 4 )
y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/tex]
Parallel lines have equal slopes, thus
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
To find c substitute (- 2, - 2) into the partial equation
- 2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← in slope- intercept form
Multiply through by 4 to clear the fractions
4y = - 3x - 14 ( add 3x to both sides )
3x + 4y = - 14 ← in standard form
Hiya can someone please help me on my maths ratio work?!?
Arthur is organising his collection of DVDs. He has 152 altogether
The ratio of comedy films to action to horror is 6:8:5
How many of each DVD does he have?
What is the answer please help! make sure to explain. thanks!! Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below. Which of the following does this situation represent? A. both a relation and a function B. a function only C. neither a relation nor a function D. a relation only
Answer:
A
achievements
Step-by-step explanation:
resolve the following into factor ab+ac-ad
Answer:
a(b+c-d)
Step-by-step explanation:
Each term has a factor of "a", so that can be factored out. The remaining factor cannot be factored any further.
ab +ac -ad = a(b +c -d)
Answer:
a(b + c - d)
Step-by-step explanation:
'a' is common to all three terms of the given expression. Thus, the expression in factored form is a(b + c - d).
If a family threw away 2.4 Kg of aluminum in a month, how many cans did they throw away?
Answer:
150 cans were thrown away
Step-by-step explanation:
If the weight of 10 aluminum cans=0.16 kilogram
Each can weighs=0.16 kilograms/10
=0.016kg per can
If the family threw away 2.4 kilogram of aluminum in a month,
How many cans did they throw away?
Total cans thrown away= Total kilogram of cans/each kilogram of cans
=2.4kg/0.016kg
=150 cans
150 cans were thrown away