Answer:
[tex](x-4)^2+(y+1)^2=29[/tex]
Step-by-step explanation:
We want to find a circle whose diameter has the endpoints (6, 4) and (2, -6).
Since this is the diameter, its midpoint will be the center of the circle. Find the midpoint:
[tex]\displaystyle M=\left(\frac{6+2}{2}, \frac{4+(-6)}2}\right)=(4, -1)[/tex]
So, the center of our circle is (4, -1).
Next, to find the radius, we can find the length of the diameter and divide it by half.
Using the distance formula, find the length of the diameter:
[tex]\begin{aligned} d&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ &=\sqrt{(2-6)^2+(-6-4)^2}\\\\&=\sqrt{(4)^2+(-10)^2}\\\\&=\sqrt{116}\\\\&=2\sqrt{29}\end{aligned}[/tex]
So, the radius will be:
[tex]\displaystyle r=\frac{1}{2}d=\frac{1}{2}\left(2\sqrt{29}\right)=\sqrt{29}[/tex]
The equation for a circle is given by:
[tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex]
Substitute:
[tex](x-4)^2+(y+1)^2=29[/tex]
the volume of a cuboid is 480cm cube,it's breadth and height are 8cm are 6cm respectively find its length
Dan, Harry and Regan sell cars.
Dan sells x cars.
Harry sells 5 more cars than Dan.
Regan sells twice as many cars as Dan.
Write an expression, in terms of x, for the mean number of cars Dan, Harry and Regan sell.
Answer:
4X+5
Step-by-step explanation:
Dan : X
Harry: X+5
Regan: 2X
X+X+5+2X
Answer:
[tex]Mean = \frac{4x + 5}{3}[/tex]
Step-by-step explanation:
Given:
Dan sold = x
Harry sold 5 more than Dan, that is = x + 5
Regan sold twice as Dan = 2x
[tex]Mean = \frac{ Total \ cars \ sold}{number\ of \ them \ sold \ it }\\\\Mean = \frac{x + ( x+ 5) +2x }{3} = \frac{4x + 5}{3}[/tex]
Two vertices of a right triangle have the coordinates (-2, 5) and (9, 5). What is the length of the side formed by these vertices?
Answer:
11 unit
Step-by-step explanation:
Applying,
s = √[(y₂-y₁)²+(x₂-x₁)²]...................... Equation 1
Where s = length of the side formed.
From the question,
Given: x₁ = -2, x₂ = 9, y₁ = 5, y₂ = 5
Substitute these values into equation 1
s = √[(9+2)²+(5-5)²]
s = √(11²)
s = 11 unit.
Hence the length of the side formed by the vertices is 11 unit
A sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. Each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. Which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?
A. t = s - 18
10t = 12s + 32
B. s = t - 18
12s = 10t + 32
C. s = t - 18
10s = 12t + 32
D. t = s - 18
12t = 10s + 32
Answer:
[tex]\text{B .}\\\begin{cases}s=t-18, \\12s=10t+32\end{cases}[/tex]
Step-by-step explanation:
The each issue of the sports magazine, [tex]s[/tex], has 18 fewer pages than each issue of the technology magazine, [tex]t[/tex], we have equation [tex]s=t-18[/tex]. This eliminates answer choices A and D.
The second equation can be written from the fact that the total number of pages in all the sports magazines, [tex]12s[/tex], is 32 more than the total number of pages in all the technology magazines, [tex]10t[/tex]. Thus, we have equation [tex]12s=10t+32[/tex], eliminating answer choice C and leaving answer choice [tex]\boxed{\text{B .}\\\begin{cases}s=t-18, \\12s=10t+32\end{cases}}[/tex]
What’s 1/2 + 1/3? Y’all please help me . And when or if you can give me the answer can you do step-by-step on how you did that so I can do it myself next time?
[tex]\longrightarrow{\green{\frac{5}{6}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{1}{2} + \frac{1}{3} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.
The L. C. M for 2 and 3 is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} [/tex]
[tex]= \frac{3}{6} + \frac{2}{6} [/tex]
Now that the denominators are equal, we can add them.
[tex]= \frac{3 + 2}{6} \\ \\ = \frac{5}{6} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Which of the following is the function f(x) if f^-1(x) = 5x - 19?
A. f(x) = x - 19 over 5
B. f(x) = x + 19 over 5
C. f(x) = 5x + 19
D. f(x) = x over 5 + 19
Answer:
number of A is correct answer
28 Marks
.
Two numbers have these properties.
Both numbers are greater than 6.
Their highest common factor (HCF) is 6.
Their lowest common multiple (LCM) is 60.
Find the two numbers, writing your answers on one line in the form,
The two numbers are ... and..
Answer:
HCF×LCM=a×b
6×60=a×b
a×b=360
So the numbers are whose product is 360 and LCM is 60
These two numbers can be 6,60 or 12,30
Identify the missing parts in the proof.
Given: ∠ABC is a right angle.
DB bisects ∠ABC.
Prove: m∠CBD = 45°
A:
B:
C:
D:
Answer:
The missing parts of the proof includes;
1) ∠ABC = m∠CBD + m∠ABD = 90° (Angle addition postulate)
2) m∠CBD = m∠ABD (Definition of angle bisector)
3) m∠CBD + m∠ABD = m∠CBD + m∠CBD (Substitution property of equality)
Step-by-step explanation:
The given details of the proof are;
∠ABC is a right angle = 90°
Line DB is a bisector of ∠ABC
Therefore;
1) ∠ABC = m∠CBD + m∠ABD = 90° by angle addition postulate
By the definition of angle bisector, we have;
The angles formed by line DB from ∠ABC are equal,
2) m∠CBD = m∠ABD by the definition of angle bisector
3) m∠CBD + m∠ABD = 90° = m∠CBD + m∠CBD = 2 × m∠CBD by substitution property of equality
2 × m∠CBD = 90°
∴ m∠CBD = 90°/2 = 45°
Answer:
A: Given
B: measure the angle ABC = 90
C: angle addition postulate
D: 2 times the measure of angle CBD = 90
Step-by-step explanation:
Hope this helps <3
What is the value of the expression 3^2 . (2^3 +4) _____________ 2^2
Answer:
The answer is [tex]3^3\times 2^2[/tex].
Step-by-step explanation:
According to the rules of exponents
a^n = a x a x a x .... n times
So,
[tex]3^{2}\times (2^{3}+4)\\\\=9\times (8 +4)\\\\=108\\\\=3^{3}\times 2^{2}[/tex]
A boat heading out to sea starts out at Point AA, at a horizontal distance of 804 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 12^{\circ} ∘ . At some later time, the crew measures the angle of elevation from point BB to be 2^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Answer:
672 feets
Step-by-step explanation:
Using the solution diagram attached, the vertical height, h of the lighthouse ;
Using trigonometry :
Tanθ = opposite / Adjacent
Tan 2 = h / 804
h = tan 2 * 804
h = 28.076 feets
Using h, we can obtain the distance CB :
Tan θ = opposite / Adjacent
Tan 2 = 28.076 / CB
CB = 28.076 / Tan 12°
CB = 132.08860 feets
Distance between A and B
804 - 132.08860
= 671.9 feets
Given csc(A) = 60/16 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator . Someone please help me!
Answer:
[tex] \frac{15 \sqrt{209} }{209} [/tex]
Step-by-step explanation:
Objective: Understand and work with trig identies.
Recall multiple trig identies and manipulate them to get from cosecant to secant.
Given
[tex] \csc(a) = \frac{60}{16} [/tex]
Apply reciprocal identity csc a = 1/sin a.
[tex] \sin(a) = \frac{16}{60} [/tex]
Apply pythagorean identity to find cos a.
[tex]( \frac{16}{60}) {}^{2} + \cos(x) {}^{2} = 1[/tex]
[tex] \frac{256}{3600} + \cos(x) {}^{2} = 1[/tex]
[tex] \cos(x) {}^{2} = \frac{3600}{3600} - \frac{256}{3600} [/tex]
We can simplify both expression
[tex] \cos(x) {}^{2} = \frac{225}{225} - \frac{16}{225} [/tex]
[tex] \cos(x) = \frac{ \sqrt{209} }{15} [/tex]
Cosine is positve on quadrant 1 so that cos(a)
Apply reciprocal identity sec a= 1/ cos a.
The answer is
[tex] \sec(a) = \frac{15}{ \sqrt{209} } [/tex]
Rationalize the denominator.
[tex] \frac{15}{ \sqrt{209} } \times \frac{ \sqrt{209} }{ \sqrt{209} } = \frac{15 \sqrt{209} }{209} [/tex]
The diameter of a circle is 6 inches. What is the circle's circumference? Use 3.14 for .
Answer: 18.84
Step-by-step explanation:
Formula for circumference of a circle is 2[tex]\pi[/tex]r. Radius is half the diameter so 6/2=3. 2(3.14)(3)= 18.84
The histogram below shows the grade ranges for Mrs. Granderson's class.
Student Scores on Test 4
10
8
6
Prequency
60-69
70 - 79
80 - 89
90 - 100
How many students earned an 80 or better on Test 4?
There were
students who earned an 80 or better on the test.
Answer:
The answer is 14.
Step-by-step explanation:
All you had to do was add all the amount of students that scored 80 to 100 and you would have got your answer.
Which of the following graphs is the solution set of -10 < 3x - 4 < 8?
Answer:
3rd option
Step-by-step explanation:
Solving the inequality
- 10 < 3x - 4 < 8 ( add 4 to each interval )
- 6 < 3x < 12 ( divide each interval by 3 )
- 2 < x < 4
Since -2 less than x and x less than 4
This is indicated by an open circle at - 2 and 4 on the number line and the line between them is shown in black.
The solution is represented on the 3rd graph
Answer:
its the 3rd graph
Step-by-step explanation:
Someone please help me ASAP!
Answer:
x + 1 y+1
Step-by-step explanation:
it translated 1 unit up the x axis and 1 unit y axis
Answer:
reflected across the y-axis and translated 1 to the right and 1 up
Step-by-step explanation:
Does this graph represent a function? Why or why not?
Answer:
B yes
Step-by-step explanation:
As long as a verticle line intercepts the graph at no more than one point it is a function
Answer:
B. Yes, because it passes the vertical line test
Step-by-step explanation:
no x values are repeated
Se tienen 25 billetes de 5 y de 20 lempiras con un monto de 350 lempiras cuantos billetes de 5 lempiras se tienen y de 20 lempiras
Answer:
El número de facturas
5 lempiras = 10 billetes
20 lempiras = 15 billetes
Step-by-step explanation:
Vamos a representar
El número de facturas de
5 lempiras = x
20 lempiras = y
Nuestro sistema de ecuaciones se da como:
x + y = 25 ..... Ecuación 1
x = 25 - y
5 × x + 20 × y = 350
5x + 20y = 350 .... Ecuación 2
Sustituiríamos x por 25 - y en la ecuación 2
5 (25 - años) + 20y = 350
125 - 5 años + 20 años = 350
125 + 15 años = 350
15 años = 350 - 125
15 años = 225
y = 225/15
y = 15
Resolviendo para x
x = 25 - y
x = 25 - 15
x = 10
Por lo tanto, el número de facturas
5 lempiras = 10 billetes
20 lempiras = 15 billetes
Help me down below
PLEASE
Answer:
there is one more zero
Step-by-step explanation:
now it's 8 million rather than 800 thousand.
A rectangle has a length of 9 mm. A similar rectangle is drawn using a scale of 1:3. What is the length of the second rectangle?
Answer:
3mm brainliest please
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
9mm times 1:3 of the rectangle is 245
Please help quadratic equation!! 20 points
Answer:
x=4,−2
Step-by-step explanation:
Because Step 1. Move all terms to one side.
{x}^{2}-2x-8=0
x
2
−2x−8=0
2 Factor {x}^{2}-2x-8x
2
−2x−8.
1 Ask: Which two numbers add up to -2−2 and multiply to -8−8?
-4−4 and 22
Step 2. Rewrite the expression using the above.
(x-4)(x+2)
(x−4)(x+2)
and going to;
(x-4)(x+2)=0
(x−4)(x+2)=0
And Step 3. Solve for xx.
1 Ask: When will (x-4)(x+2)(x−4)(x+2) equal zero?
When x-4=0x−4=0 or x+2=0x+2=0
2 Solve each of the 2 equations above.
x=4,-2
x=4,−2
x=4,-2
Our Answer is:
x=4,−2
I Hope It's Helps
Answer:
2 and -4
tso numbers when added gives -2 and 8 incase it's not clear enough.
How many possible outcomes are in spinning a spinner divided into red, yellow, orange, purple, blue, and pink?
SOMEONE ANSWER PLS
Answer:
Possible outcomes = 6
Step-by-step explanation:
Since the spinner is divided into red, yellow, orange, purple, blue and pink
Total of 6 colors.
Find the area of the shape below. GUS PLEASE HEL
Answer:
122 squared cm
Step-by-step explanation:
[tex]6*12=72[/tex]
[tex]10*5=50[/tex]
[tex]72+50=122[/tex]
Hope this helps
Answer:
122 squared cm
Step-by-step explanation:
First we split the figure into 2
12 x 6
And,
10 x 5
12 x 6 = 72
and
10 x 5 = 50
Now we add 72 + 50 = 122
Which of the quotients are equivalent to -(48/17)
Answer:
oiie4546
Step-by-step explanation:
work out 2/7 divided 7/8
Answer:
16/49
Step-by-step explanation:
2/ 7÷ 7/8
Copy dot flip
2/7 * 8/7
Multiply the numerators
2*8 =16
Multiply the denominators
7*7 = 49
numerator over denominator
16/49
Answer:
[tex]\frac{16}{49}[/tex]
Step-by-step explanation:
a right triangle has legs of lengths 7 and 2, what is the length of the hypotenuse to the nearest tenth
Answer:
hypotenuse = 7.3
Step-by-step explanation:
here 7 and 2 are the legs og the right triangle .we should find hypotenuse.
let the legs of the right triangle be a nd b respectively . And c be hypotenuse
using pythagoras theorem to find hypotenuse
a^2 + b^2 = c^2
7^2 + 2^2 = c^2
49 + 4 = c^2
53 = c^2
[tex]\sqrt{53}[/tex] = c
7.28 = c
7.3 =c
Answer:
7.3
Step-by-step explanation:
[tex]7^{2} + 2^{2} = x^{2} \\ 53 = x^{2}\\\sqrt{53} = \sqrt{x^{2}} \\x = 7.3[/tex]
A school survey asked students which candidate they supported for class president. the survey data are shown in the relative frequency table.
Answer:
C. 24%
Step-by-step explanation:
hope it works
Answer:
39%
Step-by-step explanation:
Find the product of √6*√12. A.36√2. B.6√2. C.5√6. D.4√18.
answer is
B. 6√2
hope this helps!
Solve 2x + 6 > 20. OLA X> 18 B. X>7 O c. x
someone help por favor
Answer:
2x+6>20
2x>20-6
2x/2>14/2
x>7
So your answer would be B
6x-27=-3x
solve for x:D
Answer:
6×-27=-3×
+3×
9/9×=27/9
×=3
Simplify each of the following by rationalizing the denominator.
please do answer my doubt
Answer:
(47+21√5)/2
Step-by-step explanation:
Given the expression
7+3√5/7-3√5
= 7+3√5/7-3√5 * (7+3√5)/(7+3√5)
= 49+21√5+21√5+9(5)/[7(7)-9(5)]
= 49+42√5+45/49-45
= 94+42√5/4
= 2(47+21√5)/4
=(47+21√5)/2
Hence the required expression is (47+21√5)/2
