Answer:
[tex]\large\boxed{(x-5)^2+(y-3)^2=5^2\to(x-5)^2+(y-3)^2=25}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the end points of a diameter (8, 6) and (2, 0). The midpoint of a diameter is a center of a circle. Half of a length of diameter is a length of a radius.
The formula of a midpoint of a segment:
[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
Substitute:
[tex]x=\dfrac{8+2}{2}=\dfrac{10}{2}=5\\\\y=\dfrac{6+0}{2}=\dfrac{6}{2}=3[/tex]
The center of a circle is (5, 3).
The formula of a length of a segment:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]d=\sqrt{(2-8)^2+(0-6)^2}=\sqrt{(-8)^2-(-6)^2}=\sqrt{64+36}=\sqrt{100}=10[/tex]
The length of a diameter is 10 units. The length of a radius r = 10 : 2 = 5 units.
Finally we have the equation of a circle:
[tex](x-5)^2+(y-3)^2=5^2[/tex]
Tito went to a concert given by a jazz band. The band had 5 saxophone players and 4 trumpet players. What was the ratio of trumpet players to saxophone players in the band?
Your ratio is 5:4.
We have 5 saxophone players & 4 trumpet players.
So if we have 4 trumpet players we have our first number in our ratio which would be: [tex]4:?[/tex]
Our second number is 5, that 5 represents the saxophone players.
That brings that to our equation 5:4.
Have an amazing day.
The ratio of trumpet players to saxophone players in the band is 4:5. This means there are 4 trumpet players for every 5 saxophone players.
To find the ratio of trumpet players to saxophone players in the band, we need to compare the numbers of each type of player.
The number of trumpet players is 4.The number of saxophone players is 5.We express the ratio of trumpet players to saxophone players as 4 to 5, which is written as 4:5.So, the ratio of trumpet players to saxophone players in the band is 4:5.
This means that for every 4 trumpet players, there are 5 saxophone players.
Plz help !!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
Using the rule of exponents
• [tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex], hence
[tex]16^{\frac{1}{2} }[/tex] = [tex]\sqrt[2]{16^{1} }[/tex] = 4
Answer: 4
Step-by-step explanation:
[tex]16^{\frac{1}{2}}=\sqrt{16}=\sqrt{4\cdot 4}=\boxed{4}[/tex]
Write and solve an equation that represents the
following:
Ten less than a number is equal to nine.
Let n represent the unknown number
n-10=9
+10 +10
—————
n=19
Brainliest??
Show me a graph that best represents the solution set to the system of a linear inequalities; y-x>0. y-1>0
The graph is shown in the attached image
Expand the logarithm. Log5 5x^-5
A. Log5 1/125x
B. -5 log5 5x
C. Log5 5+ -5 log5 x
D. -5 log5 5+ -5 log5 x
Answer:
[tex]\large\boxed{C.\ \log_55+-5\log_5x}[/tex]
Step-by-step explanation:
[tex]\log_ab^c=c\log_ab\\\\\log_a(bc)=\log_ab+\log_ac\\=====================\\\\\log_55x^{-5}=\log_55+\log_5x^{-5}=\log_55+-5\log_5x[/tex]
The value of logarithm log5 [tex]5x^{-5[/tex] is [tex]-5 (log_5 (5) + log_5 (x) )[/tex].
Thus, option (c) is correct.
To expand the logarithm log5 [tex]5x^{-5[/tex], use the logarithmic property.
According to power rule,
logarithm of a number raised to a power can be expressed as the product of the exponent and the logarithm of the number.
Using the power rule, we can rewrite the expression as:
[tex]{\text} log_5 5x^{-5} =[/tex][tex]\;{\text} -5 log_5 (5x)[/tex]
and, [tex]log _c (ab) = log_c (a) + log_c(b)[/tex]
So, [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex]
Thus, the simplified value is [tex]\;{\text} -5 log_5 (5x)[/tex] = [tex]-5 (log_5 (5) + log_5 (x) )[/tex].
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What is the area of a circle whose radius is 6 ft?
6 x 6 = 36 x 3.14 = 113.04
Area = 113.04
5x-12=13 what is x.
Answer:
x=5
Step-by-step explanation:
5x-12=13
Add 12 to each side
5x-12+12 =13+12
5x = 25
Divide by 5
5x/5 = 25/5
x = 5
8*10^4 is how many times as big as 4*10^-5
Answer:
80000/0.0004 = 2'000'000'000 or 2 x 10^-9
8*10^4 = 80'000
4*10^-5 = 0.00004
Step-by-step explanation:
Answer:
0,2
Step-by-step explanation:
[8*10^4] / [4*10^5]
2*[10000/100000]
0,2
Best regards
If f(x)=3x^2 and g(x)=√2, what is the value of (f×g)(8)
Number one is correct, here is how:
[tex]fgx 8 \\Simplify \\ the \\ brackets\\8\sqrt{6}[/tex]
Have a great day!
use substitution to solve the system equation.
n=3m-11
2m+3n=0
Answer:
m = 3, n = -2.
Step-by-step explanation:
Substitute n = 3m - 11 in the second equation:
2m + 3(3m - 11) = 0
2m + 9m - 33 = 0
11m = 33
m = 3.
Substitute for m in n = 3m-11:
n = 3(3) - 11
n = -2.
What is the reciprocal of 1/11
The reciprocal of the fraction 1/11 is equal to 11/1.
To answer this question you need to know what the reciprocal of a number is.
The reciprocal of a number is the number that will multiply that number and give a product of 1.
To find the reciprocal of a fraction, simply invert it such that the denominator becomes the numerator and the numerator becomes the denominator.
In this scenario therefore, the reciprocal of 1/11 is:
= 11/1
In conclusion, the reciprocal of 1/11 is 11/1.
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3. Mrs. LeBlanc is making a Pokémon box. The length of the box is 12 inches greater than its width, and its height is 5 inches less than its width. Find the dimensions of the Pokémon box formed, given that its volume is 9600 cubic inches. (Show all work including setting up the equation, simplifying the equation, listing the possible rational roots, testing the possible rational roots using synthetic division, and then identifying all of the dimensions.
Answer:
The width is 20 inches, the length is 32 inches and the height is 15 inches.
Step-by-step explanation:
Let x inches be the width of the box. If the length of the box is 12 inches greater than its width, then the length of the box is x+12 inches. If the height of the box is 5 inches less than its width, then the height of the box is x-5 inches.
The volume of box is
[tex]V=\text{length}\cdot \text{width}\cdot \text{height}\ in^3.[/tex]
Therefore,
[tex]9600=x\cdot (x+12)\cdot (x-5).[/tex]
Solve this equation:
[tex]x(x^2+12x-5x-60)=9600,\\ \\x^3+7x^2-60x-9600=0.[/tex]
The integer solutions of this equation can be among the divisors of -9600. The divisors of 9600 are:
[tex]\pm1, \pm2, \pm3, \pm4,\pm5,\pm6,\pm8,\pm10,\pm12,\pm15,\pm16,\pm20,\pm24,\pm25,\pm30,\pm32,....[/tex]
We can check all these divisors and see that x=20 is a solution, then using synthetic division
[tex]x^3+7x^2-60x-9600=(x-20)(x^2+27x+480).[/tex]
Since the quadratic factor has discriminant [tex]D=27^2-4\cdot 480=-1191<0,[/tex] we can state that the only solution is x=20 inches. The width is 20 inches, the length is 32 inches and the height is 15 inches.
NEED HELP ASAP WILL MARK BRAINLIEST
the angle of elevation from mindy to a cell phone tower is 75. if mindy is standing 28 feet from the base of the tower, find the height of the tower
A) 104.5 ft
B) 105.8 ft
C) 106.1 ft
D) 107.4 ft
E) 108.9 ft
Final answer:
To find the height of the tower given the angle of elevation and distance from the observer to the tower's base, the tangent function is used. The height is calculated as 28 feet multiplied by tan(75 degrees), resulting in approximately 105.8 feet.
Explanation:
The student is asking for help with a trigonometry problem involving the angle of elevation to calculate the height of a tower. In this case, we are given the angle of elevation as 75 degrees and the distance from Mindy to the base of the tower as 28 feet. To find the height of the tower, we use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.
So, we have:
tan(75 degrees) = opposite/adjacent
tan(75 degrees) = height of tower/28 ft
Therefore, to find the height of the tower, we can write this equation as:
height of tower = 28 ft × tan(75 degrees)
By calculating this using a calculator, we find the height of the tower to be approximately 105.8 feet, which corresponds to option B.
Justin is training for a hamburger eating competition. He is eventually able to eat 15 hamburgers in 10 minutes. What is justin’s eating rate
Answer:
1.5 hamburgers per minute
Step-by-step explanation:
In 10 minutes, Justin can eat 15 burgers.
In 1 minute, Justin can eat 15/10 burgers.
15/10 = 1.5
Answer:
1.5 hamburgers per minute
Step-by-step explanation:
15/10 = 1.5
Find the equation of the line.
Use exact numbers.
Y=___x+ ___
Please help
I just taught you how to do this, it’s really simple, try it yourself! I’ll give instructions again.
Use the equation Y=mx+b where m represents the slope and b is the y-axis point.
Finding b is easiest, so we’ll do that first. Again, b is the y axis point. So where does the line cross the y axis? That is the vertical line on the graph. The line crosses at point (0,5) so 5 is your b value.
Next find your m value, or slope. The slope is simply rise/run. Which means start at the y axis value, and count how many places you need to go down to find a perfect triangle shape. You simple go down two points, and then over one point to reach a perfect triangle. Therefore since you go down 2, your rise is -2 and since you go over 1, your run is 1. Rise/run=-2/1, this simplified is just -2. So that is your m value.
Finally, plug these into y=mx+b and get your answer of
Y=-2x+5
Best,
jrodt
Plz help me i need it
Answer: 4
Step-by-step explanation:
f(x) = 4x³ - x² + 1 g(x) = x - 1
g(2) = (2) - 1
= 1
f(1) = 4(1)³ - (1)² + 1
= 4 - 1 + 1
= 417.60 for a pack of 4. Find the unit price
Answer:
4.40 is that an option i did 17.60 divided by 4 it may be wrong
Step-by-step explanation:
This means it costs $17.60 for 4 pairs. Divide 17.60 by 4 to find the price per 1 unit. 17.60 / 4 = $4.40 per unit
Hope this helps!
X intercept for 2x +5y = -6
Answer:
(-3, 0)
Step-by-step explanation:
The x-intercept is the value of x when y = 0.
2x + 5y = -6
Set y = 0 2x + 5(0) = -6
2x = -6
Divide each side by 2 x = -3
The x-intercept is at (-3, 0).
What is the area of this figure? do not round any side lengths. Please help me.
Answer:
hmmmm lemme think
Step-by-step explanation:
Round your answers to one decimal place, if necessary. Find the mean and median of these data: 2, 5, 9, 11, 19, 21.
Answer:
mean is 11.167 the median is 10
Step-by-step explanation:
Hope this helps
The digits are 2,5,9,11,19,21
Mean is finding average by adding all value and then dividing by how many numbers
Mean=2,5,9,11,19,21 is 67 and than divide by 6 which would be 11.16 (11.2)
Median is arranging all numbers in chronological order and finding middle value
2,5,9,11,19,21
9+11 is 20 and than divide by 2 which makes it 10
Summary
Mean is 11.2
Median is 10
In ΔVWX, the measure of ∠X=90°, XV = 27 feet, and WX = 57 feet. Find the measure of ∠V to the nearest degree.
Answer:
[tex]<V=65\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle VWX
[tex]tan(V)=\frac{WX}{XV}[/tex] -----> opposite side angle V divided by the adjacent side angle V
substitute the values
[tex]tan(V)=\frac{57}{27}[/tex]
[tex]<V=arctan(\frac{57}{27})=65\°[/tex]
Final answer:
To find the measure of ∠V, we take the ratio of XV to WX (opposite to adjacent side) and use the tangent function. By calculating tan(∠V) = 27/57 and taking the inverse tangent, we get ∠V ≈ 25° to the nearest degree.
Explanation:
To find the measure of ∠V in ∆VWX, where ∠X=90°, XV = 27 feet, and WX = 57 feet, we use the trigonometric ratios, specifically the tangent function, since we are dealing with a right-angled triangle and we have the lengths of the opposite side (XV) and the adjacent side (WX) to ∠V.
Step by Step Solution:
Use the definition of the tangent function: tan(∠V) = opposite/adjacent.
Substitute the known values: tan(∠V) = XV/WX = 27/57.
Calculate tan(∠V) = 0.4737.
Find the angle whose tangent is 0.4737 using an inverse tangent function on a calculator: ∠V ≈ 25° (to the nearest degree).
Therefore, the measure of ∠V is approximately 25°.
I really need help!!
What’s 2 divided by 0.86?!?
2.32558139535 or it can just be 2.325
The answer For two divided by eighty six hundredths is forty three hundredths.
0.86/2. 0.43
Write the standard equation of a circle with center (-4,0) and radius 3.
Answer:
(x+4)^2 + y^2 = 9
Answer:
The correct answer is first option
(x + 4)² + y² = 9
Step-by-step explanation:
Formula:-
Let (x₁, y₁) and 'r' be the radius of a circle the equation of the circle is given by
(x - x₁)² + (y - y₁)² = r²
To find the equation of the circle
Here (x₁, y₁) = (-4, 0) and r = 3
we have,
(x - x₁)² + (y - y₁)² = r²
(x - -4)² + (y - 0)² = 3²
(x + 4)² + y² = 9
Therefore the equation of the given circle is (x + 4)² + y² = 9
The correct answer is first option
A line passes through the point (5,-2) and has a slope of -1/3.Which equation models the line
Answer:
[tex]y + 2= -\frac{1}{3}(x-5)[/tex]
Step-by-step explanation:
To write the equation of a line with a slope and a point, use the point slope form of the line. Substitute m = -1/3 and (5, -2).
[tex]y - y_1 = m(x-x_1)\\y --2 = -\frac{1}{3}(x - 5)\\y + 2 = -\frac{1}{3}(x-5)[/tex]
You can convert to slope intercept form.
[tex]y + 2 = -\frac{1}{3}(x-5)\\y + 2 = -\frac{1}{3}x + \frac{5}{3}\\y = -\frac{1}{3}x + \frac{5}{3} -2\\y = -\frac{1}{3}x - \frac{1}{3}[/tex]
how we make 17/24 smaller
Answer:um you simplify it
Step-by-step explanation:
To make the fraction 17/24 smaller, you can increase the denominator or decrease the numerator, but it will change the value of the fraction.
Explanation:To make the fraction 17/24 smaller, you need to increase the denominator (the bottom number) or decrease the numerator (the top number).
One simple way to do this is to add a number to 24 making it 25, 26, 27, and so forth while keeping the numerator as 17. The larger the denominator, the smaller the fraction is. Alternatively, you could decrease the numerator to 16, 15, etc, while keeping the denominator at 24. Again, the smaller the numerator, the smaller the fraction.
Also remember that the fraction must remain proper or else it will become a whole number and eventually bigger than 17/24.
Please note that these changes alter the value of the fraction, and therefore might not be accurate representations of whatever the fraction 17/24 is supposed to represent.
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Determine the intercepts of the line y+1=3(x-4)
To find the intercepts, the other number will be 0 (x-intercept: when y is 0, and vise-versa).
So:
x-intercept: 0 + 1 = 3x - 12 -> 3x = 13 -> x = 13/3, so it will be ([tex]\frac{13}{3}[/tex], 0).
y-intercept: y + 1 = 3*0 - 12 -> y = -13, so it will be (0, -13).
Answer:
x-intercept = [tex]\frac{13}{3}[/tex]
y-intercept = [tex]-13[/tex]
Step-by-step explanation:
We are given the following equation of a line and we are to find the x and y intercepts for it:
[tex] y + 1 = 3 ( x - 4 ) [/tex]
To find the x-intercept, we will put in 0 for the y to get:
[tex] 0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 } [/tex]
To find the y-intercept, we will put in 0 for the x to get:
[tex] y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13 [/tex]
So the x-intercept is [tex]\frac{13}{3}[/tex] while the y-intercept is [tex]-13[/tex].
X=10
3x+3y= 20
What is the solution (x,y) of the system
Answer:
(10, -10/3)
Step-by-step explanation:
We're told that x = 10. Substitute 10 for x in the 2nd equation:
3(10) + 3y = 20. Subtracting 30 from both sides, to isolate 3y, we get:
3y = -10
Dividing both sides by 3, we get: y = -10/3.
The desired solution is (10, -10/3).
help me please asap!!!!!!
Answer:
4a^2-19ab-5b^2
Step-by-step explanation:
What you do is the FOIL process.
F=First. The first thing that you do is times 4a and a together to get 4a^2.
O=Outer. You multiply the outer numbers 4a and -5b together to get -20ab.
I=Inner. You multiply the inner numbers b and a together to get ab.
L=Last. You multiply the last numbers b and -5b together to get -5b^2.
Put it all together to get 4a^2-19ab-5b^2 as your answer.
Determine the factors of 5x2 + 6x − 8.
Answer:
[tex]\large\boxed{5x^2+6x-8=(x+2)(5x-4)}[/tex]
Step-by-step explanation:
[tex]5x^2+6x-8\\\\=5x^2+10x-4x+8\\\\=5x(x+2)-4(x+2)\\\\=(x+2)(5x-4)[/tex]
Answer:
C
Step-by-step explanation:
use ac method
for ax^2+bx+c
multiply a and c
find what 2 numbers multiply to get ac and add to get b
split b into those 2 numbers
group
factor
factor
5x^2+6x-8
ac=5 times -8=-40
what 2 numbers multiply to get -40 and add to get 6?
-4 and 10
5x^2+10x-4x-8
group
(5x^2+10x)+(-4x-8)
factor
5x(x+2)-4(x+2)
factor
(5x-4)(x+2)
C is the answer
The results of a recent science experiment are found to have a binomial distribution the experiment consisted of 185 trials in the probability of success and age trial was .712 find the mean .
a. 6.2
b 259.8
c 131.7
d. 37.9
➷ mean = n x p
mean = 185 x 0.712
mean = 131.72
Answer is option C
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
The mean of age is 131.72. Therefore, option C is the correct answer.
Given that, a binomial distribution the experiment consisted of 185 trials in the probability of success and age trial was 0.712.
What is a binomial distribution?The binomial distribution is a commonly used discrete distribution in statistics. The normal distribution as opposed to a binomial distribution is a continuous distribution. The binomial distribution represents the probability for 'x' successes of an experiment in 'n' trials, given a success probability 'p' for each trial at the experiment.
Here, mean= 185×0.712
= 131.72
The mean of age is 131.72. Therefore, option C is the correct answer.
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