Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Since it is tangent to the center, the perpendicular line passes through the center, (2,-3). We find the slope of the perpendicular line to be -1/2 (perpendicular to a slope of 2). We can use point slope form to find the line from the tangent line to the center:
y+3=-1/2(x-2)
We can simplify this to
y= -1/2x-2
We can then check the point of intersection:
-1/2x-2=2x+3
-5=2.5x
x=-2
we can plug this in to the first equation to get y=2(-2)+3=-1
So the point of intersection of the circle and the tangent line is (-2,-1)
Then we find the distance of this point to (2,-3) and we can use pythagorean theorem.
[tex]\sqrt{(-2-2)^{2}+(-1-(-3))^{2} } =\sqrt{(-4)^{2}+2^{2} } =\sqrt{20} =2\sqrt{5}[/tex]
The radius of the circle is [tex]2\sqrt{5}[/tex]
For Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The line y=2x+3 is tangent to the circle with center (2,-3)
The distance from the center of the circle to the line is equal to the radius of the circle.
The distance from a point (x₁, y₁) to a line Ax + By + C = 0 is given by the formula:
d = |Ax₁+ By₁ + C| /√A² + B²
The equation of the line is y = 2x + 3, which can be written in the form Ax + By + C = 0 as (-2)x + y - 3 = 0.
d = |-2(2) + (-3) - 3| / √(-2)² + 1²
d=10/√5
The radius of the circle is equal to the distance from the center to the tangent line, which is:
radius = 10/√5
Hence, for Line y=2x+3 is tangent to a circle with center (2,-3) then the length of the radius of the circle is 10/√5
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can someone help pls
Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Since 1pt = 2qt, 2.75pt = 5.5qt
Can you guys please help!!!!! I need to know what 13x4=nx26 means???!!!!????
Answer:
n = 34/13
Step-by-step explanation:
13 x 4 = n x 26
=> 68 = 26n
=> n = 68/26
=> n = 34/13
Therefore, n = 34/13
Hoped this helped.
[tex]GeniusUser[/tex]
The mother is really tall (T) and the allele for this particular trait is dominant to the short (t) gene. The fathers phenotype is short (t). What will the genotype and phenotype percentages be for the the F1 generation? (hint: there may be more than one possible answer).
If tall is completely dominant over short, then the mother's genotype is either TT or Tt. The father is short so his genotype is tt.
Crossing TT with tt produces only heterzygous offspring with genotype Tt. Then the genotypic and phenotypic ratios are 0 TT : 1 Tt : 0 tt and 1 tall : 0 short, respectively. As percentages, these would
• geno: 0% TT : 100% Tt : 0% tt
• pheno: 100% tall : 0% short
Crossing Tt with tt on the other hand produces offspring with genotype either Tt or tt with equal probability, so that the geno and pheno ratios are 0 TT : 1 Tt : 1 tt and 1 tall : 1 short. As percentages,
• geno: 0% TT : 50% Tt : 50% tt
• pheno: 50% tall : 50% short
HELLP ME PLS QUICK
Oscar and Kim have $22.00 each to spend at a book fair, where all students receive a 30% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Oscar takes 30% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Kim takes 70% of the normal purchase price and then computes 110% of the reduced price. Is Oscar correct? Is Kim correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.
HELLLP ME PLS QUICK
Answer:
Both Oscar and Kim will have enough to purchase the book.
Step-by-step explanation:
Oscar takes 30% of the normal price and subtracts it from the normal price. Out of 100% price he takes 30% so the result is: 100-30%= 70% of the normal price. Oscar's first step has the same result as Kim.
Oscar takes 10% of the discounted price (70%) and adds it back. The price will become 70% + 10%*70%= 77% of original price. Kim multiplies the discounted price with 110%, so the price will be: 70% * 110%= 77%. Both also give the same result.
The final price is 77% of the original, it will be: $28.50* 77%= $21.945
Oscar :
28.50 - 0.30(28.50) = 28.50 - 8.55 = 19.95
0.10(19.95) + 19.95 = 2 + 19.95 = 21.95
Kim :
0.7(28.50) = 19.95
1.10(19.95) = 21.95
Answer:
Both Oscar and Kim got the same amount and they both had enough money to buy the book.
Given that,
Oscar and Kim have money to spend at a book fair = $22
Discount for all the students = 30% = 0.30
They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax.
Book normally sells for = $ 28.50 + 10% sales tax
According to the question,
Oscar takes 30% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount.
28.50 - 0.30(28.50) = 28.50 - 8.55 = 19.95
0.10(19.95) + 19.95 = 2 + 19.95 = $21.95
Kim takes 70% = 0.7 of the normal purchase price and then computes 110% = 1.10 of the reduced price.
0.7(28.50) = 19.95
1.10(19.95) = $21.95
Hence, Both Oscar and Kim got the same amount and they both had enough money to buy the book.
Step-by-step explanation:
Find the area and the circumference of a circle with radius 4 yd
First, let's find the area! The formula to find the area of a circle is πr²
πr²
3.14 · 4²
50.24 yds²
Now let's find the circumference. The formula for this is 2πr
2πr
2 · 3.14 · 4
25.12 yds
Hope this helps!
hello need help question below
Helpppppppppp plsssssss
Answer: You didnt give the 2 equations.
Step-by-step explanation:
Directions: Given the point and slope, write the equation of the line. 3. (1,-7); slope = -1
Answer:
y=-1x-6
Step-by-step explanation:
Using the previous problem, what is the rate at which
the shadow changes when the person is 10 ft from the wall,
if the person is walking away from the wall at a rate of 2 ft/
sec
Answer:
It grows at a rate
4/9 ft/second
Step-by-step explanation:
YOU’RE GETTING A BRAINLIST IF YOU ANSWER THESE:
If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answer:
Step-by-step explanation:
Question 1
Answer: (1, -0.5)----------------------
Explanation:
The x coordinates of the points for the restrooms and fountain are -2 and 4 in that order. Add up those values and divide by 2
(-2+4)/2 = 2/2 = 1
The midpoint of -2 and 4 on the number line is the value 1. So if the restrooms and fountain were on the x axis and at -2 and 4 respectively, then the midway point is 1 on that same number line. Note: The value 1 is exactly 3 units away from -2 and 4.
We'll use this idea for the y coordinates as well. Add them up, then divide by 2.
Add: 4+(-5) = -1
Divide by two: -1/2 = -0.5
The y coordinate of the midpoint is -0.5
Overall, the midpoint between the restrooms and fountain is the point (1, -0.5)
For more info, check out the midpoint formula.
====================================================
Question 2
Answer: (0, 0.5)----------------------
Explanation:
We'll use the same idea as before. This time we focus on the locations of the swings and ball field only.
Add the x coordinates for each point: -5+5 = 0
Divide in half: 0/2 = 0
The x coordinate of the midpoint is 0
Repeat for the y coordinates.
Add: 5+(-4) = 1
Cut in half: 1/2 = 0.5
The y coordinate of the midpoint is 0.5
We get the midpoint (0, 0.5) which is where the two pets meet.
====================================================
Question 3
Answer: Approximately 1 yard----------------------
Explanation:
Apply the distance formula for the results of the previous two questions.
So we'll apply the midpoint formula for the points (1, -0.5) and (0, 0.5)
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(1-0)^2+(-0.5-0.5)^2}\\\\d = \sqrt{(1)^2+(-1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\d \approx 1.414\\\\d \approx 1\\\\[/tex]
Temperature differences are caused by the differences in air warming from the?
1. Solar Radiation
2. Earth Convection
3. Solar Conduction
Answer:
1 solar radiationnnnnmnnmnnnnn
being timed so help me please!
derivative for the function of t3+k/t=
Answer:
Step-by-step explanation:
I will ASSUME you want the derivative with respect to "t" of the equation
f(t) = t³ + kt⁻¹
f'(t) = 3t² - kt⁻² which can also be 3t² - k/t²
It takes 82 pounds of seed to completely plant 11 acre field. How many ponds of seed are needed per acre?
Answer:
7.5lbs
Step-by-step explanation:
82/11 = 7.45454545lbs
Rounded to 7.4lbs
Hope that helps
Answer:
7 5/11
Step-by-step explanation:
you divide 82 and 11 and you get 7.45454545
please help ill mark brainliestl
Answer:
A) Yes...ABC and GFC are similar using AA.
Step-by-step explanation:
Which expression shows the result of applying the distributive property to 3 (1/5x - 1/7)
A. -3/5x + 3/7
B. 3/5x - 3/7
C. -3/5x - 3/7
D. 3/5x + 3/7
Hi,
3(1/5x - 1/7)
= 3/5x - 3/7
B
✅(◠‿◕)
Find radiuses of circles, if OO1=20cm and 3AK=2BK
Answer:
radius of smaller circle on the left = 8 centimetersradius of larger circle on the right = 12 centimeters=============================================================
Explanation:
The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.
Based on that, we can say that PQ = 20 cm.
Let x = length of PK
PK + KQ = PQ
KQ = PQ - PK
KQ = 20 - x
We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.
------------------------
We're given this equation
3AK=2BK
Let's get the numbers to one side and the letters to the other side like so:
3AK=2BK
3AK/BK = 2
AK/BK = 2/3
We'll use this later as well. I'll refer to this as "Fact 2" when it does come up later.
------------------------
Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.
The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.
The angles AKP and QKB are vertical angles, so they are congruent.
The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).
------------------------
Now that we know the triangles are similar, we can use a proportion to solve for x.
PK/KQ = AK/KB
PK/KQ = 2/3 .... use fact 2
x/(20-x) = 2/3 .... use fact 1
3x = 2(20-x) .... cross multiply
3x = 40 - 2x
3x+2x = 40
5x = 40
x = 40/5
x = 8
So,
PK = x = 8KQ = 20-x = 20-8 = 12The radius of the smaller circle on the left is 8 cm.
The radius of the larger circle on the right is 12 cm.
8 to the 2 power-28/4+2?
Answer:
59
Step-by-step explanation:
hope it helps brainliest pls
I need help bad. It's about finding angles and I can't really figure it out.
=========================================================
Explanation:
Angle BFE is 117 degrees. The adjacent angle to this (angle BFA) is 180-117 = 63 degrees since the two angles form a straight line, and must add to 180.
Now because BD is parallel to AE, we know that the alternate interior angles BFA and FBD are the same measure. This makes angle FBD to be 63 degrees.
We're told that segment BF bisects angle ABD. That indicates the two smaller pieces (angles ABF and FBD) are the same measure. Both are 63 degrees in this case.
Let x be the measure of angle DBC. This angle will add to angles ABF and FBD to form a 180 degree straight angle
(angleABF) + (angleFBD) + (angleDBC) = 180
(63) + (63) + (x) = 180
x+126 = 180
x = 180-126
x = 54
Angle DBC is 54 degrees.
-----------------------
The last set of steps has us focus on triangle BCD. The three angles of any triangle always add to 180.
B+C+D = 180
54 + 85 + D = 180
139 + D = 180
D = 180-139
D = 41
Angle CDB is 41 degrees, and so is angle CEA as they are corresponding angles. Corresponding angles are congruent when we have parallel lines like this.
Therefore, angle E is 41 degrees.
The diagram is below showing all of the angles we found.
What is 18x77 with algorithm
Answer:
1386
Step-by-step explanation:
First multiply 8 and 77 to get 616
Then multiply 10 and 77 to get 770
Finally, add them all together to get 1386
Answer:
the answer is 1,386. ......There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. How many cookies did Julio's mother bake.
Answer:
His mother baked 7 more cookies
what is the answer of solve the following equations and verify your answer
Answer:
Solution !![tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]
By cross multiplication :
[tex] \implies{\sf{ {3(p + 7)} = 1{(p - 6)} }}[/tex]
[tex]\implies{\sf{3p + 27 = p - 6 }}[/tex]
[tex]\implies{\sf{3p - p = - 6 - 21}}[/tex]
[tex]\implies{\sf{2p = - 27}}[/tex]
[tex]\implies{\sf{\underline{\underline{\red{p = \dfrac{ - 27}{2}}}}}}[/tex]
Hence, the value of p is -27/2
[tex]\begin{gathered}\end{gathered}[/tex]
Verification !![tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]
Substituting the value of (p = -27/2)
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27}{2} + 7}{ \dfrac{ - 27}{2} - 6} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27 + 14}{2}}{ \dfrac{ - 27 - 12}{2} } = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 13}{2}}{ \dfrac{ - 39}{2} } = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{2} \times \dfrac{2}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{\cancel{2}} \times \dfrac{\cancel{2}}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \cancel{\dfrac{ - 13}{ - 39}} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{1}{3} = \dfrac{1}{3}}}[/tex]
[tex]\implies{\sf{\underline{\underline{\red{LHS = RHS}}}}}[/tex]
Hence Verified!
[tex]\underline{\rule{220pt}{3pt}}[/tex]
suppose we want to choose 2 colors, without replacement from 3 colors red,bule and green
Which of the following is NOT an equivalent expression for the confidence interval given by 161.7
Choose the correct answer below.
O A. 161.7 +27.8
B. 175.6 -13.9
O C. 175.6 + 13.9
OD. (161.7.189.5)
According to the confidence interval given, the non-equivalent expression is:
A. [tex]161.7 \pm 13.9[/tex]
The interval given is:
[tex]161.7 \leq \mu \leq 189.5[/tex]
Which can also be written as: (161.7.189.5)
The point estimate is the halfway point of the interval, hence:
[tex]\overline{x} = \frac{161.7 + 189.5}{2} = 175.6[/tex]
The margin of error is half the difference of the bounds, hence:
[tex]M = \frac{189.5 - 161.7}{2} = 13.9[/tex]
According to the point estimate and to the margin of error, the interval can also be written as:
[tex]175.6 - 13.9 \leq \mu \leq 175.6 + 13.9[/tex]
[tex]175.6 \pm 13.9[/tex]
Hence, the only expression which is non-equivalent is:
A. [tex]161.7 \pm 13.9[/tex]
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Put these fractions in order from least to greatest:
Answer:
1/4, 3/8, 2/3
Step-by-step explanation:
3/8 is more than 25% (1/4) but is less than 66% (2/3) making the order 1/4 3/8 2/3.
Answer:
The answer is the 3rd option. (1/4, 3/8, 2/3)
Step-by-step explanation:
All u have to do is find a common denominator for all 3 fractions.
The common denominator in this problem would be 24
So lets convert all the fractions with a denominator of 24.
1/4 = 6/24
3/8 = 9/24
2/3 = 16/24
Since we now converted the fractions with a common denominator, we can deduce the order from least to greatest.
6/24, 9/24, then 16/24
In other words, the answer is the 3rd option. (1/4, 2/8, and 2/4)
Hope this helps! :0
૮ ・ﻌ・ა
3/4, 4/5, 7/8, 9/11, 5/6
can they be simplified? give your reasons below.
Answer:
No, none of these can be simplified
Step-by-step explanation:
Each one of these factions have a prime number in it, so therefore, you cannot simplify any of them. Prime numbers are numbers that only have 2 factors, one and itself. So, you can't simplify any of them.
Here's why:
If you take 3/4, you can't simplify because 3 is prime. 4 is NOT prime, but to reduce, you have to be able to find a GCF, or a greatest common factor.
Find the percent increase. Round to the nearest percent. From 95 books to 153 books
Answer:
62%
Step-by-step explanation:
(The part/ the whole)× 100
(95/153) = 0.62
0.62×100 = 62%
If x = (1/2)(16 - 8y), then x =
Answer:
x = 8 - 4y
Step-by-step explanation:
16/2 = 8
8y/2 = 4y
The value of x of the expression is x = 8 - 4y.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
x = (1/2)(16 - 8y)
Removing the parenthesis.
x = 16/2 - 8y/2
x = 8 - 4y
Thus,
The value of x is 8 - 4y.
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10. Saul works two part-time jobs. Last week, he worked 14 hours at a shoe store, and 19
hours as a telemarketer. His total pay was $240.30. The week before, he made
$300.00 for 19 hours at the shoe store and 22 hours telemarketing. Find his hourly
wage for each job
Answer:
shoe store $7.80/hour
telemarketer: $6.90/hour
Step-by-step explanation:
Let s = hourly salary at the shoe store.
Let t = hourly salary as a telemarketer.
14s + 19t = 240.3
19s + 22t = 300
Multiply both sides of the first equation by 19. Multiply both sides of the second equation by -14. Then add them.
266s + 361t = 4565.7
(+) -266s - 308t = -4200
----------------------------------------
53t = 365.7
t = 6.9
Substitute 6.9 for t in the first equation and solve for s.
14s + 19(6.9) = 240.3
14s + 131.1 = 240.3
14s = 109.2
s = 7.8
Answer:
shoe store $7.80/hour
telemarketer: $6.90/hour
What percent of 80 is 60
Answer:
80% of 75 is 60
Step-by-step explanation:
0.80x=60
x=60/0.80
x=75
