Answers
Use Pythagorean theorem:
[tex]x^2=3.6^2+5.5^2\\\\x^2=12.96+30.25\\\\x^2=43.21\to x=\sqrt{43.21}\\\\\boxed{x\approx6.6}[/tex]
4.
Use Pythagorean theorem:
[tex]3^2+\left(\dfrac{x}{2}\right)^2=6.5^2\\\\9+\dfrac{x^2}{4}=42.25\ \ \ |-9\\\\\dfrac{x^2}{4}=33.25\ \ \ \ |\cdot4\\\\x^2=133\to x=\sqrt{133}\\\\\boxed{x\approx11.5}[/tex]
5.
[tex]\widehat{AB}\ \cong\ \widehat{DE}[/tex]
Related Questions
Look at the table. Make a conjecture about the sum of the first 15 positive even numbers.
Answers
The conjecture about the sum of the first 15 positive even numbers is 15 * 16
Making a conjecture about the sum of the first 15 positive even numbers.
From the question, we have the following parameters that can be used in our computation:
The table of values
Where, we have
2 = 1 * 2
2 + 4 = 2 * 3
2 + 4 + 6 = 3 * 4
And so on
This means that
Sum of first n positive even numbers = n * (n + 1)
So, for the first positive even numbers, we have
n = 15
This gives
Sum of first 15 positive even numbers = 15 * (15 + 1)
Evaluate
Sum = 15 * 16
Sum = 240
Hence, the sum is 15 * 16
Write the standard form of the equation of the circle with the given center and radius.
(-3, 6); 10
Answers
Here we have (x+3)^2 + (y-6)^2 = 10^2 (answer)
Answer:
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
[tex](x+3)^2+(y-6)^2=100[/tex]
Step-by-step explanation:
This is the general standard equation for the circle centered at (h, k) with radius r
[tex](x-h)^2+(y-k)^2=r^2[/tex]
It shows all the important information at a glance: the center (h, k) and the radius r.
A circle with center at (-3, 6) and a radius of 10 has the following standard form equation
Start with:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put in (h, k) and r
[tex](x-(-3))^2+(y-6)^2=10^2\\(x+3)^2+(y-6)^2=100[/tex]
John plays a game in which he throws a baseball java questions
Answers
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 3 miles west and 4 miles south of the City Center. The park is 3 miles east and 5 miles north of the Center. How far is it from the mall to the park to the nearest tenth of a mile/12482564/8273204d?utm_source=registration
Answers
√(6² +9²) = √117 ≈ 10.8
Estimate the probability that if the company books 225 persons. not enough seats will be available. 1-.81^225
Answers
1-.81^225 = 1
What is the explicit formula for the sequence? 6, 5, 4, 3, 2, . .
Answers
an = a1 +(n-1)d
For your sequence, this is
an = 6 +(n-1)*(-1)
an = 7 - n
Answer: [tex]a_n=5+n[/tex]
Step-by-step explanation:
The explicit formula for an arithmetic sequence is given by:-
[tex]a_n=a+d(n-1)[/tex], where a is the first term , di sthe common difference and n is the number of terms.
The given sequence : 6, 5, 4, 3, 2, . .
Common difference d = 1
First term = 1
Now, the explicit formula for given arithmetic sequence will be:
[tex]a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n[/tex]
Hence, the explicit formula for given arithmetic sequence : [tex]a_n=5+n[/tex]
find the value of q in the following system so that the solution to the system is(4,2) 3x-2y=8
2x+3y=Q
Answers
3x-2y=8 -----> equation 1
2x+3y=Q----> equation 2
the solution is the point (4,2)
in the equation 2 substitute the value of
x=4
y=2
so
2x+3y=Q------> 2*4+3*2=Q-------> Q=8+6------> Q=14
the answer is
Q=14
The service plan for edith's cell phone charges her $29.50 a month for 300 minutes and 10¢ a minute for each additional minute over the 300 minutes. if edith uses 400 minutes this month, how much money will she have to pay?
Answers
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
x≈_____ feet
Answers
sin(65°) = (12.5 ft)/x
x = (12.5 ft)/sin(65°)
x ≈ 13.8 ft
Answer:
13.
Step-by-step explanation:
78 million in scientific notation
Answers
Answer:
[tex]78\ million=7.80\times 10^7[/tex]
Step-by-step explanation:
A number N can be written in scientific notation as :
[tex]N=p{\circ}0\times 10^q[/tex]
Where
p is the any real number
q is any integer
Here, the given number is 78 million. Firstly, we must know meaning of 1 million.
Since, [tex]1\ million=10^6[/tex]
[tex]78\ million=78.0\times 10^6[/tex]
To convert the above number in scientific notation, we can shift the decimal before 8 such that,
[tex]78\ million=7.80\times 10^7[/tex]
Hence, this is the required solution.
25 pt question amd will mark brainliest
Answers
The angles are supplementary meaning they add to 180°
a + 2a + 3 = 180
Combine like terms
3a + 3 = 180
Subtract 3 from both sides
3a = 177
Divide both sides by 3
a = 59
the answer is 59°
Hope this helps!
These angle are supplementary.
use the following equation to solve for a.
2a + 3 + a = 180
Solve for a now.
3a + 3 = 180
3a = 177
a = 59
Hope this helps :)
43 coins, no nickels, $4.51 equal amount amount of pennies and dimes, how many of each coin
Answers
Let the dimes = d
Let the pennies = p
Let the quarters = q
Equations
You cannot mean that the pennies and dimes have equal numbers. That would mean that each had 21.5 members. Now could you mean that the dime and penny amount could be the same with 43 coins that total 4.00. Four dollars means that you need 40 dimes alone. It must mean that you are including quarters.
p + d + p = 43 (1)
p = d (2)
p +10d +25q = 451 (3)
Note how this last equation = was derived. You have to multiply the dimes by 10 and he quarters by 100 and the total by 100 to get the numbers all in pennies.
Put the results of 2 into 1.
2p + q = 43 (4)
You need to modify equation 3 as well.
p + 10p + 25q = 451
11p + 25q = 451 (5)
Solve the new equations
2p + q = 43 (4)
11p + 25q = 451 (5)
Multiply 4 by 25
25(2p- + q = 43)
50p + 25q = 1075 (6) Subtract (5) from (6)
11p + 25q = 451
39p = 624 Divide by 39
p = 624 / 39
p = 16
Since the pennies and dimes are equal there are 16 dimes
p + d + q = 43
16 + 16 + q = 43
32 + q = 43
q = 11
Check
16 + 10*16 + 11*25 = ?
16 + 160 + 275 = ?
451 = ?
Nice problem. Thanks for posting.
The digits 1,2,3,4,5,6,7 and 8 are arranged randomly to form a three-digit number find the probability that the number is even and greater than 800
Answers
Let's start counting desired outcome.
Hundred position need to be at least 8. There is only one possible digits. So we will go with 8 and then there are 7 remaining digits.
One position can only be 2,4,6. because we need number to be even. So that's 3 possible digits. We will take one. 6 digits remaining.
Ten position can be anything so that would be 6 possible digits.
So the number of desired outcomes is 3·6 = 18.
Now count all outcomes.
Hundred, ten, and one position can get any digits
So that's 8·7·6 = 336
So the probability would be 18 / 336 = 3 / 56 ≈ 0.0536
Hope this helps.
[tex] |\Omega|=8\cdot7\cdot6=336\\
|A|=\underbrace{1\cdot6\cdot3}_{\text{8,any,even}}=18\\\\
P(A)=\dfrac{18}{336}=\dfrac{3}{56}=5\% [/tex]
which of the following best describes the English expression the product of two and a number minus eleven
Answers
2n -11
_____
It is somewhat ambiguous, so could also be interpreted to mean
2(n -11)
Wording could be changed to remove the ambiguity, if one were interested in doing that.
Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
2,000
1 + e3 − t
where P(t) is the total number of people infected after t hours. What does 2,000 represent in equation?
A) the rate at which the disease spreads
B) the number of the people in the school
C) the expected change in number of people infected
Eliminate
D) the total number of people infected after t hours
Answers
Which equation represents a hyperbola with a center at (0,0), a vertex at (0,60), and a focus at (0,-65)
Answers
Answer:
So for everybody in the future, a clarification is d)y^2/60^2 -x^2/25^2=1
Ans: [tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
The standard form equation of a hyperbola with the center at the origin (0,0), a vertical axis, a vertex at (0, a), and a focus at (0, c) is given by:
[tex]\[\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1\][/tex]
where [tex]\(c\)[/tex] is the distance from the center to the focus, and [tex]\(b\)[/tex] is related to [tex]\(a\) and \(c\)[/tex] by the equation [tex]\(c^2 = a^2 + b^2\)[/tex].
In your case, the center is at (0,0), the vertex is at (0,60), and the focus is at (0,-65). The distance from the center to the focus is [tex]\(c = 65\)[/tex], and the distance from the center to the vertex is [tex]\(a = 60\)[/tex]. Using the relationship [tex]\(c^2 = a^2 + b^2\)[/tex], we can find b:
[tex]\[65^2 = 60^2 + b^2\][/tex]
Solving for b:
[tex]\[4225 = 3600 + b^2\][/tex]
[tex]\[b^2 = 625\][/tex]
[tex]\[b = 25\][/tex]
Now, substitute [tex]\(a\), \(b\), and \((h, k) = (0, 0)\)[/tex] into the standard form equation:
[tex]\[\frac{y^2}{60^2} - \frac{x^2}{25^2} = 1\][/tex]
So, the equation of the hyperbola is:
[tex]\[\frac{y^2}{3600} - \frac{x^2}{625} = 1\][/tex]
[tex]\( \frac{y^2}{60^2} - \frac{x^2}{25^2} = 1 \)[/tex]
What is the LCD of the following rational expressions?
x/x+1 , 7x/x-1
please help I'm so confused!?
Answers
[tex] \dfrac{x (x -1)}{(x+1)(x -1)} \ , \ \dfrac{7x(x+1)}{(x-1)(x+ 1)} [/tex]
We know that (a + b)(a - b) = a² - b²:
[tex]\dfrac{x (x -1)}{x^2 - 1}} \ , \ \dfrac{7x(x+1)} {x^2 - 1}[/tex]
Answer: LCD = ( x + 1) (x - 1)
To find the least common denominator, multiply [tex] \frac{x}{x + 1} [/tex] by (x - 1) and multiply [tex] \frac{7x}{x - 1} [/tex] by (x + 1).
(x + 1)(x - 1) = x² - x + x - 1 ⇒ x² - 1
x² - 1 is the LCD.
Quadrilateral ABCD is an isosceles trapezoid. If AB || CD, AB = m + 6, CD = 3m + 2, BC = 3m, and AD = 7m - 16, solve for m.
A.) 2
B.) 3
C.) 4
D.) 5
Answers
Answer:
C.) 4
Step-by-step explanation:
we are given ABCD is an isosceles trapezoid
AB || CD
AB = m + 6
CD = 3m + 2
BC = 3m
AD = 7m - 16
Since, ABCD is an isosceles trapezoid
so, two sides must be equal
[tex]BC=AD[/tex]
now, we can plug values
[tex]3m=7m-16[/tex]
now, we can solve for m
[tex]3m-7m=7m-16-7m[/tex]
[tex]-4m=-16[/tex]
Divide both sides by -4
and we get
[tex]m=4[/tex]
Answer:
M= 4
Step-by-step explanation:
If Henry's home has a market value of $145000 and the assessment rate is 35% what is its assessed valuation
Answers
Answer:
Assessment value of Henry's home is $50750
Step-by-step explanation:
Henry's home has a market value of $145000 and the assessment rate is 35%.
This means value of home is 35% of the total cost $145000
Now we will solve it by calculating percentage
Assessment = 35% of 145000 = [tex](145000)(\frac{35}{100})=(1450).(35)=50750[/tex]
So the answer is assessment of Henry's home = $50750.
1. demand for product
2. example of fixed cost buyer's
3. sales receipts
4. credit discount
5. example of variable cost
6. moves slow-moving goods
7. business upturn
8. used for business expansion
9. depends on prime rate
10. assures profit on item sold
2/10, net 30
credit
interest rate
workers' wages
revenue
recovery
rent
markdown
markup
buyer's willingness to pay
Answers
2. example of fixed cost buyer's ----rent
3. sales receipts
4. credit discount
5. example of variable cost
6. moves slow-moving goods ---markdown
7. business upturn
8. used for business expansion
9. depends on prime rate
10. assures profit on item sold markup
2/10, net 30
credit
interest rate
workers' wages
revenue
recovery
Answer:
Interest rate - 9
Revenue - 3
Recovery - 7
Markdown - 6
Buyer's willingness to pay - 1
Markup - 10
Worker's wages - 5
2/10 net 30 - 4
Credit - 8
Rent - 2
Step-by-step explanation:
Just did this on odyssey
In Ms. Dole's class, students received grades of 87, 72, 99, 93, and 84 on yesterday's quiz. What was the mean of the quiz grades?
Answers
The mean is the average of the numbers
To find the average you add them all up and divide the sum by the amount of numbers added
87 + 72 + 99 + 93 + 84 = 435
Divide the sum by the amount of numbers added
435 / 5 = 87
The answer is 87
Hope this helps!
To find the average, or the mean, the numbers must be added together and then the sum is divided by the total amount of numbers in the set.
87 + 72 + 99 + 93 + 84 = 435
435 / 5 = 87
The mean of the quiz grades is 87
if 3 m equals 12 what is the value of 6(m-1)
Answers
3m = 12
divide both sides by 3:
m = 12/3
m = 4
now yo know m so replace m with 4 in the second equation:
6(m-1) = 6(4-1)
do the subtraction inside the parenthesis first
6(4-1) = 6(3)
now multiply 6 and 3: 6 x 3 = 18
I don't understand this problem can you help?
Answers
The question is the same as drawing a Black marble. That's one way to look at it. Another is to draw a gray and then subtract that probability of not drawing a gray. I'll do both. Choose the one that is clearest in your mind.
Method One
Total number of marbles = 21 + 11 = 32 marbles of both colors. Probability of drawing a black marble =
P(B) = P(~gray) = 11 / 32
Method Two
A. Find the probability of drawing a gray marble.
There are 21 gray marbles and 32 total
P(G) = Number of Gray's / total
P(G) = 21 / 32
P(~G) = 1 - 21/32
P(~G) = 32/32 - 21/32
P(~G) = 11/32 <<<< Answer
Which number is not in scientific notation?
A: 1.10 ⋅ 103
B: 4.0 ⋅ 1016
C: 7.03 ⋅ 10−2
D: 350 ⋅ 102
Answers
the anser would be c fo it to be in scientific notation you have to have an exponet
You scored the following grades on your first three math tests: 71, 78, 81. You only have one test remaining. What is the highest possible test average you can get?
Answers
Highest possible total scores for 4 tests = 71 + 78 + 81 + 100 = 330
Highest possible average score for 4 tests = 330 ÷ 4 = 82.5
Answer: 82.5
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth. 6, 7, 19, 7, 18, 7
Answers
Answer:
The mean is 10.7 and the standard deviation is 5.6.
Step-by-step explanation:
To find the mean, add together all of the data and divide by the number of data points:
(6+7+19+7+18+7)/6 = 64/6 = 10.7
To find the standard deviation, subtract each data point from the mean, square them and find the sum:
(6-10.7)²+(7-10.7)²+(19-10.7)²+(7-10.7)²+(18-10.7)²+(7-10.7)²
=(-4.7)²+(-3.7)²+(8.3)²+(-3.7)²+(7.3)²+(-3.7)²
=22.09+13.69+68.89+13.69+53.29+13.69 = 185.34
Next divide this by 6, the number of data points:
185.34/6 = 30.89
Lastly, take the square root:
√30.89 = 5.6
Which of the following points are more than 5 vertical units away from the point left-parenthesis 0 comma negative 2 right-parenthesis? Choose all that apply. (2 points) left-parenthesis 6 comma negative 2 right-parenthesis left-parenthesis negative 8 comma negative 2 right-parenthesis left-parenthesis 0 comma negative 8 right-parenthesis left-parenthesis 0 comma 4 right-parenthesis
Answers
Given point is (0, -2).
Given options are A(6, -2); B(-8, -2); C(0, -8); D(0, 4).
It says to select the options that are more than five units vertically away from the given point.
"Vertically away" means the x-coordinate would be same and y-coordinate would be shifted up or down.
Since it says to shift more than five units vertically away, so we must have :-
y > -2 + 5 or y < -2 - 5.
Therefore, y > 3 or y < -7.
Hence, option C and D are correct i.e. (0, -8) and (0, 4).
Please help me understand this.
Answers
Number of tiles in yellow ring = 12
Number of tiles in blue ring = 18
Observe the terms, they are forming an Arithmetic series as each term is 6 more than the previous term. We are to find the number of tiles in 30th ring, which will be the 30th term of the A.P.
So,
30th term of AP = 1st term +(30 - 1) x Common Difference
30th term of AP = 6 + 29 x 6 = 180
Thus, there will be 180 tiles in the 30th ring of white tiles
Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. Using the formula A(t) =P*e^rt , how much will you have in the account after 4 years
Answers
A = $1600*e^(0.046*4) = $1923.23 (rounded up to the nearest cent)
The histogram shows the number of vacation days taken by employees in the past year. Based on the histogram, which statement is true?
A.)Four employees took 20 vacation days in the past year.
B.) Four employees took 25 vacation days in the past year.
C.) Four employees took between 20 and 25 vacation days in the past year.
D.) Between 20 and 25 employees took four vacation days in the past year.
Answers
so answer is
C.) Four employees took between 20 and 25 vacation days in the past year.
Answer:
Option(C)
Step-by-step explanation:
As per histogram, given below
3 students took holidays between 5-10 days.
5 students took holidays between 10-15 days.
5 students took holidays between 15-20 days.
4 students took holidays between 20-25 days.
3 students took holidays between 25-30 days.
therefore, option (C) is correct.