If CD is the perpendicular bisector of AB, then the value of x is:
10.
5.
22.
11.
Answers
CD = CD [ Common side ]
AD = BD [ CD is the perpendicular "bisector" of AB ]
∠CDA = ∠CDB [ CD is the "perpendicular" bisector of AB ]
Thus, ΔCAD and ΔCBD are congruent triangles. [ SAS congruency ]
If these triangles are congruent, then AC = BC.
2x = 3x -10
x = 10.
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a car dealership has 55 cars and 11 vans.what is the ratio of cars to vans? wriiten as a fraction in simplest form?
Answers
Which expression is equivalent to x3 • x2?
A.) (x + x)5
B.) x5
C.) x-1
D.) x6
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X^3 • X^2 = X^5.
The final solution is B.
The given expression [tex]\rm x^3\times x^2[/tex] can be reduced to [tex]\rm x^5[/tex] and this can be determined by using the arithmetic operations.
Given :
Expression -- [tex]\rm x^3\times x^2[/tex]
The following steps can be used in order to evaluate the given expression:
Step 1 - The arithmetic operations can be used in order to evaluate the given expression.
Step 2 - Write the given expression.
[tex]= \rm x^3\times x^2[/tex]
Step 3 - According to the arithmetic operation if a variable 'a' is multiplied by the same variable 'a' then the expression becomes [tex]\rm a^2[/tex].
Step 4 - Applying the property mentioned in the above step in order to evaluate the given expression.
[tex]x^2\times x^3=x^5[/tex]
Therefore, the correct option is B).
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write each fraction as a sum or difference
2m-5/9
Answers
So we can simply divide each term of numerator by denominator because we can write [tex] \frac{a+b}{c} = \frac{a}{c}+ \frac{b}{c} [/tex]
So we can write given fraction as
[tex] \frac{2m-5}{9} = \frac{2m}{9} - \frac{5}{9} [/tex] which is expressed as a difference.
Your employer offers you a choice of wage scales: a monthly salary of $2800 plus commission of 8% of sales or a salary of $3300 plus a 6% commission. At what sales level would the options yield the same salary?
Answers
0.08s = 0.06s = 3300 - 2800
0.02s = 500
s = 500 / 0.02
s = 25,000 <==
At the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
Your employer offers you a choice of wage scales:
A monthly salary of $2800 plus a commission of 8% of sales or
A salary of $3300 plus a 6% commission.
First choice of wage scale:
= 2800 + 0.08s
Second choice of wage scale:
= 3300 + 0.06s
2800 + 0.08s = 3300 + 0.06s
0.08s - 0.06s = 3300 - 2800
0.02s = 500
s = 25,000
Thus, at the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.
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if the perimeter of a triangle measures 42 feet and the three sides are consecutive numbers , what are the side lengths
Answers
42/3 = 14
14-1=13
14+1= 15
13+14+15 = 42
3 numbers = 13, 14 & 15
Drag the tiles to the correct boxes to complete the pairs. A team of 10 players is to be selected from a class of 6 girls and 7 boys. Match each scenario to its probability.
Answers
Answer:
Here you go!
Step-by-step explanation:
Translate this sentence into an equation; 14 less than Julie's score is 62. Use the variable m to represent Julie's score.
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I hope this helps!
"14 less than Julie's score"
This implies that we are going to have 14 less than the variable that represents Julie's score (which in this case, is m).
m-14
"is 62"
"Is" is almost always used as a way of saying "=," and 62 is the value that it equals.
m-14=62
Using the reasoning above, we can see that an equation to represent this scenario is m-14=62.
the table below summarizes the number of children per household for a sample of 29 families
Answers
A bus traveled on a level road for 4 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 5 hours. Find the average speed on the level road if the entire trip was 449 miles.
Answers
To solve this problem, we must recall that the formula for velocity assuming linear motion:
v = d / t
Where,
v = velocity
d = distance
t = time
For condition 1: bus travelling on a level road
v1 = d1 / t1
(v2 + 20) = (449 – d2) / 4 --->1
For condition 2: bus travelling on a winding road
v2 = d2 / t2
v2 = d2 / 5 --->2
Combining equations 1 and 2:
(d2 / 5) + 20 = (449 – d2) / 4
0.8 d2 + 80 = 449 – d2
1.8 d2 = 369
d2 = 205 miles
Using equation 2, find for v2:
v2 = 205 / 5
v2 = 41 mph
Since v1 = v2 + 20
v1 = 41 + 20
v1 = 61 mph
Therefore the average speed on the level road is 61 mph.
You have learned about special right triangles. Using that knowledge, you decide to take a square cake with 10-inch sides and divide it diagonally to form two special right triangles. Find and explain how you know the exact (no decimals) measure of the hypotenuse.
Now find the exact diagonal measure of cakes that are an 8-inch square, a 12-inch square, and a 15-inch square.
Did you discover a shortcut that works with any square cake? Explain.
Please show your work
Answers
thus, using the 45-45-90 rule, for a square with sides if 8-inch, h = 8√(2), for 12-inch sides, h = 12√(2), for 15-inch sides, h = 15√(2), and so on.
The hypotenuse of a right triangle formed by dividing a square cake diagonally can be found using the Pythagorean Theorem, with the shortcut that the hypotenuse is the side length of the square multiplied by √2. Examples include a hypotenuse of 10√2 inches for a 10-inch square, 8√2 inches for an 8-inch square, 12√2 inches for a 12-inch square, and 15√2 inches for a 15-inch square.
Finding the Hypotenuse of Right Triangles in Squares
To find the length of the hypotenuse in a right triangle that is formed by dividing a square cake diagonally, we use the Pythagorean Theorem which states that for a right triangle with sides a and b and hypotenuse c, the relation is c = √(a ² + b ²). Since the sides of the square are equal in length, for a square with 10-inch sides, the hypotenuse will be √(10 inches ² + 10 inches ²) = √(100 + 100) = √200 inches = 10√2 inches.
For the other square cakes:
8-inch square: Hypotenuse = √(64 + 64) = 8√2 inches
12-inch square: Hypotenuse = √(144 + 144) = 12√2 inches
15-inch square: Hypotenuse = √(225 + 225) = 15√2 inches
The shortcut discovered is that the length of the hypotenuse is always the side length of the square multiplied by √2, because each side of the square forms a right triangle with equal sides when the square is divided diagonally.
Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h
Answers
[tex]\displaystyle=-\lim_{h\to0}\frac h{5(5+h)h}[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac1{5(5+h)}=-\frac1{25}[/tex]
Alternatively, recall that if [tex]f(x)=\dfrac1x[/tex], then [tex]f'(x)=-\dfrac1{x^2}[/tex], and so
[tex]f'(5)=\displaystyle\lim_{x\to5}\frac{\frac1x-\frac15}{x-5}[/tex]
Take [tex]h=x-5[/tex], so that [tex]x=h+5[/tex], and we have the original limit. So the limit is equivalent to the value of [tex]f'(5)[/tex], i.e.
[tex]f'(5)=-\dfrac1{5^2}=-\dfrac1{25}[/tex]
Which of these would make the number sentence true below?
3.7427 < 3.74__
A. Three thousandths
B. Two thousandths
C. Three ten-thousandths
D. Seven ten-thousandths
Answers
For football tryouts at a local school, 12 coaches and 42 players will split into groups. Each group have the same number of coaches and players. What is the greatest number of groups that can be formed? How many coaches and players will be in each of these groups?
Answers
Why does a calculator return an error when trying to find inverse sine of 1.055?
Answers
It then returns error
Answer:
1.055 is outside the domain of the sine function.
Step-by-step explanation:
When we are taking the inverse sine, we are finding an angle that gives a value of 1.055.
The sine function NEVER gives a value greater than 1 or less than -1. The domain of the sine function is between -1 and 1, inclusive.
So wanting to know which angle gives a sine value of 1.055 is futile. Sine can never be greater than 1.
That's why the calculator gives an error, because 1.055 is outside the domain of the sine function.
How many four-digit even numbers are possible if the leftmost digit cannot be zero
Answers
There are 4500 four-digit even numbers possible when the leftmost digit cannot be a zero.
Explanation:The question is about finding out the number of four-digit even numbers possible given that the first or leftmost digit cannot be a zero. In a four-digit even number, the last digit (rightmost) should be an even number, i.e., 0, 2, 4, 6, or 8. Hence, there are 5 possibilities for the last digit.
Next, since the leftmost digit cannot be a zero, it leaves us with 9 possibilities (1-9). Lastly, the middle two digits can be any digit from 0 to 9, so there are 10 possibilities each for the second and third digits.
Therefore, the total number of four-digit even numbers under the given conditions is found by multiplying these possibilities: 9 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 5 (for the last digit) = 4500.
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To find the number of four-digit even numbers where the leftmost digit cannot be zero, there are 9000 possibilities.
Explanation:To find the number of four-digit even numbers where the leftmost digit cannot be zero, we need to consider the following:
Choose the digit for the leftmost position (excluding zero). This can be done in 9 ways.Choose the digits for the other three positions (including zero for even numbers) in 10 ways each (0-9).By multiplying the number of choices for each position, we get the total number of four-digit even numbers without leading zeros: 9 * 10 * 10 * 10 = 9000.
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Mike is taking a social studies test. mike was only able to finish 1/6 of the test in 1/2 an hour. How long will it take him to finish the test.
Answers
1/6 = 1/2 hr
2/6 = 1 hr
6/6-1/6 = 5/6 left of the test
2/6 + 2/6 = 4/6 = 2 hours
4/6 + 1/6 = 2 + 1/2 = 2 1/2
so 2 1/2 more hours
Evaluate the integral. (3 + 1/4 u^4 − 2/3 u^9) du
Answers
A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.
Answers
The range of the original bill is
200 < [tex]1.2x+25[/tex] < 800, subtract each term by 25
175 < [tex]1.2x[/tex] < 775, divide each term by [tex]1.2[/tex]
145.83 < [tex]x[/tex] < 645.83
Hence, the range of the original bill is between $145.83 and $645.83
In your own words, explain the place value relationship when the same two digits are next to each number in a multi-digit number
Answers
The relationship of the two of the same digits that are next to each other in a multi-digit number lies in their place value, wherein the digits from the decimal point that is to the left, is 10 times of larger value compared to the digit in their left. And from the decimal point to the right, it is 10 times of small value that the digit in their right.
Let’s see an example:
123.45, wherein 1 is hundreds, two is tens, 3 is ones, and then after the
decimal points, is where 4 is the tenths and 5 is the hundredths.
Take note of each place value that is next to each other since each value
is 10 times in difference.
A(-3, 9) and B(5, 9) are the endpoints of the diameter of a circle. Use these points to find the standard equation of the circle.
Answers
notice the midpoint of the diameter segment, is just 1,9.
also, recall the radius is half the diameter, notice how long the radius is, just 4 units.
[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &1&9&4 \end{array} [/tex]
I got 43000 and I don't know what I did wrong
Answers
estimating wage to nearest dollar would be 22 x 40
would be 22 x 4 = 88 so 880 per week
estimating 50 weeks
88 x 5 = 440 so 44,000 per year
exact would be 21.50 x 40 = 860 per week
860 x 52 = 44,720 per year
Help me figure this out please.
Answers
Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?
Answers
45x = money Matt has
45x =50(x-.1)
45x =50x -5
5 =5x
x=$1
45x= $45
the cost of each car is $1
Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: "When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5." Which twin is talking? How do you know?
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The solve the next problem, the second lucky number (1) twice is 2. When added to the first lucky number, the sum is 4. This is tricky, because if the first lucky number was multiplied by 2 and added to the second lucky number, the sum would be 5.
In this case, the twin that lies is talking.
The average number of field mice per acre in a 5-acre wheat field is estimated to be 12. find the probability that fewer than 7 field mice are found
Answers
The probability that fewer than 7 field mice are found in the 5-acre field is 0.0458.
The probability that fewer than 7 field mice are found in the entire 5-acre field is not simply 58.10% multiplied by 5. This is because the mice are not independent on each other. The number of mice on one acre doesn't affect the number found on another.
To find the probability for the entire field, we need to consider all possible combinations of the number of mice on each acre. This can be a complex calculation involving multiple Poisson distributions.
However, if we assume that the distribution of mice across the field is approximately uniform, we can use a simpler approach. We can assume that the probability of finding fewer than 7 mice on each acre is independent of the others and multiply the individual probabilities:
P(total < 7) ≈ (0.5810)^5 ≈ 0.0458
Therefore, under the assumption of approximate uniformity, the probability of finding fewer than 7 field mice in the entire 5-acre field is approximately 0.0458%.
Complete question:
The average number of field mice per acre in a 5-acre wheat field is estimated to be 12. find the probability that fewer than 7 field mice are found on a given acre that is 5.
A small company repairs home computers. In the past 200 days, it has been quite busy, taking in and repairing 2 computers on 52 of those days; 3 computers on 84 of those days; 4 computers on 40 of those days; and 5 computers on 24 of those days. Build a probability distribution for the number of computers repaired on any given day, show it is a valid distribution, and calculate its mean and variance.
Answers
The value of [tex]x[/tex]: 2, 3, 4, and 5 shows the number of computers repaired and [tex]P(X=x)[/tex] shows the probability
Mean = (2×0.26×) + (3×0.42) + (4×0.2) + (5×0.12)
Mean = 0.52+1.26+0.80+0.6
Mean = 3.18
Variance = [(2²×0.26)+(3²×0.42)+(4²×0.2)+(5²×0.12)] - (3.18)²
Variance = 0.9076
PLEASE help me...Suck at math. find the following using the given triangle.
Answers
5+5+6 = 16
To find the area, you need to use the following formula
[tex] area = \frac{1}{2}bh[/tex]
we know b but we need to find the height. We can find the heigh by using pythagorean theorem [tex]a^2 + b^2 = c^2[/tex]
height = [tex] a^2 + 3^2 = 5^2 [/tex]
[tex] a^2 + 9 = 25 [/tex]
[tex] a^2 = 25 - 9[/tex]
[tex] a^2 = 16 [/tex]
[tex] a = \sqrt{16} = 4 [/tex]
h = height = 4
[tex] area = \frac{1}{2}\times 6\times 4 = 12cm^2[/tex]
Cost:
6.00 per cm^2 = 6.00 x 12 = $72.00 dollars
what's the cost? well is $6 per square foot, what area did you get? well, say you got A, so the cost is just A * 6.
Mabel is installing a square pool in her backyard and wants a circular fence to enclose the pool to create 4 grassy areas around the pool as show in the figure. If the pool is located at the coordinates (1, 5), (5, 8), (4, 1), and (8, 4), what is the amount of fencing Mabel needs to purchase? Round your answer to the nearest tenth. (Like 5.7 or 3.4).
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What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of probability in decimal format and round it to three decimal places.)?
Answers
Probability = n!/r!(n-r)! * p^r * q^(n-r), where n is the number of tries (n=6), r is the number tries where you get an even number (r=0), p is the probability of having an even face and q is the probability of having an odd face.
Probability = 6!/0!(6!) * (1/2)^0 * (1/2)^6
Probability = 1/64
Therefore, the probability is 1/64 or 1.56%.
The lengths of a particular type of metal rod are modeled by the equation r = |–24x + 120|, where r represents the lengths of the rod in inches, and x represents the speed at which the rods are produced, in rods per minute. If the manufacturing process is too fast or too slow, the rods will not be long enough. At what speeds will the lengths of the rods be greater than 48 inches?
A. The length of the rods will be greater than 48 inches when x > 3 or x < 7 rods per minute.
B. The length of the rods will be greater than 48 inches when x < 3 or x > 7 rods per minute.
C. The length of the rods will be greater than 48 inches when x > –3 or x < –7 rods per minute.
D. The length of the rods will be greater than 48 inches when 3 < x < 7 rods per minute
Answers
-24x + 120 > 48
-24x > 48 - 120
-24x > - 72
x < -72/-24
x < 3
-24x + 120 < -48
-24x < -48 - 120
-24x < - 168
x > -168/-24
x > 7
solution is : x < 3 or x > 7...answer B