Answers
Answer:
x = 1
Step-by-step explanation:
A right triangle is a triangle with a (90) degree angle. A box around one of the angles of a triangle indicates that this angle has a (90) degree measure. All of the triangles in the given picture are right triangles, as all of them contain a (90) degree angle. More than just being right triangles, the triangles in the diagram also have red arcs indicate that the angles are congruent. The base angles converse theorem states that in a triangle with two congruent angles, the sides opposite the congruent angles are also congruent, thus forming an isosceles triangle. Therefore, the given triangles are isosceles right triangles. One property of isosceles right triangles are that their sides follow the ratio:
\(a\ :\ a\ :\ a\sqrt{2}\)
Where the sides with a measurement of (a) are the ones opposite the congruent angles, and the side with a measure of (\(a\sqrt{2}\)) are the sides opposite the right angle. Apply this to the given triangle, refer to the attached diagram for further clarification about side namings,
\(BC*\sqrt{2}=AB\\\\BC=\frac{AB}{\sqrt{2}}\\\\BC=\frac{4}{\sqrt{2}}\)
\(BD*\sqrt{2}=BC\\\\BD=\frac{BD}{\sqrt{2}}\\\\BD=\frac{\frac{4}{\sqrt{2}}}{\sqrt{2}}\\\\BD = \frac{4}{\sqrt{2}*\sqrt{2}}\\\\BD=\frac{4}{2}=2\)
\(BE*\sqrt{2}=BD\\\\BE=\frac{BD}{\sqrt{2}}\\\\BE=\frac{2}{\sqrt{2}}\)
\(BF*\sqrt{2}=BE\\\\BF=\frac{BE}{\sqrt{2}}\\\\BF=\frac{\frac{2}{\sqrt{2}}}{\sqrt{2}}\\\\BF = \frac{2}{\sqrt{2}*\sqrt{2}}=\frac{2}{2}=1\)
\(BF = x = 1\)
Related Questions
Which shows the result of a correct substitution for the system y=2x+3 and 3x+2y=9?
o
A. y= 2y + 3
B. 3(2x + 3) + 2y = 9
C. 3x + 2(2x + 3) = 9
o
D. 2x + 2y = 3
Answers
Answer:
C. 3x + 2(2x + 3) = 9
Step-by-step explanation:
We are given the following relation:
y = 2x + 3
And we want to substitute into:
3x + 2y = 9.
So
\(3x + 2(2x + 3) = 9\)
Which is given by option C.
What best describes fraction
Answers
Answer:
a numerical quantity that is not a whole number
Step-by-step explanation:
5
Select the correct answer.
ABCD is a rectangle. AE = 3x-6 and BD=21. What is AC?
A
B
3x-6
E
2x
OA. 15
OB. 24
OC. 6
OD. 12
D
C
Answers
In the given diagram, the value of AC is 24. The correct option is B. 24
Properties of rectangleFrom the question, we are to determine the value of AC
From one of the properties of a rectangle, we have that
The diagonals of a rectangle are equal and bisect each other.
Then, in the given diagram
AC = DB
Thus,
3x - 6 + 3x - 6 = 2x + 2x
6x -12 = 4x
6x - 4x = 12
2x = 12
x = 12/2
x = 6
In the diagram,
AC = 3x - 6 + 3x - 6
AC = 3(6) -6 + 3(6) - 6
AC = 18 - 6 + 18 - 6
AC = 24
Hence, the value of AC is 24. The correct option is B. 24
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6
Step-by-step explanation:
Edmentum
Can someone help me with this problem please? I'll mark you as brainliest!
Answers
Answer:
put a closed for on -1 and go to the left with an arrow
(-4, -4), (2,3), and (-4, 6). What is the area, in square units, of this shape?
Answers
Answer:
24 sq units
Step-by-step explanation:
shape is a triangle with a height of 6 and a base of 8
A = bh/2
A = (6·8)/2
A = 24
please solve this fast
Answers
Step-by-step explanation:
1.
\(qr - pr \: + qs - ps\)
\(r(q - p) + s(q - p)\)
\((r + s)(q - p)\)
2.
\( {x}^{2} + y - xy - x\)
\( {x}^{2} - x - xy + y\)
\(x(x - 1) - y(x - 1)\)
3.
\(6xy + 6 - 9y - 4x\)
\( - 4x + 6 + 6xy - 9y\)
\(2( - 2x + 3) - 3y( - 2x + 3)\)
\((2 - 3y)( - 2x + 3)\)
4.
\( {x}^{2} - 2ax - 2ab + bx\)
\(x(x - 2a) - b(x - 2a)\)
\(-(x +b)(2a-x)\)
5.
\(axy + bcxy - az - bcz\)
\(xy(a + bc) - z(a + bc)\)
\((xy - z)(a + bc)\)
3+11+.....+(8n-5) = 4n²-n using PMI
Answers
Answer:
Basis step: S(1):
LHS: (8(1)−5)=3
RHS: 4(1)2−(1)=3
31-+=16
28+b=50
33+c=54
52-n+=24
Answers
The solution to the equations are b = 15, b = 22, c = 21 and n = 28
How to determine the solution to the equationsFrom the question, we have the following equations that can be used in our computation:
31 - b = 16
28 + b = 50
33 + c = 54
52 - n = 24
Next, we collect the like terms in each of the equation
This gives
b = 31 - 16
b = 50 - 28
c = 54 - 33
n = 52 - 24
Lastly, we evaluate the like terms
b = 15
b = 22
c = 21
n = 28
The above are the solutions to the equations
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Question
Solve the following equations:
31 - b = 16
28 + b = 50
33 + c = 54
52 - n = 24
The third and fourth grade teachers are planning a trip for their classes to the zoo. There are 173 third graders and 124 fourth graders. Each seat on the buses fits 3 students. Which expression represents the closest estimate of the number of seats on the buses that are needed for the students?
Answers
Answer:
173 - 124 = then do thatb divided by each seat 2
Step-by-step explanation:
Dr. Dominic Estores has written a prescription for a patient to take a preoperative medication at 2200 on the evening before his scheduled surgery. Using the standard time system, what time should you tell the patient to take his medication?
Answers
Using the conversion from the 24-hour system to the AM/PM system, the patient should take the medicine at 10 PM.
How to convert from 24 hours to AM/PM?If the hour is between 0 and 11:59, the hour is kept with AM.If the hour is 12, it is PM.If the hour is between 13 and 23:59, the hour the remainder of the division of the hour and 12, PM.22 divided by 12 has remainder 10, hence 22 is equivalent to 10 PM.
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The volume of a 12-inch-tall cone is 144π cubic inches.
What is the radius of this cone?
Answers
Answer:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cone is 144π cubic inches and the height is 12 inches. So we can plug these values into the formula and solve for r:
144π = (1/3)πr^2(12)
144 = 4r^2
r^2 = 36
r = ±6
Since a negative radius doesn't make sense in this context, we can discard the negative solution and conclude that the radius of the cone is 6 inches.
There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble?
25%
62.5%
20%
41.7%
Answers
Answer:
20%
Step-by-step explanation:
The theoretical probability of drawing a red marble can be found by dividing the number of red marbles by the total number of marbles in the bag:
P(red) = number of red marbles / total number of marbles
P(red) = 5 / (5 + 8 + 12)
P(red) = 5 / 25
P(red) = 0.2
So the theoretical probability of randomly drawing a red marble is 20%, which corresponds to option (C).
i really need help i have till 11:00
Answers
The expression that represents the combined inventory of these two stores is given as follows:
A. 7g²/2 - 4g/5 + 15/4.
How to obtain the combined inventory?The combined inventory is obtained adding the inventories for each store, combining the like terms.
The addition of the like terms for g² is given as follows:
1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².
The term with g is given as follows:
-4g/5.
The constant like terms are combined as follows:
7/2 + 1/4 = 14/4 + 1/4 = 15/4.
Hence the simplified expression is given as follows:
7g²/2 - 4g/5 + 15/4.
Meaning that the correct option is given by option A.
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Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
Answers
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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Find 96.1% of 146. Round to the nearest tenth.
Answers
The value of 96.1% of 146 is 140.31
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We have to find the value of 96.1% of 146.
Convert 96.1% to the decimal value by dividing with 100
96.1/100=0.961
Now multiply 0.961 with the 146 to find the value.
0.961×146
140.306
Hence, the value of 96.1% of 146 is 140.31
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To which sets does 13 belong too??
Answers
Answer: 13 is in C (the set of complex numbers)
Step-by-step explanation:
13 is in R (the set of real numbers)
13 is in Q (the set of rational number)
13 is in Z (the set of integers)
13 is in N (the set of natural numbers)
Find the value of the annuity and the interest. Round to the nearest dollar.
Periodic Deposit: $100 at the end of each year
Rate: 4% compounded annually
Time: 9 years
Answers
The value of the annuity after 9 years is approximately $1,044.56. The interest earned on the annuity after 9 years is approximately $244.56.
What is annuity?A financial contract known as an annuity offers a series of recurring payments over a predetermined length of time. A monthly, quarterly, or annual payment schedule is available when buying an annuity from an insurance provider. The payments are made until the annuitant's death or for a predetermined amount of time.
Deferred annuities and immediate annuities are the two categories under which annuities fall. Deferred annuities are a particular kind of annuity where the payments are postponed for a predetermined amount of time, typically several years. On the other hand, an instant annuity starts paying out as soon as the annuity is bought.
The value of annuity is given by the formula:
\(A = P * ((1 + r)^n - 1) / r\)
Substituting the given values we have:
\(A = $100 * ((1 + 0.04)^9 - 1) / 0.04\\A = $100 * (1.04^9 - 1) / 0.04\)
A ≈ $1,044.56
Hence, the value of the annuity after 9 years is approximately $1,044.56.
Now, the interest is givn as:
Interest = A - (P * n)
Substituting the values we have:
Interest = $1,044.56 - ($100 * 9)
Interest ≈ $244.56
Hence, the interest earned on the annuity after 9 years is approximately $244.56.
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without using a calculator or mathematical table sove 187²-87²
Answers
Hope this helps
The graph shows the position (distant from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval.
Use the equation below to calculate the bicycle rider’s average speed in kilometers per minute for the first 30 minutes of the trip
Distance(km)/time(min) = average speed
Answers
The average speed on the first 30 minutes is 0.2 km per min.
How to get the average speed?Here we have the graph for the position of a bycicle rider on a 42-minute trip.
On the vertical axis we can see the position, and on the horizontal axis we can see the time.
Remember that:
speed = distance/time.
To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.
At 30 min we can see that the position is at 6 km, then the speed will be:
S = 6km/30min = 0.2 km per min.
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The sine of 30 degrees is 1/2. What is the cosine of 60 degrees?
Answers
Answer:
Sine (30°) = cosine(90-30) = cos(60°) = 1/2
Step-by-step explanation:
The value of the \(cos 60^0\) is \(\dfrac{1}{2}\).
Recall the relationship between the sine and cosine\(cos^2\theta= 1-sin^2\theta\\cos 2\theta = cos^2\theta - sin^2\theta\)
How to find the cosine values?Given the value of \(sin30^0\) is \(\dfrac{1}{2}\).
Use the relation between the sine and cosine as-
\(\cos^230^0=1-\sin^230^0\\=1-\dfrac{1}{4}\\=\dfrac{3}{4}\\\)
Use another relation \(\cos 2\theta = \cos^2\theta -\sin^2\theta\) as-
\(\cos(2\times 30^0)=\cos^2{30^0}-\sin^2{30^0}\\=\dfrac{3}{4}-\dfrac{1}{4}\\=\dfrac{1}{2}\)
Hence, \(\cos 60^0\) is value is \(\dfrac{1}{2}\).
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How many miles does he run in one year
Answers
Answer Key:
1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.
| I just want to help you with #2 anyway
6( 3 + 5 ) 2 - 9a evaluate the expression when a = 3 and b = 5
Answers
The value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69
In this question,
we have been given an expression 6( 3 + 5 ) 2 - 9a
We need to evaluate given expression when a = 3 and b = 5
We substitute a = 3 in given expression and solve it.
6( 3 + 5 ) 2 - 9a ..........(given expression)
= 6( 3 + 5 ) 2 - 9(3) ..........(substitute a = 3)
= 6(8) 2 - 27
= 96 - 27
= 69
Therefore, the value of the expression 6( 3 + 5 ) 2 - 9a when a = 3 is 69
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no links help me
Parents are raising money for new playground equipment. They need $682.56 to purchase swings and receive a $200.00 donation. The remaining amount will be equally divided among 8 different student groups to raise. How much money will each student group need to raise in order to purchase the swings? Your answer should start with the $ and should only include numbers and a decimal point. *
Answers
Answer:
$53.57
Step-by-step explanation:
First, you have to subtract 200 from 628.56 to get 428.46
Then, you do 428.46/2 = 53.57, which is your answer
Hope this helps!
Step-by-step explanation: $682.56 - 200 of the donations = 482.56
I need help will award brainliest .
Answers
Answer:
Below
Step-by-step explanation:
Due to vertical angles:
5x+21 =9x -55 shows x = 19°
then WOZ = 9x-55 = 116 degrees
WOZ and WOY are supplemenrary (add to a 180 ° straight line)
116 + WOY = 180 so WOY = 64°
Does anyone know this answer??
Answers
Approximately 99.7% of scores lie in the shaded region.
We have,
The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
Approximately 68% of scores lie within 1 standard deviation of the mean.
Approximately 95% of scores lie within 2 standard deviations of the mean.
Approximately 99.7% of scores lie within 3 standard deviations of the mean.
Now,
In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.
This encompasses the area within 3 standard deviations of the mean.
And,
Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.
Therefore,
Approximately 99.7% of scores lie in the shaded region.
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If 2x-y=9 and 3x+4y=19, then y=
Answers
Answer:
x = 5
y = 1
Step-by-step explanation:
2x - y = 9
3x + 4y = 19
We multiply the first equation by 4
8x - 4y = 36
3x + 4y = 19
11x = 55
x = 5
Now we put 5 in for x and solve for y
2(5) - y = 9
10 - y = 9
-y = -1
y = 1
Let's Check the answer
2(5) - 1 = 9
10 - 1 = 9
9 = 9
So, x = 5 and y = 1 is the correct answer.
PLEASE ANSWER! WOLL GIVE BRAINLIEST AND LOVE U FOREVER
Answers
How many unit cubes are on each layer of the cube?
6
3
12
9
Answers
Answer:
6
Step-by-step explanation:
Remember: Each layer has 6 cubes. Step 3 Count the cubes. cubes Multiply the base and the height to check your answer. So, the volume of Jorge's rectangular prism is cubic centimeters. if wrong very sorry
Answer:
9
Step-by-step explanation:
took the test
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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A rectangular garden has a length of x + 8 units and a width of x – 4 units. Find the AREA.
Answers
Answer: i hope this helps u
(sorry if i'm wrong)
:(
The area of rectangular garden is x²+4x-32.
What is rectangle?A rectangle is a geometric figure that has four sides, opposite sides are equal, and all angles are right angles.
Given that,
The length of rectangular garden = x+8 units,
And the width of garden = x-4 units.
Area of rectangle = length × width
Area = (x+8) × (x-4)
Area = x²+8x-4x-32
Area = x²+4x-32
The area of rectangular garden is x²+4x-32.
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