As per the given rectangle, the length of EG is 5x - 7
We are given that DEFG is a rectangle, which means that its opposite sides are parallel and equal in length. Let's label the sides of the rectangle as follows:
DE = FG = a (since opposite sides of a rectangle are equal in length)
EF = DG = b (since opposite sides of a rectangle are parallel)
Now, we can use the given information to set up an equation for the length of EG:
EG = EF + FG = b + a
But we don't know the values of a and b. However, we are given that FD = 3x - 7 and EG = x + 5. We can use this information to solve for a and b.
We know that FD = DE - EF, so we can substitute the values we have:
3x - 7 = a - b
We also know that EG = FG - DG, so we can substitute the values we have:
x + 5 = a - b
Now we have two equations with two variables (a and b). We can solve for a and b by adding the two equations together:
3x - 7 + x + 5 = 2a
4x - 2 = 2a
a = 2x - 1
Now we can substitute this value for a in one of the earlier equations to solve for b:
3x - 7 = (2x - 1) - b
b = 3x - 6
Finally, we can substitute the values we found for a and b into the equation we set up earlier to find the length of EG:
EG = EF + FG = b + a = (3x - 6) + (2x - 1) = 5x - 7
Therefore, the length of EG is 5x - 7.
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20 POINTS
Given: CD is an altitude of ΔABC
Prove:
[edAsset type="image" caption="" figure="false" alt="" class="block-center img-responsive " /edAsset]In an Image of a Triangle ACB with b is the length between AC, a is the length between CB and c is the base length between AB. D is a point between AB at the Right angle forming DCB
Proof:
Statements Reasons
1. CD is an altitude of ΔABC. Given
2. ∠ADC and ∠BDC are right angles. Definition of altitude
3. ΔADC and ΔBCD are right triangles. Definition of right triangles
4.
Definition of sine
5. ? Multiplication property of equality
6. b sin(A) = a sin(b) Substitution property of equality
7.
Division property of equality
Which statement completes this proof?
A.
CD = b sin(B) and CD = a sin(A)
B.
b = CD sin(A) and a = CD sin(B)
C.
CD = b sin(A) and CD = a sin(B)
D.
b = CD sin(B) and a = CD sin(A)
In the triangle , the cοrrect οptiοn is B) b = CD sin(A) and a = CD sin(B).
What is triangle?A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.
Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.
Here the given triangle CD is altitude.
According to the given statement table , in 4th statement we have definition of sine , Then
=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]
Here simplifying this sine equation for a and b then,
=> b = CD sin(A) and a = CD sin(B).
Hence the correct option is B) b = CD sin(A) and a = CD sin(B).
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what do the slopes from part a and b tell you about the relationship between all points in the table
The slope of the line is 1. Two different points have the same slope.
What is tilt?Rise or fall is a number or ratio that determines the direction or slope of the line. The slope of a straight line is the ratio of the slope of the straight line to the course of the straight line. The point is:
-XY
twenty-five
−2 1
0 3
-7 -4
The slope of a straight line is generally calculated using the formula:
slope = [tex](y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]
Points (2, 5) and (-2, 1) of part (A).
Slope = [tex]( 1 - 5 ) / ( -2 - 2 )[/tex]
Slope = -4 / -4 = 1
Split (B) at the points ( 0, 3 ) and ( -7, - 4 ).
Slope = [tex]( -4 - 3 ) / ( -7 - 0 )[/tex]
Slope = -7 / -7 = 1
The slope of the line at two different points is the same.
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Complete question is: A table with certain points is shown. x 2 −2 0 −7 y 5 1 3 −4 Part A: Choose two points from the table and calculate the slope between them. Show all necessary work. (4 points) Part B: Choose two different points from the table and calculate the slope between them. Show all necessary work. (4 points) Part C: What do the slopes from parts A and B tell you about the relationship between the points? Explain.
The sales tax on a $44.00 purchase is $2.42. At this rate, what would be the tax on goods worth $60.00?
Answer:
We can use proportions to find out the tax on goods worth $60.00:
Let x be the tax on goods worth $60.00.
Then, we can set up the following proportion:
tax/sales = tax rate
or
2.42/44 = x/60
To solve for x, we can cross-multiply and simplify:
44x = 2.42 * 60
44x = 145.20
x = 145.20/44
x = 3.3 (rounded to the nearest cent)
Therefore, the tax on goods worth $60.00 would be $3.30.
Step-by-step explanation:
The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Write an equation and solve to determine the cost of the system with the printer.
Answer:
meaning the computer is $1246
Step-by-step explanation:
$1895-$649=$1246
In September 1998 the population of the country of West Goma in millions was modeled by f(x)=17.9e0.002x. At the same time the population of East Goma in millions was modeled by g(x)=13.6e0.017x. In both formulas x is the year, where x=0 corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.A. 19 millionB. 18 millionC. 17 millionD. 1 million
Option B, 18 million, is the answer to this question.
In September 1998, the population of West Goma in millions was modeled by the function f(x) = 17.9e0.002x, and the population of East Goma in millions was modeled by the function g(x) = 13.6e0.017x. Here, x represents the year, with x=0 corresponding to September 1998.
To find out the point of intersection where the populations are equal, we equate both formulas and solve for x:
17.9e0.002x = 13.6e0.017x
Taking the natural logarithm of both sides of the equation gives:
x ln(17.9) + 0.002x = x ln(13.6) + 0.017x
Simplifying and rearranging terms, we get:
ln(17.9) - ln(13.6) = (0.017 - 0.002)x
0.079 = 0.015x
Solving for x, we get:
x = 5.27 years
Since x is the year, when x = 5.27, it corresponds to the year 1998 + 5.27 ≈ 2003.
When the populations are equal, the population will be f(5.27) ≈ 18 million for West Goma.
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First, find the length of each edge of the cube one side is 3
Plsss help meeeeeeeereeeee
Answer: 61 degrees
Step-by-step explanation:
just trust me
Answer:
You must know the value of x
Which statements must be true? Check all that apply.
A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°
The true statements based on the shape in the given image are:
C'Q = QCLine P T⊥ A'AA'A || B'Bm∠TRB = 90°What is the Reflection of Triangles?The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.
Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.
With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.
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• F(x)=x3+2x2+5+10 factor
Answer:
F(x)=x^3+2x^2+15
Step-by-step explanation:
The Scale Used in a Map is 2 : 10,000. Two cities are 1450 km apart what will be the distance between these cities on the map? (Hint)= 2 : 10,000 means that 2cn on map corresponds with 10,000 cm of actual distance.
Answer:
3.44827586
Step-by-step explanation:
1450:10,000::x:2
=10,000x=2900
x= 10,000
----------
2900
x=3.44827586 km
Consider the following formulas.
a sin Bθ + b cos Bθ = a2 + b2 sin(Bθ + C), where C = arctan(b/a) and a > 0
a sin Bθ + b cos Bθ = a2 + b2 cos(Bθ − C), where C = arctan(a/b) and b > 0
Use the formulas given above to write the trigonometric expression in the form a sin Bθ + b cos Bθ.
11 cos (θ − π/ 4)
The trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ is 11/√2 cos θ.
What is the trigonometric expression?
The write the trigonometric expression in the required, we can start by using the second formula:
a sin Bθ + b cos Bθ = a^2 + b^2 cos(Bθ − C)
where;
C = arctan(a/b) and b > 0Let a = 11 and b = 11/√2, and Bθ = θ − π/4.
Then C = arctan(a/b) = arctan(11/(11/√2)) = arctan(√2).
Substituting these values, we get:
11 cos (θ − π/4) = 11/√2 cos (θ − π/4 + arctan(√2))
= 11/√2 cos (θ - π/4 + π/4)
= 11/√2 cos θ
Thus, we have written the trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ as 11/√2 cos θ.
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Which two statements are true???????
The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
What are perpendicular and parallel lines?Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.
From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,
FG ⊥ HB.
Also, DE ⊥ HB, thus the segments FG ║ DE.
Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
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when solving a word problem, Fiona got answer 2.05 yards. Her friend Marsha's answer was 41/2 yards. Their classmate Fredic got 20.5. What was the answer to the problem if two out of three fifth graders have the correct answer?
Answer:
2.05 yards, Fredic and Fioana's answers are in the same range.
SOMEBODY HELP ME OUT
Answer:
Below
Step-by-step explanation:
Area of a triangle = 1/2 base * height
this triangle has base = 4 ( 3 in) = 12 in and height = 3 (3 in) = 9 in
area = 1/2 * 12 * 9 = 54 in^2
54 in^2 * $ 2.75 /in^2 = $ 148.50
If the window is scaled down by .5 then the dimensions would be
base = 6 in height = 4.5 in
area = 1/2 * 6 * 4.5 = 13.5 in^2
cost would be 13.5 in^2 * $ 2.75/in^2 =~ $37.13
using two water heaters as the inspection unit, calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?
The probability is 0.05.
When using two water heaters as the inspection unit, the center line and control limits consistent with the past 22 days of inspection data are calculated as follows:
Center line (CL) = (X1 + X2)/2
Upper control limit (UCL) = CL + 3 * s/2
Lower control limit (LCL) = CL - 3 * s/2
Where X1 and X2 are the means of the two water heaters, and
s is the standard deviation of the sample data.
The probability of type I error for the control chart in part (b) is typically set at 0.05,
meaning that there is a 5% chance of rejecting the null hypothesis when it is actually true.
Complete question:
When using two water heaters as the inspection unit, (b) calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?
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A wide receiver catches a ball and begins to run for the endzone following a path defined by (x-5, y-50) = t(0,10). A defensive player chases the receiver as soon as he starts running following a path defined by (x-10, y-54) = t(-0. 9, -10. 72)
Write Parametric equations for the path of each player.
A. Receiver: x=50,y=5-10t
Defensive: x=10-0. 9t, y=54-10. 72
B. Receiver: x=5, y=50-10t
Defensive: x=10-0. 9t, y=54-10. 72t
C. Receiver: x=5, y=50-10t
Defensive: x=54-10. 72t, y=10-0. 9t
D. Receiver: x=10-0. 9t, y=54-10. 72t
Defensive: x=5, y=50-10t
The correct answer is B Parametric equations for the path of each player is Receiver: x=5, y=50-10t Defensive: x=10-0. 9t, y=54-10. 72t
The given paths of the receiver and defensive player can be described parametrically, using the parameter t, as:
Receiver: x = 5, y = 50 - 10t
Defensive: x = 10 - 0.9t, y = 54 - 10.72t
We can use the parameter t to represent the time that has elapsed since they started moving. The parametric equations describe the x and y coordinates of each player as functions of t.
By plugging in different values of t, we can determine the positions of the players at different points in time. In this case, the receiver moves horizontally while the defensive player moves at an angle, so their equations are different.
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Five friends went to an amusement park. The group wanted to calculate the total cost, so Kathie wrote the expression 5x + 70. Each of her friends wrote expressions, too.
Determine which friends' expressions are equivalent to Kathie's. Show or explain your reasoning.
Kathie: 5x+70
Stephanie: 3(x+30)+2x−20
Jon: 3x+30+2x−20
Mary: 5(x+14)
Nicole: 3(x+30−20)+2x
Answer:
Stephanie Mary and Nicole
Step-by-step explanation:
Find x.
Please help, and thank you!
Answer: 42
Step-by-step explanation:
We start by looking at the 49 degree angle. A common method of solving geometric problems is to bring things together. To follow this concept, we can say that the 49 degree angle has a vertical angle inside the triangle, which means that angle is 49 degrees. We now work with the 91 degree angle. We can see the 91 degree angle falls on a line, so the other side of the angle equals 180-91=89. All angles in a triangle add up to 180 degrees, so x + 49 + 89 = 180, so x=180 - 138 = 42.
Pls help question in photo
Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.
Expression : What is it?With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.
Here,
The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:
=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)
Condensing each term:
=> 3x³ - 5x²- 3x - 3x² + 5x + 3
=> 3x³ - 8x²+ 2x + 3
Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.
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Calculate the perimeter of the following.
Last month Carmen made $480 working for 30 hours this month she will get a 15% increase in the amount she earns per hour what will be her hourly rate in dollars after the increase enter your answer in the space provided
After the 15% increase in her hourly rate, Carmen's new hourly rate will be $18.40 per hour.
Carmen currently makes $480 in a month by working 30 hours. To find her hourly rate, we can divide her total earnings by the number of hours she worked:
Hourly rate = Total earnings ÷ Number of hours worked
So Carmen's current hourly rate is:
Hourly rate = $480 ÷ 30 = $16 per hour
If Carmen gets a 15% increase in her hourly rate, we can calculate her new hourly rate by multiplying her current hourly rate by 1.15 (since a 15% increase means the new rate is 115% of the current rate):
New hourly rate = Current hourly rate x 1.15
New hourly rate = $16 x 1.15
New hourly rate = $18.40 per hour
This means she will earn $2.40 more per hour than she did before the increase.
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Please help me somebody
The surface area of the cone is 1,966.896 mm²
How to find the surface area of the cone?We can see that the surface area of a cone of slant height H and radius R is:
SA = pi*R² + pi*R*H
Here we can see that R = 27mm/2 = 13.5mm
And H = 32.9 mm
And we know that pi = 3.14
So, replacing that we will get:
SA = 3.14*(13.5mm)² + 3.14*13.5mm*32.9mm
SA = 1,966.896 mm²
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Manny walked around a basketball court the court is 27 m long and 17 m wide what is the perimeter A. G, O. N, S. A. Grade 4 pls help
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m
The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.
Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:
= Length + Length + Width + Width
Slotting the figures in will give:
= 27 + 27 + 17 + 17
= 88 m
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Would a yardstick be a reeasonable tool to use to measure the length of a canoe paddle explain
In conclusion, a yardstick or ruler can be a reasonable tool to use to measure the length of a canoe paddle.
Then, move the yardstick along the length of the paddle, counting the marks until you reach the other end. This will give you an estimate of the length of the paddle in terms of the number of yardstick marks.
For a more precise measurement, you can also use a ruler. Place the zero mark of the ruler at the tip of the paddle and move the ruler along the length of the paddle, counting the small marks that correspond to 1/16th of an inch. This will give you a more precise estimate of the length of the paddle.
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In a class, we have 61 students of different majors. There are 23 chemistry majors (C), 12 math majors (M), 9 engineering majors (E), and 17 students who are undecided (U). Of these students, 4 of them have declared both math and engineering majors. A student will randomly be chosen to win a scholarship. Find the probability of awarding the scholarship to a student who is either a math major or an engineering major. 0.0290 0.7213 0.2787 0.3443
The probability of awarding the scholarship to a student who is either a math major or an engineering major is 0.2787 .Option (c) is the correct answer.
In this question, we are asked to find the probability of awarding the scholarship to a student who is either a math major or an engineering major. Total students (n) = 61 Chemistry majors (C) = 23 Math majors (M) = 12 Engineering majors (E) = 9 Undecided (U) = 17Students with declared majors in Math and Engineering (M ∩ E) = 4
We have to find P(A) = P(student is either a math major or an engineering major).To solve this problem, we will use the addition rule of probability. The addition rule states that the probability of event A or B occurring equals the probability of event A plus the probability of event B minus the probability of both A and B occurring. P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)
Here, P(M) = probability that the student is a math major= number of math majors / total students = 12/61 P(E) = probability that the student is an engineering major= number of engineering majors / total students = 9/61 P(M ∩ E) = probability that the student has declared both math and engineering majors = 4/61So,P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)P(A) = 12/61 + 9/61 - 4/61= 17/61≈ 0.2787
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the midpoint is at -8
Step-by-step explanation:
Write a system of equations to represent the number of each type of basket Jake scored. Explain your thinking.
The system of equations that represents the number of each type of basket Jake scored is given by:
x + y = 13
2x + 3y = 28
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of 2-point shots.
Variable y: Number of 3-point shots.
Jake scored 28 points in his basketball game by shooting only 2-point and 3-point shots, hence:
2x + 3y = 28.
He scored a total of 13 baskets, hence:
x + y = 13.
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(6-y) (6-y)=0
Solve.
Answer:
6
Step-by-step explanation:
y is 6..
Quality Progress, February 2005, reports on improvements in customer satisfaction and loyalty made by Bank of America. A key measure of customer satisfaction is the response (on a scale from 1 to 10) to the question: "Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?" Here, a response of 9 or 10 represents "customer delight." Suppose that the survey selected 350 customers. Assume that 48% of Bank of America customers would currently express customer delight. That is, assume p = .48.
Find the probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within three percentage points of the population proportion. That is, find P(.45 < Picture < .51). (Round your answer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.) P(.45 < Picture < .51) .7372
Find the probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within six percentage points of the population proportion. That is, find P(.42 < Picture < .54). (Round your answer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.) P(.42 < Picture < .54)
From the given data, the probability that the sample proportion is between 0.45 and 0.51 is approximately 0.7372 and between 0.42 and 0.54 is 0.9772.
To solve this problem, we can use the central limit theorem, which states that the distribution of sample proportions will be approximately normal for large sample sizes.
Given that the population proportion is p = 0.48 and the sample size is n = 350, we can calculate the standard error of the sample proportion as:
SE = √(p × (1 - p) / n) = √(0.48 × 0.52 / 350) = 0.025
We want to find the probability that the sample proportion is within three percentage points of the population proportion, or in other words, between 0.45 and 0.51. To do this, we can standardize the sample proportion using the standard error:
z = (P - p) / SE = (0.45 - 0.48) / 0.025 = -1.2
z = (P - p) / SE = (0.51 - 0.48) / 0.025 = 1.2
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values, which represents the probability that the sample proportion is within three percentage points of the population proportion:
P(-1.2 < z < 1.2) = 0.7372
To find the probability that the sample proportion is within six percentage points of the population proportion, or between 0.42 and 0.54, we can use the same approach:
z = (P - p) / SE = (0.42 - 0.48) / 0.025 = -2.4
z = (P - p) / SE = (0.54 - 0.48) / 0.025 = 2.4
Again, using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values:
P(-2.4 < z < 2.4) = 0.9772
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Answer for this please!
Step-by-step explanation:
See image below