Triangle ABD is a right-angled triangle. The value of s which is the hypotenuse of the triangle ABD is 17 units.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Here,
Given information:
From the given figure, the following information can be extracted:
Triangle ABD is a right-angled triangle.
Base AB is 8 units, Height BD is 15 units.
s is the hypotenuse of the triangle ABD.
Use the Pythagoras theorem to solve for the value of s or AD,
AD²=AB²+BD²
s²=8²+15²
s²=289
s=17 units
Therefore, the value of s which is the hypotenuse of the triangle ABD is 17 units.
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Using the regression line, or line of best fit, predict the resale value of an 8-year-old car with an original cost of $15,000.a.The 8-year-old car could be worth approximately $2000.b.The 8-year-old car could be worth approximately $5000.c.The 8-year-old car could be worth approximately $3000.d.The 8-year-old car could be worth approximately $4500.
The 8-year-old car could be worth approximately $3000.
The graphs that show the association between two variables in a data collection are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.
The X-axis is used to represent the independent variable or characteristic, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.
In the graph attached below, we can see that when the age of the car is 8 years, the resale value of the car is between points 40 and 20.
Thus, The 8-year-old car could be worth approximately $3000.
(Refer to the image attached for the complete question and graph)
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The ratio of the sides of a triangle is 3:5:6. If the perimeter of the triangle is 154 feet, what are the side lengths?
The side length of the triangle are
33 feet55 feet66 feetHow to find the side length of the triangleA triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is
= a + b + c
where
a, b, and c are the dimensions of the side length of the triangle:
Using the values given in the problem we have
let the ratio be a multiple of x such that
154 = 3x + 5x + 6x
154 = 14x
x = 11
a = 3 * 11 = 33 feet
b = 5 * 11 = 55 feet
c = 6 * 11= 66 feet
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1. Circle which of the following ways to prove that a quadrilateral is a parallelogram. (5 pts.)
I. quadrilateral with both pairs of opposite sides congruent
II. quadrilateral with both pairs of opposite angles congruent
ILI. quadrilateral with one pair of opposite sides both congruent and parallel
A. I only
B. II only
C. I, II and III
D. III only
E. I and II
quadrilateral with both pairs of opposite sides congruent
What is a parallelogram?
A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
If both pairs of opposite sides of a quadrilateral are congruent , then the quadrilateral is a parallelogram.
So, the option I only is correct
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Do the sides 12 16 and 20 make a right triangle?
A triangle with side lengths 12,16, and 20 is a right triangle.
A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.
The formula states that in a right triangle:
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
The three numbers which satisfy the above formula are the Pythagorean triplets
properties of right angle:
The largest angle is always 90º and called the hypotenuse which is always the side opposite to the right angle.
The measurements of the sides follow the Pythagoras rule, which cannot have any obtuse angle.
consider c=20 a=12, b=16 substitute in above formula:
20²=12²+16²
⇒400=144+256
⇒400=400
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Find y for 0.5y-2 2/5=1/2y+2.4
To solve this equation for y, you can follow these steps:
First, get all the terms with y on one side of the equation and all the other terms on the other side. To do this, you can add 2/5 to both sides to get rid of the 2/5 on the left side:
0.5y - 2 2/5 + 2/5 = 1/2y + 2.4 + 2/5
Simplify the left side of the equation:
0.5y - 2 + 2/5 = 1/2y + 2.4 + 2/5
0.5y - 2 + 2/5 + 2/5 = 1/2y + 2.4 + 2/5 + 2/5
0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
(0.5y + 4/5) - 2 = (1/2y + 2.4) + 4/5
Simplify:
0.5y + 4/5 - 2 = 1/2y + 2.4 + 4/5
0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
(0.5y + 4/5) = (1/2y + 2.4) + 4/5
Simplify:
0.5y + 4/5 = 1/2y + 2.4 + 4/5
Combine like terms on each side:
0.5y = 1/2y + 2.4
Subtract 1/2y from both sides:
0.5y - 1/2y = 1/2y - 1/2y + 2.4
0 = 2.4
Solve for y:
0 = 2.4
This equation has no solution, so there is no value of y that satisfies the given equation.
Answer:
Step-by-step explanation:nosoulution
a. Is this a function? Why or why not?
Independent
Variable
Dependent
Variable
4
3
6
12
14
15
8
11
20
22
[tex](m-9)(m-3)[/tex]
Answer:
m^2-11m+27
Step-by-step explanation:
Find the measure of the missing angles.
Answer:
g = 92
K = 91
h = 88
m = 89
Step-by-step explanation:
g = 92; because of vertical angle theorem
k = 91; because of vertical angle theorem
h = 88; because a line is 180 degrees in total so just subtract 180 - 92
m = 89; same thing as h but subtract 180 - 91
Answer:
Step-by-step explanation:
h=180-92=88
g=180-h g=180-88=92 or straight up 92 because the angle across is also 92
m=180-91=89
k=180-k m=180-89=91 or straight up the 91 because the angle across is 91
Question 5
Describe the reflection that maps ST, with vertices S(-7, 1) and T(-7, 5), onto itself. Use decimals, if necessary.
reflection in the line y =______
The reflection that maps ST onto itself is a reflection in the line y = -7.
What is the line of symmetry?
Reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry.
A reflection maps a geometric figure onto itself by "flipping" it across a line of symmetry. In this case, the reflection maps ST onto itself, so the line of symmetry must be a line that ST is reflected across.
To find this line, we can look at the two given vertices of ST, S(-7, 1) and T(-7, 5).
We can see that these points have the same x-coordinate (-7), which means that the line of symmetry must be a vertical line passing through the x-coordinate of -7.
Therefore, the reflection that maps ST onto itself is a reflection in the line y = -7.
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What is undecidable problem give two examples?
An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:
The Whitehead problem The halting problemWhat the halting problem?The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.
A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.
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How do you graph the polar curve r=5cosθ? Drag an equation, variable, or phrase into each box to correctly complete the statements.
Answer:
See graph below
Step-by-step explanation:
The equation r=5cosθ basically means the graph is going to be a circle with a radius of 5/2=2.5 to the right on the horizontal axis since it's cosine.
To graph the function r=5cosθ, we graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ and a radius of 2.5
How to graph the function?The function is given as:
r=5cosθ
The above means that, we want to graph the function f(x) = 4cos(x), such that functional values are used as the corresponding values of θ.
The radius r is calculated using;
r = 5/2
r = 2.5
Hence, the graph of r=5cosθ has a radius of 2.5
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Please hurry its timed
The best option regarding the solutions of the trigonometric equation 2sin(θ) + 1 = 0 in this problem is given as follows:
d. θ = 330º + 360ºn, θ = 210 + 360ºn.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
2sin(θ) + 1 = 0
Then, isolating the sine, we have that:
2sin(θ) = -1
sin(θ) = -1/2.
The values of theta for which the sine is of negative 1/2 are given as follows:
θ = 210º, θ = 330º.
(as the sine is negative for the third and fourth quadrant, hence we have to find the equivalent angle to 30º in each of these quadrants).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option d is correct.
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Choose the correct answer for the problem
Answer:
D
Step-by-step explanation:
You would multiply the -5 and the -1 from the -5x^4 and the -x^5 this would make 5. Also the 4 and the 5 exponets, since they are exponets you need to add if multiplying so it would just be 4+5=9.
For y its just multiplying the exponets which is y^4xy^4=y^8.
Final answer if you bring everything together is 5x^9y^8 also answer D.
Answer:
5x9y8
Step-by-step explanation:
Multiplying two negatives equals a positive ( - ) × ( - ) = ( + )
Write a system of equations modeling the given conditions. Then solve the system by the substitution method and find the two numbers. The sum of two numbers is 71. One number is 27 more than the other. Find the numbers. D Let x be the smaller number and y be the larger number. Write an equation that represents the fact that the sum of the numbers is 71. =71 (Simplify your answer.)
Given that the sum of two numbers is 71 and one number is 27 more than the other, we can set up the following system of equations:
What is the straightforward definition of a system of equations solution?
A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
x + y = 71 (equation 1 represents the fact that the sum of the numbers is 71)
y = x + 27 (equation 2 represents the fact that one number is 27 more than the other)
To solve the system of equations, we can use the substitution method. We'll substitute equation 2 into equation 1:
x + (x + 27) = 71
Combining like terms:
2x + 27 = 71
Subtracting 27 from both sides:
2x = 44
Dividing both sides by 2:
x = 22
Now we can substitute x = 22 back into equation 2 to find the value of y:
y = x + 27
y = 22 + 27
y = 49
So the two numbers are x = 22 and y = 49, and they satisfy the given conditions that the sum of the two numbers is 71 and one number is 27 more than the other.
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Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution and histogram for the data using a lower class limit of 49.5 and a class width of 10. Describe the shape of the distribution Search Search Select an answer variable(s), the correct graph to make is a a) Since data were collected for? Select answer b) For this one the class width is given to be the following: class width Complete the frequency relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Frequency Relative Frequency Classes 495 c) Which of the following is the correct histogram for the given data? Frey 495 595 695 795 Histogram for Test I Score 895 995 Q Search Search 5 Spring ZOO) Final El Pl E U M QUI PUUVITU 495 595 69.5 79.5 Histogram for Test / Score 89.5 99.5 Q a Frequency 49.5 595 695 795895995 Histogram for Test / Score Frequency 595 603 795 Histogram for Tere d) What shape is the histogram above? Select an ant Q Search Search LE
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
What is histogram ?
A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
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please help with math question!!
Answer:
b. cubic
Step-by-step explanation:
hope this helps :)
The CEO of a large company claims that 85% of customers are repeat customers. They define a repeat customer as someone who makes more than one purchase per month. A random sample of 200 customers shows that 162 are repeat customers. Do these data provide convincing evidence at the 5% significance level that less than 85% of customers of this company are repeat customers?
If needed, use the z-table to answer the question.
What is the value of the test statistic? (Round to 2 decimal places.)
What is the P-value of the test? (Enter 4 decimal places.)
Answer:
-1.58
0.0571
Got it right on edge:)
Answer:
-1.58
0.0571
Step-by-step explanation:
EDGE2022
103M) solve on the interval 0 ≤ x < 2pi
sin ( 4x ) = √3 / 2
solving sin ( 4x ) = √3 / 2 , the value of x is 15°
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
For angle of 30° and 60°
sin 30° = 1/2
cos 60° = √3/2
tan60° = √3
for angle 60 °
sin60° = √3/2
cos 60° = 1/2
tan60° = 1/√3
since sin(4x) = √3/2
and sin 60° = √3/2
sin60° = sin(4x)
this means 60° = 4x
divide both sides 4
x = 60/4
x = 15°
therefore the value of x is 15°
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Can you help solve this.
The equation that best represents the line on the first graph is
5x + 3y = 3
Option C is the correct answer.
The equation that best represents the line on the second graph is
x - y = -7
Option A is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Pick two coordinates that the line passes through in each graph.
First graph:
(0, 1) and (-3, 6)
m = (6 - 1)/ (-3 - 0) = 5/-3 = -5/3
(0, 1) = (x, y)
1 = (-5/3)0 + c
c = 1
Now,
y = (-5/3)x + 1
3y = -5x + 3
5x + 3y = 3
Second graph:
(0, 7) and (-5, 2)
m = (2 - 7) / (-5 - 0) = -5/-5 = 1
(0, 7) = (x, y)
7 = 1 x 0 + c
c = 7
y = x + 7
x - y = -7
Thus,
The equation of the first graph is 5x + 3y = 3.
The equation of the second graph is x - y = -7.
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Mhanifa please help! Find the length of the missing side in the following examples. Round your answers to the nearest tenth, if necessary.
Answer:
Use Pythagorean to solve for the missing side.
#4
[tex]x = \sqrt{5.2^2-2.4^2} = \sqrt{21.28} = 4.6 m[/tex]#5
[tex]x = \sqrt{10^2+3^2} = \sqrt{109} = 10.4 cm[/tex]#6
[tex]x = \sqrt{30^2 - 8^2} = \sqrt{836} = 28.9 m[/tex](x-2)(x-1)= in standard form
Answer:
[tex]x^{2} -3x+2[/tex]
Step-by-step explanation:
A function has a y-intercept of -6 and x-intercepts at (2,0) and (6,0). Which graph represents this function?
Answer: I'm guessing it would be a parabola, with the line going through -6 on the y-axis and passing through 2 and 6 on the x-axis, but we cannot see any answers, so therefore we can't answer it accurately.
Step-by-step explanation:
Since the the graph is not given it can be identified by the graph passing through the three coordinate points given.
What are coordinates of a graph?Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate). The origin is located at (0,0).
We have a function that has a y-intercept of -6 and x-intercepts at (2,0) and (6,0).
Since, the graph is not given it cannot be identified clearly what would be the possible graph. But the following points can be concluded -
The graph of the function will cut the y - axis at y = -6.The graph of the function cuts the x - axis at two points i.e. at x = 2 and at x = 6.Any graph passing through the 3 points will be the required graph.
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June and the total of 4/6 hour on her math and reading homework which pair of models could show the amount of time in hours she spends on each subject.
Am I right?
Answer:
yh
Step-by-step explanation:
I need help to get the answer
The length BC of the right triangle is 18 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:
Therefore, using proportion because triangle ABC is similar to triangle BDC.
x / 36 = 9 / x
cross multiply
x × x = 36 × 9
x² = 324
square root both sides of the equation
x = √324
x = 18 units
Therefore,
BC = 18 units
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Isosceles triangle ABC is shown below. Triangle A B C. Angles B and C are x. Sides C A and B A extend to form an exterior angle at point A with a measure of 22 degrees. What is the value of x? 22° 79° 136° 158°
Answer:
79°
Step-by-step explanation:
Assuming the diagram need to complete the question is the same as the one attached below,
From the diagram,
∠A+∠B+∠C = 180 (sum of the angles in a triangle is 180)..................... Equation 1
Given: ∠A = 22° (Vertically opposite angles are equal), ∠B = x, ∠C = x
Substitute these values into equation 1
22+x+x = 180
2x+22 = 180
2x = 180-22
2x = 158
x = 158/2
x = 79°
Hence the value of x is 79°
Answer:
79
Step-by-step explanation:
i got it right
[(-7)+9]+(______)=9+[-7+4]
Fill in the blanks
Answer:
[(-7)+9]+(+4)=9+[-7+4]
Simplify:- 3/11of(1/3+5/9)÷9/15
Answer:
=3/11 of (1×3+5/9)÷9/15
=3/11 of (8/9)÷9/15
=3/11 of 8/9÷9/15
=8/33÷9/15
=8/33×15/9
=40/99
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Missy is saving to attend a week at summer camp. She needs $250.00 to register. Her parents will contribute $75.00. She needs to raise the rest of the money babysitting for $12.00 per hour. What is the minimum number of hours she must babysit in order to attend camp?
Answer:
At least 15 hours
Step-by-step explanation:
First, subtract the $75 that her parents will contribute:
250 - 75
= 175
So, from babysitting, she will have to raise $175
Divide this by 12 to find how many hours she has to babysit:
175/12
= 14.583
We have to round this up to a whole number, which will be 15.
So, Missy will have to babysit for a minimum of 15 hours
Lori's bookcase has 5 mystery novels and 8 romance novels. She randomly picks out 2 mysteries and 3 romances. How many different sets of 5 novels could Lori pick out?
Answer:
I would say 6 sets
Step-by-step explanation:
Mystery = 5 | Romance = 8
0 5
1 4
2 3
3 2
4 1
5 0
each time she picks out 5 novels. There is only 5 mystery novels so you cant go past that
....but that's just me personally
Answer:
Step-by-step explanation:
560
Identify the figure that illustrates "a reflection in line k."
Answer:
A
Step-by-step explanation:
The figure that illustrates a reflection in line k is figure A.
We have given that the figure
We have to determine the correct option a reflection in line k.
What is the reflection?
A reflecting line is a perpendicular bisector. When a figure is reflected, the reflecting line is the perpendicular bisector of all segments that connect pre-image points to their corresponding image points.
Therefore option A is correct.
Therefore the figure that illustrates a reflection in line k is figure A.
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