Step-by-step explanation:
the area of a triangle is base times height divided by 2.
A = (b × h) / 2
so, when b = 3 and h = 4, then
A = (3 × 4) / 2 = 12 / 2 = 6
correct.
now the other way around
we know the area (6).
=> 6 = (b × h) / 2
=> 12 = b × h
well, b=3, h=4 is one possible solution for this.
but so is e.g. b=2, h=6, or b=12, h=1, or ...
and that is just the natural numbers. then there are rational numbers and so on.
therefore there is an infinite set of possible (b, h) pairs that satisfy the equation 12 = b × h.
therefore the statement that we can conclude out of a given triangle area of 6 that b must be then 3 and h must be 4 is wrong.
simple - it is one equation with 2 variables and has therefore usually not just one solution.
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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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
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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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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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
Which inequality correctly orders the numbers -2/3, -11/3, and 2.5 if you tell me right now then i will send you the newest phone and 1,000,000 dollors
Answer: As for the inequality question you asked,
-2/3, -11/3, and 2.5 are decimal numbers.
-11/3 is smaller than -2/3 because -3.67 is smaller than -0.67
-2/3 is smaller than 2.5 because -0.67 is smaller than 2.5
So the inequality that correctly orders the numbers -2/3, -11/3, and 2.5 is -11/3 < -2/3 < 2.5
It's worth noting that this inequality uses the less than (<) symbol to show the order of the numbers from the smallest to the largest, and it's also worth to remember that this inequality is true only for these specific values, if any of the values were changed it would've resulted in a different inequality.
Step-by-step explanation:
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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[tex](m-9)(m-3)[/tex]
Answer:
m^2-11m+27
Step-by-step explanation:
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
a. Is this a function? Why or why not?
Independent
Variable
Dependent
Variable
4
3
6
12
14
15
8
11
20
22
Find the inverse of A in order to decode "-66, 186, 2, 98".
The decoded message is
Answer: look up zodiac signs and if that dont work look up ailian signs
Step-by-step explanation:
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 ( - ) × ( - ) = ( + )
What is 2x10-2+6 please help
Answer:
24
Step-by-step explanation:
What is 2x10-2+6?
2 × 10 - 2 + 6 = (remember PEMDAS)
20 - 2 + 6 =
18 + 6 =
24
Answer:
24 should be your answer
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]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
[(-7)+9]+(______)=9+[-7+4]
Fill in the blanks
Answer:
[(-7)+9]+(+4)=9+[-7+4]
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
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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(x-2)(x-1)= in standard form
Answer:
[tex]x^{2} -3x+2[/tex]
Step-by-step explanation:
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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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
please help with math question!!
Answer:
b. cubic
Step-by-step explanation:
hope this helps :)
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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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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PLS ANSWER QUICK THANK YOU
Answer:
Option A is correct
8.96×10^7
What did Ponyboy think might have separated the Greasers from the
Socs? *
5 ро
money
grades
cars
O
girls
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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Work out
m
and
c
for the line:
2
y
−
4
x
=
2
Answer:
General equation : y = mx + c
2y - 4x = 2
2y = 4x + 2
y = 2x + 1
Therefore m = 2 and c = 1.
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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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: