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Explanation:
For this answer choice, we have p = 43, q = 133, and r = 89. Note how p+r = 43+89 = 132, which is not larger than the third remaining side q = 133. Therefore, p+r > q is false and a triangle cannot be formed.
A triangle is only possible if and only if adding any two sides leads to a sum larger than the third side (triangle inequality theorem).
Put another way, we must have these three conditions hold true for a triangle to form:
p+q > rp+r > qq+r > pIf any of those three are false, then we cannot make a triangle with side lengths p,q,r
-----------------
Let's go over choice C for an example in which we can form a triangle
p = 5, q = 6, r = 7
We can see that,
p+q = 5+6 = 11 which is greater than r = 7. So p+q > r is true.p+r = 5+7 = 12 which is greater than q = 6. So p+r > q is true.q+r = 6+7 = 13 which is greater than p = 5. So q+r > p is true.All three conditions are true, and therefore we have a triangle that is possible with side lengths p = 5, q = 6, r = 7. I recommend cutting out slips of paper with these lengths to try it out yourself, so you have a real world example to play with. Choices A and D are a similar story to choice C, so we can rule out all three of these choices.
A right triangle RST is drawn. A square is drawn onto each side of the triangle. The area of the square A is 49 square meters and the area of the square B is 144 square meters. Determine the length, x, of the indicated side of the right triangle.
Answer:
144+49=x²
193. =x²
X =√193
x. =+-13.89
Graph the function.
g(x) = -1/5(x+5)^2-2
Answer:
Step-by-step explanation:
The first one is Crosses the axis at (1, 0). The second one is Crosses the axis at (−4, 0). The third one is touching the axis at (−5, 0).
To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²
5 units right and 9 units down
Step-by-step explanation:
Let us revise the translation
1. If the function f(x) translated horizontally to the right by h units, then
its image is g(x) = f(x - h)
2. If the function f(x) translated horizontally to the left by h units, then
its image is g(x) = f(x + h)
3. If the function f(x) translated vertically up by k units, then its image
is g(x) = f(x) + k
4. If the function f(x) translated vertically down by k units, then its image
is g(x) = f(x) - k
∵ f(x) = x²
∵ g(x) = (x - 5)² - 9
∴ g(x) = f(x - 5)² - 9
∴ h = 5 ⇒ 5 units right
∴ k = -9 ⇒ 9 units down
∴ f(x) translated 5 units to the right
∴ f(x) translated 9 units down
To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²
5 units right and 9 units down
The graph of g(x) = -1/5(x + 5)² - 2 is plotted making use of the points it passes.
What is a function?A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.
The given function is g(x) = -1/5(x + 5)² - 2.
In order to plot its graph, consider following values of x and y as follows,
For x = 0,
g(x) = -1/5(0 + 5)² - 2
= -7
For x = -5,
g(x) = -1/5(-5 + 5)² - 2
= -2
Now as the given function has its degree as 2, it is parabolic.
Thus, its graph can be drawn as follows,
Hence, the graph of the given function is drawn clearly.
To know more about function click on,
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Jane got scores of 67, 83, and 79 on three math tests. What must her score be on the fourth test for the average of the four to be 80?
What is the surface area of this figure? Round to the nearest tenth if necessary.
10 ft
12 ft
6 ft
8 ft
18ft times 12ft long
Answer:
216 ft
Step-by-step explanation:
18 x 12 = 216 so ya ezzzzzz :)))))
How many real solutions does the quadratic equation below have?
y = 2? + 5x + 10
Answer:
their are 2
Step-by-step explanation:
Classify the triangle by its sides and angles.
100 m
100 m
120 m
Which is the height of the triangle?
O A. 40 m
B. 60 m
O C. 80 m
D. 100 m
O e 110 m
B. 60 m is the height of the triangle
Answer:
B. 60m
Step-by-step explanation:
i took the test
Pls help
What is the magnitude of the vector u = <4, 7>?
[tex]\sqrt{4^{2}+7^{2}}=\sqrt{16+49}=\boxed{\sqrt{65}}[/tex]
Pls help me with this question I need to turn this in
please help as soon as possible
18. 23 units
19. x = 1
Which of the following is a typical number of books one student checked out?
Answer:
2 Books
Step-by-step explanation:
Because more kids checked out 2 books than any other number
Translate algebraic words to symbols.
W
Twelve more than x is greater than
two
A. 12x>2
B. 12/x < 2
C. x + 12>2
D. 12-x>2
Answer:
C. x + 12 > 2
Step-by-step explanation:
Given:
Twelve more than x is greater than two
Required:
Translate to symbols
Solution:
Twelve more than x can be represented as "x + 12"
Greater than is represented by the symbol ">"
Two represented as "2"
Therefore, the translation to symbols would be:
x + 12 > 2
1. 8x – 4 = 12x + 12
2. 7(x – 2) + 3x = 46
are 2 different questions, answer the 2 if you can
On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.
Answer:
After a quick online search, I've found that the complete question is:
a) Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs the same amount, complete the table of values representing the cost of gummy candy in pounds.
Then we want to graph the points, and then comes our question:
c) On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.
So first, we know that this is a proportional relationship (each pound of candy costs the same)
And 0 pounds of candy should cost $0.
Then the relation between y (price) and x (number of lb) is:
y = k*lb
where k is the cost per lb.
Knowing that Parker paid $4.50 for three pounds of gummy candy, the relation is:
$4.50 = k*3lb
($4.50/3lb) = k = $1.50/lb
Then the linear relation is:
y = ($1.50/lb)*x
Now, in this question we can see that Parker's friend was charged $5 for ( 1 and 1/2) lb of candy.
If we replace those values in the equation, we get:
$5 = ($1.50/lb)*(1 + 1/2)lb = $2.25
This equation is false, then, in terms of the graph, the point ( (1 and 1/2)lb, $5) does not belong on the graph that you found in the previous points.
What is the 5004300 in standard form
Answer:
In standard form,
5004300. Five Millon four thousand and three hundred.
The standard form of 5004300 is [tex]50.043[/tex] × [tex]10^{5}[/tex].
What is standard form of a number?The standard form of a number is a way of writing the numbers in a form that follows a certain rule.
According to the given question.
We have a number 5004300.
The standard form of 5004300 is given by
[tex]50.043[/tex] × [tex]10^{5}[/tex]
Hence, the standard form of 5004300 is [tex]50.043[/tex] × [tex]10^{5}[/tex].
Find out more information about standard form of a number here:
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calculate the lateral area and volume of a truncated cone of radii 10cm and 12cm and a slant height of 15cm
Answer:
The lateral surface is 212
Step-by-step explanation:
Lateeal surface area is = Ph
12+12+10+10(15)=212
Pablo planted a tomato plant for his neighbor.
The tomato plant has 2 tomatoes. Pablo said
that he expects the number of tomatoes to
triple each month. After a certain number of
months, he expects there to be 54 tomatoes.
If m represents the number of months, which
equation could Pablo's neighbor use to
determine when Pablo expects there to be
54 tomatoes?
A. 3.2 = 54
B. 3.m2 = 54
C. 2.3" = 54
D. 2 m² = 54
Answer:
i think its 2m²=54, not sure thought
can ace and expert help me help
Answer:
24
Step-by-step explanation:
Highest 33
lowest 9
range = 33 - 9 = 24
What is the range of fat grams for the five sandwiches?
15162121.224 ____________________Solution :-Given Information :-Highest grams fat in sandwich ➢ 33 gLowest grams fat in sandwich ➢ 9 gTo Find :-Range of fat grams for the five sandwiches. Formula Used :-Range = Highest limit - Lowest limit Calculation :-⇒ Range of fat grams for the five sandwiches = 33 - 9
Calculating further, We get,
⇒ Range of fat grams for the five sandwiches = 24 g
Since, 24 is also given as option E. 24. Therefore, option E. 24 is the correct answer.
____________________Final Answer :-Option E. 24 is the correct answer. ____________________
Find the number of degrees in the third angle of
the triangle
The figure is not drawn to scale.
The measure of the missing angle I'd 100 43
Answer:
37
Step-by-step explanation:
triangles' inside angles always equal 180. so 100+43=143. 180-143=37
Gracie bought a bag of 70 marshminnows. She wants to divide them evenly among herself, Lilly, and Gilda. How many marshminnows will be left over after she has evenly divided them?
what is the surface area of a rectangular prism if the length is 14.5 square inches, the width is 11 square inches, and the height is 2 square inches?
PLEASE HELP ITS DUE TODAY
I need formulas for volumes of cones and cylinders. And other 8th grade math formulas if you have any, preping for eog.
Answer:
(Shown below)
Step-by-step explanation:
Here are a few formulas for shapes:
Perimeter of a rectangle: Length + Length + Width + Width = PerimeterArea of a rectangle: Length * Width = AreaPerimeter of a triangle: Base + Height + Hypotenuse = PerimeterArea of a triangle: (Base * Height)/2 = AreaTo find the missing side length in a right triangle: [tex]a^{2} + b^{2} = c^{2}[/tex]Circumference of a circle: (2 * [tex]\pi[/tex] * r) = CircumferenceArea of a circle: [tex]\pi (r)^{2}[/tex] = AreaSurface area of a rectangular prism: All sides added up = Surface areaVolume of a rectangular prism: Length * Width * Height = AreaVolume for a sphere: [tex]\frac{4}{3}\pi r^{3}[/tex] = VolumeVolume for a cylinder: [tex]pi (r^{2})h[/tex] = VolumeVolume for a cone: [tex](pi (r^{2})h)/3[/tex] = VolumeHere a few formulas for functions, if you need it:
Linear function: y = mx + bQuadratic function: [tex]ax^2+bx+c = 0[/tex]Quadratic formula: (Shown at the bottom)Hope this helps!
Find the scale factor of the similar shapes below. For your answer please only input the number. Do not include units with your answer.
Answer:
x is 12
Step-by-step explanation:
7.5÷5=1.5
1.5×8=12
Jennifer made a baby blanket that is 2 feet by 3 feet. She has a queen-size blanket that is 6 feet by 9 fee How does the area of the baby blanket compare to the area of the queen-size blanket?
Answer:
1/9
Step-by-step explanation:
2x3=6
6x9=54
54 divided by 6 = 9
Therefore 6 is 1/9 of 54
Hope this helps.
An Olympic-size swimming pool is approximately 50 meters long by 25 meters wide. What distance will a swimmer travel if they swim from one corner to the
opposite?
type your answer...
meters
Answer:
56m
Step-by-step explanation:
Diagram:-[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier (0,0)(0,0)(5,0)\qbezier (0,0)(0,0)(0,3)\qbezier (0,3)(0,3)(5,3)\qbezier (5,3)(5,3)(5,0)\qbezier (0,3)(5,0)(5,0)\qbezier (0,0)(0,0)(5,3)\put (-0.4,-0.2){\sf D}\put (-0.2,3.1){\sf A}\put (5.2,3.1){\sf B}\put (5.2,-0.2){\sf C}\put (2.4,1){\sf O}\put (2,-0.4){\bf 50\:m}\put (-1,1.5){\sf 25\:m}\end {picture}[/tex]
Length=50m
Breadth=25m
Diagonal be x
It will form right angle triangle Like below[tex]\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 25m}\put(2.8,.3){\large\bf 50m}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\put(3.8,1.3){\large\bf $\Theta$}\end{picture}[/tex]
So
➝x^2=50^2+25^2
➝x=√(50)^2+(25)^2
➝x=√2500+625
➝x=√3125
➝x=55.9m
➝x=56m(approx)
To those who can make a poem about math, please help me with this. I really need it right now but please answer it correctly. :(
Directions: Write a poem using the following words in the box.
Function
Range
Relation
Vertical Line
Imaginary
Domain
Variable
not Function
Thank you in advance!
Answer:
Poem:
Function is binary relation of two sets
have a single output but
not Function is having no function
have multiple output.
Range is a function refer to two closely concepts
but
Domain is a set of possible input values with concepts.
All the function are relation but
not all relation are function.
Relation is a collection of ordered pair but
imaginary is a collection of complex number written in imaginary unit.
Vertical line is parallel to y-axis but
horizontal line is parallel to x-axis.
What angle is this? A: Adjacent. B: Vertical. C: Complementary. D: Supplementary.
I WILL GIVE BRAINLIST TO RIGHT ANSWER
Answer:
Supplementary!
Answer:
Complementary I believe.
correct me if I’m wrong
if not adjacent
the cylindrical part of an architectural column has a height of 320 cm and a diameter of 30 cm. find the volume of the cyndrical part of the coulmn . use 3.14 for and round your answer to the nearest cubic centimeter if needed.
I need help if your an ap student 5!∛54-3.14
Answer:
100-.idrk
Step-by-step explanation:
im the best