Answer:
D. 6 < x < 22
Step-by-step explanation:
For a triangle, the third side must be less than the sum of the other two sides and it must greater than the difference between the other two sides.
The possible length of the third side of the triangular pen, given the Triangle Inequality Theorem and two given side measures, is best described by the inequality D. 6 < x < 22.
Explanation:To find the possible length of the third side of a triangle, we use the Triangle Inequality Theorem. The theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and greater than the absolute difference of the lengths of the other two sides. Here, we have the lengths of two sides as 14 ft and 8 ft.
So the sum of these two sides is 14 + 8 = 22 ft. The difference is |14 - 8| = 6 ft. Therefore, the length of the third side 'x' can range between the sum and the difference of the other two sides. Hence, the correct answer is D. 6 < x < 22.
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Anastasia thinks of a positive integer.
Barry doubles Anastasia's number.
Connor trebles Barry's number.
Damion multiplies Connor's number by 6.
Eve notices that the total of the four numbers is a perfect square.
What is the smallest positive integer that Anastasia could have thought of?
Answer:
6
Step-by-step explanation:
Anastasia thinks of a positive integer, say x
Barry doubles Anastasia's number.
Barry's Number=2xConnor trebles Barry's number.
Connor's Number=3xDamion multiplies Connor's number by 6.
Damions Number=6(3x)=18xTotal of the Four Numbers=x+2x+3x+18x=24x
To find the value of x that makes 24x the smallest perfect square
First, express it as a product of prime factors
[tex]24x=2 X 2 X 2 X 3 X x=2^3X3Xx\\$Multiply both sides by 2 and 3 to make the powers even\\24 X 2 X 3=2^3X3X2 X 3=2^4X3^2\\$24 X [2 X 3]=144 which is a perfect square\\Therefore, x=6[/tex]
Anastasia's initial number could be denoted as 'a'. This number is modified by Barry, Connor, and Damion, and the sum of all these numbers is a perfect square. The smallest positive integer for 'a' that achieves this is 1.
Explanation:Let's denote the number that Anastasia thought of as 'a'. Barry doubles this number, so his number becomes '2a'. Connor triples Barry's number, so his number becomes '6a'. Damion multiplies Connor's number by 6, so his number becomes '36a'. The total of these four numbers must be a perfect square. So the sum 'a + 2a + 6a + 36a' equals a perfect square. That simplifies to '45a', which is equal to a perfect square.
The smallest positive integer when multiplied by 45 and is a perfect square would be when 'a = 1' as 45 itself is not a perfect square. So, the smallest positive integer that Anastasia could have thought of is 1.
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what is the area of a triangle whose side is 17 meters long
Answer:
125.141
Step-by-step explanation:
Assuming that this is an equilateral triangle, I am going to divide this triangle in half to get a right triangle.
17 is our hypotenuse
17/2 = 8.5, this is one of our legs
The other leg is our height, which we will find.
We use Pythagoras Theorem to find the height/leg: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]17^{2} -8.5^{2} = 216.75[/tex]
[tex]\sqrt{216.75}[/tex] = 14.72243186
Now, we use another formula to find the area of the triangle: [tex]\frac{Base*Height}{2}[/tex]
14.72243186 × 17 = 250.2813416
250.2813416 ÷ 2 = 125.1406708
A decorative steel is shown and it is made from circular circle and 6 stems.
The length of each stem is 45cm.
Workout the total length of steel used in the frame
The total length of the steel used in the frame is 270 cm, if the decorative steel up of 6 stems and each stem is 45 cm.
Step-by-step explanation:
The given is,
Decorative steel made from circular circle of 6 stems
The length of the stem is 45 cm
Step:1
We need to find the total length of the steel used in the decorative steel,
Let, T - Total length of the steel
L - Length of the stem
n - Number of stems used in steel frame
Step:2
Formula to find the total length of the steel is,
[tex]T=[/tex] [tex]l[/tex] × [tex]n[/tex]
From given,
[tex]l[/tex] = 45 cm
[tex]n[/tex] = 6 stems
Substitute the values in formula,
[tex]T =[/tex] ( 45 × 6 )
= 270
[tex]T =[/tex] 270 cm
Result:
The total length of the steel used in the frame is 270 cm.
The total length of steel used in the decorative steel frame, made with 6 stems of 45cm each, is 270cm.
Explanation:To solve this question, we simply need to multiply the length of each stem by the number of stems used in the decorative steel. As stated, each stem measures 45cm, and there are 6 stems used in total.
Therefore, the total length of steel used in the frame would be calculated as follows:
Determine the length of an individual stem: 45cmDetermine the total number of stems: 6Multiply these two figures together: 45cm * 6 = 270cmSo, the total length of steel used in the frame is 270cm.
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10. A basketball court is being painted. Everything
shown below will be painted blue. How any square
feet will be painted blue?
Solve the following inequality. Negative one-half p less-than negative 16 Which graph shows the correct solution?
Answer:
p > 10.67
Step-by-step explanation:
Given the inequality -1 1/2p < -16
Before we can represent the inequality on a graph we just simplify it first. On simplification:
-1 1/2p < -16
(-3/2)p < -16
Multiplying both sides by 2
-3p < -32
Dividing both sides by -3 will change the sense of the inequality as shown:
p > -32/-3
p > 32/3
p > 10.67
Find the graph of the resulting inequality in the attachment.
Answer:
Graph A since these idiots cant just put the answer.
Step-by-step explanation:
The variables x and y are related proportionally. When x = 6, y = 14. Find y when x = 48.
When x = 48, y =
Answer:
112
Step-by-step explanation:
When something is related proportionally, that means that multiply by some value constant k, will result in the output.
Thus, to find k, all you have to do is divide y/x
14/6 = 7/3 = k
kx = y
48*7/3 = y = 112
Two candles of equal height start to burn simultaneously. One of the candles is thicker than the other one and burns out in 4 hours, while the thinner one burns out in 2 hours. Both of the candles are extinguished after some time, and the remaining height of the thicker candle is now 3 times as long as the thinner one. How many minutes were the candles burning for?
Answer:
hope this helps you to understand
Use the distributive property to simplify the expression 15(14a)
Answer:
[tex]15(14a) = 210a[/tex]
Step-by-step explanation:
We want to simplify the expression 15(14a) using the distributive property.
We rewrite as:
[tex]15(14a) = 15(10a + 4a)[/tex]
According to the distributive property:
[tex]a(b + c) = ab + ac[/tex]
This implies that:
[tex]15(14a) = 15 \times 10a + 15 \times 4a[/tex]
We simplify to obtain:
[tex]15(14a) = 150a + 60a[/tex]
Add on the right to get:
[tex]15(14a) = 210a[/tex]
Express z=−10\sqrt{3} −10i in polar form.
Express your answer in exact terms, using radians, where your angle is between 0 and 2π radians, inclusive.
Answer:
z = [20/sqrt(3][cos(-2π/3) + isin(-2π/3)]
Step-by-step explanation:
Polar form is
r(cos(theta) + isin(theta))
r = sqrt[(-10/sqrt3)² + (10)²]
r = sqrt(400/3)
r = 20/sqrt(3)
tan^-1[10 ÷ (10/sqrt(3))] = π/3
Theta: -π + π/3 = -2π/3
z = [20/sqrt(3][cos(-2π/3) + isin(-2π/3)]
What is the value of 3 to the 3rd power + 4 to the 2nd power?
Answer:
43
Step-by-step explanation:
3^3= 27
4^2= 16
27+16=43
Answer:
The value of 3 to the 3rd power + 4 to the 2nd power is 43
Step-by-step explanation:
3^3= 27
4^2= 16
27+16= 43
What is the volume of a cylinder with base radius
2and height 9???
Volume of a cylinder will be 113.112cm³.
The volume of a cylinder can be calculated using the formula
V = π r² h,
where r is the base radius and h is the height
Plugging in the values, we get
V = 3.142 × (2 cm)² × 9 cm
V = 113.112 cm³
Samira is playing a game with the spinner shown.
a. What is the theoretical probability that the pointer will land in a section labeled with the letter A on a given spin? Enter as a fraction.
b. Predict how many times the pointer will land in a section labeled with the letter A after 300 spins.
Answer:
A:⅕ and B:60
Step-by-step explanation:
⅕•300/1=300/5=60
Answer:
Answer:
A:⅕ and B:60
Step-by-step explanation:
⅕•300/1=300/5=60
Step-by-step explanation:
Answer:
A:⅕ and B:60
Step-by-step explanation:
⅕•300/1=300/5=60
2x-4y=8
Y=3/2x
solution
Answer:
(- 2, - 3 )
Step-by-step explanation:
Given the 2 equations
2x - 4y = 8 → (1)
y = [tex]\frac{3}{2}[/tex] x → (2)
Substitute y = [tex]\frac{3}{2}[/tex] x into (1)
2x - 4([tex]\frac{3}{2}[/tex] x ) = 8
2x - 6x = 8
- 4x = 8 ( divide both sides by - 4 )
x = - 2
Substitute x = - 2 into (2) for corresponding value of y
y = [tex]\frac{3}{2}[/tex] × - 2 = - 3
Solution is (- 2, - 3 )
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
k² − 4k +
Answer:
4.
Step-by-step explanation:
Hope this helps!
Answer:
k² − 4k + 4
Step-by-step explanation:
recall the following property of perfect square quadratics
(a-b)² = a²- 2ab + b² --------------( eq1)
We are given:
k² − 4k + ? --------------(eq 2)
and we are asked to determine ? for which the expression above is a perfect square.
Manipulating the given equation:
k² − 4k + ? (factor out 2 from the 2nd term), we get:
k² −(2)(k)(2) + ?
now we compare this with the right side of (eq1)
a²- 2 a b + b²
we can clearly see that a = k and b = 2,
substituting this back into eq 2,
k² − 4k + 2²
= k² − 4k + 4
The resulting ΔR'S'T' is an example of what kind of transformation?
Answer:
reflecting across y-axis
Step-by-step explanation:
I hope this helps :)
what is the product of 4^4(4^-7)(4)
Answer:
0.0625
Step-by-step explanation:
Answer: [tex]4^{-2}[/tex]
Step-by-step explanation:
Equation:
[tex]4^4*4^{-7} *4^1[/tex]
When multiplying exponents with the same base, you can add the exponents together to find your answer:
4 + (-7) + 1
How many permutations can you make from the letters A,B,C,D And E?
Answer:
25
Step-by-step explanation:
5x5
A cube has and edge length of 2 centimeters. What is it’s volume, in cubic centimeters?
Answer:
8
Step-by-step explanation:
2x2 is 4 and x 2 is 8. I think im right?
Answer: 8
Step-by-step explanation:
1The volumes of two similar prisms are 972 cm3 and 36 cm3. The surface area of the larger prism is 594 cm2.
What is the scale factor for the similar figures? What is the surface area of the smaller prism?
Answer:
Part 1)
The scale factor of the smaller prism to the larger prism is 3
or
The scale factor of the larger prism to the smaller prism is 1/3
Part 2) The surface area of the smaller prism is 66 square centimeters
Step-by-step explanation:
Part 1) What is the scale factor for the similar figures?
we know that
If two figures are similar, then the ratio of their volumes is equal to the scale factor raised to the cube
Let
z ----> the scale factor
x ---> volume of the larger prism
y ---> volume of the smaller prism
so
[tex]z^3=\frac{x}{y}[/tex]
we have
[tex]x=972\ cm^3\\y=36\ cm^3[/tex]
substitute
[tex]z^3=\frac{972}{36}[/tex]
Simplify
[tex]z^3=27\\z=3[/tex]
therefore
The scale factor of the smaller prism to the larger prism is 3
or
The scale factor of the larger prism to the smaller prism is 1/3
Part 2) What is the surface area of the smaller prism?
we know that
If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared
Let
z ----> the scale factor
x ---> surface area of the larger prism
y ---> surface area of the smaller prism
so
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]x=594\ cm^2[/tex]
[tex]z=3[/tex]
substitute
[tex]3^2=\frac{594}{y}[/tex]
solve for y
[tex]y=\frac{594}{9}=66\ cm^2[/tex]
therefore
The surface area of the smaller prism is 66 square centimeters
I need help with this
Answer: D.
Step-by-step explanation:
7 x (2+3) = 7 x (3+2)
7 x (5) = 7 x (5)
35 = 35
Due to the Commutative Property of Multiplication
Answer:
D
Step-by-step explanation:
7 times 5 equal 35,
and 7 times (3+2) equals 35,
so the D equation are right.
at least $7500 with this event. Tickets for the fundraiser are $75.00 per couple, and they have to pay a $375 fee for renting the community center. Write and solve an inequality to determine the minimum number of tickets they need to sell to reach their goal.
Answer:
75x + 375 [tex]\geq[/tex] 7500
-375 -375
_________________
75x [tex]\geq[/tex] 7125
divide both sides by 75
x is greater than or equal to 95
95 or more to reach goal
Step-by-step explanation:
Principal value of Arccos(-1)
You may have wondered what Euler's Identity means
[tex]e^{i \pi} = -1[/tex]
I hate to break it to you but it just means
[tex]\cos \pi + i \sin \pi = -1 + 0i[/tex]
Equating respective real and imaginary parts,
[tex]\cos \pi = -1, \qquad \sin \pi = 0[/tex]
which you probably already knew.
From the first part,
[tex]\pi = \arccos(-1)[/tex]
That's in the principal value range of cosine.
[tex]\pi = \textrm{Arccos}(-1)[/tex]
Answer: π
A shape is randomly selected from the following quadrilaterals: parallelogram, rhombus, rectangle, square, and trapezoid. What is the probability that it has four right angles, given that it has four congruent sides?
Answer:
1/2.
Step-by-step explanation:
There are 2 quadrilaterals which have 4 congruent sides in the list: A square and a rhombus, The square is the one with four right angles.
So the required probability is 1/2.
The probability that the shape has four right angles, given that it has four congruent sides is 1/2.
What is probability?Probability is the ratio that shows the likelihood of an event occurring from a given set of other events.
It is given that there are 5 shapes.
There are 2 shapes that have congruent sides. They are rhombus and square.
There are 2 shapes that have right angles. They are the square and the rectangle.
P( shape has four right angles, given that it has four congruent sides ) = number of shapes with four congruent sides and four right angles/number of shapes with congruent sides = 1/2
Therefore, we have found that the probability that the shape has four right angles, given that it has four congruent sides is 1/2.
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pls help me i’ll give u a brainlest
Answer:
6 inches
Step-by-step explanation:
The volume of a box can be calculated with the simple formula [tex]l\cdot w\cdot h[/tex], where l represents length, w represents width, and h represents height. You know that [tex]6\cdot 13\cdot h=468[/tex], so dividing both sides by 13 and 6 yields h=6 inches. Hope this helps!
Answer:
The height is 6
Step-by-step explanation:
468 divided by (13 x 6) = height
13 x 6 = 78
468 divided by 78 = 6
What is the simplified quotient?
•0
•1
• x2 - 6x + 9
______________
4x2 + 20x + 25
•4x2 + 20x + 25
______________
x2 - 6x + 9
The correct answer is (1)
Answer:
Is 1
Step-by-step explanation:
Just got it right people. Trust me
(04.01 LC)
The coordinates of point A on a grid are (−3, −2). Point A is reflected across the y-axis to obtain point B. The coordinates of point B are (___, −2). (1 point)
Answer:
(3,-2)
Step-by-step explanation:
reflection over why axis will make the x coordinate positive.
Winona has 4 quarters and 1 nickel. Which does not represent the value of 4 quarters and 1 nickel?
Anything that doesn't show $1.04 is wrong.
Score: 0 O 1 PL
2.3.1
Solve the equation. Check your solution.
2x + 4x - 5= 37
x=
(Simplify your answer.)
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
combine 2x and 4x to get 6x. Add 5 to 37 to get 42. divide the 6 and 42 to get x=7
Find the output, k, when the input, t, is 3.
K=13t-2
K=
The value of the variable 'K' at t = 3 will be 37.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The equation is given below.
K = 13t - 2
The value of the variable K at t = 3 will be given as,
K = 13t - 2
K = 13 x 3 - 2
K = 39 - 2
K = 37
The value of the variable 'K' at t = 3 will be 37.
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Five brothers picked 5 pounds of apples. Two of the
brothers will share 3 pounds of apples equally and the
other 3 brothers will share 2 pounds of the apples
equally. In which group does each brother get a greater
amount of the apples?
Use what you know about division and fractions to
explain why your answer is reasonable. worth 29 points will mark you.
Answer:
Step-by-step explanation:
Two brothers get three pounds to share is the answee.
2 brothers will share 3 pounds. Divide 3 pounds by 2 people:
3/2 = 1-1/2 pounds per person.
3 brothers will share 2 pounds. Divide 2 pounds by 3 people:
2/3 = 2/3 pounds per person.
The 2 brothers sharing 3 pounds will have more apples each.