The length of the envelope is 6.3 inches
Step-by-step explanation:
Width of the envelope = 3 inches
Diagonal of the envelope = 7 inches
To find:
The length of the envelope.
Let the length of the envelope be 'l'
We can use pythogoras theorem to calculate the length.
l = √(49-9)
l = √(40)
l = 6.3 inches
The length of the envelope is 6.3 inches
Problem Solving
11. Maya's family is building a deck. The deck has
6 sides. Each side of the deck is 12 feet long
What is the perimeter of the deck?
Answer:
72 feet
Step-by-step explanation:
The deck has 6 SidesEach side of the deck is 12 feet longThis is an example of a regular hexagon. A hexagon is a polygon that has 6 sides. It is regular because all the sides are equal.
Perimeter of a Regular Hexagon=6l
Length of one side, l=12 feet
Therefore:
Perimeter of the deck = 6 X 12 =72 feet
Name
1. Oscar and Eli set up a lemonade
stand. If they have prepared 23
gallons of lemonade, how many
1-cup servings can they sell?
Oscar and Eli can sell 368 1-cup servings of lemonade because there are 16 cups in 1 gallon, and they have 23 gallons of lemonade.
Explanation:Calculating Servings of LemonadeOscar and Eli have prepared 23 gallons of lemonade and want to know how many 1-cup servings they can sell. First, we need to know the equivalent of gallons to cups. There are 16 cups in 1 gallon. Therefore, we multiply 23 gallons by 16 cups per gallon to find the total number of cups available:
23 gallons x 16 cups/gallon = 368 cups. Thus, they can sell 368 1-cup servings of lemonade.
To summarize the conversion:
1. Identify the conversion rate between gallons and cups (1 gallon = 16 cups).
2. Multiply the total gallons of lemonade by the conversion rate to get the total cups (23 gallons x 16 cups/gallon).
Is 6 to the 3rd power equal to 2•2•2•3•3•3? Full explaination and reasoning.
Answer:
yes
Step-by-step explanation:
if you do 6^3 you get 216
6*6*6=216
6*6=36
36*6=216
2*2*2*3*3*3=216
2*2=4
4*2=8
8*3=24
24*3=72
72*3=216
Circle C has diameter AB. The coordinates of A are (5,1) and the coordinates of C are (6,10). Find the coordinates of B.
Answer:
(7, 19)
Step-by-step explanation:
We know that we are talking about circle C, which means that the center is point C. Since the diameter is AB, that means that AB goes through the center C and that center C is the midpoint of the segment AB.
Say the coordinates of B are (x, y). We can use the Midpoint Theorem to figure out B. The Midpoint Theorem states that for two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the coordinates of the midpoint are: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex].
Here, our two points are A(5, 1) and B(x, y). Then, the midpoint is: [tex](\frac{5+x}{2} ,\frac{1+y}{2} )[/tex]. We already know the midpoint is C(6, 10), so we can just set 6 equal to [tex]\frac{5+x}{2}[/tex] and set 10 equal to [tex]\frac{1+y}{2}[/tex]:
6 = [tex]\frac{5+x}{2}[/tex] ⇒ 12 = 5 + x ⇒ x = 12 - 5 = 7
AND
10 = [tex]\frac{1+y}{2}[/tex] ⇒ 20 = 1 + y ⇒ y = 20 - 1 = 19
So, the coordinates of B is: (7, 19).
Hope this helps!
Answer:
(7 , 19)
Step-by-step explanation:
Centre is the midpoint of the diameter
C = Midpoint of AB
Let B: (x,y)
(6,10) = (x+5)/2, (y+1)/2
12 = x + 5
x = 7
20 = y + 1
y = 19
The equation x^2 - 3x + a = 0 has two roots. One root of the equation is 2. What is the other root?
a. -2
b. -1
c. 1
d. 3
The other root is 1, and the correct answer is: c. 1
The quadratic equation [tex]x^2 - 3x + a = 0[/tex] has two roots, and given that one of the roots is 2, we can use the fact that the sum of the roots is equal to the coefficient of the linear term (-b/a).
In this case, the linear term is −3x, so the sum of the roots is 3. Since we know one root is 2, the other root must be such that when added to 2, the sum equals 3.
Therefore, the other root is 3 − 2 = 1.
This demonstrates the application of the sum of roots formula in solving for the other root when one root is known. Hence, the correct answer is 1, which is option (c).
What gives the range of the function y=|x-1|+7
The range of the function y=|x-1|+7 is all real numbers greater than or equal to 7, as the absolute value ensures non-negative values to which 7 is added.
The range of the function y=|x-1|+7 can be determined by analyzing the nature of the absolute value function and the constant term. The absolute value function, |x-1|, ensures that the output is always non-negative for any value of x, since it represents the distance from 1 on the number line, which cannot be negative. Therefore, when we add 7 to this non-negative value, the smallest value y can take is when |x-1|=0, which is when x=1. So, at x=1, y will be 7 since we have 0+7. For any other value of x, |x-1| will be positive, and when adding 7, y will be greater than 7. Hence, the range of y is all values greater than or equal to 7.
What is the value of k?
k=
Answer:k=2
Step-by-step explanation:
Rewrite the equation by completing the square.
x^2-2x+1=0
Answer:
(x - 1)² = 0
Step-by-step explanation:
Given
x² - 2x + 1 = 0 ( subtract 1 from both sides )
x² - 2x = - 1
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 1)x + 1 = - 1 + 1
(x - 1)² = 0
Write an equation that represents “Eight more than the quotient of a number and two is fourteen.”
Answer:
I think it's supposed to be 8x+2=14
Cylinder A
What is the ratio of the volume of Cylinder A to the volume of Cylinder B?
Given:
For cylinder A:
Radius = 3 unit
Height = 4 unit
For cylinder B:
Radius = 4 unit
Height = 3 unit
To find the ratio of the volume of cylinder A to the volume of cylinder B.
Formula
The volume of a cylinder is,
[tex]V = \pi r^{2} h[/tex]
where, r be the radius and
h be the volume of the cylinder.
Now,
For cylinder A
Putting, r = 3 and h = 4 we get,
Volume [tex]V_{A}[/tex] = [tex]\pi (3^{2} )(4)[/tex]
or, [tex]V_{A} = 36\pi[/tex]
For cylinder B
Putting, r = 4 and h = 3 we get
Volume [tex]V_{B}=\pi (4^{2} )(3)[/tex]
or, [tex]V_{B}= 48\pi[/tex]
Now,
The ratio [tex]\frac{V_{A} }{V_{B}} = \frac{36\pi}{48\pi}[/tex]
or, [tex]\frac{V_{A} }{V_{B}} = \frac{3}{4}[/tex]
Hence,
The ratio of the volume of Cylinder A to the volume of Cylinder B is [tex]\frac{3}{4}[/tex]. Option A
can someone please help me match the vocabulary to the graph!
Answer: A2, B3, E1, C5, D4
Step-by-step explanation:
1. A is Maxium because it is the highest point on the graph
2.B is Midline because it is the “middle”
3.C is Peroid because the graph in a way ends or meets back in the middle
4.D is Minimum because it is the lowest point on the graph
5.E is Amplitude
a square pizza box has a width of 24 in. What is the area of the largest circular pizza that could fit in the box?
Answer: 72 in
Step-by-step explanation:
If the area is 96 inches the it would be 72
In Tammy's video game, she receives a treasure box for completing a mission. Each treasure box gives Tammy a special item. Every treasure box has a 17%
chance of having an amulet, a 29% chance of having a wand, and a 54% chance of having a ring.
Tammy wants to simulate what could happen for the next ten treasure boxes.
Let 1 to 17 represent a treasure box having an amulet, 18 to 46 a wand, and 47 to '100 a ring.
A random whole number from 1 to 100 is generated for each simulated treasure box.
Here is Tammy's simulation.
Treasure box 1
Random number 55
2 3 4
57 100 32
5
13
6
23
7
14
8
60
9
6
10
2
X
5
?
In the simulation, which item was in each treasure box?
(a) Treasure box 2: (Choose one)
(b) Treasure box 4: (Choose one)
(c) Treasure box 7: (Choose one)
Write an exponential function in the form
y
=
a
b
x
y=ab
x
that goes through points
(
0
,
4
)
(0,4) and
(
3
,
2916
)
(3,2916).
Answer:
y = 4[tex](9)^{x}[/tex]
Step-by-step explanation:
Using the given points to find a and b
Using (0, 4), then
4 = a[tex]b^{0}[/tex] ⇒ a = 4, thus
y = 4[tex]b^{x}[/tex]
Using (3, 2916), then
2916 = 4 b³ ( divide both sides by 4 )
729 = b³ ( take the cube root of both sides )
b = [tex]\sqrt[3]{729}[/tex] = 9
Thus
y = 4 [tex]9^{x}[/tex] ← is the exponential function
The sizes of seven exterior angles of an octagon are: 42, 110, 13, 67, 55, 11 and 53. What is the size of the eighth exterior angle?
Answer:
9 degrees.
Step-by-step explanation:
For ALL polygons, the exterior angles add up to 360 degrees.
Therefore the 8th exterior angle = 360 - (42+110+13+67+55+11+53)
= 360 - 351
= 9 degrees.
Answer:
9°
Step-by-step explanation:
Always some of exterior angle of any polygon is 360
42 + 110 + 13 + 67 + 55 +11 + 53 + x = 360
351 +x = 360
x = 360 - 351
x = 9
Triangle ABC has vertices A(-2, 3), B(0, 3), and C(-1,-1). Find the coordinates of the image after a reflection over the
x-axis.
Given:
Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).
We need to determine the coordinates of the image after a reflection over the x - axis.
Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.
Coordinates of the point A':
The general rule to reflect the coordinate across the x - axis is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Substituting the point A(-2,3), we get;
[tex](-2,3)\rightarrow (-2,-3)[/tex]
Thus, the coordinates of the point A' is (-2,-3)
Coordinates of the point B':
The general rule to reflect the coordinate across the x - axis is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Substituting the point B(0,3), we get;
[tex](0,3)\rightarrow (0,-3)[/tex]
Thus, the coordinates of the point B' is (0,-3)
Coordinates of the point C':
The general rule to reflect the coordinate across the x - axis is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Substituting the point C(-1,-1), we get;
[tex](-1,-1)\rightarrow (-1,1)[/tex]
Thus, the coordinates of the point C' is (-1,1)
Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)
Answer:
A - (-2,-3)
B - (0,-3)
C - (-1,1)
Step-by-step explanation:
A picture is to be mounted on a board.
Show that the picture and the board are not mathematically similar.
A picture and the board it is mounted on are not mathematically similar because their corresponding sides do not have the same proportions, with the board generally having extra space around the picture that alters the length-to-width ratio. Additionally, artistic elements like tension and abstractness in images disrupt dimensional consistency that similarity requires.
Explanation:To show that a picture and the board it is mounted on are not mathematically similar, we must understand similarity in a mathematical context. For two figures to be similar, they must have the same shape but not necessarily the same size, meaning their corresponding angles are equal, and their corresponding sides are in proportion. When we mount a picture on a board, the picture itself has dimensions that are different from that of the board - the board is usually larger to provide a border or frame around the picture. Since the additional border provided by the board changes the overall dimensions, the two objects cannot be considered mathematically similar.
The concept of similarity also involves dimensional consistency. If the picture and the board were to be similar, the ratio of the length to width in the picture would have to be the same as that of the board. However, in most scenarios, a picture needs to be mounted with additional space around it, thus altering the ratio.
Additionally, from an artistic point of view, tension within a painting or an abstract representation might disrupt the dimensional consistency that mathematical similarity requires. Various factors such as perspective can create a visual illusion that skews perceived dimensions, making it impossible for the two to be similar. When a picture includes a pattern that has a specific repetition with variation, it does not satisfy the conditions of mathematical similarity when placed on a uniform board.
Plz help
Thank you very much!
Answer:
I believe the answer is 8.
Step-by-step explanation:
8.02 rounded to the nearest tenth is 8
3 times a number plus 5 is the equal to the same number increased by 17. what is the number
Answer:
The number is 6
Step-by-step explanation:
Let the number be x
3 times a number plus 5 = 3x +5
Same number increased by 17 = x + 17
3x + 5 = x + 17
3x -x + 5 = 17
2x + 5 = 17
2x = 17 - 5
2x = 12
x = 12/2
x = 6
The solution to the problem 3x + 5 = x + 17 is x = 6. This involves setting up an algebraic equation using the given conditions and then solving for x.
Explanation:This problem seems to be a basic algebra problem. You can begin by setting up the equation based on the sentence given. The sentence translates into the equation: 3x + 5 = x + 17 where x is the unknown number you’re solving for. Then, you need to solve for x by isolating it on one side of the equation.
Step-by-step explanation: Subtract x from both sides of the equation to get 2x + 5 = 17. Then, subtract 5 from both sides to get 2x = 12. Finally, divide by 2 to solve for x. This will give you: x = 6. Therefore, the number that fits the condition in the problem is 6.
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Which of the following is the triangle proportionality theorem
Answer: a line parallel to one side of a triangle divides the other two sides proportionally. you’re welcome :)
Tracy has 5 cans of vegetable juice in her refrigerator. Four of the cans each have 6 ounces of juice. Write an expression for the total ounces of juice Tracy has in her refrigerator. if the fifth can has 12 ounces, what's the total ounces of juice Tracy has?
Answer:
4(6)+12=36
Step-by-step explanation:
The required, Tracy has a total of 36 ounces of juice in her refrigerator.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The expression for the total ounces of juice Tracy has in her refrigerator is:
4(6) + 12
The expression shown above shows the sum of the ounces of juice in the four cans that have 6 ounces each, plus the ounces of juice in the fifth can that has 12 ounces.
Evaluating this expression:
4(6) + 12 = 24 + 12 = 36
Therefore, Tracy has a total of 36 ounces of juice in her refrigerator.
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Danila breeds peregrine falcons. She recorded the breadth (in mm) of each egg and the mass (in g) of the falcon
chick that hatched from it.
After plotting her results, Danila noticed that the relationship between the two variables was fairly linear, so she
used the data to calculate the following least squares regression equation for predicting the mass of the chick
from the breadth of the egg:
y = -47 + 2x
What is the residual of a 29 g falcon chick who hatches from an egg with a breadth of 40 mm ?
Answer:
residual = - 4
Step-by-step explanation:
The residual is the difference between the actual mass of the falcon chick and the mass our regression line would have predicted.
residual = actual mass - predicted mass
actual mass = 29 grams
The predicted mass of 40 mm breadth of egg can be calculated by using the regression equation Danila came up with.
predicted mass
y = -47 + 2(40)
y = -47 + 80
y = 33 grams
residual = actual mass - predicted mass
residual = 29 - 33
residual = - 4
Answer:
-4
Step-by-step explanation:
trust me.
Write 63 as a product of prime factors in ascending order. I don't need the answer but the explanation as to my friends one was not enough
Answer:
Step-by-step explanation:
63= 3 * 3 * 7
63 will come in 7th table. 7*9. here 7 is a prime and 9 is composite number. 3*3 = 9. So 63 = 3*3*7
Answer:
63 = 3 × 3 × 7
Step-by-step explanation:
Start dividing by the smallest prime divisor till you reach 1
Which is 3
63/3 = 21
21/3 = 7
7/7 = 1
So the prime factors are: 3,3,7
determine the number and type of zeros of the quadratic function based on the value of the discriminant? discriminant=0, discriminant=-36, discriminant=3, discriminant=2, discriminant=100, discriminant=-4
Answer with Step-by-step explanation:
We know that
Number of zeroes of a quadratic function are 2.
When discriminant D
D=0
Roots are equal and real
D>0
Roots are real and different
D<0
Roots are not exist.
a.D=0
Number of zeroes=2
Zeroes are equal and real.
b.D=-36
Zeroes of quadratic function does not exist.
c.D=3
Number of zeroes=2
zeroes are real and different
d.D=2
Number of zeroes=2
zeroes are real and different
e.D=100
Number of zeroes=2
zeroes are real and different
D=-4
Zeroes of quadratic function does not exist.
please help !!! :(
1 and 2 form a linear pair, if the measure of 1 is 113 find the measure of 2
Answer:
67
Step-by-step explanation:
A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2
The measure of angle 2 is 67°.
It is required to find the measure of angle 2.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given :
<1=113°
We know that
A linear pair adds to 180 degrees.
<1 + <2 =180°
113°+ <2 = 180°
<2 = 180°-113°
<2 =67°
Hence, the measure of angle 2 is 67°.
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The shape is a quadrilateral.
The shape has no right angles.
The shape has 4 sides of equal length.
A rhombus is a type of polygon distinct from squares and rectangles due to its lack of right angles.
This description fits a geometric shape known as a rhombus. A rhombus is a type of polygon that is a quadrilateral with all four sides of equal length. Unlike a square, a rhombus does not have to have right angles, which distinguishes it from rectangles and squares. The sum of the interior angles in a quadrilateral is always 360°, a property that applies to rhombuses as well.
Functions f(x) and g(x) are shown below:
f(x) = x2
g(x) = x2 - 8x + 1
In which direction and by how many units should f(x) be shifted to obtain g(x)? (1 poi
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
Answer:
f(x) should shifted Right by 4 units to obtain g(x) ⇒ B
Step-by-step explanation:
Let us put g(x) in the form of g(x) = (x - h)² + k, where h is the the horizontal shift (x - h) to right, (x + h) to left and k is the vertical shift (k) up and (-k) down
In the quadratic function y = ax² + bx + c, h = [tex]-\frac{b}{2a}[/tex] and k = y at x = h
∵ g(x) = x² - 8x + 1
∵ a is the coefficient of x² and b is the coefficient of x
∴ a = 1 and b = -8
∵ h = [tex]-\frac{b}{2a}[/tex]
∴ h = [tex]-\frac{-8}{2(1)}=\frac{8}{2}[/tex]
∴ h = 4
∵ k = g(x) at x = h
- Substitute x by 4 in g(x) to find k
∴ k = (4)² - 8(4) + 1 = 16 - 32 + 1
∴ k = -15
- Substitute them in the form of g(x) = (x - h)² + k
∴ g(x) = (x - 4)² + (-15)
∵ h is the horizontal shift
∵ (x - h) means shift to right h units
∵ f(x) = x²
∵ g(x) = (x - 4)² + (-15)
- That means f(x) is shifted 4 units to the right
∴ f(x) should shifted right by 4 units to obtain g(x)
Answer:
B. Right by 4 units
Step-by-step explanation:
You leave your ranch in South Texas to drive your cattle to the railroad in Abilene, Kansas. You have 2,000 head of cattle and 10 cowboys (not including you.) Along the trail, you are attacked by some cattle rustlers, the herd stampedes during a thunderstorm, and you have trouble finding water. As a result, when you get to Abilene, you have lost 10% of the herd. You sell the cattle in Abilene for $35 a head. You pay each of the cowboys $100 and the rest of the money is yours. How much did you make?
Answer:
You get $5727.27
Step-by-step explanation:
At the start, you have 2000
After you are attacked, stampeded and have trouble finding water, you have lost 10% of your cattle
2000 * 10% is 200
2000 - 200 is 1800
Multiply 1800 cattle by $35 per cow
1800 * $35 = $63000
10 cowboys + 1 (you) is 11 people
Divide $63000 by 11
63000 / 11 = $5727.27
You get $5727.27
Which graph grows the fastest?
A) black
B) blue
C) green
D) pink
Answer:
b
Step-by-step explanation:
Answer:
do u have a pic?
Step-by-step explanation:
find the surface area of the composite 3D figure below. leave in terms of pi, numerical value only
Given:
The diameter of the cylinder = 34 m
So, the radius (r) = 17 m
The height (h) of the cylinder = 12 m
The slant height (l) of the cone = 20 m
To find the surface area of the given figure.
Surface area of the given fig = surface area of cylinder + surface area of the cone
Formula:
The surface area of the cylinder is [tex]2 \pi r(r+h)[/tex]
The surface area of the cone is [tex]\pi rs[/tex]
Now,
The surface area of the cylinder is given by
[tex]SA=2 \pi 17(17+12)[/tex]
[tex]=2 \pi 17(29)[/tex]
[tex]=2 \pi (493)[/tex]
[tex]SA=986 \pi[/tex]
The surface area of the cylinder is 986π m²
The surface area of the cone is given by
[tex]SA=\pi rs[/tex]
[tex]SA=\pi (17)(20)[/tex]
[tex]=340 \pi[/tex]
Thus, the surface area of the cone is 340π m²
The surface area of the composite figure is given by
Surface area = Surface area of cylinder + Surface area of cone
Substituting the values, we get;
[tex]SA=986\pi +340 \pi=1326 \pi \ m^2[/tex]
Thus, the surface area of the composite figure is 1326π m²