The gardener's expression correctly calculates the area of the entire garden after extension, not just the extension itself. The error was in misinterpreting the question and focusing solely on the extension, leading to the incorrect answer of 13 square feet.
Explanation:Expanding the expression: 6(x + 7) = 6x + 42. This represents the total area of the garden after extending its length by 7 feet.
Error analysis: The gardener likely assumed they needed to calculate the area added by the extension. This could be due to:
Misunderstanding the question and focusing on the 7-foot extension instead of the total area change.
Mistakenly interpreting "area of the extension" as the area of the rectangle formed only by the additional 7-foot length and the original width.
Therefore, while the expression itself is correct, the gardener misinterpreted the question and made an error in interpreting what "area of the extension" referred to.
Simplify: (x - 7)(6x - 3)
Answer:
C. 6x² -45x + 21
Step-by-step explanation:
( x - 7) (6x - 3)
= x(6x - 3) -7 ( 6x - 3)
= 6x² - 3x - 42x + 21
= 6x² - 45x + 21
Hope it will help you :)
Answer
the answer is c
Step-by-step explanation:
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
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
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.
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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What is the product enter your answer as a fraction in simplest form in the box -4/5 • 10/16
Answer:
-1/2
Step-by-step explanation:
The first thing you do is cross cancel because when you cross cancel 4 and 16 it would be -1/5 * 10/4 then you cross cancel 5 and 10 and then you faction would look like -1/1 * 2/4 then you multiply those fractions together and get -2/4 but simplified would be -1/2.
All else being equal, a study with which of the following error ranges would be
the most reliable?
O
A. 17 percentage points
O
B. +22 percentage points
O
C. 17 percentage points
O
D. 112 percentage points
Answer:
it would be A and C because they are the lowest
Step-by-step explanation:
The correct option is C
Percentage point : It is defined as a unit for the arithmetic difference of two percentages and greater the difference more will be the error range.
So, the most reliable error range is the one whose percentage point is minimum.
Now, among the provided options , 2 percentage points is minimum so it will be the most reliable error range.
Hence, Option C. 2 percentage points is correct
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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)
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
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
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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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
an international company has 24,500 employees in one country. if this repersents 24.8% of the company's employees, how many employees does it have in total?
Answer:
98,790
Step-by-step explanation:
The given relation is ...
0.248 · (total employees) = 24,500
Dividing by the coefficient of the variable, we have ...
(total employees) = 24,500/0.248 = 98,790
The company has 98,790 employees in total.
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:
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
−8 ≤ −3; Add 11 to both sides
Three ballet dancers are positioned on stage. Elizabeth is straight behind Hannah and directly left of Manuel. If Hannah and Elizabeth are 3 meters apart, and Manuel and Hannah are 5 meters apart, what is the distance between Elizabeth and Manuel?
Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Final answer:
To calculate the distance between Elizabeth and Manuel, the Pythagorean theorem is used. Given the 3-meter distance between Hannah and Elizabeth, and the 5-meter distance between Hannah and Manuel, the distance between Elizabeth and Manuel is calculated to be the square root of 34, which is approximately 5.83 meters.
Explanation:
The question pertains to finding the distance between Elizabeth and Manuel, given their respective positions on a stage in relation to Hannah.
To find the distance between Elizabeth and Manuel, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the distances between Hannah and the other two dancers form two sides of a right-angled triangle with Elizabeth and Manuel's positions marking the ends of the hypotenuse.
Since Hannah is 3 meters from Elizabeth and 5 meters from Manuel, we can calculate the distance between Elizabeth and Manuel (hypotenuse) with the following equation:
c^2 = a^2 + b^2
Where c is the distance between Elizabeth and Manuel, a is the distance between Hannah and Elizabeth (3 meters), and b is the distance between Hannah and Manuel (5 meters).
So, c^2 = 3^2 + 5^2 which simplifies to c^2 = 9 + 25, and further to c^2 = 34. This implies that c = [tex]\sqrt{34}[/tex].
Therefore, the distance between Elizabeth and Manuel is the square root of 34, which is approximately 5.83 meters. We can round this to the nearest hundredth for a precise measurement.
The distance between Elizabeth and Manuel is approximately 5.83 meters.
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.
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).
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:
What is the volume of this container ? HELP
Answer:
56 [tex]in^{3}[/tex]
Step-by-step explanation:
Volume of bigger rectangular prism is 4*3*4 (48[tex]in^{3}[/tex]).
Volume of smaller rectangular prism is 1*2*4 (8[tex]in^{3}[/tex]).
48 + 8 = 56[tex]in^{3}[/tex].
The expression 1.5t + 20 predicts the height in centimeters of a plant t days from today. What is the predicted height of the plant 15 days from today?
Answer:
42.5
Step-by-step explanation:
so you start with adding 15 to the equations because that is how many days
1.5 15 +20
1.5 x 15 =22.5
22.5+20=42.5
so 42.5 is the answer
The predicted height of the plant 15 days from today is 42.5 cm.
The given expression for the height of a plant is 1.5t + 20, where t represents the number of days from today. To find the predicted height of the plant 15 days from today, we need to substitute t = 15 into the expression.
Substitute t = 15 into the expression:height of the plant 15 days from today = 1.5(15)+20 cm
height of the plant 15 days from today = 22.5 + 20 cm = 42.5 cm
Therefore, the predicted height of the plant 15 days from today is 42.5 cm.
What is the area of triangle ABC?
3 square units
7 square units
11 square units
15 square units
Answer:
7 units
Step-by-step explanation:
use the distnce formula to get the riangles legs, multiply them and divide by two
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
The door code outside a house often consists of either pressing A or B and then a code with free digits. Suppose you do not know the code, but try your way. How long would it take to test all combinations if each trial takes 10 seconds?
Round to whole hours.
Answer:
6 hours
Step-by-step explanation:
2 option for letter
10 for each digit
2×10×10×10
2000 trials
2000×10
20,000 seconds
20000/3600
5.5555555556 hours
The total number of combinations is 2000. Testing each one at a rate of 10 seconds per test would take approximately 20,000 seconds, which is around 6 hours when rounded to the nearest hour.
Explanation:This problem deals with the concept of combinations in mathematics. To find out how long it would take to try all possible combinations, you first need to determine how many combinations there are. The door code consists of either A or B (2 options) followed by a three-digit code (10 options for each digit, from 0-9). Therefore, there are 2 * 10 * 10 * 10 = 2000 possible combinations. If each combination takes 10 seconds to try, it would take 2000 * 10 = 20,000 seconds. To convert this to hours, divide by 3600 (as there are 3600 seconds in one hour), rounding to the nearest whole number, would give approximately 6 hours.
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On your first day of work, you get $1. On your second day of work, you get $4. On your third day of work, you get $9. On your fourth day of work, you get $16. It continues this way for 30 days and then once you’ve completed the 30 days you receive a completion bonus of $500,000. How much would I earn after?
Answer:
Money earned after 30 days is $509455
Step-by-step explanation:
If on the first day, that is n = 1, where n is the day and you earn $1.
On the second day (n = 2), you earn $4, On the third day (i.e n = 3) you earn $9 and on the fourth day (n = 4) you then earn $16. That is the money earned on the nth day is given by:
Money earned on the nth day = n².
That is on the 30th day, the money earned = 30² = $900
Once you’ve completed the 30 days you receive a completion bonus of $500,000, in given by:
Money earned after 30 days = [tex]\Sigma}n^2 ;n=1 to30+$500000=(1^2+2^2+3^2+4^2+5^2+...+29^2+30^2)+500000\\=9455+500000=509455[/tex]
Money earned after 30 days = $509455
Answer:
y = x^2 = 30^2 = $900
He would earn $900 on the 30th day and the bonus of $500,000
Step-by-step explanation:
Given
let y represent the amount earned
x represent the day.
At x = 1 y = 1
x = 2 y = 4
x= 3 y = 9
x = 4 y = 16
This satisfies the function;
y = x^2
So, on the 30th day;
x = 30
y = x^2 = 30^2 = $900
He would earn $900 on the 30th day and the bonus of $500,000
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).
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