The standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5 is (x - 5)^2 = 20y.
Explanation:The standard form of the equation of a parabola with a focus at (h, k) and a directrix at x = d is given by (x - h)^2 = 4p(y - k), where p is the distance between the vertex and the focus or directrix.
In this case, the focus is at (5, 0) and the directrix is at x = -5. Since the directrix is a vertical line, the parabola opens to the right. The distance between the vertex and the focus or directrix is given by p = |5 - (-5)|/2 = 5 units.
Substituting the values into the standard form equation gives (x - 5)^2 = 4(5)(y - 0), which simplifies to (x - 5)^2 = 20(y - 0). Therefore, the standard form of the equation of the parabola is (x - 5)^2 = 20y.
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Angle A and Angle B are Complementary Angles. If Angle A measures 40 degrees, what is the measure of Angle B? *
40 degrees
45 degrees
50 degrees
140 degrees
Answer:
50 degrees
Step-by-step explanation:
If angle A and angle B are complementary, that would mean that their sum is 90 degrees. A + B = 90 . We know that angle A is 40, so 40 + B = 90. It becomes a one step equation. Subtract both sides by 40. 90 - 40 = 50. Angle B is equal to 50 degrees.
Answer:
50 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
so
A+B=90°
we have
A=40°
substitute and solve for B
40°+B=90°
B=90°-40°=50°
For f(x) = √x-3 find f(f^-1(4))
Answer:
4
Step-by-step explanation:
f⁻¹(x) = x²+3, but none of that matters, since f(f⁻¹(x)) = x
identify the midline of the graph
Answer:
-4.5
Step-by-step explanation:
ANSWER
The midline y=3.6
EXPLANATION
The midline is the midpoint of the peak value and the least value.
The peak value is 5.20
The least value is 2
The midline is
[tex]y = \frac{5.20 + 2}{2} = \frac{7.2}{2} = 3.6[/tex]
Therefore the mid value is y=3.6
help plz thank you so so much
Answer:
[tex]\frac{95}{99}[/tex]
Step-by-step explanation:
The bar above 95 denotes that 95 is repeated, that is
0.959595,,,,
Create 2 equations with the repeating values after the decimal point, thus
let x = 0.9595.... → (1) ← multiply both sides by 100
100x = 95.9595.... → (2)
Subtract (1) from (2) eliminating the repeated value, so
99x = 95 ( divide both sides by 99 )
x = [tex]\frac{95}{99}[/tex]
(HELP ASAP PLEASE)
Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Nick has passed 5 scales, whereas his friend Mary has passed 12 of them. Going forward, Nick has committed to passing 4 scales per week, and Mary has committed to passing 3 per week. At some point soon, the two friends will have passed the same number of scales. How many scales will that be? How long will that take?
The friends will each have passed ___ scales in ___ weeks.
Answer:
The friends will each have passed _33_ scales in _7_ weeks.
Step-by-step explanation:
We must write an equation for the number of scales that Nick approves and an equation for the number of scales that Mary approves.
For Nick we have:
5 initial scales
Nick has committed to approve 4 scales per week. Let's call x the number of weeks.
So the number of scales and for Nick is:
[tex]y = 5 + 4x[/tex]
For Mary we have:
12 initial scales
Mary has committed to approve 3 scales per week. Let's call x the number of weeks.
So the number of scales and for Mary is:
[tex]y = 12 + 3x[/tex]
To know when the two friends have passed the same number of scales we must equal both equations and solve for x:
[tex]12 + 3x = 5 + 4x[/tex]
[tex]12-5= 4x-3x[/tex]
[tex]x= 7\ weeks[/tex]
And
[tex]y=12+3*7\\\\y=33\ scales[/tex]
Final answer:
Nick and Mary will both have passed 33 scales in 7 weeks. This is determined by setting the equation for the number of scales Nick will pass equal to the number for Mary and solving for the number of weeks.
Explanation:
To determine when Nick and Mary will have passed the same number of scales, we can set up an equation based on the given information. Nick has currently passed 5 scales and will pass 4 scales each week. Mary has passed 12 scales and will pass 3 scales each week. The point at which they will have passed the same number of scales is when their total passed scales are equal.
Let's denote the number of weeks it will take to reach this point as w. For Nick, the total number of scales passed after w weeks will be 5 + 4w (his current count plus 4 times the number of weeks). For Mary, it will be 12 + 3w (her current count plus 3 times the number of weeks). Setting these two expressions equal to each other:
5 + 4w = 12 + 3w
Subtract 3w from both sides:
5 + w = 12
Subtract 5 from both sides:
w = 7
So, it will take 7 weeks for Nick and Mary to have passed the same number of scales. At that point, to find the total number of scales:
Nick: 5 + 4 x 7 = 33 scales
Mary: 12 + 3 x 7 = 33 scales
The friends will each have passed 33 scales in 7 weeks.
z + mx = yx , for x can you pls give me the answer I need it fast
To solve the equation Z + mx = yx for x, we first move 'mx' to the right side to get 'yx - mx = Z'. We then factor out 'x' to get 'x(y - m) = Z'. Finally, we divide by '(y - m)' to get 'x = Z / (y - m)'. This solution holds as long as y ≠ m.
Explanation:Here, we're going to solve the equation for x: Z + mx = yx.
We can start by grouping the terms with 'x' together. This gives us: yx - mx = Z. Now, we can factor x out of the left side of the equation. This results in: x(y - m) = Z. Finally, to solve for x, we divide both sides of the equation by (y - m). This gives us the solution: x = Z / (y - m).
Note: This solution is under the assumption that y ≠ m because division by zero is undefined.
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Find the range and interquartile range of the
data. Round to the nearest tenth.
259, 125, 158, 168, 187,334, 198
Answer: the range is 209
Step-by-step explanation: the biggest number minus the smallest will give you the range
The answer is 209. Hope this helps
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 The length of a rectangle is 6 inches, and the width is 5 inches. When each dimension is increased by x inches, the area triples. Which equation models this situation?
A)(6x)(5x) = 60B)(6x)(5x) = 90C)(x + 6)(x + 5) = 60D)(x + 6)(x + 5) = 90
Answer:
D
Step-by-step explanation:
Before the increase, the length is 6 and the width is 5, so the area is 5×6 = 30.
After the increase, the length is x+6, the width is x+5, and the area is tripled: 30×3 = 90.
Therefore:
(x+6) (x+5) = 90
you have 13 coins in your wallet some are nickels and some are dimes altogether you have 0.85. how many nickels do you have
Answer:
4 Dimes
9 Nickels
Step-by-step explanation:
I did guess and check (if you have an equation leave a comment or answer!)
So I did kept playing with the numbers making them go down until I could subtract the number of coins and divide to get the rest:
85-40 (4 dimes)=45
45/5=9 nickels
4+9=13
I hope this helps!
To solve for the number of nickels and dimes amounting to $0.85 in 13 coins, we set up and solve a system of equations. We found that there are 9 nickels and 4 dimes in the wallet.
To find out how many nickels you have when you have 13 coins composed of nickels and dimes amounting to $0.85, we can set up a system of equations where the number of nickels is represented by n and the number of dimes by d.
The first equation comes from the total number of coins: n + d = 13.
The second is derived from the total amount of money: 0.05n + 0.10d = 0.85.
We have two equations:
n + d = 13
0.05n + 0.10d = 0.85
Now, let's multiply the second equation by 20 to get rid of the decimals:
n + 2d = 17
By subtracting the first equation from this new equation:
d = 4
Substitute d back into the first equation:
n + 4 = 13
Thus:
n = 9
So you have 9 nickels and 4 dimes.
let f(x) =2x and g(x)= x - 2 the graph of (f.g )(x) is shown below
What is the domain of ?
x >0
all real numbers except x =0
x <0
all real numbers
Answer:
The domain of the graph is all real number ⇒ the last answer
Step-by-step explanation:
* Remember that our original exponential formula was y = ab^x
- The b value is the growth factor
* Lets revise how to find the domain of this function
- The domain is all values of x that make the function defined
* Lets revise the composite function
- A composite function is a function that depends on another function.
- A composite function is created when one function is substituted
into another function.
- For example, f(g(x)) is the composite function that is formed when
g(x) is substituted for x in f(x).
∵ f(x) = 2^x
∵ g(x) = x - 2
∴ (f · g)(x) = f(x - 2)
∵ f(x) = 2^x
∴ (f · g)(x) = f(x - 2) = 2^(x - 2)
- For this function there is no values of x make the function undefined
∴ The Domain is all real numbers
- Look to the graph, the values of x go from -∞ to ∞
* The domain of the graph is all real number
¿What is the density of a rock if it has a mass of 50 g and a volume of 10 mL?
Final answer:
Explaining how to calculate density using the mass and volume of a rock.
Explanation:
Density can be calculated using the formula: Density = Mass/Volume. Given that the mass of the rock is 50 g and the volume is 10 mL, we can plug these values into the formula to find the density.
Mass = 50 g
Volume = 10 mL = 10 cm³
Density = Mass/Volume = 50 g / 10 cm³ = 5 g/cm³
polygon A i simllar to polgon B. find the perimeer of polygon B if one side of polygon A is 24 A sde to polygon B is 15 and the perimeter of polgon A is 128
Answer:
Perimeter of polygon B = 80 units
Step-by-step explanation:
Since both polygons are similar, their corresponding sides and perimeters are proportional. Knowing this we can setup a proportion to find the perimeter of polygon B.
[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]
Let [tex]x[/tex] be the perimeter of polygon B. We know from our problem that the side of polygon A is 24, the side of polygon B is 15, and the perimeter of polygon A is 128.
Let's replace those value sin our proportion and solve for [tex]x[/tex]:
[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]
[tex]\frac{24}{15} =\frac{128}{x}[/tex]
[tex]x=\frac{128*15}{24}[/tex]
[tex]x=\frac{1920}{24}[/tex]
[tex]x=80[/tex]
We can conclude that the perimeter of polygon B is 80 units.
Answer:80 units
Step-by-step explanation:
I'm doing it right now. You got this have a great day!
The center of Circle D is (0,0). The circumference of the circle passes through Point E (-7,-4).
Find the length of the radius of Circle D.
Answer:
[tex]\boxed{\sqrt{65}}[/tex]
Step-by-step explanation:
The radius of circle D is the distance from the origin to (-4, -7).
In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):
[tex]d = \sqrt{(x _{2}-x_{1})^{2} +(y _{2}-y_{1})^{2}}[/tex]
You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.
For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is
[tex]d = \sqrt{(0 - (-4))^{2} +(0 -(- 7))^{2}}\\\\ = \sqrt{4^{2} +7^{2}}\\ = \sqrt{16 + 49}\\=\sqrt{65}[/tex]
[tex]\text{The radius of the circle is }\boxed{\mathbf{\sqrt{65}}}[/tex]
Find the solution set. (x+7)(x+7)=0
For this case we must find the solution of the following expression:
[tex](x + 7) (x + 7) = 0[/tex]
If we isolate a term and we equate to zero, we have:
[tex]x + 7 = 0[/tex]
Subtracting 7 on both sides of the equation we have:
[tex]x + 7-7 = 0-7\\x = -7[/tex]
Thus, the solution of the expression is given by:
[tex]x = -7[/tex]
ANswer:
[tex]x = -7[/tex]
Answer:
x = -7, multiplicity 2.
Writing it as a set it is {-7, -7}.
Step-by-step explanation:
(x + 7)(x + 7 )= 0
When 2 expressions are multiplied and the result is zero either of them can be zero, so
x + 7 = 0
x = -7.
In this case, since the 2 factors are the same, there are duplicate roots.
We write this as x = -7, multiplicity 2.
Determine the vertex of the function f(x) = 2(x − 5)2 + 8.
(8, −5)
(8, 5)
(−5, 8)
(5, 8)
Answer:
Vertex ( 5 ,8) .
Step-by-step explanation:
Given : f(x) = 2(x − 5)² + 8.
To find : Determine the vertex of the function .
Solution : We have given
f(x) = 2(x − 5)² + 8.
Vertex form of parabola : f (x) = a(x - h)² + k, where (h, k) is the vertex.
On comparing f(x) = 2(x − 5)² + 8. with vertex form of parabola.
a = 2 , h = 5 , k = 8 .
Vertex ( 5 ,8) .
Therefore, Vertex ( 5 ,8) .
Answer: (5,8)
Step-by-step explanation:
The given function :[tex]f(x) = 2(x - 5)^2 + 8.[/tex]
We know that the vertex form of a quadratic equation is given by :
[tex]f (x) = m(x - a)^2+ b[/tex] (1)
, where (a,b)= Vertex of the function f(x).
When we compare the given function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] to equation (1) , we conclude that the given function is already in its vertex form.
with a= 5 and b= 8
Therefore , the vertex of the function [tex]f(x) = 2(x - 5)^2 + 8.[/tex] = (5,8)
DUDE washed 5 windows in 35 minutes. At this rate, how long
will it take DUDE to wash 12 windows?
Answer:
35/5 = 7 Minutes per Window thus: 12*7 = 84 Minutes
Step-by-step explanation:
Answer:
84 minutes or 1 hour and 24minutes
Step-by-step explanation:
12*35=420
420/5=84
Can someone help me with this please
Answer:
the answer is: 6z^3
Step-by-step explanation:
We need to solve this equation:
[tex]\sqrt{36z^6}[/tex]
We know that 6X6 = 36
and √ = 1/2
Solving:
[tex]=\sqrt{6*6*z*z*z*z*z*z}\\We\,\,know\,\,6X6=6^2\,\, and \,\,z*z=z^2\\=\sqrt{6^2*z^2*z^2*z^2} \\=(6^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}\\=6*z*z*z\\=6z^3[/tex]
So, the answer is: 6z^3
The graph represents Daniel's bike ride to the ball park. Determine the slope from point D to point E. What does the slope indicate about Daniel's speed between points D and E?
A) 1; The slope indicates that Daniel's speed is 1 meter per minute.
Eliminate
B) undefined; The slope indicates that Daniel's speed varies from minute to minute.
C) 0; The slope indicates that Daniel is not moving.
D) −1 The slope indicates that Daniel's speed is less than 1 meter per minute..
Answer:
The correct answer to this problem is
C) 0; The slope indicates that Daniel is not moving.
Step-by-step explanation:
I know this because I just did the test
The slope from point D to point E on the graph represents Daniel's speed between these two points. The slope is 10 meters per minute.
Explanation:The slope from point D to point E on the graph represents Daniel's speed between these two points. To determine the slope, we need to find the change in position and the change in time between the two points. The slope is calculated by dividing the change in position by the change in time.
Let's assume that the change in position from D to E is 100 meters and the change in time is 10 minutes. The slope would then be 100 meters divided by 10 minutes, which is equal to 10 meters per minute.
Therefore, the correct answer is A) 10; The slope indicates that Daniel's speed is 10 meters per minute.
Find the area of the regular 15-gon with radius 10mm.
318.83484250503 mm^2
The area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².
Formula for a Regular Polygon Area:
The area (A) of a regular polygon can be calculated using the following formula:
A = 1/2 * n * s^2 * r
where:
n is the number of sides in the polygon (15 for this case)
s is the side length of the polygon
r is the radius of the polygon
Finding the Side Length (s):
We don't directly have the side length (s) of the regular 15-gon. However, we can relate it to the radius (r) using the following formula:
s = 2r * sin(π / n)
In this case:
r = 10mm
n = 15
Substituting these values:
s = 2 * 10mm * sin(π / 15)
s ≈ 8.24mm (round to 2 decimal places)
Calculating the Area (A):
Now that we have the side length (s) and the radius (r), we can calculate the area (A) of the regular 15-gon:
A = 1/2 * 15 * 8.24mm² * 10mm
A ≈ 247.2mm^2 (round to 1 decimal place)
Therefore, the area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².
11. In this figure, ∠a and ∠b are
In this figure, ∠a and ∠b are supplementary. The answer is OPTION C.
A. Complementary angles are two angles whose sum is equal to 90 degrees. Since no information is given about the angles Za and Zb in the figure, we cannot determine if they are complementary. Therefore, this answer choice is not supported by the given information.
B. Equal angles have the same measure. Again, no information is given about the angles Za and Zb, so we cannot determine if they are equal. Thus, this answer choice is not supported by the given information.
C. Supplementary angles are two angles whose sum is equal to 180 degrees. Since the figure does not provide any specific angle measurements, we cannot directly determine if Za and Zb are supplementary. However, this answer choice is a possibility as supplementary angles are commonly encountered in geometry.
D. Vertical angles are a pair of non-adjacent angles formed by intersecting lines. Without any information about the lines or angles in the figure, we cannot determine if Za and Zb are vertical angles. Therefore, this answer choice is not supported by the given information.
In conclusion, the most accurate answer choice based on the given information is C. supplementary. However, without additional context or measurements, we cannot definitively determine the relationship between Za and Zb.
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According to the given figure, ∠a and ∠b are complementary angles.
The correct answer to the given question is option A.
These two could be any pair of angles and the relationship between them depends on their relative positions. If ∠a and ∠b are complementary, that means that the sum of their angle measures is 90 degrees.
This usually happens when two angles together form a right angle. On the other hand, if ∠a and ∠b are equal, that means that they have the same angle measure.
This usually happens when the angles are opposite each other in a shape with symmetry, such as an isosceles triangle or a rectangle. Should ∠a and ∠b be supplementary, it means that the sum of their angle measures is 180 degrees.
This usually happens when two angles form a straight line or the angles on a straight line sum to 180 degrees.
Finally, if ∠a and ∠b are vertical, that means they are opposite each other when two lines intersect.
Hence, ∠a and ∠b are complementary angles.
Therefore, the correct answer to the given question is option A.
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A 5-mile race takes place along a straight course. The number line shows the distance, in miles, from start to finish. The race director would like to place a water station along the course such that the distance from the start to the water station and the water station to the finish line is in a 7:5 ratio. Where would the water station be located? Round to the nearest tenth of a mile, if necessary. The water station will be placed about miles from the start.
The water station would be located approximately 2.9 miles from the start.
What is the distance?A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.
Let's call the distance from the start to the water station x. The distance from the water station to the finish line is 5 - x.
We know that the ratio of these two distances is 7:5, so we can write the following equation:
x / (5 - x) = 7/5
Expanding and solving for x, we get:
5x = 7(5) - 7x
12x = 35
x = 35/12 = 2.92 miles
So, the water station would be located approximately 2.92 miles from the start. Round to the nearest tenth of a mile, the answer is 2.9 miles.
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The water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.
To find where to place the water station at a 7:5 ratio along a 5-mile race course, we must determine how many parts out of the total 12 parts (7+5) each section of the race is. Since the total race is 5 miles, we divide 5 miles by 12 parts, which gives us the length of one part. Multiplying that length by 7 will give us the distance from the start to the water station.
First, we find the length of one part:
5 miles ÷ 12 parts = 0.4167 miles per partThen, we find the distance to the water station:
0.4167 miles per part × 7 parts = 2.9169 milesThe water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.
I need help on NS part b plz help me!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Any number between 0.390 and 0.400 will work. For example, 0.391, 0.392, and 0.393.
A cereal box is 9 inches by 2.5 inches by 10 inches. What is the volume of the box?
When doing volume you do Length x Width x Height (9 x 2.5 x 10) the answer is 225 if I’m not mistaken
The volume of the cereal box is 225 in³
What is volume?Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Given that, a cereal box is 9 inches by 2.5 inches by 10 inches., we need to find its volume,
Volume of box = length x width x height
= 9 x 2.5 x 10
= 225
Hence, the volume of the cereal box is 225 in³
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This Data set represents the number
of children in 8 families
4,2,1,2,4,2,6,3
The mean of this data set is 3. what is the mean absolute deviation
A. 1.25
B. 3
C. 3.3
D. 8
Answer:
The answer would be A. 1.25
Identify the roots of the quadratic function.
A) x = 0 and x = 4
B) y = 0 and y = 4
C) x = 0 and x = -4
D) y = 0 and y = -4
Answer:
A. x=0 and x=4
Step-by-step explanation:
The roots of a quadratic function are the x intercepts of the parabola. In this case, the roots are 0 and 4 because the parabola intercepts the x axis twice in these points.
Your answer is A. x=0 and x=4
Hope I helped!
Answer:
A
Step-by-step explanation:
Suppose y varies directly as x, and y = 8 when x = -2. Which of the following is the correct equation to set up to solve for the constant of variation?
A) 8 = k(-2)
B) -2 = k(8)
C) -2/8 = k/1
D) k = (-2) - 8
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} y=8\\ x=-2 \end{cases}\implies 8=k(-2)[/tex]
17) There are 15 boys and 18 girls in seventh grade. Find the ratio of boys to girls in seventh grade.
18) Janet bought 12 guavas and 16 apples. What is the ratio of guavas to apples?
19) Sandy has 8 candies and Tabitha has 10 candies. Find the ratio of Sandy’s candies to Tabitha’s candies.
20) For a birthday party, Evelyn orders 10 chicken pizzas and 15 vegetable pizzas. Find the ratio
of chicken pizzas to the vegetable pizzas.
21) In a local animal sanctuary, there are 48 deer and 64 monkeys. Find the ratio of deer to monkeys.
22) Gerry scored 56 in Math and 84 in Science. Find the ratio of his scores in Math to Science.
23) A fruit seller bought 75 mangoes and 125 apples from vendor. Find the ratio mangoes to apples bought.
24) Yulee primary school maintains a library with 81 English books to every 90 Math books. Find the ratio of English books to the Math books.
17) 5:6
18) 3:4
19) 4:5
20) 2:3
21) 3:4
22) 2:3
23) 3:5
24) 9:10
These answers are all simplified ratios
Final answer:
The questions involve finding the ratio of two quantities and simplifying them by dividing both numbers by their greatest common divisor. Each ratio gives a comparative relationship between two different counts of items or scores in different subjects.
Explanation:
The questions provided all relate to finding the ratio of two quantities.
The ratio of boys to girls in seventh grade is 15:18, which can also be simplified to 5:6 by dividing both numbers by 3.The ratio of guavas to apples Janet bought is 12:16, which simplifies to 3:4 after dividing both numbers by 4.For Sandy and Tabitha's candies, the ratio is 8:10, which simplifies to 4:5 once both numbers are divided by 2.Evelyn orders chicken and vegetable pizzas at a ratio of 10:15, which is equal to 2:3 after dividing both numbers by 5.In the animal sanctuary, the ratio of deer to monkeys is 48:64, simplifying to 3:4 after dividing by 16.Gerry's scores in Math to Science are at a ratio of 56:84, which can be reduced to 2:3 by dividing by 28.The ratio of mangoes to apples the fruit seller bought is 75:125, simplified to 3:5 after dividing both by 25.Lastly, the ratio of English books to Math books in Yulee primary school's library is 81:90, which simplifies to 9:10 upon division by 9.In each case, the ratio is found by comparing two quantities and simplifying by dividing both numbers by their greatest common divisor (GCD).
Ted buys wood to build his guitars. Find the number of blocks of mahogany that Ted can afford to buy if he wishes to spend a total of $5000 this month, mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each
Answer:
Sorry, all I know is that after he got the 7 blocks of spruce he will have $3,600 left over. I don't know how many blocks he can buy with that.
Step-by-step explanation:
Answer:
Ted can buy 8 blocks of mahogany.
Step-by-step explanation:
Total amount Ted wishes to spend this month is $5000.
Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.
So, money spent on spruce = [tex]7\times200=1400[/tex] dollars
Money left after buying spruce = [tex]5000-1400=3600[/tex] dollars
Now as $450 will be spent on buying 1 block of mahogany.
So, $3600 will be spent on buying [tex]\frac{3600}{450}= 8[/tex] blocks of mahogany.
The answer is 8 blocks.
Josh simplified 4x - 8x ÷ 2 and said the answer was -2x. What was josh's error? What should his answer have been?
Answer:
see explanation
Step-by-step explanation:
Given
4x - 8x ÷ 2
Under the rules of PEMDAS , division must be performed before subtraction.
Hence
4x - 8x ÷ 2 = 4x - 4x ← dividing - 8x by 2, then
4x - 4x = 0 ← correct answer
Without calculating, which has a bigger volume. A cube that has a length, width, and height of 18 m. Or a sphere with a radius of 9 m? Explain.
Weird. A period appears above this... huh.
Answer:
[Th]e cube has a greater value.
Step-by-step explanation:
What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4[tex]\pi[/tex]r^2 when r = 9? And here's how to solve that.
Starting with the[ c]ube we have A=6a^2. A bit t[o]o simple, right?
A=6(18)^2 Substitute numbers.
A=6(324) Solve ex[p]onents.
A=1944 Mult[i]ply.
So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4[tex]\pi[/tex]r^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.
A=4(3.14)(9)^2 Subst[i]tute numbers.
A=4(3.14)(81) Solve expone[n]ts.
A=12.56(81) Multip[ly].
A=1017.36 Multiply again[.]
Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.
And PLEASE don't copy this guys. Make your own iteration. Change it up!