What is the result of dividing x3−4 by x + 2?
x2−2x+4+4x+2
x2−2x+4+12x+2
x2−2x+4−12x+2
x2−2x+4−4x+2
Answer:
x3−4 by x + 2? equals to (x-3)/(4)=(x)/(2)
Step-by-step explanation:
Here, we are required to determine the result of dividing x³ - 4 by x + 2.
The result is Choice C;. x²−2x+4−12/(x+2)
The steps required for the division of
x³ - 4 by x + 2
can be made easier by assuming x³ - 4 to take the form;
x³ + 0x² + 0x - 4.
The step by step process for the division is attached to the image.
Ultimately, the division results into;
x²−2x+4−12/(x+2).
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Simplify 2x-2y +5z-2x-y+3z
Answer:
-3y+8z
Step-by-step explanation:
Add like terms which would be 2x-2x, -27-y, 5z+3z.
Answer:
-y+8z
Step-by-step explanation
Find a mixture that will make a different shade of green that is bluer
:
Mix a pthalo green and alizarin crimson with ultramarine blue
This new mixture will contain 2 cups of yellow and 7 cups of blue, resulting in a bluer shade of green compared to the original mixture.
To create a bluer shade of green, we need to increase the proportion of blue relative to yellow in the mixture. We can achieve this by increasing the amount of blue while keeping the amount of yellow constant.
Given that the original mixture ratio is 2 cups of yellow to 3.5 cups of blue, let's increase the amount of blue relative to yellow. We can try doubling the amount of blue while keeping the amount of yellow constant.
So, to create a bluer shade of green, we can use:
- 2 cups of yellow (constant)
- 2 * 3.5 = 7 cups of blue
This new mixture will contain 2 cups of yellow and 7 cups of blue, resulting in a bluer shade of green compared to the original mixture.
complete question given below:
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the different shade of green that is bluer
3)June 2019-In the diagram below of AABC, D is a
point on BA, E is a point on BC, and DE is drawn.
If BD = 5, DA= 12, and BE = 7, what is the length of
BC so that AC || DE?
Answer:
BC = 23.8
Step-by-step explanation:
See the diagram attached.
Given AC ║ DE and BD = 5, DA = 12 and BE = 7.
We have to find BC.
Since, AC ║ DE, so, Δ ABC and Δ DBE are similar.
If two triangles are similar then the ratio of their corresponding sides remains the same.
Hence, [tex]\frac{BD}{BA} = \frac{BE}{BC}[/tex]
⇒ [tex]\frac{5}{12 + 5} = \frac{7}{BC}[/tex]
⇒ [tex]BC = \frac{7 \times 17}{5} = 23.8[/tex] (Answer)
Answer:
23.8
Step-by-step explanation:
If-1 is a root of f(x), which of the following must be true?
A factor of f(x) is (x - 1).
Afactor of f(x) is (x + 1).
Both (x - 1) and (x + 1) are factors of f(x).
Neither (x - 1) nor (x + 1) is a factor of f(x).
A factor of f(x) is (x + 1) must be true ⇒ 2nd answer
Step-by-step explanation:
In a quadratic equation y = ax² + bx + c, the roots of it are:
The values of x when y = 0They can called the x-interceptsIf the roots of it are m and n, then the factors of the equation are (x - m) and (x - n)∵ -1 is a root of f(x)
∵ The roots of f(x) are the values of x when f(x) = 0
∴ At f(x) = 0, x = -1
When f(x) = 0, then all factors of f(x) must be equate by 0
∵ f(x) = 0
∵ x = -1 ⇒ when f(x) = 0
- Add to sides by 1
∵ x + 1 = 0
∴ (x + 1) is one factor of f(x)
A factor of f(x) is (x + 1) must be true
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I’ll make u the brainliest if right
Answer:
38
Step-by-step explanation:
To evaluate h(8) substitute x = 8 into h(x)
h(8) = 5(8) - 2 = 40 - 2 = 38
Answer:
38
Step-by-step explanation:
can someone solve this
-4x − 7y = 21
find the y intercept
Answer:
[tex]\displaystyle [0, -3][/tex]
Step-by-step explanation:
The y-intercept is when zero is set to x, so you will end up with this:
[tex]\displaystyle -\frac{21}{7} = -\frac{7y}{7} \\ \\ -3 = y[/tex]
I am joyous to assist you anytime.
Given a square pyramid with a height of 21 feet and a volume of 3969 cubic feet, find the length of one side of the square base.
Answer:
The length of one side of the square base is 24 feet.
Step-by-step explanation:
Given:
Volume of square pyramid(V) = 3969 cubic feet, and its height(h) = 21 feet.
Now, we need to find the length of one side(a) of the square base.
So. by putting the formula of square pyramid we get our length of one side(a):
[tex]V=a^{2}\frac{h}{3}[/tex]
[tex]3969=a^{2}\times \frac{21}{3}[/tex]
[tex]3969= a^{2}\times 7[/tex]
Dividing both sides by 7 we get:
[tex]567=a^{2}[/tex]
Using square root both sides we get:
[tex]23.81=a[/tex]
a = 24 feet (approximately).
Therefore, the length of one side of the square base is 24 feet.
The length of one side of the square base of the pyramid is approximately 23.8 feet. This was determined using the volume formula for a square pyramid and solving for the side length. The base area and height were key in finding this solution.
To find the length of one side of the square base of the pyramid, we can use the formula for the volume of a square pyramid:
Volume = (1/3) × Base Area × Height
Given:
Volume = 3969 cubic feetHeight = 21 feetLet the side length of the square base be s feet. The base area of the square is s².
Using the volume formula, we get:
3969 = (1/3) × s² × 21
First, solve for s²:
3969 = 7 × s²
s² = 3969 / 7
s² = 567
Now, take the square root of both sides to find s:
s = √567 ≈ 23.8 feet
Therefore, the length of one side of the square base of the pyramid is approximately 23.8 feet.
A book was on sale for 40% off its original price. If
the sale price of the book was $18.00, what was the
original price of the book? (Assume there is no sales
tax.)
A) $7.20
B) $10.80
C) $30.00
D) $45.00
Answer:
Option (c) $30.00
Explanation:
Let the original price be $x
Given the rate of discount is 40%
Selling (or sale) price of the book is = $18
The original price is calculated by the formula,
Selling Price = Original Price(1 – r%)
Substituting the values in the above equation,
[tex]18 = x (1-\frac{40}{100})[/tex]
[tex]18 = x (\frac{60}{100})[/tex]
[tex]x=\frac{1800}{60}[/tex]
Therefore, x = 30
Hence, option (c)is correct
The original price of the book was $30.00, which, after a 40% discount, results in the $18.00 sale price. To find the original price, divide the sale price by 0.60 (which represents the remaining 60% after the discount). So the correct option is C.
Explanation:To find the original price of the book before the sale, you need to consider that the sale price represents 60% of the original price, because the book was discounted by 40%. The calculation that needs to be done is to divide the sale price by 0.60.
Here are the steps:
Represent the sale price: $18.00Determine the percentage of the original price that $18.00 corresponds to 100% - 40% = 60%.Convert the percentage to a decimal to perform the calculation: 60% = 0.60.Divide the sale price by the decimal equivalent of the percentage: $18.00 / 0.60 = $30.00.Therefore, the original price of the book was $30.00.
Reiko started a business selling home medical supplies. She spent $ 5200 to obtain her merchandise, and it cost her $550 per week for general expenses. She earns $900 per week in sales. What is the minimum number of weeks it will take Reiko to make a profit?
Answer:
The minimum number of weeks is 15 weeks after that it will take Reiko to make profit.
Step-by-step explanation:
Reiko spent $5200 to obtain her merchandise and it cost her $550 per week for general expenses.
So, the total cost for her business after w weeks will be
C = 5200 + 550w ........ (1)
Now, she earns $900 per week in sales.
So, after w weeks her total earning is given by
E = 900w ......... (2)
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200 + 550w = 900w
⇒ 350w = 5200
⇒ w = 14.85
So, the minimum number of weeks is 15 weeks after that it will take Reiko to make a profit. (Answer)
Answer:
900w>6500+550w
From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees. How far apart are the two ships?
Answer:
189.8 m
Step-by-step explanation:
See the diagram attached.
Now, the plane is at B and the two ships are at C and at D.
So, angle of depression of C from B is ∠ OBC = ∠ ACB = 35°
Again, the angle of depression of D from B is ∠ OBD = ∠ ADB = 25° ,
Now, from the right triangle Δ ACB,
[tex]\tan 35 = \frac{AB}{AC} = \frac{265}{AC}[/tex]
⇒ [tex]AC = \frac{265}{\tan 35} = 378.5[/tex] m.
Similarly, from the right triangle Δ ADB,
[tex]\tan 25 = \frac{AB}{AD} = \frac{265}{AD}[/tex]
⇒ [tex]AD = \frac{265}{\tan 25} = 568.3[/tex] m.
Hence, the distance between the ships = CD = AD - AC = 568.3 - 378.5 = 189.8 m (Approx.) (Answer)
The distance apart is the two ships is 189.8 meters.
Given
A plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35 degrees and 25 degrees.
What is the angle of depression?The angle of elevation, the angle of depression is the angle at which you would draw a line from a point on a horizontal line to intersect another point that falls below the line.
The plane is at B and the two ships are at C and at D.
Then,
The angle of depression of C from B is ∠ OBC = ∠ ACB = 35°.
And the angle of depression of D from B is ∠ OBD = ∠ ADB = 25°.
From the right triangle Δ ACB,
[tex]\rm Tan35= \dfrac{AB}{AC}\\\\ AC= \dfrac{265}{Tan35}\\\\AC = \dfrac{265}{0.70}\\\\AC =378.57[/tex]
Again in the right triangle Δ ADB,
[tex]\rm Tan 25=\dfrac{AB}{AD}\\\\AD =\dfrac{265}{Tan25}\\\\ AD = \dfrac{265}{0.46}\\\\AD =569.30[/tex]
Therefore,
The distance apart are the two ships is;
= 568.3 - 378.5 = 189.8 m
Hence, the distance apart is the two ships is 189.8 meters.
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Write an equation in point slope form line passing through (-4,3), (3,-4)
Answer:
y-3=-(x+4)
Step-by-step explanation:
Point Slope Form: y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=(y2-y1)/(x2-x1)
m=(-4-3)/(3-(-4))=-7/(3+4)=-7/7=-1
y-3=-1(x-(-4))
y-3=-(x+4)
QA is tangent to circle M at point D and the m angle QMD=40 what is the measure of angle MQA?
Answer:
the answer is MQA =130°
Wen u draw a parallel line with respect to MD through Q, the angle between the line become 40 degree - alternate angles
so the rest is 90 degree, therefore 90 + 40 = 130 degree
Answer:
∠MQA = 130°
Step-by-step explanation:
∠MDQ = 90° ( angle between tangent and radius )
Given ∠QMD = 40°, then
∠MQD = 180° - (90 + 40)° = 180° - 130° = 50° ( sum of angles in a triangle )
∠MQD and ∠MQA form a straight angle and are supplementary, thus
∠MQA = 180° - 50° = 130°
OR
The external angle of a triangle is equal to the sum of the 2 opposite interior angles
∠MQA is an exterior angle of the triangle, thus
∠MQA = 90° + 40° = 130°
helppppppppppppppp!!!! rate 5 stars
Answer:
11) a or d 12) b
Step-by-step explanation:
sorry, I don't feel like looking at number 11 properly I'm half asleep
mason calculated sales tax on his clothing purchase 5.57375 round to the nearest hundredth
Answer:
The nearest hundredth is 5.57. Hope I helped! ☺
Which is the graph of 2x + 3y > -3?
Answer:
The third one
Step-by-step explanation:
You can plug the equation into Desmos and it graphs the equation for you, it's actually really helpful if you have more questions like this.
Answer:
C
Step-by-step explanation:
Someone help me please!
12a = 28 ÷ 2/3
Answer:
a = 3.5
Step-by-step explanation:
12a = 28 ÷ 2/3
12a = 28 × 3/2
a = 28 × 3/2 ÷ 12
a = 3.5
Answer:
a = 3.5
Step-by-step explanation:
12a = 28 ÷ 2/3
12a = 28 × 3/2
a = 28 × 3/2 ÷ 12
a = 3.5
2x+3y=7 3x-y=5 find the value of x and y
Answer:
that seem hard but it is 123times 6
Step-by-step explanation:
123×6
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
2x+3y=7
3x-y=5
-------------
y=3x-5
2x+3(3x-5)=7
2x+9x-15=7
11x-15=7
11x=7+15
11x=22
x=22/11=2
y=3(2)-5=6-5=1
Compare and contrast linear and exponential functions
Answer:
A linear function is one that is changing at a constant rate as well as it changes. As for a exponential function is one that changes at a rate that's always proportional to the value of the function.
Answer:
a linear function is in which the rate of change is constant, and because you are adding the same amount every time in the graph, the change is the same. In an exponential function, it’s where your graph is not constant, the rate of change increases, or decreases because you are adding or subtracting more each time.
Step-by-step explanation:
hope it helps
A pastry recipe calls for 3 cups of flour to make 9 servings. How many cups of flour are needed to make 6 servings?
A) 2.25 cups
B) 2.5 cups
C) 4.5 cups
D) 16 Cups
Answer:
2 cups of flour.
Step-by-step explanation:
9 servings require 3 cups of flour, so:
1 serving requires 3/ 9 = 1/3 of a cup of flour.
6 servings require 1/3 * 6 = 2 cups of flour.
Simplify: 9x - (-19 + 11x)
i’m really bad at math so please help.
Answer:
-2x+19
Step-by-step explanation:
9x-(-19+11x)=9x+19-11x=-2x+19
Answer:
-2x + 19
Step-by-step explanation:
9x - (-19 + 11x)
Distribute the (-) sign
9x + 19 - 11x
9x - 11x + 19
Simplify
-2x + 19
what is the formula for a semicircle
Answer:
Area = πr^2/2, and Perimeter πr+2r
Step-by-step explanation:
so the formula for a circle is πr^2, and a semicircle is half of a circle....... so we do the formula of a circle, πr^2, divided by 2 to get the area of it, πr^2/2. now we kind of do the same thing for perimeter. we do the circumference/2, so 2πr/2, or πr but we need to add the bottom of the semicircle so we add 2r to it . so this whole equation would be πr+2r.
the answer to 0.92 into a percentage
Answer:
92%
Step-by-step explanation:
This is because all you have to do to turn a decimal into percentage is to move the decimal over 2 spots, and drop the Zero.
Your friend has improved in his math class. On his first test he scored 50 points, and then he scored 53, 56, 59, and 62 points on his next 4 tests. His tests continued to improve following this pattern. If he took 15 tests, how many points did he score on the last test?
Answer:
95
Step-by-step explanation:
We need to add up by 3 from 50 until we get the 15th number so we do this:
1. 53
2. 56
3. 59
4. 62
5. 65
6. 68
7. 71
8. 74
9. 77
10. 80
11. 83
12. 86
13. 89
14. 92
15. 95
The 15th term is 92.
What is an Arithmetic Sequence ?A sequence of numbers where each number is linked with its consecutive term by a fixed number is called Arithmetic Sequence.
It is given that
The test score results are
50 , 53 , 56 , 59 , 32 ..................
The common difference is 3
Then the nth term is given by
Tn = a₁ + (n-1)d
a₁ is the first term = 50
n = 15
Then the 15th term is
T₁₅ = 50 + (15-1) * 3
T₁₅ = 92
The 15th term is 92.
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Solve: -7(3+6x)=9(-5x+7)
Answer:
x=28
Step-by-step explanation:
-7(3+6x)=9(-5x+7)
-21-42x=-45x+63
-21-42x-(-45x)=63
-21-42x+45x=63
-21+3x=63
3x=63-(-21)
3x=63+21
3x=84
x=84/3
x=28
Find the distance between (-8,-2) and (7,6)
Answer:
23 grids
Step-by-step explanation:
|-8|+7=8+7=15
|-2|+6=2+6=8
15+8=23
Tracy’s trip she traveled 2884 miles her trip took 7 days find a unit rate to represent the average miles she traveled per day during the trip
Answer:
Average miles travelled per day =412.
Step-by-step explanation:
If Tracy travels 2884 in 7 days, then to know the average miles she travelled per day, we just have to divide 2884 into the 7 days.[tex]\frac{2884}{7} =412[/tex], then she travelled on average 412 miles per day.A parabolà can be drawn given a focus of (7,9) and a
directrix of y = 5. Write the equation of the parabola
in any form.
from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".
keeping in mind the vertex is half-way between these two fellows, Check the picture below.
[tex]\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}[/tex]
Final answer:
The equation of the parabola with a focus of (7,9) and a directrix of y = 5 can be written as (x-7)^2 = 16(y-5).
Explanation:
The equation of a parabola in standard form is given by:
(x-h)^2=4p(y-k)
Where (h,k) is the vertex of the parabola and p is the distance from the vertex to the focus and to the directrix. In this case, the focus is (7,9) and the directrix is y = 5. To find the equation of the parabola, we need to determine the value of p.
From the given information, we can see that the focus is a point on the parabola and the directrix is a line that is perpendicular to the axis of symmetry and does not pass through the vertex. Therefore, the distance from the vertex to the focus is equal to the distance from the vertex to the directrix. In other words, the value of p is the distance from the vertex to the line y = 5.
Since the directrix is a horizontal line, the vertex of the parabola is on the line y = 5. Therefore, k = 5. The distance from the vertex to the line y = 5 is equal to the distance from the vertex to the focus, which is p. Therefore, we have:
p = 9 - 5 = 4
So the equation of the parabola is:
(x-7)^2 = 4 * 4(y-5)
Simplifying, we get:
(x-7)^2 = 16(y-5)
Therefore, the equation of the parabola is (x-7)^2 = 16(y-5).
evey y-value is the sum of one half of x and 15
Answer:
y = 1/2 x + 15
Step-by-step explanation:
The equation for the word problem is y = 1/2 x + 15.
"one half" is 1/2
sum means addition
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -5t^2 + 20t + 4 gives the height h, in meters, of the ball t seconds after it is launched.
A. What equation can be used to tell whether the ball reaches a height of 12 m ?
B. Does the ball reach a height of 12m? (yes or no)
The maximum height reached is greater than 12m, hence the ball reach a height of 12m
The height of the toy cannon all launched is expressed as [tex]h(t) = -5t^2 + 20t + 4[/tex]
h is the height reached by the ball
t is the time taken by the ball to reach its maximum height
A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:
[tex]12= -5t^2 + 20t + 4\\ -5t^2 + 20t + 4 -12=0\\ 5t^2 - 20t +8=0\\[/tex]
Hence the equation that can be used to tell whether the ball reaches a height of 12 is [tex]5t^2-20t+8=0[/tex]
B) At the maximum height
dh/dt = 0
-10t + 20 = 0
-10t = -20
t = 20/10
t = 2
Get the maximum height reached
h(2) = -5(2)^2 + 20t + 4
h(2) = -5(4) + 20t + 4
h(2) = -20 + 20(2) + 4
h(2) = -20+40+4
h(2) = 24 m
Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m
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To determine whether the ball reaches a height of 12 meters, we set the height equation equal to 12 and solve the quadratic equation. Upon solving, we find that the ball reaches 12 meters, hence the answer to whether the ball reaches 12 meters is yes.
Explanation:To determine whether the toy cannon ball reaches a height of 12 meters, we can set the height equation h(t) equal to 12 meters:
12 = -5t^2 + 20t + 4.
To solve for t, we need to rearrange the equation and solve the resulting quadratic equation:
0 = -5t^2 + 20t + 4 - 12
0 = -5t^2 + 20t - 8
This is the equation that can be used to tell whether the ball reaches a height of 12 meters. To determine if the ball does reach 12 meters, we solve for the roots of the equation:
-5t^2 + 20t - 8 = 0
Using the quadratic formula, we find the possible values for t. If there are real, positive solutions, it means the ball does reach 12 meters at those times.
Upon solving, we find that the ball indeed reaches a height of 12 meters because there are real, positive solutions for t.
Therefore, the answer to Part B is yes; the ball does reach a height of 12 meters.
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