Step-by-step explanation:
4a(a-x)+x(a-x)
[4a]2-4ax+ax-(x)2
(4a)2-3ax-(x)2
Chandler wants to buy a bike
that costs $345. He has a job that
pays an hourly wage of $6. He
needs to pay back $35 that he
borrowed from his mom. How
many hours does Chandler need to
work to have enough money to
purchase the bike?
Solve. Be sure to eliminate any extraneous solutions. X= square -2x+48
Answer: X = 6
Step-by-step explanation:
Substitute the x’s in the equation for the answer options that are provided.
Solutions of quadratic equation x = √(-2x + 48) are x = -8 and x = 6.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given, quadratic equation;
x = √(-2x + 48)
Squaring on both sides,
x² = -2x + 48
x² + 2x - 48 = 0
Now, we have to solve for x.
Simplifying,
x² + 8x - 6x - 48 = 0
(x + 8)(x -6) = 0
(x + 8) = 0 and (x -6) = 0
x = -8 and x = 6
After eliminating the extraneous solutions;
we have,
x = -8 and x = 6.
Therefore, the solutions are x = -8 and x = 6.
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The box plots show the average wind speeds, in miles per hour, for two different islands.
Average Wind Speeds on Island A
H
++
2 3 4 5 6 7 8 9 10 11
Average Wind Speeds on Island B
Which explains, on a given day, which island is more likely to have a wind speed close to its median
the answer would be 240 because wind speed is close to its median
Triangle DEF is shown on the xy-coordinate plane. The triangle will be rotated 180° clockwise around point (4, 8) to create AD'E'F'. Which
characteristic of AD'E'F' will NOT be the same for the corresponding characteristic of ADEF?
O the coordinates of D'
O the coordinates of F
O the area of AD'E'F'
O the perimeter of AD'E'F'
Answer: the coordinates of D'
Step-by-step explanation:
Reflections are rigid motions, so area and perimeter are preserved.
However, the preimage of a point is only the same as the image of that same point if that point is the center of rotation. Since point D is not the center of rotation, the coordinates of D' will not be the same as those of D.
Choose two number sentences below that equal 39:
A) 71 - 32
B) 49 - 20
C) 85 - 46
D) 50 - 29
What is the Length of CG
Answer: 32
Step-by-step explanation:
Since [tex]\overline{FG} \parallel \overline{AC}[/tex], we know that by the corresponding angles theorem, [tex]\angle BFG \cong \angle BAC[/tex] and [tex]\angle BGF \cong \angle BCA[/tex].
Thus, [tex]\triangle BFG \sim \triangle BAC[/tex] by AA.
It follows that since corresponding sides of similar triangles are proportional,
[tex]\frac{36+90}{90}=\frac{CG+80}{80}\\ \\\frac{126}{90}=\frac{CG+80}{80}\\\left(\frac{126}{90} \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}[/tex]
Find and solve a system of linear equations to answer the question below.
Joanne buys one kilogram of French Roast and one kilogram of Boxer Blend
from the Java Hut. Jacob buys two kilograms of French Roast and three
kilograms of Boxer Blend. If Joanne spends $14 for her purchase, and Jacob
spends $36 for his, what is the price of one kilogram of Boxer Blend coffee? Please help!!
Answer:
$8
Step-by-step explanation:
Let f = 1 kg of French Roast coffee
Let b = 1 kg of Boxer Blend coffee
Given:
Joanne buys 1 kg of French Roast and 1 kg of Boxer Blend. Joanne spends $14 for her purchase.⇒ f + b = 14
Given:
Jacob buys 2 kg of French Roast and 3 kg of Boxer Blend. Jacob spends $36 for his purchase.⇒ 2f + 3b = 36
Rewrite the first equation to make f the subject:
⇒ f + b = 14
⇒ f = 14 - b
Substitute this into the second equation and solve for b:
⇒ 2f + 3b = 36
⇒ 2(14 - b) + 3b = 36
⇒ 28 - 2b + 3b = 36
⇒ 28 + b = 36
⇒ 28 + b - 28 = 36 - 28
⇒ b = 8
Therefore, the price of 1 kg of Boxer Blend coffee is $8
If you had 36 cookies and gave 1/2 to one friend and 1/4 to another, how many could you have left?
Step-by-step explanation:
[tex] \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} [/tex]
[tex] \frac{3}{4} 36 = 27[/tex]
Find the lateral area of the prism. 8cm 6cm, I 1 13cm I 10cm Lateral Area = [?]cm² 2008-2012 International Academy of Science, All Rights Reserved. Aid Enter
The lateral area of the prism is 270cm²
What is the lateral area of a prism?
The lateral area of a prism is defined as the sum of the areas of its lateral faces.
How to determine the lateral area of a prismUsing the formula;
Lateral area = (a+ b+ c) h
Where a, b, c, are all the lateral faces and h is the height
Lateral area = (8 + 6 + 13) × 10 = 27 × 10 = 270cm²
Therefore, the lateral area of the prism is 270cm²
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Identify the first five terms of the sequence in which an = 3n − 1 + 1.
The first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13
How to determine the first five terms?The formula of the sequence is given as:
an = 3(n -1) + 1
The above sequence is an arithmetic sequence, and the first five terms are the values of the sequence when the value of n is from 1 to 5
i.e. n = 1, 2, 3, 4 and 5
Next, we set n = 1, 2, 3, 4 and 5, and substitute these values for n in an = 3(n -1) + 1
So, we have the following equations
First term
a1 = 3(1 -1) + 1 = 1
Second term
a2 = 3(2 -1) + 1 = 4
Third term
a3 = 3(3 -1) + 1 = 7
Fourth term
a4 = 3(4 -1) + 1 = 10
Fifth term
a5 = 3(5 -1) + 1 = 13
Hence, the first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13
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if the volume of a cube is 27cm³ what are the dimensions of the cube
Answer:
3 cmStep-by-step explanation:
if the volume of a cube is 27cm³ what are the dimensions of the cube
Cube Volume = l³
we use the inverse formula
∛V = l
so
∛27 =
3 cm
A scale model of a building is 3 inches tall. If the building is 90 feet tall, find the scale of the model.
The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
Scaling of measurementScaling is the way of enlarging or reducing the image of an object.
Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;
Convert both measures to same units
Since 1 feet. = 12 in
90 feet = 90/12 in = 7.5 in
Take the ratio
3 : 7.5 = 30: 75
Reduce to lowest term
30: 75 = 2 : 5
Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5
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simplify:
x² - 25
x²-3x -15
Answer:
x² - 25=(x-5)(X+5)
x²-3x -15=5.6 or. -2.6
The total area of town C and town D is 120,000 square miles. The area of town C is 30,000 square miles more than that of town D. Find the area land of each town.
Answer:
Find the area land of each town.
Let x be the area of town D
then, x+ 30000 is the area of town C
we know that,
the total area of town C and town D is 120,000 square miles.
x+x+30000=120000
2x= 90000
x=45000
Area of town D= 45000 square miles
Area of town C= 45000+30000= 75000 square miles.
The graph below represents which system of inequalities?
A) y > 2x − 3
y > −x − 3
b) y < 2x − 2
y < −x + 3
C) y ≤ 2x − 2
y > −x + 3
D) None of the above
The system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
Equation of a lineA line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b
For the broken line, the coordinate points will be(0, 3) and (3, 0)
m = -3/3
m = -1
The equation of the line will be y > -x + 3
For the solid line, the coordinate points will be(0, -2) and (1, 0)
m = 2/1
m = 2
The equation of the line will be y ≤ 2x - 2
Hence the system of inequalities that represents the graph are y > -x + 3 and y ≤ 2x - 2
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What is the y-intercept for this function?
a
(0, −3)
b
(3, 0)
c
(−9, 0)
d
(0, −9)
Answer:
d
Step-by-step explanation:
the y- intercept is the point on the y- axis where the graph crosses
the graph crosses the y- axis at point (0, - 9 )
then y- intercept = (0, - 9 )
WILL MARK BRAINLIEDT If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central angle associated with the arc? Use 3.14 for π. Give your answer in degrees and radians (approximate to two decimals and exact).
The angle that defines the arc is 1.57 radians or 90°.
How to get the angle of the arc?For a circle of radius R, the length of an arc defined by an angle θ in radians is given by:
L = θ*R.
Here we know that the radius is R = 7cm, and the length of the arc is 10.99 cm. Replacing these in the above equation:
10.99 cm = θ*7cm
θ = (10.99 cm/7 cm) = 1.57
Then the angle is 1.57 radians. Remember that:
3.14 radians = 180°
Then:
θ = (1.57/3.14)*180° = 90°
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[tex]\\ \rm\Rrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180\ell}{r\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{180(10.99}{7(3.14)}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=\dfrac{1978.2}{7\pi}[/tex]
[tex]\\ \rm\Rrightarrow \Theta=90^{\circ}[/tex]
On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of
100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions
are on the test?
04
0 8
0 12
O 16
help asap please
Which of the points shown below are on the line given by the equation y = x + 4? Check all that apply
A) -1, 3
B) 2, 6
C) -2, -2
D) 2, 4
The points on the line are points B and D
How to determine the points on the line?The equation is given as:
y = x + 4
The above means that the output value is 4 more than the input value
Using the above rule, the points that satisfy the equation are:
B) 2, 6 and D) 2, 4
This is so because:
6 = 2 + 4
4 = 2 + 2
Hence, the points on the line are points B and D
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which expression is equivalent to sin(2x) cosx
Answer:
[tex]2sin(x)cos^2(x)[/tex]
Step-by-step explanation:
To solve the problem, you must expand the trigonometric expression using the information given.
[tex]sin(2x)cosx\\sin(2x)\\=2sin(x)\\=2sin(x)cos^2(x)[/tex]
Suppose you have $600 to invest in a savings plan,Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding.
Answer:
P(1+[tex]\frac{r}{100}[/tex])ⁿ
600(1+[tex]\frac{5}{100}[/tex])¹
600(1+0.05)¹
600(1.05)
630
Note:
P= participle
R= rate
N= years
Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?
(0, 4)
(–1, 0) and (1, 0)
(–1, 0), (0, 4), and (1, 0)
(–4, 0), (–1, 0), (0, 4), and (1, 0)
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
If we plot the function, y = 4x⁴ - 8x² + 4, then it can be observed that the lists all of the turning points of the graphs are (–1, 0), (0, 4), and (1, 0).
Hence, the correct option is C.
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Suppose a high school student is selected at random.Let event A = junior and event B = earbuds. Are events A and B independent
Answer:
yes
Step-by-step explanation:
independence means the object or so are completely unreliant of eachother or does not have order.
for example a dependent situation would be sports players getting picked because there is order.
The sides of a triangle measure 10 feet, 13 feet, and 17 feet.
How would you explain to a friend that the triangle is not a right triangle?
Step-by-step explanation:
if the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle
bbc
10 squared = 100
13 squared = 169
17 squared = 289
100 + 169 = 269 NOT 289 so
there is no right angle and so its not a right triangle
A rain drop hitting a lake makes a circular ripple.. if the radius, in inches,, grows as a function of time in minutes according to R(t)=20sqrt(t+2), find the area of the ripple as a function of time. What is the area of the circular ripple at t=2?
Answer:
Step-by-step explanation:
Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)
A(2) = 400π (2 + 2) = 1600π = 5026.5 in²
please help me.............
I apologize for the handwriting it's not the best :)
What is Logically equivalent? Yeah
answer:
c
step by step explanation:
I did it on edge.
Line segment AB with endpoints A (5, 8) and B (7, 8) is translated 2 units down and 2
units left. Identify the coordinates of the endpoints of the translated line segment?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of the translated line segment will be A' (3,6) and B' (5,6).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Since AB is a line segment the changes will occur on both the coordinates, therefore, if the line segment is translated 2 units down and 2 units left, the coordinates will be,
A = (5,8) → 2 units down ⇒ (5, 8-2) → 2 units left ⇒ (5-2, 8-2) = (3, 6)
B = (7,8) → 2 units down ⇒ (7, 8-2) → 2 units left ⇒ (7-2, 8-2) = (5, 6)
Hence, the coordinates of the translated line segment will be A' (3,6) and B' (5,6).
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Simon is riding a bike at 12 km/h away from his friend Keesha. He throws a ball at 5 km/h back to Keesha, who is standing still on a sidewalk.
How fast would Keesha say the ball is traveling?
5 km/h
7 km/h
12 km/h
17 km/h
Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h
What is relative velocity?Relative velocity is defined as the velocity of an object with respect to another observer.
From the question, we are to determine how fast Keesha would say the ball is traveling. That is, the relative velocity
Relative velocity of the ball = 12 km/h - 5 km/h
Relative velocity of the ball = 7 km/h
Hence, Keesha would say the ball is traveling at 7 km/h. The correct option is the second option 7 km/h
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Answer:
7 km/h
Step-by-step explanation:
|2/13t-11|-10=-16
solve for t
[tex]\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset[/tex]