Answer:
Final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].
Step-by-step explanation:
Given rational expressions are [tex]\frac{x+2}{x-4}[/tex] and [tex]\frac{3x}{x+4}[/tex].
Now we need to find about what is the product of given rational expressions.
to multiply the rational expressions, we simply multiply numerator with numerator. Then multiply denominator with denominator.
[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]
[tex]=\frac{\left(x+2\right)\cdot3x}{\left(x-4\right)\cdot\left(x+4\right)}[/tex]
[tex]=\frac{3x^2+6x}{x^2+4x-4x-16}[/tex]
[tex]=\frac{3x^2+6x}{x^2-16}[/tex]
Hence final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].
Explain the following terms: positive slope, negative slope, x-intercept, y-intercept
The volume of a sphere is 2,143.572,ft cubed. To the nearest foot, what is the radius of the sphere? Use 3.14 for pi.
Volume of a sphere is defined:
[tex]V=\frac{4\pi r}{3}[/tex]
Solve for radius.
[tex]3V=4\pi r\Longrightarrow r=\frac{3V}{4\pi}[/tex]
Now put in the data.
[tex]
r=\frac{3\cdot2143.572}{4\cdot3.14} \\ \\
r=\frac{6430.716}{12.56}\approx\boxed{30010}
[/tex]
The radius of the sphere is 30010ft.
Hope this helps.
r3t40
x and y intercepts if y=3(x-1)^2-12
The x-intercepts are: (-1,0) and (3,0).
The y-intercept is: (0,-9).
Hope this helps!
In 1983, a pair of jeans cost $66.35. If a pair of jeans costs $118.10 today, what is the CPI? a. 152 b. 156 c. 178 d. 184
Answer:
ddddddd
Step-by-step explanation:
Answer:
The correct answer is C on edge 2020
Step-by-step explanation:
Given that ba bisects DBC which statements must be true
Answer: the answer is m∠ABD = m∠ABC
The answer is, m∠ABD = m∠ABC.
What does bisects mean?To cut or divide into two equal or nearly equal parts. Geometry to cut or divide into two equal parts: to bisect an angle.What is an example of bisector?Example of Line Segment Bisector: Consider a line AB = 4cm. A line segment bisector will cut it into two equal parts of 2cm each. If a bisector cuts the line segment into two equal parts at 90o, then the bisector is known as perpendicular bisector.What is bisecting a shape?Bisect means to cut or divide something into two equal parts.
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Reflection all symmetry is the quality a design has if it maintains all characteristics when it is (blank) lying in its plane.
A) rotated about an axis
B) translated along a line
C) rotated about a point
Answer:
Rotated about an axis
Step-by-step explanation:
APEX
Reflectional symmetry is the quality a design has if it maintains all characteristics when it is (blank) lying in its plane Option: A) rotated about an axis.
What is reflectional symmetry?Consider a plane. Consider a design or shape on that plane. Now consider an axis.
If we think of that axis as a mirror, and on the opposite side of that axis create the image of the considered shape, then if the shape's image looks exactly as the shape itself, then that shape is called to have a reflectional symmetry.
Instead of that mirror intuition, we can also think that we sort of rotated that image about that considered axis, and after half rotation, the figure is again onto its plane. If that rotated figure looks alike to the initial figure, then that figure has rotational symmetry.
Thus, reflectional symmetry is the quality a design has if it maintains all characteristics when it is (blank) lying in its plane Option: A) rotated about an axis.
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Which statement best compares the spread of the data sets?
Answer:
Choice B is correct
Step-by-step explanation:
The Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.
The spread of a data set is a measure of the dispersion or variability of the data set. The spread can be measured by various statistical quantities depending on the nature of the data (skewed or symmetric);
The IQR
Variance
Standard Deviation
Range
A box plot is a graphical representation of the five number summary;
The minimum, first quartile, median, third quartile, and the maximum value in that order.
The IQR is defined as;
third quartile - first quartile
With this definition, the Interquartile Range (IQR) for Florida is;
28 - 17 = 11
while the Interquartile Range (IQR) for Australia is;
14 - 10 = 4
Therefore, the Interquartile Range (IQR) for Florida, 11, is greater than the IQR for Australia, 4.
The Sun is vvv kilometers from the upper edge of the Earth's atmosphere and qqq kilometers from the surface of the Earth. Which of the following expressions always represents the distance between the Earth’s surface and the upper edge of the Earth's atmosphere?
Choose 1 answer:
(Choice A)
v+q
(Choice B)
| v-q|
(Choice C)
None of the above
Answer:
The distance between the Earth's surface and the upper edge of the Earth's atmosphere would be Q - V.
The distance from the Sun to the Earth is Q. The distance from the Sun to the upper edge of the atmosphere is V. If you subtract V from Q, the remaining distance is that of the Earth's atmosphere. Q - V = the atmosphere
Step-by-step explanation:
Answer:
Choice B
Step-by-step explanation:
I just did the question on khan
Factor the polynomial: -x^3-2x^2-3x
Answer:
-x(x^2+2x+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
-x is common to all three terms. Thus, -x^3-2x^2-3x = -x(x^2 + 2x + 3).
Use the quadratic formula to find the roots (and thus the factors) of
x^2 + 2x + 3: a = 1; b = 2; c = 3.
Thus, the discriminant is b^2-4ac, or 4 - 4(1)(3), or -8.
Because this discriminant is negative, x^2 + 2x + 3 has two complex, unequal roots. They are:
-2 ± i√8
x = -------------- or -1 ± i*2*√2
Thus, the three factors of the given polynomial are:
-x, (x + 1 + 2i√2), and (x + 1 - 2i√2)
2
Sarah bought a car last year to drive back and forth to work after she spent $1,098 on gas this year she spent $1,562 what is the inflation rate rounded to the nearest percent
Answer:
its 42%
Step-by-step explanation:
the answer above is wrong
The inflation rate in the car is 42%.
What is the inflation rate?Inflation Rate (CPI, annual variation in %) Inflation refers to an overall increase in the Consumer Price Index (CPI), which is a weighted average of prices for different goods.
Sarah bought a car last year to drive back and forth to work after she spent $1,098 on gas this year she spent $1,562.
Based on the above information, the calculation is as follows:
[tex]\rm Inflation \ rate=\dfrac{1562-1098}{1098}\\\\ Inflation \ rate=\dfrac{464}{1098}\\\\ Inflation \ rate=0.42\\\\ Inflation \ rate=0.42 \times 100\\\\ Inflation \ rate= 42 \ percent[/tex]
Hence, the inflation rate of the car is 42%.
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a hockey team ordered 12 wooden pedestals to mount their brass trophies on. The design pedestal is shown below. The teal is charge $0.08 per cubic inch of wood. What is the total cost of the order, rounded to the nearest dollar?
56 cause u need 12 divide by 0.08 12 times
Answer:
Total charge for wooden pedestal will be $1136
Step-by-step explanation:
Volume of the pedestal will be = volume of cube + volume of the cone
= (Side)³ + [tex]\frac{1}{3}(\pi r^{2}h)[/tex]
= 10³ + [tex]\frac{1}{3}[\pi (\frac{10}{2})^{2}(7)][/tex]
= 1000 + [tex]\frac{1}{3}[\pi 5^{2}(7)][/tex]
= 1000 + [tex]\frac{1}{3}[\pi (25)(7)][/tex]
= 1000 + [tex]\frac{1}{3}[(3.14)(25)(7)][/tex]
= 1000 + 183.17
= 1183.17 cubic inch
Total volume of 12 wooden pedestals = 12 × 1183.17 = 14198 cubic inch
Since charges of the wood is $0.08 per cubic inch
So total charges for pedestal will be = 0.08 × 14198 = $1135.84 ≈ $1136
A rectangle has an area of 22 square miles and a base of 5 miles. What is the height? miles
Answer:
4.4 miles is the height
Step-by-step explanation:
Area = base x height
22= 5 x 4.4
Answer:22=5*4.4
Step-by-step explanation:
the base is 5 miles so you do 22 / 5 and it gives you 4.4 for the height
Juice boxes are sold in a local store for 65 cents each. The factory has $1400 in fixed costs plus 15 cents of additional expense for each juice box made. Assuming all juice boxes manufactured can be sold, find the break-even point.
Answer:
Production of 2800 juice boxes is the break even point.
Step-by-step explanation:
Break-even point is the point where profit is zero and number of manufactured goods are all sold
Let number of juice boxes be y
charges of local store for 1 juice box= $0.65
charges of local store for y juice box=$0.65y
Factory cost of y juices boxes= $1400 + $0.15y
Assuming all juice boxes manufactured can be sold, to find the break-even point
charges of local store for y juice box= Factory cost of y juices boxes
$0.65y=$1400 + $0.15y
$0.65y-$0.15y= $1400
$0.50y=$1400
y= 1400/0.5
y=2800
hence production of 2800 juice boxes is the break even point!
You buy a laptop that costs £899, including VAT at 20%. How much of the purchase price is VAT?
I’m not sure if it’s right try it
For this case we propose a rule of three:
£ 899 ----------------> 100%
x ----------------------> 20%
Where "x" represents the amount of money corresponding to the VAT.
[tex]x = \frac {20 * 899} {100}\\x = 179.8[/tex]
So, the VAT is £ 179.8
ANswer:
The purchse price of VAT is £ 179.8
simplify: cos2x+cos4 all over sin2x - sin 4x
1400 answer choice B
Answer:
[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}=-\cot\left(x\right)[/tex]
Step-by-step explanation:
[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}[/tex]
Apply formula:
[tex]\cos\left(A\right)+\cos\left(B\right)=2\cdot\cos\left(\frac{A+B}{2}\right)\cdot\cos\left(\frac{A-B}{2}\right)[/tex] and
[tex]\sin\left(A\right)-\sin\left(B\right)=2\cdot\cos\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex]
We get:
[tex]=\frac{2\cdot\cos\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}{2\cdot\cos\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}[/tex]
[tex]=\frac{\cos\left(\frac{2x-4x}{2}\right)}{\sin\left(\frac{2x-4x}{2}\right)}[/tex]
[tex]=\frac{\cos\left(\frac{-2x}{2}\right)}{\sin\left(-\frac{2x}{2}\right)}[/tex]
[tex]=\frac{\cos\left(-x\right)}{\sin\left(-x\right)}[/tex]
[tex]=\frac{\cos\left(x\right)}{-\sin\left(x\right)}[/tex]
[tex]=-\cot\left(x\right)[/tex]
Hence final answer is
[tex]\frac{\cos\left(2x\right)+\cos\left(4x\right)}{\sin\left(2x\right)-\sin\left(4x\right)}=-\cot\left(x\right)[/tex]
find the missing term of each equivalent ratio. 90:15=_____:7
ANSWER
The missing term is 42.
EXPLANATION.
We want to find the missing term of the equivalent ratio. 90:15=_____:7
Let y be the missing term, then
90:15=y:7
We rewrite as fractions to get;
[tex] \frac{90}{15} = \frac{y}{7} [/tex]
Simplify the left ratio:
[tex] \frac{6}{1} = \frac{y}{7} [/tex]
Cross multiply:
[tex]6 \times 7 = 1 \times y[/tex]
[tex]42 = y[/tex]
Therefore the missing term is 42.
Determine (a+h) - @) for f(x) = x2 + 5x and simplify.
To determine (f(a+h) - f(a)) for f(x) = x² + 5x, we substitute a+h and a into the function, expand, and subtract to ultimately simplify to 2ah + h² + 5h.
To determine (f(a+h) - f(a)) for f(x) = x² + 5x and simplify, we need to substitute x with a+h and a into the function separately and then find the difference. Here are the steps:
Substitute a+h into f(x) to get f(a+h) = (a+h)² + 5(a+h).
Expand the equation: f(a+h) = a² + 2ah + h² + 5a + 5h.
Substitute a into f(x) to get f(a) = a² + 5a.
Find the difference: (f(a+h) - f(a)) = (a² + 2ah + h² + 5a + 5h) - (a² + 5a).
Simplify the expression: (f(a+h) - f(a)) = 2ah + h² + 5h.
Our math team had m students last year, but this year it has already n students! By what percent did the number of students grow? need percentage only 24 points
Answer:
Since is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. Then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100
What are the coordinates of a point that partitions segments ab in a ratio of 1:5?
(3,6) I think is the answer
Answer:
I believe it's (19,10)
Daniel sites 5 feet away Mia . Juliette sites 64 inches away from Mia. who sits closer to Mia.
daniel sits closer to mia
What is the domain of g?
Answer:
The answer is -9,9 Its funny cuz I just did this problem on Khan academy
Step-by-step explanation:
Can I get brainliest
-9,9 should be the answer
The points (0,8),(5,3),(4,2) and (-1,7) are vertices of a rectangle. Determine the coordinates of the midpoints for each side and determine if the midpoints are the vertices of a rectangle
The area of the triangle is 16.
You can find this by plotting each of the points and drawing the triangle. You can then use the distance formula to determine each side length. The rectangle will be 2 on one side and 4 on the other. When multiplied together, it will give you the above answer
The coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
And, yes, the midpoints are the vertices of a rectangle, as its opposite sides are the same in length.
Use the formula for the midpoint of two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are,
[tex][\dfrac{(x_1 + x_2)}{2} , \dfrac{(y_1 + y_2)}{2} ][/tex]
Given that,
Vertices of the rectangle are (0, 8), (5, 3), (4, 2), and (- 1, 7).
Hence, the coordinates of the midpoints for each side are calculated by using the above formula,
The midpoint of two points (0, 8) and (5, 3) are,
[tex](\dfrac{(0 + 5)}{2} , \dfrac{(8 + 3)}{2} )[/tex]
[tex](2.5, 5.5)[/tex]
The midpoint of two points (5, 3) and (4, 2) are,
[tex](\dfrac{(5 + 4)}{2} , \dfrac{(3 + 2)}{2} )[/tex]
[tex](4.5, 2.5)[/tex]
The midpoint of two points (4, 2) and (-1, 7) are,
[tex](\dfrac{(4 - 1)}{2} , \dfrac{(2 + 7)}{2} )[/tex]
[tex](1.5, 4.5)[/tex]
The midpoint of two points (-1, 7) and (0, 8) are,
[tex](\dfrac{(-1 + 0)}{2} , \dfrac{(8 + 7)}{2} )[/tex]
[tex](-0.5, 7.5)[/tex]
Therefore, the coordinates of the midpoints for each side are (2.5, 5.5) , (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
When the coordinates of vertices are rectangular then opposite sides are equal to each other.
So, we can check the length of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5).
Used the distance formula,
The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, The distance between the two points [tex](2.5, 5.5)[/tex] and [tex](4.5, 2.5)[/tex],
[tex]d = \sqrt{(4.5- 2.5)^2 + (2.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](4.5, 2.5)[/tex] and [tex](1.5, 4.5)[/tex],
[tex]d = \sqrt{(4.5- 1.5)^2 + (2.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points [tex](1.5, 4.5)[/tex] and [tex](-0.5, 7.5)[/tex]
[tex]d = \sqrt{(1.5+ 0.5)^2 + (7.5 - 4.5)^2}[/tex]
[tex]d = \sqrt{4 + 9}[/tex]
[tex]d = \sqrt{13}[/tex]
The distance between the two points[tex](-0.5, 7.5)[/tex] and [tex](2.5, 5.5)[/tex]
[tex]d = \sqrt{(2.5+ 0.5)^2 + (7.5 - 5.5)^2}[/tex]
[tex]d = \sqrt{9 + 4}[/tex]
[tex]d = \sqrt{13}[/tex]
Clearly, All the lengths of each side of the coordinates of the midpoints (2.5, 5.5), (4.5, 2.5), (1.5, 4.5), and (- 0.5, 7.5) are the same.
Hence, it forms a rectangle, as its opposite sides are also the same in length.
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need answer will name the brainliest!!!!!!! PLZ PLZ
What question do you need answered?
Answer:
Option A.
Step-by-step explanation:
Anastasia worked for = 7 hours per day
Number of weeks she worked = 52 weeks
Number of hours she worked = 7×52
= 364 hours
Per hour earning of Anastasia = $20
Total earning of Anastasia = 364×20
= $7280
Let the monthly expenses of Anastasia = $x
Then total expenses = $12x
At the end of the year total saving = Total earning - Total expenses
= $7280 - 12x
Since she saved $2000 in a year therefore, expression that represents the savings will be
2000 = 7280 - 12x
12x = 7280 - 2000
12x = 5280
x = [tex]\frac{5280}{12}[/tex]
x = $440
Option A will be the answer.
Melanie is taking flute lessons. Her flute teacher charges $32.50 per hour. If Melanie has 2.5 hours of lessons each week, what is the weekly charge for her lessons?
2.5 x 32.50 = 81.25 a week
Answer:
32.50× 2 = 65
32.50 ÷ 2 = 16.25
65+16.25 = 81.25(this is the answer)
If m1=45 degrees, which other angles have a measure of 45 degrees? Select all that apply.
∠ 2
∠3
∠4
∠5
∠6
Answer:
∠4 and ∠5
Step-by-step explanation:
we know that
If a is parallel to b
then
∠5=∠1 -----> by corresponding angles
∠4=∠1 -----> by alternate interior angles
which of the following graphs represents the solution(s) of the following system x^2+y=7 x^2+y^2=49
UPDATE : its B
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]x^{2} +y=7[/tex]
[tex]y=-x^{2}+7[/tex] ----> equation A
This is the equation of a vertical parabola open downward
The vertex is the point (0,7)
[tex]x^{2} +y^{2}=49[/tex]
[tex]x^{2} +y^{2}=7^{2}[/tex] ----> equation B
This is the equation of a circle with center at (0,0) and radius equal to 7 units
The y-intercepts of the circle are the points (0,7) and (0,-7)
therefore
The graph in the attached figure
Answer:
B
Step-by-step explanation:
In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?
4 units
5 units
6 units
9 units
Answer:
The correct option is 2. The length of JG is 5 units.
Step-by-step explanation:
Given information: ∠EDH ≅ ∠EDG, EH=9, EJ=4.
Corresponding sides of two triangles are congruent.
[tex]EH=EG[/tex] (CPCTC)
[tex]9=EG[/tex] .... (1)
From the given figure it is clear that
[tex]EG=EJ+JG[/tex]
[tex]EG=4+JG[/tex] ... (2)
Using (1) and (2), we get
[tex]9=4+JG[/tex]
Subtract 4 from both the sides.
[tex]9-4=JG[/tex]
[tex]5=JG[/tex]
The measure of JG is 5 units, therefore the correct option is 2.
Answer:
Step-by-step explanation:
OPTION 2 OR B!!!
1. Which of the following equations have rational solutions?
Select TWO that apply.
A. (X+5)^2=49
B. X^2=12
C. X^2=81
D. (X-1)^2=20
2. Which quadratic equation is a perfect square trinomial with only one root, x=-6?
A. 3x^2+x-2=0
B. X^2-15x+36=0
C. X^2+12x+36=0
Answer:
1. A. and C.2. C.Step-by-step explanation:
[tex]1.\\\bold{YES}\\A.\ (x+5)^2=49\iff x+5=\pm\sqrt{49}\\\\x+5=\pm7\qquad\text{subtract 5 from both sides}\\\\x=-13\in\mathbb{Q}\ or\ x=2\in\mathbb{Q}\\\\C.\ x^2=81\iff x=\pm\sqrt{81}\\\\x=\pm9\in\mathbb{Q}\\\\\bold{NOT}\\B.\ x^2=12\to x=\pm\sqrt{12}\notin\mathbb{Q}\\D.\ (x-1)^2=20\to x-1=\pm\sqrt{20}\notin\mathbb{Q}[/tex]
[tex]\bold{YES}\\C.\\x^2+12x+36=0\\\\x^2+2(x)(6)+6^2=0\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+6)^2=0\iff x+6=0\qquad\text{subtract 6 from both sides}\\\\x=-6\\\\\bold{NOT}\\A.\\3x^2+x-2=0\\3x^2+3x-2x-2=0\\3x(x+1)-2(x+1)=0\\(x+1)(3x-2)=0\iff x+1=0\ \vee\ 3x-2=0\\\text{two different solutions}\\B.\\x^2-15x+36=0\\x^2-12x-3x+36=0\\x(x-12)-3(x-12)=0\\(x-12)(x-3)=0\iff x-12=0\ \vee\ x-3=0\\\text{two different solutions}[/tex]
a 28 foot ladder leaning against a building forms a 15 degree angle with the side of the building. how y’all is the building?
Check the picture below.
make sure your calculator is in Degree mode.
Please help me with this
Please Show a picture or either a text so that I can help you
Answer:
for x = 1 , y = 40(1) -5 ⇒ y = 35
for x = 1 , y = 40(2) -5 ⇒ y = 75
for x = 1 , y = 40(3) -5 ⇒ y = 115
for x = 1 , y = 40(4) -5 ⇒ y = 155
for x = 1 , y = 40(5) -5 ⇒ y = 195