The quotient of the rational expressions given is obtained by converting the division to multiplication by the reciprocal leading to \((\frac{3x \times (x+5)}{2x \times (2x+5)})\). The final simplification depends on specific values of x.
Explanation:The question asks to find the quotient of the following rational expressions: \((\frac{3x}{2x+5}) \div (\frac{2x}{x+5})\). To solve this, we first recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, the problem becomes \((\frac{3x}{2x+5}) \times (\frac{x+5}{2x})\).
We simplify this further by multiplying the numerators together and the denominators together: \((\frac{3x \times (x+5)}{2x \times (2x+5)})\).
To solve the more difficult problem, as hinted, we might consider factoring or simplifying further. However, the key calculation here reveals that the certain factors in the numerator and denominator might not simplify directly in this expression, leading to a more nuanced understanding of rational expressions. As such, detailed simplification depends on the specific values of x and further factorization may not lead to a simpler form without more context.
The correct answer is: [tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex].
To find the quotient of the given rational expressions, you divide the first rational expression by the second one.
[tex]\frac{\frac{3 x}{2 x+5}}{\frac{2 x}{x+5}}=\frac{3 x}{2 x+5} \cdot \frac{x+5}{2 x}[/tex]
Now, you can simplify this expression:
[tex]=\frac{3 x(x+5)}{2 x(2 x+5)}[/tex]
Cancel out x from both numerator and the denominator.
[tex]=\frac{3 (x+5)}{2 (2 x+5)}[/tex]
[tex]=\frac{3x+15}{4x+10}[/tex]
This value matches with the option B. Thus, B is the correct answer.
Complete Question:
Which of the following is the quotient of the rational expressions shown below?
[tex]\frac{3 x}{2 x+5} \div \frac{2 x}{x+5}[/tex]
[tex]\text { A. } \frac{4 x^2+10 x}{3 x^2+15 x}[/tex]
[tex]\text { B. } \frac{3 x+15}{4 x+10}[/tex]
[tex]\text { C. } \frac{6 x^2}{2 x^2+15 x+25}[/tex]
[tex]\text { D. } \frac{3}{4}[/tex]
Find the area of a trapezoid if the altitude is 6 inches and the median is 8 inches. (Hint: Recall that the median of a
trapezoid is equal to half the sum of the bases.)
24 sq units
48 sq. units
96 sq. units
Answer:
48 sq. units
Step-by-step explanation:
The area of a trapezoid is given by half sum of the bases multiplied by the height
[tex]=\frac{1}{2} (a+b)h[/tex]
where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid
But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae is covered by the median
[tex]Median=\frac{1}{2} (a+b)[/tex]
Hence area, A, of a trapezoid is simplified to product of median and amplitude
[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]
Answer:
=48 sq. units.
Step-by-step explanation:
Area of a trapezoid =h× (a+b)/2
(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.
Median=8 inches
Altitude is the distance between the two parallel sides= 6 inches
A=6 inches×8 inches
=48 sq. units.
How can you verify that the solution to a proportion is correct?
Final answer:
To verify a proportion solution, substitute the answer back into the original equation, check that the units are consistent, and ensure the answer's reasonableness in terms of magnitude, sign, and units.
Explanation:
To verify that a solution to a proportion is correct, one effective method is to perform a check by substituting the solution back into the original proportion equation. Here's how you can ensure the correctness of the solution step by step:
First, solve the proportion problem and record your answer.Next, substitute the solution for the unknown in the original proportion to see if the two ratios are equivalent.Ensure that the units make sense both in the proportions and when substituting the solution back in.Check to see if the answer is reasonable: Does it seem too large or too small? Does it have the correct sign? Are the units consistent with the problem?Please help me Find a, b, and c
Answer:
It is A.
Step-by-step explanation:
To solve for b, use the 45-45-90 triangle theorem, in which each of the legs is x, so the legs would be 8. The hypotenuse would therefore be 8√2.
So without further solving the answer is A, since it's the only one with 8√2.
However, I will still solve for A and C. Using the 30-60-90 theorem, we have the sides as x, x√3, and 2x. The second longest side is b. Using this, we find a = 4√6 and c to be 4√2
Sketch the graph of the given function. The state the functions domain and range
f(x)=-2{1/4}^x
Answer:
Domain: -∞ < x < ∞
Range: f(x) < 0
Step-by-step explanation:
[tex]f(x)=-2(\frac{1}{4})^x[/tex]
We need to sketch the graph and identify domain and range of the function f(x).
The graph is attached in the figure below.
Domain:
The domain of the function is all the values of x that gives the real values for f(x).
So, in our case all values of x gives real values for f(x). So domain is:
-∞ < x < ∞
Range:
The range of the function is the resulting f(x) values when we put all the values of x.
In our case the value of f(x) will always be less than zero because of the negative sign.
Range is:
f(x) < 0
Find the equation of a circle with its center at (2,7) and a radius of 5.
Final answer:
The equation of a circle with center (2,7) and a radius of 5 is (x - 2)² + (y - 7)² = 25.
Explanation:
To find the equation of a circle with its center at (2,7) and a radius of 5, we use the standard form of the equation for a circle which is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle and r is the radius.
Plugging in the given values for our circle we have:
(x - 2)² + (y - 7)² = 5²
Expanding the right side of the equation gives us:
(x - 2)² + (y - 7)² = 25
This is the desired equation of the circle. It represents a circle with a radius of 5, centered at the point (2,7).
. You deposit $10,000 in an account that pays 6.92% annual interest. Find the balance after 5 years if the interest is compounded with the given frequency.
Final answer:
To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, use the formula A = P(1 + r/n)^(nt). The balance after 5 years will be $13,933.16.
Explanation:
To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, you can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal is $10,000, the annual interest rate is 6.92%, and n is 1 (compounded annually), and t is 5 years.
Calculate (1 + r/n)^(nt): (1 + 0.0692/1)^(1 * 5) = 1.0692^5 = 1.39331595
Calculate the final amount using the formula: A = 10,000 * 1.39331595 = $13,933.16
Therefore, the balance after 5 years will be $13,933.16.
You manage inventory for Swim Chem, a large distributor of chemicals for indoor and outdoor pool companies. Your division sold 2.4 tone of chlorine on Monday, 4.4 on Tuesday, 1.8 on Wednesday, and 2.8 on Thursday. If last week's sales totaled 14.4 tons, how much chlorine sold on Friday?
Answer:
[tex]\boxed{\text{3.0 T}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]
Answer: There are 3 tons of chlorine sold on Friday.
Step-by-step explanation:
Since we have given that
Number of tone of chlorine on Monday = 2.4
Number of tone of chlorine on Tuesday = 4.4
Number of tone of chlorine on Wednesday = 1.8
Number of tone of chlorine on Thursday = 2.8
Total number of week's sales = 14.4 tons
So, we need to find the number of tone of chlorine on Friday.
According to question we get that
[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]
Hence, there are 3 tons of chlorine sold on Friday.
What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?
Answer:
see explanation
Step-by-step explanation:
Let u = x² ( choice of variable is flexible ), then
4u² - 21u + 20 = 0 ← expressed as a quadratic
This can now be solved for u and converted back into terms of x
Answer:
refer the explanation
Step-by-step explanation:
this question can be written as
X^2=y
so,x^4=y^2
so it will be 4y^2-21y+20=0
please could someone answer this
Answer:
29/12
Step-by-step explanation:
In an isosceles triangle, two sides are equal.
Therefore:
25/6+25/6+u = 10 3/4
50/6+u=43/4
u=43/4-50/6
u=43/4-25/3
u=129/12-100/12
u=29/12
A.) x+7/x-1
B.) x+1/x+7
C.) x-1/x+7
Answer:
C
Step-by-step explanation:
If there is an expression such as:
[tex]\frac{A*B}{A*C}[/tex]
we can cancel out A from top and bottom and that will leave us with [tex]\frac{B}{C}[/tex]
Note: Let A, B, C, be any algebraic expression
For the problem given, we can simply cut (x+1) from top and bottom by rules of algebra. So the remaining terms are:
[tex]\frac{(x-1)}{(x+7)}[/tex]
This is option C
Answer:
C)
Step-by-step explanation:
When you have a*b/c*a, a crosses out, simplifying to b/c:
(x+1)(x-1)/
(x+1)(x+7)
When "crossing out", you are really just simplifying it to 1/1:
1*(x-1)/
1*(x+7)
Which is the same as:
(x-1)/(x+7)
Therefore, C is the correct answer
-3 < n < 1
n is an integer
write down the possible values of n
The notation of the above inequality:
[tex]-3<n<1[/tex]
Can be written as an interval:
[tex]n\in(-3,1)[/tex]
Or group of points on a line that satisfy the linear inequality.
[tex]n\in\mathbb{G}=\{n; -3<n<1\wedge n\in\mathbb{Z}\}[/tex]
Or simply:
[tex]n\in\mathbb{G}=\{-2,-1,0\}[/tex]
Hope this helps.
r3t40
Which graph is a function of X? Explanation, please?
Answer:
V looking graph
(absolute value function)
Step-by-step explanation:
We are looking for a relation that passes the vertical line test.
Basically if you can play a vertical line on your graph and it touches more than once on that vertical line (your graph) then it isn't a function.
The only one that is a function here is the V looking graph.
The graph in the shape of a V (absolute value function)
We want a partnership that can withstand the vertical line test.Fundamentally, Whenever you really can play a vertical line in the graphs so it touches the vertical line (your graphs) more than once, it isn't a function.The only one that is a function here is the V-shaped graph.Learn more:
brainly.com/question/9214547
Please help with this question
Answer:
all pairs are congruent
1) Congruent by SAS (Side-Angle-Side)
2) Congruent by SAS (Side-Angle-Side)
3) Congruent by HL (Hypotenuse-leg)
Answer:
• Each pair of triangles is congruent
~You can tell that each pair is congruent for the following reasons: (1) The legs, or sides, of the triangles in both #1 & #3 are both the same number. (2) The tick marks in #2 are the same, meaning the side lengths are similar.
• Both triangles in each pair are right triangles.
• The triangle pairs in #1 & #3 are rotations, while the triangle pair for #2 is a translation.
I was unaware of any specific answers, so I hope this is helpful!!!
What is the value of Y? WILL GIVE BRAINLIEST
Answer
54 degrees
Step-by-step explanation:
Using angle sum property(angles in a triangle add up to 180),
y+y+72=180
2y+72=180
2y=180-72
2y=108
y=108/2
y=54 degrees
pls mark brainliest
hope it helped
Answer:
A 54
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
72+y+y = 180
Combine like terms
72 +2y = 180
Subtract 72 from each side
72-72 +2y = 180-72
2y = 108
Divide by 2 on each side
2y/2 = 108/2
y = 54
Which is the graph of f(x) = 3(2/3)?
Answer:
Last graph on the right.
Step-by-step explanation:
Try substituting some values for x and see which graph is valid.
when x = 0, y = f(0) = 3 [tex](2/3)^{0}[/tex] = 3 (1) = 3
When we compare this to the graphs, we immediately see that the first 2 are not correct because in those cases, when x=0, y = 6 (i.e not 3).
Next we try x = 1
when x = 1, y = f(1) = 3 [tex](2/3)^{1}[/tex] = 3 ([tex]\frac{2}{3}[/tex]) = 2
Comparing the graphs ones again, show that only the last graph has x=1 and y = 2.
Answer:
D
Step-by-step explanation:
What is the equation of the tangent line passing through the point (1, 3) of the graph of the function f(x) = x2 + x + 1?
ANSWER
[tex]y = 3x[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + x + 1[/tex]
To find the gradient function, we find the first derivative;
[tex]f'(x) = 2x+ 1[/tex]
To find the gradient at (1,3), we put x=1 into the gradient function to get;
[tex]f'(1) = 2(1)+ 1 = 3[/tex]
The equation of the tangent line is
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get,
[tex]y-3=3(x-1)[/tex]
This simplifies to
[tex]y = 3x - 3 + 3[/tex]
[tex]y = 3x[/tex]
find the values of angles x, y, and z.
Answer:
x = 80, y = 140 and z = 20
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles in the triangle with x and equate to 180
x + 60 + 40 = 180
x + 100 = 180 ( subtract 100 from both sides )
x = 80
40° and y form a straight angle and are supplementary, hence
40 + y = 180 ( subtract 40 from both sides )
y = 140
Sum the 3 angles in the triangle with z and equate to 180
z + y + 20 = 180, that is
z + 140 + 20 = 180
z + 160 = 180 ( subtract 160 from both sides )
z = 20
Match each inequality to the number line that represents its solution
Answer:
Part 1) shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]
Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
see the attached figure
Step-by-step explanation:
Part 1) we have
[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Multiply by -10 both sides
[tex]x-2 \leq 6[/tex]
Adds 2 both sides
[tex]x \leq 6+2[/tex]
[tex]x \leq 8[/tex]
The solution is the interval -----> (-∞,8]
All real numbers less than or equal to 8
In a number line the solution is the shaded area at left of x=8 (close circle)
Part 2) we have
[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Multiply by -6 both sides
[tex]100x+11 \leq -489[/tex]
Subtract 11 both sides
[tex]100x \leq -489-11[/tex]
[tex]100x \leq -500[/tex]
Divide by 100 both sides
[tex]x \leq -5[/tex]
The solution is the interval -----> (-∞,-5]
All real numbers less than or equal to -5
In a number line the solution is the shaded area at left of x=-5 (close circle)
Part 3) we have
[tex]\frac{3x}{2}+105 \leq 96[/tex]
Multiply by 2 both sides
[tex]3x+210 \leq 192[/tex]
Subtract 210 both sides
[tex]3x \leq 192-210[/tex]
[tex]3x \leq -18[/tex]
Divide by 3 both sides
[tex]x \leq -18/3[/tex]
[tex]x \leq -6[/tex]
The solution is the interval -----> (-∞,-6]
All real numbers less than or equal to -6
In a number line the solution is the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
Multiply by -18 both sides
[tex]13x-10 \leq 81[/tex]
Adds 10 both sides
[tex]13x \leq 91[/tex]
Divide by 13 both sides
[tex]x \leq 91/13[/tex]
[tex]x \leq 7[/tex]
The solution is the interval -----> (-∞,7]
All real numbers less than or equal to 7
In a number line the solution is the shaded area at left of x=7 (close circle)
PLEASE HELP 12 POINTS
Answer:
5:5 (first box, pencils to pens)
7:3 (second box, coloured pencils to crayons)
The probability of picking a pen (1st box): 5/10
The probability of picking a crayon (2nd box): 3/10
Probability of picking both: 5/10*3/10 = 15/100
What is the ordered pair of M’ after point M (5, 6) is rotated 90° counterclockwise?
ANSWER
(-6,5)
EXPLANATION
The mapping for 90° counterclockwise rotation has mapping
[tex](x,y)\to (-y,x)[/tex]
The coordinates of M are (5, 6)
To find the coordinates of M' we substitute the coordinates of M into the rule.
[tex]M(5, 6)\to M'(-6,5)[/tex]
Hence the ordered pair of M' after point M (5, 6) is rotated 90° counterclockwise is (-6,5)
cant fully understand, help would be appreciated lol
Simplify the expression.
the quantity x to the one fifteenth power end quantity to the power of 5
Answer:
[tex]\sqrt[3]{x}[/tex]
Step-by-step explanation:
we have
[tex](x^{\frac{1}{15}})^{5}[/tex]
Simplify
Multiply the exponents
[tex](x^{\frac{1}{15}})^{5}=x^{\frac{1}{15}*5}=x^{\frac{5}{15}}=x^{\frac{1}{3}}=\sqrt[3]{x}[/tex]
Answer:
[tex]\sqrt[3]{x}[/tex].
Step-by-step explanation:
We have been given an expression [tex](x^{\frac{1}{15}})^5[/tex]. We are asked to simplify our given expression.
We will use power rule of exponents [tex](a^b)^c=a^{b\cdot c}[/tex] to simplify our given expression as:
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{15}\times 5}[/tex]
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}\times 1}[/tex]
[tex](x^{\frac{1}{15}})^5=x^{\frac{1}{3}}[/tex]
Using fractional exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex], we can write our expression as:
[tex](x^{\frac{1}{15}})^5=\sqrt[3]{x}[/tex]
Therefore, the simplified form of our given expression would be [tex]\sqrt[3]{x}[/tex].
What is the area of a sector with a central angle of 5π6 radians and a radius of 5.6 ft? Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
41.03 square feet
Step-by-step explanation:
The area of a sector is given by the formula:
[tex]A=\frac{1}{2}r^2\theta[/tex]
Where A is the area, r is the radius and [tex]\theta[/tex] is the angle in radians.
Given the values, we plug into the formula and solve:
[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(5.6)^2(\frac{5\pi}{6})\\A=41.03[/tex]
Which situation is most likely to have a constant rate of change?
O
A. Distance a school bus travels compared with the number of stops
O
B. Number of trees in a park compared with the area of the park
C. Length of a bead necklace compared with the number of identical
beads
D. Number of runs scored in a baseball game compared with the
number of innings
Final answer:
The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.
Explanation:
The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.
In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.
For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.
This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.
From a point P, two tangents PA and PB
are drawn to a circle with center 0. If OP is equal to diameter of the circle, show
that triangle APB is equilateral.
Answer:bsdaosdfhaodsifhaosdfaidfhaoif
have a nice time reading and understanding his:)
Step-by-step explanation:
considering APB as the triangle
AP is the tangent to the circle.
∴ OA ⊥ AP (Radius is perpendicular to the tangent at the point of contact)
⇒ ∠OAP = 90º
In Δ OAP,
sin ∠OPA = OA/OP = r/2r [Diameter of the circle]
∴ sin ∠OPA = 1/2 = sin 30º
⇒ ∠OPA = 30º
Similarly, it can he prayed that ∠OPB = 30
How, LAB = LOP + LOB = 30° + 30° = 60°
In APB,
PA = PB [lengths &tangents drawn from an external point to circle areequal]
⇒ ∠PAB = ∠PBA --- (1) [Equal sides have equal angles apposite to them]
∠PAB + ∠PBA + ∠APB = 180° [Angle sum property]
∠PAB + ∠PBA + ∠APB = 180° - 60° [Using (1)]
⇒ 2∠PAB = 120°
⇒ ∠PAB = 60°
From (1) and (2)
∠PAB = ∠PBA = ∠APB = 60°
APB is an equilateral triangle.
Find the distance CA
C' ( 0, 3)
A' ( 2 , 1)
C'A' = CA
C'A' = √(2^2 + 2^2) = √8 = 2√2
C'A' = CA = 2√2
The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.
We have,
The coordinates of point A =(2, 1) and C = (-2, 2)
Now,
To find the distance between two points, (x₁, y₁) and (x₂, y₂), we can use the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Given the points (2, 1) and (-2, 2), we can substitute the values into the formula:
Distance = √[(-2 - 2)² + (2 - 1)²]
Distance = √[(-4)² + 1²]
Distance = √[16 + 1]
Distance = √17
Therefore,
The distance between the points (2, 1) and (-2, 2) is √17, which is approximately 4.123 units.
Learn more about the distance of a line here:
https://brainly.com/question/14645718
#SPJ2
Which shows a reasonable estimation for 124% of 42 using the distributive property?
Answer:
B 48
Step-by-step explanation:
it is b I know because I got it correct
Answer:
Its b
Step-by-step explanation:
You have to estimate the numbers so b is the best answer
Carly withdraws $18 from her bank account which number line represents this amount ?
Answer:
it would be D
Step-by-step explanation:
Answer:
The number line D)
Step-by-step explanation:
Carly withdraws $18 from her bank account.
We assume that Carly has $x in her account. She withdraws $18 from her bank account.
So we have to subtract $18 from $x amount.
Which is $x - 18.
So we are subtracting $18 from her account.
It should be represented by an integer -18.
Now we have to identify the which number line represents -18.
It is D)
What is the EQUATION of a HORIZONTAL LINE passing through THE POINT (-7, 5)?
A.y = 5
B.y=-7
C.x = 5
D.x= -7
Answer:
A. y = 5Step-by-step explanation:
A horizontal line has an equation: y = a (a - any real number).
Each point on a horizontal line y = a, has coordinates (x, a) (x - any real number).
We have the point (-7, 5) → y = 5
Subtract.
(6x2 + 5) - (4x - 3)
Answer:
6x^2 -4x +8
Step-by-step explanation:
(6x^2 + 5) - (4x - 3)
Distribute the negative sign
(6x^2 + 5) - 4x + 3
Combine like terms
6x^2 -4x +5+3
6x^2 -4x +8