Answer:
the option Si mark as light green are correct
Rewrite as equivalent rational expressions with denominator (x+3)(x−4)(x+4)
An equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
The given denominator are (x+3), (x−4) and (x+4).
What is a rational expressions?A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.
Here, an equivalent rational expressions is
\(\frac{1}{x+3}+\frac{1}{x-4} +\frac{1}{x+4}\)
The LCM of denominators is (x+3)(x-4)(x+4)
= (x+3)(x²-16)
= x(x²-16)+3(x²-16)
= x³-16x+3x²-48
= x³+3x²-16x-48
Now, \(\frac{(x-4((x+4)+(x+3)(x+4)+(x+3)(x-4)}{x^3+3x^2-16x-48}\)
= (x²-16+x²+7x+12+x²-x-12)/(x³+3x²-16x-48)
= (3x²+6x-16)/(x³+3x²-16x-48)
Hence, an equivalent rational expressions with denominator (x+3), (x−4) and (x+4) is (3x²+6x-16)/(x³+3x²-16x-48).
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Pete was building a doghouse for his dog, Chip. He made the door 27 inches tall. The height of the door was three times the height of the window in the doghouse.
Write an equation to determine the height of the window.
27 = 3 + h
27 = h − 3
27 = 3h
27 equals h over 3
The equation to determine the height of the window is 27 = 3h.
The correct answer option is option C
How to write algebraic equation?Height of the door, d = 27 inchesHeight of the window = hThe height of the door was three times the height of the window in the doghouse. d = 3h27 = 3 × h
27 = 3h
Therefore, the equation 27 = 3h can be used to determine the height of the window.
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\(\sqrt{4x-5}-\sqrt{16-5x}\)
Answer:
[5/4,16/5]
Step-by-step explanation:
Maggie has a collection of 1,200 pennies. Of these, 25% are dated before 1980, 35% are dated from 1980-2000, and the rest are dated after 2000. How many pennies in Maggie's collection are dated after 2000?
Answer: 780
Step-by-step explanation:
Simplify the following
(2p^2)^5
Answer:
32p^10
Step-by-step explanation:
(2p^2)^5
(2)^5 * (p^2*5)
32p^10
5/8k=25
how do i do this?
Answer:
\( \frac{5}{8} k = 25 \\ \frac{5k}{8} = 25 \\ 5k = 25 \times 8 \\ 5k = 200 \\ k = \frac{200}{5} \\ k = 40\)
I hope it helped U
stay safe stay happy
Answer:
k=1/40
Step-by-step explanation:
multiple both sides by 8k
5= 25×8k
simplify 25×8k to 200k
5=200k
divide both sides by 200
5/200=k
simplify 5/200 to 1/40
1/40= k
switch sides
k=1/40
What is the solution to the system of equations below?
(2, 2)
(-2, 2)
(2, -2)
(-2, -2)
Answer:
(2,2)
Step-by-step explanation:
The lines cross in quadrant 1(the top right), so both x and y have to be positive.
Answer:
2,2
Step-by-step explanation:
PLEASE HELP, I NEED THIS OR I WILL FAIL MY CLASS PLZZZZ.
30 POINTS AND BRANILEST
Study and Learn
pasagutan plss..
Which expression is equivalent to 3 sqrt32x8y10?
O 4x2y3(3 sqrt2x2y)
O 2x4y5(3 sqrt4)
O 2x2y3(3 sqrt4x2y)
O 4x4y5(3 sqrt2)
Answer: \(2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)
Step-by-step explanation:
\(\sqrt[3]{32x^{8} y^{10} } =\sqrt[3]{2^{3} \cdot 2^{2} \cdot x^{2} \cdot (x^{2} )^{3} \cdot y \cdot (y^{3})^{3} } =2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)
Answer:
Option C :
\(\sqrt[3]{32x^8y^10} = 2x^2 y^3 \sqrt[3]{4x^2 y}\)
Step-by-step explanation:
\(\sqrt[3]{32x^8y^{10}}} = ( 32 x^8 y^{10})^{\frac{1}{3}}\)
\(= ( 2^5 \times x^8 \times y^{10})^{\frac{1}{3}}\\\\= ( 2^{5\times\frac{1}{3}} \times x^{8 \times \frac{1}{3}} \times y^{10 \times \frac{1}{3}})\\\\=(2^{\frac{3}{3} + \frac{2}{3}}} \times x^{\frac{6}{3} + \frac{2}{3}} \times y^{\frac{9}{3} + \frac{1}{3}})\\\\= 2 \times 2^{\frac{2}{3}} x^2 \times x^{\frac{2}{3}} \times y^3 \times y^\frac{1}{3}\\\\=2x^2 y^3 \times 2^{\frac{2}{3} \times }x^{\frac{2}{3}} \times y^{\frac{1}{3}}\\\\=2x^2 y^3 (2^2x^2 y)^{\frac{1}{3}}\\\\= 2x^2y^3 \ \sqrt[3]{ \ 4 x^2 \ y }\)
x+y=24
75x+60y=1710
Solve using any method
Answer:
\(x=18,\:y=6\)
Step-by-step explanation:
Solve by substitution
\(\begin{bmatrix}x+y=24\\ 75x+60y=1710\end{bmatrix}\)
\(\mathrm{Substitute\:}x=24-y\)
\(\begin{bmatrix}75\left(24-y\right)+60y=1710\end{bmatrix}\)
\(\begin{bmatrix}1800-15y=1710\end{bmatrix}\)
\(\mathrm{For\:}x=24-y\)
\(\mathrm{Substitute\:}y=6\)
\(x=24-6\)
\(x=18\)
\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)
\(x=18,\:y=6\)
Use the formula for the general term (the nth term) of a geometric sequence to find a(sub5) with the given first term a(sub1)=9, and a common ratio, r=5sub=subscript
The general expression for the n terms :
\(a_n=a_1r^{n-1}\)From the given data :
first term = 9, Common Ratio: r = 5
we need to find the fifth term : n = 5
Substitute the given value in the expression for
In the figure below, lines m and n are parallel.
what is the measure of
A. 20
B. 35
C. 40
D. 15
HELP i’ll mark brainlist !!!
6.3 divided by 2.5 HELP ME PLZZZZZZZZZZZZZZZ
Answer:
6.3/2.5=2.52
Step-by-step explanation:
Answer:
2.52
Step-by-step explanation:
Answer:
Explanation:
the total cost of the tiles is £68 plus VAT
the rate of VAT is 20%
(b) work out 20% of £52
Answer:
a) 81-6
b) 10.4
Step-by-step explanation:
a) assuming that the VAT is 20% of the 68 pounds,
you calculate 120% of 68 (convert percentage to decimal)
= 1,20 * 68 = 81.6 pounds
or
calculate 20% of 68 pounds and add the answer to 68 pounds:
(0.2 * 68) + 68 = 81.6 pounds
b) 20% of 52
first convert the percentage to decimals:
0.2 * 52 = 10.4 pounds
What is the prime factorization of -14x^4
Suppose that in January of a certain year, 77.6% of domestic flights flown by the top 18 U.S. airlines arrived on time. Represent this in terms of a random circumstance and an associated probability. The random circumstance is whether or not a flight from one of the top 18 U.S. aidines_______and the associated probability is_________ .
The random circumstance in this case is whether or not a flight from one of the top 18 U.S. airlines arrives on time. Let's denote this random circumstance as "A." The associated probability, given that 77.6% of flights arrived on time, can be represented as P(A) = 0.776 or 77.6%.
Let's clarify the representation of the random circumstance and associated probability based on the given information.
The random circumstance in this case is whether or not a flight from one of the top 18 U.S. airlines arrives on time. Let's denote this random circumstance as event "A." The associated probability, given that 77.6% of flights arrived on time, can be represented as P(A) = 0.776 or 77.6%.
To explain in more detail, let's consider a large sample of domestic flights flown by the top 18 U.S. airlines in January of that certain year. Each flight in this sample can be seen as a random trial, where the outcome is whether the flight arrives on time or not.
In this context, event A represents the specific outcome of a flight arriving on time, and the complementary event, denoted as event "A'", represents the outcome of a flight being delayed or not arriving on time.
The given information states that 77.6% of domestic flights arrived on time. Therefore, the associated probability P(A) represents the probability of a flight from one of the top 18 U.S. airlines being on time, and it is equal to 0.776 or 77.6%.
It's important to note that this probability represents an average value based on historical data and may vary from month to month or between different airlines. Additionally, this probability assumes that each flight's on-time performance is independent of the others, which may not always hold true in practice.
Overall, the random circumstance "A" refers to a flight from one of the top 18 U.S. airlines arriving on time, and the associated probability P(A) represents the likelihood of this occurrence based on the given information.
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simplify and rewrite so the expression contains no radicals.
√64+√8
A) 8+8^(1/2)
B) 8^(3/2)
C) 8+2•2^(1/2)
D) 8+2^(1/2)
The simplified expression for √64 + √8, with no radicals, is 8 + 2√2.
To simplify the expression, we need to find the square roots of 64 and 8 separately and then combine them.
The square root of 64 is 8, since 8 * 8 = 64.
The square root of 8 can be further simplified by recognizing that 8 can be expressed as 4 * 2. The square root of 4 is 2, and the square root of 2 cannot be simplified further.
Therefore, the square root of 8 is equal to 2√2.
Now, we can rewrite the original expression: √64 + √8 = 8 + 2√2.
Hence, the correct answer is option C) 8 + 2•2^(1/2).
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proving triangle similarity
could someone explain this to me? kinda confused
Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.
What is the AA Similarity Theorem?The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.
With the information given, the proof that shows that the two triangles are similar as as follows:
Statements Reasons
1. ∠QPR ≅ ∠STR 1. Given
2. QR ⊥ PT 2. Given
3. ∠QRP ≅ ∠SRT 3. def. of perpendicular
4. ΔPQR ~ ΔTSR 4. AA Similarity Theorem
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find the domain and range of fx= 2-3sinx
Answer:
domain expansion
Step-by-step explanation:
jujutsu kaisen brúh
Elsa has two coupons for a jacket coupon a: 45% off a $73 jacket coupon B: $30 rebate off $73 jacket which coupon has a lower price
Answer: 45% off a $73 jacket coupon
Step-by-step explanation:If you multiply 45% by 73 (.45 x 73) you get $32.85.. which means that is how much money would be reduced from the original price. If you have have a $30 rebate off a $73 jacket, you would be paying a higher price if you used the rebate instead of the coupon
how to solve the value for x
Answer:
x>6;x>2 or just x>2 if u combine intervals
Step-by-step explanation:
x^2-8x+12>0
factor: (x-6)(x-2)>0
split: x-6>0; x-2>0
add 6 and 2: x>6;x>2
combine intervals: x>2
Please help me solve
Answer:
I could but can you please put down the problem.
Step-by-step explanation:
Which system has no solution because exactly two of the planes are parallel?
(x-y-z-3
A -y-2=-4
(x +2y + z-1
1x - 3y + 2-4
B
-+ 3y + 2 - 4
(.x - 3y + 2z - 4
(2.x + y + 3 - 4
С
{2x + y +2 -1
(2x + y + z = 5
(r-4
D
{y-7
(x + y + 2 - 6
Answer:
confusing confusing actually
1. A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of vinegar are needed to make 1/2 cup of salad dressing?
Answer: The answer is 8
Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup
Which of the following statements are correct?
Select only those statements you know to be correct because negative marking is applied within this question (although it is not possible to get a negative mark for the question overall).
a.
Cost machines and cost related to machining are considered to be part of inventory
b.
Ordering costs decrease with respect to lot size
c.
It is good to have fixed interval ordering systems for products that have independent demand
d.
Companies using ABC approach need not use EOQ
e.
Taxes and insurance costs can be considered as carrying costs of inventory
f.
Costs incurred for defective products identified after the products are shipped are classified as internal failure costs
g.
Costs spent to prevent low quality goods in production are classified as cost of reengineering
h.
Costs of repairing faulty products under warranty are limited to external failure costs
i.
Returned goods cannot be classified under internal failure costs
j.
Under EOQ inventory model there is an assumption which states that there is no possibility of inventory stockout to occur
The correct statements are:
b) Ordering costs decrease with respect to lot size,
c) It is good to have fixed interval ordering systems for products that have independent demand,
e) Taxes and insurance costs can be considered as carrying costs of inventory,
f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs,
h) Costs of repairing faulty products under warranty are limited to external failure costs, and j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur.
b) Ordering costs decrease with respect to lot size: Ordering costs involve the expenses incurred when placing orders for inventory, such as administrative costs, processing fees, and transportation costs.
When the lot size increases, the frequency of placing orders decreases, resulting in lower ordering costs per unit. This is because the fixed costs associated with ordering are spread over a larger quantity of inventory.
c) It is good to have fixed interval ordering systems for products that have independent demand: Fixed interval ordering systems involve placing orders at regular intervals, regardless of the inventory level.
This approach is suitable for products with independent demand, where the demand is unpredictable or sporadic. By setting fixed intervals, the company can ensure a consistent replenishment schedule and avoid stockouts while optimizing inventory levels.
e) Taxes and insurance costs can be considered as carrying costs of inventory: Carrying costs are the expenses associated with holding and storing inventory.
They include costs such as storage fees, insurance premiums, taxes on inventory, and the opportunity cost of tying up capital in inventory. Taxes and insurance costs directly impact the financial burden of inventory holding and are considered as components of carrying costs.
f) Costs incurred for defective products identified after the products are shipped are classified as internal failure costs: Internal failure costs are expenses incurred due to quality issues discovered within the company's operations.
In the context of inventory, costs related to defective products identified after they are shipped, but before reaching the customer, fall under internal failure costs. These costs include rework, scrap, and any necessary corrective actions taken to address the quality problems.
h) Costs of repairing faulty products under warranty are limited to external failure costs: External failure costs are the expenses incurred due to quality issues discovered by customers after the products have been delivered.
When faulty products are repaired under warranty, the costs associated with the repairs are considered external failure costs. This includes the direct costs of repairing or replacing the faulty products and any associated customer service expenses.
j) Under EOQ inventory model, there is an assumption which states that there is no possibility of inventory stockout to occur: The Economic Order Quantity (EOQ) model is a widely used inventory management technique.
It assumes that demand for the product is constant and known with certainty, there are no quantity discounts or price variations, and there is no possibility of stockouts occurring.
The assumption of no stockouts simplifies the calculations and ensures that the optimal order quantity obtained from the model will meet the demand without interruptions.
However, in real-world scenarios, stockouts can occur due to unforeseen factors, variability in demand, or supply chain disruptions.
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A road sign is in the shape of a square. What is the measure of each angle on the sign? Round to the nearest tenth.
Each angle on a square road sign measures 90 degrees.
A square is a quadrilateral with four equal sides and four right angles. In a square, all angles are congruent, meaning they have the same measure. Since a square has four angles, each angle is equal to the total sum of the interior angles of a square divided by four.
The total sum of the interior angles of a square can be calculated using the formula (n - 2) * 180 degrees, where n is the number of sides. For a square, n = 4, so the total sum of the interior angles is (4 - 2) * 180 = 2 * 180 = 360 degrees.
To find the measure of each angle, we divide the total sum of the interior angles by the number of angles, which is 4 in the case of a square:
360 degrees / 4 angles = 90 degrees.
Therefore, each angle on a square road sign measures 90 degrees.
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Triangles E F G and K L M are shown. Angles E F G and K L M are congruent. The length of side K L is 6, the length of side M L is 5, and the length of K M is 8. The length of E G is 24, the length of G F is 15, and the length of E F is 18.
Can the triangles be proven similar using the SSS or SAS similarity theorems?
Yes, △EFG ~ △KLM only by SSS.
Yes, △EFG ~ △KLM only by SAS.
Yes, △EFG ~ △KLM by SSS or SAS.
No, they cannot be proven similar by SSS or SAS
Based on the given information, we cannot prove that △EFG and △KLM are similar using the SSS or SAS similarity theorems. The correct answer is option D) No, they cannot be proven similar by SSS or SAS.
To determine if the triangles △EFG and △KLM can be proven similar using the SSS (Side-Side-Side) or SAS (Side-Angle-Side) similarity theorems, we need to compare their corresponding sides and angles.
SSS Similarity Theorem states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
SAS Similarity Theorem states that if two corresponding sides of two triangles are proportional, and the included angles are congruent, then the triangles are similar.
Let's examine the given information:
Side lengths of △EFG: EF = 18, EG = 24, FG = 15.
Side lengths of △KLM: KL = 6, KM = 8, LM = 5.
By comparing the side lengths, we can see that they are not proportional. For example, the ratio of EF/KL is 18/6 = 3, while the ratio of EG/KM is 24/8 = 3. Therefore, the corresponding sides of △EFG and △KLM are not proportional, which means we cannot establish similarity using the SSS theorem.
Now, let's consider the SAS theorem. For this, we also need to compare the included angles.
Angles of △EFG: ∠EFG, ∠EFG, ∠EGF.
Angles of △KLM: ∠KLM, ∠KML, ∠KLM.
The given information states that ∠EFG and ∠KLM are congruent. However, we don't have any information about the other angles. Without knowing the congruency of the remaining angles, we cannot establish similarity using the SAS theorem
Option D.
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Answer: Its C
Step-by-step explanation:
For what values of x does the following geometric series converge? Solve f(x) = 5. f (g) = sigma^infinity_k = 0 (x - 3/5)^k The series converges if -_____ < x < ____. (Simplify your answer.) The solution for f(x) = 5 is x = ___.
The series converges if 2/5 < x < 8/5, and the solution for f(x) = 5 is x = 4/5.
The given series is a geometric series with the common ratio (x - 3/5), and the first term is 1. For a geometric series to converge, the absolute value of the common ratio must be less than 1. Therefore,
| x - 3/5 | < 1
Simplifying this inequality, we get
-1 < x - 3/5 < 1
Adding 3/5 to all sides, we get
2/5 < x < 8/5
So, the series converges if 2/5 < x < 8/5.
To solve f(x) = 5, we can use the formula for the sum of an infinite geometric series
f(x) = 1/(1 - (x - 3/5)) = 5
Multiplying both sides by (1 - (x - 3/5)), we get
1 = 5(1 - (x - 3/5))
Simplifying and solving for x, we get
x = 4/5
Therefore, the solution for f(x) = 5 is x = 4/5.
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sadadjskjdlfhsadidshoichuedhhefhksjdhfihdpihdifhjehj;fhsuhfehkjfjkshxjhf
Answer:
\(x<5\)
Step-by-step explanation:
Lol, y did you post this question twice?
\(4-x<9\)
Subtract 4 to both sides
\(x<5\)
Answer:
x > -5
Step-by-step explanation:
Lets start by bringing the 4 to the right as -4. We are now at -x < 5. We now divide the total by -1, which flips the sign so now x > -5