I need help figuring out which of these four options is equivalent to\((x + 3)(4 {x}^{2} + 5)\)
(4 {x}^{2} + 5)[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Vci3kjXepOPNySB4caIY3s3YJQSxNx8R.png)
Answers
The distributive property for the multiplication states that:
\(a\cdot(b+c)=a\cdot b+a\cdot c.\)(1) Choosing:
• a = (x + 3),
,• b = 4x²,
,• c = 5.
We have:
\((x+3)\cdot(4x^2+5)=a\cdot(b+c).\)(2) Applying the distributive property for the multiplication, we have:
\((x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c.\)(3) Replacing a = (x + 3), b = 4x² and c = 5, we get:
\((x+3)\cdot(4x^2+5)=a\cdot(b+c)=a\cdot b+a\cdot c=(x+3)\cdot(4x^2)+(x+3)\cdot(5).\)Answer(A)
\((x+3)\cdot(4x^2)+(x+3)\cdot(5)\)Related Questions
One week, Gabriel bought 2 bags of beans and 3 bags of rice. The next week, he bought 4 bags of beans and 1 bag of rice. Let b represent the cost of each bag of beans and r represent the cost of each bag of rice. Simplify the expression for the total cost, shown below.
(2b + 3r) + (4b+ r)
Answers
= 6b + 4r
190 is what percent of 360
Answers
Answer:
190 / 360 = 0.52777777
0.527777 x 100 = 52,78%
Factorizie completely 2ap+aq-bq-2bp
Answers
Answer:
2ap + aq - bq -2bp = (a - b)(2p + q)
Step-by-step explanation:
(2ap + aq) - (bq -2bp)
a(2p +q) -b(q + 2p) [ taking a common from the first, and b from the second]
(2p + q) [a - b] [takin (2p + q)]
(2p + q)(a - b)
The completely factored form of the expression 2ap + aq - bq - 2bp is
(a - b)(2p + q).
In order to completely factorize the given expression, we need to look for common factors and apply factorization techniques.
Given expression: 2ap + aq - bq - 2bp
Step 1: Look for common factors.
Notice that 'a' is common in the first two terms, and '-b' is common in the last two terms.
Step 2: Factor out the common terms.
We can factor 'a' from the first two terms: a(2p + q)
And factor '-b' from the last two terms: -b(q + 2p)
Step 3: Rearrange the expression.
Now we have: a(2p + q) - b(q + 2p)
Step 4: Factor by grouping.
We can see that (2p + q) is common in both terms, so we can factor it out: (2p + q)(a - b)
Step 5: Final result.
Thus, the completely factored form of the given expression is
(a - b)(2p + q).
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The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
Answers
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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You consider buying a phone from one of two cell phone carriers. The table shows the total costs (in dollars) of the phone and service for different numbers of months at Carrier A. The total cost $y$y (in dollars) of the phone and x$x$x months of service at Carrier B is represented by the equation y is equal to 55 x plus 300$y=55x+300$y=55x+300 . Which carrier has the lower initial fee?
Answers
Answer:
Carrier B
Step-by-step explanation:
The linear equation that represents Carrier B is y=55x+300. it's a linear equation so 55 represent the monthly fee and 300 represents the initial fee. So the initial fee of carrier B is 300. In case of Carrier A, the total cost increases by $150 as months increases by 3. So The initial fee of Carrier A is 500-150=$350 . Hence, Carrier B has lower initial fee.
Please help me!!!!!!!!!!!!!!!
Answers
Answer:0.03
Step-by-step explanation:
Answer:
Answer: 0.03Step-by-step explanation:
I hope it helps you ❤❤❤Allison is choosing between two rental car companies. Countrywide Auto charges $27 plus $0.27 per mile, and Smart Auto charges $45 plus $0.21 per mile.
Use the following system of equations, where y represents total cost and x represents miles, to answer the question:
y = 0.27x + 27
y = 0.21x + 45
At what point would the two lines intersect if graphed? (4 points)
(300, 108)
(108, 300)
(45, 27)
(27, 45)
Answers
The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).
How to Solve a System of Linear Equations?Given that:
y = total cost
x = miles
We are also given the system of linear equations that models the scenario given as:
y = 0.27x + 27 --> equation 1
y = 0.21x + 45 --> equation 2
To find the value of x, make both equations equal to each other and solve:
0.27x + 27 = 0.21x + 45
Combine like terms
0.27x - 0.21x = -27 + 45
0.06x = 18
Divide both sides by 0.06
0.06x/0.06 = 18/0.06
x = 300
To find the value of y, plug in the value of x into equation 1, and find y:
y = 0.27(300) + 27
y = 81 + 27
y = 108
Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).
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Desperate Need Of Help
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The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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A company received orders for 1.500
erasers, and then a batch of orders
came in for 3,200 more. The company
has 800 erasers in stock, but 5,500 are
due in next week. How many erasers
will the company have in stock after
this shipment comes in and has
fulfilled all orders?
Answers
Answer:
0
Step-by-step explanation:
A rope is 15 meters long, you cut off 12/5 meters. What is the length of the remaining rope?
Answers
Answer:
12.6
Step-by-step explanation:
15/2 = 2.4
15-2.4= 12.6
Answer:
12.6
Step-by-step explanation:
YOu just subtract 15 and 12/5
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answers
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
Without graphing, tell if this pair is on the graph
5x-3y=14, (-1,-6)
Answers
On one day, 4 chefs and 5 helpers earned $650.
On another day working the same number of hours
at the same rate of pay, 5 chefs and 6 helpers
earned $800.
How much does a chef earn each
day?
Answers
5c + 6h = 800 where c are chefs, h are helpers
Start by finding an expression for c
4c + 5h = 650
4c = 650 -5h
c = (650- 5h)/4
Then substitute that into the second equation and solve for a number value for h
5 (650-5h)/4 + 6h = 800
(3250-25h)/4 + 6h = 800
Multiply both sides by 4
3250-25h + 24h = 3200
-h = -50
h = 50
Take that 50 and substitute it into the expression we have for c to get a number value for c
C= 650-5(50)/4
C = 650-250/4
C = 400/4
C= 100
Check your first equations, substituting $50 for the helpers and $100 for the chefs.
4 (100) + 5(50) =
400 + 250 = 650
5(100) + 6(50) =
500 + 300 = 800
21. Sandra is 4 feet tall. Pablo is 10% taller than Sandra, and Michaela is 8% taller than Pablo. a. Explain how to find Michaela's height with the given information.
Answers
Answer:
Step-by-step explanation:
Find 10% of Sandra’s height then find 8% of Pablo’s height, then combine. 4 feet 9 inches.
the amount of blank needed too make an object change it’s blank depends on the blank of the object? PLEASE HELP URGENT
Answers
Answer:
force
Step-by-step explanation:
by applying fore to an object at rest it will b acted upon so therefore force is the answer and force is the push or pull to an object
Answer:
2nd law, acceleration, position, mass, force
Step-by-step explanation:
I hope that helps =)
Katie is mixing a new blend of perfume. Her formula calls for 12% lavender solution. She has two bottles. One is 15% and the other is 6%. How many ounces of each does she need to make 18 ounces of 12%?
Answers
Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". The percentage can be calculated by dividing the value by the total value and then multiplying the result by 100.01
First, determine the total amount of lavender solution needed for the 18 ounces of perfume.
This is 18 ounces x 12% = 2.16 ounces.
Next, determine the amount of lavender solution in the 15% solution. This is 2.16 ounces / 0.15 = 14.4 ounces.
Subtract the amount of lavender solution in the 15% solution from the total amount needed. 2.16 - 14.4 = 0.76 oz
Determine how many ounces of the 6% solution are needed. This is 0.76 oz / 0.06 = 12.67 oz
Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.
Hence, Katie should use 14.4 oz of the 15% solution and 12.67 oz of the 6% solution to make 18 ounces of a 12% lavender solution.
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Complete the square to re-write the quadratic function in vertex form:
y= x2 - 5x +9
Answer: y =
Submit Answer
Answers
In right ∆ABC the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find BC if AD = 8 cm and DH = 4 cm.
Answers
The measure of side BC is 12 units in a right ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.
What is meant by right angle?A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.
Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.
Given,
m∠CAL = m∠BAL
m∠C = 90°
AD = 8 cm
DH = 4 cm
We have to apply sine rule for ΔADH,
sinθ=opposite side/hypotenuse
sin(∠DAH)=DH/AD
=4/8
=1/2
∠DAH=sin⁻¹(1/2)
∠DAH=30°
Therefore, ∠CAB=2(∠DAH)
=2(30°)
=60°
Now, we have to apply tangent rule in ∆AHD
tan( ∠DAH)=DH/AH
tan(30°)=4/AH
1/√3=4/AH
AH=4√3
Now, we have to apply cosine rule in ∆AHC
cos(60°)=AH/AC
1/2=4√3/AC
AC=8√3
Now, we have to apply tangent rule in ∆ACB
tan(∠CAB)=opposite side/adjacent side
tan(60°)=BC/AC
√3=BC/8√3
BC=8√3(√3)
BC=24units.
Therefore, the measure of side BC is 12 units in a right ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.
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Riley is building a pool with a surrounding deck in their backyard. The pool has a fixed area, A m2, but the pool's dimensions can vary (For instance, a 4 m2 pool can have infinitely many length-width combinations, including 2×2, 4×1, 1×4, or π2×8π).The width of the pool deck extends beyond the pool on both sides, as does the length of the pool deck. Because the pool has a fixed area, the pool length depends on the pool width and vice versa.The width in the applet, W, varies between .5 meters and 12 meters. Find the minimum area for a pool and deck built as in the application such that the pool's area is 1800 square meters, the deck extends an extra 10 meters wide on both sides of the pool, and the deck extends an extra 5 meters long on the corresponding sides of the pool. Your solution should contain a justification for why your found area is indeed the minimizing area.
Answers
The minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters is 1400 meter square.
Given that,
We have to find the minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters on each side of the pool and a further 5 meters along the corresponding sides of the pool. The pool's area is 1800 square meters.
We know that,
Area of the Total space = (l+10)(b+20)
Here,
b=1800/l
l= 30
So,
b=60
Area of the total space is (30+10)(60+20) = 40×80 = 3200 m²
The minimum area of deck = 3200-1800 = 1400 m²
Therefore, The minimal size for a pool and deck constructed as in the application, with the deck extending an additional 10 meters is 1400 meter square.
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tan alpha = -4/3, alpha lies in quadrant II, and cos ß = 2/3, ß lies in quadrant I.
a.) cos (alpha + ß)
b.) sin (alpha + ß)
c.) tan (alpha + ß)
Answers
The trigonometric function is cos (alpha + ß)
What are trigonometric identities?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
We are given that tan α= -4/3, alpha lies in quadrant II,
cos ß = 2/3, ß lies in quadrant I.
We know that, tan(−θ) = − tan(θ)
α= -4/3
As we know cos(−θ) = cos(θ)
cos ß = - 2/3
The answer is cos (alpha + ß).
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the area of a table top is a whole number of square feet. Could the length and width be decimal numbers each one with decimal place?
Answers
Yes, the length and width can be decimal numbers each one with decimal place, but not in every case.
Define areaThe size of a two-dimensional surface or region is expressed in terms of area. Square units like square inches, square feet, or square metres are frequently used to measure it. The area of a shape or region is determined by counting the number of unit squares that can fit inside it without overlap.
for example, lets take length =2.5 feet
and width=3.2 feet
area of table top=8 feet²
Taking another case:
length =1.2 feet
and width=3.5 feet
area of table top=4.2 feet²
if the length and width are decimal numbers, then the area would also be a decimal number or whole number, But, this is not possible in every cases.
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The complete question is:
The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.
Find the value of X.
Answers
Answer:
x = 36
Step-by-step explanation:
Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.
RelationThe product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.
24² = 12(12 +x)
2·24 = 12 +x . . . . . . . divide by 12
36 = x . . . . . . . . . subtract 12
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What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
Answers
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
In Exercises 15-18, find the coordinates of the centroid of the triangle with the given vertices. (See Example 2.) 15. A(2,3), B(8,1), C(5,7)
Answers
9514 1404 393
Answer:
(5, 3 2/3)
Step-by-step explanation:
The centroid coordinates are the average of the vertex coordinates.
(A+B+C)/3 = ((2, 3) +(8, 1) +(5, 7))/3 = (2+8+5, 3+1+7)/3 = (15, 11)/3
The centroid is (5, 3 2/3).
_____
The graph shows the intersection of the medians. It is the centroid, (5, 3 2/3), as we calculated.
The difference of seven times a number and 6 is the quotient of the number and 4 .
Which of the following equations could be used to find the number, n ?
Answers
According to the given equation, the value of the number is 8/9.
Let's break down the statement: "The difference of seven times a number and 6 is the quotient of the number and 4." We can translate this into a mathematical equation by first defining the number as "n":
7n - 6 = n/4
In this equation, 7n represents seven times the number, and n/4 represents the quotient of the number and 4. The difference between the two is given by subtracting 6 from 7n.
Now, we can solve for the value of n by manipulating the equation to isolate n on one side. To do this, we can start by multiplying both sides of the equation by 4 to eliminate the fraction:
28n - 24 = n
Next, we can simplify the equation by bringing all the n terms to one side:
28n - n = 24
Combining like terms, we get:
27n = 24
Finally, we can solve for n by dividing both sides by 27:
n = 24/27
Simplifying the fraction, we get:
n = 8/9
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If a jar of grape jelly has a sell price of $1.25. The sale price 75% off the original price. What was the original price.
Answers
Answer:
i believe its $0.31
Step-by-step explanation:
Use differences to find a pattern in the sequence.
3,8,15,28,51,88,143
Assuming that the pattern continues, the eighth term should be
Answers
Answer:
220
Step-by-step explanation:
You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.
First differencesSubtracting each term from the next, we find the sequence of first differences to be ...
5, 7, 13, 23, 37, 55
Second differencesThe first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.
The second differences are the differences of the sequence of first differences. They are ...
2, 6, 10, 14, 18
Third differencesThe differences of the terms of the 2nd-difference sequence are constant: 4.
4, 4, 4, 4, 4
Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.
Next termSince we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.
next 2nd difference = 18 +4 = 22
next 1st difference = 55 +22 = 77
next sequence term = 143 +77 = 220
The eighth term should be 220.
__
Additional comment
The n-th term is ...
f(n) = 2/3n^3 -3n^2 +28/3n -4
ingredients: f(6)-20 = (?)cups of sugar. use f(x) = x² - 2x - 3
Answers
Answer:-18 mm sugar
Step-by-step explanation:
Thanks me later
Need help with how to do this one...
Find the domain of
x ¹ -2
x + 1
A. x ≠ -1
B. x ≠ 1
C. x ≠ -2
D. x ≠ -1, 1
E. x ≠ 2
F. x ≠ 0
Answers
What happens at equilibrium price and quanity? 1.The quantity supplied equals the quantity demanded.
2.The price demanded equals the price supplied.
3.The priced demanded equals the quantity supplied.
4.The quantity supplied equals the price demanded.
Answers
Answer:
Step-by-step explanation:
At equilibrium price and quantity, the answer is 1. The quantity supplied equals the quantity demanded.
This means that the market is in a state of balance, where the quantity of a good or service that producers are willing to supply is exactly the same as the quantity that consumers are willing to buy. As a result, there is no excess supply or excess demand, and the price of the good or service is stable.