The expression 4sr²(2rs + 3s) is not completely factored.
How to factor an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
An expression is completely factored when no further factoring is possible.
Therefore, let's check if the expression is completely factored.
4sr²(2rs + 3s)
The expression still have a common factor which is s. This means its not completely factored.
The complete factorisation is as follows;
4sr²(2rs + 3s) = 4s²r²(2r + 3)
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hi please help me tysmYour mother places 6 flowers in a vase. How many vases does your mother need for 30 flowers?A. 9B. 7C. 5D. 3
SOLUTION:
Step 1:
In this question, we are given the following:
Your mother placed 6 flowers in a vase.
How many vases does your mother need for 30 flowers?
Step 2:
The details of the solutions are as follows:
[tex]\begin{gathered} 6\text{ flowers = 1 vase} \\ \text{Then, we have that:} \\ 30\text{ flowers = }\frac{(30\text{ x 1)}}{6}=\frac{30}{6}=\text{ 5 vases ( OPTION C)} \end{gathered}[/tex]
based on the side lengths given (a, b, and c), which triangles are right triangles????A. a=4, b=6, c=8B. a=6, b=8, c=10C. a=5, b=6, c=(square root of) 61D. a=6, b=9, c=12 PLEASE HELP!!
Explanation
From the question, a right-angle triangle must obey Pythagoras theorem. Therefore, we can see that
[tex]6^2+8^2=10^2\text{ also, }5^2+6^2=(\sqrt{61})^2[/tex]The rest of the values do not obey Pythagoras theorem. Therefore;
Answer: Option B and Option C
Which sequence of rigid motions will definitely work to take triangle RPQ onto triangle CAB?
RPQ to CAB transform
Rotation needed = RPQ using C as center ,an angle ACP
Translations= Line RC
Reflections= None
Then answer is
Option D)
Translate RPQ by the direct line segment RC
A department store is offering a promotion on candles. The promotion is "Buy 2 candles, get 40% off the 3rd Candle". If you are buying three of thesame candles with the same price, which two expressions below can be used to represent the cost of buying 3 candles.c+0.6c2.6cOc+c+0.4c2c +0.6c2.4c
Given:
it is given that a department store is offering a promotion on candles. The promotion is "Buy 2 candles, get 40% off the 3rd Candle".
Find:
we have to find the total cost of buying 3 same candles.
Explanation:
Let c be the cost of one candle.
Then 2c is the cost of two candles.
and, as per offer , the price of the third candle is 40% off.
if c is the price of one candle , then the cost of third candle is
c - (40% of c) = c - 0.4c = (1 - 0.4)c = 0.6c
Therefore, cost of third candle is 0.6c.
Now, the total cost of buying three same candles = 2c + 0.6c = 2.6c
Therefore, the options 2c + 0.6c and 2.6c are correct options
3. When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.Let f(x) refer to the amount of drug left in the body after I hours.(a) Write down an exponential function to model this situation. Write your answer using functionnotation(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
When people take medicine, the drug gets metabolized by the body and eliminated at a constant rate.
Suppose the initial amount of a drug in the body is 549 mg and it is eliminated at a rate of 12% per hour.
Let f(x) refer to the amount of drug left in the body after I hours.
(a) Write down an exponential function to model this situation. Write your answer using function
notation
(b) How much of the drug is left in the body after 12 hours? Round to the nearest whole number.
(c) How much of the drug is left in the body after 180 minutes? Round to the nearest whole number
Part a)
Let
t -----> number of hours
f(x)=a(1+r)^t
where
a=549 mg
r=12%=0.12
substitute
f(x)=549(1+0.12)^t
f(x)=549(1.12)^tPart b)
For t=12 hours
substitute in the function
f(12)=549(1.12)^12
f(12)=2,139 mgPart c)
For t=180 minutes
Remember that
1 h=60 minutes
so
180 minutes=180/60=3 hours
For t=3 hours
substitute
f(3)=549(1.12)^3
f(3)=771 mgThe answers to choose from are -40, 130, 53, -63, -140, 265, 234
First we need to know how to convert radians to degrees
[tex]d=\text{r}\cdot\frac{180}{\pi}[/tex]where r is the measure in radians and d is the measure in degrees
for A.
r=53pi/36
[tex]d=\frac{53\pi}{36}\cdot\frac{180}{\pi}=265[/tex]the measure in degrees is 265°
for B.
r= 13pi/18
[tex]d=\frac{13\pi}{18}\cdot\frac{180}{\pi}=130[/tex]the measure in degrees is 130°
for C.
r=-7pi/20
[tex]d=-\frac{7\pi}{20}\cdot\frac{180}{\pi}=-63[/tex]the measure in degrees is -63°
for D.
r=-2pi/9
[tex]d=-\frac{2\pi}{9}\cdot\frac{180}{\pi}=-40[/tex]the measure in degrees is -40°
Please help solve the following questions using the exponential equation
SOLUTION
We want to solve
[tex]7^{2x+4}=2^{x-5}[/tex]Taking logarithm of both sides, we have
[tex]\begin{gathered} \log 7^{2x+4}=\log 2^{x-5} \\ (2x+4)\log 7=(x-5)\log 2 \\ \text{expanding we have } \\ (2x)\log 7+(4)\log 7=(x)\log 2-(5)\log 2 \end{gathered}[/tex]Collecting like terms we have
[tex]\begin{gathered} (2x)\log 7-(x)\log 2=-(4)\log 7-(5)\log 2 \\ x(2\log 7-\log 2)=-4\log 7-5\log 2 \\ \text{dividing both sides by }(2\log 7-\log 2),\text{ we have } \\ x=\frac{-4\log 7-5\log 2}{2\log 7-\log 2} \end{gathered}[/tex]Hence the solution set expressed in terms of logarithm is
[tex]x=\frac{-4\log7-5\log2}{2\log7-\log2}[/tex]Using a calculator to obtain a decimal approximation, we have
[tex]\begin{gathered} x=\frac{-4\log7-5\log2}{2\log7-\log2} \\ x=\frac{-3.3804-1.5051}{1.6902-0.3010} \\ x=\frac{-4.8855}{1.3892} \\ x=-3.51677 \\ x=-3.52 \end{gathered}[/tex]Hence the answer is -3.52 to 2 decimal places
#3) Ulices was charged $140 plus a pick up charge of $20 to ship 4 identical boxesbys Fast Ship. The pick up charge applies regardless of how many boxes are pickedup. What would have been the change to Ulices' account if he had shipped just 1box?
To determine the Ulices's account if he shipped just 1 box, calculate the charge for one box. To calculate the charge, compute the quotient between the charge for 4 boxes between 4 boxes, just as folow:
charge per one box = 140/4 = 35
Hence, for 1 box the charge is $35
Due to it is necessary to pay $20 idependenty of the number of boxex, you sum $20 to the cost for one box:
New Ulices's account = $35 + $20 = $55
Hence, Ulices's account would have been of $55
Use the distributive property of operations and choose the correct equivalent expression for 15 - 21p1(5 - 2p)15(5 - 7p)3(5 - 7p)None of these answers are correct.3(5 - 21p)
According to the given data we have the following:
15 - 21p
correct expression?
To find the correct expression we need to check which expression is the correct one by multiplying the number which is outside of parentesis to the numbers inside of the parentesis.
Therefore,
15 - 21p
The right option in this case is:
3(5 - 7p)
3 times 5 is=15
3 times -7=21
Therefore 3(5 - 7p)= 15 - 21p
Hi I need help with this question, please and thank you
real part = 8
imaginary part = -√245
Explanation:[tex]\begin{gathered} \text{Given:} \\ 8\text{ - }\sqrt[]{-245} \end{gathered}[/tex][tex]\begin{gathered} \text{For a complex number:} \\ a\text{ + bi} \\ a\text{ = real part} \\ b\text{ = imaginary part} \end{gathered}[/tex]since we can't find square root of a negative number, we will introduce the complex number:
i² = -1
[tex]\begin{gathered} 8-\sqrt[]{-245}\text{ = 8-}\sqrt[]{245i^2} \\ =\text{ 8-i}\sqrt[]{245} \\ \\ \text{writing in the form of real and imainary number:} \\ \text{8-}\sqrt[]{245i}\text{ = 8 + (i}\times\text{-}\sqrt[]{245}) \end{gathered}[/tex][tex]\begin{gathered} \text{real part = 8} \\ \text{imaginary part = -}\sqrt[]{245} \end{gathered}[/tex]Abrha lives in an apartment and pays the following expenses each month: electric bill, $44.90; TV streaming service, $24.99; and rent, $625.85 Estimate his total expenses for the month by first rounding each value to the nearest tens place.
Answer: $700
Abrha will be spending $701 monthly, just by arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Abrha lives in an apartment,
electric bill, $44.90 = $50
TV streaming service, $24.99 = $25
Rent, $625.85 = $626
So the Total expenses will be (50+25+626) = $701 just by arithmetic operation
Hence Abrha will be spending $701 monthly.
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Use the factor theorem to determine whether x-2 is a factor
Factor theorem is usually used to factor and find the roots of polynomials. A root or zero is where the polynomial is equal to zero. Therefore, the theorem simply states that when f(k) = 0, then (x – k) is a factor of f(x).
In this case here, let's find out if 2 is a root of the polynomial given.
As we can see in the box below, 2 is not a root of the polynomial, therefore (x-2) isn't a factor.
[tex]\begin{gathered} P(x)=-2x^3+4x^2-4x-7 \\ P(2)=-2\cdot2^3+4\cdot2^2-4\cdot2-7 \\ P(2)=-16+16-8-7 \\ P(2)=-15 \end{gathered}[/tex]If h(x) = 3(x2 + 1) - 6, what is the value of h(10)?
write the following equation in a function form.x-3y=-9
the given equation is
x - 3y = -9
-3y = -9 - x
-3y = - (9 + x )
3y = 9 + x
y = x/3 + 3
so the answer is
y = x/3 + 3
i need help asap with this (Its ACD and not AGD just incase that confuses you)
4)
In the case of a square, its diagonals are equal and bisect each other, meeting at 90°.
In our case, using a diagram,
Therefore,
[tex]\begin{gathered} a+2b=90 \\ and \\ 2a-b=90 \end{gathered}[/tex]Solving the system of equations for a and b,
[tex]\begin{gathered} \Rightarrow a=90-2b \\ \Rightarrow2(90-2b)-b=90 \\ \Rightarrow5b=90 \\ \Rightarrow b=18 \end{gathered}[/tex]Finding a,
[tex]\begin{gathered} b=18 \\ \Rightarrow a=90-2*18=90-36=54 \end{gathered}[/tex]The answers are a=54, b=18The functions f(x) and g(x) are shown on the graph.F(x)=x^2What is g(x)?A. g(x)= -x^2+3B. g(x)=(-x)^2-3C. g(x)=(-x)^2+3D.g(x)= -x^2-3
On observation of the graphs of the two functions, we can see that f(x) has undergone some transformation to give g(x).
The original function is given as
[tex]f(x)=x^2[/tex]The function is reflected over the x-axis.
The rule for the reflection over the x-axis is given as
[tex]f(x)\to-f(x)[/tex]Applying this to the function, we have the new function to be
[tex]-x^2[/tex]The graph is also shifted downwards by 3 units.
This shift can be represented as
[tex]f(x)\to f(x)-3[/tex]Applying this to our function, we have the new function, g(x), to be
[tex]g(x)=-x^2-3[/tex]The correct option is OPTION D.
S-7>3Help please !Don’t really understand
The given inequality is
[tex]s-7>3[/tex]To solve it, we need to isolate s on one side and the numerical terms on the other side
To do that we need to move 7 from the left side to the right side with 3, so
Add 7 to both sides
[tex]\begin{gathered} s-7+7>3+7 \\ s+0>10 \\ s>10 \end{gathered}[/tex]The solution of the inequality is s > 10
We can represent it on the number line
If the product is 900, and the two of its three factors are 3 and 50, what is the third factor?
We have the multiplication of 3 factors, one of them unknown, that give 900 as a result.
We can write this as:
[tex]\begin{gathered} 3\cdot50\cdot x=900 \\ 150x=900 \\ x=\frac{900}{150} \\ x=6 \end{gathered}[/tex]The third factor is 6.
[tex]4a ^{2} - 12a - 16[/tex]I need help factoring
4(a-4)(a+1)
1) Factorizing 4a²-12a -16
4a²-12a -16 Note that the GCD (4,12,16) is 4, Rewrite them
4a²- 4*3a - 4* 4
2) 4(a² -3a -4) Rewrite a² -3a -4 answering the question, What are the numbers whose sum is 3 and product is 4?
Answer:
1 -4 = -3
1 x -4 = -4
3) Hence, the answer is:
4a²-12a -16= 4(a-4)(a+1)
Solve equations x-27=56
Answer:
x = 83
Step-by-step explanation:
Add 27 to both sides
x - 27 +27 = 56 + 27
x = 83
An eighth-grade student estimated that she needs $8,800 for tuition and fees for each year of college. She already has $5,000 in a savings account. The table shows the projected future value of the account in five years based on different monthly deposits.future value of a savings account. initial balance, dollars, $5000, $5000, $5000, $5000. Monthly deposit, dollars. $100, $200, $300, $400. Account value in five years, dollars. $12,273; $18,737; $25,202; $31,667.The student wants to have enough money saved in five years to pay the tuition and fees for her first two years of college. Based on the table, what is the minimum amount she should deposit in the savings account every month?AnswerF$200G$300H$100J$400
Since each year cost $8,800 for two years tuition he will need $17,600 then if he want to save at least this much in five years according to the table he needs to save $200 monthly
Find the z-value so that the area to the left of z (shaded in the picture) is 0.9131.
area shaded to the left = 0.9131
by using the Z cumulative table , we can see that the value that corresponds with Z= 0.913 is 0.838
Consider the polynomial
1/2a^4 + 3a³ + a.
1) What is the coefficient of the third term?
2) What is the constant term?
1) The coefficient of the third term is one.
2) The constant term is zero.
We are given a polynomial. A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive integer powers of variables. The polynomial is (1/2)a^4 + 3a³ + a. The polynomial has the variable "a". The polynomial has three terms. So, it is a trinomial. The third term of the polynomial is "a". The coefficient of the third term is 1. There is no constant term in the polynomial. So, we can say that the constant term is 0.
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Yea I think and if it’s ok we
Explanation: To solve a derivate we can use a simple technique presented below
- First, we take the exponent and multiply it by the function. Second, we subtract a unit of the exponent. Let's visualize it better on the drawing below
Step 1: Now we can use the same concept to calculate all the derivates we need as follows
Final answer: So the final answers are
[tex]\begin{gathered} letter_{\text{ }}a=5x^4 \\ letter_{\text{ }}b=20x^3 \\ letter_{\text{ }}c=60x^2 \\ letter_{\text{ }}d=120x \end{gathered}[/tex].
If there are 25 people in a room and 15 chairs, how many different seating arrangements are possible?A)3268760B)7.41x10^11C)4.27x10^18D)4.27x10^19
We will investigate the counting principles that are used for cases of probability evaluation.
There are two possible types of counting principles.
Combinations:
It gives us the total number of possible selections that you can make "given" - " for " something. It is a simple selection process between the subejct and an object. The notation used for determining the number of selections/combinations is expressed as:
[tex]^nC_r[/tex]Where,
[tex]\begin{gathered} n\colon\text{ Total number of subjects} \\ r\colon\text{ Total number of ob}\imaginaryJ ects \end{gathered}[/tex]Then we can use the calculator infused functions of " C " combinatorics!
Permutations:
It gives us the total number of possible arrangements comprised of selections and shuffling that you can make "given" - " for " something. It is a simple selection and shuffling process of subject and object. The notation used for determining the number of selections/combinations and re-shuffling is expressed as:
[tex]^nC_r\cdot\text{ r!}[/tex]The above means that to determine arrangements we first need to find the number of combinations " C " between the subject and object then we will re-shhuffle the order of each combination paired with an object!
We are given the following:
[tex]\begin{gathered} \text{Subject : people} \\ \text{Object : chairs} \end{gathered}[/tex]The corresponding variables are:
[tex]\begin{gathered} n\text{ = 25} \\ r\text{ = 15} \end{gathered}[/tex]We are to determine the total number of possible arrangements that are possible. Hence, we are looking at the case of permutations that involves the selection and re-shuffle process.
The total number of arrangements can be made as such:
[tex]\begin{gathered} ^{25}C_{15}\cdot15! \\ 4.27\cdot10^{18}\text{ possible arrangements} \end{gathered}[/tex]
1 금35Lolo19.Which type of variation is modeled in the table?jointdirectcombinedInverse
The answer to your question is inverse varaiation.
Explanation: Inverse variation is a reciprocal term. Or say a variable is increasing while the other is decreasing.
So it is observed that as when y increases, then x decreases.
And also when y decreases, then x increases.
Thus, It is an inverse variation.
Translate thefollowing phaseinto an inequality-3 times r is at least 33A) inequality B) Solve the equality for r.C) express the solution in interval notation.
Given the phrase:
-3 times r is at least 33
Let's translate the given phrase into an inequality.
• Part A.
Let's figure out the inequality in steps.
-3 times r is written as:
-3r
-3 times s is at least 33 means that -3r is greater than or equal to 33.
Hence, we have the inequality:
[tex]-3r\ge33[/tex]• Part B.
Let's solve the inequality for r.
To solve for r, divide both sides of the inequality by -3:
[tex]\begin{gathered} \frac{-3r}{-3}\ge\frac{33}{-3} \\ \\ r\le-11 \end{gathered}[/tex]• Part C.
Let's express the solution in interval notation.
Here, the solution is:
[tex]r\le-11[/tex]It means s must be less than or equal to 11.
Therefore, the solution in interval notation is:
[tex](-\infty,-11\rbrack[/tex]ANSWER:
• A) -3r ≥ 33
• B) r ≤ -11
• C) (-∞, -11]
Two electrical lines are parallel to each other. One of the lines is represented by theequation - 4x + y = 8. What is the slope of the other electrical line?
Solve the system by substitution.y =10xY=4x+22
Given the system:
[tex]\begin{cases}y=10x \\ y=4x+22\end{cases}[/tex]Let's clear x from equation 1:
[tex]\begin{gathered} y=10x\rightarrow\frac{y}{10}=x \\ \rightarrow x=\frac{y}{10}\text{ (A)} \end{gathered}[/tex]And substitute (A) in equation 2:
[tex]\begin{gathered} y=4x+22 \\ \rightarrow y=4(\frac{y}{10})+22 \\ \rightarrow y=\frac{4}{10}y+22 \end{gathered}[/tex]Solving for y:
[tex]\begin{gathered} y=\frac{4}{10}y+22 \\ \rightarrow y-\frac{4}{10}y=22 \\ \rightarrow\frac{3}{5}y=22\rightarrow3y=110\rightarrow y=\frac{110}{3} \end{gathered}[/tex]Now, let's use (A) to calculate x:
[tex]\begin{gathered} x=\frac{y}{10} \\ \rightarrow x=\frac{\frac{110}{3}}{\frac{10}{1}}\rightarrow x=\frac{110}{30}\rightarrow x=\frac{11}{3} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{11}{3} \\ \\ y=\frac{110}{3} \end{gathered}[/tex]Use the Angle Bisector Theorem to set up an equation and solve for X.
1. AB is the Angle Bisector of 4CAD.
33° B (4x + 1)º A D
Step-by-step explanation:
what happens, if I cut something in half ?
not just into 2 pieces, but outright in half ?
a pizza or a cake ?
well, I get 2 identical pieces.
a bisector (bi = 2 or double, sector = part) splits an angle into 2 equal parts.
that means
33 = 4x + 1
from there we get
32 = 4x
x = 32/4 = 8