Answer:
\(x^3+x^2-5x+5-\frac{30}{x+5}\)
Step-by-step explanation:
\(\frac{x^4 + 6x^3 -20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^3-20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x^2-20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x(x+5)+5x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x(x+5)+5(x+5)-30}{x+5} \\ \\ =x^3+x^2-5x+5-\frac{30}{x+5}\)
What is the domain of ggg? Choose 1 answer: Choose 1 answer: (Choice A) A The xxx-values -7−7minus, 7, -4−4minus, 4, 000, 333, and 444 (Choice B) B -4 \leq x \leq 8−4≤x≤8minus, 4, is less than or equal to, x, is less than or equal to, 8 (Choice C) C The xxx-values -4−4minus, 4, -3−3minus, 3, 000, 222, and 888 (Choice D) D -7 \leq x \leq 4−7≤x≤4
The domain of ggg is option D: -7 ≤ x ≤ 4.
To determine the domain of a function, we need to identify the set of all possible values for the independent variable, in this case, x, for which the function is defined.
In option D, the domain is specified as -7 ≤ x ≤ 4. This means that x can take any value within the closed interval from -7 to 4, inclusive.
In other words, the domain of ggg includes all real numbers between -7 and 4, including -7 and 4 themselves. This interval represents the range of values for x that satisfy the given conditions for the function ggg.
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Use the given scale factor and the side lengths of the scale drawing to
determine the side lengths of the real object.
A. Side a is 12 inches long and side b is 3 inches long.
B. Side a is 45 inches long and side b is 18 inches long.
C. Side a is 5 inches long and side b is 2 inches long.
D. Side a is 12 inches long and side b is 4 inches long.
Answer:
C is the correct answer
Step-by-step explanation:
i got it right on my test
Given g(x) = 2x ^ 2 - 3x + 5 find g(- 2)
The value of the function when evaluated is 3
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = 2x ^ 2 - 3x + 5
Express properly
So, we have the following representation
g(x) = 2x^2 - 3x + 5
Substitute the known values in the above equation, so, we have the following representation
g(-2) = 2(-2)^2 - 3(-2) + 5
Evaluate the like terms
g(-2) = -8 + 6 + 5
So, we have
g(-2) =
Hence, the function value is 3
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help with parallel lines please
Answer:
angle 2 = 38° { because they are corresponding angles ,so they are equal }
Answer:
Step-by-step explanation:
∠2 = 38 {corresponding angles}
A pair of angles on the same side of the transversal, one of which is and interior angle and the other one is an exterior angles, but do not form a linear pair, is known as corresponding angles
Math is multi-cultural, analytical, timeless and hands-on. Provide a piece of mathematical concept, hypothesis, law, paradox, rule or theorem to prove this statement.
It should be noted that mathematics is multicultural. This implies that mathematics applies to different cultures.
Mathematics is multicultural and it's neutral from the issues of races, gender, class, etc. Also, it should be noted that mathematics is analytical.Furthermore, mathematics is timeless and hands-on. This implies that students need to touch and feel what they're learning through a concrete experience.Learn more about mathematics on:
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Where do you stash your allowance, birthday cash or paycheck? There are lots of ways to keep your money safe, but knowing which option is best for you means researching your choices. After the videos watched in class, write down four facts that you learn about each type of institution below. Watch the videos twice if needed to fill in the chart. Then, decide which one you would choose to put your money in and why.
I stash my allowance, birthday cash or paycheck in a bank.
The facts about Banks include the following:
They are profit oriented.They accepts deposits with a lower interest rate.They give loan at a higher rate.They provide a larger range of services.The facts about Credit union include the following:
They are not profit oriented.They accepts deposits with a higher interest rate.They give loan at a lower rate.They provide a smaller range of services.What is a Credit union?These are non profit organizations that exist to serve their members and offer some banking services.
They accepts deposits with a higher interest rate and give loan at a lower rate which is why my decision in where to put my money will be in a credit union due to the high interest rate.
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please help me i really don’t understand!
Answer:
Step-by-step explanation:
f(x)=-89-76-88
Calculate The Constant of Proportionality (k) and Write an Equation for the line in the Graph Below:
Answer:
K = ½
Equation: y = ½x
Step-by-step explanation:
✔️Constant of proportionality (k) = y/x
Using a point on the line, (2, 1),
k = ½
✔️Equation of a proportional relationship would be in the form of y = kx
To write an equation, substitute k = ½, into y = kx
Thus:
y = ½x
could anyone give me these answers!!
Answer
5 and 6 are NOT functions but 4 IS a function
Step-by-step explanation:
A number cannot repeat in the x axis
Manuel made $80 for 5 hours of work.
At the same rate, how many hours would he have to work to make $208 ?
Answer:
13 hours
Step-by-step explanation:
Let's first start by finding how much he makes in 1 hours:
\(\frac{\$80}{5} =\$16\)
Now we can set up two ratios
\(\frac{16}{1} = \frac{208}{x} \)
Solve by cross multiplying (multiply the numerator of the first fraction with the denominator of the second fraction and the numerator of the second fraction with the denominator of the first fraction)
16x=208
Divide both sides by 16 to isolate x
x=13
He would have to work 13 hours to make $208
Multiply: (2x + 5)(3x + 2)
Simplify and write your answer in standard form
Answer:
Hey,
\( \rm \: =6x^2+19x+10\)
Step-by-step explanation:
=(2x+5)(3x+2)
=(2x)(3x)+(2x)(2)+(5)(3x)+(5)(2)
=6x^2+4x+15x+10
=6x^2+19x+10(ANS)
Answer:
The answer is 6x^2+19x+10
Step-by-step explanation:
What is the graph of one cycle of a sine curve with amplitude 5, period pi, and a>0?
What is an equation for the sine curve in the form y=asinb0?
a. y=2sin50
b. y=5sinpi0
c. y=5sin20
d. y=5sin1/2 0
Answer:
c is correct
Step-by-step explanation:
if u have the equation y = a sin b (x),
a is the amplitue (regardless of + or - before it) and 2pi / b = period. so we can deduce that a = +5 or -5 and b = 2, but then it says a>0, so therefore a must be 5 and b is still 2, so the equation is y= 5 sin2(O)
-8 + 5 ( 1 + x) = 2x - 20
multi step equation, please solve ill give brainliest (with steps)
Answer:
The answer is x=-17/3
Step-by-step explanation:
The Steps:
-8 + 5(1 + x) = 2x - 20
-8 + 5 + 5x = 2x - 20
-3 + 5x = 2x - 20
-3 + 3x = -20
3x = -17
x = -17/3
What are the solutions of the system? y = -6x – 6 y = x2 – 5x – 6
Answer:
Answer is 0
Step-by-step explanation:
-6x-6=x²-5x-6
-6(x+1)=(x+1)(x-6)
-6=x-6
x=0
which expression results in an irrational number? (see image)
a) II
b) III
c) I, III, IV
d) II, III, IV
The _____ of the correlation coefficient indicates the direction of the correlation, positive or negative
The __sign__ of the correlation coefficient indicates the direction of the correlation, whether it is positive or negative.
The correlation coefficient, often denoted by the symbol "r," is a statistical measure that quantifies the strength and direction of the linear relationship between two variables.
It ranges between -1 and 1, where a value of -1 indicates a perfect negative correlation, a value of 1 indicates a perfect positive correlation, and a value of 0 indicates no correlation.
When the correlation coefficient is positive, it suggests that the two variables have a positive linear relationship. This means that as one variable increases, the other variable tends to increase as well.
For example, a positive correlation may be observed between the amount of studying a student does and their test scores. As the study time increases, the test scores also tend to increase.
Conversely, when the correlation coefficient is negative, it indicates a negative linear relationship between the variables. In this case, as one variable increases, the other variable tends to decrease.
For instance, a negative correlation may exist between the amount of rainfall and the number of hours spent outdoors. As rainfall increases, the time spent outdoors typically decreases.
Therefore, the sign of the correlation coefficient is crucial in understanding the direction of the correlation.
It provides valuable insights into how two variables are related to each other and helps researchers and analysts interpret the nature of their relationship.
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Part B. How much would it cost to buy a cover for the pool that costs $0.30 per square foot? Enter your answer in the box. Image above
use the ratio test to determine whether the series is convergent or divergent. [infinity] ∑ 9/k! k=1 identify ak. =____evaluate the following limit. lim k → [infinity] | ak+1 / ak |
The value of following limit is zero which is less than one so the series is convergent.
What is convergent or divergent series?
The term "convergent series" refers to a series whose partial sums tend to a limit. A divergent series is one whose partial sums, in contrast, do not approach a limit. The Divergent series often reach, reach, or don't reach a particular number.
As given,
Infinity ∑ (k = 1) (9/K!)
Suppose that ak = 9/K!
Apply ratio test:
I (ak + 1)/ak I = I 9/(K + 1)! (K!/9) I
Simplify values,
I (ak + 1)/ak I = I K!/(K + 1)K! I
= I 1/(K + 1) I
So, that Left hand limit is,
Lim (n⇒∞) I (ak + 1)/ak I = Lim (n⇒∞) I 1/(K + 1) I
= 1/(∞ + 1)
= 0
Since Right hand limit is,
Lim (n⇒∞) I (ak + 1)/ak I = 0
Which is less than one.
So, the given series is Convergent series.
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how many feet are in one story on the empire state building
Answer:
The building itself is 1,250 feet and 102 stories high.
Uhm what class is this for
Which rational exponent represents a square root?
A. 1 / 2
B. 3/2
C. 1/3
D. 1/4
Answer:
1/2 rational exponent represents a square root.
Therefore, option A is correct.
Step-by-step explanation:
As we know that raising to the one-half power i.e. \(\frac{1}{2}\) is the same
as taking the square root.
so \(x^{\frac{1}{2}}\) is the same as the square root of \(x\).For example, taking the square root of 4 will determine:
\(4^{\frac{1}{2}}\)
\(\mathrm{Factor\:the\:number:\:}\:4=2^2\)
\(4^{\frac{1}{2}}=\left(2^2\right)^{\frac{1}{2}}\)
\(\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\)
\(\left(2^2\right)^{\frac{1}{2}}=2^{2\cdot \frac{1}{2}}\)
so the expression becomes
\(4^{\frac{1}{2}}=2^{2\cdot \:\frac{1}{2}}\)
\(=2^1\)
\(=2\) ∵ \(\mathrm{Apply\:exponent\:rule}:\quad \:a^1=a\)
so, 1/2 rational exponent represents a square root.
Therefore, option A is correct.
Answer: A.) 1/2 is the correct answer
Step-by-step explanation:
Pls help thank you will mark the Brainliest
Learning mathematics online can be more interesting than learning it in the classroom. It can also be different from learning other topics online because special tools can be used for this area.
What is it like to learn mathematics online?Learning mathematics online is a process through which a person acquires skills and knowledge to solve mathematical problems through an online platform. This process can be enriching for the student because it will allow him to develop his knowledge of it.
How is it different from learning other topics online?Learning math online is different from learning other topics online because there are different platforms on the web that offer useful tools for different math topics such as geometry, arithmetic, algebra, among others. Therefore, it can be more interesting because the student can interact more directly with the knowledge.
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PLEASE HELP
Rihanna wants to find the distance, AB, across a river. She starts at point B and walks along the edge of the river 215 ft and marks point C. Then she walks 25 ft further and marks point D. She turns 85° and walks until her final location and marks point E. Point E, point A, and point C are collinear.
The congruence theorem used is the SAS theorem and the measure of the side AB is 525feet
Congruence theoremThe congruence theorem used is expressed is the SAS rule which states that:
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
To get the length of DE, we will use the similarity theorem of the triangle as shown:
DE/25 = AB/215
105/25 = AB/125
25AB = 105 * 125
AB = 105 * 5
AB = 525feet
Hence the measure of the side AB is 525feet
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Answer:
The congruence theorem used is the SAS theorem and the measure of the side AB is 525feet
Congruence theorem
The congruence theorem used is expressed is the SAS rule which states that:
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
To get the length of DE, we will use the similarity theorem of the triangle as shown:
DE/25 = AB/215
105/25 = AB/125
25AB = 105 * 125
AB = 105 * 5
AB = 525feet
Hence the measure of the side AB is 525feet
Please help me! I really need it.
Answer:
1. 11x
2. 5x+7
3. 5x+8
4. 8x+9y
5. x+8y+12
6. 12x+3y
7. 10a+7b+4
8. 19a+11
9. a+16b+10
10. 13a+9b+11
11. 12a+2b+24
12. 4a+3b+1
13. 8x+6
14. 11x+20
15. 4x+27
16. 11x+8y
17. 5x+3y+18
18. 7x+15y+30
19. 7x+7y
20. 5x+10y+33
21. 2x+7y+37
22. 9x+7y+9
23. x+2x+7+3x+1= 6x+8
24. 3x+x+x+5+x+5+2x+3= 8x+13
Step-by-step explanation:
Like variables can be added together and simplified. Like variables are things like 2x and 4x. They both have x. This works for y,z, etc...
Cara made some cookies for the Math Club
She sold 3/5 of them in the morning and 1/4 of THE REMAINING in the afternoon.
How many cookies did Cara make? How many cookies did Cara sell in the afternoon?
Answer: There are multiple solutions.
Step-by-step explanation:
Let's say she made 50 cookies. If she sold 3/5 of them in the morning, that means she sold 3/5 * 50 = 30 cookies. If she sold 1/4 of the remaining 20, she sold 1/4 * 20 = 5 cookies. So she would have 15 remaining.
However, the same logic could be applied if she started with 100 cookies, or 200, or 1000. There are an infinite number of solutions.
o check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?
Answer:
No this is a not good experimental design
Step-by-step explanation:
In an experiment, we seek to establish cause an effect relationship. The effect of one variable on another is examined while keeping other variables constant. A control often establishes the validity of the experiment.
Now the ten rubber bands were selected at random from each box. The experimental group was put in a freezer while the control group was maintained at room temperature.
Comparison of the mean stretch before breakage of the rubber bands in both groups establishes the effect of cold temperature on elasticity of rubber bands.
However, this is not a good experimental design because the sample rubber bands should have been picked from different boxes of brand A and B and not from the same box.
Secondly, samples from the two brands should have been put in the freezer and kept at room temperature. That is, ten rubber bands from A are put on the freezer and another 10 are left at room temperature. 10 rubber bands from B are put in the freezer and another 10 are left at room temperature.
The mean elasticity of the both groups can now be meaningfully compared from the data obtained.
A student always catches his train if class ends on time. However, 30% of classes run late and then there's a 45% chance he'll miss it. What is the probability that he misses the train today?
The probability that he misses the train today is 0.135 or 13.5%.
P(Class runs late)=30%=0.30
P(Miss train ∣ Class runs late)=45%=0.45
General multiplication rule:
P(A and B)=P(A)×P(B ∣ A)
Using the general multiplication rule, we then obtain (and using that the student always catches his train if the class ends on time) :-
P( Miss train)=P( Miss train and Class runs late)=P(Class runs late)×P(Miss train ∣ Class runs late)
= 0.30×0.45
= 0.135
= or 13.5%.
So, the the probability that he misses the train today is 0.135 or 13.5%.
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problem 5. let w1 and w2 be subspaces of a vector space v . show that the following holds. w1 ∪w2 is a subspace of v ⇐⇒ w1 ⊆w2 or w2 ⊆w1
The statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, meaning that the union of two subspaces is a subspace if and only if one subspace is contained within the other.
To show that the statement "w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1" holds, we need to prove both directions of the implication.
Direction 1: If w1 ∪ w2 is a subspace of V, then w1 ⊆ w2 or w2 ⊆ w1.
Assume that w1 ∪ w2 is a subspace of V. We will prove that either w1 ⊆ w2 or w2 ⊆ w1.
Suppose there exists an element v in w1 that is not in w2. Since w1 ∪ w2 is a subspace, it must be closed under scalar multiplication. Therefore, av is in w1 for any scalar a. But av is not in w2, which contradicts the assumption that w1 ∪ w2 is a subspace. Thus, we conclude that if w1 ∪ w2 is a subspace, then w1 ⊆ w2.
Similarly, we can prove that if w1 ∪ w2 is a subspace, then w2 ⊆ w1.
Direction 2: If w1 ⊆ w2 or w2 ⊆ w1, then w1 ∪ w2 is a subspace of V.
Assume that w1 ⊆ w2. To show that w1 ∪ w2 is a subspace, we need to demonstrate that it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.
Closure under addition: Take any two vectors u and v in w1 ∪ w2. Since w1 ⊆ w2, u and v are both in w2. Therefore, u + v is also in w2, and thus in w1 ∪ w2.
Closure under scalar multiplication: Take any vector u in w1 ∪ w2 and any scalar a. Since u is in w2, au is also in w2, and thus in w1 ∪ w2.
Contains the zero vector: The zero vector is in both w1 and w2, so it is in w1 ∪ w2.
Therefore, if w1 ⊆ w2, then w1 ∪ w2 is a subspace. Similarly, if w2 ⊆ w1, then w1 ∪ w2 is a subspace.
By proving both directions of the implication, we conclude that w1 ∪ w2 is a subspace of V if and only if w1 ⊆ w2 or w2 ⊆ w1.
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g(x) =
x if x < 1
6 if x = 1
2 − x2 if 1 < x ≤ 2
x − 2 if x > 2
(a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)
(i) lim x→1− g(x)
___________
(ii) lim x→1+ g(x)
____________
(iii) g(1)
____________
(iv) lim x→2− g(x)
____________
(v) lim x→2+ g(x)
____________
(vi) lim x→2 g(x)
____________
DONE
(i) lim x→1− g(x) = 1
(ii) lim x→1+ g(x) = 6
(iii) g(1) = 6
(iv) lim x→2− g(x) = 4
(v) lim x→2+ g(x) = 0
(vi) lim x→2 g(x) = DONE
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On a coordinate plane, parallelogram A B C D, parallelogram A prime B prime C prime D prime, and parallelogram A double prime, B double prime, C double prime, D double prime are on the graph.
In the pre-image of the parallelogram, the slope of AD is −3 and the slope of BC is −3. The image is translated down 7 units and then reflected over the y−axis.
The slope of A"D" is
.
The slope of B"C" is
.
What can you determine about the line segments A"D" and B"C"?
Using translation concepts, we have that:
The slope of A"D" is of 3.The slope of B"C" is 3.The lines are parallel.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
When the function is translated down, the slope remains constant, while when the function is reflected over the y-axis, the slope is multiplied by -1, hence both lines will have a slope of 3, and since they have the same slope, they are parallel.
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15. pls help will give brainliest
Answer:
Point-slope form: y - 120 = 2(x - 25)
Slope-intercept form: y = 2x + 70