Answer:
gg
Step-by-step explanation:
Select the correct answer. Solve for x. x2 + 4x - 21 = 0 A. -3, -7 B. -3, 7 C. 3, -7 D. 3, 7
Answer:
Answer: the correct option is(C) 3, -7.
Step-by-step explanation:
How do I take an antiderivative of the following equation?
[tex]dy/dx+ky-77k=0[/tex]
The required anti derivative of given function is -(ky^2)/2 + 77ky.
What is integration(anti-derivative)?Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.
According to question:We have,
dy/dx +ky - 77k = 0
dy/dx = -ky + 77k
Integrate with respect to x
∫dy/dx = ∫(-ky + 77k)
∫dy/dx = -∫ky +∫77k
y = -(ky^2)/2 + 77ky
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The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
What is antiderivative?
In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.
[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]
Hence, The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15
After solving the given equation, we know that the value of c is -11.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
Sc, we have the equation:
3c + 7 = c - 15
Now, calculate this equation for c as follows:
3c + 7 = c - 15
3c - c = -15 - 7
2c = -22
c = -22/2
c = -11
Therefore, after solving the given equation, we know that the value of c is -11.
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Three times the quantity of a number c increased by 7 is equal to the same number, c, decreased by 15. What is c in this situation?
Find the equation of a line parallel to y=−7+4x that passes through the point (-2,-1)
To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.
We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:
y - (-1) = 4(x - (-2))
Simplifying this expression gives us:
y + 1 = 4(x + 2)
Which simplifies to:
y = 4x + 5
So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.
Cailen needs at least $150 to buy an X-box. She earns $15 for each lawn she mows and has $30 in savings. Write an inequality to determine how many lawns Cailen must mow to buy an x-box. How many lawns must she mow to buy the x-box?
total = 15x + 30
EDIT: She has to mow 8 lawns. I didn't read the question
there you go its that simple
Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph is a line that goes through points (0, 0) and (7.5, 7.5).
The graph is a line that goes through points (0, 0) and (15, 2).
The graph is a line that goes through points (0, 0) and (7.5, 1).
The graph is a line that goes through points (0, 0) and (1, 7.5).
The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)
What is a graph of linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
considering the given equation y = 7.5x.
c = 0
hence the graph passed through (0, 0)
substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point
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From question 28 -29
Help please
By using the concept of vector, it can be calculated that
28) First option is correct
29) Fourth option is correct
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
28) The vectors are
[tex]\vec{v} = -2i-5j,[/tex]
[tex]\vec{w} = -3i+j[/tex]
[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]
[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]
First option is correct
29) P = (1, 2) and Q = (-6, -1)
Position vector = (-6-1)i + (-1-2)j = -7i - 3j
Fourth option is correct
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Use the formula A=P\left(1+r/n)^nt to solve the compound interest problem.
Find how long it takes a 1700$ investment to earn 500$ interest if it is invested at 2% interest compounded quarterly.
500$ interest will be earned in approximately years. (Round to the nearest tenth.)
It will take 12.91 years to earn $ 500 in interest
What is Compound interest:
Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest.
The formula used for
Amount, A = P(1+r/n)^ntP = Principal amount
r = Rate of interest
n = Number of compounds in a year
t = Time period in years
And the formula for
Compound Interest, C.I = A - P
Here we have
Principal amount = 1700,
Rate of interest = 2% = 2/100 = 0.02 on decimals
Given that compound interest gained = $ 500
Number of compounds = 4 times
Let a be the time period
By the given formula,
Amount, A = 1700(1+0.02/4)^4t
= 1700(1+0.005)^4t
= 1700 (1.005)^4t
Compound interest = 1700 (1.005)^4t - 1700
From the given data,
Compound interest = $ 500
=> 1700 (1.005)^4t - 1700 = 500
=> 1700 (1.005)^4t = 2200
=> (1.005)^4t = 1.294
Take logs on both sides
=> log (1.005)^4t = log 1.294
=> 4t log (1.005) = log (1.294)
=> 4t = log(1.294)/log(1.005)
=> 4t = 0.111934276/ 0.00216606176
[ Use calculator for log(1.294) and log(1.005) ]
=> 4t = 51.6764012
=> t = 12.9191003
=> t = 12.91
Therefore,
It will take 12.91 years to earn $ 500 in interest
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Evaluate the following:
Logc1 = ?
The given logarithmic expression can be evaluated as Logc1 = 0.
What is Logarithm?Logarithm function is defined as the inverse of the exponential function.
If a^(b) = c, then b = log(c) at the base of a.
Logarithm of any number is always positive.
For negative numbers, the logarithm are complex numbers.
The given expression is Logc1.
It implies that it is the logarithm of 1 with c as a base.
Sine, the logarithm of 1 to any base is equal to zero, the given expression can be evaluated as follows,
Logc1 = 0
Hence, the value of the given expression is 0.
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Find a rectangular equation for the plane curve defined by the parametric equations.
X = t + 4, y = t^2 ; - ∞ < t < ∞
Answer:
[tex]y=x^2-8x+16[/tex]
Step-by-step explanation:
[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]
olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%.If she has a 92 test average and 100% HW average, what must her quiz average be? Let x = the average of the
Olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%. The quiz average is 82%.
What do you mean by Average?It is forming the outcome of multiplying the total of multiple quantities by their sum and then dividing this result by the number of quantities
Given,
She has test count = 55%,
quizzes count = 30%,
homework counts = 15%
If she had
test count = 92%
Homework counts = 100%
quizzes count = ?
Let x be the test count
x = (90 - (0.55(92) + 0.15(100)))/0.30x
= 82
Olivia must have an 82 average on quizzes in order to have a 90 average in algebra.
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Divide. Give the quotient and remainder.
133 2
Answer:
Quotient: 66
Remainder: 1
Step-by-step explanation:
133/2 = 66.5
66.5 =
66 + 0.5 =
66 + 1/2 = 66 1/2
1/2 * 2 = 1 ==> Remainder: 1
Whole number : 66
Quotient: 66
Remainder: 1
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A table of 1,022 guests are attending a reception. If each table can seat exactly 12 people,what is the least number of tables needed to seat all guests?
Answer:
86
Step-by-step explanation:
If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.
If ABTS = AGHD, BS = 25, IS = 14, BT = 31, GD = 4x - 11, m2S = 56, mLB = 21°, and mLH = (7y + 5)°, find the values of x and y.
Answer:
x = 8
y = 2
Step-by-step explanation:
If you sold 30% of a business for 500 dollars how much is the bussnis worth
it would be 1600 i hope this helps
26034 i hope this help man pls pls
A container is a hemisphere of radius 30cm.
Sand fills the container at a rate of 4000 cm³ per minute.
Does it take less than a quarter of an hour to fill the container?
You must show your working.
Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container
How to determine if it takes less than a quarter of an hour to fill the container?Given: A container is a hemisphere of radius 30cm
Sand fills the container at a rate of 4000 cm³ per minute
A hemisphere is half a sphere. Thus:
The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³
The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³
Rate = Volume / Time
Time = Volume/Rate
Time = 56548.67 /4000 = 14.14 minutes
In hours: Time = 14.14/60 = 0.24 hour
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The expected return on HiLo stock is 13.69 percent while the expected return on the
market is 11.5 percent. The beta of HiLo is 1.3. What is the market risk premium?
The risk-free rate of return on Hilo stock is 1.58%
What is the market risk premium?
Expected return on the stock=risk free rate beta x (expected market return-risk free rate)
14.08%=risk free rate+1.26 x (11.5%-risk free rate)
14.08%=risk free rate+14.49%-1.26 x risk free rate
0.41=0.26 x risk-free rate
risk-free rate=[tex]\frac{0.41}{0.26} %=1.58%[/tex]%=1.58%
The hazard-free price is the price of going back offered by means of funding that carries 0 risks. each investment asset incorporates a few degrees of threat, however small, So the risk-free price is something of a theoretical concept. In practice, it is taken into consideration to be the hobby price paid on short-time period government debt. the risk-free rate threat-unfastened price of going back no longer genuinely exists, as each investment carries at least a small quantity of hazard.To calculate the actual chance-unfastened charge, subtract the inflation rate from the yield of the Treasury bond matching your funding duration. Crucial banks control the threat-loose fee – nicely understood as the yield on short-term authorities’ payments.That is a risk-free rate fact of financial life but not one that we frequently think about. The capital asset pricing model and present-day portfolio idea take the danger-loose price as “given” instead of as “determined”.To learn more about risk-free rates visit here:
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Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?
Time in years =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]
[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]
WILL MARK BRAINLIEST PLEASE HELP ME ‼️‼️‼️‼️‼️‼️
NEED #13 AND #14 ‼️‼️
PLEASE HELP ME I NEED THIS FINISHED ASAP IM DOING OVERDUE ASSIGNMENTS FOR MATH I NEED THIS PELASE
Answer:
Step-by-step explanation: Q13 Find the perimeter of the shape
42x *2=84x
72x*2=72x
Perimeter=84x+72x=156x
Q14 Find the perimeter of the shape just add up 3x +(4x+8)+3(x-2)
=3x+4x+8+3*x+3 *-2
=3x+4x+8+3x-6
=3x+4x+3x+8-6......add together like terms and number terms
=10x+2
Answer:
13.) 156x
14.) 10x + 2 or 2( 5x + 1)
Step-by-step explanation:
13.)perimeter of a parallelogram is
p = 2(a + b)
P = 2( 36x + 42x)
P = 2( 78x )
P = 156x
14.) perimeter of a scalene triangle
P = a + b + c
P = 3x + 3(x – 2) + 4x + 8
P = 3x + 3x –6 + 4x +8
P = 6x + 4x –6 + 8
P = 10x + 2
in factorise form
P = 2(5x + 1)
I hope this helps pls rate as brainliest
ABCD is a rhombus and side AE Is congruent to EC prove triangle AEB is congruent to CEB
ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given that the side AE is congruent to EC of rhombus.
That means, AE ≅ EC.
And the diagonals of rhombus bisects each other.
Both the triangle AEB and triangle CEB share the same side which is BE.
That means BE ≅ BE, by the reflexive property.
And the sides AB and BC are the sides of rhombus.
So, AE ≅ BC.
Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The top 18 percent of scores fall within two standard deviations of the mean.
What is publicly recognized?Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.
Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.
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Solve the equation -3.98=x-11.24
x = 7.26
Step-by-step explanation:How to solve your problem:1. Add 11.24 to both sides
-3.98 = x - 11.24
-3.98 + 11.24 = x - 11.24 + 11.24
2. Simplify
Add the numbers:
-3.98 + 11.24 = x - 11.24 + 11.24
7.26 = x - 11.24 + 11.24
Add the numbers:
7.26 = x - 11.24 + 11.24
7.26 = x
Move the variable to the left:
7.26 = x
x = 7.26
Solution:
x = 7.26
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer:
x = 7.26
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
First, add 11.24 to both sides of the equation:
-3.98 = x - 11.24
-3.98 (+11.24) = x - 11.24 (+11.24)
Next, simplify.
11.24 - 3.98 = x
x = 7.26
x = 7.26 is your answer.
~
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i have no idea how to do this can anyone help
The long term behavior of the rational function f(x) = (x² - 3) / (x³ + 2) is 0, for the rational function g(x) = (x³ - 3) / (x³ + 2) is 1 and for the rational function h(x) = (x⁴ - 3) / (x³ + 2) does not exist.
How to determine the long run behavior of a rational function
In this case we find three rational functions, that is, functions of the form:
m(x) = p(x) / q(x)
Where:
p(x) - Function numerator.q(x) - Function denominator.Please notice that both numerator and denominator are polynomic functions, the long run behavior of the function depends on the grades of numerator and denominator according to these rules:
If the grade of the numerator is greater than the grade of the denominator, then long run behavior is divergent as x → ± ∞.If the grade of the numerator and the grade of the denominator are the same, then the function tends to a / b as x → ± ∞, where a and b are the lead coefficients of the numerator and the denominator, respectively.If the grade of the numerator is less than the grade of the denominator, the function tends to be 0 as x → ± ∞.Now we proceed to analyze the long run behavior of each rational function:
Case 1: f(x) = (x² - 3) / (x³ + 2)
Grade of numerator: 2, grade of denominator: 3
Result: 0
Case 2: g(x) = (x³ - 3) / (x³ + 2)
Grade of numerator: 3, grade of denominator: 3
Result: 1
Case 3: h(x) = (x⁴ - 3) / (x³ + 2)
Grade of numerator: 4, grade of denominator: 3
Result: N / A
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From the graph, estimate what numbers should go into the empty cells in the first two columns. Do not complete the columns on the right of the dividing line.
The first two columns of the table, considering logarithms, are completed as follows:
2 - 10^0.3.5 - 10^0.7.9 - 10^(0.95).4 - 10^(0.6).2.51 - 10^(0.4).How to complete the table?The table is completed in this problem applying the logarithms.
This is because on the first column we had that:
10^(0.3) = 2, which means that log10(2) = 0.3.
(log10(x) represents the logarithm of base 10 of x).
For the second row, the decimal approximation is found applying the power of 10^0.7, hence:
10^0.7 = 5.
For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:
log10(9) = 0.95.log10(4) = 0.6.Hence the power of 10 expressions are given as follows:
9 = 10^(0.95).4 = 10^(0.6).For the fifth row, we just need to calculate the exponential expression, hence:
10^(0.4) = 2.51.
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x^-3=1/343 what does x equals please show all work.
Answer:
Step-by-step explanation:
X^-3=1/343
X^-3=1/7^3
X^-3=7^-3
Since the powers are equal, the bases should also be equal.
Therefore, X=7
help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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3. Diana uses 30 grams of coffee beans to
make 48 fluid ounces of coffee. When
company comes she makes 96 fluid ounces of coffee. How many grams of coffee
beans does Diana use when company comes?
A. 160
B. 60
C. 98.2
D. 14.4
Answer:
Step-by-step explanation:
The grams of coffee beans Diana uses when the company comes is:
62.5 grams
Which of the following statements is correct based on the number line below?
-8
-6
A
B
C
D
-4 -2
P
200
808
Q
0 2 4
6
√68 is to the right of Point Q because it is less than 8.
√68 is between points P and Q because it is less than 0 and greater than 8.
√68 is between points P and Q because it is greater than 0 and less than 8.
68 is to the right of Point Q because it is greater than 8.
John Morse corporation buys a van for $16,000. The estimated life of the van is four years. The residual value of the van is $4,000. After two years, the van is sold for $8,000. What was the difference between the book value and the amount received from selling the van if John used the straight-line method of depreciation?
A.$4,000
B. $12,000
C. $8,000
D. $2,000
The difference between book value and the amount received is $2000
What was the difference between the book value and the amount received ?
van cost = $16000
Estimated life= 4 years
Residual value= $4000
using straight line method of depreciation
Depreciation per year= 16000-4000/4= 3000
Therefore book value after two years = $16000- 2*3000= $10000
Selling price of book after 2 years= $8000
hence the difference between book value and the amount received
10000-8000= $2000
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What is an equation of the line that passes through the points (-4, 8)(−4,8) and (6, 3)(6,3)
Answer:
y=-1/2x+6
Step-by-step explanation:
slope: -5/10 = -1/2
y=mx+b
y=-1/2x+b
substitute points to find b: 8=-1/2(-4)+b
8=2+b
6=b