Write the log equation as an exponential equation. You do not need to solve for x.
log (x^2– 5x + 14) = 2x + 4
Answers
9514 1404 393
Answer:
x^2 -5x +14 = 10^(2x +4)
Step-by-step explanation:
The relationship is ...
log(a) = b ⇔ a = 10^b
__
Using this with a=x^2-5x+14 and b=2x+4, we have ...
x^2 -5x +14 = 10^(2x +4)
_____
Additional comments
In plain text, the exponent needs parentheses, because superscript formatting is not available to tell what is and isn't part of the exponent.
The base of "log" is assumed to be 10 in high school algebra. In the larger world, "log" is often used in place of "ln" to mean the logarithm to base 'e'.
__
The one solution is approximately x = −1.32505947996.
Related Questions
The area of a rectangular field is the product of its length and width. If each dimension of the rectangular field is multiplied by 3, then the area of the enlarged field is how many times the area of the original field?
Answers
Step 1
The area of the rectangular field is given as;
\(A=\text{length(l)}\times width(w)=lw\)If the dimensions of the field are multiplied by 3, then we will have;
\(\begin{gathered} 3(\text{length)}=3l \\ 3(\text{width)}=3w \end{gathered}\)Step 2
Find by how many times the area of the enlarged field is bigger than the area of the original field.
\(\begin{gathered} \text{Area of enlarged field= 3}l\times3w=9lw \\ \text{Number of times the enlarged field is bigger=}\frac{9lw}{lw}=9 \end{gathered}\)Therefore the area of the enlarged field is 9 times the area of the original field.
what is 3 +(-4) on a number line
Answers
solve for x. show your work.
Answers
Hello!
\(\large\boxed{x = 8}\)
The two angles pictured are corresponding angles, so they are congruent.
Therefore:
17x - 4 = 12 + 15x
Isolate for x by subtracting 15x from both sides:
2x - 4 = 12
Add 4 to both sides:
2x = 16
Divide both sides by 2:
x = 8.
Answer:
x=8
Step-by-step explanation:
These angles are what we call corresponding angles. This simply means that they are the same. Therefore, we set 17x-4 equal to 12+15x. To isolate x, add 4 to both sides, and subtract 15x from both sides. 2x=16. x=8. To check, both angles = 132 degrees.
Complete the following sentence (select all that apply). The expected count of females who are not pierced is what we would expect to see in the sample if ___________________________. Group of answer choices gender and piercing were significantly related. gender and piercing are independent. the null hypothesis is true. the null hypothesis is not true.
Answers
The statement that completes the blank is (c) the null hypothesis is true.
In sampling techniques, the expected count of a variable is dependent on the null hypothesis.
This means that, if the null hypothesis is true, then the expected count is what is expected to be seen in the sample.
This in other words, means that the complete statement is:
The expected count of females who are not pierced is what we would expect to see in the sample if the null hypothesis is true.
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3 people can build a shed in 8 hours how long would it take 5 people
Answers
Answer:
3howers
Step-by-step explanation:
Step-by-step exaplanation
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48
Answers
Answer:
c. y=2x−48
Explanation:
It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept
It also says he earns $2 per hot dog, so that will be our slope (rate of change)
Hope it helps! :]
y = 2x - 48 equation represents the profit earned by the x hot dog sold.
What is linear equation?A linear equation is an algebraic expression in which highest power of the given variable is equals to one.
Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.
It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.
We need to establish an equation that represents the total profit,
According to the question,
x represents the number of hot dogs sold
y represents the total profit earned
Cost required for supply = $48
Profit on each hot dog sold = $2
As per the condition given, the required linear equation is =
y = 2x - 48
Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.
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In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answers
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
A and B are mutually exclusive events. P(A) = 0.20 and P(B) =
0.50.
What is P(A or B)?
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A furnace is designed to heat a 10,000 cubic feet of space. Will this furnace be adequate for a 1,400 square foot house with a 9foot ceiling.
Answers
To determine whether the furnace will be adequate for a 1,400 square foot house with a 9-foot ceiling, we need to calculate the volume of the house and compare it to the volume the furnace is designed to heat.
The volume of the house can be found by multiplying the square footage by the ceiling height:
1,400 sq ft x 9 ft = 12,600 cubic feet
Since the furnace is designed to heat 10,000 cubic feet, and the house has a volume of 12,600 cubic feet, the furnace may not be adequate for heating the house. The furnace is not capable to heat the entire house.
solve the simuteneous equation
4x+2y=6
x-2y=9
Answers
Answer:
find the same x-value and the same y-value that satisfies both ... 1 2 3. + 4 5 6. 5 7 9 ... + (4x – 2y + 9 = 0).
Step-by-step explanation:
Answer:
x=3 y= -3
Step-by-step explanation:
Add the two equations to eliminate y
4x+2y=6
x-2y=9
-------------
5x = 15
Divide by 5
5x/5 = 15/5
x = 3
Now find y
x - 2y = 9
3 -2y = 9
Subtract 3 from each side
3-2y-3 = 9-3
-2y = 6
Divide by -2
-2y/-2 = 6/-2
y = -3
Ellen bought 18 boxes of paper clips. Each box had 150 paper clips. How many paper clips did Ellen buy
Answers
Answer:
Ellen bought 2700 paper clips.
Step-by-step explanation:
Total boxes=18
Paper Clips in 1 box=150
Total paper clips=18×150
=2700
Answer:
ellen bought 2700 paper clips
Step-by-step explanation:
total paper clips in a box = 150
total boxes = 18
multiplication = 150×18=2700
Calculate the product
20 (-15)
Answers
Answer:
Step-by-step explanation:
Product means multiply.
-300
Carlos plays college soccer, and will attempt two goals in a row.
A = the event Carlos is successful on his first attempt. P(A) = 0.60.
B = the event Carlos is successful on his second attempt. P(B) = 0.55.
The probability that he makes the second goal GIVEN that he made the first goal is
0.35
What is the probability that he makes both goals?
Answers
Since Carlos needs to make both goals, we must multiply the probability that he makes goal 1 with the dependent probability that he makes goal 2 after goal 1. Since we are given these values as 0.60 and 0.35, we multiply them to find a probability of (0.6)(0.35) = 0.21
m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
Answers
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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(need help asap please this is urgent)
Use the systems of inequalities graphed below to answer the questions.
what is the inequality symbol of the green line?
-y is greater than ax+b -y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
what is the inequality symbol of the green line?
-y is greater than ax+b
-y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
is the point (-3, -5) a solution to the system of inequalities?
-yes -no
is the point (1,6) a solution to the system of inequalities?
-yes -no
Answers
Answer:
Green line: y is greater than or equal to ax+b
Purple line: y is less than ax+b
(-3, -5) : Yes
(1, 6) : No
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Green line
From inspection of the given graph, the green line is a solid line and the shading is above the line.
Therefore, the inequality symbol of the green line is ≥.
"y is greater than or equal to ax+b"
Purple line
From inspection of the given graph, the purple line is a dashed line and the shading is below the line.
Therefore, the inequality symbol of the purple line is <.
"y is less than ax+b"
The solutions to a graphed system of inequalities are found in the overlapping shaded region.
Yes, point (-3, -5) is a solution to the system of inequalities as this point is in the overlapping shaded region.
No, point (1, 6) is not a solution to the system of inequalities as this point is not in the overlapping shaded region.
answer the question for me
Answers
Answer: 1, 2, and 4.
Step-by-step explanation: Each must be wider than the angle than a "L" has.
A drone flying over a field of corn identifies a dry area. The coordinates of the vertices of the area are shown. To what coordinates should the portable irrigation system be sent to water the dry area? Explain your reasoning.
Answers
The coordinates to which the portable irrigation system should be sent to water the area are:
(495.75, 672).
Where to send the portable irrigation system?The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.
Hence the coordinates are given as follows:
x-coordinate: Mean of the x-coordinates of x = 56, x = 144, x = 888, x = 895.y-coordinate: Mean of the y-coordinates of y = 289, y = 332, y = 1012, y = 1055.Hence the x-coordinate of the point to which the system should be sent is:
x = (56 + 144 + 888 + 895)/4 = 495.75.
(the mean is given by the sum of the observations divided by the number of observations).
The y-coordinate of the point to which the system should be sent is:
y = (289 + 332 + 1012 + 1055)/4 = 672.
Missing InformationThe area is given by the image at the end of the answer.
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Rocio deposits $3,200 in a one year CD at
3.1% interest, compounded daily. What is
her APY to the nearest hundredth of a
percent?
Answers
The annual percentage yield (APY) of Rocio is 3.11 %
What is Annual Percentage Yield?
The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.
Given data ,
Deposit amount of Russ = $ 3200
Interest rate R = 3.1 %
And it is given that the interest rate is compounded daily , so
Interest rate R = 3.1 % / 365
= 0.031 / 365
= 0.000084
Now , The annual percentage yield (APY) is calculated as
The interest amount = 3200 x ( 1 + 0.000084 )³⁶⁵
= 3200 x ( 1.000084 )³⁶⁵
= 3200 x 1.031133
= 3299.6272
≈ 3299.627
Therefore , the interest will be
= 3299.627 - 3200
= $ 99.627
Now , the annual percentage yield (APY) is given by
= Interest / Deposit
= 99.627 / 3200
= 0.03113
≈ 3.11 %
Hence , annual percentage yield (APY) of Rocio is 3.11 %
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9.215
627
How to work the problem
Answers
Answer:
multiply
Step-by-step explanation:
Please use the Quadratic Formula to find the zeros of the function below.
g(x) = 2x2 + x + 25
Answers
Answer:
Step-by-step explanation:
PR and SU are parallel lines. Which angles are alternate interior angles
Answers
Answer:
RQT AND STQ
Step-by-step explanation:
I'm not sure but that's what I think it is
9514 1404 393
Answer:
(d) ∠RQT and ∠STQ
Step-by-step explanation:
Alternate interior angles are on opposite sides of the transversal, and between the parallel lines. Of the answer choices, the only one that fits is ...
∠RQT and ∠STQ
__
In the attached, pairs of alternate interior angles are identified in the same color (red or blue).
You deposit $400 in an account earning 8% interest compounded annually. How much will you have in the account in 15 years?
Answers
Answer:
you will gain 280,462.92 in peso.but you convert in in dollar you will gain $5,520.00
1 = 104
2 = 79
find the measure of the third angle
Answers
Answer:
?
Step-by-step explanation:
What is the coordinate of the vertex of this following parabola?
Answers
Comparing the parabola's equation to the formula \(y = ax^2 + bx + c\) in standard form is the first step. In step 2 Apply the formula h = -b/2a to find the vertex's x-coordinate. In step 3 Substitute x = h in the expression \(y = ax^2 + bx + c\) to obtain the vertex's y-coordinate (k).
How are the axis and vertex determined?The equation of the parabola's axis of symmetry is the vertex's x-coordinate. The axis of symmetry for a quadratic function in standard form, \(y = ax^2 + bx + c\) is a vertical line, \(x=b^2a\).
What exactly is a vertex?The intersection of two lines or rays that create an angle is known as the vertex of the angle.
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Determine whose method is the most fair, based on probability. Show your work. If needed, use a 6 × 6 array when analyzing Keenan’s method.
Explain why Gerard’s method isn’t fair.
Explain why Elena’s method would be unfair.
Elena, Keenan, and Gerard are planning a movie night, but can’t decide which movie to watch. Elena wants to watch an action movie, Keenan wants to watch a comedy, and Gerard wants to watch a science fiction movie. Since no one is budging on their movie preference, the three friends propose different methods for choosing the movie they’ll watch:
Elena suggests they call up her sister and have her make the choice for them.
Keenan suggests they roll two dice and find the sum of the dice. If the sum equals 2, 3, 4, or 7, then they’ll watch an action movie. If the sum equals 8, 9, or 10, then they’ll watch a comedy. If the sum equals 5, 6, 11, or 12, then they’ll watch the science fiction movie.
Gerard suggests they flip a coin two times. If both flips land on heads, then they watch an action movie. If both flips land on tails, then they watch a comedy. And if one flip lands on heads and one lands on tails, then they watch a science fiction movie.
Answers
Answer: Gerard's method isn't fair because it has a higher chance for his movie than any other movie and Elena's method isn't fair because her sister will choose what Elena wants. so Keenan's method is the fairest because it has a chance for all.
Answer:
Answer from PLATO just reworded a bit
Find the value of X in the diagram. (See below)
1. 25
2. 10
3. 180
4. 50
Answers
Answer:
17
Step-by-step explanation:
STUDY HARD GUYS I NEED HW HELP
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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write equation that has slope of 1/2 and y intercept of -5
Answers
The equation of the straight line with a slope of 1/2 and a y-intercept of -5 is y = (1/2)x - 5
What is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions.
For example, the equation 2 + 3 = 5 shows that the expression 2 + 3 is equal to the expression 5. In this equation, the expressions on both sides of the equals sign have the same value.
The equation of a straight line can be written in slope-intercept form as:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Given that the slope is 1/2 and the y-intercept is -5, we can substitute these values into the equation above to get:
Therefore, the equation of the straight line with a slope of 1/2 and a y-intercept of -5 is y = (1/2)x - 5
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First if is an Eigenvector of the matrix A with Eigenvalue 4, will also be an Eigenvalue for any linear combination of the matrix A.
Answers
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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PLEASE HELP WILL MARK BRAINLIEST
Answers
9514 1404 393
Answer:
x = 10/3 = 3 1/3 ≈ 3.33
Step-by-step explanation:
Triangles ABC and ADE are similar, so corresponding sides are proportional.
DE/DA = BC/BA
x/(4+6) = 2/6
x = 10(2/6) = 10/3 = 3 1/3