The domain of g(x) = log (7x - 10) is all real numbers greater than 10/7.
Set-builder notation: x > 10/7. Interval notation: (10/7,∞)
What is the domain of the function?Given the function in the question:
g(x) = log( 7x - 10 )
For the function g(x) = log (7x - 10), the domain consists of all the possible values of x that can be plugged into the function without resulting in an undefined expression.
Here, the logarithm (in this case, (7x - 10) must be greater than zero, since the logarithm of zero or a negative number is undefined in the real numbers.
So we set the argument of the logarithm to be greater than zero, and solve for x:
7x - 10 > 0
Solve for x
7x - 10 + 10 > 0 + 10
7x > 10
Dividing both sides by 7:
7x/7 > 10/7
x > 10/7
Therefore, the domain of g(x) = log (7x - 10) is x > 10/7
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Mr. McGill is buying a car worth $35,000 and taking out a loan for the full amount. If
it is increasing at 2.5 percent yearly. How much will the loan increase to in 5 years?
A.) $39,599.29
B.)$36,599.29
C.)$18,382,656.25
D.)$40,269,30
The loan will increase to $39599.29 in 5 years
How much will the loan increase to in 5 years?From the question, we have the following parameters that can be used in our computation:
Mr. McGill is buying a car worth $35,0002.5% interest compounded annualyUsing the above as a guide, we have the following:
Amount = P * (1 + r)ᵗ
Where
P = Principal = 35000
r = Rate = 2.5%
t = time = 5
Substitute the known values in the above equation, so, we have the following representation
Amount = 35000 * (1 + 2.5%)⁵
Evaluate
Amount = 39599.29
Hence, the amount is 39599.29
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Think about prime numbers and composite numbers.list all the digits that are the last digit of at least one prime number.
Answer:
1,3,5,7,9
Step-by-step explanation:
0 can't be, let's take 10 or 20 or 30 for example, not a prime number.
1 can be because let's take 11, 31 as example, they're prime numbers.
2, 4, 6, 8 can't be the answer because they have factors
The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59
AABC-ADEC. 1 and 2 have the same measure. Find DC and
DE. (Hint: Let DC = x and AC=x+4, Use the figure shown to the right.)
DC is unit(s) long.
(Round to the nearest tenth as needed.)
D
4
A
14
E
B
Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.
Using the properties of similar triangles, we can set up the following proportion:
$\frac{CE}{CA}=\frac{CD}{CB}$
Substituting the given values:
$\frac{CE}{x+4}=\frac{x}{14}$
Cross-multiplying:
$14CE = x(x+4)$
$14CE=x^2+4x$
We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:
$\frac{DE}{AB}=\frac{AE}{AC}$
Substituting the given values:
$\frac{DE}{18}=\frac{AE}{x+4}$
Cross-multiplying:
$AE = 18\frac{DE}{x+4}$
Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:
$14CE=x^2+4x$
$14\frac{DE}{x+4}=x^2+4x$
$14DE=x^2+4x(x+4)$
$14DE=x^2+4x^2+16x$
$18x^2+16x-14DE=0$
We can now use the quadratic formula to solve for $x$:
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$
$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$
Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:
$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$
$DC\approx 2.3$ or $DC\approx -3.1$
Since distance cannot be negative, we choose the positive solution:
$DC\approx 2.3$ units.
To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:
$\frac{CE}{x+4}=\frac{x}{14}$
$\frac{CE}{2.3+4}=\frac{2.3}{14}$
$CE\approx 1.34$ units
Now we can use the second similarity proportion to find $DE$:
$\frac{DE}{18}=\frac{AE}{x+4}$
$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$
$DE\approx 3.64$ units
Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.
Step-by-step explanation:
Compute the area of the following triangle. (Express answer in cm^2)
b= 20in
h= 4in
A= ? Cm^2
Answer:
A = 40 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 20) (4)
A = 40 cm^2
Answer:
40in²
Step-by-step explanation:
The formula to find the area of a triangle is:
[tex]\sf Area = \frac{1}{2}*Base*Height[/tex]
Accordingly, let us solve it now.
[tex]\sf \frac{1}{2}*Base*Height\\\\\sf \frac{1}{2}*20*4\\\\40\:in^2[/tex]
-5-4-3-2
y
5
3
+ do
Mark this and return
23
Which equation represents a circle with the same
radius as the circle shown but with a center at (-1, 1)?
(x-1)2 + (y + 1)² = 16
(x-1)² + (y + 1)² = 4
(x + 1)² + (y-1)² = 4
O(x + 1)² + (y-1)² = 16
Save and Exit
Next
Submis
The equation that represents the circle is (x + 1)² + (y - 1)² = 16
Writing the equation that represents a circleThe equation of a circle with center (h,k) and radius r is:
(x - h)² + (y - k)² = r²
To find the equation of the circle with center (-1,1) and radius 4, we need to shift the center of the circle to (-1,1).
We can do this by replacing x with (x - (-1)) = (x + 1) and y with (y - 1) in the equation of the original circle. This gives:
(x + 1)² + (y - 1)² = 16
This equation represents a circle with center (-1,1) and radius 4.
Therefore, the correct option is (O) (x + 1)² + (y - 1)² = 16.
The other options do not have the correct center or radius to describe the circle.
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This table shows all of the values for the function y = f(x).
y = f(x)
Checkpoint Function transformations (L
-5-28
-3
-2
0
0
7
1 26
Based on those values, complete a table for the function y=f(x)-5.
=F(x)-5
The table for the function y = f(x) - 5 is
x f(x) - 5
5 -33
-3 -5
-2 2
0 21
Creating a table for the function y = f(x) - 5From the question, we have the following parameters that can be used in our computation:
x f(x)
5 -28
-3 0
-2 7
0 26
To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)
using the above as a guide, we have the following:
x f(x) - 5
5 -28 - 5
-3 0 - 5
-2 7 - 5
0 26 - 5
Evaluate
x f(x) - 5
5 -33
-3 -5
-2 2
0 21
This represents the table for the function y = f(x) - 5
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 8.2 mg and a standard deviation of 1.45 mg. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 42 cigarettes with a mean nicotine amount of 7.73 mg.
Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 42 cigarettes with a mean of 7.73 mg or less.
P(M < 7.73 mg) = ???
The probability of randomly selecting 42 cigarettes with a mean of 7.73 mg or less is: 0.0179
How to find the p-value from z-score?The formula to find the z-score of the given normal distribution is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given:
x' = 7.73 mg
μ = 8.2 mg
σ = 1.45 mg
n = 42
Thus:
z = (7.73 - 8.2)/(1.45/√42))
z = -2.1
From online p-value from z-score calculator, we have:
p = 0.0179
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True or False Deductive reasoning is when someone uses lots of data to make a conjecture.
Answer:
Step-by-step explanation:
5^-2 x ³√8
answer as a decimal
Answer: We can start by simplifying the cube root of 8:
³√8 = 2
Next, we can rewrite 5^-2 as 1/5^2:
1/5^2 x 2 = 1/25 x 2 = 2/25
So the answer, as a decimal, is 0.08 (or 0.08 rounded to two decimal places).
Determine the equation of the circle. Center: (1,5) Radius: 2
The equation of the circle is x² + y² - 2x - 10y + 22 = 0
Define circleAny locations on a plane that are a certain distance from a fixed point (referred to as the radius) are considered to be parts of a circle, which is a two-dimensional geometric shape (is called the center). Each point on the circle may be found at the same distance from the circle's centre.
The following is the equation for a circle with centre (h,k) and radius r:
r²=(x - h)² + (y - k)²
In this case, the center of the circle is (1,5) and the radius is 2. So, we may change these values in the equation:
(x - 1)² + (y - 5)² = 2²
Simplifying and expanding the equation, we get:
(x - 1)×(x - 1) + (y - 5)(y - 5) = 4
x² - 2x + 1 + y² - 10y + 25 = 4
x² + y² - 2x - 10y + 22 = 0
Therefore, the equation of the circle is:
x² + y² - 2x - 10y + 22 = 0
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Wendy is customizing shirts for the debate team. She can choose from 8 styles, 7 colors, and 7 collars. How many different shirts is it possible for Wendy to customize?
Answer:
392 conbinations
Step-by-step explanation:
multiply all 3 numbers to find conbinations.
8x7x7
=56x7(or 49x8)
=392
its prob wrong cuz i guessed so yeah
what number is 8% larger than 230
Answer:
That number is 230 × 1.08 = 248.4.
To find this number, we calculated 8% of 230, which is 18.4 , and then added it to 230, Hence The number that is 8% larger than 230 is 248.4.
How to solve for the numberTo find a number that is 8% larger than 230, we can calculate the 8% increase of 230 and add it to the original number.
Step 1: Calculate the 8% increase of 230:
8% of 230 = (8/100) * 230 = 0.08 * 230 = 18.4
Step 2: Add the 8% increase to 230:
230 + 18.4 = 248.4
Therefore, a number that is 8% larger than 230 is 248.4.
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Sin-1 (-1/2) exact value
Step-by-step explanation:
Just use your calculator
arcsin( -1/2) = -30 degrees ( or 330 degrees or 210 degrees)
If the price of a round trip airline to Ireland is $1300 per person and Jan can spend at most $6000 what is the largest number of people for whom she can buy tickets
The largest number of people for whom she can buy tickets, is 4 people.
:: Available money = $6000
:: Cost per person = $1300
So,
No. of maximum tickets = 6000/1300 = 4.6
That is,
Only 4.6 persons can have the tickets, and since, number of persons can only be a positive integer, so we have to only take the integer part of the number and eliminate the decimal part.
Therefore, the largest number of people for whom she can buy tickets, is 4 people.
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This is ixl olease help
Answer:
m<H = 62.7°
Step-by-step explanation:
If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.
Answer:
H = 62.7 degrees
Step-by-step explanation:
Because this is a right triangle, we can use one of the trigonometric functions to find angle H:
Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):
sin(H) = 8/9
We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:
arcsin(8/9) = H = 62.7 degrees
After a scientific balloon was launched, it rose at a rate of about 440 feet per minute to a final
altitude of 92400 feet. Use function notation to write an equation giving the altitude of the
balloon as a function of time. Find out how long (in minutes) it took the balloon to reach its final
altitude.
Let h be the altitude of the balloon in feet and t be the time in minutes. At time t = 0, the balloon is at an altitude of h = 0. Since the balloon rises at a rate of 440 feet per minute, the equation that gives the altitude of the balloon as a function of time is:
h(t) = 440t
To find out how long it took the balloon to reach its final altitude of 92400 feet, we can set h(t) equal to 92400 and solve for t:
440t = 92400
t = 210
Therefore, it took the balloon 210 minutes to reach its final altitude.
PLEASE HELP ME WITH THIS IM SO CONFUSED
The probability of hitting the shaded region is 0.755 or 75.5%.
What is the probability of hitting the shaded region?To find the probability of hitting the shaded region, we need to find the area of the shaded region and divide it by the area of the entire square.
Let's label the side length of the small square as x.
Then, we know that the diagonal of the small square is 7, so we can use the Pythagorean theorem to solve for x:
x^2 + x^2 = 7^2
2x^2 = 49
x^2 = 24.5
So the area of each white square is x^2 = 24.5 square units.
Let's label the side length of the large square as y.
Then, we know that the diagonal of the large square is 20, so we can use the Pythagorean theorem to solve for y:
y^2 + y^2 = 20^2
2y^2 = 400
y^2 = 200
So the area of the large square is y^2 = 200 square units.
Now, we can find the area of the shaded region by subtracting the area of the two white squares from the area of the large square:
Area of shaded region = Area of large square - 2 * Area of white square
= 200 - 2(24.5)
= 151
Therefore, the probability of hitting the shaded region is:
Probability = Area of shaded region / Area of entire square
Probability = 151 / 200
Probability = 0.755 or 75.5% (rounded to one decimal place)
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Is the following function even, odd, or neither? f(x)=x^4-2x^2
The given function, f(x) = x⁴ - 2x², is even function.
What is the function?The nature of the function, whether it is even or odd can be determined by applying the following rules.
Even function, f(x) = f(-x)
Odd function; f(x) = -f(-x)
The given function, f(x) = x⁴ - 2x²
Test of for even function;
f(-x) = (-x)⁴ - 2(-x)²
f(-x) = x⁴ - 2x²
so f(x) = f(-x), the function is even.
Test for odd function;
-f(-x) = - [(-x)⁴ - 2(-x)²]
-f(-x) = -x⁴ + 2x²
so, f(x) ≠ -f(-x), the function is not odd.
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Is it an integer?
19/20 - yes or no
32/4 - yes or no
74 - yes or no
23 - yes or no
5.95 - yes or no
Answer:
19/20--no
32/4--yes (32/4 = 8)
74--yes
23--yes
5.95--no
Write the equation of a line that is perpendicular and passes through the midpoint of AB with A(-3, 5) and B(1, -1).
The given line AB is having endpoints A(-3,5) & B(1,-1).
To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]
Substituting the given points
[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]
y=-(3/2)x+1/2
For two perpendicular lines [tex]m_1*m_2=-1[/tex]
Therefore, (-3/2)*[tex]m_2[/tex]=-1
or [tex]m_2[/tex] = 2/3
Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).
The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows
(y-3)=(2/3)(x-2)
3y-9=2x-4
3y=2x+5 is the required equation of the line.
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The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 73.6% of their carbon-14. How old were the bones at the time they were discovered?
The bones were about how many years old?
The age of the radioactive element of half-life 5750 years is 11047.8 years.
What is a radioactive element?Radioactive elements are atoms that are unstable in normal conditions and are converted in another different atoms.
To calculate how old is the bone at the time it was discovered, we use the formula below.
Formula:
R/R' = [tex]2^{t/n}[/tex]...................... Equation 1Where:
R = Original percentage of the boneR' = Percentage of the bone after decayt = Years of the bonen = Half-lifeFrom the question,
Given:
R = 100%R' = 100-73.6 = 26.4%n = 5750 yearsSubstitute these values into equation 1 and solve for t
100/26.4 = [tex]2^{t/5750}[/tex][tex]2^{t/5750}[/tex] = 3.7878 t/5750 = log[tex]2^{3.7878}[/tex][tex]{t/5750}[/tex] = t/5750 = 1.921t = 1.921×5750t = 11047.8 yearsLearn more about radioactive element here: https://brainly.com/question/23759636
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Which linear equation is represented in the graph?
*If correct giving brainlyest*
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
Answer:
C
x1=2
-2(2)+1=3
which is the answer for y1
Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies
The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
What does an expression means?An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.
The total number of cookies Anna baked is:
= 3 batches * c cookies/batch
= 3c cookies
After eating 8 cookies, Anna has left:
= 3c cookies - 8 cookies
So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.
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Which equation has the variable, or missing number, in the correct place to match the given situation? The Mansour family drove a total of 687 miles, starting on Friday and ending on Sunday. They drove 313 miles on Friday and 164 miles on Saturday. How many miles did they drive on Sunday?
part a.
The equation that has the variable in the correct place to match the given situation is: Sunday's mile
part b
the Mansour family drove 210 miles on Sunday.
What is an equation?An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..
We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile
Sunday's miles = Total miles - Friday's miles - Saturday's miles
Sunday's miles = 687 - 313 - 164
Sunday's miles = 210
In conclusion, the Mansour family drove 210 miles on Sunday.
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What is 2 1/4 divided by 1 1/2?
Answer:
2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.
Step-by-step explanation:
To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:
2 1/4 = (2 × 4 + 1) / 4 = 9 / 4
1 1/2 = (1 × 2 + 1) / 2 = 3 / 2
Now we can divide by multiplying by the reciprocal of the second fraction:
(9/4) / (3/2) = (9/4) * (2/3)
We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:
(9/4) * (2/3) = (33/4) * (2/13) = 9/2
So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.
[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]
2. Convert the mixed fractions into improper fractions.[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]
[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]
3. Rewrite the division.[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]
4. Rewrite again using the properties of fractions.• Check the attached image.
[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]
5. Calculate and simplify.[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]
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On a sample tray, 3 out of 6 cake samples are chocolate.
What is the probability that a randomly selected piece of cake will be chocolate?
Write your answer as a fraction or whole number.
The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.
The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.
In this case, there are 3 chocolate cakes out of a total of 6 cakes.
So the probability of selecting a chocolate cake is:
3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)
Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.
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10. The time it takes to drain a swimming pool varies inversely with the amount of water being
pumped per hour. If a large pool takes 12 hours to empty at 400 gallons an hour, how many
hours faster can the pool be drained if the pumping rate is increased to 500 gallons per hour?
(teal)
To solve this problem, we can use the formula for inverse variation, which is:
time = k/ rate
where k is a constant of proportionality.
We can start by finding the value of k using the given information. We know that when the pumping rate is 400 gallons per hour, it takes 12 hours to drain the pool. Therefore:
12 = k/400
Multiplying both sides by 400 gives us:
k = 4800
Now we can use this value of k to answer the second part of the question. We want to know how many hours faster the pool can be drained if the pumping rate is increased to 500 gallons per hour. Let's call this new time t:
t = 4800/500
t = 9.6 hours
So the pool can be drained 12 - 9.6 = 2.4 hours faster if the pumping rate is increased to 500 gallons per hour.
Enter your answer by filling in the boxes.
The correct statement regarding the end behavior of the function is given as follows:
As x -> -∞, f(x) -> +∞.As x -> +∞, f(x) -> +∞.What is the end behavior of a function?The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.
The function in this problem is given as follows:
f(x) = 2(x - 4)² + 3.
We have the square of a number, which is always positive, hence the function goes to positive infinity when the input goes to negative infinity/positive infinity.
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Lou is 1,200 feet from the base of a building that stands 500 feet tall. Assuming Lou's height is negligible, determine the angle of elevation from him to the top of the building. First, choose which angle represents the angle of elevation and then select the measure of that angle from the choices provided.
Select TWO correct answers.
We can see from the calculation that the angle of elevation of the building is 22.6 degrees.
Explain angle of elevation
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object that is above the observer's level. It is the upward angle from the observer's eye to the object being observed.
We have that;
Tan θ = 500/1200
θ = tan-1 (500/1200)
θ = 22.6 degrees
Thus the angle of elevation is obtained as 22.6 degrees as we can see here.
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Vase A has height 10 cm. Vase B has height 15 cm. The difference between the volume of vase A and the volume of vase B is 1197 cm' Calculate the volume of vase A
The volume of vase A is given as follows:
504 cm³.
How to obtain the volume?The volume of vase A is obtained applying the proportions in the context of the problem.
Vase A has height 10 cm. Vase B has height 15 cm, hence the ratio between the heights is given as follows:
[tex]\frac{h_B}{h_A}[/tex] = 15/10
[tex]\frac{h_B}{h_A}[/tex] = 1.5.
The heights are given in units, while the volumes are given in cubic units, hence the rate between the volumes is given as follows:
[tex]\frac{vB}{vA}[/tex] = 1.5³
[tex]\frac{vB}{vA}[/tex]= 3.375
[tex]v_B = 3.375v_A[/tex].
The difference between the volume of vase A and the volume of vase B is 1197 cm³, hence:
[tex]v_B - v_A = 1197[/tex]
[tex]3.375v_A - v_A = 1197[/tex]
[tex]v_A = 1197/2.375[/tex]
[tex]v_A[/tex] = 504 cm³.
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