A horizontal shift happens when you add or subtract a value from the input value of x.
To shift left the number would be added to the x.
The answers are:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Answer:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Step-by-step explanation:
The parent function given to us is: [tex]f(x)=\ln x[/tex].
A horizontal translation to the left k units is of the form [tex]y=\ln (x+k)[/tex].
This implies that;
h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.
r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.
p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.
Find the area of a regular hexagon with the given measurement.
4-inch side
A = sq. in.
bruh what is the answer
Answer: [tex]24\sqrt{3}in^2[/tex] or [tex]41.56in^2[/tex]
Step-by-step explanation:
You can find the area of a regular hexagon with the following formula:
[tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex]
Where "s" is any side of the regular hexagon.
For this hexagon you know that the length of each side is 4 inches. Then, you must substitute [tex]s=4in[/tex] into the formula [tex]A_{(hexagon)}=\frac{3\sqrt{3}s^2}{2}[/tex].
Therefore, the area of this regular hexagon is:
[tex]A_{(hexagon)}=\frac{3\sqrt{3}(4in)^2}{2}[/tex]
[tex]A_{(hexagon)}=24\sqrt{3}in^2[/tex] or [tex]A_{(hexagon)}=41.56in^2[/tex]
Answer:
the answer is 24 square root 3
Step-by-step explanation:
38. Express these rates in the lowest terms.
a. $56: 16 kg
b. There are six teachers for every 108 students
39. Change to unit rates.
a. $20 for five T-shirts
b. 45 miles in half an hour
Answer:
38: is A
39: is A
Step-by-step explanation:
To express rates in the lowest terms, divide both the numerator and denominator by their greatest common divisor. For unit rates, calculate the rate per single unit of item or time. Example: $7 for 2 kg simplifies to a rate of $3.50 per kg, six teachers for 108 students simplifies to one teacher for 18 students, $20 for 5 T-shirts becomes $4 per T-shirt, and 45 miles in half an hour translates to 90 miles per hour.
Explanation:Question 38: Our goal is to express the rates in the lowest terms.
$56 for 16 kg: To find the simplest form, we divide both the numerator (dollars) and the denominator (kilograms) by the greatest common divisor. $56 and 16 kg both are divisible by 8, so dividing by 8 gives us $7 for 2 kg.Six teachers for every 108 students: The simplest form is found by dividing both numbers by their greatest common divisor, which is 6 in this case. So, 1 teacher for every 18 students is the rate in the lowest terms.Question 39: Here, we will convert the given rates to unit rates.
$20 for five T-shirts: A unit rate is the rate for one unit of the item. To find the unit rate for one T-shirt, divide $20 by 5. This gives $4 per T-shirt.45 miles in half an hour: To find the distance traveled in one hour (unit time), multiply the distance by 2. So, the unit rate is 90 miles per hour.The radius of a small ornament in the shape of a sphere is 2 inches. What is the approximate volume of the ornament? Use 3.14 for pi. Round to the nearest tenth of a cubic inch.
Answer:
34
Step-by-step explanation:
The volume is calculated as approximately 33.5 cubic inches when rounded to the nearest tenth.
The question asks us to calculate the volume of a sphere with a known radius using the value of 3.14 for pi. The formula for the volume of a sphere is V = (4/3)πr³. Given that the radius (r) is 2 inches, we substitute the given values into the formula to find the volume:
V = (4/3)πr³
V = (4/3) × 3.14 × (2 inches)³
V = (4/3) × 3.14 × 8
V ≈ 33.51 cubic inches
We then round the result to the nearest tenth to get the final answer:
The approximate volume of the ornament is 33.5 cubic inches.
Colleen can paint a room in 12 hours.Rebecca can paint the same room in 20 hours.How long does it take for both Colleen and Rebecca to paint the room if they are working together? Write an equation that using the variable t to represent the time it takes to paint the room together that can be used to solve the problem.
The answer is:
It will take 7.5 hours to paint the room together.
Why?Using the given information we need to write an equation considering both Colleen and Rebecca rates.
For Colleen we know that she can paint a room in 12 hours, so, her equation will be:
[tex]\frac{1Room}{12hours}*t=\frac{t}{12}[/tex]
Being "t" the time used to paint.
For Rebecca, we know that she can paint a room in 20 hours, so, her equation will be:
[tex]\frac{1Room}{20hours}*t=\frac{t}{20}[/tex]
Now, if we want to calculate the time needed to paint 1 room, we have:
[tex]\frac{t}{12}+\frac{t}{20}=1\\\\\frac{12*t+20*t}{12*20}=1\\\\\frac{12t+20t}{240}=1\\\\\frac{32t}{240}=1\\\\32t=240*1\\\\t=\frac{240}{32}=7.5[/tex]
Hence, we have that it will take 7.5 hours to paint the room together.
Have a nice day!
Simplify the following.
7^1=
4^0=
6^-1=
Answer:
7
1
0.1666666667
The following exponents can be simplified as follows:
[tex]7^1=7[/tex][tex]4^0=1[/tex][tex]6^-1=1/6[/tex]What are exponents?The exponent of a number says how many times to use the number in a multiplication.
For example: 8 to the Power 2( or 8^2)
In 8^2 the "2" says to use 8 twice in a multiplication,
so 8^2 = 8 × 8 = 64
In words: 8^2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".
So coming to the question:
a) 7^1 = 7 times 1 from definition that 7*1=7
b)To prove this one, I will go with the property of exponents:
[tex]a^{(b-c)}=\dfrac{a^b}{a^c}[/tex]
implies:
[tex]4^0=4^{(2-2)}=\dfrac{4^2}{4^2} =1[/tex]
c)Applying the previous property:
[tex]6^{-1}=6^{0-1}=\dfrac{6^0}{6^1}=\dfrac{1}{6}[/tex]
Therefore, with the help of definitions and property of exponent, we can simplify it.
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Curtis wants to save money for a trip overseas. Curtis invests 800 in an account that pays an interest rate of 6.25%. How many years will it take for the account to reach $10800? round your answer to the nearest hundredth
Answer:
the answer is 42.93
Step-by-step explanation:
just did it
An Internet store charges a base fee plus $1.50 per pound to ship items. The table shows samples of their shipping rates.
Shipping Rates
Weight of Package Shipping Cost
(pounds) (dollars)
2 8.00
5 12.50
7
9 18.50
10
17 30.50
Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. How much more does Keisha pay for shipping than Derek?
A)$4.50
B)$6.00
C)$9.50
D)$12.00
Answer: For Last Question 4.50
Step-by-step explanation:It depends on the price per pound. Let's say the price per pound is 50 cents (or 0.50). (This is an example, the answer I'm giving will most likely NOT be correct, due to the nature of your question - sorry!) To calculate the price of Derek's package, you would multiply 7 (the weight of the package) by 0.50 (the price per pound), which totals to 3.50 Next, to calculate the price for Keisha's package, you'd do the same thing, but instead of multiplying 7 by the price per pound, you would multiply 10 by the price per pound, or 0.50. This multiplies out to 5 dollars. Next you'd subtract Derek's price from Keisha's, which is 5 - 3.50 or 1.50. If it is asking for a percentage, it would be about 150%.
Find the area of the circle with the given radius or diameter. Use pi = 3.14.
r = 4
A =
50.24 sq. units
100.48 sq. units
25.12 sq. units
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=4 \end{cases}\implies A=\pi 4^2\implies A=16\pi \implies \stackrel{\pi =3.14}{A=50.24}[/tex]
Answer:
50.24 sq units
Step-by-step explanation:
PLZ HURRY IT'S URGENT!
What is the distance between the points (4, 7) and (4, –5)? A. 2 units B. 0 units C. 4 units D. 12 units
Answer:
D. 12 units
Step-by-step explanation:
The distance between two points is found by
d = sqrt( (x2-x1)^2 + (y2-y1)^2)
sqrt( (4 -4)^2 + (-5-7)^2)
sqrt((0^2 + (-12)^2)
sqrt(0+144)
sqrt(144)
12
A store is having a sale in which all items are 20% off. If p is the original price of an item, then the equation p - 0.2 = 0.8 can be used to find the sale price. Which statement does the equation represent?
A. Decreasing the original price by 20% is the same as dividing the original price by 80%.
B. Decreasing the original price by 80% is the same as dividing the original price by 20%.
C. Decreasing the original price by 20% is the same as multiplying the original price by 80%
D. Decreasing the original price by 80% is the same as multiplying the original price by 20%.
Answer:
d
Step-by-step explanation: 0.2 x 100% = 102.1/ 20%= d
look below and can i have brainlyplus Start with the original price, $80.
If you take 20% off, then you will be paying 80% of the original price. Calculate 80% of $80.
80% of $80 = 80% * $80 = 0.8 * $80 = $64
After applying the 20% discount, the new price is $64.
Now you apply the 10% coupon.
Since you are taking 10% off the discounted price, you will be paying 90% of the discounted price.
90% of $64 = 0.9 * $64 = $57.6
The final discounted price is $57.60
Step-by-step explanation:
Does the graph represent a function and if so, why?
Yes, no two ordered pairs on this graph have the same second element.
Yes, there is more than one ordered pair on this graph.
Yes, no two ordered pairs on this graph have the same first element
No, there is a limited number of ordered pairs on this graph
ANSWER
Yes,no two ordered pairs on this graph have the same first element
EXPLANATION
For a set of ordered pairs to be a function,there must not be any two points that have the same first elements.
This means that, the x-coordinates must not repeat for any two given points.
The graph given represents a function because,no two ordered pairs on this graph have the same first element.
Hence it would pass the vertical line test.
The third choice is correct.
The correct answer is: Yes, no two ordered pairs on this graph have the same second element.
To determine if a graph represents a function, one must apply the Vertical Line Test. This test states that a graph represents a function if no vertical line intersects the graph at more than one point. In other words, for every input (x-value), there is exactly one output (y-value). This is equivalent to saying that no two ordered pairs on the graph have the same first element (x-value) and different second elements (y-values).
The statement Yes, no two ordered pairs on this graph have the same second element correctly describes the condition for a graph to represent a function. It implies that for every y-value, there is only one x-value associated with it, which is the definition of a function.
The other options are incorrect for the following reasons:
- Yes, there is more than one ordered pair on this graph. While this statement may be true, it does not address the condition necessary for a graph to represent a function. A graph with multiple ordered pairs could still fail to be a function if any vertical line intersects the graph more than once.
- Yes, no two ordered pairs on this graph have the same first element. This statement is not relevant to the definition of a function. A function can have the same x-value associated with different y-values (which would be multiple ordered pairs with the same first element). The key is that for each x-value, there can only be one y-value.
- No, there is a limited number of ordered pairs on this graph. The number of ordered pairs being limited does not affect whether the graph represents a function. A function can have a finite or infinite number of ordered pairs. The defining characteristic is that there is exactly one output for each input, not the total number of ordered pairs.
Therefore, the correct justification for the graph representing a function is that no two ordered pairs on the graph have the same second element, ensuring that the graph passes the Vertical Line Test.
find the volume of the prism.
a)152.4cm^3
b)158.3cm^3
c)163.9cm^3
d)167.1cm^3
Answer: option a
Step-by-step explanation:
You can calculate the volume of a prism with this formula:
[tex]V_{prism}=lwh[/tex]
Where l is the lenght, w is the width and h is the height.
You can identify from the figure that:
[tex]l=12cm\\w=5cm\\h=2.54cm[/tex]
Then, substituting these values into the formula, you get that the volume of this prism is:
[tex]V_{prism}=(12cm)(5cm)(2.54cm)=152.4cm^3[/tex]
Answer:
Final answer is choice a) [tex]Volume = 152.4 \, cm^3[/tex]
Step-by-step explanation:
Given that length of the prism = 12 cm
Given that width of the prism = 5 cm
Given that height of the prism = 2.54 cm
Then volume of the rectangular prism is given by formula:
[tex]Volume = (Length)(Width)(Height)[/tex]
[tex]Volume = (12 cm)(5 cm)(2.54 cm)[/tex]
[tex]Volume = 152.4 \, cm^3[/tex]
Hence final answer is choice a) [tex]Volume = 152.4 \, cm^3[/tex]
I need help on this question
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Compare the ratio of the measure of corresponding sides, that is
AB = 6 and A'B' = 2
BC = 3 and B'C' = 1
Calculate the ratio of A'B'C' to ABC, then
scale factor = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
a small refrigerator is a cube with a side length of 16in use the formula s equals 6s to the second power to find the surface area of the cube
Answer:
1536 in²
Step-by-step explanation:
S = 6s²
We are told that s = 16 inches, so plugging in:
S = 6 (16)²
S = 1536 in²
What are the real zeros of the function g(x) = x3 + 2x2 − x − 2?
For this case, to find the roots of the function, we equate to zero.
[tex]x ^ 3 + 2x ^ 2-x-2 = 0[/tex]
We rewrite how:
[tex]x ^ 3 + 2x ^ 2- (x + 2) = 0[/tex]
We factor the maximum common denominator of each group:
[tex]x ^ 2 (x + 2) -1 (x + 2) = 0[/tex]
We factor the polynomial, factoring the maximum common denominator[tex](x + 2):[/tex]
[tex](x + 2) (x ^ 2-1) = 0[/tex]
By definition of perfect squares we have to:
[tex]a ^ 2-b ^ 2 = (a + b) (a-b)[/tex]
ON the expression[tex](x ^ 2-1):[/tex]
[tex]a = x\\b = 1[/tex]
So:
[tex](x ^ 2-1) = (x + 1) (x-1)[/tex]
Thus, the factorization of the polynomial is:
[tex](x + 2) (x + 1) (x-1) = 0[/tex]
[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
ANswer:[tex]x_ {1} = - 2\\x_ {2} = - 1\\x_ {3} = 1[/tex]
Solve using the quadratic equation for all values of x in simplest form !! Please answer this !!
Answer:
Step-by-step explanation:
simplify both sides of the equation
-x^2+16=-7
subtract 16 form both sides
-x^2= -23
divide by -1
x^2=23
take square root
and your answer is x= plus or minus (square root) of 23 or -23
Answer:
Step by STEP explanation
Determine the coordinates of the y-intercept of 5x − 5y = 4
Final answer:
The coordinates of the y-intercept of 5x − 5y = 4 are (0, -4/5).
Explanation:
The y-intercept of a linear equation represents the point where the line intersects the y-axis. To determine the coordinates of the y-intercept, we set the x-coordinate to 0 and solve for y. In the equation 5x - 5y = 4, To determine the coordinates of the y-intercept of the equation 5x − 5y = 4, we set the x-value to 0 since, by definition, the y-intercept occurs where the line crosses the y-axis (x=0). The equation simplifies to -5y = 4. we substitute x=0 and solve for y:
5(0) - 5y = 4
-5y = 4
y = -4/5
Therefore, the coordinate of the y-intercept is (0, -4/5).
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
PLZZZZZ I NEED LE HELP FROM LE FELLOW STUDENTS!!!
Answer:
44 and 46
Step-by-step explanation:
Let
x,x+2-----> the two consecutive positive even integers
we know that
[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048[/tex]
Solve for x
[tex](x+x+2)^{2}=x^{2}+(x+2)^{2} +4,048\\ \\4x^{2} +8x+4=x^{2}+x^{2} +4x+4+4,048\\ \\2x^{2} +4x-4,048=0[/tex]
Solve the quadratic equation by graphing
The solution is x=44
see the attached figure
therefore
the numbers are
x=44
x+2=46
Find the measure of the third angle of a triangle given the measure of two angles: x and 50
Answer:
is it a right triangle or no ?
Step-by-step explanation:
Probability question. Please answer with work attached.
Step-by-step Answer:
There is a total of 10 coins, 5 dimes, 2 quarters and three pennies.
By picking a coin, it could be any that shows up out of the 10, so the probability of picking any coin in particular is 1 / 10.
If there are 5 dimes, the probability of picking ANY one particular dime is 1/10, so with 5, the probability of picking ANY of the five dimes is 5/10 = 1/2.
Going along the same line of thought, the probability of picking any of quarters and pennies would be 2/10+3/10 = 5/10 = 1/2 as well.
The following examples illustrate the associative property of multiplication.
(5 · 3) · 6 = 5 · (3 · 6)
2 · (1.1 · 0.1) = (2 · 1.1) · 0.1
Study the examples, then choose the statement that best describes the property.
a · (b · c) = (a · b) · c
a · b · c = c · a · b
b · c · a = (b · c · a)
(a · b) · c = a · b
Answer:
The first example: a · (b · c) = (a · b) · c
Step-by-step explanation:
The associative property regroups values by changing the location of parentheses. If you notice, the order of the values is not changed. Both sides have a x b x c, only the parentheses have been moved. Moving the parentheses changes the progression of what is multiplied (whatever is in the parentheses is multiplied together first) but doesn't change the final answer.
The statement a. (b . c) = ( a . b ) . c describes the correct property.
What is associative property ?Associative property for multiplication states that rearranging the terms and brackets places in a multiplication of two or more than two terms does not change the result of the multiplication.
There are more properties multiplication is commutative also for example a×b = b×a
a . ( b . c ) = ( a . b) . c is the right answer here brackets have been changed according to the statement.
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Solve for X
A: 12.5
B: 5
C: 6[tex]\sqrt{3}[/tex]
D:12
Answer:
D. 12Step-by-step explanation:
(LOOK AT THE PICTURE)
ΔADC and ΔCDB are similar (AAA). Therefore the corresponding sides are in proportion:
[tex]\dfrac{AD}{CD}=\dfrac{CD}{DB}[/tex]
We have
[tex]AD=16,\ CD=x,\ DB=9[/tex]
Substitute:
[tex]\dfrac{16}{x}=\dfrac{x}{9}[/tex] cross multiply
[tex]x^2=(9)(16)\to x=\sqrt{(9)(16)}\\\\x=(\sqrt9)(\sqrt{16})\\\\x=(3)(4)\\\\x=12[/tex]
bear in mind that, a perpendicular line stemming from the right-angle like so, creates three similar triangles, a large one, containing the other two smaller ones, a medium and a small.
so.. .we can just use the medium and small proportions.
Check the picture below.
Solve each equation. 6.97a = 27.88
Answer:
a=4
Step-by-step explanation:
6.97a = 27.88
Divide 6.97a on both sides
6.97a/6.97a = 27.88/6.97a
a=4
6.97a = 27.88
Divide both sides by 6.97.
6.97a/6.97 = 27.88/6.97
a = 4
Find volume of cylinder
Show work
For this case we have that by definition, the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
A: It is the radius of the cylinder
h: It's the height
We have according to the data that:
[tex]r = \frac {34} {2} = 17 \ m\\h = 27 \ m[/tex]
Substituting in the equation we have:
[tex]V = \pi * (17) ^ 2 * 27\\V = \pi * 289 * 27\\V = 24501.42\ m^3[/tex]
ANswer:
[tex]V = 24501.42\ m^3[/tex]
Please someone help i really need it :( The original 25 colored pencils have all been placed back in the box and another 11 colored pencils have been added to the box. The new pencils are either red, blue, or green. The likelyhood of drawing a green pencil is now greater than the likelyhood of drawing a red pencil, but less than the likelyhood of drawing a blue pencil.
What is the question?
I would say there would be 5 blue pencils, 4 green pencils, and 2 red pencils. I say this because the chance of grabbing a green pencil is smaller than the blue, and the chance of grabbing a red one is smaller than the green one, as a result, we are left wit 5 blue pencils, 4 green pencils, and 2 red pencils.
How many 2/3 cup servings of rice are in a 6 cup bag
Answer:
9
Step-by-step explanation:
namely, how many times does 2/3 go in 6?
[tex]\bf 6\div\cfrac{2}{3}\implies \cfrac{6}{1}\div\cfrac{2}{3}\implies \cfrac{6}{1}\cdot \cfrac{3}{2}\implies \cfrac{3}{1}\cdot \cfrac{6}{2}\implies 3\cdot 3\implies 9[/tex]
The graph shows the population of a school from year to year what is the rate of change in terms of number of students per year?
Answer:
The number of students per year increasing
What is the value of x?
A. 13
B. 17
C. 119
D. 169
Answer:
13
Step-by-step explanation:
x² = 5²+12²
x² = 25+144
x² = 169
x² = 13²
x = 13
An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure. Which of the following is the angle formed by the sun's rays and the ground?
Answer:
The angle is 50.2°.
Step-by-step explanation:
The tree and its shadow from a right triangle with the tree being the perpendicular and the shadow being the base as shown in the figure attached.
Therefore the angle θ formed by the sun's rays and the ground is:
[tex]\theta = tan^-1(\frac{18}{15} )=\boxed{50.2^o}[/tex]
The angle formed by the sun's rays and the ground can be found using trigonometry and it is approximately 50.19°
Given: length of tree is 18 ft. and the shadow of tree is 15 ft.
To find: angle formed by suns rays and the ground
This question involves using trigonometry to find the angle formed by the sun's rays and the ground. We can use the tangent function which is:
[tex]\tan \theta = \frac{\text{perpendicular}}{\text{base}}[/tex]
Here the perpendicular is the length of the tree, base is the shadow of the tree and θ is the angle formed by suns rays and ground. So, plugging the values we get:
[tex]\tan \theta = \frac{18}{15}[/tex]
We see that 15 and 18 have 3 as a common factor so we can divide the numerator and denominator by 3 to simply the fraction and we get:
[tex]\tan \theta = \frac{6}{5} = 1.2[/tex]
To find the angle, we take the inverse tangent of the ratio:
[tex]\theta = tan^{-1} (1.2)[/tex]
θ ≈ 50.19°
Thus, the angle formed by the sun's rays and the ground is approximately 50.19°.
PLEASE HELP!!! ASAP
An expression can often be used to model a real-life situation. For each of the following expressions, write a real-life situation using money as the context. Then, evaluate the expression and interpret the result in terms of the situation. Here's an example.
The following situation is modeled by the expression -24.50 + 100.00: Jonathan overdrew his checking account by $24.50. He then transferred $100.00 from his savings account to his checking account. His new checking account total is $75.50.
Make sure to use complete sentences in your answers.
1. $8.15 + $11.99
2. $20 - $18.04
3. 7($1.45)
4. $42.08/4