Answer:
f(x)
Step-by-step explanation:
This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].
Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.
Can someone help me please
Answer:
y = 3x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 6) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-(-6)}{2-0}[/tex] = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6
y = 3x - 6 ← equation of line L
Point R is between points Q and S. Label the
picture, then find x and the measure of QS.
3x+7
1---
8x
28
The measure of angle QS based on the information given when Point R is between points Q and S is 11x + 35.
How to depict the information?From the information given,
PR = 3x + 7
QR = 8x + 28
The value of QS will be:
PR + QR
= (3x + 7) + (8x + 28)
= 11x + 35
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please help asap ill appreciate the help.
Answer:
B and D
Step-by-step explanation:
check where the points are. If they are in shaded triangle they are solutions
If the acute angle made by lines /and mis 24° and AABC is reflected across line /
followed by a reflection across line m, find the angle through which AABC is rotated.
B
m
The angle through which ΔABC is rotated is; Option A: 48°
How to Interpret Transformation Reflection?Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but preserves its length and shape. Thus, a rotational transformation is formed by two reflections.
In the given question, image ABCD is reflected over lines I, then m at an angle of 24° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 24 * 2 = 48°
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Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY.
The area of BXYC is 71.5 square units. What is the area of ABCD?
99 square units
110 square units
126 square units
143 square units
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the opposite sides are equal and parallel to each other. We can write,
AD ≅ BC
Since BX ≅ DY, therefore, we can write,
AB = CD
AX + XB = DY + YC
XB = DY, cancelling both the sides,
AX = YC.
Also, XY is the common side.
Since all the sides are equal also the angle are equal, therefore, it can be written,
AXDY ≅ CYXB
Given the area of CYXB is 71.5 square units. Therefore,
ABCD = CYXB + AXDY
ABCD = 2(CYXB)
ABCD = 143 square units.
Hence, the correct option is D.
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Verify csc^2t-cos t sect= cot^2 t
Rewriting the left hand side,
csc²t - cost sec t
= (1/sin²t)-(cost)(1/cost)
= 1/sin²t - 1
= 1/sin²t - sin²t/sin²t
= (1-sin²t)/sin²t
= cos²t/sin²t
= cot²t
Step-by-step explanation:
assuming this is correct, you can really manipulate either side and you should arrive eventually arrive to same sides. But in this case you usually manipulate the more complex side. So I'll manipulate the left side.
Original Equation:
[tex]csc^2(t)-cos(t)*sec(t)=cot^2(t)[/tex]
Rewrite csc and sec, using the reciprocal identities:
[tex](\frac{1}{sin(t)})^2-cos(t)*\frac{1}{cos(t)}=cot^2(t)[/tex]
multiply cos(t) and 1/cos(t) and also distribute the exponent:
[tex]\frac{1}{sin^2t}-1=cot(t)^2[/tex]
Multiply 1 by sin^2(t)/sin^2(t)
[tex]\frac{1}{sin^2(t)}-\frac{sin^2(t)}{sin^2(t)}[/tex]
subtract the numerator
[tex]\frac{1-sin^2(t)}{sin^2(t)}[/tex]
Pythagorean Identity:
[tex]sin^2(t)+cos^2(t)=1[/tex]
subtract sin^2(t) from both sides
[tex]cos^2(t)=1-sin^2(t)[/tex]
Use this to rewrite the numerator:
[tex]\frac{cos^2(t)}{sin^2(t)}[/tex]
Rewrite using the reciprocal identities:
[tex]cot^2(t) = cot^2(t)[/tex]
Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the y-axis of the graph of f(x) = -(x + 3)2. Write a rule for g.
Answer:
6
Step-by-step explanation:
2+2+2
How many different student body governments are possible if there are 7 seniors, 3 juniors, and 4 sophomores running for the student body offices of senior class president, junior class president, and sophomore class president
There are 84 possible student body governments
The number of student body governmentsThe given parameters are:
Senior = 7
Junior = 3
Sophomore = 4
The number of student body governments is calculated as:
n = Senior * Junior * Sophomore
This gives
n = 7 * 3 * 4
Evaluate
n = 84
Hence, there are 84 possible student body governments
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6. The city needs to buy grass to cover
the driving range. The measurement of the
driving range is 100 by 372 yards. If one bag
of grass seed covers 75 square yards, how.
many bags will the city need to buy to seed.
the driving range?
(A) 160
(B) 357
(C) 496
(D) 653
Answer:
(C) 496
Step-by-step explanation:
area = 100 yd × 372 yd = 37,200 yd²
37,200 yd² / 75 yd² = 496
Answer: (C) 496
A number has 7 added to it and the sum is multiplied by 5. When the value is divided by 11, the quotient obtained is 10. Find the original number.
In the following exercises, multiply the binomials. Use any method.
248. (m + 11)(m − 4)
Answer:
Hence the expression [tex]$$(m+11)(m-4)=m^2+7m-44$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (m+11)(m-4).We have to multiply the given expression.Multiply the (m+11) by -4, multiply the (m+11) by m then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$[/tex]
Suppose a and b are independent events if p(a|b)=0.55 and p(b)=0.2, what is P(AnB)?
A. 0.275
B. 0.22
C. 0.11
D. 0.165
The value of the probability P(AnB) is 0.11
How to evaluate the probability?The given parameters are:
P(a|b)=0.55 and P(b)=0.2
The value of P(AnB) is calculated using:
P(AnB) = P(a|b) * P(b)
Substitute the known values
P(AnB) = 0.55 * 0.2
Evaluate the product
P(AnB) = 0.11
Hence, the value of the probability P(AnB) is 0.11
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Can someone answer this please. Trolls will be reported
Answer: D
Step-by-step explanation:
See attached image.
You are driving on a freeway with a posted speed of 65 mph. Nearly all of the cars are traveling between 35 and 40 mph. What would be a safe speed for you to drive
30 mph would be a safe speed for you to drive.
Collisions are much more likely to occur when one driver travels greater speedy or more slowly than the alternative motors on the road. You have to input a throughway at or near the velocity of visitors except if the speed of site visitors exceeds the prison speed restrict.
A pedestrian has a 90 percent threat of survival if hit by a vehicle transferring at 30 km ph (18.64 mph). This decreases to 70 percent at 40 kmph (24. eighty five mph) and much less than 20 percent at 50kmph (31 mph). driving at decreased speeds also enables drivers to stop within a shorter distance.
Retaining high speeds on highways is straightforward, as roads are wider and traffic is usually mild. If there are signs that show a pace restriction of 80kph, use them as a guide and stick near them. it's also an excellent exercise to assess road situations and set your pace thus.
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What is the value of the logarithm below? (Round your answer to two decimal
places.)
log₂7
A. 0.58
B. 2.11
C. 0.85
D. 2.81
I am totally horrible at geometry! can someone help me please
Answer: 6
Step-by-step explanation:
We will set up a proportion to solve. Let x be equal to ?.
[tex]\displaystyle \frac{3}{5} =\frac{x}{x+4}[/tex]
Now, we will cross-multiply.
3 * (x + 4) = 5 * x
3x + 12 = 5x
12 = 2x
6 = x
HURRY I NEED HELP 80p
Select the correct answer from each drop-down menu. A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. What is the surface area of all 27 blocks compared to the surface area of the box? The side length of the blocks is (3,4 or 5) inches, so the total surface area of the 27 blocks is (150, 4,050 or 1350) square inches. This is (5 times, 3 times, one third or one-fifth) the surface area of the box.
I need someone to answer the answers in the ( )
Answer:
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Step-by-step explanation:
Surface area of a cube
SA = 6s² (where s is the side length)
Given the side length of the box is 15 inches:
⇒ SA of box = 6 · 15² = 1350 in²
Surface Area of blocks with 3 inch side lengths:
⇒ SA = 6 · 3² = 54 in²
⇒ SA of 27 blocks = 27 · 54 = 1458 in²
Surface Area of blocks with 4 inch side lengths:
⇒ SA = 6 · 4² = 96 in²
⇒ SA of 27 blocks = 27 · 96 = 2592 in²
Surface Area of blocks with 5 inch side lengths:
⇒ SA = 6 · 5² = 150 in²
⇒ SA of 27 blocks = 27 · 150 = 4050 in²
Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
[tex]\implies \dfrac{\textsf{SA of 27 blocks}}{\textsf{SA of box}}=\sf \dfrac{4050}{1350}=3[/tex]
Summary
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
A pipe fills 11/15 liters of tub in 22/45 minutes. What is it's flow rate in terms of liters per minute?
The flow rate of the given fluid in the pipe is gotten as; 3/2 liters per minute
How to calculate the rate of flow?We are told that a pipe fills 11/15 liters in 22/45 minutes.
Now, to get the flow rate of this pipe, we will use the formula;
Flow rate = Quantity of fluid/Time
Thus;
Flow rate = 11/15 ÷ 22/45
⇒ 11/15 * 45/22
⇒ 3/2 liters per minute
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helpppppppppppppppppppppppppp!
Answer:
[tex] \boxed{ \tt{x = - 26}}[/tex]- Please see the attached picture for full solution!:)
------------------ HappY LearninG<3 -------------
Answer:
x = -26
Step-by-step explanation:
[tex]5^7^x^+^5 =125^2^x^-^7\\\\5^7^x^+^5 =5^3^(^2^x^-^7^)\\\\5^7^x^+^5 =5^6^x^-^2^1[/tex]
∴ 7x + 5 = 6x - 21
7x - 6x + 5 = -21
x = -21 - 5
x = -26
A thunderstorm cloud holds about 6,200,000,000 raindrops .which of the following shows this number in scientific notation?
Answer: [tex]6.2 *10^9[/tex]
Step-by-step explanation:
Scientific notation is large numbers expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10
So the first number cannot be 6200 or 62 or 0.6, it has to be 6.2 because 6.2 > 1 and 6.2 < 10
count your numbers right of the decimal and you should get:
[tex]6.2 *10^9[/tex]
(06.01 MC)
The following data show the number of times different students of a class practice swimming
in a month:
Considering the given data-set, the dot plot is incorrect for the number 1.
What does a dot plot shows?The dot plot shows the number of times each measure appears in the data-set.
In this problem, number 1 appears only twice on the data-set, but has 3 dots, hence it is incorrect, it should be 2 dots.
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You know that a pair of triangles has two pairs of congruent corresponding angles. What other information do you need to show that the triangles are congruent?
Answer: A pair of congruent, corresponding sides
Step-by-step explanation:
This will make the triangles congruent by either AAS or ASA.
A pair of congruent, corresponding sides will make the triangles congruent by either AAS or ASA property.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Consider it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. A Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written.
For ΔABC ≅ ΔDEF, since all of their corresponding elements like angle and sides congruent.
The ASA congruent rule state that If corresponding two angles and one corresponding side of two triangles are of same measurement, then the considered pair of triangles are congruent.
This will make the triangles congruent by either AAS or ASA property.
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In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of the cocktail is orange juice?
Give your answer as a fraction in its simplest form.
30+20+50 = 100 ml total. 20 ml is orange juice.
So, 30/100 reduce by dividing top and bottom by 30 gives
3/10 is the proportion of orange juice in the fruit cocktail.
Hope this helps! :)
Answer:
3/10
Step-by-step explanation:
First, find the total amount of liquid for a drink with 30 mls of orange juice
Assume volumes can be added
30+20+50 = 100 ml
the percentage/proportion of orange juice in the drink is the number of mls of orange juice divided by the total volume
so
30/100
which can be reduced to 3/10
(but does not require a calculator).
Calculate the density of an irregularly shaped solid reporting to the correct number of significant
figures. The volume of the solid was found by placing the solid into a graduated cylinder filled with
water with an initial volume of 15.0-mL. The final water level volume with the solid was 17.0-mL.
The mass of the solid was 10.0 g.
• This calculation involves multiple operations. Make sure you do the operations separately and
round at end.
O 5 g/mL
O 5.00 g/mL
O 2.0 g/mL
5.0 g/mL
O 2.00 g/mL
The density is:
D = 10g/2mL = 5 g/mL
The correct option is the first one.
How to get the density?Remember that density is defined as the quotient between mass and volume.
We know that the mass of the solid is 10.0 grams.
And the volume of the solid is given by the difference between the volume of the water alone (15.0 mL) and the water with the solid (17 mL).
V = 17mL - 15mL = 2mL
Then the density is:
D = 10g/2mL = 5 g/mL
The correct option is the first one.
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Find all angles between 0° and 180° satisfying the given equation. Round your answer to one decimal place. (Enter your answers as a comma-separated list.) cos() = 5/6
(don't bother answering if you wont give an explanation lol)
By using the concepts of direct and inverse trigonometric expressions, the angles that represents the trigonometric function cos 5/6 are θ₁ ≈ 33.557° and θ₂ ≈ 326.443°.
How to determine the possible angles of a given trigonometric relationship
Cosine are trigonometric functions whose period is 360°. Cosine is positive both for the first and fourth quadrants. Thus, the two angles associated to the given trigonometric expression are by inverse trigonometric functions:
θ₁ ≈ 33.557°, θ₂ ≈ 326.443°
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When given the original measurements and a scale factor for a figure, how easily can you visualize the scaled figure?
Answer:
pretty 5
Step-by-step explanation:
5
hahaha
got it on khan
A scale factor is defined as the ratio between the scale of the new object and the original object.
If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.
What is a scale factor?A scale factor is defined as the ratio between the scale of the new object and the original object.
We have,
The original measurement = x
The scale factor = m
The scale factor figure measurement = y
Now,
A scale factor is defined as the ratio between the scale of a given original object and a new object,
This means,
m = y/x
y = mx
This means,
The scaled figure measurement is the multiplication of the scale factor with the original measurement
Thus,
If the original measurements and a scale factor for a figure are given, we can easily visualize the scaled figure measurement by multiplying the scale factor with the original figure measurement.
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Please helppp! I’ve been stuck for almost 45 minutes now.
The system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have a line showing the graph.
First, we have to calculate the equation of the line:
The horizontal line:
y = 3
The region represents the inequality:
y > 3
Second inequality line:
[tex]\rm \dfrac{x}{-2}+\dfrac{y}{3} < 1[/tex]
3x -2y < 1
Thus, the system of inequality is y > 3 and 3x -2y < 1 these are the inequalities that represent the region.
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Find the value of a.
The value of a is (c) 86
How to solve for a?The given parameter is:
Angle C = 86
By vertical angle theorem, we have:
Angle A = Angle C = 86
This implies that:
Angle A = 86
The arc A subtends angle A
This means that:
Arc A = 86
Hence, the value of a is (c) 86
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The intersection of lines y=-14x+3 and y=-32x+3 is .
The intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)
How to determine the intersection of the lines?The lines are given as:
y = -14x + 3 and y = -32x+3
Substitute y = -32x+3 in
-32x+3 = -14x + 3
Evaluate the like terms
-18x = 0
Divide by -18
x = 0
Substitute x = 0 in y = -14x + 3
y = -14(0) + 3
Evaluate
y = 3
Hence, the intersection of lines y=-14x+3 and y=-32x+3 is (0, 3)
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Translate the statement into a mathematical equation.
9 times a number subtracted from 7 times the number is 26.
Answer:
7x - 9x = 26
Step-by-step explanation:
9 times a number = 9x
7 times the number = 7x
=26 because it says so
and 9x subtracted from 7x is 7x - 9x