Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².
stretched vertically by a factor of fourShifted 9 units to the left.What exactly is a translation?In mathematics, a translation is the movement of a shape to the left or right and/or down or up. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There's no change in shape because it is simply moved from one location to another.A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.
The base function g(x) = x² in this problem was.Multiplied by 4, such that, stretched vertically by a factor of four.Shifted 9 units to the left.Thus, the resultant function is obtained as (X)=4(X+9)²
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Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 7)(0,7) and (2, 112)(2,112).
An exponential function in the form y=abˣ is y = 7×4ˣ .
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Write the equation of the function:
y = abˣ
For point (0 , 7)
7 = ab⁰
for point (2 , 112)
x = 2
y = 112
Substitute:
112 = ab²
Swap the sides:
ab⁰ = 7
ab² = 112
Find the quotient of the equations:
ab²/ ab⁰ = 112/7
Simplify the equations:
b² = 16
b = ±√16
Split into two equations: b = +√16 or b = -√16
Simplify the radical expression:
b = 4
b = -4
Combine the results: b = 4 or b = -4
Any fraction with a denominator of 1 is equal to its numerator:
a = 7
7 = a (±4)°
Substitute into one of the equations:
a = 7
b = ± 4
y = 7×4ˣ
Hence , y =7×4ˣ is an exponential function with the formula y=abˣ.
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Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scaleA. x=1.86feet, y=4.41 feet and z=65 degreeB.x=4.41 feet, y=1.69 feet, and z=155 degreeC. x=8.58 feet, y=9.46 feet and z=65 degreeD.x=9.46 feet, y=8.58 feet and z=155 degree
Since the triangle is a right-angled triangle, we can use SohCahToa to find x
Using the ratio
[tex]Tan25=\frac{\text{opposite}}{\text{adjacent}}[/tex]Opposite = 4ft
adjacent = x
Substituting these values yield
[tex]\begin{gathered} \text{Tan 25 =}\frac{4}{x} \\ x\text{ =}\frac{4}{\tan 25} \\ x\text{ =8.57}8ft \\ x\approx8.58ft \end{gathered}[/tex]To find Z we use the fact that the sum of angles in a triangle is 180 degrees
so that in triangle XYZ
90 + 25 +Z = 180
Z = 180 - 115
Z= 65 degrees
We will now use Pythagoras theorem to find y
[tex]\begin{gathered} \text{For that} \\ y^2=x^2+4^2 \\ \text{but x = 8.58ft} \\ y^2=8.58^2+4^2 \\ y=\sqrt[]{73.6164\text{ +16}} \\ y\text{ =9.46 ft} \end{gathered}[/tex]
Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C
Just need a simple explanation.
The square roots for each side of the equation are not correct, as the square root of 36 is of -6 or 6, not -36 or 36, hence the correct solutions are:
x = -3 or x = 9.
Are the steps correct?The equation in Step 6 is given as follows:
[tex]\sqrt{(x - 3)^2} = \sqrt{36}[/tex]
Simplifying the square roots, the variable x can be isolated, as follows:
x - 3 = 6.x - 3 = -6.Both -6 and 6 are correct results for the square root of 36, because:
6² = 36.(-6)² = 36.His mistake when removing the square root is that he did not calculate the root, he just removed the square root from the 36, hence the correct solutions will be found as follows:
x - 3 = 6. -> x = 9.x - 3 = -6. -> x = -3.From the (x - 3)² term, the square root is removed along with the square. However 36 = (6)² or (-6)², hence sqrt(36) = 6 or sqrt(36) = -6.;
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I need to solve this to get zero can you help?
sin 0 = 26/30
sin 0 = 0.87
0 = 60°
Result 0 = 60°
A quadrilateral has two angles that measure 210° and 82º. The other two angles are in aratio of 7:10. What are the measures of those two angles?o andSubmit
Solution
The interior angles of a quadrilateral measure to 360 degrees
Two of them are known and are 210 and 82. They add to 292 degrees.
The other two angles must sum to (360-292)=68 degrees.
They are in a ratio of 7:10
The sum of these two numbers is 17
[tex]\frac{68}{17}=4[/tex][tex]\begin{gathered} 7\times4=28^0 \\ 10\times4=40^0 \end{gathered}[/tex]The other two angles are 28 and 40 degrees respectively.
The sum of all 4 angles is 360 degrees.
The final answer
The other two angles are 28 and 40 degrees respectively.
HELP PLEASEEEEEEEEE!!!!!!!!
Answer:
n∧4 basically its n to the power of 14
Step-by-step explanation:
your work is in the pic below check it out sorry if incorrect have a wonderful day:)
There are 2 buses. Bus A can travel 125 miles in 3 hours, and bus B can travel 85 more miles than bus A within the same time what is the speed of bus B?
Answer:
70 miles an hour
Step-by-step explanation:
First, you want to know how fast bus A can go. So you want to do 125/3 since the bus travels 3 hours. you get 41.6666667. keep that number. then you want to divide 85 by 3 since bus B is going for 3 hours. you get 28.3333333. then you add those numbers to get how fast bus B is going and you get 70 miles per hour for bus B
SHOW ALL WORK PLEASE!
Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the larger. Only the smaller pyramid is shown.
She calculates the area of the base of the pyramid (through long, hard work) to be 110.11 square units. The height of the pyramid is 15 units. Now she needs to calculate the volume of the pyramid.
(a) Calculate the volume of the pyramid for Sarah.
(b) "Oh, no!" Sarah exclaims. "Now I have to go through all this hard work again to find the volume of the larger pyramid!" Does she? Explain.
(c) Calculate the volume of the larger pyramid for Sarah.
Answer: a) The volume of the pyramid 440.44 cube units
(b) No she doesn't
(c) The volume of the larger pyramid is 1,486.485 cube units
Step-by-step explanation: The given parameters are;
The scale factor of the pyramids, S.F. = 2:3
The base area of the small pyramid, = 110.11 square units
The height of the small pyramid, h₁ = 12 units
(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid
Therefore;
The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units
V₁ = 440.44 cube units
The volume of the small pyramid, V₁ = 440.44 cube units
(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid
She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid
The volume scale factor = (The linear scale factor)³
(c) The linear scale factor of the pyramids = 2:3 = 2/3
Therefore;
The volume scale factor of the pyramids = (2/3)³ = 8/27
To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;
V₂ = V₁ × (27/8)
Therefore;
The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units
The volume of the larger pyramid, V₂ = 1,486.485 cube units.
PLS GIVE ME BRAINLIESTA DN FRIEND REQUEST ME PLS AND THANK YOU
Given the following sets, find the set (A UB) n (AUC).U={1, 2, 3, ...,9}A = {1, 2, 4, 8}B = {3, 7, 9)C={1, 2, 3, 4, 6}Select the correct choice below and, if necessary, fill in the answer box to complete your choice.O A. (AUB) n (AUC)=0(Use a comma to separate answers as needed. Use ascending order.)O B. (A UB) n (AUC) is the empty set.
From the data sets given
(A U B) = ( 1, 2 ,3 ,4 , 7, 8 , 9)
(A U C) = (1, 2 ,3 ,4 ,6 ,8)
(A U B) n ( A U C) = ( 1 ,2, 3, 4 ,8)
V =Y(r+ B) solve for r
an insurance company claims the probability of surviving a certain type of cancer is 20%. what are the odds of surviving? express your answer in the form a:b
The probability of surviving is given as 20%.
It is required to find the odds of surviving.
Let the event "surviving a certain type of cancer" be X.
It follows that the probability can be written as:
[tex]\begin{gathered} P(X)=20\%=\frac{20}{100}=\frac{\cancel{20}^1}{\cancel{100}^5} \\ \Rightarrow P(X)=\frac{1}{5} \end{gathered}[/tex]Recall that for an event X, the odds in favor of the event happening are given by the ratio:
[tex]\begin{gathered} \frac{P(X)}{P(\overline{X})} \\ \text{Where }P(\overline{X})\text{ is the probability of the event not happening} \end{gathered}[/tex]The probability of event X not happening is given as:
[tex]\begin{gathered} P(\overline{X})=1-P(X) \\ \text{Substitute }P(X)=\frac{1}{5}\text{ into the equation:} \\ P(\overline{X})=1-\frac{1}{5}=\frac{4}{5} \\ \Rightarrow P(\overline{X})=\frac{4}{5} \end{gathered}[/tex]Substitute the probabilities into the odds formula:
[tex]\frac{P\mleft(X\mright)}{P(\overline{X})}=\frac{\frac{1}{5}}{\frac{4}{5}}=\frac{1}{4}[/tex]The odds of surviving is 1:4.
The odds of surviving in the ratio from is 4 : 1.
What are odds in favor and odds against?The odds in favor is the ratio of the number of ways that an outcome can occur compared to how many ways it cannot occur.
The odds against is the ratio of the number of ways that an outcome cannot occur compared to in how many ways it can occur.
Given, An insurance company claims the probability of surviving a certain type of cancer is 20%.
So, The probability of not surviving a certain type of cancer is 80%.
∴ The odds of surviving is 2/8 = 1/4.
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Essential Question How can you write an algebraic expression?
Answer:
Step-by-step explanation:
In algebraic expressions that use variables (written as letters), you can write them directly after a normal number, with no symbol between them.
...
Use a ⋅ or × sign if you see words like double, per, or product.
Twice 16 → 2 ⋅ 16.
Five per day → 5 ⋅ d or 5d. ...
The product of 8 and 20 → 8 ⋅ 20.
Lana has a three-year lease that requires her to pay $395 rent permonth. What is the total amount she will pay for rent during the term ofher lease?a. $1,185b. $14,220c. $4,740d. $1,422
Step 1. Since Lana Pays the rent monthly, and the lease is for a 3 year period, the first step will be to calculate the number of months that are in 3 years.
Since there are 12 months in just 1 year, we multiply 12 by 3 to get the number of moths in 3 years:
[tex]12\times3=36[/tex]There are 36 months in 3 years.
Step 2. Multiply the number of months by the monthly payment of the rent.
We multiply $395 by the 36 months:
[tex]395\times36[/tex]And the result is:
[tex]395\times36=14,220[/tex]$14,220 is the total amount she will pay for rent during the term of her lease.
Answer:
b. $14,220
what is the slope of the line through (-9, 6) and (-3,9)
Solution
For this case we have the following points:
(-9, 6) and (-3, 9)
and we can find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{9-6}{-3+9}=\frac{3}{6}=\frac{1}{2}[/tex]Then the solution would be:
B ) 1/2
Let X be a discrete random variable for the outcome of a toss of a coin with sides 0 and 1,with P(X = 0) = 0.5 and P(X = 1) = 0.5. Moreover let Y be another variable associatedwith a biased coin with sides 1 and 2, such that P(Y = 1) = 0.4 and P(Y = 2) = 0.6. IfZ = X + Y , what is P(Z < 3)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} P(X=0)=0.5,P(X=1)=0.5 \\ P(Y=1)=0.4,P(Y=2)=0.6 \\ Z=X+Y \end{gathered}[/tex]STEP 2: Write the formula for calculating the required probability
[tex]P(Z<3)=P(Z=1)+P(Z=2)[/tex]STEP 3: Find P(Z=1)
[tex]\begin{gathered} P(Z=1)=P(X=0)\text{ and }P(Y=1) \\ =0.5\times0.4=0.2 \end{gathered}[/tex]STEP 4: Find P(Z=2)
[tex]\begin{gathered} P(Z=2)=P(X=0)\cdot P(Y=2)\text{ or }\times P(X=1)\cdot P(Y=1) \\ (0.5\times0.6)+(0.5\times0.4) \\ =0.3+0.2=0.5 \end{gathered}[/tex]STEP 5: Find the P(Z<3)
[tex]P(Z<3)=0.5+0.2=0.7[/tex]Hence, the answer is 0.7
express in simplest form: sec 0 • cot 0 • sin 0
Note that;
secθ = 1/cosθ cotθ= cosθ/sinθ
substitute into into the expression
[tex]\sec \theta.\cot \theta.\sin \theta=\frac{1}{\cos\theta}.\frac{\cos \theta}{\sin \theta}\text{. sin}\theta[/tex]cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator
[tex]=1[/tex]which is more 95 fluid ounces or 3 quarts
95 fluid ounces or 3 quarts.
To solve htis problem, convert the ounces to quarts and compare the results.
1 ounce ----------------------- 0.03125 quart
95 ounces ------------------- x
x = (95 x 0.03125) / 1
x = 2.97 quarts
2.97 ounces < 3 quarts
Three quarts is more
A restaurant bill for four people is 122 route leave the $8018 tip what percentage tip is that A restaurant beer for four people is 120 the group me is a tip of $18 what percent of tip is that
The total tip for a four-person meal at a restaurant is $122, people $8018. The percentage of the tip is 22%.
Given that,
The total tip for a four-person meal at a restaurant is $122, people $8018. What proportion of a tip is that? Four restaurant beers cost 120 each, and the group tip is $180.
We have to calculate the how much percentage of a tip is there.
In a variety of situations, such as restaurants, hotels, salons, and other establishments in the service sector, leaving a tip is common. Knowing how to compute a tip and knowing how much to tip is crucial for a variety of reasons, including the fact that many service sector personnel, like waiters, rely heavily on gratuities for the majority of their income. This means that these experts might not be able to support themselves and their families without tips.
Percentage= tip/amount
Percentage= $180/$8018
Percentage= 22%
Therefore, the percentage of the tip is 22%
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Help me pleaseeeeeeeeee
The side lengths of the right triangle in exact form are z = (15√3)/2, x = 15/2, y = (15√3)/4, a = 15/4 and b = 45/4.
How determine the sides of a right triangle using trigonometric ratios?Three out of the six functions used in trigonometry is expressed as;
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
From diagram, we solve for side z of the right triangle.
cosθ = adjacent / hypotenuse
cos( 30° ) = z / 15
Solve for z
z = cos( 30° ) × 15
z = (√3)/2 × 15
z = (15√3)/2
Next solve for side x
sinθ = opposite / hypotenuse
sin( 30° ) = x / 15
x = sin( 30° ) × 15
x = 15/2
Solve for side y
sinθ = opposite / hypotenuse
sin( 60° ) = y / 15/2
y = sin( 60° ) × 15/2
y = (15√3)/4
Solve for side a
cosθ = adjacent / hypotenuse
cos( 60° ) = a / 15/2
a = cos( 60° ) × 15/2
a = 15/4
Solve for side b
b = 15 - a
b = 15 - 15/4
b = 45/4
Therefore the length of side of b is 45/4
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Formula?
$268 is deposited into savings account at 4% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $427?
Answer: 12 years
5. A ja contains 11 green marbles, 7 red marbles, and 6 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability ofselecting a blue marble followed by a green marble?
Answer: 11/92
Explanation:
Probability is expressed as
number of favorable outcomes/number of total outcomes
From the information given,
number of green marbles = 11
number of red marbles = 7
number of blue marbles = 6
Total number of marbles = 11 + 7 + 6 = 24
Probability of selecting a blue marble = 6/24 = 1/4
Since the marble is not replaced, total number of marbles left = 24 - 1 = 23
Probability of selecting a green marble = 11/23
The probability of selecting a blue marble followed by a green marble is
1/4 x 11/23
= 11/92
Find the inverse
g(x) =
10 –5x
2
The most appropriate choice for inverse of a function will be given by-
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
What is inverse of a function?
At first, it is important to know about function
A function from A to B is a rule that maps to each element of A a unique element of B.
A is called the domain of the function and B is called the co domain of the function.
[tex]f^{-1}[/tex] is said to be the inverse of [tex]f[/tex] if [tex]f[/tex] [tex]o[/tex] [tex]f^{-1}[/tex] = [tex]f^{-1} o[/tex] [tex]f[/tex] = [tex]I[/tex], I is the identity function.
Let g(x) = y
[tex]\frac{10-5x}{2} = y\\10 - 5x = 2y\\5x = 10-2y\\x = \frac{10 - 2y}{5}[/tex]
[tex]f^{-1}(x) = \frac{10 - 2x}{5}[/tex]
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help please for my homework
A. The similar triangles are: B. ΔABC ~ ΔDBE
B. AC = 16
What is the Angle-Angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if two angles in one triangle are congruent to two corresponding angles in the other triangles.
The side lengths of two similar triangles are proportional to each other, which means they have ratio that is equal to one another.
Part A:
In the given diagram, triangles ABC and DBE have two pairs of corresponding angles that are congruent to each other which are: angle ABC ≅ DBE, and angle BCA ≅ BED.
Therefore, based on the AA similarity theorem: B. triangle ABC ~ triangle DBE.
Part B:
Since triangles ABC and DBE are similar triangles, therefore, BC/BE = AC/DE
Substitute
12/15 = (x + 1)/(x + 5)
Cross multiply
12(x + 5) = 15(x + 1)
12x + 60 = 15x + 15
Combine like terms
12x - 15x = -60 + 15
-3x = -45
-3x/-3 = -45/-3
x = 15
AC = x + 1 = 15 + 1
AC = 16
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Which of these is the northern-most countries? Responses
A Colombia
B Brazil
C Ecuador
D Peru
3 thousandths times 0.001
the answer would be 3
Please help with these two problems.
Answer:
7. x = 25
8. x = 28
Step-by-step explanation:
7. Alternate interior angles are congruent.
[tex]x + 25 = 2x[/tex]
[tex]x = 25[/tex]
8. Consecutive angles add up to 180°.
[tex]4x + 2x + 12 = 180[/tex]
[tex]6x + 12 = 180[/tex]
[tex]6x = 168[/tex]
[tex]x = 28[/tex]
A, taken two at a time 4) a. ** Evaluate each expression. 5) P2
we have
4P2
the formula is equal to
n!/(n-r)!
n=4
r=2
substitute
4!/(4-2)!
4!/2!=(4*3*2!)/2!
simplify
4*3=12
answer is 12For the polynomial f(x) = 2x3 – 9x2 +117 - 20 as x → -0,f(x) > 0 O A. True O B. False
Given the function;
[tex]\begin{gathered} f(x)=2x^3-9x^2+11x-20 \\ \end{gathered}[/tex]The leading exponent is odd and the leading coeeficient is positive, so as x tends to positive infinity, f(x) also tends to positive infinity and as x tends to negative infinity, f(x) also tends to negative infinity.
Thus, the correct answer is FALSE.
2. Which of the following represents a quadratic function? (Circle all that apply!) (2 pts)a, y = 9x2 + 4x - 6b. y = 3x + 8c. y = 1223 - 6x2 + 4x - 9
A quadratic function is a function in the form,
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{where a, b, c are real } \\ a\ne0 \end{gathered}[/tex]Option A is a quadratic function,
Option B, is not a quadratic function because it is not the form of the equation written above and also,
[tex]a=0[/tex]Option C is also not a quadratic function because it has the highest degree of x to be 3.
In option D the function is given by the function is defined by
[tex]\begin{gathered} y=x^2 \\ \text{thus} \\ a=1\ne0 \end{gathered}[/tex]This implies that the function in option D is a quadratic function
Option E is not a quadratic function
a regular octagon (a polygon with 8 equal sid3s) is inscribed in a circle of radius 19.9cm. find the perimeter of the octagon
Perimeter of an octagon
radius R = 19.9 cm
then To find perimeter
Multiply 8 times lenghts of octagon
with height=
internal angle is= 360/8 = 45°
Now apply rule of Sines
then sin 45/ lside = sin ( 180-45)/2/ radius
Therefore
Lside = sin 45• (19.9) / sin (67.5) = 15.23 cm
Now multiply 8 times this lenght side to find perimeter
8x 15.23 = 121.84 cm
