The rule for the translated function is:
g(x) = 3*(x + 10)^2 - 7
How to find the rule for g(x)?
First, we know that for a function f(x) a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.
if N < 0, the translation is to the right.
A translation of 5 units to the left is written as:
g(x) = f(x + 5)
Replacing f(x) we get:
g(x) = 3*(x + 5 + 5)^2 - 7
g(x) = 3*(x + 10)^2 - 7
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
solve for X using cross multiplication 4x-3/3 = x+8/2 x= []
Answer:
x=6
Explanation:
Given the equation:
[tex]\frac{4x-3}{3}=\frac{x+8}{2}[/tex]First, cross multiply:
[tex]2(4x-3)=3(x+8)[/tex]Next, open the brackets:
[tex]8x-6=3x+24[/tex]Subtract 3x from both sides of the equation:
[tex]\begin{gathered} 8x-3x-6=3x-3x+24 \\ 5x-6=24 \end{gathered}[/tex]Add 6 to both sides of the equation:
[tex]\begin{gathered} 5x-6+6=24+6 \\ 5x=30 \end{gathered}[/tex]Finally, divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{30}{5} \\ x=\frac{6\times5}{5} \\ x=6 \end{gathered}[/tex]The value of x is 6.
Transversal c intersects lines a and b. Prove that a // b in each case.
The required solutions are m∠1 + m∠7 = 143° + 37° = 180° and 'a' is parallel to 'b' due to the same-side exterior angle.
Transversal c intersects lines a and b which is given in the question.
As per the given figure,
m∠1 + m∠7 = 143 degrees + 37 degrees = 180 degrees
m∠1 = 143° and m∠7 = 37°.
First, we can write m∠1 + m∠7 and then substitute angles with their actual degree measure:
143° + 37° = 180 degrees
The first statement will be:
m∠1 + m∠7 = 143° + 37° = 180°
Exterior indicates that both angles are on the same side, or outside, of the parallel lines.
Angles a, b, c, and d in the figure are outside of the parallel lines.
We can then state;
a and b are parallel since they both agree with the same-side exterior theorem.
As a result, 'a' and 'b' are parallel because they both satisfy the same-side exterior theorem.
Learn more about Alternate Interior Angles here:
brainly.com/question/2125016
#SPJ1
Solve right triangle ABC for all missing parts. Express angles in decimal degrees.a = 200.7 km, c= 401.5 kmRound to the nearest hundred
Using the Pythagorean Theorem we get:
[tex]c^2=a^2+b^2\text{.}[/tex]Therefore:
[tex]b^2=c^2-a^2\text{.}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]b^2=(401.5km)^2-(200.7km)^2.[/tex]Solving the above equation for b we get:
[tex]\begin{gathered} b=\sqrt[]{(401.5km)^2-(200.7km)^2} \\ =\sqrt[]{161202.25km^2-40280.79km^2} \\ =\sqrt[]{120921.76km^2}\approx347.74km\text{.} \end{gathered}[/tex]Now, from the given diagram we get that:
[tex]\begin{gathered} \cos B=\frac{a}{c}, \\ \sin A=\frac{a}{c}\text{.} \end{gathered}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]\begin{gathered} \cos B=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \\ \sin A=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} B=\cos ^{-1}(\frac{2007}{4015})\approx60.00^{\circ}, \\ A=\sin ^{-1}(\frac{2007}{4015})\approx30.00^{\circ}, \end{gathered}[/tex]Answer:
[tex]\begin{gathered} b=347.74\operatorname{km}, \\ B=60.00^{\circ}, \\ A=30.00^{\circ} \end{gathered}[/tex]
9. Mrs. Sorenstam bought one ruler, one compass, and one mechanical pencil at the prices shown in the table for each a. Suppose Mrs. Sorenstam had 36 cents left after buying the school supplies. Write an equation to find the amount of money Mrs. Sorenstam initially had to spend on each student. b. Describe a two-step process you could use to solve your equation. 5020 02/03 Due Price ($) Item 1.49 of her 12 students. compass 0.59 mechanical pencil 0.49 ruler Then solve the equation.
Let A be the total amount of money that Mrs. Sorenstam had before buying the school supplies. Let C be the unit price of the compass, M the unit price of the mechanical pencil and R the unit price of the ruler.
The total amount of money required for the school supplies of one student, is C+M+R. Since there are 12 students, the total amount of money required for school supplies is:
[tex]12(C+M+R)[/tex]Since Mrs. Sorenstam had a total A of money and she bought the school supplies for 12 students, with 36 cents left after the transaction, then:
[tex]A-12(C+M+R)=0.36[/tex]Since C=1.49, M=0.59 and R=0.49, then:
[tex]\begin{gathered} C+M+R=1.49+0.59+0.49 \\ =2.57 \end{gathered}[/tex]Then, our equation is equivalent to:
[tex]A-12\times2.57=0.36[/tex]which is the equation that we may write for the first part of the problem.
For the second part, one step is to multiply 12 times 2.57, and then add the result to both sides of the equation to solve for A:
1.- Multiply 12 times 2.57:
[tex]A-30.84=0.36[/tex]2.- Add 30.84 to both sides of the equation:
[tex]\begin{gathered} A-30.84+30.84=0.36+30.84 \\ \Rightarrow A=31.2 \end{gathered}[/tex]Math help please help
Answer:
2,6
Step-by-step explanation:
△I'J'K' is a translation of △IJK. Write the translation rule.
The △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K' by applying translation rule.
What is the translation rule?
An example of a transformation is a translation, which moves every point in a figure uniformly and in one direction. Slides are a common term used to describe translations. You can use notation or words to express a translation, such as "moved up 3 and over 5 to the left."
The coordinate of the vertices of △IJK are K(3, 7), I(1,2), J(6, 5).
The coordinate of the vertices of △I'J'K' are K(-6, -3), I(-8, -8), J(-3, -5).
The difference between x-coordinate of △IJK and △I'J'K' corresponding vertices are 3 - (-6) = 1 - (-8) = 6 - (-3) = 9
The difference between y-coordinate of △IJK and △I'J'K' corresponding vertices are 7 - (-3) = 2 - (-8) = 5 - (-5) = 10.
Thus △IJK is shifted 9 units toward left and then shifted 10 units toward down to get △I'J'K'.
To learn more about translation rule, click on below link:
https://brainly.com/question/933695
#SPJ1
2. The Access to University course in the college has 252 full-time and 140 part-
time students enrolled this year. What fraction of students are studying part-
time?
Answer:
[tex]\frac{5}{14}[/tex]
Step-by-step explanation:
First, find the total number of students:
[tex]252+140=392[/tex]
Then, divide the number of students at hand by the total number:
[tex]\frac{140}{392}[/tex]
When possible, reduce the fraction to its simpliest form:
[tex]\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}[/tex]
in an election, suppose that 55% of the voters in fact support funding the new crc library building. a news organization wants to predict the outcome of the election by sampling 80 voters. what is the probability that less than 49% of the sampled voters support the new crc library building? this would result in the news organization making a wrong prediciton.
The new organization making a wrong prediction cannot be determined.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
According to the problem,
p = 55% ≅ 0.55
n = 80 voters
The probability that less than 49% ≅ 0.49 of the sampled voters support the new library building can be calculated as,
p( p < 0.49 ) = p( z < (0.49 - 0.55) / √(0.55*(1 - 0.55)/80) )
where, z = { p - p/ √(p(1 - p)/n) }
p( p < 0.49 ) = p( z < ( -0.06) / √(0.55*0.45/80))
= p( z < ( -0.06) / √(0.2475/80))
= p( z < ( -0.06) / [tex]\sqrt{0.00309375}[/tex] )
= p( z < ( -0.06) / 0.055621488 )
= p( z < ( -1.078719793) )
p( p < 0.49 ) = p( z < ( -1.079) )
p( p < 0.49 ) ≅ 0.140071 ( From the normal standard table )
The calculated probability is unpredictable. Therefore, We cannot say that the new organization is making a wrong prediction.
To know more about probability with z-score refer to:
https://brainly.com/question/28213251
#SPJ4
please help me identify an alternate exterior, an alternate interior, a vertical, linear pair, consecutive interior, and corresponding angles that fit the given type m || n and a || b :)
We have that (Some) alternate exterior angles in this graph are:
1 & 7
2 & 8
9 & 15
10 & 16
(Some) Alternate interior angles are:
3 & 5
4 & 6
12 & 14
11 & 13
Some linear pairs are:
1 & 2
9 & 10
4 & 3
12 & 11
5 & 6
13 & 14
8 & 7
16 & 15
(Some) Consecutive interior angles are:
4 & 5
3 & 6
12 & 13
11 & 14
(Some) Corresponding angles are:
1 & 5
2 & 6
9 & 13
10 & 14
(Some) Vertical angles:
1 & 3
2 & 4
9 & 11
10 & 12
5 & 7
6 & 8
13 & 15
14 & 16
The scale along each als is 1.State the interval where f (2)
We have the following:
replacing:
[tex]\begin{gathered} f(2)The answer is the interval (-6, 9)Which relationship between x and y in the equation shows a proportional relationship? o y=+3 o y y= 12 O y = 2x + 6 o y = 12x
Please help me ASAP
3. You deposit $1575 in a bank account that earns 3.75% interest per year for 5 years. How much will the balance be if it's compounded continuously?
4. From #3, How much will the balance be if it's compounded monthly?
5. You buy a boat for $35,000 that depreciates in value at about 17% per year. How much will it be worth in 3 years?
3) $1,899.81
4) $1,899.26
6) $17,150
Please help me with this..
Answer:
40/36=20/x
X=18
Step-by-step explanation:
it solve by Proportion and proportion
Answer:
Area of the small rectangle is 9m²
I need to find the surface area. it's a cut sphere with a diameter of 14.
Given data:
The diameter of the cut sphere, D=14 in.
The radius of the cut sphere is,
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{14}{2} \\ r=7\text{ in} \end{gathered}[/tex]The cut sphere is called a hemisphere.
The surface area of a sphere is
[tex]A_1=4\pi r^2[/tex]So, the lateral surface area of a hemisphere is half the surface area of sphere. Therefore, the lateral surface area of a hemisphere is,
[tex]\begin{gathered} A_2=\frac{4\pi r^2}{2} \\ A_2=2\pi r^2 \end{gathered}[/tex]The hemisphere has a lateral surface and a circular surface. The area of the circular surface is,
[tex]A_3=\pi r^2[/tex]Therefore, the total area of the hemisphere is,
[tex]\begin{gathered} A=A_2+A_3 \\ A=2\text{ }\pi r^2+\pi r^2 \\ A=3\text{ }\pi r^2 \end{gathered}[/tex]The total surface area of a hemisphere is,
[tex]\begin{gathered} A_{}=3\text{ }\pi r^2 \\ A=3\text{ }\pi\times7^2 \\ A=461.8in^2 \end{gathered}[/tex]Therefore, the total surface area of the cut sphere is 461.8 square inches.
I need haled on this question so air was wondering what was the equation for r-c=p
The equation r-c= p represents the profit equation
What does the equation r-c = p stands for?Profit can be defined as the difference between revenue and cost i.e. revenue minus cost. The formula for profit can be written as:
p = r - c
where r is the revenue and c is the cost
Notice that the equation, r-c = p is the same as p = r-c when rearranged.
Therefore, the equation r-c=p stands for the profit equation
Learn more about the profit equation on:
https://brainly.com/question/19104371
#SPJ1
In circle M with m \angle LMN= 42m∠LMN=42 and LM=14LM=14 units, find the length of arc LN. Round to the nearest hundredth.
The length of the arc is 1.63
In circle M with m \angle LMN= 42m∠LMN=42
The diagram shows a sector of a circle, center M
The radius of the circle is 14 units
The angle LMN = 42
We need to find the perimeter of the sector
s = r∅
Where ∅ is the angle subtended by the arc
r is the radius of the circle
s = 14 (42/360)
s = 14 (7/60)
s = 1.63
Therefore, the length of the arc is 1.633
To learn more about sector refer here
brainly.com/question/28108430
#SPJ1
Each basket contains 3 identical bags of stuffing and 6 pound bag of rice.
The total pounds of rice will be 18 pounds.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, each basket contains 3 identical bags of stuffing and 6 pound bag of rice. The total pounds will be:
= 3 × 6
= 18 pounds
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Complete question
Each basket contains 3 identical bags of stuffing and 6 pound bag of rice. What is the total pounds of rice?
503,000
3,200,000
Scientific Notations
Answer:5.03x10^5 and 3.2x10^6
Step-by-step explanation:
Number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10
503,000 divide by 10 until the number before decimal point digit becomes less than 10
A parabola opening up or down has vertex 0, – 3 and passes through – 12,15. Write its equation in vertex form.
y = 0.125x² - 3 is equation of parabola in vertex form
The standard form of the parabola is [tex]y = ax^{2} + bx + c[/tex]
The vertex form of parabola is [tex]y = a(x-h)^{2} + k[/tex]
where h and k are vertex of parabola. The vertex formula is used to find vertex coordinate of parabola .
Vertex point of parabola are usually represented by (h, k).
Given that the vertex of parabola is 0, -3
(h, k) = (0, -3)
h = 0 and k = -3
substituting the values of h and k in vertex form of parabola,
[tex]y = a(x-0)^{2} -3\\y = ax^{2} - 3[/tex]
Parabola is also passing through (12,15) means it should satisfy vertex equation of parabola
[tex]15= a(-12)^{2} -3\\15+3 = 144a\\18 = 144a\\a = \frac{18}{144}\\\\a = 0.125[/tex]
Substituting value of a
Vertex form of parabola is [tex]y = 0.125x^{2} - 3[/tex]
To know more about Vertex form of parabola here ,
https://brainly.com/question/27973602
#SPJ1
Select the step in the solution that shows the first error. Step 1: 5x – 3 = 2x + 6 Step 2: 3x – 3 = 2x + 6 Step 3: x – 3 = 6 Step 4: x = 3
The error is in step 2 that is 3x-3=2x+6 as in step 2 we shifted 2x to LHS side of calculation.
What is error?Error is the difference between a true value and an estimate, or approximate, representation of that value in applied mathematics. The difference between the mean of the entire population and the mean of a sample taken from that population is a frequent example in statistics. Three types of errors can occur when solving math problems: factual, procedural, and computational. Students can make a variety of math mistakes, and it's crucial to know how to avoid them and how to take lessons from them. An error is an inaccurate or incorrect action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake. The term "error" in statistics describes the discrepancy between the computed value and the correct value.
Here,
5x-3=2x+6
3x-3=6
3x=9
x=3
The mistake is in step 2, which reads 3x-3=2x+6 because we shifted 2x to the LHS side of the calculation in step 1.
To know more about error,
https://brainly.com/question/17738182?referrer=searchResults
#SPJ1
What is the vertical change from Point A to Point B?
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth, if
necessary
The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given,
Point A translate to point B on a straight line.
The Coordinate of point A is (2,1).
The Coordinate of point B is (4,2).
Vertical change = 2 - 1 = 1
Horizontal change = 4 - 2 = 2
Slope = vertical change / horizontal change
Slope = 1/2 = 0.5
Hence "The vertical change from point A to point B is 1. The horizontal change from point A to point B is 2. The rate of change in the graph is 0.5".
To learn more about graphs,
brainly.com/question/16608196
#SPJ1
Please please please help me and show the steps too I really need to understand this!
Yes I will mark brainliest!
The value of x for the ΔPRT is 7.
As its given in the question that ΔKMN ≅ ΔPRT (congruent)
MN = 20
KN = 25
KM = 15
RT = 3x - 1
Therefore,
MN = RT
KM = PR
KN = PT
So, RT = MN
3x - 1 = 20
3x = 20 + 1
3x = 21
x = 21/7
x = 7
Hence, x = 7.
Learn more about value of x on:
https://brainly.com/question/28787935
#SPJ1
Solve four-sixths minus three-twelfths equals blank. Solve five-sixths minus three-fourths equals blank. Solve five-ninths minus two-sixths equals blank. Solve nine-twelfths minus eleven-eighteenths equals blank. Solve four-ninths minus four-tenths equals blank. Solve six-sevenths minus five-fourteenths equals blank.
Solve two-fifths minus one-seventh equals blank. Solve four-sixths minus three-fifths equals blank. Solve four-sixths minus three-eighths equals blank. Solve seven-eighths minus nine-sixteenths equals blank. Please solve all 10 questions no explanation needed but you can add one if you want
Answer:
Step-by-step explanation:
first you need to make sure that the fractions you are adding and subtracting have like denominators. To do this you need to find the least common multiple between the two
1. 4/6 - 3/12= 8/12 - 3/12 Answer: 5/12
2. 5/6 - 3/4 = 10/12 - 9/12 Answer: 1/12
3. 5/9 - 2/6= 10/18 - 6/18 Answer 4/ 18 (reduces to 2/9 for simplest terms)
4. 9/12 - 11/18 = 27/36 - 22/36 Answer: 5/36
5. 4/9 - 4/10 = 40/90 - 36/90= 4/90 ( reduces to 2/45)
6. 6/7 - 5/14= 12/14-5/14 Answer 7/14 (reduces to 1/2
7. 2/5- 1/7= 14/35 - 5/35 Answer 8/35
8. 4/6 - 3/5 = 20/30 - 18/30 Answer 2/30 (1/15 simplified
Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job. If each is working alone, Janice typically takes 2 less hours than Donald to build a picnic table. Based on this information, how long would it have taken for Janice to build the picnic table alone? Do not include the units in your answer.
To solve this problem the first thing we have to do is identify our variables
The time taken by Janice will be represented by a j, and the time taken by Donald by a d.
• Donald builds the picnic table in hours: , 1/d, of the picnic table per hour
,• Janice builds the picnic table ,j=d-2, in hours: ,1/(d-2), of the picnic table per hour
Now we will get our equation to solve
Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job.
[tex]\begin{gathered} 2(\frac{1}{d}+\frac{1}{d-2})+1(\frac{1}{d})=1Table \\ \frac{2}{d}+\frac{2}{d-2}+\frac{1}{d}=1Table \\ \frac{3}{d}+\frac{2}{d-2}=1\text{Table} \\ \frac{2d+3(d-2)}{d(d-2)}=1\text{table} \\ 2d+3d-6=d^2-2d \\ d^2-2d-5d+6=0 \\ d^2-7d+6 \end{gathered}[/tex]We factor our equation to find Donald's time
[tex]\begin{gathered} (d-6)(d-1)=0 \\ d_1=6 \\ d_2=1 \end{gathered}[/tex]They gave us 2 values but we discarded the value of d=1 because the joint calculations would give negative calculations then
[tex]\begin{gathered} j=d-2 \\ j=6-2 \\ j=4 \end{gathered}[/tex]Donald takes 6 hours to set up a table and Janice takes 4 hours.Find the value of 3a + 2b if a = 4 and b = (-9) (*Substitute*)
Question:
Find the value of 3a + 2b if a = 4 and b = (-9) .
Solution:
Let the following expression
[tex]3a\text{ + 2b}[/tex]now, if a = 4 and b = -9, and we substitute them in the previous expression, we obtain:
[tex]3(4)\text{ + 2(-9) = 12 - 18 = -6}[/tex]then, we can conclude that the correct answer is:
[tex]-6[/tex]Convert form the giving stand and Form of a linear equation to the slope-intercept form of a linear equation x + 5y = 5
The slope-intercept form of a linear equation is given by the expression:
y=mx+b, so in this case you just have to solve the equation for y by inverse operations to solve equations:
x+5y=5
5y=5-x
y=5/5-x/5
y=-1/5x+1
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How much would an order of 1 slice of cheese pizza and 3 sodas cost?
An order of 1 slice of cheese pizza and 3 sodas cost will be $5.25.
Define simultaneous equation.Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.
Given data -
Cost of 3 slices of cheese pizza and 2 sodas = $8.75
Cost of 2 slices of cheese pizza and 4 sodas = $8.50
Let x be the cost of 1 slice of cheese pizza
and y be the cost of 1 soda
According to the given data,
3x + 2y = $8.75 -------------equation 1
2x + 4y = $8.50 -------------equation 2
Equation 1 by equation 2 multiplied results in
6x + 4y = $17.5 ------------equation 3
By subtracting equation 2 from equation 3 to get the cost of 1 slice of cheese pizza, we will get
4x = $9
x = $2.25
By substituting the value of x in equation 2 so that we can get the cost of 1 soda, we will get
2*2.25 + 4y = $8.50
4.5 + 4y = $8.50
4y = $8.50 - 4.5
4y = $4
y = $1
To get the cost of 3 sodas, multiplying the value of y by 3
Therefore the cost of 3 sodas will be $1*3 = $3
The total cost of 1 slice of cheese pizza and 3 sodas cost = $2.25 + $3
= $5.25
To know more about simultaneous equation, visit:
https://brainly.com/question/15165519
#SPJ1
Can someone explain how to answer this problem
Write an equation in point-slope form given the following: (1,2); m=7
thanks
Answer:
Step-by-step explanation:
Answer:
y-2 = 7(x-1)
match the correct base shape to each prism. some cards may be used more than once.
Looking at figure A, we have a prism with a triangular base that looks like a right triangle.
Since the prism has a right triangular base, the base shape is a right triangle (shape 5).
Looking at figure B, we have a prism with a pentagonal base.
Since the prism has a pentagonal base, the base shape is a pentagon (shape 1).
Looking at figure C, we have a prism with a triangular base that looks like an equilateral triangle.
Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).
Looking at figure D, we have a prism with a triangular base that looks like an equilateral triangle.
Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).
Two planes, which are 2660 miles apart, fly toward each other. Their speeds differ by 65mph. If they pass each other in 4 hours, what is the speed of each?
EXPLANATION
Since the two planes are 3400 miles apart, and their speed differs by 80 mph, we can apply the following relationship:
2660 / 4 = 665 mph
Assuming that x is the speed of the slower plane and y is the speed of the faster, we have:
(1) x + 65 = y
(2) x + y = 665 [Combined speed of both planes]
Plugging in (1) in (2):
x + (x + 65) = 665
Removing the parentheses:
x + x + 65 = 665
Adding like terms:
2x + 65 = 665
Subtracting -50 to both sides:
2x = 665 - 65
Subtracting numbers:
2x = 600
Dividing both sides by 2:
x = 300
Plugging in x=315 into (1):
300 + 65 = 365
In conclusion, the speed of both planes is:
Slower plane = 300 mph
Fastest plane = 365 mph