Given the expression:
[tex]\sin (x)=\frac{5}{14}[/tex]to find the angle, we use the invers sine function to get x:
[tex]\begin{gathered} \sin (x)=\frac{5}{14} \\ \Rightarrow x=\sin ^{-1}(\frac{5}{14})=20.92 \\ x=20.92 \end{gathered}[/tex]therefore, the angle x = 20.92°
all you need is in the photo please don't put the step by step ANSWER FAST
The given expression is
[tex]3x^2+12x-15=0[/tex]First, we factor our the number 3.
[tex]3(x^2+4x-5)=0[/tex]Then,
[tex]x^2+4x-5=0[/tex]Now, we look for two numbers whose product is 5, and whose difference is 4, those numbers are 5 and 1.
[tex](x+5)(x-1)=0[/tex]Hence, the solutions are x = -5 and x = 1.Which represents the inverse of the function f(x) = 4x?Oh(x) = x + 4O h(x) = x - 4Oh(x) =O h(x) = x
Let y=f(x). To find the inverse of f, isolate x:
[tex]\begin{gathered} f(x)=4x \\ \Rightarrow y=4x \\ \Rightarrow x=\frac{1}{4}y \end{gathered}[/tex]Let x=f^{-1](y). Then:
[tex]f^{-1}(y)=\frac{1}{4}y[/tex]Evaluate the inverse of f at y=x:
[tex]f^{-1}(x)=\frac{1}{4}x[/tex]Therefore, the rule of correspondence of the inverse of f is given by the expression:
[tex]\frac{1}{4}x[/tex]1. If(x)= 5x-2, find(-3)a. -13b. 13c. -17d. 172. If(x)= 5x-2, find x such that f(x)= -3a. -1/5b. 1/5c. -1(Also explain what's the difference between the questions)
1. f ( -3 ) = 5 ( -3 ) - 2 = - 15 - 2 = -17
2. f (x) = 5x - 2 = -3
5x = -3 + 2
5x = -1
x = -1/5 ( dividing both sides by 5 )
The difference between the equations is that -3 is the value for the variable x in the first equation but the function is equal to -3 in the second.
What is the cardinal number of the set H={}?
The set is empty that is null set, so the cardinal number is zero.
The cardinal number of a finite set A is the number of distinct members present in the set and it is denoted by n(A). The cardinal number of the empty set, Ø, is 0 because Ø has zero members or no members. so n(Ø) = 0. And the cardinal number of an infinite set, cannot be found because such a set has countless members.
for example
i) If A = (-3,-2,-1,0,1,2,3) then n(A)=7.
ii) If A = (x/x is a letter of the word HYDERABAD) then n(A) = 7 because writing in the tabular form, A = (H,Y,D,E,R,A,B)
Here, the set is empty that is null set, so the cardinal number is zero.
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the architectures that group of elementary students and teachers from 32 schools who pick up trash at the Lock of parts
the answer is: each school picked up 12/128 tons
if I get the graph correct, every cross indicate the quantity under it. (an x above 1/8 means that there is 1/8 of a ton collected)
then, we need to add up the total amount of tons they collected.
we have 6 crosses in 1/8, 8 crosses in 1/4 and 2 crosses in 1/2. then we do:
[tex]6\cdot\frac{1}{8}=\frac{6}{8}=\frac{3}{4}[/tex][tex]8\cdot\frac{1}{4}=\frac{8}{4}=2[/tex][tex]2\cdot\frac{1}{2}=1[/tex]we add everithing:
[tex]\frac{3}{4}+2+1=3+\frac{3}{4}=\frac{12}{4}+\frac{3}{4}=\frac{15}{4}[/tex]the total amount of trash collected is 15/4 tons (3.75 tons)
there are 32 schools, then we need to divide the amount of trash by the amount of schools:
[tex]\frac{15}{4}\div32=\frac{15}{4}\cdot\frac{1}{32}=\frac{15}{4\cdot32}=\frac{15}{128}[/tex]every school got 15/128 tons of trash
Predict using the equation of the trend line y=25X+150 what will the y value be when x =23?
Given the equation of the line :
[tex]y=25X+150[/tex]We need to find the value of y when x = 23
So, substitute with x = 23 at the given equation
[tex]\begin{gathered} y=25\cdot23+150 \\ y=575+150 \\ \\ y=725 \end{gathered}[/tex]So, the answer is : y = 725
Answer:
725
Step-by-step explanation:
Hello!
You can substitute 23 for x in the equation y = 25x + 150, to find the predicted y-value.
Solve for y
y = 25x + 150; x = 23y = 25(23) +150y = 575 + 150y = 725The value of y at x = 23 is 725.
Which relations are functions?
The most appropriate choice for functions will be given by -
First and second options are correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here Domain of function is obtained from x axis and range of the function is obtained from y axis
For the first option
Every element of domain has a unique image
So first graph is a function.
First option is correct
For the second option
Every element of domain has a unique image
So second graph is a function.
Second option is correct
For the third option
x = 3 has been mapped to every element of y axis
So ]x = 3 has infinite number of images.
Third graph is not a function.
Third option is wrong
For the fourth option
Every point on x axis has been mapped to two elements
So every element of x axis has two images.
Fourth graph is not a function
Fourth option is wrong.
So First and second option are correct
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a rectangle measures 12 inches by 20 inches. what size squares can tile the rectangle completely? choose all that apply
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
What is HCF?
The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF).
HCF for 12 and 20 is equal to 4. Factors of 12 & 20 = 1, 2, 3, 4, 6, and, respectively, 1, 2, 4, 5, 10, 20. In this case, 4 is the biggest number that can be found in the factors for 12 and 20.
We interpret the study released as the component of the product factors in order to determine the HCF by listing common factors in prime factorization.
Consequently, 12 and 20 can be written as;
12 equals 2 × 2 × 3
20 equals 2 × 2 × 5
2 and 2 are frequent prime factors for 12 and 20.
Therefore,
HCF (12, 20) equals 2 × 2 = 4
Therefore, supplying 4X4 square tiles can tile the rectangle completely with the help of the HCF concept.
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Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. <1 and <3 <3 and <7 <8 and <10<4 and <14<6 and <14<2 and <3
EXPLANATION:
To make a correct classification we must do the following:
First we must know the following terms:
-Corresponding angles:
They are on the same side of the parallels and on the same side of the transversal.
For example: <1 <3 ; <6 and <14
-Alternate interior:
They are found within the parallel lines and on the opposite sides to the transversal
For example: <3 and <7 ; <8 and <10
-Alternate Exterior:
they lie outside the parallel lines and on the opposite sides to the transversal.
For example: <4 and <14
-Consecutive interior angles:
They are the pairs of angles on one side of the transversal that are between the lines.
For example: <2 and <3
[20 points]Practice analyzing stretches and shrinks of exponential
functions.
Consider the exponential function f(x) = 2(3¹) and its
graph.
ty
8
The initial value of the function is
The base of the function is
The function shows exponential
The function's initial value is 2, its base value is 3, and it exhibits exponential growth.
What is meant by initial value?An initial value of a function denotes the function's y-intercept. The constant of an equation can also be used to find initial values. Understanding the y-intercept will help you with graph functions. Substitute 0 0 for x x and solve for y y to confirm the initial value. A differential equation with some initial conditions is used to solve an initial value problem. For instance, with initial conditions y(0)=1, dy/dx = x. An initial value problem (IVP) in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.To learn more about initial value, refer to:
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Simplify this question for me thanks!
Answer:
2[tex]x^{\\2}[/tex][tex]y^{5}[/tex][tex]\sqrt{x} 7xy^{3}[/tex]
Step-by-step explanation:
Answer:
2x[tex]2x^{2} \sqrt[5]{7xy} }^{38}[/tex]
Step-by-step explanation:
Kristen make $16 per hour and worked 34 hours last week. How many dollars she made : Mark make $14 per hour and worked 46 hours last week. How many dollars he make :How many hours must Kristen and mark work in order for their pay/savings to be equal ?If Kristen and mark combine their saving how many they will have ?
first question
Kristen make $16 per hour
last week he worked for 34 hours
1 hour ==== $16
35 hours ==== $x
cross multiplication
x * 1 = 16 x 34
x = $544
Second question
for mark
make $14 per hour
he worked 46 hours last week
total amount made
1 hour ===== $14
46 hours =====$x
1 * x = 14 x 46
x = $644
Mark make $644 last week
for the fourth question
if mark and kristen combined their savings
mark make $644 and kristen make $544
their saving combines is
$644 + $544
= $1,188
Their saving combines is $1, 188
if mark works for 46 hours and make $644
if marks works for 34 hours and make $544
how many hours will they work
let the number of hours be x
equating the two equation
iif there is 3 kids and they wanted to share one cup of celery and one cupof carrots how many cups doe each kid get
Each kid will get the fraction 1/3 of a cup of carrots .
A common fraction is a number that represents a rational number. The same number may be expressed as a decimal, percent, or negative exponent.
For instance, the numbers 0.01, 1%, and 102 are equal to the fraction 1/100. The term "set of rational numbers" refers to the collection of all numbers that can be expressed in the form a / b, where a and b are integers and b is not zero. This collection is represented by the letter Q, which stands for quotient. A denominator of one can be considered to be inherent in an integer. A number is said to be logical when it can be stated in that manner (i.e., as a common fraction).There is 1 cup of the carrots and it is to be divided among 3 kids.
therefore each kid will get:
1÷3 = 1/3 cups of carrot.
Hence the kids will each have 1/3 cups of carrot .
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Determine if the pair of solids are similar. If NO explain
Given:
There are given that the two solid to find the similar or not.
Explanation:
To determine whether the solid pair are similar or not, we need to set their dimension with proportion.
So,
From the dimensions of solid:
The radius of the given solids is 14 yd and 4 yd.
The height of the solids is 20 yd and 6 yad.
Now,
We need to set the proportion:
[tex]\begin{gathered} \frac{14}{4}=\frac{7}{2} \\ \frac{20}{6}=\frac{10}{3} \end{gathered}[/tex]So,
[tex]\frac{7}{2}\ne\frac{10}{3}[/tex]Final answer:
Hence, the given pair of solid is not similar because their proportion has not equal.
What is the solution to this equation?4x - 6 + 2x = 18OA. x = 6OB. X= 4OC. X = 2OD. x = 12
In order to solve this equation, we can do the following steps:
[tex]\begin{gathered} 4x-6+2x=18\\ \\ 6x-6=18\\ \\ 6x=18+6\\ \\ 6x=24\\ \\ x=\frac{24}{6}\\ \\ x=4 \end{gathered}[/tex]Therefore the correct option is B.
Find the area and perimeter of the following rectangle guru angad education
1.
[tex]A=l\times w=11\times8=88\operatorname{cm}\text{ }[/tex][tex]P=2l+2w=2(11)+2(8)=22+16=38\text{ cm}[/tex]2.
[tex]\begin{gathered} A=11\times11=121 \\ P=2(11)+2(11)=22+22=44 \end{gathered}[/tex]3.
[tex]\begin{gathered} A=8\times6=48 \\ P=2(8)+2(6)=16+12=28 \end{gathered}[/tex]4.
[tex]\begin{gathered} A=7\times2=14 \\ P=2(7)+2(2)=14+4=18 \end{gathered}[/tex]5.
[tex]\begin{gathered} 35=7\times w \\ \frac{35}{7}=\frac{7w}{7} \\ w=5 \\ P=2(7)+2(5)=14+10=24\text{ units} \end{gathered}[/tex][tex]\begin{gathered} 25=l\times5 \\ \frac{25}{5}=\frac{5l}{5} \\ l=5 \\ P=2(5)+2(5)=10+10=20\text{ units} \end{gathered}[/tex]6.
[tex]P=11+18+9+3+3+8+5+7=64[/tex]Jeanette wants to raise $3, 200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
It’s not 92
Jeanette need to run 91.42 km to get $3,200
How to calculate the distance :
The amount Jeanette wants to raise = $3,200
Amount her sponsers donate = $35 per KM
To find total distance she need to run is divide 3,200 by 35
so we get the distance which she need to cover.
Distance Jeanette need to run = 3200/35 = 91.42 km
The basic operation applied is division.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.There are four important terms used in division. These are dividend, divisor, quotient and remainder.Dividend: The number to be divided by another number is called the dividend.Divisor: The number by which we divide another number (dividend) into equal parts is called the divisor.Quotient: The result of division is called a quotient.Remainder: The leftover number after division is called the remainder.To learn more about division refer :
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a parabola can be drawn given a focus of (4, -7) and a directrix of y=-1
The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
What is Parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
Any point on the parabola is equidistant from the focus an directrix.
Distance of a point (x,y) from y=-1 is (y+1)
Distance of a point (x,y) from (4,-7) say L, then
L² = (x - 4)² + (y+7)²
since, L = y + 1
(y + 1)² = (x - 4)² + (y+7)²
y² + 1 + 2y = (x - 4)² + y² + 49 + 14y
-12y - 48 = (x-4)²
-12(y + 4) = (x-4)²
Therefore, The equation of parabola is -12(y + 4) = (x-4)² with vertex(4, -7) and Latus rectum 12.
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Will picks a Marble random puts it back and then picks another Marble at random are these 2 events depended or independent
When Will puts back the marble, the number of marbles in the sample space has not changed. This is similar to having a replacement marble. The event therefore, is independent.
What is the word for added and subtracted parts of an expression
Answer:
Step-by-step explanation:
answer: terms
hope that is what you mean!
The diagram shows a field.
66 m
140m
102 m
Work out the area of the field.
4
Answer:
The area of the field will be 60504 Sq. m
Step by Step calculation:
Area of the cuboidal field
A cuboid is a three-dimensional figure bounded by six rectangular planes that have different lengths, widths, and heights. If you look around and see a box, brick, or anything in the shape of a rectangle, it might be a cuboid. A cuboid ([tex]3[/tex]-dimensional) can be seen as composed of rectangles ([tex]2[/tex]-dimensional) of different dimensions when viewed from either end
Total area of block = lh + lh + lb+ lb+ hb+ hb=[tex]2[/tex](lb+bh+hl).......(1)
where l means length h means height and b means the breadth of the cuboid
Put the value of length, breadth, and height in (1)
We get TSA of field as= 2(66*140+140*102+102*66 ) = 60504 m^2
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thanks for the help!!!
The value of expression cos(A + B) is equivalent to 0.9902.
What is the relation between sinФ and cosФ?The relation between sinФ and cosФ is as follows -
sin²Ф + cos²Ф = 1
Given is sin(A) = -11/61 and sin(B) = 9/41
We have -
sin(A) = -11/61
sin(B) = 9/41
Evaluating the expression -
cos(A + B)
We can write -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
Now, we know -
sin²Ф + cos²Ф = 1
cos²A = 1 - sin²A = 1 - 0.033 = 0.97
cos A = 0.98
cos²B = 1 - sin²B = 1 - 0.04 = 0.95
cos B = 0.97
Using the values -
cos(A + B) = cos[A] cos[B] - sin[A] sin[B]
cos(A + B) = 0.98 x 0.97 + 0.18 x 0.22
cos(A + B) = 0.9902
Therefore, the value of expression cos(A + B) is equivalent to 0.9902.
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Mr. Pryor's second period consists of 25 students. The mean grade on the first exam was 80, the median was also 80, and the standard deviation was 6.07. Find the standardized scores (z-scores) for each of the following students. Interpret each value in context.
a) Katie, who scored 93.
b) Norman, who scored 72
c) Ted, who scored an 80.
d) Jenny earned an 82 on Mr. Goldstone's chemistry test. Mr. Goldstone told the class that the distribution was fairly symmetric with a mean of 76 and a standard deviation of 4. She scored an 86 in Mr. Pryor's exam, on which test did Jenny perform better relative to the class? Justify your answer.
Answer:
See explanation
Step-by-step explanation:
a. (93-80)/6.07=
13/6.07=2.14
b. (72-80)/6.07=
8/6.07=1.317957
1.317957=1.32
c. (80-80)/6.07=
0/6.07=0
d. (82-76)/4=
6/4=1.5
(86-80)/6.07=
6/6.07=0.988
1.5>0.98, so Jenny did better on Mr. Goldstone's test.
I need help solving this problem.( I had a tutor helping a min ago, but Brainly crashed)
See graph below
Explanation:Given:
Rate water is added = 30 l/min
The initial amount in the pond = 600l
To find:
The equation relating the amount of water in the pond to the number of minutes the water is being added
W = amount of water in the pond
T = number of minutes that water has been added
Amount of water in the pond = rate water is added (number of minutes that water has been added) + the initial amount in the pond
[tex]\begin{gathered} W\text{ = 30\lparen T\rparen + 600} \\ W\text{ = 30T + 600 \lparen equation\rparen} \end{gathered}[/tex]Graphing the equation:
To graph the equation, we will assign values to T
when T = 0, W = 600
when T = 2, W = 660
when T = 4, W = 720
when T = 6, W = 780
Given f(x)
= 3x + 1, solve for x when
f(x) = 7.
Answer:
Answer:
x=2
Step-by-step explanation:
7=3x+1
6=3x
2=x
Hopes this help please mark brainliest
Nancy went to the mall on Saturday to buy clothes. She paid $14.95 on pants and
$4.05 on a jacket with a $20 bill. How much money did Nancy get in change?
Answer:
$1.00
Step-by-step explanation:
Total cost = $14.95 + $4.05 = $19.00
Change = $20.00 - $19.00 = $1.00
find the unit price of 16 oz of candy with sells for $4.82
The price of 16 oz candy is $4.82.
Determine the unit price of candy.
[tex]\begin{gathered} s=\frac{4.82}{16} \\ =0.30125 \end{gathered}[/tex]Rectangle ABCD is given by these coordinates: A(4,1), B(2,3), C(5,6), D(7,4). Select all the transformations that will carry the rectangle onto itself. First option: a rotation 270° counterclockwise, then a rotation 90° counterclockwise Second option: a translation 10 units left, 5 units down, 10 units right, and 5 units up Third option: a reflection across the y-axis, then a rotation 270º counterclockwise about the origin Fourth option: a reflection across the x-axis, then a translation 5 units left, then a reflection across the y-axis, then a translation 5 units right Fifth option: a reflection across the y-axis, then a translation 9 units right
Given the rectangle ABCD, whose vertices are:
[tex]A\mleft(4,1\mright),B\mleft(2,3\mright),C\mleft(5,6\mright),D\mleft(7,4\mright)[/tex]You can apply the transformations shown in each option, in order to determine all the transformations that will carry the figure onto itself:
• First option:
By definition, the rule for a rotation of 270 degrees counterclockwise is:
[tex](x,y)\rightarrow(y,-x)[/tex]And the rule for a rotation of 90 degrees counterclockwise is:
[tex](x,y)\to(-y,x)[/tex]Therefore, you can choose any vertex of the rectangle and apply the first rule and then the second rule:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(1,-4\mright)\rightarrow A^{\doubleprime}\rightarrow(4,1)[/tex]Notice that the coordinates of point A'' are equal to the original point A.
• Second option:
The rule for a translation of 10 units left and 5 units down is:
[tex](x,y)\rightarrow(x-10,y-5)[/tex]And the rule for a translation of 10 units right, and 5 units up is:
[tex](x,y)\rightarrow(x+10,y+5)[/tex]Then, applying the transformations indicated, you get:
[tex]\begin{gathered} A\mleft(4,1\mright)\rightarrow A^{\prime}(4-10,1-5)=A^{\prime}(-6,-4) \\ \\ A^{\prime}(-6,-4)\rightarrow A^{\prime\prime}(-6+10,-4+5)=A^{\doubleprime}(4,1) \end{gathered}[/tex]Notice that point A'' and point A are equal.
• Third option:
The rule for a reflection across the y-axis is:
[tex](x,y)\rightarrow\mleft(-x,y\mright)[/tex]Then, applying that transformation and then applying the rule for a rotation of 270 degrees counterclockwise about the Origin (shown in the explanation of the First option), you get:
[tex]A(4,1)\rightarrow A^{\prime}(-4,1)\rightarrow A^{\doubleprime}(1,4)[/tex]The points A and A'' are different.
• Fourth option:
The rule for a reflection across the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]For a translation of 5 units left is:
[tex](x,y)\rightarrow(x-5,y)[/tex]And for a translation of 5 units right:
[tex](x,y)\rightarrow(x+5,y)[/tex]Therefore, knowing those rules and also knowing the rule for a reflection across the y-axis, you can apply all the transformations indicated in the third option, you get:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(4,-1\mright)\rightarrow A^{\doubleprime}(4-5,-1)=A^{\doubleprime}(-1,-1)[/tex][tex]A^{\doubleprime}(-1,-1)\rightarrow A^{\doubleprime}^{\prime}(1,-1)\rightarrow A^{\doubleprime\prime^{\prime}}(6,-1)[/tex]Notice that the points A and A'''' do not have the same coordinates.
• Fifth option:
Knowing the rule for a reflection across the y-axis, and knowing that to translate a point 9 units right you must add 9 to the x-coordinate of the points, you get:
[tex]A\mleft(4,1\mright)\rightarrow A^{\prime}\mleft(-4,1\mright)\rightarrow A^{\doubleprime}(-4+9,1)=A^{\doubleprime}(5,1)[/tex]Notice that the points A and A'' do not have the same coordinates.
Hence, the answers are:
• First option.
,• Second option.
Graph the inequality on the numberlineA + 5/3 > 1/2
Okay, here we have this:
Let's solve first A + 5/3 > 1/2:
[tex]\begin{gathered} A+\frac{5}{3}>\frac{1}{2} \\ A>-\frac{7}{6} \end{gathered}[/tex]So, according with this we obtain the following in the number line:
(05.01)Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:YearAnnual Tutoring Fee2005$12002008$1350A. What is the rate of change and initial value for Neil’s business? How do you know?B. Write an equation in slope-intercept form to represent the fees that Neil charges each year.
Solution:
Given that, the initial year (2005), the tutoring fee is $1200. Three years later (2008), the tutoring fee is $1350.
Thus, the rate of change, m, is;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ x_1=0,y_1=1200,x_2=3,y_2=1350 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{1350-1200}{3-0} \\ \\ m=\frac{150}{3} \\ \\ m=50 \end{gathered}[/tex]Then, the rate of change for Neil's business is 50 and the initial value is $1200.
(b) The slope-intercept form is written as;
[tex]\begin{gathered} y=mx+b \\ \\ \text{ Where }m\text{ is the rate of change, }b\text{ is the initial value;} \\ y\text{ is the annnua tutoring fee,}x=year \end{gathered}[/tex]ANSWER:
[tex]y(x)=50x+1200[/tex]