Answers
Answer:
-x^2-2
Step-by-step explanation:
So by looking at the two curves it appears that g(x) is simply a reflection of f(x) over the x-axis and then shifted 2 units down. So to reflect the parabola you simply make the x^2 negative to get -x^2 and then to go 2 units down you subtract 2 from the -x^2. This gives you the equation
[tex]g(x)=-x^2-2[/tex]
Related Questions
What is the product of (x² + x + 2) and (x² − 2x + 3)
Answers
Answer:
[tex]x^4-x^3+3x^2-x+6[/tex]
Step-by-step explanation:
Multiply each term in the first equation by all the terms in the second and add them together.
Calcular la edades actuales de una madre y sus dos hijos sabiendo que hace 14 años la dad de la madre era 5
veces la suma de las edades de los hijos en aquel momento, que dentro de 10 madre será la suma de las edades
que los hijos tendrán en ese momento y que cuando el hijo mayor tenga la edad actual de la madre, el hijo
menor tendrá 42 años.
Answers
The present age of mother and her daughter respectively are; 40 and 10 years respectively.
How to Solve Algebra Word Problems?Let x and y be the present age of mother and her daughter respectively.
Therefore;
x + y = 50
x = 50 − y .....(1)
After 20 years, mother's age will be twice her daughter's age at the time. Thus;
x + 20 = 2(y + 20)
x − 2y = 20 .....(2)
Plugging eq 1 into eq 2 gives us;
50 − y − 2y = 20
3y = 30
y = 10
Thus;
x = 50 − 10
x = 40
Thus, the present age of mother and her daughter is 40 and 10 years respectively.
Translation of the question into English is;
The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at the time. Find their present ages.
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P, Q and R are points in the same
horizontal plane. The bearing of
Q from P is 150° and the bearing
of R from Q is 060°.
If |PQ| = 5m and QR = 3m,
Find the bearing of R from P.
correct to the nearest degree./
Answers
Answer: 119°
Step-by-step explanation:
From the positive y-axis, all angles are measured clockwise
PR = PQ + QR = 5[150°] + 3[60°]
X = 5*sin150 + 3*sin60 = 5.1
Y = 5*Cos150 + 3*Cos60 = -2.83
TanA = X/Y
A = -61° = 61° East of South = 119° Clockwise
Therefore, the bearing of R from P is 119°
ASAP!!!!!!!!!!!!
PLEASE GIVE A STEP BY STEP EXPLANATION!!!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answers
The two transformations for fx and gx would be to shift by 6 units and also go up by 18.
What is a transformation?This is the term that is used in mathematics to describe the manipulation of a line or a shape.
a. The possible transformations that can be gotten here would be to shift to the left by 6 units from what we have in the graph and also shift to the top by 18.
b. How to solve for K in the transformationg of x = f(x - k) then
g(x)= f(x) + k
C. The value of k should be based on the way it changes based on the given points.
Vertically, g(x)=f(x) +18
Horizontally , g(x)=f(x-6)
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Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12? O X= -2. x = 1 O x= -2 x = 4 O x = 2. x = 4 O x = 2, x = 4
Answers
The values are x= -2 and x =4 of the given function f (x) =-5|x+1| +3
What is function?
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
According to the question,
The given function is
[tex]f(x) = -5|x + 1| + 3[/tex]
Here f(x) = -12
Substitute f(x) and solve for x
[tex]- 12 = -5|x + 1| + 3[/tex]
By subtracting 3 on both sides
[tex]- 12 - 3 = -5|x + 1| + 3 - 3[/tex]
[tex]- 15 = -5|x + 1|[/tex]
By dividing -5 on both sides
[tex]3 = |x + 1|[/tex]
We get absolute values for the function.
[tex]x + 1 = 3 , x + 1 = -3[/tex]
By subtracting 1 on both sides
[tex]x + 1 - 1 = 3 - 1 = 2\\\\x + 1 - 1 = - 3 - 1 = -4\\\\x = 2 , x = - 4[/tex]
Therefore, the values of x are 2 and - 4 of the given function f (x) =-5|x+1| +3
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An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the box as a function of the length of a side of the base, x.
Answers
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
[tex]= (5x \times x) + 2(h \times x) + 2(5x \times h)\\\\= (5x^2) + 2(\dfrac{12}{5x^2} \times x) + 2(5x \times \dfrac{12}{5x^2})\\\\\\= 5x^2 + \dfrac{24}{5x} + \dfrac{24}{x}[/tex]
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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A hostel has food for 60 days if after 15 days 500 more students joined th hostel and the food lasted for 40days only. How many students were there in hostel
Answers
Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
Need help with this geometric question
Answers
Answer: 95 degrees (not an answer choice)
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so the left part of the angle is 40 degrees.
Adjacent angles of a parallelogram are supplementary, so the right part of the angle is 55 degrees.
Adding these together, we get 95 degrees.
please solve using whatver method u want!
+brainest
ASAP
Answers
Answer:
System has no solutions.
Step-by-step explanation:
Double the first, change sign to the second. You get
[tex]6x-4y=8\\6x-4y=-7[/tex]
You need a quantity ([tex]6x-4y[/tex]) which, at the same time is both equal to 8 and -7, which is obviously impossible.
System has no solutions.
If the ordered pair (-5/2, y) lies on the graph of y=7-2x, find the value of y.
19/2
012
02
Answers
The correct answer is option B which is the value of Y will be 12.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
If the ordered pair (-5/2, y) lies on the graph of y=7-2x,
The value of Y will be calculated as:-
Y = 7 - 2x
Y = 7 - 2 ( -5/2 )
Y = 7 - ( - 5 )
Y = 7 + 5
Y = 12
Therefore the correct answer is option B which is the value of Y will be 12.
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Answer please! I need this!
Answers
Step-by-step explanation:
The top has been multiplied by 5 so multiply the bottom by 5, 2 x 5 = 10. also why is there a pig lol
The length of a golden rectangle is 35 cm. Find the width to the nearest centimeter.
17cm
25cm
22cm
29cm
16cm
Answers
Answer:
22 cm
Step-by-step explanation:
First we need to know that The golden number
= (1+√(5))÷2
= 1.61803398875 (in decimal)
………………………………………………
We get the length of a golden rectangle
by multiplying its width by the golden number itself.
Then
The width = 35÷ 1.61803398875
=21.631189606245
Solve the system of equation for y using Cramer's rule. Hint: The determinant of the coefficient matrix is -23.
Answers
Answer:
-4 option (c)
Step-by-step explanation:
Cramer rule : In this method, the values of the variables in the system are to be calculated using the determinants of matrices
if , D :determinant of the coefficient matrix
[tex]{D}_{x}:[/tex]determinant of the matrix with coefficients except x
then,
[tex]x=\frac{{D}_{x}}{D}[/tex]
similarly,
[tex]y=\frac{{D}_{y}}{D}[/tex]
[tex]z=\frac{{D}_{z}}{D}[/tex]
given,
D = -23
[tex]D_{y}[/tex] = [tex]det\left[\begin{array}{ccc}5&7&-1\\2&6&-2\\3&-7&2\end{array}\right][/tex]
[tex]D_{y}[/tex] = 92
therefore, y = 92/(-23)
y = -4 answer
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Which statement is correct when a scatterplot is constructed?
The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
Answers
Option A is the correct answer.
The independent variable is the input variable and should be represented by the x-axis.
What is Variable?A variable is a symbol and placeholder for a quantity that may change, or any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.
For the Scatterplot, out of given options,
Option A is the correct option which represents The independent variable is the input variable and should be represented by the x-axis.
Thus, The independent variable is the input variable and should be represented by the x-axis.
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An airplane is flying at an altitude of 26,843 feet. The plane descends (goes down) 1,284 feet. Then the plane ascends (goes up) another 5,832 feet.
Let a represent the altitude of the plane.
Which equation could be used to find the final altitude of the plane?
A. a = 26,843 + 1,284 + 5,832
B. a=26,843+1,284−5,832
C. a=26,843−1,284+5,832
D. a=26,843−1,284−5,832
Answers
Answer:
Hi
The answer is C
Step-by-step explanation:
Because it descend means goes down so it's minus and after that it ascends means goes up so it's plus so the answer will be -
26,843-1,284+5832
f(a)=3a^2+2a+7 find the value of f(a)
Answers
Answer:
Step-by-step explanation:
If a = 0, f(a) = f(0) = 0 + 0 + 7 = 7;
If a = 1, f(1) = 3(1^2) + 2(1) + 7 = 12;
and so on. Normally an 'a' value would be given as part of this problem.
Actually, the value of f(a) is given and is f(a) = 3a^2+2a+7 for input value a.
Using Triangle Congruence Theorems
Answers
There are a total of five theorems congruent triangles. They are summarized as:
SASSSSAASRHS and ASA.What are the definitions of the Theorems of Congruent Triangles?SAS - Side Angle Side
According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.
SSS - Side Side Side Rule
According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.
AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.
ASA - Angle Side Angle rule
According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.
RHS - Right Angle- Hypotenuse side Rule
According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.
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Answer:
AD=BC (given)
DC=DC (reflexive property)
DE=CE (converse of isosceles triangle thm)
<BCD=<ADC (given)
<ECD=<EDC (CPCTC)
TriangleADC=TriangleBCD (SAS)
Suppose that an examination consists of 10 questions with the choice A, B, C, and D. Assume that a student has no knowledge of the subject matter. Then what is the probability that: Guessing at most two correct answers? Guessing at least seven correct answers? Which type of probability distribution it has? Why? average five smokers pass a crain traat B. C. Suppose that an examination consists of 10 questions with the choice A , B , C , and D. Assume that a student has no knowledge of the subject matter . Then what is the probability that : Guessing at most two correct answers ? Guessing at least seven correct answers ? Which type of probability distribution it has ? Why ?
Answers
The probability of getting two correct answers will be 0.0625.
How to calculate the probability?The probability of getting two correct answers will be:
Probability of getting the correct answer will be:
= 1/4 = 0.25
The probability of getting two correct answers will be:
= 0.25 × 0.25
= 0.0625
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You are choosing between two different cell phone plans. The first plan charges a rate of
24 cents per minute. The second plan charges a monthly fee of $49.95 plus 11 cents per
minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first
and second plans. Give an equation for each in terms of t, and then find the number of
talk minutes that would produce the same cost for both plans (Round your answer to one
decimal place).
C₁ =____
C₂ =____
If you talk for
_____ minutes the two plans will have the same cost.
Answers
If you talk for 384.23 minutes the two plans will have the same cost.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
x is the number of minutes that will be used during a month:
C₁ = 0.24x
C₂ = 49.95 + 0.11x
So, when 1st = 2nd
0.24x = 49.95 + 0.11x
0.24x - 0.11x = 49.95
0.13x = 49.95
x = 49.95/0.13
x = 384.23 minutes
Hence, If you talk for 384.23 minutes the two plans will have the same cost.
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Maria rides her bicycle to school at a constant speed of 15 miles per hour.If the distance to school is 6 miles,how many minutes will it take Maria to get to school?EXPLAIN PLEASE
E. 10
F.15
G.24
H.30
Answers
Answer:
24 minutes
Explanation:
Given:
speed: 15 miles/hdistance: 6 milesFormula:
time taken = distance/speed
Applying the formula:
time taken = 6/15 = 0.4 hours = 24 minutes
Now
Speed=Distance/TimeTime=Distance/SpeedTime =6/15=0.4h=24minThe angles of a quadrilateral have measures m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =
(6x + 15)◦, m∠D = (6x −5)◦. Find the value of x. If a diagonal bisects ∠B and ∠D, what
type of quadrilateral is ABCD?
Answers
The value of x is 15° and the type of quadrilateral is a rhombus.
Quadrilateral
A quadrilateral is a polygon that has four sides.The sum of all angles of a quadrilateral is 360°.
Here, we are given,
m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦
So, we will have
7x+4x+5+6x+15+6x-5=360°
23x+15°=360°
23x=345°
x=345°/23°
x=15°
Hence, the angles of the quadrilateral are:
m∠A = (7x)◦=105°,
m∠B = (4x + 5)◦ =65°
m∠C =105°
m∠D = (6x −5)◦ =85°
Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.
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At a certain time of day, the angle of elevation of the sun is 80degree. Find the height of a tree whose shadow is 44 feet long.
Answers
The height of the tree is 249.5 feet
How to determine the height of the tree?The given parameters are:
Elevation angle = 80 degreesShadow length (L) = 44 feetLet the height of the tree be x.
So, we have:
tan(80) = x/44
Multiply both sides by 44
x = 44 * tan(80)
Evaluate
x = 249.5
Hence, the height of the tree is 249.5 feet
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What is the vertex of the quadratic function given in the table?
Answers
Answer:
The vertex is (-3,-2)
The vertex is basically the very top or very lowest, so you will notice how values around (-3,-2) are relatively the same in the y coordinate, but -2 is the "highest/lowest" so that's how you know it's a vertex.
If you try picturing the points in your head, you will see it make a U and at the bottom of the U is the vertex.
The y values are symmetric either side of x = -3 so the vertex is at (-3, -2)
This is enough information to identify the function is y =(x + 3)^2 - 2
If you currently makes 425 What is the gross they will earn If they work every week If the year
Answers
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
Answers
The width of the cooling tower at the base of the structure will be A. 36 meters.
How to calculate the width?From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.
Therefore, the width of the cooling tower at the base of the structure will be:
= 2 × ✓324
= 2 × 18
= 36
In conclusion, the width is 36 meters.
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Answer:
It is actually D
Step-by-step explanation:
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answers
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
Answers
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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what is the range of the ordered pairs shown in the graph?
Answers
D
Step-by-step explanation:
The points dx are at -1, 1, 2 and 3 so it must be D
Answer:
To find the range,
first see the value of each points -
first = (3,5)
second = (2,0)
third = ( 1,3)
fourth, ( -1, 2)
let's take X Axix to find the range
so the range is ( -1, 1 , 2 ,3)
Option D is correct
the length of a cell is 2/3 mm. If the area of the cell is 1/12 square mm, whtat is the width of the cell
Answers
Answer:
0.125 mm
Step-by-step explanation:
A/L=W
W=0.125
Find the greatest number which divides 6168, 2447, and 3118 leaving the same remainder in each case.
Answers
Answer:
Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.
