Answers
Answer:
x = 3Step-by-step explanation:
given:
f(x) = g(x)
f(x) = x³ - 3x² + 2
g(x) = x² - 6x + 11
find: the value of x
solution:
as given f(x) = g(x) equate each side x³ - 3x² + 2 = x² - 6x + 11 combine similar terms and equate to zero: x³ - 4x² + 6x - 9 = 0 solve by factoring: (x - 3) (x² - x + 3) use the Zero factor principle: x - 3 = 0 x = 3 for x² - x + 3 = 0 ----this is a complex solution.
therefore, the value of x = 3
Step-by-step explanation:
[tex]
\underline{\bf{Given\::}}
Given:
\underline{\bf{To\:find\::}}
Tofind:
\underline{\bf{Explanation\::}}
Explanation:
\boxed{\bf{\frac{1}{f} =\frac{1}{v} -\frac{1}{u} }}}}
\begin{gathered}\longrightarrow\sf{\dfrac{1}{-10} =\dfrac{1}{v} -\dfrac{1}{-30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-10} +\dfrac{1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{-3+1}{30} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\cancel{\dfrac{-2}{30} }}\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{-15} }\\\\\\\longrightarrow\sf{v=-15\:cm}\end{gathered}
⟶
−10
1
=
v
1
−
−30
1
⟶
v
1
=
−10
1
+
30
1
⟶
v
1
=
30
−3+1
⟶
v
1
=
30
−2
⟶
v
1
=
−15
1
⟶v=−15cm
\boxed{\bf{M \:A \:G \:N\: I \:F \:I \:C\: A\: T \:I \:O\: N :}}
MAGNIFICATION:
\begin{gathered}\mapsto\sf{m=\dfrac{Height\:of\:image\:(I)}{Height\:of\:object\:(O)} =\dfrac{Distance\:of\:image}{Distance\:of\:object} =\dfrac{v}{u} }\\\\\\\mapsto\sf{m=\cancel{\dfrac{-30}{-15}} }\\\\\\\mapsto\bf{m=2\:cm}\end{gathered}
↦m=
Heightofobject(O)
Heightofimage(I)
=
Distanceofobject
Distanceofimage
=
u
v
↦m=
−15
−30
↦m=2cm
Thus;
The magnification will be 2 cm .
[/tex]
Related Questions
What is the x-intercept ?
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Answer:
-3
Step-by-step explanation:
What is the answer to the meaning of life, the universe, and everything
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Answer:
no idea
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
The answer to this question is 42 this is calculated by a super computer named deep for over 7.5 million years.
Solve for a
3a +1=4. With a 7 under it
Answers
Answer:
a=9
Step-by-step explanation:
(3a+1)/7=4
This deals with linear equations with one unknown.
Overview
Steps
Terms and topics
1 result(s) found
a=9
See steps
Step by Step Solution:
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(3*a+1)/7-(4)=0
Step by step solution :
STEP
1
:
3a + 1
Simplify ——————
7
Equation at the end of step
1
:
(3a + 1)
———————— - 4 = 0
7
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 7 as the denominator :
4 4 • 7
4 = — = —————
1 7
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(3a+1) - (4 • 7) 3a - 27
———————————————— = ———————
7 7
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
3a - 27 = 3 • (a - 9)
Equation at the end of step
3
:
3 • (a - 9)
——————————— = 0
7
STEP
4
:
When a fraction equals zero
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
3•(a-9)
——————— • 7 = 0 • 7
7
Now, on the left hand side, the 7 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
3 • (a-9) = 0
Equations which are never true:
4.2 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
4.3 Solve : a-9 = 0
Add 9 to both sides of the equation :
a = 9
One solution was found :
a = 9
Hope this helps! Please mark Brainliest!
us
How many milliliters are in
12 teaspoons?
1 tsp = 5 mL
12 tsp = [?] mL
Enter
Answers
explanation: 12x5=60
Please help!! I don’t know it
Answers
B=8
Y=2x+8
2) the slop is 2
3)the slope is 0
4)the slop is -4/3
2
The units of the floor plan at the right are in feet. Find the
perimeter and area of each room.
a. the kitchen
Kitchen
Bedroom
b. the bedroom
c. the bathroom
20 ft
Main
hallway
d. the closet
Closet
Bathroom
e. What is the area of the main hallway? Explain how
you could find this area using the area of each room
20 ft
Answers
Answer:
Step-by-step explanation:
a). Perimeter of the kitchen = total length of all sides
= 4 + 2 + 2 + 6 + 6 + 12 + 10 (Since side of one smallest square = 2 feet)
= 42 ft
Area of the kitchen = Area of the composite figure
= 4² + 2² + (6 × 12)
= 16 + 4 + 72
= 92 square feet
b). Perimeter of bedroom = 2(length + width)
= 2(12 + 8)
= 40 feet
Area of the bedroom = Length × Width
= 12 × 8
= 96 square feet
c). Perimeter of the bathroom = 2(9 + 4) = 26 feet
Area of the bathroom = 9 × 4 = 36 square feet
d). Perimeter of the closet = 2(6 + 8) = 28 feet
Area of the closet = 6 × 8 = 48 square feet
e). Area of the hallway = Total area of the floor plan - area of the (kitchen + bathroom + bedroom + closet)
Area of the floor plan = 20 × 20 = 400 square feet
Area of the hallway = 400 - (92 + 96 + 36 + 48)
= 400 - 272
= 128 square feet
What is the equation of this graph?
A. y = 2x + 7
B. y = -2x + 7
C. y = -2/7x + 7
D. y = -7/2x + 7
E. y = -7/2x + 2
Answers
(-9.5) to the power of 0
Answers
3. A new a bank customer with $3,000 wants to open
a money market account. The bank is offering a
simple interest rate of 1.9%
a. How much interest will the customer earn in 20 years?
Answers
Answer:
In 20 years, the customer earns 1330
Step-by-step explanation:
I =Prt
the formula for simple interest
P= 3000
r = 1.9% (0.019)
t = 20 years
(3500)(0.019)(20)= 1330
which is a unit rate? plis help :c
Answers
Answer:
6 hours : 1 book
Step-by-step explanation:
A unit rate is a rate with 1 in the denominator. If you have a rate, such as a price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.
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Answers
Answer:
6^9 over 6^9 is 1
Hope that helps
What is 0.233 as a fraction in simplest form.
Answers
Answer:
233/1000
Step-by-step explanation:
(i think) probably wrong
Answer:
i thing it's 236/1000
Step-by-step explanation:
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Steve and Brian are both avid bicyclists. Each week, Steve rides for a total of 2x hours at an average speed of x miles per hour.
sBrian rides 6 more hours a week than Steve, but at an average speed that is 4 miles per hour less than Steve's average speed.
Which of the following functions will give the total distance that Brian rides each week, in miles?
Answers
Answer:
m(x) = 2x^2 - 2x - 24
Step-by-step explanation:
We will use the speed formula for this.
d/t = s
d is distance
t is time
s is speed
since we are looking for a function that gives the distance, we must rewrite
the equation to have d on one side of the equation by itself. We will do this by multiplying both sides by t.
(d/t)t = (s)t
which simplifies to:
d = st
Now we must find out what s and t are.
t: Steve's time riding is 2x hours, and Brian's is 6 more hours, so
Brian's time riding is 2x + 6.
so t = 2x + 6.
s: Steve's speed is x mph. Brian's is 4 less than that so
s = x - 4.
Now we can plug in what we know the the formula we made: d=st
d = (2x + 6)(x-4)
now we can FOIL.
(2x)(x)= 2x^2
(2x)(-4)= -8x
(6)(x) = 6x
(6)(-4) = -24
d = 2x^2 - 8x + 6x - 24
simplify:
Answer: d = 2x^2 -2x - 24
p.s. This was my first time answering a question on Brainly, sorry if it
was not explained well. Let me know if you have questions.
What is the solution to
−(6m+8) =4(17−m)
Answers
Answer:
[tex]\boxed{m = -38}[/tex]
Step-by-step explanation:
[tex]-(6m+8) =4(17-m)[/tex]
→ Expand brackets
[tex]-6m-8=68-4m[/tex]
→ Add 8 to both sides to collect the whole numbers
[tex]-6m = 76-4m[/tex]
→ Add -4m to both sides to collect the m terms
[tex]-2m=76[/tex]
→ Divide both sides by -10 to isolate m
[tex]m=-38[/tex]
A number x minus 7 is at most 22?
Answers
The value of 30 - (2 - 4) ÷ (-2) is _____.
-16
31
-14
29
Answers
Answer:
29.
Step-by-step explanation:
Lois Lane leaves Metropolis driving 50 km/h. Three hours later, Superman leaves Metropolis to catch up to her, flying at 300 km/h.
When does Superman catch up with Lois?
Superman will catch up ____ hours after Lois left Metropolis.
Answers
Answer:
0.6 hours
Step-by-step explanation:
50t=300(t-3)
50t= 300t - 900
-250t=-900
t=3.6
dont forget to subtract supermans time as well
3.6-3= 0.6
Answer:
0.6 hours
Step-by-step explanation:
Select the correct answer.
Which statement is true about the slope of the graphed line?
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Answer:
A
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
0
What is the value of 12?
Answers
Answer:
1
Step-by-step explanation:
[remember: any number raised to the power of 0 is 1]
∴ 12^0 = 1
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What is the answer I don’t understand how to do it
Answers
Answer:
= -22
Step-by-step explanation:
In a simple way to say it, all you have to do is add.
Remember that two negatives being added together will remain a negative.
Think of a number line, -11 would be on the left side of the 0. If you subtract another 11, you move 11 spaces more to the left. This gives you -22.
Or simply add the 11 and then add the negative sign next to it.
-(11+11)= -22
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Given: Lines a and b are parallel and line c is a transversal. Prove: Angle2 is supplementary to Angle8 Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the missing reason in the proof? Statement Reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
Answers
Answer:
The correct option is;
Corresponding angles theorem
Step-by-step explanation:
Type of lines of lines a and b = Horizontal and parallel lines
The transversal to a and b = Line c
The angles between a and c labelled clockwise from the upper left quarter segment = 1, 2, 4 and 3
The angles between b and c labelled clockwise from the upper left segment = 5, 6, 8 and 7
Therefore, we have;
Statement [tex]{}[/tex] Reason
1. a║b, c is a transversal [tex]{}[/tex] Given
2. ∠6 ≅ ∠2 [tex]{}[/tex] Corresponding angles theorem
3. m∠6 = m∠2 [tex]{}[/tex] Definition of congruent
4. ∠6 is supp. to ∠8 [tex]{}[/tex] Definition of linear pair
5. ∠2 is supp. to ∠8 [tex]{}[/tex] Congruent supplement theorem
Corresponding angles are the angles located in spatially similar or matching corners of two lines that have been crossed by the same transversal. When the two lines having a common transversal are parallel, the corresponding angles will be congruent.
674
x 38
Multiply by the ones.
Multiply by the tens.
+ Add the partial products.
+
Answers
Answer:
25612
Step-by-Step Explanation:
Simple multiplication
There are 20 teachers and 705 students in Corey's school. What is the ratio of teachers to students?
Answers
Answer:
4:141
Step-by-step explanation:
first, wright out a ratio with what's given
20(teachers):705(students)
next, simplify the ratio by dividing both sides by the gcf
20: 705
20/5 : 705/5
4 : 141
Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of -36.14 degrees Celsius and a boiling point of 324.84 degrees Celsius . What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state?
Answers
Answer:
i. When the temperature is above [tex]616.712^{o}[/tex]F, it changes to gas.
ii. When the temperature is below [tex]-33.052^{o}[/tex]F, it changes to solid.
Step-by-step explanation:
Matter generally exists in either a solid, liquid or gaseous form. With each phase having a certain range of temperature.
Temperature scale of a given substance can be either in Celsius, Fahrenheit or Kelvin. And conversion from one scale to another can be achieved. Example, Celsius scale can be converted to Fahrenheit by:
F = [tex]\frac{9}{5}[/tex] θ + 32
where: F is the equivalent temperature in Fahrenheit, θ is the value of temperature in degree Celsius.
Given that: melting point of the substance = [tex]-36.14^{o}[/tex]C
⇒ F = [tex]\frac{9}{5}[/tex] x [tex]-36.14^{o}[/tex] + 32
= [tex]-33.052^{o}[/tex]F
The boiling point = [tex]324.84^{o}[/tex]C
F = [tex]\frac{9}{5}[/tex] x [tex]324.84^{o}[/tex] + 32
= [tex]616.712^{o}[/tex]F
The melting point of the substance is [tex]-33.052^{o}[/tex]F, and boiling point is [tex]616.712^{o}[/tex]F.
Therefore, the range of temperatures for which the substance is not in a liquid state are:
i. When the temperature is above [tex]616.712^{o}[/tex]F, it changes to gas.
ii. When the temperature is below [tex]-33.052^{o}[/tex]F, it changes to solid.
You start at (-3,0). You move down 2 units and left 1 unit. Where do you end?
Answers
Answer: should end up on (-4 , -2)
Step-by-step explanation:
place the items in order from lowest to highest degree of internal organization
stomach
digestive system
epithelial stomach cell
stomach lining tissue
Answers
Answer:
Simplest
1)Epithelial stomach cell
2)Stomach lining tissue
3)Stomach
4)Digestive system
Most complex
Answer:
1)Epithelial stomach cell
2)Stomach lining tissue
3)Stomach
4)Digestive system
I hope this helps
Are rational numbers closed under squaring?
Answers
Answer:
The integers are "closed" under addition, multiplication and subtraction, ... The rational numbers are "closed" under addition, subtraction, and multiplication
Step-by-step explanation:
4. 700 J of work is used to push an object for 12 seconds. What is the power of this machine?
Answers
Answer:
58.3333333333
Step-by-step explanation:
Last year at a certain high school, there were 50 boys on the honor roll and 100 girls on the honor roll. This year, the number of boys on the honor roll decreased by 8% and the number of girls on the honor roll decreased by 15%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary). pls help
Answers
Answer:
46 for boys and 85 for girls
Step-by-step explanation: