we have the expression
[tex](\frac{2m^6n^4}{6m^4})^3[/tex][tex](\frac{2m^6n^4}{6m^4})^3=\frac{(2^3)(m^{(18)})(n^{(12)})}{(6^3)(m^{(12)})}[/tex]simplify
[tex]\frac{(8)(m^{(18-12)})(n^{(12)})}{216}=\frac{(m^6)(n^{(12)})}{27}[/tex]Determine whether the graph represents a function.
A, the relation is not a function
in order for something to be a function, x (the input) can't repeat itself more than once
Larry says all numbers that have a 2 in the one's place are composite numbers. Explain if Larry is correct or incorrect.
A composite number is defined as a whole number that have more than two factors; from this definition we conclude that all whole numbers that are not prime are composite numbers.
Since all even numbers are not prime we conclude that Larry is correct; all numbers that have a 2 in the one's place are composite. In fact all even numbers are composite with exception of 2 itself.
Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
entionaction f(x) = 4.12x +12. If f(x) = -2(5)*, what is f(2)?A100B.20fC227-2050C. -20D. -50boioht of 144I
Problem
We have the following expression given:
f(x)= -2(5)^x
And we want to find f(2)
Solution
so we can do the following:
f(2)= -2 (5)^2 = -2*25 = -50
5 cm3 cm3 cm5 cm3 cmPrisma5 cmPrism BWhich of the following statements are true about the solids shown above?Check all that apply.A. Prisms A and B have different values for lateral surface area.O B. Prism B has a total surface area of 110 cm?O C. Prism A has a lateral surface area of 60 cm?D D. Prism B has a larger surface area.
Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.
The lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_A=2(5\times3)+2(5\times3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}[/tex]Similarly, the lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_B=2(3\times5)+2(5\times5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}[/tex]Clearly, prisms A and B have different values of lateral surface area.
So option A is the correct statement.
The total surface area is the sum of all the faces of the solid.
Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.
The total cross section area of prism B is calculated as,
[tex]\begin{gathered} A_B=2(5\times3) \\ A_B=30 \end{gathered}[/tex]So the total surface area of prism B becomes,
[tex]\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}[/tex]The total surface area of prism B is 110 sq. cm.
So option B is also correct.
Note that we have already found that the lateral surface area of prism A is 60 sq. cm.
Therefore, option C is also correct.
The total cross section area of prism A is calculated as,
[tex]\begin{gathered} A_A=2(3\times5) \\ A_A=30 \end{gathered}[/tex]So the total surface area of prism A becomes,
[tex]\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}[/tex]The total surface area of prism A is 90 sq. cm.
It is oberved that prism B has a larger surface area.
So, option D is also correct.
Hence, we can conclude that all the given statements are correct.
10.1.3The hour hand of a clock moves from 5 to 9 o'clock. Through how many degrees does it move?
Step 1: Lets calculate angle on each hour hand
since the wall clock takes the shape of a cirle
Therefore,
The total angles in a walk clock is 360°
Angle on each hour hand is
There are 12 hour hands on the clock ,
Therefore,
[tex]\begin{gathered} \text{Angle on each hour hand is =}\frac{360^0}{hands\text{ on the clock}}^{} \\ \text{Angle on each hour hand =}\frac{360^0}{12}=30^0 \end{gathered}[/tex]Since the hour hand moved from 5 o'clock to 9 o'clock
It has moved a distance of (9 - 5)= 4 hands on the clock
If each hand on the clock=30°
Therefore,
The angle in degrees moved through 4 hour hands on the clock will be calculated as,
[tex]\begin{gathered} \text{Angle moved = angle on each hand}\times no\text{ of hands moved} \\ \text{Angle moved=30}^0\times4=120^0 \end{gathered}[/tex]The hour hand of the clock moved from 5 o'clock to 9 o'clock through an angle of 120°
I Need some help on this assignment Also the second half to the problem how much will be spent on the job from the 10 to 20th day
Explanation
[tex]f(x)=4.1x+1.9[/tex]
where x is the number of days since the start of the job
and f(x) is the rate of change
Step 1
a)find the total expenditure if the job takes 12 days
so, as x represents the number of days, just replace and calculate
let x= 12
[tex]\begin{gathered} f(x)=4.1x+1.9 \\ f(12)=4.1(12)+1.9 \\ f(12)=49.2+1.9 \\ f(12)=51.1 \end{gathered}[/tex]so
a) 51.1
Step 2
now, let's find the total spent on the job from the 10 to 20th day
a) find the x value ( number of days since the job started)
x= 20 days-10dys= 10
so
x= 10
may ou solve the system of linear equations by substitution
y= 11 + 4x
3x +2y = 0
Put the first equation into the second one. (replace the value of y)
3x +2 (11 + 4x) = 0
Solve for x:
3x + 22 + 8x = 0
3x+8x = -22
11x = -22
x = -22/11
x = -2
Replace x=-2 in the first equation and solve for y
y= 11 + 4 (-2)
y= 11-8
y= 3
Solution:
x= -2 , y=3
A population grows according to an exponential growth model. The initial population is 224 and the population after one year is 263. Complete the formula where P is the population and n is the number of years.: P=224*(___)n
Round your answer to three decimal places.
The equation of the population function is is P = 224(1.17)ⁿ
How to complete the equation?From the question, the given parameters are:
Initial population = 224Population after one year = 263The above parameters imply that the rate of change of the population every year is
Rate = Population after one year/Initial population
Substitute the known values in the above equation
So, we have
Rate = 263/224
Evaluate the quotient
Rate = 1.17
The exponential function can be represented as
P = Initial population * (Rate)ⁿ
So, we have
P = 224(1.17)ⁿ
Hence, the complete equation is P = 224(1.17)ⁿ
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The required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
As per the question, the population of the 2 years are given as 224 and the preceding year's population is 263 and equation is illustrated the exponential growth is given as P = 224(__)ⁿ. The blank space in the equation is to be filled.
The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
The given function of the population is incomplete as rate of growth is missing, So,
The rate is given as,
Rate = 263 - 224 / 224
Rate = 0.17 or 17%
Growth = 1 + 0.17 = 1.17
now, put this growth rate in the blank space.
So,
P = 224 (1.17)ⁿ
Thus, the required rate of the increase in the population is 17% and the equation is fulfilled as P = 224 (1.17)ⁿ.
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What is the complement of P(A) if P(A) = 0.52P(A) =
Given
P(A) = 0.52
Find
complement of P(A)
Explanation
As we know sum of probabilities is equal to one,
so ,
[tex]\begin{gathered} P(A)+P^{\prime}(A)=1 \\ P^{\prime}(A)=1-0.52 \\ P^{\prime}(A)=0.48 \end{gathered}[/tex]Final Answer
Therefore, the complement of P(A) = 0.48
find the exact values of the six trigonometric functions of the angle 0 shown in the figure(Use the Pythagorean theorem to find the third side of the triangle)
The right angled triangle is given with reference angle theta.
The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;
[tex]\begin{gathered} \text{Adj}^2+3^2=5^2 \\ \text{Adj}^2=5^2-3^2 \\ \text{Adj}^2=25-9 \\ \text{Adj}^2=16 \\ \text{Adj}=\sqrt[]{16} \\ \text{Adj}=4 \end{gathered}[/tex]Therefore, the trigonometric functions of angle theta are shown as follows;
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp}=\frac{3}{5} \\ \cos \theta=\frac{adj}{hyp}=\frac{4}{5} \\ \tan \theta=\frac{opp}{adj}=\frac{3}{4} \\ \csc \theta=\frac{hyp}{opp}=\frac{5}{3} \\ \sec \theta=\frac{hyp}{adj}=\frac{5}{4} \\ \cot \theta=\frac{adj}{opp}=\frac{4}{3} \end{gathered}[/tex]Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
If f(x) = x + 1, find f(x + 7). Hint: Replace x in the formula by x+7.f(x + 7) =
The original function is:
[tex]f(x)\text{ = x+1}[/tex]We want to find the value of the function when the input is "x + 7". So in the place of the original "x" we will add "x+7".
[tex]\begin{gathered} f(x+7)\text{ = (x+7)+1} \\ f(x+7)\text{ = x+7+1} \\ f(x+7)\text{ = x+8} \end{gathered}[/tex]The value of the expression is "x + 8"
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
price of gas at store was 4.29 per gallon the next week it went up .55 and down .25 and back up 8.30 and finally it went down$.15 what is the price per gallon now
The final price of gas per gallon after number of reduction and increment is $12.74.
Given,
The price of gas at store = 4.29 per gallon
The increased amount of gas = 0.55
The new price of gas = 4.29 + 0.55 = 4.84 per gallon
Then decreased 0.25. So, the price of gas = 4.84 - 0.25 = 4.59 per gallon
Again the price increases 8.30 and the new price become, 4.59 + 8.30 = 12.89 per gallon
Then, the price of gas finally went down to .15.
Therefore, the price of gas now is:
12.89 - 0.15 = 12.74
That is, the final price of gas per gallon after number of reduction and increment is $12.74.
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Which compound inequality does the number line represent
The compound ineqality which the number line represents will be 5x ≥ -15 or 5x ≤ 10 so option (B) must be correct.
What is inequality?
A difference between two values reveals whether one is greater, smaller, or fundamentally different from the other.If the sides are not equal, an expression in mathematics is said to be unequal. The result of comparing any two values is a determination of whether one is smaller, bigger, or equal to the value on the opposite side of the equation.In option (B) given that
5x ≥ -15
⇒ x ≥ -15/5
⇒ x ≥ -3
And
5x ≤ 10
⇒ x ≤ 10/5
⇒ x ≤ 2
By looking at the number line it is clear that the blue line is greater than -3 and less than 2 hence it will be correct.
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X -5x+4 =015.x+6=0A rectangular painting is 3 feet shorter in length than it is tall (height).12. Write a polynomial to represent the area of the painting.13. Write a polynomial to represent the perimeter of the painting.14. The painting has the unique quality of having an area that has a value that is equal to the value of theperimeter. Find the height of the painting.15. What is the extraneous solution to the polynomial created when the area is set equal to the perimeter?
The rectangular painting is 3 feet shorter in length than in height.
Let "x" represent the painting height, then its length can be expressed as "x-3"
12.
The area of the rectangular painting can be calculated by multiplying its length by its height.
[tex]A=l\cdot h[/tex]For the painting
h=x
l=x-3
-Replace the formula with the expressions for both measurements:
[tex]A=(x-3)x[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} A=x\cdot x-3\cdot x \\ A=x^2-3x \end{gathered}[/tex]The polynomial that represents the area of the painting is:
[tex]A=x^2-3x[/tex]13.
The perimeter of a rectangle is calculated by adding all of its sides, or two times its length and two times its height. You can calculate the perimeter of the painting as follows:
[tex]P=2l+2h[/tex]We know that
h=x
l=x-3
Then the perimeter can be expressed as follows:
[tex]P=2(x-3)+2(x)[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} P=2\cdot x-2\cdot3+2x \\ P=2x-6+2x \end{gathered}[/tex]-Order the like terms together and simplify them to reach the polynomial:
[tex]\begin{gathered} P=2x+2x-6 \\ P=4x-6 \end{gathered}[/tex]14.
The painting has the unique quality of having an area that is equal to the value of the perimeter, then we can say that:
[tex]A=P[/tex]-Replace this expression with the polynomials that represent both measures:
[tex]x^2-3x=4x-6[/tex]To solve the expression for x, first, you have to zero the equation, which means that you have to pass all therm to the left side of the equation. Do so by applying the opposite operation to both sides of the equal sign.
[tex]\begin{gathered} x^2-3x-4x=4x-4x-6 \\ x^2-7x=-6 \\ x^2-7x+6=-6+6 \\ x^2-7x+6=0 \end{gathered}[/tex]We have determined the following quadratic equation:
[tex]x^2-7x+6=0[/tex]Using the quadratic formula we can calculate the possible values for x. The formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient that multiplies the quadratic term
b is the coefficient that multiplies the x term
c is the constant of the quadratic equation
For our equation the coefficients have the following values:
a=1
b=-7
c=6
Replace these values in the formula and simplify:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]Next is to calculate the addition and subtraction separately:
-Addition
[tex]\begin{gathered} x=\frac{7+5}{2} \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{7-5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]The possible values of x, i.e., the possible heights of the painting are:
x= 6ft
x=1 ft
15.
To determine the extraneous solution created when the area was set equal to the perimeter you have to calculate the corresponding length for both possible values of the height:
For the height x= 1ft, the corresponding length of the painting would be -2ft. This value, although mathematically correct, is not a possible measurement for the painting's length since these types of measures cannot be negative.
HELP ASAP
QUESTION IS ATTACHED!
Answer:
(2,8) and (-6,0)Step-by-step explanation:
(3,9)
(-5*3) +( 3*9) > 12
-15 + 27 > 12
12 > 12
not true
(-5,5)
(-5*5) + (3*5) > 12
-25 + 15 > 12
-10 > 12
not true
(3,-6)
(-5*3) + (3*-6) > 12
-15 + -18 > 12
-33 > 12
not true
(-2,-5)
(-5*-2) + (3*-5) > 12
10 + -15 > 12
5 > 12
not true
(2,8)
(-5*2) + (3*8) > 12
-10 + 24 > 12
14 > 12
true(-6,0)
(-5*-6) + (3*0) > 12
30 + 0 > 12
30 > 12
trueQuestion 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo
If :
[tex]x^2-16[/tex][tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{16}=4 \end{gathered}[/tex]Then:
[tex]x^2-16\text{ =(x-4)(x+4)}[/tex]Answer: ( x - 4 ) ( x + 4 )
Solve the equation 2x^3 – 5x² + x + 2 = 0 given that 2 is a zero of f (x) = 2x^3 – 5x^2 + x +2.
Hence, 2 is a zero of f(x). That is x - 2 is a factor of f(x).
So we can find
[tex]\frac{2x^3-5x^2+x+2}{x-2}[/tex][tex]\Rightarrow\frac{2x^3-5x^2+x+2}{x-2}=2x^2-x-1[/tex][tex]\text{Next we solve }2x^2-x-1=0[/tex][tex]\begin{gathered} \Rightarrow2x^2-x-1=0 \\ 2x^2+x-2x-1=0 \\ x(2x+1)-1(2x+1)=0 \\ \Rightarrow(x-1)(2x+1)=0 \\ \Rightarrow x-1=0\text{ or 2x+1=0} \\ \Rightarrow x=1\text{ or 2x=-1} \\ x=1\text{ or x =-}\frac{1}{2} \end{gathered}[/tex]Hence,
[tex]x=2,1,\text{ or -}\frac{1}{2}[/tex]Swine Flu is attacking Springfield. The function below determines how many people have swine where t=time in days and S=the number of people in thousands.
A.find s(4)
[tex]\begin{gathered} s(4)=9(4)-4 \\ s(4)=36-4 \\ s(4)=32 \end{gathered}[/tex]B. means that in 4 days there will be 32000 infected people
C. find t to S(t)=23
[tex]\begin{gathered} 23=9t-4 \\ 9t=23+4 \\ t=\frac{27}{9} \\ t=3 \end{gathered}[/tex]D. means there will be 23,000 infected people after 3 days
E. Graph
to draw the line we need two points which we already have but we will add another to make a table of 3 values the new value is t=1
[tex]\begin{gathered} s(1)=9(1)-4 \\ s(1)=5 \end{gathered}[/tex]table
graph
How do you Graph g(x)=x^5-2x^4 ?
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
If I complete this review, then I will do well on the test. If I do well on the test. If I do well on the test, then I will get an “A” on my progress report. Make a conclusion using the law of syllogism
Law of syllogism:
If p, then q
If q, then r
Conclude:
If p, then r
Given situation:
p: complete this review
q: do well on the test
r: get an “A” on my progress report
If p, then q: If I complete this review, then I will do well on the test
If q, then r: If I do well on the test, then I will get an “A” on my progress report
Conclusion:
If p, then r: If I complete this review, then I will get an “A” on my progress report
Using the GCF you found in Part B, rewrite 72 + 81 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work.
The factors of 72 and 81 are
[tex]\begin{gathered} 72=2^3\cdot3^2 \\ 81=3^4 \end{gathered}[/tex]Therefore, their GCF is equal to 3^2=9
Then,
[tex]72+81=9\cdot8+9\cdot9=9(8+9)[/tex]The answer is 9(8+9).
The factors of 8 and 9 are
[tex]\begin{gathered} 8\to2,4,8 \\ 9\to3,9 \end{gathered}[/tex]The Terrell Middle School wants to plant a community garden. They plan togrow and harvest vegetables, which will then be sold to raise funds for futuregardening.1. The science teacher, Ms. Maeda, wants the school to start composting.She borrows $392 from a school fund for supplies to make thecompost bins.Part AStudents plan to pay back half the debt now through fundraising,and the rest after the harvest. Write and solve an equation to representthe debt they will repay through fundraising. Use a negative integer toshow debt.
Total money $392
half of $392 is 196
one half would be paid through fundraising
The debt would be the other half
[tex]\begin{gathered} The\text{ debt} \\ x=\frac{-1}{2}(392) \\ x=-196\text{ dollars} \end{gathered}[/tex]THE FINAL ANSWER
x=-196 dollars
Ready for me for a quadratic function with vertex (3,9)
We have to write an equation of a quadratic function that has a vertex at (3,9) and pass through the origin.
We can use the vertex form of the quadratic equation:
[tex]y=a(x-h)^2+k[/tex]where the vertex has coordinates (h,k).
In this case, (h,k) = (3,9).
From the formula we can see that the parameter a that can take any value and still have the same vertex. We will use the parameter "a" to make it pass through the origin.
The vertex form of the equation is then:
[tex]y=a(x-3)^2+9[/tex]As it pass through the origin, then the equation should be satisfied when x = 0 and y = 0:
[tex]\begin{gathered} 0=a(0-3)^2+9 \\ 0=a(-3)^2+9 \\ 0=a\cdot9+9 \\ -9=9a \\ -\frac{9}{9}=a \\ a=-1 \end{gathered}[/tex]Then, as a = -1, we can write the equation as:
[tex]y=-(x-3)^2+9[/tex]Answer: An example of quadratic function with vertex (3,9) that pass through the origin is y = -(x-3)² + 9.
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 6. A(-3, 8), B(3, 2), C(7,1), D(5,-1)m(AB) m(CD) Types of Lines
in which quadrant is the given point located (2,-4)
Answer: 4th Quadrant
Step-by-step explanation:
When plotted, the point (2, -4) lies in the 4th quadrant.
A cubic equation has zeros at -2, 1, and 3 a) Write an eqn for a polynomial function that meets the given conditions.b) Draw the graph of a polynomial function that meets the given conditions.
we know that
A cubic equation has zeros at -2, 1, and 3
so
the factors of the cubic equation are
(x+2), (x-1) and (x-3)
Part a
The equation of a polynomial is
[tex]P(x)=(x+2)\cdot(x-1)\cdot(x-3)[/tex]Applying distributive property
[tex]\begin{gathered} P(x)=(x^2-x+2x-2)\cdot(x-3) \\ P(x)=(x^2+x-2)\cdot(x-3) \end{gathered}[/tex]Applying distributive property again
[tex]P(x)=x^3-3x^2+x^2-3x-2x+6[/tex]Combine like terms
[tex]P(x)=x^3-2x^2^{}-5x+6[/tex]Part b
using a graphing tool
see the attached figure below
jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Jessica bought 4 gallons of paint. Of that, she used 3/4 to paint. So the ammount she used was
[tex]4\cdot(\frac{3}{4})=\frac{4\cdot3}{4}=3[/tex]So she used 3 gallons of paint.
