We are given the following expression:
[tex]8.\mleft(2+3\mright)^2-4^2[/tex]To solve the expression we will add the numbers inside the parenthesis:
[tex]8.(2+3)^2-4^2=8(5^2)-4^2[/tex]Now we solve the squares:
[tex]8(5^2)-4^2=8(25)-16[/tex]Now we solve the product:
[tex]8(25)-16=200-16[/tex]Now we solve the operation:
[tex]200-16=184[/tex]Therefore, the expression is equivalent to 184.
of the arithmetic sequence -10, -25, -40, ...
Find the 81st term
The 81st term of the arithmetic sequence -10, -25, -40, ... is -1210
Here is a step-by-step explanation The common difference in this sequence,
d = a2 -a1
let a2 = -25 and a1 = -10
d= -25 - (-10)
d = -15
the common difference (d) = -15
To find the n term we use :
an= a1+ (n-1)d
Therefore,
a81 = -10 + (81-1)(-15)
= -1210
The 81stterm of the arithmetic sequence -10, -25, -40, ... -1210
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The distance to the grocery store is 13.456 miles round this distance to the nearest tenth
Answer:
Your answer is 13.50
Classify the following lines Y = 1 X – 2 3 & – 60 + 2y = 18 Intersecting, but not perpendicular Parallel Perpendicular The same line
7) We rearrange the second equation to compare it to the first one:
[tex]\begin{gathered} -6x+2y=18 \\ 2y=6x+18 \\ y=3x+9 \end{gathered}[/tex]The slopes are m1=1/3 and m2=3. They are not equal, nor negative reciprocals, so they are not parallel nor perpendicular. As they don't have the same slope, they will intersect.
Answer: Intersecting but not perpendicular.
8)
[tex]\begin{gathered} 2x+3y=10 \\ 3y=-2x+10 \\ y=-\frac{2}{3}x+\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} -3x+2y=11 \\ 2y=3x+11 \\ y=\frac{3}{2}x+\frac{11}{2} \end{gathered}[/tex]The slopes are negative reciprocals:
[tex]m_1=-\frac{1}{m_2}[/tex]As the slopes are negative reciprocals, both lines are perpendicular.
Answer: Perpendicular.
Sammi had a total of 25 ft of ribbon. She cut off 13 ½ feet to keep, the remaining fabric she cut into 3 inch sections to make ribbons. How many ribbons would she be able to make?
First, find the total length of the remaining fabric by substracting 13 1/2 from 25:
[tex]\begin{gathered} 25-13\frac{1}{2} \\ =25-13-\frac{1}{2} \\ =12-\frac{1}{2} \\ =11\frac{1}{2} \end{gathered}[/tex]Since one feet equals 12 inches, multiply 11 1/2 by 12 to find the total length of the remaining fabric in inches:
[tex]\begin{gathered} 11\frac{1}{2}\times12=11\times12+\frac{1}{2}\times12 \\ =132+\frac{12}{2} \\ =132+6 \\ =138 \end{gathered}[/tex]Since each ribbon takes 3 inches, divide 138 over 3 to find the total amount of ribbons that can be made:
[tex]\frac{138}{3}=46[/tex]Therefore, Sammi is able to make 46 ribbons.
6.0 x 10^4 ÷ 4.0 x 10^8
Scientific notation
The scientific notation for 6.0 x 10^4 ÷ 4.0 x 10^8 is 1.5 × 10^-4.
Whet is scientific notation?It should be noted that scientific notation simply means the power format that is used for expressing numbers that are too large or two small.
Based on the information given, the number illustrated is given as:
6.0 x 10^4 ÷ 4.0 x 10^8
It should be noted that since we are dividing,, we'll have to subtract the powers. This will be illustrated this
= 6.0 x 10^4 ÷ 4.0 x 10^8
= (6.0 / 4.0) × 10^(4 - 8)
= 1.5 × 10^-4
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Keywords Key Concept The total area of all surfaces, or faces, of a solid is called the surface area of the solid. Think of painting all the faces of a toy box for a baby's room. The paint covers the surface area of the toy box. net prism pyramid surface area Area of each face combined - surface area You can use the net of a three-dimensional figure, like a prism or pyramid to find the surface area of the solid. A soild can be unfolded into a net made up of polygons. The polygons within the net are the faces of the solld. You can use formulas to find the area of the pol zons vithin the net and find the sum of these areas. The sum equals the surface area of the solid
Solution
The solution is given in the image below
Brief Explanation
Let the sides of the cube be x
Each sides are squares
[tex]Area=x^2[/tex]Therefore, the surface area is
[tex]Surface\text{ }Area=6x^2[/tex]Help with number one a-f is all part of number one.Part e is: P(7).
Given the spinner that goes from 1 to 8, you can identify that the total number in the spinner is:
[tex]TotalNumbers=8\text{ }[/tex]a. By definition, Odds Numbers are those numbers that are not divisible by 2.
In this case, you can identify that the Odd Numbers the spinner has are:
[tex]1,3,5,7[/tex]Knowing that there are four Odd Numbers, you can determine that:
[tex]P(odds)=\frac{4}{8}[/tex][tex]P(odds)=\frac{1}{2}[/tex]b. By definition, Even Numbers are divisible by 2.
In this case, you can identify that the Even Numbers in the spinner are:
[tex]2,4,6,8[/tex]Knowing that there are four Even Numbers, you get:
[tex]P(evens)=\frac{4}{8}[/tex][tex]P(evens)=\frac{1}{2}[/tex]c. Since there is only one number 3:
[tex]P(3)=\frac{1}{8}[/tex]d. By definition:
[tex]P(A\text{ or}B)=P(A)+P(B)[/tex]Then:
[tex]P(4\text{ or }6)=P(4)+P(6)[/tex]Since there is only one number 4 and only one number 6:
[tex]P(4)=P(6)=\frac{1}{8}[/tex]Therefore:
[tex]P(4\text{ or }6)=\frac{1}{8}+\frac{1}{8}[/tex][tex]P(4\text{ or }6)=\frac{2}{8}[/tex][tex]P(4\text{ or }6)=\frac{1}{4}[/tex]e. Since there is only one number 7:
[tex]P(7)=\frac{1}{8}[/tex]f. Knowing that there is only one number 1:
[tex]P(1)=\frac{1}{8}[/tex]Hence, the answers are:
a.
[tex]P(odds)=\frac{1}{2}[/tex]b.
[tex]P(evens)=\frac{1}{2}[/tex]c.
[tex]P(3)=\frac{1}{8}[/tex]d.
[tex]P(4\text{ or }6)=\frac{1}{4}[/tex]e.
[tex]P(7)=\frac{1}{8}[/tex]f.
[tex]P(1)=\frac{1}{8}[/tex]3 feeding 54C 3. What is the constant of proportionality? What does it tell us about the situation? day 4. If we switched the columns in the table, what would be the constant of proportionality? Explain your reasoning. 5. Use d for number of days and f for amount of food in grams that a shrimp eats to write two equations that represent the relationship between d and f. 6. If a tank has 10 shrimp in it, how much food is added to the tank each day? 7. If the aquarium manager has 300 grams of shrimp food for this tank of 10 shrimp, how many days will it last? Explain or show your reasoning.
3) 0.6 grams per day
4) 1.67 grams per day
5) f = kd
k = f/d
Explanation:3) y = kx
where k = constant of proportionality
from the table, let x = number of days
y = food in grams
when x = 1, y = 0.6
we find k:
0.6 = k(1)
0.6 = k
Hence, the constant of proportionality is 0.6
It means the rate at which the shrimp is fed is 0.6grams per day
4) if columns are switched, the number of days = y
food in grams = x
let's use the same values but it will be interchanged:
when x = 0.6, y = 1
y = kx
1 = k(0.6)
1 = 0.6k
k = 1/0.6
k = 1.67 or 5/3
The rate at which the shrimp is fed is 1.67 grams per day
Here the rate is higher than the previous result. This is because the y value is greater then the x value.
5) if f = amount of food in grams
d = number of days
Since the relationship between the amount of food and number of days is proportional (it has beeen established previously), we would use the proportional equation:
y = f = amount of food in grams
x = d = number of days
f = kd (one equation)
it can also be written as:
f = kd
k = f/d (2nd equation)
it is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 19 students in the class, what is the probability that the first 3 presentations will be by Mika, Todd and Kelly? Express your answer as a fraction.
The probability of an event is the number of outcomes in which the event happens divided by the number of total outcomes.
The outcome we want is that the first 3 will be Mika, Todd and Kelly, in this order.
For this, we can thing in picks:
The first pick we can only pick Mika, so there is 1 possibilitie1:
[tex]1[/tex]For the second pick, we can pick only Todd, so 1 possibility:
[tex]1\times1[/tex]And for the third there is only Kelly, so 1 possibility:
[tex]1\times1\times1[/tex]For the following pick, we can pick any of the 16 students left, so 16 possibilities:
[tex]1\times1\times1\times16[/tex]And for the next we have one less, so 15 and so on until we picked everyone:
[tex]1\times1\times1\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1[/tex]We don't need to multiply all of this, because some of them will cancel afterwards.
Let's go the all possible outcomes. In this case, the first pick can be any of the 19 students:
[tex]19[/tex]And the next we have one less, and so on:
[tex]19\times18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1[/tex]The probability will be the number of outcomes of the event we want over the number of total outcomes, so:
[tex]P=\frac{1\times1\times1\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{19\times18\times17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}[/tex]Notice that all from 16 down will cancel out, so:
[tex]P=\frac{1\times1\times1}{19\times18\times17}=\frac{1}{5814}[/tex]So, the probability is 1/5814.
what is 200000000000000000000000000000 divided 4
Answer:5e+28
Step-by-step explanation:
It's very complicated.
in the graphs state wether these represent a function or not. PLEASE HELP !!
Answer:
graph 1 is a function
graph 2 is not
graph 3 is not
graph 4 is not
graph 5 is not
graph 6 is a function
Step-by-step explanation:
the statement below always sometimes or never true give at least two examples to support your reasoning the LMC of two numbers is the product of the two numbers discuss with a partner
Multiply (6 – 5i)2.Question 20 options:A) 11 – 60iB) 36 – 25iC) 11 + 60iD) 36 + 25i
Multiply (6 – 5i)2
Apply distributive property
6(2)+(-5i)(2)
12-10i
the answer is
12-10i
Part 2
we have
(6-5i)^2
so
(6)^2-2(6)(5i)+(5i)^2
36-60i+25i^2
Remember that
i^2=-1
substitute
36-60i+25(-1)
36-60i-25
combine like terms
11-60i
the answer is option A. Find the Value of x. SHOW YOUR WORK OR NO CREDITIMI
we can use pythagoras to solve the triangle
[tex]a^2+b^2=h^2[/tex]where a and b are sides and h the hypotenuse on this case we use half triangle to make a rigth triangle and apply pythagoras
a is 9, b is 20 and h the x
so replacing
[tex]\begin{gathered} 9^2+20^2=x^2 \\ \end{gathered}[/tex]solve for x
[tex]x=\sqrt[]{9^2+20^2}[/tex]and do the operatios
[tex]\begin{gathered} x=\sqrt[]{81+400} \\ x=\sqrt[]{481}\approx21.93 \end{gathered}[/tex]the value of x is 21.93 units
which trig function should you pick ? solve for x
To find the value of x and according to the given information, it is necessary to use cosine, which is the ratio between the adjacent side and the hypotenuse.
In this case the given angle is 43, it means that cos 43 is the ratio between 36 (adjacent side) and x (hypotenuse). Solve for x, this way:
[tex]\begin{gathered} \sin 43=\frac{36}{x} \\ x=\frac{36}{\sin 43} \\ x=52.8 \end{gathered}[/tex]x has a value of 52.8 (approximately).
a+3 divided by b =c
solve for a
The value of a in the equation given as a+3 divided by b =c is a = bc - 3.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario
From the information, a+3 divided by b =c. We have to make a the subject of the formula. This will be:
a + 3 / b = c
Cross multiply
a + 3 = bc
Subtract 3 from both sides
a + 3 - 3 = bc - 3
a = bc - 3
Therefore, a = bc - 3.
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Please help on this if m=45 fund m3
In m=45 fund m3 then 55;<3and <4 are complementary angles so m<3=90-m<4. Two complimentary angles add up to 90 degrees, and one is referred to as the other's "complement." Therefore, an angle's complement can be calculated by deducting it from 90 degrees. 90-x° is the counterpart of x°.
What is complementary angles?complementary angles are a pair of two angles that add up to give us 90 degree.Two angles are said to be supplementary if their sums total 180 degrees.When two angles add up to 90 degrees, they are said to be complementary. By deducting an angle from 90, one can find its complement. For instance, 90° - 40° = 50° is the complement of 40°. thus angle 4 and angle 3 are complementary anglesm<ACD=90 degree m<4=35 degree thereforem<ACD=m<4+m<390 degree=35 degree + m<3substract 35 from both sides90-35=35+m<3-3555=m<3m<3=55 degreeTo learn more about complementary angles refer to:
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Draw an angle in standard position such that the terminal side passes through the given point. (7, 4)
we have the point (7,4)
the x-coordinate and the y-coordinate are positive numbers
that means
The point lies on the First quadrant
see the figure below to better understand the problem
the value of the angle θ is equal to
tanθ=4/7
θ=29.7 degrees
A train goes at a constant speed. If it covers 150 miles in 2 1/2 hours, a What distance would it cover in 7 hours
Parent Function Description: A cubic (cubing) function that is reflected over thex axis, has a vertical stretch of 3 units, is shifted right 2 units, and is shifted down4 units.
Parent function:
f(x) = x³
that is reflected over the x axis
f(x) = -x³
has a vertical stretch of 3 units:
f(x) = -3x³
is shifted right 2 units:
f(x) = -3(x - 2)³
and is shifted down 4 units:
f(x) = -3(x - 2)³ - 4
Find the amplitude and period of ft=-tan0.4t
For function f(t)=-tan(0.4t) , there is no amplitude for tan function and period is equal to 5π/2.
As given in the question,
Given function:
f(t)=-tan(0.4t)
Standard equation for tan function:
f(x) =a tan(bx)
Compare both given and standard equation of a function,
a =-1
b =0.4
=4/10
=2/5
Period of a tangent function, y=a tan(bx),is the distance between any two consecutive vertical asymptotes.
Period of the given function =π/b
=π/(2/5)
=5π/2
Amplitude:
Tangent function have no amplitude as it has no maximum or minimum value.
It tends to ∞ to both the side of y -axis.
Therefore, for function f(t)=-tan(0.4t) , there is no amplitude for tan function and period is equal to 5π/2.
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A four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft is to be fenced. How many feet of fencing are required?
307.3 feet is the perimeter of fencing that is required to fence a four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.
What is perimeter?The distance around a shape or space is measured by its perimeter. The length of a shape's outline is what it is, simply put.
Children may have an easier time understanding this new term if they are given an analogy like walking completely around a shape or erecting a fence around a field.
When determining the size of a space, such as a garden or a room in your home, the perimeter is frequently used. The distance around your living room or garden, for instance, would be necessary if you wanted a new carpet or garden fence.
We need to simply find the perimeter of the polygon lot to find measure of fencing required.
Perimeter = sum of sides
= 12.7 + 85.3 + 110.8 + 98.5
= 307.3 ft
Thus, 307.3 feet of fencing are required to fence a four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.
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Solve |3x +18| = 6x
Please help
Answer: x = 2, 6
Step-by-step explanation:
To solve, we will isolate the variable. Since this deals with absolute value, we can assume we'll have two answers.
|3x + 18| = 6x
3x + 18 = 6x 3x + 18 = - 6x
18 = 3x 18 = 9x
6 = x 2 = x
x = 2, 6
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 9
Step-by-step explanation:
87 + 36 = 123
180 - 123 = 57
6x + 3 = 57
57 - 3 = 54
54/6 = 9
Please help!! College Algebra. Need answer fast!!
On the graph of y=25-x², a rectangle has four corners: one at the origin. The area of the rectangle is A=25x-x³.
Given that,
On the graph of y=25-x², a rectangle has four corners: one at the origin, one in quadrant I, one in the positive y-axis, and one in the positive x-axis. Refer to Figure.
We have to find as a function of x, express the rectangle's area A.
The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle.
The area of rectangle is A=xy
A=x(25-x²)
A=25x-x³
Therefore, the area of the rectangle is A=25x-x³.
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I need help with this problem. The table below shows that the number of miles driven by Samuel is directly proportional to the number of gallons he used. \text{Gallons Used}Gallons Used \text{Miles Driven}Miles Driven 3030 10411041 4646 1596.21596.2 4848 1665.61665.6 \text{What is the rate of gas usage, in miles per gallon?} What is the rate of gas usage, in miles per gallon?
The rate of gas usage, in miles per gallon is 34.7 miles per gallon.
What is a direct proportion?A direct proportion is used to show the constant of proportionality.
In this case, at 30 gallons, the miles used was 1041. Therefore the rate of gas usage will be:
= Miles travelled / Number of gallons
= 1041 / 30
= 34.7 miles per gallon
This shows the rate.
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Can you help me solve the problem by multiplying or dividing.
Given:
The width (w) of a rectangular swimming pool is
[tex]w=7x^2[/tex]The area (A) of the pool is
[tex]A=7x^3-42x^2[/tex]Required:
The expression for the length (l) of the pool.
Answer:
Let us find the expression for the length (l) of the pool.
The area (A) of the rectangular swimming pool is,
[tex]\begin{gathered} A=l\times w \\ 7x^3-42x^2=l\times7x^2 \\ l=\frac{7x^3-42x^2}{7x^2} \\ l=\frac{7x^3}{7x^2}-\frac{42x^2}{7x^2} \\ l=x-6 \end{gathered}[/tex]Final Answer:
The expression for the length (l) of the pool is,
[tex]l=x-6[/tex]Fred has a spinner that is split into four equal sections: red, blue, green, and yellow. Fred spun the spinner 500 times. Which of the following would be a good estimate of the number of times the spinner lands on the green section? A. 142 B. 175 C. 250 D. 415
Answer
I don't know
asdnsiuuuuuuuuuuuuuuuuuuuuuuuuuuwlefnhiug4efbglvliaufngkrhbg
The Jacksons bought a $276,000 condominium. They made a down payment of S43,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1396.96 on their mortgage until it was paid off.Х$?(a) What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?si(b) How much interest did they pay on the mortgage?si
(a) What was the total amount they ended up paying for the condominium
(including the down payment and monthly payments)?
We need to calculate the total monthly payments, plus the down payment.
[tex]=1396.96\cdot30\cdot12+43000=545905.60[/tex]So, the total amount they ended up paying was $545,905.60
(b) How much interest did they pay on the mortgage?
The interest they pay is: $269,905.60
[tex]=545905.60-276000.00=269905.60[/tex]16) F(x) = (x + 1)exponetn (2) Identify the function family to which this belongs. A Absolute Value B Constant CLinear D Quadratic
D quadratic
Explanation
[tex]f(x)=(x+1)^2[/tex]
you can easily identify a function with this :
if the exponent of the variable (x) is 1 , then it is a linear function:example
[tex]\begin{gathered} y=x,\text{ linear function} \\ y=3x+8 \end{gathered}[/tex]if the exponent of the variable (x) is 2 , then it is a quadratic function
[tex]\begin{gathered} y=x^2 \\ y=(x+1)^2 \end{gathered}[/tex]the absolute value has this symbol
[tex]y=\left|x\right|[/tex]a constant function is a number, with no variable, example
[tex]\begin{gathered} y=4 \\ Y=-7 \end{gathered}[/tex]so, the answer is D quadratic
