Given the following functions:
[tex]\begin{gathered} f(x)=6x^6+8x \\ g(x)=2x \end{gathered}[/tex]The weight of a bacterium is defined by multiplying the functions of f(x) and g(x).
So, the product of the functions will be as follows:
[tex]f(x)*g(x)=(6x^6+8x)*2x[/tex]We will use the distributive property to find the result as follows:
[tex]\begin{gathered} f(x)*g(x)=6x^6*2x+8x*2x \\ f(x)*g(x)=12x^7+16x^2 \end{gathered}[/tex]So, the answer will be 12x⁷+16x²
The table and the graph represent the rate at which two machines arebottling milk in gallons per second.
Given:
There are given the information about the two machines, one is in table form and another is in the graph.
Explanation:
We need to find the rate of change from both of the machines.
So,
For machine 1:
Choose two-point and find the slope by using the slope formula:
So,
The points are;
[tex](1,0.6),and,(2,1.2)[/tex]From the formula to find the rate of change:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]Then,
[tex]\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{1.2-0.6}{2-1} \\ r=\frac{0.6}{1} \\ r=0.6 \end{gathered}[/tex]Now,
For machine 2:
We need to choose two points from the graph.
So,
Two points are:
[tex](8,6),and,(16,12)[/tex]Then,
From the formula:
[tex]\begin{gathered} r=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ r=\frac{12-6}{16-8} \\ r=\frac{6}{8} \\ r=0.75 \end{gathered}[/tex]Final answer:
Hence, the machine 2 is faster at botting milk because the value of the rate of machine 2 is greater than the value of rate of machine 1.
Which statement about the following equation is true?
2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.
Answer:
The discriminant is greater than 0, so there are two real roots.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.2 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\If $b^2-4ac > 0 \implies$ two real roots\\If $b^2-4ac=0 \implies$ one real root\\If $b^2-4ac < 0 \implies$ no real roots\\\end{minipage}}[/tex]
Given equation:
[tex]2x^2-9x+2=-1[/tex]
Add 1 to both sides of the equation so that the equation equals zero:
[tex]\implies 2x^2-9x+2+1=-1+1[/tex]
[tex]\implies 2x^2-9x+3=0[/tex]
Compare the equation with ax²+bx+c=0:
a = 2b = -9c = 3Substitute the values of a, b and c into the discriminant formula and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(-9)^2-4(2)(3)\\&=81-4(2)(3)\\&=81-8(3)\\&=81-24\\&=57\end{aligned}[/tex]
As 57 > 0, the discriminant is greater than zero, so there are two real roots.
Answer:
B on Edge 23
Step-by-step explanation:
trust me bro
which number set(s) does -10 belong toirrational numberswhole numbersrational numbersintegersreal numberscounting or natural numbersNo number set describes this number.
Given:
The number is -10.
To describe the number:
Explanation:
Since 10 is a whole number and it has a minus sign.
So, -10 is an integer number.
Since it is an integer number.
So, it must be a rational number as well as the real number.
Therefore, -10 is a number that belongs to the sets
Integer numbers
Rational numbers
Real numbers
Final answer:
• Integer numbers
,• Rational numbers
,• Real numbers
please help me I’m really not understanding this my answer was completely wrong
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the table, we can see that:
Gross profit for Q 1 = 85 x 1000= 85,000
Gross profit for Q 2= 94 x 1000 = 94, 000
Hence the increase in Gross profit = 94,000 - 85,000 = 9000
Then,
[tex]\begin{gathered} \text{Percentage change = }\frac{9000}{85000}\text{ x 100} \\ =\frac{900000}{85000} \\ =\text{ 10}.58823529 \\ \approx\text{ 10. 6 \% ( to the nearest tenth )} \end{gathered}[/tex]CONCLUSION:
The percent change = 10. 6 % ( to the nearest tenth)
Find the coordinate point for that would make ABCD a rhombus. Answer Choices: (3,5), (5,1), (1,1), (3,4)
A rhomus has te following shape:
therefore, the top part is missing, if we analyze, it should be 5 on the y axis and 3 on the x axis.
Answer: (3,5)
1.Emily needs to make party hats in the shape of a cone. Shewants the hat to have a radius of 6 inches and a height of15 inches. What is the volume of the party hat?a) 565.2b) 94.2c) 2260.8d) 188.4
Emily needs to make party hats in the shape of a cone. She
wants the hat to have a radius of 6 inches and a height of
15 inches. What is the volume of the party hat?
a) 565.2
b) 94.2
c) 2260.8
d) 188.4
the volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
pi=3.14
r=6 in
h=15 in
substitute
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot6^2\cdot15 \\ V=565.2\text{ in3} \end{gathered}[/tex]answer is option A
The average American student is in class 330 minutes/day. How many seconds/day is this?
The given time duration is
330 minutes/day
So converting it into seconds, we know that 60 seconds is 1 minute, therefore,
[tex]330\frac{\text{ minutes}}{\text{day}}=330\times\frac{60\sec onds}{day}=19800\text{ seconds/day}[/tex]Thus the answer is 19800 seconds/day.
Patsy’s pizza sells one 20-inch cheese pizza or two 12-inch cheese pizzas for 11.99. Determine which size gives more pizza (A= 3.14r^2)
Since 20-inch pizza, means it is a circle with a diameter of 20 inches
Since the diameter is twice the radius, then
The raduis = 20/2 = 10 inches
Then the area of it is
[tex]\begin{gathered} A_1=\pi(r)^2 \\ A_1=3.14(10)^2 \\ A_1=3.14(100) \\ A_1=314 \end{gathered}[/tex]The area of the first pizza is 314 square inches
Since the diameter of the other area is 12 inches, then
The radius = 12/2 = 6 inches
Then the area of it is
[tex]\begin{gathered} A_2=3.14(6)^2 \\ A_2=3.14(36) \\ A_2=113.04 \end{gathered}[/tex]Then the area of the second pizza is 113.04 x 2 = 226.08 square inches
Since the area of the first offer is greater than the area of the second offer, then
The first size gives more pizza
If h(x) = 2x and k(x) =2x -k, what is h(k(x))?
If h(x) = 2x and k(x) =2x -k, then h(k(x)) would be:
h(k(x))= 2*(2x-k)
h(k(x))= 4x - 2k Using distributive property
Final answer is: h(k(x))= 4x - 2k
the trapezoids shown below are similar. find Y
Since it is given that trapezoids are similar so,
[tex]\begin{gathered} \frac{y}{25}=\frac{12}{15} \\ y=\frac{4}{5}\times25 \\ y=20 \end{gathered}[/tex]So value of y is 20.
Solve for the variable: 1 - p = 7
Given,
Solve for the variable,
[tex]1-p=7[/tex]Solution:
Take the variable on one side of the equation and the constant on another side of the equation.
[tex]\begin{gathered} -p=7-1 \\ -p=6 \\ p=-6 \end{gathered}[/tex]Thus, the value of p is -6.
Which statement about this equatiin is true? 3+x=2-3x
1. The equation has no solution
2. The equation has one solution
3. The equation has infinitely many solutions
The equation has only one solution.
What is solution of equation?Equation solutions are numerical numbers that meet the requirements of the equation. When our answers are used to replace the variables in the equations, true assertions are obtained.
A mathematical equation proves the equality of two expressions. There is a mathematical formula: 4 + 4 = 8. A mathematical formula that has one or more variables is called an algebraic equation. Therefore, (2x + 5 = 35) is a linear equation with one variable. Its graph is a straight line, and its first-degree variable is (x).
Given
3+x = 2-3x
3-2 = -3x - x
1 = -4x
x = -1/4
Hence, x has only one value.
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Match each equation with its solution set.2(5 – 4x) = 8x + 2a. no solution8(x + 5) = 8x + 40b. all real numbers2(5 – 4x) = 2 – 8xc. 1/28(x + 5) = 8x + 5d. 2
To match the equation with its solution set we need to solve each of them. Let's do that
First equation:
[tex]\begin{gathered} 2(5-4x)=8x+2 \\ 10-8x=8x+2 \\ 8x+8x=10-2 \\ 16x=8 \\ x=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Second equation:
[tex]\begin{gathered} 8(x+5)=8x+40 \\ 8x+40=8x+40 \end{gathered}[/tex]Since both sides of the equation are exactly the same expression we conclude that this equation is satisfied by all real numbers.
Third equation:
[tex]\begin{gathered} 2(5-4x)=2-8x \\ 10-8x=2-8x \\ 8x-8x=2-10 \\ 0=-8 \end{gathered}[/tex]Since the last line is a contradiction we conclude that this equation has no solutions.
Fourth equation:
[tex]\begin{gathered} 8(x+5)=8x+5 \\ 8x+40=8x+5 \\ 8x-8x=5-40 \\ 0=-35 \end{gathered}[/tex]Once again we have a contradiction in the last line, then this equation has no solutions.
Then the correct match is:
First equation with c.
Second equation with b.
Third equation with a.
Fourth equation with a.
Which numbers are irrational numbers?
Select each correct answer.
Responses
110−−√
square root of fraction 1 over 10 end fraction
116−−√
square root of fraction 1 over 16 end fraction
14√
square root of fraction 1 over 4 end fraction
12√
square root of fraction 1 over 2 end fraction
18√
square root of fraction 1 over 8 end fraction
Answer:Here I hope this helps
1/10=irrational
1/16=rational
1/4=rational
1/2=irrational
1/8=irrational
Step-by-step explanation: you can go into desmos graphing calculator and plug in each number into the square root and it will tell you if its irrational or not.
Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter
Explanation:
Taking into account the law of cosines, we can write the following equation:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Then, replacing the values for a, b, and c, we get:
[tex]\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}[/tex]Solving for cos A, we get:
[tex]\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ \frac{-15}{-24}=\frac{-24\cos A}{-24} \\ 0.625=\cos A \end{gathered}[/tex]Therefore, the value of angle A is:
[tex]\begin{gathered} \cos ^{-1}(0.625)=A \\ 51.3=A \end{gathered}[/tex]Now, we can use the law of sines, we can write the following equation:
[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]So, replacing the values and solving for B, we get:
[tex]\begin{gathered} \frac{\sin B}{2}=\frac{\sin 51.3}{5} \\ \sin B=\frac{\sin 51.3}{5}\times2 \\ \sin B=0.3121 \\ B=\sin ^{-1}(0.3121) \\ B=18.2 \end{gathered}[/tex]In the same way, Angle C is equal to:
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \frac{\sin C}{6}=\frac{\sin 51.3}{5} \\ \sin C=\frac{\sin51.3}{5}\times6 \\ \sin C=0.9365 \\ C=\sin ^{-1}(0.9365) \\ C=69.5 \end{gathered}[/tex]So, the answers are:
A = 51.3°
B = 18.2°
C = 69.5°
Heather is six years younger than her husband Ryan. Thesum of their ages is 52. How old is Ryan23293146
Let's begin by listing out the information given to us:
Ryan (r) = r
Heather (h) = r - 6
[tex]\begin{gathered} r+h=52 \\ h=r-6 \\ r+r-6=52 \\ 2r-6=52 \\ 2r=52+6 \\ 2r=58 \\ r=\frac{58}{2}=29 \\ r=29 \\ \\ \therefore Ryan^{\prime}s\text{ age is 29 years old} \end{gathered}[/tex]Therefore, Ryan is 29 years old
Answer:74
Step-by-step explanation:
How many times can 2/7 be subtracted from 6/7
Answer:
Exactly three times.
Step-by-step explanation:
(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3
2ax-b=cx+d solve for x
We have to solve the following equation for the variable x:
[tex]2ax-b=cx+d[/tex]For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.
[tex]\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}[/tex]Now, we will factor the variable x, as we want to have just one expression with x, thus:
[tex](2a-c)x=d+b[/tex]And lastly, we will divide both sides by 2a-c, and we obtain:
[tex]x=\frac{d+b}{2a-c}[/tex]Which is the asked expression for x.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.2 minus twice a number.
Given the statement:
2 minus twice a number.
Let's represent the sentence as an algebraic expression where the number is the letter x.
To represent the statement as an algebraic expression, we have:
A number is the letter x ==> x
• 2 minus twice the number ==> 2 - 2x.
Therefore, the algebraic expression that represents the sentence is:
2 - 2x
ANSWER:
2 - 2x
Perform the indicated operation. 22 6/11 x 1 1/2
Multiplying the two fractions gives us the result 372/11
Here, we are given an expression- 22 6/11 x 1 1/2
To multiply these fractions, we first need to first convert the mixed fraction into an improper fraction. This can be done as follows-
22 6/11 = (22 * 11 + 6)/ 11
= (242 + 6)/ 11
= 248/ 11
similarly we have,
1 1/2 = (1*2 + 1)/2
= (2 + 1)/2
= 3/2
Thus, the given expression becomes-
248/ 11 x 3/ 2
= (248 * 3)/ (11 * 2)
= 744/ 22
= 372/ 11
We cannot simplify this fraction further.
Thus, multiplying the two fractions gives us the result 372/11
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I am trying to simplify a composition of functions.(f o g) (7.5)f(x) = -x + 7f(g) = -4x -2
There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have
[tex]\begin{gathered} (f\circ g)(x)=-(-4x-2)+7 \\ (f\circ g)(x)=4x+2+7 \\ (f\circ g)(x)=4x+9 \end{gathered}[/tex]We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get
[tex]\begin{gathered} (f\circ g)(7.5)=4(7.5)+9 \\ (f\circ g)(7.5)=39 \end{gathered}[/tex]The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got
[tex]\begin{gathered} g(7.5)=-4(7.5)-2 \\ g(7.5)=-32 \\ \Rightarrow\Rightarrow f(-32)=-(-32)+7=39 \end{gathered}[/tex]The accompanying table shows the median household income (in dollars) for 25 randomly selected regions. Complete parts (a) through (g) below.B!: Click the icon to view the table of data.(a) Construct a frequency distribution. Use a first class having a lower class limit of 35,000 and a class width of 5000.IncomeFrequency
Step 1:
Draw a table with class intervals to construct the frequency distribution table.
Step 2:
Choose a lower class and a class interval.
Lower class limit = 35,000
Class interval = 5000
Step 3:
Get the smallest and largest values from the table
Smallest value = 39712
Largest value = 67729
Step 4:
Draw the table using the class interval.
a) Frequency distribution table
Brad stands 30 feet from a tree. He estimates the angle of elevation from a point onthe ground 30 feet from the tree to the top of the tree to be 60° as shown below.60°30 feetWhich of the following is closest to the height of the tree?
To determine the height of tree using trigonometric ratio,
please answer this question
It's important to know that similar figures have equal angles, for example, if two triangles are similar, then their corresponding angles are congruent.
Having said that, D is true because all rectangles have equal angles.
help meee
solve for system of equations with steps shown please
1.
x+4y=0
3x+2y= 20
2.
6x+3y=54
2x+y=18
3.
x-3y=-2
10x+8y=-20
4.
3x-y=-8
5x+2y=5
The solutions to the equations are :
1. x= 8 ; y = -2
2.infinitely many solutions.
3. x= - 2 ; y = 0
4. x= -1 ; y = 5
How are the equations solved?
1. x+4y=0 --(1)
3x+2y= 20 ---(2)
(1)*3
3x+ 12y =0 ---(3)
(3) - (2)
(3x+ 12y) -(3x+2y -20)
10y +20= 0
10 y = -20
y = - 2
Substituting y in equation(1)
x+ 4 (-2) = 0
x = 8
The solutions to the equations are x= 8 and y = -2
2. 6x+3y=54 --(1)
2x+y=18 ----(2)
(2)*3
6x+3y=54 --(3)
(3) = (1)
0 = 0
The equations have infinitely many solutions.
3. x -3y= -2 --(1)
10x+8y=-20 ---(2)
(1)*10
10x - 30y +20 = 0--(3)
(3) - (2)
(10x - 30y +20 )- (10x+8y +20)
-38y = 0
y = 0
Substituting y in equation(1)
x - 0 = -2
x = -2
The solutions to the equations are x= - 2 and y = 0
4.
3x-y=-8 ---(1)
5x+2y=5 ---(2)
(1)*2
6x -2y+16 =0---(3)
(3) +(2)
(6x -2y+16) +(5x+2y-5)
11x +11 = 0
11x = -11
x = -1
Substituting x in equation(1)
3(-1) -y = -8
-3- y = - 8
- y = -8+3
-y = -5
y = 5
The solutions to the equations are x= -1 and y = 5
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A motorcycle can be purchased for $9000 or leased for a down payment of $400 and $290 per month. Find a function that describes how the cost of the lease depends on time. Assuming that the monthly payments are made, how long can the motorcycle be leased before more than the purchase price has been paid?Question content area bottomPart 1The function that models the situation is p= enter your response here, where p is the amount paid on the lease in dollars and t is the time in months.(Simplify your answer.)
Let's find the function p that describes that situation, at the initial time we must pay 400, then
400 - 0
After one month we must pay 290, it will sum with the previous 400 that we have paid
400 - 0
690 - 1 month
In the third month, we must add 400, the previous 290 and 290 again, two times.
400 - 0
690 - 1 month
980 - 2 months
If we repeat that we will see that we will have 290*3 plus 400, in other words, more 290 per month. We can write an expression to do it, it's
[tex]p=400+290\cdot t[/tex]Where t is the time in months, verify that our expression is coherent with our previous logic, now we have our expression let's go to the next step. The lease will be equal to the purchase price when p = 9000, which means that the person paid 9000 on the lease, if we use it in our equation we can solve it for t
[tex]9000=400+290\cdot t[/tex]Let's solve it for t
[tex]\begin{gathered} 9000=400+290t \\ \\ 290t=9000-400 \\ \\ 290t=8600 \\ \\ t=\frac{8600}{290} \\ \\ t=29.65 \end{gathered}[/tex]Then, if we lease the motorcycle for 30 months, we will pay $9100, more than the purchase price, if we lease it for 29 months, we will pay $8810.
Final answer:
Expression:
[tex]p=400+290t[/tex]How long you can lease it before it costs more than the purchase price:
[tex]t=29[/tex]I need help with my algebra
N 1
we have the ordered pairs
(1,1) and (4,2)
m=(2-1)/(4-1)
m=1/3
the slope is 1/3If a full air container has a volume of 2.3 m3, and 78.1 % of that air is nitrogen, what is the volume of nitrogen in the container. Quote your answer to an appropriate number of significant figures.
The amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
From the data given:
The total volume of the air container = 2.3 cubic meters
78.1 % is nitrogen.
The amount of nitrogen = 78.1 % of 2.3
= (78.1/100)x2.3
= 1.7963 cubic meters
The number 1.7963 to three Significant Figures is 1.80
The amount of nitrogen = 1.80 cubic meters
Thus, the amount of nitrogen is 1.80 cubic meters if a full air container has a volume of 2.3 m³, and 78.1 % of that air is nitrogen.
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Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.
Explanation:
The given information is
m∠4 = m∠2
m∠5 = m∠3
m∠DBE = 180
The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation
m∠4 + m∠1 + m∠5 = m∠DBE
But, we know that m∠DBE = 180, so by transitivity, we get:
m∠4 + m∠1 + m∠5 = 180
Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get
m∠2 + m∠1 + m∠3 = 180
Therefore, we can change the order by the commutative property to get
m∠1 + m∠2 + m∠3 = 180
Answer:
So, the answer is
What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter? In fraction in simplest form
SOLUTION
We want to find the area of the rectangle with the given side lengths as indicated in the question.
The area of a rectangle is given as
[tex]\text{Area = leghth }\times\text{ width}[/tex]So, this means to get the area, we will multiply the side lengths, we have
[tex]\begin{gathered} \text{Area = leghth }\times\text{ width} \\ \text{Area = }\frac{6}{8}\times\frac{4}{10} \end{gathered}[/tex]Solving the fraction, we have
[tex]\begin{gathered} \text{Area = }\frac{6}{8}\times\frac{4}{10} \\ 4\text{ divide itself is 1, }8\text{ divide 4 is 2, we have } \\ \text{Area = }\frac{6}{2}\times\frac{1}{10} \\ \text{now, 2 divide itself is 1, 6 divide 2 is 3, we have } \\ \text{Area = }\frac{3}{1}\times\frac{1}{10} \\ \text{Area = }\frac{3}{10} \end{gathered}[/tex]Hence the area in fraction in the simplest form is
[tex]\frac{3}{10}\text{ meter}[/tex]