Answer:
y=1/5x+4
Step-by-step explanation:
7. The length (in centimeters) of a scalloped hammerhead shark can be
modeled by the function = 266-219e-0.05t, where t is the age (in years) of
the shark.
a. How old is a shark that is 200 centimeters long?
2.11
b. How long is a shark that is twice as old as the shark in part (a)?
Answer: a. To find the age of a shark that is 200 centimeters long, we can set the function equal to 200 and solve for t:
L = 266 - 219e^(-0.05t)
200 = 266 - 219e^(-0.05t)
Solving this equation for t, we get t ≈ 2.11 years.
b. To find the length of a shark that is twice as old as the shark in part (a), we can substitute 2.11*2= 4.22 for t into the function:
L = 266 - 219e^(-0.05(4.22))
This will give us the length of the shark that is twice as old as the shark in part (a) in centimeters.
what is the value of K such that (x^3-2x^2+kx-12)/(x-5) has a remainder of 0
Answer:
k = -12.6
Step-by-step explanation:
Given rational polynomial:
[tex]\dfrac{x^3-2x^2+kx-12}{x-5}[/tex]
When we divide a polynomial f(x) by (x − d) the remainder is f(d).
If the remainder is zero, then (x - d) must be a factor of f(x).
If a cubic polynomial is divided by (x - d) then:
[tex]\implies (x-d)(ax^2+bx+c)[/tex]
where:
a is the leading coefficient-cd is the constantIf the constant of the cubic polynomial is -12 and d = 5:
[tex]\implies -cd=-12[/tex]
[tex]\implies -5c=-12[/tex]
[tex]\implies c=2.4[/tex]
The leading coefficient of the cubic polynomial is one. Therefore:
[tex]\implies (x-5)(x^2+bx+2.4)[/tex]
Expand and collect like terms:
[tex]\implies x^3+bx^2+2.4x-5x^2-5bx-12[/tex]
[tex]\implies x^3+(b-5)x^2+(2.4-5b)x-12[/tex]
The find the value of b, compare the coefficients of the term in x²:
[tex]\implies b-5=-2[/tex]
[tex]\implies b=3[/tex]
To find k, substitute the found value of b into the coefficient of x:
[tex]\implies k=2.4-5b[/tex]
[tex]\implies k=2.4-5(3)[/tex]
[tex]\implies k=-12.6[/tex]
Answer:
–12.6
Step-by-step explanation:
[tex] \frac{ \\ {x }^{3} - {2x}^{2} + kx - 12}{x - 5} = 0[/tex]
that means (x–5) is a factor of x³ – 2x² +kx – 12
since it resulted to zero according to the rules of zeros of polynomial.
x–5 = 0
x = 5
by substituting
f(x) = 5³ – 2(5)² + k(5) – 12 = 0
125 – 50 + 5k – 12 = 0
75 + 5k – 12 = 0
5k + 75 – 12 = 0
5k + 63 = 0
5k = –63
[tex] \frac{ \\ 5k}{5} = \frac{ - 63}{5} [/tex]
[tex]k = - 12.6 \: or \: - 12 \frac{3}{5} [/tex]
I hope I helped
Above are two different models of the same rectangular dog run. If the area of the model on the left is 54 sq cm, what is the area of the model on the right?
Answer:
48 sq cm
Step-by-step explanation:
The smaller square is 3' x 3' = 9 square feet.
The larger square is 9' x 9' = 81 square feet.
9 goes into 81 exactly 9 times (81 / 9 = 9), so we could just multiply the 54 cm by 9 and get your answer in centimetres.
54 x 9 = 486 cm
Which has a greater absolute value 10 or -9
Answer:
10
Step-by-step explanation:
10 is 10 units away from 0 on a number line
-9 is only 9 units away from 0 on a number line
The farthest away from 0 would be 10
ANYONE GOOD AT MATH PLEASE I BEG OF YOU FOR HELP!
Answer: 5
Step-by-step explanation: To solve f(x), g(x), or f(g(x)) problems, we place the value of x in the functions with the value that we are given. This value will be f(g(5)) or g(3) or f(27). We plug in the number in the parentheses.
In this problem, we have to first plugin 5 to g(x) then plug g(5) into f(x).
First, we do g(5)=sqrt((5^2)+2). This gives us 3. Then we plug in 3 which is g(5) into f(x). This gives us f(g(5)) or f(3)=sqrt((3^3)-2) which is 5.
The measures of the interior angles of a quadrilateral are 2°, 3x", 5x°, and 7x°. Find the measures of all the interior angles.
X= ?
3x= ?
5x= ?
7x= ?
HURRY PLEASE !
Answer:
x = 22.5°
3x = 67.5°
5x = 112.5°
7x = 157.5°
Step-by-step explanation:
You have both 2° and x for the measure of the first angle. I used x°.
Sum of the measures of the interior angles of a polygon
For an n-sided polygon:
(n - 2)180° = 2(180°) = 360°
x° + 3x° + 5x° + 7x° = 360°
16x = 360
x = 22.5°
3x = 67.5°
5x = 112.5°
7x = 157.5°
Find the exact circumference of each circle
By dividing the circle's diameter by, you may determine a circle's circumference (pi). By dividing 2radius by pi, or 3.14, you may also determine the circumference.
What is Circle’s Circumference?The diameter of a circle, also known as its circumference or perimeter, is the measurement of the circle's edge. As opposed to this, a circle's area indicates the space it occupies. The circumference of a circle is its length when we cut it open and draw a straight line from it. Units like centimeters or meters are typically used to measure it.The circle's radius is taken into consideration when applying the formula to determine the circumference of the circle. Therefore, in order to calculate the circumference of a circle, we must know its radius or diameter.The perimeter (or circumference) of a circle is equal to two R.where,R denotes the circle's radius.
The mathematical constant has a value that is around 3.14 (to the nearest two decimal places).Again,
As the ratio of any circle's circumference to diameter, pi () is a unique mathematical constant.and C = D
C represents a circle's circumference.D represents the circle's diameter.Calculate the circle's circumference, for instance, if its radius is 4 cm.Radius is given as 4 cm.Circumference = 2r
= 2 x 3.14 x 4
= 25.12 cm
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PLEASE ANSWER FAST FOR TEST
Represent the following scenario as a rate and a unit rate.
Write your Unsimplfied Rates as unsimplified fractions.
Write your Simplified Unit Rates as whole numbers or decimals rounded to two decimal places.
Form
Representing Rates and Unit Rates in Multiple Ways
Unsimplified Rate
Simplfied Unit Rate
"per language"
Dawn spent $32.2 on 14 gallons of gas.
Rate of Dollars to Gallons
dollars
gallons
dollars per gallon
Rate of Gallons to Dollars
gallons
dollars
gallons per dollar
The amount per gallon that Dawn will spend is $2.3 per gallon.
How to calculate the value in the word problem?It should be noted that a word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In the information given, it was stated that Dawn spent $32.2 in 14 gallons of gas. The amount per gallon will be:
= Total amount / Number of gallons
= $32.2 / 14
= $2.3
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Solve the following problem using the substitution method. Please make sure to show all of your work.
x + y = 3
y = x + 5
Answer: x=-1,y=4
Step-by-step explanation:
x + y = 3
y = x + 5
subtract x from both sides of the equation so you get
x + y = 3
-x + y = 5
use the elimination method and you'll get
2y = 8
simplify and
y = 4
now use that to get x
x + 4 = 3
x = -1
Therefore, the answer is
x = -1, y = 4
Answer:
x=-1, y=4. (-1, 4).
Step-by-step explanation:
x+y=3
y=x+5
----------
x+(x+5)=3
x+x+5=3
2x+5=3
2x=3-5
2x=-2
x=-2/2
x=-1
y=-1+5=4
How do the interior and exterior angles of a polygon relate? *
They are congruent
O They are supplementary
O They are complementary
There is no relationsh
Which graph is the graph of this function? F(x) = { 1/2x - 2 if x <_ 6 -x - 1 if x > 6
34x56x79447886447567
Please help!
Graph y= -3/2 x -3.
Answer:there you go
Step-by-step explanation:
use a graphing calc
Which of the numbers below correctly describes 25 A?
The required number below correctly describes 25 A is 0.025 KA. Option A is correct.
What is a unit of measurement?Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
25 A is the unit of current,
Now,
This unit can be further written as,
25 A = 25 × KA / 1000 = 0.025 KA
The required number below correctly describes 25 A is 0.025 KA. Option A is correct.
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Complete question-
which of the numbers below correctly describes 25 A? a) .025 KA, b) .25KA, c) 25,000 uA, d) 2500 mA
please help! math factorization
Factors of [tex]$$4(x-y)^3-x+y$$[/tex] are [tex]4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y[/tex] and [tex]$16 x^{16}-1$[/tex], respectively, are [tex]\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex].
What do you meant by factorization ?Let's incrementally simplify.
[tex]$$4(x-y)^3-x+y$$[/tex]
Distribute:
[tex]$$=4 x^3+-12 x^2 y+12 x y^2+-4 y^3+-x+y$$$=4 x^3-12 x^2 y+12 x y^2-4 y^3-x+y$[/tex]
Factor [tex]$16 x^{16}-1$[/tex]
[tex]$$\begin{aligned}& 16 x^{16}-1 \\& =\left(4 x^8+1\right)\left(2 x^4+1\right)\left(2 x^4-1\right)\end{aligned}$$[/tex]
When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. When you factorize a number in mathematics, you divide it into smaller numbers that, when multiplied together, give you the original number. Factorization occurs when a number is divided into its components or divisors. For illustration, the factorization of the integer 12 can appear as 3 times 4. Each check takes longer on average due to the larger size of our product and the larger size of the numbers we use to verify it.
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Can someone help me? Or explain this please I will give all stars!!
Answer:
The slope is 1. It is the number before the x. If we do not see a number, we assume that the number is 1.
Step-by-step explanation:
Answer:
The slope: 1
Step-by-step explanation:
The slope is simply the number in front of the x ONLY in the form y=mx+b, which it is currently in. If it is not in that form, try and manipulate the equation to put it into that form.
Moreover, if it is just x by itself imagine there being a 1 in front of it.
The answer: 1
Evaluate the expression 6x + 4 9/10when x =23.
142 9/10
6*23=138, 138+4 9/10=142 9/10
PLEASEEEEE HELPPPPPP!!!!
The combinations between the linear function g(x) = 4 · x + 1 and the quadratic function g(x) = 4 · x + 1 are f ° g (x) = 16 · x² + 44 · x + 10 and g ° f (x) = 4 · x² + 36 · x + 1, respectively.
How to use composition between two functions
Let be f(x) and g(x) a linear function and a quadratic function, respectively. The composition between two functions is represented below:
f ° g (x) = f [g(x)]
g ° f (x) = g [f(x)]
Where the input of the former function is substituted by the latter function. Now we proceed to find the resulting function:
f(x) = x² + 9 · x
g(x) = 4 · x + 1
f ° g (x) = (4 · x + 1)² + 9 · (4 · x + 1)
f ° g (x) = 16 · x² + 8 · x + 1 + 36 · x + 9
f ° g (x) = 16 · x² + 44 · x + 10
g ° f (x) = 4 · (x² + 9 · x) + 1
g ° f (x) = 4 · x² + 36 · x + 1
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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
The equivalent exponential equations are given as follows:
[tex]2^{4x} = 2^{3(x - 3)}[/tex]
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
[tex]2^{4x} = 8^{x - 3}[/tex]
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
[tex]8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}[/tex]
Meaning that the correct option is given by the fourth option.
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What is the central angle of a circle whose radius is 8cm and intercepted arc length is 7.2cm?
What is the radians as a decimal
Answer:
≈51.55
Step-by-step explanation:
∆/360 πD = 7.2
x/360 *22/7*16= 7.2
x/360 *50/2/7= 7.2
x/360 = 63/440
x =51.54545455
≈51.55
Whats 35 divided by 375?
Answer:0.093333333333
Step-by-step explanation:
If the null hypothesis is µ ≥ 200, then a two-tail test is being conducted.
True Or False
Answer:
False
Step-by-step explanation:
A two-tailed test requires that the null hypothesis use the equal (=) sign. Rejection of the null can happen in either direction. (Ex. a test statistic that i either too high, or too low). Anything other than equal (Ex. the null hypothesis is either, "greater than or equal to", or, "less than or equal to"), indicates a one-tailed test.
Kristy made 33 cookies for a bake
sale. She is putting the cookies in
packages to sell. Each package will
hold 4 cookies. How many complete
packages of cookies can she make?
Solve the system of equations.
3x-2y=3
-4x+5y=-11
The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7). An equation is a proposition that has two equal sides as well as an equal sign .
what is equation ?
It is thought that a number's simplest form is represented by its smallest equivalent fraction. finding the simplest form: what to do. For shared factors, look into the numerator and denominator. Examine a fractional integer to determine if it is a prime number. An equation is a proposition that has two equal sides as well as an equal sign in the middle. In the general form of any equation, the degrees of all the variables are listed in descending order. The common representation of a system of equations is an x + b = 0. x + b y + c = 0 is the general form of a two-variable linear equation (or something similar). Identity or conditional equations are the two categories under which equations fall. An identity holds true regardless of how the variables are valued.
given
Equation substitution is another name for combining the equations. When one variable is added to another equation, this is done.
-8x - 5y = -13
-4x - 5y = 11
Let's make the second equation a one-variable-on-each-side equation.
-5y = 4x + 11
y = -4/5x - 11/5
Put this into your first equation right now.
-8x - 5(-4/5x - 11/5) = -13
Give out the -5 symbol.
-8x + 4x + 11 = -13
Stack similar phrases.
-4x + 11 = -13
-4x = -24
Divide both sides by -4 to isolate x.
x = -24/-4
x = 6
Reintroduce this to either equation now.
y = -4/5(6) - 11/5
Multiply.
y = -24/5 - 11/5
Subtract.
y = -35/5
Simplify.
y = -7
The answer to the system of equations 3x-2y=3 and -4x+5y=-11 is (6, 7).
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HELP ASAP!
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 15:73 represents.
The ratio 15:73 represents the ratio of total athletes to 7th grade football players.
The ratio 15:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
The ratio 15:73 represents the ratio of 6th grade athletes to total athletes.
Answer:The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
Step-by-step explanation:
Jada has challenged herself to do at least 100 full push-ups this week On Sunday, she does 30 push-ups Her arms are sore, so she decides to do fewer push-ups on the remaining days of the week She wants to do the same number of push- ups each day for the rest of the week. Write and solve an inequality for the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups Which answer choice best interprets the solution in the context of the problem?
A. Jada needs to do at least 11 and 2 thirds
B. Jada needs to do push-ups for at least 12 more days to meet her goal
C. Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal
D. Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal
a) The inequality showing the number of push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups for the week is 30 + 6x ≥ 100.
b) The solution to the inequality shows D. Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal
What is inequality?Inequality is a mathematical statement that two or more mathematical expressions are unequal and not equivalent.
Inequalities are depicted in the following ways:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total number of full push-ups for the week = 100
The number of push-ups done on Sunday = 30
The remaining number of push-ups for 6 days = 70 (100 - 30)
Inequality:30 + 6x ≥ 100
6x ≥ 70
x ≥ 12
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Maria makes a fruit salad. The table shows the amounts of different kinds of fruit that she uses. Kind of Fruit Amount Grapes 3 2/3 cups Melon 2 1/4 cups Pineapple 23/4 cups Strawberries? The amount of strawberries that Maria uses is 3/8 times the amount of the other fruits combined. How many cups of strawberries does Maria use?
Proportionately, the number of cups of strawberries that Maria needs to use is 3¹/₈ cups.
What is proportion?Proportion refers to a part of a whole.
Proportion is a ratio of one value to another.
Proportions are depicted as decimals, fractions, or percentages.
In this situation, we know that the amount of strawberries is a fractional value of the combined fruits.
Thus, we can multiply the fraction of strawberries against the combined value of the other fruits to determine the number of cups of strawberries needed.
Kind of Fruit Amount
Grapes 3²/₃ cups
Melon 2¹/₄ cups
Pineapple 2³/₄ cups
Total of other fruits = 8²/₃ cups
Strawberries ?
Strawberries = 3¹/₈ (8²/₃ x ³/₈)
Thus, Maria needs 3¹/₈ cups of strawberries.
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Find the savings plan balance after 9 months with an APR of 3% and monthly payments of $200.
Answer: To calculate the balance of the savings plan after 9 months with an APR of 3% and monthly payments of $200, we need to take into account the interest earned on the account.
First, we will calculate the interest earned by multiplying the principal (initial amount) by the interest rate (APR) and the number of months.
Interest = Principal * Interest Rate * Number of months
Interest = 200 * 0.03 * 9 = 54
Then, we will add the interest earned to the total amount of payments made.
Total = Principal + Interest + Payments
Total = 200 + 54 + (200 * 9) = 200 + 54 + 1800 = 2054
So the savings plan balance after 9 months with an APR of 3% and monthly payments of $200 is $2054.
Step-by-step explanation:
how do i do this and whats the answer
Answer:
3 - 1
12 - 4
21 - 7
Step-by-step explanation:
Answer:
youd start and see that you can divide 12/3 this gives you 4 you then divide 4/4 and find 1 so he can do 3 lawns in 1 hour thus you just mutiplltiply each side by 7 so it'd be 21 and 7
Step-by-step explanation:
should look like this
3 1
12 4
21 7
C
27 cm
A) 18.9 cm
C) 20.8 cm
74°
A
9 cm
B
B) 26 cm
D) 22.7 cm
The length of other side is 20.8 in the given triangle.
What is a triangle ?
triangle can be defined in which it consists of three sides and three angles and sum of all the angles is always 180 degrees .
Given in the triangle ,
AC = 27 cm
AB = 9 cm
CAB = 74 degrees
a2 = b2 + c2 – 2bc cos ∠x
a2 = 27*27 + 9*9 - 2*27*9*cos74
a2 = 529 + 81 - 486*0.27
a2 = 610-486*0.27
a2 = 610-131.22
a2 = 479
a= [tex]\sqrt{479}[/tex]
a = 20.8 (approximately)
Hence the length of other side is 20.8 in the given triangle.
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(URGENT) lWhich pair of functions are inverses of each other?
If the two graphs are mirror images of one another across the line y = x, then they are inverse functions.[tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex]
How do you find a pair of inverse functions?As for looking at the graphs, we already knew that. You should keep in mind that inverse functions are represented by two graphs that are mirror images of one another over the line y = x. The broadest definition of an inverse function is one that "reverses" another function.
The inverse, for instance, must take b to an if a function goes from a to b. When the first and second elements of each pair in the original function are switched, a set of ordered pairs is obtained that is known as the inverse of the function. The act of switching the x and y coordinates is known as obtaining an inverse. They aren't opposites. The output of the first function is sent through an inverse function, which then generates an output whose input was the first function.
So, option A) [tex]$f(x)=\frac{x}{3}+10$ \\[/tex] and [tex]$g(x)=3 x-10$[/tex] is the appropriate response.
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