Answer:
1,215
Step-by-step explanation:
39/13=3
45*(3)^x
45*(3)^3
45*(27)
1,215
Final answer:
To find the number of foxes after 39 years, use the population growth function y = 45 *[tex]3^x[/tex]. Since 39 years corresponds to 3 periods of 13 years each, the equation becomes y = 45 * [tex]3^3,[/tex] resulting in 1215 foxes.
Explanation:
The student has asked how many foxes will there be after 39 years, given the population growth function y equals 45 times 3 to the x power, where x represents the number of 13-year periods. To solve this, we calculate the value of x by dividing the total time of population observation (39 years) by the duration of one population tripling period (13 years). This gives us:
x = 39 years / 13 years/period = 3 periods
We then substitute x into the equation and get:
y = 45 *[tex]3^3,[/tex] = 45 * 27 = 1215 foxes
Therefore, there will be 1215 foxes in the wildlife preserve after 39 years.
How many ways are there to answer a $10$-question true/false test, where at least $3$ of the questions have been answered with a false?
Answer:
968 ways
Step-by-step explanation:
This is a question of permutation and combination.
Each equation can have two different answers.
Thus the total number of cases will be (for 10 questions) :
[tex]2*2*2*2*.....10times=2^{10}[/tex] cases.
Now to find the number of ways to at least answer 3 questions False will be total minus the number of question with at most 2 False answers.
Number of ways in which no answer is False : 1 ( all are true )Number of ways in which ONLY one answer is False : [tex]10_C_1[/tex] where [tex]n_C_r=\frac{n!}{(n-r)!r!}[/tex]Number of ways in which ONLY two answers are False :[tex]10_C_2[/tex]Total ways (at most 2 answers false) = [tex]1+10_C_1+10_C_2[/tex] ;
∴
The number of ways in which at least 3 have False as the answer is :
[tex]2^{10}-(1+10_C_1+10_C_2)\\=968[/tex] WAYS.
What is the value of x when solving the equation 4x+(-4) = -2x+8
Answer:
You have to simplify the equation and find the answer
Step-by-step explanation:
[tex]4x + ( - 4) = - 2x + 8 \\ \\ 4x + 2x = 4 + 8 \\ \\ 6x = 12 \\ \\ x = 2[/tex]
Answer:
Step-by-step explanation:
4x+(-4) = -2x+8
4x - 4 = -2x + 8
Collecting like terms
4x + 2x = 8 + 4
6x = 12
Dividing through by 6
x = 12/6
x = 2
How many 1/3 are in 1 2/3
Answer:12
Step-by-step explanation:bcs in 1/3 it has the same denominatoor
The lengths of the diagonals of a rhombus are 2x and 10x. What expression gives the perimeter of the rhombus?
A. 42
B.
196
Answer:
[tex]P=4x\sqrt{26}\ units[/tex]
Step-by-step explanation:
we know that
The sides of a rhombus are all congruent and the diagonals are perpendicular bisectors of each other
so
Applying the Pythagorean Theorem
[tex]c^2=a^2+b^2[/tex]
where
c is the length side of the rhombus
a and b are the semi-diagonals
we have
[tex]a=2x/2=x\ units\\b=10x/2=5x\ units[/tex]
substitute the values
[tex]c^2=x^2+(5x)^2[/tex]
[tex]c^2=26x^2[/tex]
[tex]c=x\sqrt{26}\ units[/tex]
To find out the perimeter of the rhombus multiply the length side by 4
[tex]P=(4)(x\sqrt{26})[/tex]
[tex]P=4x\sqrt{26}\ units[/tex]
Bobby’s football team received four five-yard penalties in the first quarter, which meant his team lost yardage in their progress toward the goal line. What was the change in their progression down the field as a result of these penalties?
Answer: they lost 20 yards.
Step-by-step explanation
Answer:
A -20
Step-by-step explanation:
A candidate for mayor plans to campaign at 5 shopping malls before the election
In how many different ways can the candidate schedule the vists?
Enter your answer as a whole number
I’ll put you as brainliest
Answer:
120 ways
Step-by-step explanation:
⭐ Please consider brainliest! ⭐
✉️ If any further questions, inbox me! ✉️
Answer:
56
Step-by-step explanation:
add
Complete the inequality statement.
14 ft ____ 4 1/2 yd.
<
>
='
PLEASE ANSWER CORRECTLY
DO NOY ANSWER INCORRECTLY JUST FOT POINTS TY
Answer: 14ft > 41/2
Step-by-step explanation:
Your answer is:
14ft > 41/2yd
I hope this helped! If so, please mark brainliest!
evaluate the indicated function for f(x)=x^2-7 and g(x) =x-2
Answer:
f(g(x))=(x-2)^2 - 7
(x-2)(x-2) - 7
x^2-2x-2x+4-7
x^2-4x-3
g(f(x))=x^2-2-7
x^2-9
(x+3)(x-3)
Step-by-step explanation:
to solve for f(x), replace x with the g(x).since we don't multiply a bracket with the negative or the positive signs to the exponent, you have to factor into two binomials.use the FOIL method to eliminate the brackets.add like-termsto find g(x), replace x with the f(x).add like-termssince there's difference of square, factor them into two binomialsTo evaluate functions, you substitute x with the given value in the function and perform the calculation. For example, evaluating f(3) for the function f(x)=x^2-7 gives f(3)=2, while evaluating g(3) for the function g(x)=x-2 gives g(3)=1.
Explanation:The functions given are f(x)=x^2-7 and g(x)=x-2. To evaluate these functions, we substitute a value for x into the function and perform the calculation. For example, if we want to evaluate f(3), we replace x in the function f(x) with 3.
So for f(3)=3^2-7, we do the following: f(3)=9-7=2.
For g(3), we substitute x in the function g(x) with 3: g(3)=3-2=1
It's important to note that the value you're evaluating might change depending on the question, but this is the basic process for evaluating a function at a given value or values.
Learn more about functions here:https://brainly.com/question/35114770
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Write the function f(x)6x^2+7x+2 in vertex form, and identify its vertex
Answer:
Step-by-step explanation:
Complete the square to do this. This one is a bit of a pain because of the 7 as our linear term, but a little hard work never killed anyone!
The rules for completing the square are very strict and cannot be strayed from. The first rule is that the leading coefficient HAS to be a positive 1; ours is a positive 6 so we have to factor it out. Let's do that first then we can get to rule number 2.
Set the quadratic equal to 0, then move the constant over to the other side. This is not a rule, per se, but I teach it this way to avoid unnecessary confusion in an already confusing process.
[tex]6x^2+7x=-2[/tex] and to factor out the 6:
[tex]6(x^2+\frac{7}{6}x)=-2[/tex]
Now for rule #2: take half the linear term, square it, and add it to both sides. Our linear term is 7/6. Half of that is 7/12, and 7/12 squared is 49/144. BUT we cannot forget about that 6 hanging around out front, refusing to be ignored. It is a multiplier, so when we add 49/144 inside the parenthesis on the left, we have to add 6(49/144) to the right, giving us:
[tex]6(x^2+\frac{7}{6}x+\frac{49}{144})=-2+\frac{294}{144}[/tex]
We will rewrite now by simplifying. The left side can be written into a perfect square binomial (which is why we did this in the first place) and the right side can be added. The left side becomes
[tex]6(x+\frac{7}{12})^2[/tex]
The 7/12 comes from the square root of 49/144, and the x comes from the square root of x-squared. The right side requires a common denominator:
[tex]-2+\frac{294}{144}=-\frac{288}{144}+\frac{294}{144}=\frac{6}{144}=\frac{1}{24}[/tex]
So now we have
[tex]6(x+\frac{7}{12})^2=\frac{1}{24}[/tex]
Put evertyhing back onto the left side and set it back to equal y and you're done!
[tex]y=6(x+\frac{7}{12})^2-\frac{1}{24}[/tex]
Because the vertex form of a quadratic does not allow us to stray from the format "x -", we have to interpret our h coordinate as "x - (-7/12))" which is movement to the left. This gives us a vertex of
[tex](-\frac{7}{12},-\frac{1}{24})[/tex]
two lines have the given equations. Use the LINEAR COMBINATION METHOD to solve.
2x-y=1
3x-y=-6
Using linear combination method, the solution to given system of equations are (-7, -15)
Solution:Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated
Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.
Given system of equations are:
2x - y = 1 ---- eqn 1
3x - y = -6 ------ eqn 2
Subtract eqn 2 from eqn 1
2x - y = 1
3x - y = -6
(-) -------------
-x = 7
x = -7Substitute x = -7 in eqn 1
2(-7) - y = 1
-14 - y = 1
y = -14 - 1 = -15
y = -15Thus the solution to given system of equations are (-7, -15)
Greg wants to find the amount of concrete needed to cast a pillar he has designed. The pillar will have a base area of square yard and a height of yard. How much concrete does he need to cast the pillar?
Answer:
1/392 cubic yard
Step-by-step explanation:
V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³
Answer:
1/392
Step-by-step explanation:
i was foing this test and turns out this is right.
A toll collector on a highway receives $8 for trucks and $5 for sedans. At the end of a 3-hour period, she collected $208. How many trucks and sedans passed through the toll booth during that period? List all possible solutions.
Answer:
The number of trucks and sedans can be
(0 trucks ,26 sedans)
(8 trucks ,21 sedans)
(24 trucks ,11 sedans)
(25 trucks ,1 sedans)
(32 trucks ,6 sedans)
(16 trucks ,16 sedans)
Step-by-step explanation:
Given:
The cost for trucks =$5
The cost for sedans =$8
The total amount collected = $208
To Find:
Number of trucks and sedans passed through the toll booth =?
Solution:
Let the number of trucks be x and the number of sedans be y
Then
5x + 8y = 208-------------------------------(1)
By Trail and error method
5(0) + 8(26) = 208
5(8) + 8(21) = 208
5(24) +8(11) =208
5(25) + 8(1) = 208
5(32) + 8(6) =208
5(16) + 8(16) = 208
A card is drawn at random from a standard 52-card deck. What is the probability that it is an odd number (3,5,7,9) or a spade (or both)?
Answer:
The probability of selecting the given event = [tex]\frac{25}{52}[/tex]
Step-by-step explanation:
A card is drawn at random from a standard 52-card deck.
We have to find the probability of selecting an odd numbered card(3,5,7,9) or spade or both.For this we have to find the number of favourable cases.
Favorable cases = 13 (all the spades) + 12(4 odd numbered cards from each of the remaining 3 )
= 25
Final probability = [tex]\frac{number of favourable cases}{total number of cases}[/tex]
= [tex]\frac{25}{52}[/tex]
Hence the probability = [tex]\frac{25}{52}[/tex]
5( q + 27 ) - -30=95
STEPS:
First distribute the 5 through the parentheses to get 5q + 135. So the problem now reads 5q + 135 - (-30) = 95.
Now, minus a negative can be changed to plus a positive so - (-30) can be changed to +30 so our equation now reads 5q + 135 + 30 = 95.
Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. Notice that we can add 135 and 30 to get 165 so the left side simplifies to 5q + 165 = 95.
Now we can simply subtract 165 from both sides of the equation to get 5q = -70.
Now simply divide both sides of the equation by 5 to get q = -14.
What is the slope of the line passing through the point 3,5 and -1,7
Answer:
m = -1/2
Step-by-step explanation:
As we move from the point (-1, 7) to the point (3, 5), x increases by 4 (this is the "run") and y decreases by 2 (this is the "rise").
Thus, the slope of the line connecting these two points is
m = rise / run = -2/4, or m = -1/2.
Answer:
1/2
Step-by-step explanation:
Given the equations, identify which way the parabola opens by matching an equation on the left with a term on the
right
Answer:
1) up
2) correct
3) left
4) down
Step-by-step explanation:
do you not have a graphing calculator, it really helps you with these.
The parabola opens by matching an equation are as follows,
[tex]&x^{2}=3 y \\[/tex] up[tex]&y^{2}=6 x \\[/tex] Right[tex]&y^{2}=-2 x \\[/tex] Left[tex]&x^{2}=-10 y[/tex] DownWhat is Parabola?The standard equation of a regular parabola exists [tex]y^{2} = 4ax.[/tex] Some of the important representations below are helpful to understanding the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
A positive value denotes the parabola opens up, and a negative value means the parabola opens down. That stands If the quadratic exists given in standard or vertex form.If a exists positive, then the parabola opens up. If a stands negative, then the parabola opens down.A parabola is a plane curve that exists mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be established to define the same curves.
The parabola opens by matching an equation are as follows,
[tex]&x^{2}=3 y \\[/tex] up[tex]&y^{2}=6 x \\[/tex] Right[tex]&y^{2}=-2 x \\[/tex] Left[tex]&x^{2}=-10 y[/tex] DownTo learn more about Parabola refer to:
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what is the solution to 3x+5+4x=5x+27
｡☆✼★ ━━━━━━━━━━━━━━ ☾
3x + 5 + 4x = 5x + 27
7x + 5 = 5x + 27
- 5
7x = 5x + 22
- 5x
2x = 22
/2
x = 11
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
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Answer:
Step-by-step explanation:
3x + 5 + 4x = 5x + 27
collect like terms
7x - 5x = 27 -5
2x = 22
divide both side by 2
x = 11
I WILL MARK BRAINLIST!!
Which of the following shows that polynomials are closed under subtraction when two polynomials, (5x2 + 2x − 6) − (3x2 − 6x + 2), are subtracted?
2x2 − 4x − 4; will be a polynomial
2x2 − 4x − 4; may or may not be a polynomial
2x2 + 8x − 8; will be a polynomial
2x2 + 8x − 8; may or may not be a polynomial
Answer:
For [tex](2x^2 + 8x - 8)[/tex], the group is CLOSED as it a polynomial.
Step-by-step explanation:
Here, the given polynomials are:
[tex]P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)[/tex]
Now, a group G is said to be CLOSED UNDER SUBTRACTION if,
a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G
Now, here:
[tex]R(x) = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)[/tex]
or, [tex]R(x) = (2x^2 + 8x - 8)[/tex]
Also, R(x) is a POLYNOMIAL.
So, R(x) is an Element of group G.
So, the set G of polynomials.
Hence, for the polynomial [tex](2x^2 + 8x - 8)[/tex], it will be a polynomial the group is CLOSED.
Answer:
The answer would be C
Step-by-step explanation:
Can you plz tell me the answer to:
1. Make w the subject of
y-aw=2w-1
2. Make q the subject of
2(q+p)=1+5q
3. Make r the subject of
t=r/r-3
4. Make r the subject of
P=10(q-3r)/r
Answer: see attached file
Step-by-step explanation: see attached file for explanation. Thanks!
What is 272,062 rounded to the nearest hundred?
Answer:
272,100
This is because 62 rounds up
Answer:
272,100
You get this answer by looking at the hundreds place and then looking at the right of it. The hundreds place is the 0 and the the right of it is 6, so 5 and up round up 4 and down round down and in this case, 6 is above 5, so it rounds up to 272,100!
Hope this helped!
which if the following statements is true about the triangles below
Answer:
Step-by-step explanation:
ΔABC ≅ ΔABD by ASA
I need help with Algebra 2a
Answer:
Step-by-step explanation:
Summation means that you are adding together all the numbers that result from putting in the numbers 5-11 for i:
(-7 - 6(5)) + (-7 - 6(6)) + (-7 - 6(7)) + ( -7 - 6(8)) + ( -7 - 6(9)) + ( -7 - 6(10)) + ( -7 - 6(11)) which gives you the numbers:
-37 + -43 + -49 + -55 + -61 + -67 + -73 = -385
Theo wants to use a cokkie recipe that makes 36 cookies but he wants to reduce the number of cookies to 24.if the recipe specifes using 2 cups of sugar, how many sugar should he use ?
Answer:
Theo Should use 1.3 cups of Sugar to make 24 cookies.
Step-by-step explanation:
Given;
Number of cookies required by recipe = 36 cookies
Number of cookies Theo wants to use = 24 cookies
Number of cups sugar recipe requires = 2 cups
We need to find Number of cups sugar Theo should use to make cookie according to recipe.
Now,
For 36 cookies = 2 cups of sugar
So For 24 cookies = Number of cups of sugar required for 24 cookies.
By Using Cross Multiplication we get;
Number of cups of sugar required for 24 cookies = [tex]\frac{24\times2}{36}= 1.33\ cups[/tex]
Hence Theo Should use 1.3 cups of Sugar to make 24 cookies.
Can someone help me with these problems? I'm in k12 and this assignment was in classkick, so if anyone already completed this and can help, please do. I also am going to be asking some more questions, if you can help with those too. Thanks! (Will give brainliest.)
Answer:
See the explanation
Step-by-step explanation:
Given function
[tex]Y=3x+1[/tex]
We need to find [tex]y[/tex] value corresponding to each [tex]x[/tex] value.
So, plug each [tex]x[/tex] value in equation we get,
[tex]plug\ x=4\\y=3(4)+1\\y=12+1\\y=13\\\\plug\ x=6\\y=3(6)+1\\y=18+1\\y=19\\\\plug\ x=10\\y=3(10)+1\\y=30+1\\y=31[/tex]
Now in next part of question it ask us to check each ordered pair.
Let us plug each [tex]x[/tex] value and [tex]y[/tex] value in the function [tex]y=-3x-5[/tex]
[tex]plug\ (1,-8)\\-8=-3(1)-5\\-8=-3-5\\-8=-8\\\\plug(-5,0)\\0=-3(-5)-5\\0=15-5\\0\neq10\\\\plug\ (-2,1)\\1=-3(-2)-5\\1=6-5\\1=1\\\\plug\ (-1,-2)\\-2=-3(-1)-5\\-2=3-5\\-2=-2\\[/tex]
we can see ordered pair [tex](1,8),(-2,1)and(-1,-2)[/tex] true for function [tex]y=-3x-5[/tex]
Rewrite the equation 2x + 3y = 6 in slope-intercept form. y = -2 x + 6 y = - x + 2 y = 2 x + 6 3 y = -2 x + 6
Answer:
y=-2/3x+2
\\\\\\\\\\\\\\\\\\\\\
alexandra earns 12$ an hour babysitting. she babysat 10 hours last week and 12 hours this week what equation shows how to find how much money (m) she earned in all
$120 +$144 =$264
Alexndra earns $264
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that
apply.
The question is incomplete. Here is the complete question:
The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which
characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that apply.
(A) The coordinates of A'.
(B) The coordinates of B'.
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Answer:
(C) The perimeter of Δ A'B'C'.
(D) The area of Δ A'B'C'.
(E) The measure of ∠B'.
(F) The length of segment A'B'.
Step-by-step explanation:
Given:
A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.
Now, a rotation is a rigid motion transformation. In rigid transformation, the size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.
Rotation only changes the position of the points on the figure.
Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.
So, the correct options are (C), (D), (E), and (F).
Please help me with this I’m crying
Answer:
640 cm²
Step-by-step explanation:
The ratio between the area two similar polygon are the ratio between their sides squared.
Given side S₁ and side S₂, you can find the area of the second shape by multiplying the area of the first shape by a factor of (S₂/S₁)².
This might sound confusing if you're not used to hearing math terms so lets solve it in this problem.
The side of the first trapezoid is 5cm, so S₁ = 5
The side of the second trapezoid is 20cm so S₂ = 20.
The ratio between them is 20/5=4
To find the area of the second shape, we just have to multiply the area of the first one by the ratio², ie. (S₂/S₁)².
40(4)² = 40(16) = 640 cm²
wiple Choice which equation describes the relationship
20. Multiple
the table?
0 0 1 2 3 4 5 6
16 10 20 30 40 50 60 70
A. C= 10n
B. C= 10 +n
C. C= 10
D. C= 10 + 10n
answer:C=10+10n
proof: 10+10 (1)=20
10+10 (.6)=16
10+10 (-.4)=6
What do the expressions (3up3)and (3up4) have in common
Answer:
They both have 3 up ig
Step-by-step explanation: