Answer:
A. y = x^2 -6x + 13
Step-by-step explanation:
The parabola that opens up and has line of symmetry x=3 and a minimum at x=3 is
[tex]y=x^2-6x+13[/tex]
The reason is that, we can write this function in the vertex form to get;
[tex]y=x^2-6x+(-3)^2+13-(-3)^2[/tex]
[tex]y=(x-3)^2+13-9[/tex]
[tex]y=(x-3)^2+4[/tex]
Hence the line of symmetry is x=3 and the vertex is (3,4)
Answer:
option A
y = x² - 6x + 5
Step-by-step explanation:
step 1
Find out if a is positive or negative.
'a' is the coefficent of x
If the parabola is facing up , then a must be positive.
a = 1
Step 2
To find the minimum point
x = -b/2a
using the standard equation y = ax² + bx + c
x must be equal to 3
Equation 1
y = x² -6x + 13
x = -(-6)/2(1)
x = 3(ACCEPTED)
Equation 2
y = x² + 6x + 5
x = -6/2(1)
x = -3
Equation 3
x² - 3x + 6
x = 3/2(1)
x = 3/2
Equation 4
x² + 8x + 19
x = -8/2(1)
x = -4
Step 3
At the minimum point there will be line of symmetry hence x = 3
decide whether each statement is possible or impossible for some angle theta. tan theata =-35.4 possible or impossible
Answer:
It is possible
Step-by-step explanation:
x = 1.5990374 + π n , for any integer n
If x = 15 in, y = 20 in, and z = 25 in, what is the surface area of the geometric shape formed by this net?
A. 1,650 in2
B. 2,100 in2
C. 1,100 in2
D. 1,800 in2
Answer:
the answer is D: 1800 square in
Step-by-step explanation:
find the area of the triangle
area = 1/2 bh
=1/2 (15 inch) (20 inch)
=150 square inch
***then multiply by 2 which gives you 300 square inch***
find the area of the 3 rectangular faces
A=lw
= (25 in) (15 in)
= 375 square inch
A = lw
= (25 in) (20 in)
= 500 square inch
A = lw
= (25 in) (25 in)
= 625 square inch
then add all 3 rectangular faces which equals to 1500 square inch
then add the triangular and rectangular
300 square inch + 1500 square inch = 1800 square inch
Answer:
The answer for study island would be D. 1,800 in2
hope i helped :)
Multiple choice
How many degrees are in angle A?
There are 70 degrees in angle A.
PLS HELP. Find the first four terms of the recursive sequence defined by the following formula:
Answer:
see explanation
Step-by-step explanation:
Given the recursive formula [tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex] and
[tex]a_{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex], then
[tex]\frac{a_{3} }{4}[/tex] = [tex]\frac{9}{4}[/tex] ( multiply both sides by 4 )
a₃ = 4 × [tex]\frac{9}{4}[/tex] = 9
[tex]\frac{a_{2} }{4}[/tex] = 9 ( multiply both sides by 4 )
a₂ = 36
[tex]\frac{a_{1} }{4}[/tex] = 36 ( multiply both sides by 4 )
a₁ = 144
The first 4 terms are
144, 36, 9, 2 [tex]\frac{1}{4}[/tex]
The first four terms of the recursive formula are 144, 36, 9, 9/4 .
What is a recursive sequence ?A recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its before or after number. In a recursive sequence, the series of the number present follows a particular sequence of logic.
How to solve the given recursive sequence ?Given series is an = (an-1)/4 and also a4 = 9/4
Putting n = 4 in the given recursive sequence,
⇒ a3/4 = a4
∴ a3 = a4 * 4 = 9/4 * 4 = 9
Again putting n = 3 in the given recursive sequence,
⇒ a2 = 4*a3
∴ a2 = 4 * 9 = 36
Finally putting n = 2 in the recursive sequence,
⇒ a1 = 4 * a2
∴ a1 = 4 * 36 = 144
Therefore, the first four terms of the recursive formula are 144, 36, 9, 9/4 .
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write the number .00000000000000193 in scientific notation
Answer:
1.93 x 10^-15
Step-by-step explanation:
You want to move the decimal just past the first real number and count the spaces moved, which is 15. Since the decimal is being moved to the right the spaces moved will be negative. Therefore you remove the zeroes and get 1.93 times 10 to the negative 15th power.
scientific notation means, moving the dot in a way that only one integer is to its left, namely the in this case it'll look like 1.93, so we'll have to move the dot all the way from the left to the right that many slots.
[tex]\bf 0.00000000000000193\implies \stackrel{\textit{moved }\stackrel{\downarrow }{15} \textit{ slots to the right}}{0000000000000001.93}\implies 1.93\times 10^{\stackrel{\downarrow }{-15}}[/tex]
an equilateral triangle has a perimeter of 36 cm. what is the area?
Answer:
Each side of this equilateral triangle is 12 cm.
A = (1/2)(12)(6√3) = 36√3 cm²
The equilateral triangle, with a perimeter of 36 cm, has a side length of 12 cm. Its area is [tex]\(36\sqrt{3} \, \text{cm}^2\)[/tex], calculated using the formula [tex]\(\frac{\sqrt{3}}{4} \cdot s^2\)[/tex].
For an equilateral triangle, the perimeter (P) is related to the side length (s) by the formula P = 3s. From this, you can find the side length s by dividing the perimeter by 3:
[tex]\[ s = \frac{P}{3} = \frac{36}{3} = 12 \, \text{cm} \][/tex]
Now, you can use the side length to find the area (A) of the equilateral triangle. The formula for the area of an equilateral triangle is:
[tex]\[ A = \frac{\sqrt{3}}{4} \cdot s^2 \][/tex]
Substitute the value of (s):
[tex]\[ A = \frac{\sqrt{3}}{4} \cdot 12^2 \]\[ A = \frac{\sqrt{3}}{4} \cdot 144 \]\[ A = \frac{144\sqrt{3}}{4} \]\[ A = 36\sqrt{3} \, \text{cm}^2 \][/tex]
Therefore, the area of the equilateral triangle is [tex]\(36\sqrt{3} \, \text{cm}^2\)[/tex].
The graph of f(x) = x3 is given. Which equation will translate the graph 1 unit up?
A)
g(x) = x3 - 1
B)
g(x) = x3 + 1
C)
g(x) = -x3 + 1
D)
g(x) = (x - 1)3
Answer:
B: g(x) = x^3 + 1
Step-by-step explanation:
Please use " ^ " to denote exponentiation: f(x) = x^3.
This graph starts (increasing) in Quadrant III and grows without bound in Quadrant IV. It passes thru the origin (0, 0).
If we want to translate the graph 1 unit up, then the function f(x) becomes
g(x) = f(x) + 1, or x^3 + 1.
Answer:B: g(x) = x^3 + 1
Step-by-step explanation:
Factor to find the zeros of the function defined by the quadratic expression.
4x2 − 24x − 108
A) x = 3 or x = 9
B) x = 3 or x = −9
C) x = −3 or x = 9
D) x = −3 or x = −9
ANSWER
C) x = −3 or x = 9
EXPLANATION
The given quadratic function is:
[tex]4 {x}^{2} - 24x - 108[/tex]
To find the zeros, we equate to zero.
[tex]4 {x}^{2} - 24x - 108 = 0[/tex]
Divide through by 4
[tex] {x}^{2} - 6x - 27 = 0[/tex]
Factor to get,
[tex] {x}^{2} + 3x - 9x - 27 = 0[/tex]
[tex]x(x + 3) - 9(x + 3) = 0[/tex]
[tex](x + 3)(x - 9) = 0[/tex]
Use the zero product property,
[tex]x = - 3 \: or \: x = 9[/tex]
how many parallel sides can a triangle have
Answer:
a triangle will always have 0 parallel sides
Step-by-step explanation:
Don’t know how to do this type of problem !:(
Answer:
Step-by-step explanation:
Alright. I can't really explain much but i can get your answer.
AS A DECIMAL: 1.047197551196597746154214461093167628065723133125035273658
As a property:
π/3
Sorry if its wrong... I tried lol
Answer:
The answer would be 2
Step-by-step explanation:
Complete the ratio
4 : ? = 1 : 6
I think the answer is 4:24
Answer:
4 : 24
Step-by-step explanation:
1:6
We need to make the 1 a 4, so we will multiply by 4
What we do to one side, we do to the other
1 *4 = 4
6*4 = 24
1: 6 becomes 4: 24
I need help in this one please thankyou (explanation) ill give 20pts
Answer: (y-3)(4y-5)
Step-by-step explanation:
4*15= 60. 60= -12 x -5
4(y-12)(y-5)
(y-3)(4y-5)
what is the slope of the line that passes through (-2,2) and (-4,-2)
Answer:
slope = 2
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (- 4, - 2)
m = [tex]\frac{-2-2}{-4+2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2
Fifty years ago, bed bugs were nearly eliminated in the United States by using of pesticides like DDT. Today bed bugs are back in beds and theaters. DDT is no longer used due to environmental issues. Pyrethrums are currently the top choice for bed bug infestations. Pyrethrums are especially useful to us because they generally have a stronger effect on bugs than on humans and animals.
Bed bugs have become resistant to even this chemical pesticide. What happened that allowed the bug population to increase?
A) the chemicals used currently are weaker
B) the chemicals no longer can penetrate bed bugs brains
C) the bed bugs of today are exactly the same as the bed bugs of fifty years ago
D) the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring
Answer:
The most reasonable Answer is *D.) the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.*
Step-by-step explanation:
Answer:
The answer is D) The bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.
Step-by-step explanation:
The bed bug population has increased because the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.
Please explain your answer as well. THX!!
Answer:
option b
6 C 2 + 6
Step-by-step explanation:
Given in the question that,
number of pink beans = 87
number of purple beans = 74
number of white beans = 35
number of black beans = 70
number of orange beans = 25
number of green beans = 47
Step 1if two beans selected are different
6 C 2
(6 colours of beans)
Step 2if two beans selected are same
6 C 1 = 6
(6 colours of beans)
Step 3total sample space will be
6 C 2 + 6
What is the value of x?
Enter your answer in the box.
Answer:
50 =x
Step-by-step explanation:
The two angles are vertical angles, so they are equal
2 (x+10) = 3x-30
Distribute the 2
2x+20 = 3x-30
Subtract 2x from each side
2x-2x+20 = 3x-2x-30
20 = x-30
Add 30 to each side
20+30 = x-30+30
50 =x
Answer:
x = 50
Step-by-step explanation:
We are given a diagram showing two vertically opposite angles and we are to find the value of x.
We know that when two lines intersect each other, vertically opposite angles are formed which are equal to each other.
Therefore, we can write them as:
[tex] 2 ( x + 1 0 ) = 3 x - 3 0 [/tex]
[tex] 2 x + 2 0 = 3 x - 3 0 [/tex]
[tex] 3 x - 2 x = 2 0 + 3 0 [/tex]
x = 50
CHORDS AND ARCs: Find the value of x
The answer is probably 14, but I don't know how to prove it correctly, I mean by using the mathematical language. So if it will work, I can try to guess how I got this answer. So if you will draw radiuses, like I did on the screenshot, you will get 2 equal to each other triangles, but the thing is that I have no idea why they should be equal. So if the first step is right the value of x should be equal to 14, as the side below is equal to 14 too. That's it, I guess I helped you at least a little!
The value of x in the chord and arc circle figure is 8[tex]\sqrt{2}[/tex] units.
What is the value of the x in the given circle figure?Given:
The radius of the circle is given as 9 units.The length of one chord is 2*7 = 14 units.Find:
The length of the other chord that is represented by x.Solution:
As it is given that the radius of the circle is 9 units.
So, from here the diameter is 2*9 units = 18 units.
Now, we will draw a line from A to B, we will then Right triangle.
From the right-angled triangle we can calculate the value of x by Pythagoras Theorem, we get;
[tex]x^{2} = (18)^{2} - (14)^{2}[/tex]
[tex]x^{2} = 324 - 196[/tex]
[tex]x^{2} = 128[/tex]
[tex]x = \sqrt{128} = 8\sqrt{2}[/tex]
Hence, the value of x is 8[tex]\sqrt{2}[/tex] units.
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Please help and thank you
Answer:
I think the answer is B
What is two times the quantity of a number minus 12
Answer: B Or Option 2
Step-by-step explanation: Your Answer Will Be The Second Choice Have A Great Day!
what is the value of z in the diagram?
Answer:
2
Step-by-step explanation:
Find a
a. 4
b. 6
c. 9
ANSWER
C. 9
EXPLANATION
We use the Altitude Theorem,to find the value of a.
According to the altitude theorem, the height of the triangle of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.
[tex]6 = \sqrt{4a} [/tex]
Square both sides to get,
[tex]36 = 4a[/tex]
[tex]9 = a[/tex]
The correct choice is option C.
Answer:
C
Step-by-step explanation:
the answer is 9
hurry i need this!!!!!!!!!!!!!
ANSWER
[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]
EXPLANATION
The given equation that models the height is
[tex]h(x) = - 2 \sin(\pi(t + \frac{1}{2} )) + 5[/tex]
This is sine a sine function that is reflected in the x-axis.
This function will coincide with the cosine function with the same amplitude, period, phase shift and vertical translation.
The function that can also model this height is
[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]
The last choice is correct.
How large is the greatest possible error for measurement of 77 inches
Answer:
0.5
Step-by-step explanation:
Its too hard to explain
subtract 3x from 7x-3
Answer:
The answer is 4x-3 because all your doing is subtracting 3x from 4x
In a drawer, there are 8 knives, 8 spoons, and 5 forks. What is the probability of randomly drawing a knife or a spoon?
8+8=16 so 16/5 16÷5=3.2 32%
32% is the answer I think. Hope this helps
Answer:
32%
Step-by-step explanation:
8 + 8 = 16.
16/5
16 ÷ 5
= 3.2
= 32%
the sum of 2 numbers is 21. one number is 18 less than two times the other. find the numbers.
hence the numbers are 8 and 13
hope it helps you!!!!!!!!
Final answer:
The two numbers that satisfy the conditions of summing up to 21 and one being 18 less than twice the other are 8 and 13.
Explanation:
To solve the problem, let’s denote the two numbers as x and y. According to the question, the sum of the two numbers is 21, which can be expressed as an equation: x + y = 21. Additionally, we are told that one number is 18 less than two times the other, which gives us another equation: x = 2y - 18.
We can use the method of substitution to solve these equations. First, we will solve the second equation for x, which we already have as x = 2y - 18. Then we will substitute this expression for x in the first equation: (2y - 18) + y = 21. Simplifying we get: 3y - 18 = 21. Adding 18 to both sides gives us 3y = 39. So, dividing both sides by 3 yields y = 13. Now that we have the value of y, we can substitute it back into the equation x = 2y - 18 to get x = 2(13) - 18 which simplifies to x = 8.
Thus, the two numbers in question are 8 and 13.
Plz help me with this
Answer: [tex]\bold{A)\quad y=5sin\bigg(\dfrac{6}{5}x-\pi\bigg)-4}[/tex]
Step-by-step explanation:
The general form of a sin/cos function is: y = A sin/cos (Bx-C) + D where the period (P) = 2π ÷ B
In the given function, [tex]B=\dfrac{6}{5}[/tex] → [tex]P=2\pi \cdot \dfrac{5}{6}=\dfrac{10\pi}{3}[/tex]
Half of that period is: [tex]\dfrac{1}{2}\cdot \dfrac{10\pi}{3}=\large\boxed{\dfrac{5\pi}{3}}[/tex]
Calculate the period for each of the options to find a match:
[tex]A)\quad B=\dfrac{6}{5}:\quad 2\pi \div \dfrac{6}{5}=2\pi \cdot \dfrac{5}{6}=\dfrac{5\pi}{3}\quad \leftarrow\text{THIS WORKS!}\\\\\\B)\quad B=\dfrac{6}{10}:\quad 2\pi \div \dfrac{6}{10}=2\pi \cdot \dfrac{10}{6}=\dfrac{10\pi}{3}\\\\\\C)\quad B=\dfrac{5}{6}:\quad 2\pi \div \dfrac{5}{6}=2\pi \cdot \dfrac{6}{5}=\dfrac{12\pi}{5}\\\\\\D)\quad B=\dfrac{3}{10}:\quad 2\pi \div \dfrac{3}{10}=2\pi \cdot \dfrac{10}{3}=\dfrac{20\pi}{3}[/tex]
in any inequality or equation a number that does not change is called
In any inequality or equation, a number that does not change is called a constant.
A number that does not change in any inequality or equation is called a constant.
What are inequalities?Equations are not always balanced on both sides using an "equal to" sign in mathematics. Sometimes it might be about a "not equal to" connection, meaning that something is superior to or inferior to another. In mathematics, an inequality is a connection between two numbers or other mathematical expressions that results in an unequal comparison.
A constant in algebra is a single integer or, occasionally, a letter (such as a, b, or c) that stands in for a fixed number. something constant or unalterable a number that is supposed not to change the value in a particular mathematical discussion, for example, a number that has a fixed value in a certain scenario, globally, or that is distinctive of some substance or instrument
a concept in logic with a predetermined name
Therefore, A constant is a quantity that does not alter in any inequality or equation.
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Need help with this math. find the Slope of a line That contains the points (5,6) (1, 4).
Answer:
The slope can 1/2 or 0.5
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
The slope of a line is defined as ...
slope = (change in y)/(change in x)
Given two points, (x1, y1) and (x2, y2), the slope can be computed using ...
slope = (y2 -y1)/(x2 -x1)
It does not matter which points you call point 1 and point 2. You just need to be consistent.
Using the point values in the order given in the problem statement, we have ...
slope = (4 -6)/(1 -5) = -2/-4
slope = 1/2
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a factor of k, where k>0.
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.
Answer:
a) Similar
b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)
c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)
Step-by-step explanation:
Given:
Rectangle 1 has length = x
Rectangle 1 has width = y
Rectangle 2 has length = kx
Rectangle 2 has width = ky
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
Perimeter of Rectangle = 2*(Length + Width)
Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y
Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky
= k(2x+2y)
= k(Perimeter of Rectangle 1)
Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.
Area of Rectangle = Length * width
Area of Rectangle 1 = x * y
Area of Rectangle 2 = kx*ky
= k^2 (xy)
= k^2 (Area of rectangle 1)
Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.
Final answer:
Rectangles 1 and 2 are similar due to proportional dimensions. The perimeter of Rectangle 2 is proven to be k times the perimeter of Rectangle 1 by factoring out the scale factor. Similarly, the area of Rectangle 2 is k² times the area of Rectangle 1, as shown by multiplying the scaled dimensions.
Explanation:
(a) Yes, Rectangle 1 and Rectangle 2 are similar because the sides of Rectangle 2 are proportional to the sides of Rectangle 1. This means that the two rectangles have the same shape but different sizes, which is the definition of similarity in geometry.
(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, consider the perimeter of Rectangle 1, which is 2x + 2y. When each dimension is multiplied by k, the new length is kx and the new width is ky, so the perimeter of Rectangle 2 is 2(kx) + 2(ky) = 2kx + 2ky. Factoring out the common factor of k gives k(2x + 2y), which is k times the perimeter of Rectangle 1.
(c) For the area of Rectangle 2, the area of Rectangle 1 is xy. After scaling by k, the new dimensions of Rectangle 2 are kx and ky, so its area is (kx)(ky) = k²(xy), which shows that the area of Rectangle 2 is k² times the area of Rectangle 1.