The zeros of function p(x) = 5 - x² are x = √5 and x = -√5
Consider given polynomial function.
p(x) = 5 - x²
We know that the zeros of a function are the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.
⇒ p(x) = 0
⇒ 5 - x² = 0
⇒ 5 - x² - 5 = 0 - 5 ....(subtract 5 from each side of equation)
⇒ -x² = -5
⇒ x² = 5 ......(multiply both the sides by -1)
⇒ x = ±√5 .........(taking square-root of both the sides)
Thus x = √5 and x = -√5 are zeros.
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The complete question is:
What are the zeros of p(x) = 5 - x²?.
PLEASE HELP!!!!!!
Which expression is equal to 511√
Answer:
[tex]\frac{5\sqrt{11} }{11}[/tex]
Step-by-step explanation:
To cancel out a square-rooted number at the denominator, we can multiply the square-rooted number by multiplying the square root number over again:
[tex]\frac{5}{\sqrt{11}}[/tex] * [tex]\frac{\sqrt{11}}{\sqrt{11}}[/tex]
Now, any same number of square root times another same number of a square root will cancel out the root. So [tex]\sqrt{11}[/tex] * [tex]\sqrt{11}[/tex] will equal 11.
With this information, we can now go back to the problem, so we will get:
[tex]\frac{5\sqrt{11}}{11}[/tex]
4) Zombies and vampires are taking over. There are 100 zombies and 100
vampires. In function z(t), the zombies increase in population by 1000 per day,
and in function V(t), the vampire population increases by 25% each day, Which
population will reach 50,000 first?
!!PLEASE SOLVE THIS!!
For given functions for zombies and vampires, zombies will reach 50,000 first.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
Initial numbers, 100 Zombies and 100 Vampires.
In function z(t), the zombies increase in population by 1000 per day,
and in function V(t), the vampire population increases by 25% each day,
Therefore, z(t)=100+1000t where t=no, of days and
v(t)=100+25t where t= no. of days
for z(t)=50000
100+1000t=50000
t=49900/1000=49.9≈50days
for v(t)=50000
100+25t=50000
t=49900/25=1996 days
Hence,
zombies will reach 50,000 first.
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For given functions for zombies and vampires, zombies will reach 50,000 first.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
Initial numbers, 100 Zombies and 100 Vampires.
In function z(t), the zombies increase in population by 1000 per day,
and in function V(t), the vampire population increases by 25% each day,
Therefore, z(t)=100+1000t where t=no, of days and
v(t)=100+25t where t= no. of days
for z(t)=50000
100+1000t=50000
t=49900/1000=49.9≈50days
for v(t)=50000
100+25t=50000
t=49900/25=1996 days
Hence,
zombies will reach 50,000 first.
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helppp
i don't understand any of this
Here you go mate!
7x + 10 = -11
answer : x = -3
-12(x + 5) = -144
Answer : x = 7
-9x - 9 = 27
Answer : x = -4
x/4 + 2 = 10
Answer : x = 32
Given the following practical problem, what is the y-intercept of the linear function?
Desmond decided to babysit for extra money over the summer. He decided to charge a flat rate of $15 to babysit and then charged $10 for every hour he babysat.
A( 3
B(10
C(15
D(5
step by step pleaseee!
The y-intercept of the linear function is: C. 15.
What is the Y-intercept of a Linear Function?The y-intercept of a linear function is defined as the starting or initial value, which is also the point on the y-axis where the line of the equation crosses.
In a given function represented as y = mx + b, the y-intercept is the value of b.
From the information given above, we have:
Initial value/y-intercept (b) = flat rate = $15
Slope/unit rate (m) = $10
Therefore, the y-intercept of the function is: C. 15.
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Apply 9. The table shows the amount a restaurant is donating to a local school based on various dinner bills. Is the amount of the donation proportional to the dinner bill? If so, what would be the donation for a dinner bill of $50? If not, explain. Donations Dinner Bill ($) 25 30 35 40 Donation ($ 4.50 5.40 6.30 7.20
Answer: Yes, $9.
Step-by-step explanation:
From what I understand, since the table isn't showing: \
Dinner bill $25:$4.50 tip, $30:$5.40, etc..
To find if Bill is proportional, we need to find the rate of each tip to Bill and see if they match.
$25/$4.50 =5.555555555...
$30/$5.40 =5.555555555...
$35/$6.30 =5.555555555...
$40/$7.20 =5.555555555...
The rate is the same for each one, so yes, the amount of the donation proportional to the dinner bill.
To find the donation for a bill of $50, divide by the rate we found above.
[tex]Tip=$50/5.555555555=9.000...[/tex]
Find (fog)(x) where f(x)=x²+2, g(x)=x-3.
Step-by-step explanation:
fog(x)=f(x-3)
=(x-3)²+2
=x²-6x+9+2
=x²-6x+11
A planet has a circular orbit around a star it is distance of 67,000,000 km from the center of the star it orbits at an average speed of 35,000 km/h how many earth days does it take the planet to orbit the star give your answer to 2sf
The number of earth days that it will take the planet to orbit the star is 500 earth days.
Speed of an object.The rate of distance moved in a specific direction to the time taken can be referred to as the speed.
i.e speed = distance/ time taken
In the given question, the total distance covered is the length of the orbit.
So that,
length of the orbit = 2πR
where R is the radius i.e the distance of the star to the planet.
length of the orbit = 2 * 3.142 * 67000000
= 421028000 km
speed = distance/ time taken
⇒ time taken = distance/ speed
= 421028000 km/ 35,000 km/h
= 12029.37 h
But,
1 earth day = 24 hours
x = 12029.37 h
x = 12029.37 h * 1 earth day/ 24 h
= 501.2238 earth days
The number of earth days it will take the planet to orbit the star is 500 earth days.
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How many angles are there in a triangle ABC?.
A triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex.
There are three angles in a triangle ABC. A triangle is a three-sided polygon and it has three angles. Each angle is formed by the intersection of two sides of the triangle.
In a triangle, the angle between two sides is measured in degrees and these angles are formed by the intersection of the two lines that represent the sides of the triangle. The three angles in a triangle are labeled with the corresponding vertex, for example, angle A, angle B, and angle C.
In a triangle, the sum of the three angles is always 180 degrees. This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.
Therefore, In short, a triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex. The sum of the three angles in a triangle is always 180 degrees.
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What is the factor of a polynomial x² +6x 8 )?.
The factors of a polynomial x² +6x + 8 ( binomial, power of variable x is 2) are equals to the ( x + 2) ( x + 2).
In Mathematics, Factorisation of an algebraic expression is a process of writing the given expression as a product of its factors. These factors can be any type like numbers, variables, or an algebraic expression. To make the factor of a number means to break it up or decompose into numbers such that the multiplication of these can be get the original number. For example, In case of x² – 9 is (x – 3) (x + 3). In other words
(x- 3) and (x + 3) are the factors of x² – 9. We have, a polynomial say, p(x) = x² +6x + 8 and we have to factorize it. Now, x² +6x + 8 ----(*)
Split the middel term of above expression such that sum/difference of split terms is equal to 6x and multiplication of these give 8x².
=> x² + 4x + 2x + 8
group the pairs, => (x² + 2x ) + (4x + 8)
factor each group of pairs,
=> x( x + 2) + 2( x + 2)
Factor out the common term (x + 2)
=> (x + 2) ( x + 2)
Hence, required factors are ( x + 2) (x + 2).
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14. One of the classic proofs of the Pythagorean Theorem involves the
diagram below where square ABCD has had points E, F, G, and H located
on its sides such that AE = BF=CG= DH as shown. The proof then
relies on quadrilateral EFGH being a square.
(a) First, explain why EFGH must be a rhombus. Use a paragraph proof
style, but carefully justify all of your statements with reasons.
(b) Give an explanation for why all interior angles of EFGH must be right angles? Explain why this fact in
combination with your proof in part (a) show that EFGH is a square?
We showed that EFGH is a square by proving that EFGH is a rhombus and all the angles are right angles. This is one of the classic proofs of the Pythagorean theorem.
How do you solve equations?(a) First, explain why the EFGH must be a rhombus.
In the figure, square ABCD has points E, F, G, and H on each side, so AE = BF = CG = DH, as shown. This means that all four sides of the rectangle EFGH are the same length. This is because they are all congruent with the side lengths of square ABCD. According to the definition of a rhombus, a rhombus is a quadrilateral with all four sides congruent. All four sides of the quadrilateral EFGH are congruent, so it must be a rhombus.
(b) Explain why all interior angles in EFGH must be right angles?
In square ABCD, by definition, all interior angles are right angles (90 degrees). Since the points E, F, G, and H lie on the sides of the square ABCD, the angles EFG and FGH are congruent to the right angle of the square ABCD. Similarly, the angles FGH and HGE are congruent to the right angle of the square ABCD.
Therefore, all four interior angles of quadrilateral EFGH are congruent with right angles of square ABCD, and all four interior angles of quadrilateral EFGH are right angles.
A square is a quadrilateral with all four sides congruent and all four angles congruent at right angles. And since it has already been proved that the quadrilateral EFGH is a rhombus and all its angles are right angles, we know that the quadrilateral EFGH is a square.
We showed that EFGH is a square by proving that EFGH is a rhombus and all the angles are right angles. This is one of the classic proofs of the Pythagorean theorem.
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Place these events from "Let George Do It!" in the right sequence by choosing the correct step from each blue box.
A strange feeling developed in his stomach.
"George, come with us for a ride," the boys called.
They looked toward the shore and saw the large sand dunes.
"George, do you want to be like this always?"
Tall, lanky George walked along the dusty path in Alderdale, Washington.
George reached the boys, and with one quick jump, leaped into the boat.
They were now approaching home.
The events from "Let George Do It!" in the right sequence will be:
Tall, lanky George walked along the dusty path in Alderdale, Washington."George, come with us for a ride," the boys called.George reached the boys, and with one quick jump, leaped into the boat.They looked toward the shore and saw the large sand dunes.They were now approaching home.A strange feeling developed in his stomach."George, do you want to be like this always?"What is the program about?From 1946 to 1954, Owen and Pauline Vinson produced the radio drama series Let George Do It in the United States.
In 1954, Olan Soule voiced the role of private eye George Valentine, which was portrayed by Bob Bailey. The scripts by David Victor and Jackson Gillis were directed by Don Clark.
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the sum of two numbers is 30. the
difference between the two numbers is four. what are the two numbers?
Answer:
the numbers are 13 and 17
Step-by-step explanation:
let the first number be a
let the second number be b
a+b=30.......a=30-b
a-b=4
substitute the first eq into the second one
30-b-b=4
30-2b=4
30-4=2b
26=2b
13=b
a=30-b
a=30-13
a=17
Take a factor out of the square root.
[tex]\sqrt{x^3}[/tex]
Answer:
[tex]x\sqrt{x}[/tex]
Step-by-step explanation:
Use Exponent Power rule:
[tex]b^{1/n} =\sqrt[n]{b}[/tex]
Given [tex]\sqrt{x^3}[/tex] also known as [tex]\sqrt[2]{x^3}[/tex], rewrite with exponent power rule as [tex]x^{3/2}[/tex].
Factor [tex]x[/tex] from [tex]x^{3/2}[/tex] = [tex]x(x^{1/2})[/tex]
Rewrite as [tex]x\sqrt{x}[/tex]
Temasa has a 1:10 scale drawing of her doll house in the drawing the dimensions of the rectangular house are 7 1/5 inches by 4 4/5 inches.The actual length is 72
inches
12 inches equals 1 feet, what is the area of Temasa's doll house
to the nearest SQUARE FOOT?
The area of the Temasa's doll house is 31.5 square feet.
What is the scale factor?
The scale factor is a ratio that compares the measurements of an object on a drawing or map to the actual measurements of that same object in real life. It is usually expressed as a ratio in the format 1:n (or 1/n) where n is the scale factor.
We can start by using the scale factor of 1:10 to find the actual dimensions of the doll house.
Since the scale factor is 1:10, this means that for every 1 inch on the drawing, the actual measurement is 10 inches. So, to find the actual length and width of the doll house, we can multiply the measurements on the drawing by 10.
7 1/5 inches * 10 = 71 inches + 2 inches
4 4/5 inches * 10 = 44 inches + 8 inches
So, the actual length of the doll house is 71 inches + 2 inches = 73 inches, and the actual width is 44 inches + 8 inches = 52 inches.
To find the area of the doll house, we can multiply the length and width:
73 inches * 52 inches = 3788 square inches
To convert this to square feet, we can divide by 12^2, since 1 foot = 12 inches:
3788 square inches / (12 inches)^2 = 31.5 square feet (rounded to the nearest square foot)
Hence, the area of the Temasa's doll house is 31.5 square feet.
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Triangle TUV is dilated by a scale factor of 1/3 to from triangle T'U'V. Side U'V' measures 3. What is the measure of side UV
Answer:
9
Step-by-step explanation:
The pre-image is larger than the image because the scale factor is 1/3. That means that the scale factor going from the image to the pre-image is 3.
3 x 3 = 9
what is 3 and 1/6 as an improper fraction
Answer:
Step-by-step explanation: 3×6+1,3×6 is 18+1 is 19/6 is your answer
Find the median of these numbers:
15
22
13
24
Answer: The median is 19
Step-by-step explanation:
To find the median you have to arrange the numbers from lowest to highest.
It would go like this: 13, 15, 16, 22, 24, 28
Pick the number that is in the middle. In this case, it would be 16 and 22. The median of these numbers is the mean of these 2.
To find the mean you add 16 and 22 together to get 38 and divided it by 2 to get 19.
I hope this was able to help you :D
How do you solve complex fractions with rational expressions?.
To solve a complex fraction, which is a fraction that contains one or more fractions in its numerator and/or denominator, you can follow these steps:
Factor the numerator and denominator of the complex fraction if possible. This will make it easier to cancel common factors.
Multiply both the numerator and denominator by the reciprocal of the fraction(s) in the denominator. This will eliminate the fraction(s) in the denominator, leaving a simplified expression.
Simplify the resulting expression by combining like terms, if possible.
Check your work by multiplying the numerator and denominator of the original complex fraction by the reciprocal of the fraction(s) in the denominator, and verifying that the simplified expression you obtained is equivalent.
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What is the product of X+ a and x b )?.
The product of (X + A) + (X + B) is- [tex]x2 + xb + ax + ab[/tex]
The information provided in the question,
The outcome of multiplying two numbers together is known as the product. 12 is the result of the addition of 3 and 4, 20 is the sum of 4 and 5, and so on. Discovering the Product A multiplication problem has a solution in the product.
We must determine the of (x + a) and (x + b).
The product is the result of multiplying two numbers, as we all know.
So,
[tex]( x+ a)[/tex] x [tex]( x + b)[/tex]
[tex]x( x+b) + a( x + b)[/tex]
[tex]x[/tex]²[tex]+ bx + ax + ab[/tex]
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What’s the answer to this simpflied?
g(x) = 2x + 4, h(x) = x² +1
Find g(h(24))
Using Composition of functions, the value of g(h(24)) = 1158.
What is meant by Composition of functions?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
The new function h is created by combining the two functions f and g, where h(x) = f(g(x)) for all x in g's domain where g(x) is in f's domain. Function composition is denoted by the notation h = f • g, also written as h(x) = (f • g)(x), which can be interpreted as "f of g of x."
Given,
g(x) = 2x + 4, h(x) = x² +1
Using composition of functions,
⇒ h(24) = 24² + 1
⇒ g(h(24)) = 2 (24² + 1) + 4
⇒ g(h(24)) = 2 × 577 + 4
⇒ g(h(24)) = 1158
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Help please! I will reward brainiest.
Answer:
follow me first
Step-by-step explanation:
i will answer that in 60 sec
Answer:
B
Step-by-step explanation:
1. Before anything, figure out the inequality symbol. Why? In the solutions, all of the inequalities are different so you narrow it down by figuring out the inequality sign.
2. "At most 50 pounds" means we can't go over 50 pounds, but the package can still equal 50, that's just the most it can be. This means we will have a line underneath because it includes the maximum number, 50, in the solution.
3. "At most" also means the package (x) cannot be over 50. The sign opening must face 50 because that shows x has to be less than. But it can equal 50, so the sign is [tex]x\leq 50[/tex]. That would be B.
4. About the numbers, the box weighs 2 pounds. This means it is x+2 because weight is not negative and it is ADDING weight to what we don't know. To isolate x, just do 50-2, and you get 48. That again proves b is the answer.
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2
Identify one pair of supplementary angles.
Figure 1
Ꮋ
E
A HJC & ZHJG
B) /AJB & /BJC
c) ZGJE & ZEJD
D_ /HCJ & /HᏀᎫ
&
B
Answer:
B) /AJB & /BJC are a pair of supplementary angles.
Step-by-step explanation:
Sam can paint an apartment living room in 3 hours, and Pam can paint the same room in 2 hours. The solution to the equation §+ £ = 1 describes how long it will take them to paint the living room if they work together. Before solving this problem, make a guess about the answer. Then solve the equation. How did your guess compare?
Answer:
sorry its so long
Step-by-step explanation:
We multiply the entire equation by the number
6
6 in order to get rid of the fractions.
2
�
+
3
�
=
6
5
�
=
6
�
=
6
5
=
1
1
5
1
1
5
ℎ
=
1
hour
12
minutes
2x+3x
5x
x
1
5
1
h
=6
=6
=
5
6
=1
5
1
Can a 2-digit number start with 0?.
No, a 2-digit number cannot start from Zero (0), as it can only have values ranging from 1 to 9.
When a number has two digits, it is called a 2-digit number. 2-digit numbers have two digits and range from 10 to 99. They are unable to begin with zero since it will then be regarded as a single-digit number. Any number between 1 and 9 can be used as the digit in the tens place.
The placement of each digit in a number is known as place value. There is just one place value that matters when discussing 1-digit numbers, and that is the ones place. There are two place values for 2-digit numbers: ones and tens. Two-digit numbers can be expressed verbally, numerically, or in their expanded form. 45 is a 2-digit number, for instance.
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For the following dilation, do, k = (5, 0) (10, 0), the scale factor is equal to ______. 10 2 5 0. 5.
The scale factor is equal to 2.
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
as given, K =(5,0) (10,0)
Solution:
Initial Coordinates=(5,0)=(xi,yi)→xi=5, yi=0
Final Coordinates=(10,0)=(xf,yf)→xf=10, yf=0
Scale factor=xf/xi=yf/yi
We divide the final coordinates by the initial coordinates. In this case the ordinates (yf and yi) are zero and we can't divide by zero, but the abscissas (xf and xi) are different of zero, then we can use them:
Scale factor=xf/xi=10/5
Scale factor=2
Therefore, the scale factor is equal to 2.
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If Alice fed her fish 1/4 tsp, of food before school and 3/4 tsp of food after school, how much did she have left if the container had 2 tsp total at the beginning of the day?
The amount left in the container by Alice is solved to be 3/8 tsp
How to solve for the amount left in the containerTo find the amount left in the container the amount used to feed the fish in each case will factored and then used for subsequent feeding. of the fish.
From the problem it can be deduced that the initial amount in the container was 2 tsp
The routine feeding of the fish include:
Alice fed her fish 1/4 tsp, of food before school = 1/4 * 2 = 1/2
The 2 tsp has reduced to 1/2, this is further used as shown below
Alice fed her fish 3/4 tsp, of food after school = 3/4 * 1/2 = 3/8 tsp
We can therefore say that the amount left in the container is 3/8 tsp
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Triangle ABC is a right triangle with the right angle at angle B. If the sine of angle A is ? and the longer leg is 52 inches, what is the length of the shorter leg of the triangle?
Answer:
The length of the shorter leg of the triangle can be calculated using the Pythagorean Theorem. The formula is a^2 + b^2 = c^2, where a is the length of the shorter leg, b is the length of the longer leg and c is the length of the hypotenuse. In this case, a^2 + 52^2 = c^2. The hypotenuse can be calculated by using the sine formula. c = (52/sinA). Substituting this value into the Pythagorean Theorem equation, a^2 + 52^2 = (52/sinA)^2. Solving for a, a = sqrt(52^2 - (52/sinA)^2).
What is the remainder when x4 x³ 2x² X 1 is divided by x 1?.
After solving, the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex] is divided by x − 1 is 2.
In the given question, we have to find the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex] is divided by x − 1.
The given polynomial is [tex]x^4 + x^3 - 2x^2 + x + 1[/tex].
We have to find the remainder of the polynomial when we divide this polynomial x - 1.
To find the polynomial we equate x - 1 equal to zero to find the value of x.
x - 1 = 0
x = 1
Now putting x = 1 in the given equation [tex]x^4 + x^3 - 2x^2 + x + 1[/tex].
P(x) = [tex](1)^4 + (1)^3 - 2(1)^2 + 1 + 1[/tex]
P(x) = 1 + 1 - 2×1 + 1 + 1
P(x) = 2 - 2 + 2
P(x) = 2
Hence, the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex] is divided by x − 1 is 2.
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The complete question is:
What is the remainder when [tex]x^4 + x^3 - 2x^2 + x + 1[/tex] is divided by x − 1?
Find triangle perimeter Please help quick, answer will be not useful after 4 hours
The perimeter of the triangle is given by the equation P = 4√3 feet
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the perimeter of the triangle be P
Let the triangle be represented as LMX
Now , An equilateral triangle is a triangle in which all three sides have the same length.
∠L = ∠M = ∠X = 60° and LM = MX = LX
The height of the triangle is LW = 2 feet
Now , from the trigonometric relations ,
sin 60° = opposite side / hypotenuse
Substituting the values in the equation , we get
√3 / 2 = 2 / LX
Multiply by LX on both sides of the equation , we get
LX ( √3/2 ) = 2
Multiply by ( 2/√3 )on both sides of the equation , we get
LX = 4/√3
Now , the perimeter of the triangle = LX + LM + MX
Perimeter of the triangle P = 3 ( 4/√3 )
Perimeter of the triangle P = 4√3 feet
Hence , the perimeter is 4√3 feet
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