Symmetry is when an image or being is halved into two, and both sides are the exact same to each other.
Final answer:
Symmetry in mathematics refers to an object's balanced or invariant properties under transformations like reflection, rotation, or translation. It is significant in physics for understanding conservation laws and is observed in various aspects of nature and art, providing balance and stability.
Explanation:
Symmetry is a fundamental concept in mathematics, physics, and the natural world. It implies that an object or system possesses a form of invariance or balance under certain transformations, such as reflection, rotation, or translation. In mathematical terms, symmetry refers to a situation where a figure can be manipulated in various ways, such as being flipped over a mirror plane (reflective symmetry), rotated around a central point (rotational symmetry), or shifted along a direction without changing its appearance (translational symmetry).
An example of symmetry in nature is bilateral symmetry, where an object can be divided into two symmetrical parts across a unique plane. This type of symmetry is easily observed in some living organisms, like humans, who have a left and right side that are mirror images of each other. In the realm of physics, symmetry plays an impactful role, especially in the study of sub-atomic particles through the use of particle accelerators like the Large Hadron Collider at CERN. Emmy Noether's work highlighted the deep connection between symmetries and conservation laws, illustrating the significance of symmetry in understanding the foundational principles of our universe.
In art, symmetry is associated with balance and harmony. Symmetrical balance is visually stable, often featuring compositions that are identical, or nearly so, on either side of a central axis. Optical devices, such as mirrors and lenses, also exploit principles of symmetry, with their function heavily dependent on a specific optical axis to guide light appropriately.
11 fives and 3 ones =
Answer:
If you mean the sum ?
55 + 3 = 58
Answer:
58
Step-by-step explanation:
11 x5=55
3x1=3
55+3=58
Create a system of equation.
The following system of equations represents the given statement;
x = y+z
y = 2z
10x+15y+40z = 600
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Step-by-step explanation:
Let,
Small pizza = x
Medium Pizza = y
Large Pizza = z
Cost of one small pizza = $10
Cost of one medium pizza = $15
Cost of one large pizza = $40
According to given statement;
They usually sells as many small pizzas as medium and large pizzas combined.
x = y+z
The number of medium pizzas sold is usually twice as many as large ones.
y = 2z
How many of each pizza must they sell to get $600.
10x+15y+40z = 600
The following system of equations represents the given statement;
x = y+z Eqn 1
y = 2z Eqn 2
10x+15y+40z = 600 Eqn 3
Putting value of x and y from Eqn 1 and 2 in Eqn 3;
[tex]10(y+z)+15(2z)+40z=600\\[/tex]
We know that y=2z from Eqn 2,
[tex]10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600[/tex]
Dividing both sides by 100;
[tex]\frac{100z}{100}=\frac{600}{100}\\z=6[/tex]
Putting z=6 in Eqn 2;
[tex]y=2(6)\\y=12[/tex]
Putting value of y and z in Eqn 1;
[tex]x=12+6\\x=18[/tex]
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Keywords: linear equations, substitution method
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what is 1/8 x 3/4 iready
1/8*3/4
multiply the numerators together
1*3=3
multiply the denominators together
8*4=32
answer:
3/32
Answer:
The answer is 3/32.
Step-by-step explanation:
You multiply 1/8 x 3/4. 1x3 equals 3 so that is the numerator and 8x4 equals 32 so that is the denominator.
Jamal is having a football party with 10 people he orders 2 1/3 large pizzas for the party he gives equal amounts of pizza to each person what fraction of the pizza does each person get?
Each person will get 7/30 fraction of pizza
Step-by-step explanation:
Given
[tex]Total\ pizza = 2\frac{1}{3} = \frac{7}{3}\\Total\ people = 10[/tex]
In order to find the fraction of pizza each person will get, we have to divide the total pizza by total number of people
So,
[tex]Share\ of\ one\ person = \frac{\frac{7}{3}}{10}\\=\frac{7}{3} * \frac{1}{10}\\=\frac{7}{30}[/tex]
Hence,
Each person will get 7/30 fraction of pizza
Keywords: Fractions, Division
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Triangle ABC is similar to triangle DEF
Which of the following statements is NOT true?
a. Segment BC is congruent to segment DE
b. m angle D = 80 degrees
c. a/c = 2
d. 3/c = 6/a
Answer:
a. Segment BC is congruent to segment DE
Step-by-step explanation:
what is the lowest common denominator of:11/5+2/3+1/6
Answer:
30
5 × 6 = 30
3 ×10 = 30
6 × 5 = 30
Answer:
LCD = 30Step-by-step explanation:
[tex]LCD\ of\ \dfrac{2}{3}\ and\ \dfrac{1}{6}\ is\ 6:\\\\\dfrac{2}{3}=\dfrac{2\cdot2}{3\cdot2}=\dfrac{4}{6}\\\\LCD\ of\ \dfrac{1}{6}\ ond\ \dfrac{11}{5}\ is\ 30:\\\\\dfrac{11}{5}=\dfrac{(11)(6)}{(5)(6)}=\dfrac{66}{30}\\\\\dfrac{1}{6}=\dfrac{(1)(5)}{(6)(5)}=\dfrac{5}{30}\\\\\dfrac{2}{3}=\dfrac{4}{6}=\dfrac{(4)(5)}{(6)(5)}=\dfrac{20}{30}\\\\\text{Therefore:}\\\\\dfrac{11}{5}+\dfrac{2}{3}+\dfrac{1}{6}=\dfrac{66}{30}+\dfrac{20}{30}+\dfrac{5}{30}=\dfrac{66+20+5}{30}=\dfrac{91}{30}=3\dfrac{1}{30}[/tex]
PLEASE HELP!
3. A certain can of soup has a radius of 4 cm and a height of 10 cm. For a new can, the height
and the radius will each be increased by x cm. Find the polynomial that gives the volume of the
new can in cm'. Leave your answer in terms of . [Use V = pi r^2h
Answer:
The volume of the new can is [tex]V_2=160x^3\pi\ cm^3[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z ----> the scale factor
In this problem
[tex]z=x[/tex]
The volume of the original can is
[tex]V_1=\pi r^{2}h[/tex]
The volume of the new can is
[tex]V_2=z^{3}V_1[/tex]
[tex]V_2=x^3(\pi r^{2}h)[/tex]
we have
[tex]r=4\ cm\\h=10\ cm[/tex]
substitute
[tex]V_2=x^3(\pi (4)^{2}10)[/tex]
[tex]V_2=160x^3\pi\ cm^3[/tex]
A rectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. At what value of x will the area of the walkway equal the area of the pool?
Answer:
x = 1 mStep-by-step explanation:
Area of pool:
6*4= 24 m²Area of walkway:
(6+2x)(4 +2x) - 24 =24 + 12x + 8x + 4x² - 24 =4x² + 20xIf the areas are equal, then:
4x² + 20x = 24x² + 5x - 6 = 0x = (-5 ±√25+24)/2x = (-5 ± 7)/2x = 1 and x = -6 (excluded as negative)Final answer:
To find the value of x when the area of the walkway equals the area of the pool, set up an equation and solve for x. The value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
Explanation:
To find the value of x when the area of the walkway equals the area of the pool, we need to set up an equation. The area of the pool is the length multiplied by the width, which is 6 meters multiplied by 4 meters, or 24 square meters. The area of the walkway is the total area of the larger rectangle minus the area of the pool.
The total area of the larger rectangle is the length plus twice the width, all multiplied by the width. So, the area of the walkway is x(6 + 2x - 4). Setting the area of the walkway equal to the area of the pool gives us the equation: x(6 + 2x - 4) = 24.
To solve this equation, we can first simplify it by distributing the x through the parentheses: 6x + 2x^2 - 4x = 24. Combining like terms, we have 2x^2 + 2x - 24 = 0. To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring gives us 2(x + 6)(x - 2) = 0. So either (x + 6) = 0 or (x - 2) = 0. Solving for x, we find that x = -6 or x = 2.
Since we are dealing with width, the negative solution x = -6 is not applicable. Therefore, the value of x that will make the area of the walkway equal to the area of the pool is x = 2 meters.
please answer this fast thank you for your help
Answer:
Prices of Toys: As we move to the right, toy sales decrease and suddenly jump up to a certain point when advertising begins. advertising lasts for a while, but as soon as it stops, the toy sales go down. X axis is time and y axis is sales in thousands
Step-by-step explanation:
A runner runs 8 miles in 92 minutes what is the runner’s unit rate?
Answer:
The runner's unit rate is 0.09 miles/minute.
Step-by-step explanation:
Given:
Distance cover by runner = 8 miles and the time taken = 92 minutes.
Now, to calculate the runner's unit rate.
We put the formula to get the unit rate:
Velocity = distance/time
[tex]v=\frac{d}{t}[/tex]
[tex]v=\frac{8}{92}[/tex]
[tex]v=0.0869[/tex]
v = 0.09 miles/minute (approximately)
Therefore, the runner's unit rate is 0.09 miles/minute.
Final answer:
To find the runner's unit rate, divide the total miles (8) by the total minutes (92), resulting in a rate of 0.08695652 miles per minute or 5.217 miles per hour when converted.
Explanation:
The question is asking to find the unit rate of a runner who runs 8 miles in 92 minutes. To find the unit rate, we need to calculate how many miles the runner can run in one minute. This involves dividing the total miles run by the total minutes taken.
Calculation:
Unit Rate = Total Miles / Total Minutes = 8 miles / 92 minutes = 0.08695652 miles per minute.
For practical purposes and better understanding, it might be useful to convert this unit rate into miles per hour. Since there are 60 minutes in an hour, we simply multiply the unit rate per minute by 60.
Miles per hour = 0.08695652 miles/minute * 60 minutes/hour = 5.217 miles per hour.
Therefore, the runner's unit rate is 0.08695652 miles per minute, or equivalently, 5.217 miles per hour.
plant a is 4.7 centimeters tall and growing at the rate of 3.5 centimeters a month. plant b is 5.2 centimeters tall and growing at the rate of 2.5 centimeters a month. When will plant a axceed the height of plant b? what will the hights of the plants be after 3 months
After 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
To find when to plant A will exceed the height of plant B, we need to set up an equation:
Let t be the number of months, then the height of plant A after t months is:
Height of plant A = 4.7 + 3.5t
The height of plant B after t months is:
Height of plant B = 5.2 + 2.5t
We want to find when to plant A will exceed the height of plant B, so we need to solve the equation:
4.7 + 3.5t = 5.2 + 2.5t
Simplifying, we get:
t = 1.0
Therefore, plant A will exceed the height of plant B after 1 month.
To find the heights of the plants after 3 months, we substitute t = 3 into the equations:
Height of plant A = 4.7 + 3.5(3) = 14.2 centimeters
Height of plant B = 5.2 + 2.5(3) = 12.7 centimeters
Therefore, after 3 months, plant A will be 14.2 centimetres tall and plant B will be 12.7 centimetres tall.
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Final answer:
After solving linear equations for growth over time, Plant A will exceed the height of Plant B after 1 month. After 3 months, Plant A will be 15.2 cm tall and Plant B will be 13.7 cm tall.
Explanation:
The question involves two plants with different initial heights and growth rates. To find out when Plant A will exceed the height of Plant B and their heights after 3 months, we can use linear equations.
Calculation for Exceeding Height:
Let x represent the number of months it will take for Plant A to exceed the height of Plant B. The equation for Plant A's height over time is:
Height of Plant A = 4.7 + 3.5x (in centimeters)
The equation for Plant B's height over time is:
Height of Plant B = 5.2 + 2.5x (in centimeters)
To find out when Plant A exceeds Plant B, we set the equations equal and solve for x:
4.7 + 3.5x = 5.2 + 2.5x
Solving for x, we find that x = 1. Therefore, after 1 month, Plant A will exceed the height of Plant B.
Heights After 3 Months:
Height of Plant A = 4.7 + 3.5(3) = 15.2 cm
Height of Plant B = 5.2 + 2.5(3) = 13.7 cm
Which of the following is a solution to this inequality? y greater than one half times x plus 2 (1, 4) (−1, 1) (2, 3) (0, 2)
Answer:
(1, 4)
Step-by-step explanation:
Lets show first the inequality. Putting in numbers what greater than one half times x plus 2 means is:
y > (1/2)x + 2
The procedure is simple: take the points and replace them in the inequality to see which verifies.
(1, 4):
4 > (1/2)*1 + 2
4> 1/2+ 2
4 > 1/2 + 4/2
4> 5/2
8/2> 5/2 ---> I verifies!!!
(-1, 1)
1 > (1/2)(-1) + 2
1> -1/2 + 2
1 > -1/2 + 4/2
1 > 3/2 ---> Not verify!!
(2, 3):
2 > (1/2)*2 + 2
2 > 1 + 2
2 > 3 ---> Not verify!!!
(0, 2)
2 > (1/2)*0 + 2
2 > 2 ---> Not verify!!!
So, the only pair that verifies is (1, 4)
Elliott has some yarn that she wants to use to make hats and scarves. Each hat uses 0.2, point, 2 kilograms of yarn and each scarf uses 0.1, point, 1 kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, and she wants to make a total of 20 items.
Answer:
Elliot will make 4 hats and 16 scarves
Step-by-step explanation:
Let x be the number of hats and y be the number of scarves Elliot will make.
Elliott wants to make a total of 20 items, then
x + y = 20
Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then
0.1y = 2(0.2x)
Thus,
0.1y = 0.4x
y = 4x
Substitute it into the first equation:
x + 4x = 20
5x = 20
x = 4
y = 20 - 4
y = 16
Hence, Elliot will make 4 hats and 16 scarves
Answer:
0.1s=2.0.2h
h+s=20
Step-by-step explanation:
PLEASE HELP ASAP!!!
Which of these sentences is an independent clause?
1. While Marvin plays air guitar in the back seat.
2. Unless she can get the gum out of her hair in time for the big dance.
3. The superhero is afraid of heights.
4. Until Thanksgiving is over.
Answer:
3. The superhero is afraid of heights.
"The superhero is afraid of heights." is independent clause because the sentence contains a subject and verb and it's a complete sentence.
Step-by-step explanation:
An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.
Jim studied in the Sweet Shop for his chemistry quiz.
A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word. A dependent marker word is a word added to the beginning of an independent clause that makes it into a dependent clause. Some common dependent markers are: after, although, as, as if, because, before, even if, even though, if, in order to, since, though, unless, until, whatever, when, whenever, whether, and while.
When Jim studied in the Sweet Shop for his chemistry quiz . . .
(What happened when he studied? The thought is incomplete.)
Hope this helps!!!Answer: choice 3. The superhero is afraid of heights
The other choices are sentences that are incomplete because they need more structue to them. For example, sentence 1 implies that something else is going on during Marvin's guitar time. The other sentences have cliffhangers as well and they arent fully independent or on their own. Sentence 3 expesses a single complete thought without introducing some other related or tangential thought needed to complete that idea.
The product of two consecutive even integers is 440.. what are the positive and negative integers?
Positive integers are 20,22 and negative integers are -22,-20.
Step-by-step explanation:
Let,
2 positive integers are x, x+2
According to given statement;
[tex]x(x+2)=440\\x^{2}+2x=440\\x^{2}+2x-440=0\\x^{2}+22x-20x-440=0\\x(x+22)-20(x+22)=0\\(x+22)(x-20)=0\\Either,\\x+22=0\\x=-22\\Or,\\x-20=0\\x=20[/tex]
If x=-22
Then,
x+2 = -22+2 = -20
Or,
x=20
x+2 = 20+2 = 22
Positive integers are 20,22 and negative integers are -22,-20.
Keywords: Integers, Multiplication
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The two consecutive even integers whose product is 440 are 20 and 22. When considered as positive and negative, they are +20 and -20, +22 and -22, respectively.
Explanation:To find the two consecutive even integers whose product is 440, we need to employ some algebraic reasoning. Let's denote the first of the two consecutive even integers as x.
Given that even integers follow a pattern of +2, we can denote the next consecutive even integer as x + 2.
Hence, we're solving for the equation x * (x + 2) = 440. Solving this equation will give us our consecutive even integers, which are 20 and 22. In terms of positive and negative integers, they would be represented as +20 and -20, +22 and -22, respectively.
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A large soup pot holds 20 quarts. What could be its volume in liters?
Answer:
In litres the volume of the pot of soup is 18.93litre
Step-by-step explanation:
This problem seeks to examine our understanding of unit conversion
Step one
Convert quarts to liters
Definition of quart (symbol: qt)
Quart is a unit of volume in the United States customary and imperial systems of measurement. Multiple.
Step two
If 1 qt=0.946353 litre
20qt=x litre
By cross multiplication we have
x litre = 20*0.946353 litre
x=18.93litre
In litres the volume of the pot of soup is 18.93litre
To convert 20 quarts to liters, you would use the conversion factor of 1 liter equating to 1.06 quarts. Following this conversion, the volume of the soup pot would be approximately 18.87 liters.
Explanation:You're asked about the volume of a soup pot that contains 20 quarts and wants it to be converted to liters. Based on our comparison, 1 liter is approximately equivalent to 1.06 quarts. So to convert from quarts to liters, you'd divide the amount in quarts by the conversion factor.
Here is a step-by-step process to convert 20 quarts to liters:
Identify the conversion factor: 1 liter = 1.06 quarts
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what is 139.5 as a fraction?
Answer:
139.5/1 or 1395/10
Step-by-step explanation:
The quadrilateral shown is a parallelogram. If m∠ADC = 125° and m∠1 = 30°, what is m∠2? A) 15° B) 25° C) 35° D) 55°
Answer:
B) 25°
Step-by-step explanation:
Assuming the quadrilateral is the one shown in the picture attached, then a triangle ADC is form, where m∠ADC = 125° and m∠1 = 30°. The addition of the three angles of a triangle is equal to 180°, so:
m∠ADC + m∠1 + m∠2 = 180°
Replacing with the known values and isolating m∠2 we get:
125° + 30° + m∠2 = 180°
m∠2 = 180° - 125° - 30°
m∠2 = 25°
Answer:
it is 25 degrees
Step-by-step explanation:
thanks for your help
plz mark as brainlest.
Find the solution for -2y + 10 < -14.
1 y > -12
2 y < -12
3 y > 12
4 y < 12
Answer:
y > 12Step-by-step explanation:
[tex]-2y+10<-14\qquad\text{subtract 10 from both sides}\\\\-2y+10-10<-14-10\\\\-2y<-24\qquad\text{change the signs}\\\\2y>24\qquad\text{divide both sides by 2}\\\\\dfrac{2y}{2}>\dfrac{24}{2}\\\\y>12[/tex]
solve 2x + 3 = 9 nowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
x=3
Step-by-step explanation:
2
x
+
3
=
9
We want to find the variable
x
, so we have to make it alone. To do so, first subtract
3
from both sides of the equation:
2
x
+
3
−
3
=
9
−
3
2
x
=
6
Now divide both sides by
2
:
2
x
2
=
6
2
So the final answer is:
x
=
3
Hope this helps!
Answer: x = 3
Step-by-step explanation: To solve for x in the equation you see here, our goal is to get x by itself.
Our first step will be to isolate the term containing x which in this case is 2x. To isolate 2x, we have to get rid of the 3 by subtracting 3 from both sides of the equation.
On the left, the 3's cancel each other out and we are left with 2x. On the right, 9 - 3 simplifies to 6 and we are left with 2x = 6 which is a one step equation.
To get x by itself, since it's being multiplied by 2, we just divide both sides of the equation by 2. On the left, the 2's cancel and we are left with x. On the right, 6 over 2 simplifies to 3.
Therefore, our answer is x = 3.
Find the least common denominator (LCD) of 1/6 and 11/12
Answer:
12
Step-by-step explanation:
12 is the smallest number that divisible by 6 and 12
please help solve with steps: Order of operation with integers.
5 - 6x (-7)
Thank you
Answer:
5 + 42
Step-by-step explanation:
Given
5 - 6x(- 7)
= 5 - 6 × - 7 ← perform multiplication before subtraction
= 5 + 42
= 47
Answer:
47Step-by-step explanation:
Use PEMDAS:
P Parentheses first
E Exponents
MD Multiplication and Division
AS Addition and Subtraction
[tex]5-6\times(-7)[/tex] first - multiplication
[tex]=5+(-6)(-7)=5+42[/tex] next - addition
[tex]=47[/tex]
Each side of rhombus 7 cm find the perimeter of a rhombus
Answer:
P = 28cm
Step-by-step explanation:
First, all four sides of a rhombus are congruent, meaning that if we find one side, we can simply multiply by four to find the perimeter. Second, the diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half.
Hope this helps!!!The new merry go round can hold a total weight of 500 pounds. Susie weighs 45.67 pounds, Johnny weighs 76.9 pounds, Grace weighs 66.72 pounds, and Max weighs 89.3 pounds. Can the merry go round hold all of the children? Show and explain your answer.
Answer:
Yes, it can
Step-by-step explanation:
45.67+76.9+66.72+89.3= 278.59
278.59 is less than 500
The merry-go-round can hold all the children.
To find if the merry go around can hold all children, we need to find the total weight of all the children.
[tex]\text{total weight of all children} = Susie\ +\ Johnny\ +\ Grace\ +\ Max\\\\\text{total weight of all children} = (45.67 +76.9+ 66.72+ 89.3)\ pounds = 278.59\ pounds[/tex]
The total weight of all the children is 278.59 pounds, which is less than the maximum capacity of the merry-go-round which is 500 pounds.
So, the merry-go-round can hold all the children.
can someone explain to me and give me the answer cause i don’t get it
Answer:
ONP and JKI
Step-by-step explanation:
exterior angles are the angles on the outside and if your looking for the alternate exterior angle you would go and find the equivalent angle on the opposite side of the bisector or the ray cutting the parallel lines in half
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 55 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all
Answer:
The number of large boxes is 55 and the number of small boxes is 70
Step-by-step explanation:
The complete question is
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 50 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4150 pounds in boxes, how many of each type of box is it carrying?
Let
x ------> the number of large boxes
y -----> the number of small boxes
we know that
[tex]x+y=125[/tex] -----> equation A
[tex]50x+20y=4,150[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is (55,70)
therefore
The number of large boxes is 55 and the number of small boxes is 70
What is 4(2a) + 7(-4b) + (3•c•5) writing in standard form
Answer:
8a-28b+15c
Step-by-step explanation:
4(2a)+7(-4b)+(3*c*5)
8a-28b+15c
A yoga studio offers memberships that cost $60 per month for unlimited classes. The studio also accepts walk-ins, charging $10 per class. If someone attends enough classes in a month, the two options cost the same total amount. How many classes is that? What is that total amount?
pls help (kinda easy)
A function is shown: f(x) = 4x2 − 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
f(x) = (4x + 1)(4x − 1)
f(x) = (2x + 1)(2x − 1)
f(x) = 4(x2 + 1)
f(x) = 2(x2 − 1)
Answer:
[tex]f(x)=(2x+1)(2x-1)[/tex].
Step-by-step explanation:
We want to convert the function into the form that let's us easily find the x-intercept, and it would be for the form [tex](ax+b)(cx+d)[/tex] because then we can find the x-intercept in the following manner:
[tex](ax+b)(cx+d)=0[/tex]
[tex]x=-b/a[/tex]
[tex]x=-d/c[/tex]
We factor our function [tex]f(x)=4x^2-1[/tex] and get
[tex]\boxed{f(x)=(2x+1)(2x-1)}[/tex]
Now this form let's us easily find the x-intercepts:
[tex]x=-1/2[/tex]
[tex]x=1/2[/tex]
and so we pick the second choice: f(x)=(2x+1)(2x-1).
Answer:
b
Step-by-step explanation:
solve using substitution -9x+7y=-15 and -8x+y=18
Answer:
x=-3, y=-6. (-3, -6).
Step-by-step explanation:
-9x+7y=-15
-8x+y=18
------------------
y=18-(-8x)=18+8x=8x+18
----------------------------------
-9x+7(8x+18)=-15
-9x+56x+126=-15
47x+126=-15
47x=-15-126
47x=-141
x=-141/47
x=-3
-8(-3)+y=18
24+y=18
y=18-24=-6
x=-3, y=-6.
Answer:
x = 51/28
y= 24/7
Step-by-step explanation: