Given:
The given quadratic polynomial is :
[tex]x^2-x-12[/tex]
To find:
The quadratic polynomial whose zeroes are negatives of the zeroes of the given polynomial.
Solution:
We have,
[tex]x^2-x-12[/tex]
Equate the polynomial with 0 to find the zeroes.
[tex]x^2-x-12=0[/tex]
Splitting the middle term, we get
[tex]x^2-4x+3x-12=0[/tex]
[tex]x(x-4)+3(x-4)=0[/tex]
[tex](x+3)(x-4)=0[/tex]
[tex]x=-3,4[/tex]
The zeroes of the given polynomial are -3 and 4.
The zeroes of a quadratic polynomial are negatives of the zeroes of the given polynomial. So, the zeroes of the required polynomial are 3 and -4.
A quadratic polynomial is defined as:
[tex]x^2-(\text{Sum of zeroes})x+\text{Product of zeroes}[/tex]
[tex]x^2-(3+(-4))x+(3)(-4)[/tex]
[tex]x^2-(-1)x+(-12)[/tex]
[tex]x^2+x-12[/tex]
Therefore, the required polynomial is [tex]x^2+x-12[/tex].
There is 2/3 of a pan of brownies left on the
counter. If you eat 2/3 of the brownies left in the
pan, what is the fraction of the whole pan that
you ate?
Answer:
He ate 4/9 of the pan of brownies.
Step-by-step explanation:
So the question might seem hard but when you read it, it said that there were 2/3 of brownies left and he ate 2/3 of that 2/3 in that pan so to figure 2/3 of 2/3 I divided 2/3 by 3 which is 2/9, 2/9 is 1/3 of 2/3 to figure out 2/3 of 2/3 you need to add by itself which you get 4/9.
Alex and Nick collect baseball cards. Alex has three more than twice as many cards as Nick. Together they have 27 cards.
How many cards does Alex have?
A culture of bacteria has an initial population of 860 bacteria and doubles every 9 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after hours, P_0P 0 is the initial population, is the time in hours and is the doubling time, what is the population of bacteria in the culture after 4 hours, ?
Answer:
1170
Step-by-step explanation:P_0=860
P
0
=860
The initial population
t=4
t=4
Time elapsed
d=9
d=9
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=860\cdot 2^\frac{4}{9}
P
t
=860⋅2
9
4
Plug in
P_t=1170.2794\approx1170
P
t
=1170.2794≈1170
Erica bought a road bike using the
store's payment plan. She made a
$320 down payment and makes
monthly payments of $91. If the total
cost is $1,867, how many months will
Erica be paying for the bike? Write and
solve an equation.
Answer:
17 months i think
Step-by-step explanation:
1867$-320$=1547
1547:91=17
The number of months Erica will be paying for the bike, if She made a $320 down payment and makes monthly payments of $91 is 17 months.
What is the equation?A formula known as an equation uses the equals sign to denote the equality of two expressions. It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given:
The down payment = $320,
The amount of monthly installment = $91,
The total cost = $1867
Calculate the remaining amount after the down payment as shown below,
The remaining amount = The total cost - The down payment
The remaining amount = 1867 - 320
The remaining amount = $1547
Calculate the number of months as shown below,
The number of months = The remaining amount / The amount of monthly installment
The number of months = 1547 / 91
The number of months = 17 months
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HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
C?
Step-by-step explanation:
I think it is C but I am not sure.
9% of 40 is what number?
Answer:
3.6
Step-by-step explanation:
Answer:
3.6
Step-by-step explanation:
(using proportion method)
40 x 9 = 360
100 x C = 100c
360 / 100c = 3.6
I need this ASAP!
( Fractions and whole numbers)
Answer:
C. [tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
One way of approaching this problem is to multiply the numbers the numerators together and then divide by the denominator to receive the quotient and the remainder.
Firstly 6 can be written as a fraction like so: [tex]\frac{6}{1}[/tex] because 6 divided by 1 is equal to 6.
To multiply two fractions together, we simply multiply the numerators and multiply the denominators:
[tex]\frac{7}{9}* \frac{6}{1} =\frac{7*6}{9*1}[/tex]
Which gives us the improper fraction of: [tex]\frac{42}{9}[/tex]
Next, we find the highest multiple of 9 which is smaller than 42. If we write out the multiples of 9 we will find that it is 36:
1x9=9, 2x9=18, 3x9=27, 4x9=36, 5x9=45
Since we know that at least 4 whole 9s go into 42 we can conclude that the coefficient of the fraction will be 4.
To find the fraction itself, we must find the remainder which we can do by subtracting 36 from 42: 42-36 = 6
The remainder is the numerator of the fraction as there are 6 ninths left over after we have divided 42 by 9.
Therefore our answer is [tex]4\frac{6}{9}[/tex]
If we divide 6 and 9 by 3 we will find that 6/9 is equivalent to 2/3 therefore our final answer is [tex]4\frac{2}{3}[/tex].
Option C is correct.
someone pls help this is an emergency
Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. Which histogram represents Blanca’s lap times for the three days of practice?
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds
What is endurance race?
A type of motorsport racing known as endurance racing is designed to test both the participants' and the equipment's endurance. Teams of several drivers attempt to travel a long distance in a single race while being allowed to change drivers at any time.
The given table is attached below.
The number of laps in the range 82 to 84 seconds = 1
The number of laps in the range 84 to 86 seconds = 4
The number of laps in the range 86 to 88 seconds = 2
The number of laps in the range 88 to 90 seconds = 4
The number of laps in the range 90 to 92 seconds = 6
The number of laps in the range 92 to 94 seconds = 5
The number of laps in the range 94 to 96 seconds = 2
The number of laps in the range 96 to 98 seconds = 0
Therefore, the histogram that represents Blanca's lap times for the three days of practice is described as follows;
A graph shows lap time (seconds) labeled 82 to 98 on the horizontal axis and the number of laps on the vertical axis. 1 lap was 82 to 84 seconds. 4 laps were 84 to 86 seconds. 2 laps were 86 to 88 seconds. 4 laps were 88 to 90 seconds. 6 laps were 90 to 92 seconds. 5 laps were 92 to 94 seconds. 2 laps were 94 to 96 seconds. 0 laps were 96 to 98 seconds.
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Answer:A
Step-by-step explanation:
One of the adjacent angles of the parallelogram is 50° more than the other. The measure of the least angle in the parallelogram is ___
Answer:
65
Step-by-step explanation:
A parallelogram is a quadrilateral (a four sided object) with parallel sides
Some of the characteristics of a parallelogram includes :
1. Opposite sides and angles are congruent .
2. Opposite angels are congruent
3. Consecutive angles are supplementary
4. The diagonals bisect each other
one side measures = 50 + x
the opposite side measures 50 + x
and the 2 other sides measure x
sum of angles in a parallelogram = 360
50 + x + 50 + x + x + x = 360
100 + 4x = 360
4x = 260
x = 65
In indirect variation where y =
[tex]\frac{k}{x}[/tex]
if y = 20 and x = 2, what is the value of y when x = 10 ?
Step-by-step explanation:
y=k/x
y=20, x=2
Substitute this first to get "k"
20=k/2
k=40
Value of y when x=10... is now
y= 40/10
y=4.
For your birthday, you received a $30 McDonald’s gift certificate. You decided that every day, you’d buy a McGriddle on your way to school. After 4 days, you had $19 remaining on your gift card. a. What is the cost of one McGriddle? Show all work and circle your final answer.
Answer:
3.29
Step-by-step explanation:
What is the area of a circle if the diameter is 40 meters PLEASE HELP PLEASE IM TIMED
Answer:
Half of 40 is 20(new radius)
20^2 = 400
400 x 3.14 = 1256 meters^2
Formula of area of a circle:
πr2
pi(3.14 or 22/7 whatever they tell you to use for pi) x radius(half of your diameter or your given radius) being squared(^2 to the power of 2)
What are the factors of the expression x² 4x 3?
The factors of the expression x² 4x 3 are (x + 3)(x − 3).
What is factor?Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.
This is determined by using the factoring technique called factoring by grouping.
First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.
Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.
Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).
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Can someone please answer this
Original price: $__
Percent of Discount: 25%
Sale price after discount: $40
What is the original sale price?
Answer:
$53.33
Step-by-step explanation:
A whole (100%)- 25% is 0.75
x*0.75=40
/0.75 /0.75
x=53.33333
round to the 2 decimal since this is money
Therefore the original sale price was $53.33
Have a nice day and I hope this helped. :D
A carpenter needs to be sure that a frame he has built is rectangular. He knows that the opposite sides of his frame are congruent. Which additional fact would be sufficient to prove that the frame is a rectangle?
A)
If two adjacent angles are supplementary, then the frame must be rectangular.
cross out
B)
If the adjacent sides are also congruent, then the frame must be rectangular.
cross out
C)
If opposite angles are congruent, then the frame must be rectangular.
cross out
D)
If one angle is a right angle, then the frame must be rectangular
The answer is D) If one angle is a right angle, then the frame must be rectangular,
What is angle?An angle is a measure of the amount of rotation between two lines or planes. It is measured in degrees or radians. Angles are formed by the intersection of two lines, called the sides of the angle, and a point, called the vertex of the angle. There are different types of angles such as acute angle, right angle, obtuse angle, and straight angle.
What is rectangle?A rectangle is a four-sided polygon with four right angles. It has opposite sides that are parallel and congruent, and the opposite angles are also congruent. A rectangle can be defined by its length and width or by the coordinates of its vertices. Rectangles are a special case of parallelograms, which have opposite sides parallel but not necessarily congruent. The special properties of rectangles make them a popular shape in design and construction, such as in building and engineering.
A rectangle is defined as a four-sided polygon with four right angles. Opposite sides of a rectangle are congruent, but adjacent sides may or may not be congruent. Therefore, A and B are not sufficient to prove that the frame is a rectangle. Also, two adjacent angles being supplementary does not guarantee that the frame is a rectangle. The only way to be sure that the frame is a rectangle is if it has one right angle, this is the only way to ensure that all angles are right angles. Therefore, D) is the correct answer.
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Quadrilaterals A and B are similar. The area of quadrilateral A is 5cm². Calculate the area of quadrilateral B. 3cm 63° 87° 120° A 90° 15cm 63 87° B 120° 90°
Answer: 25cm²
Step-by-step explanation:
Ok, so I haven't actually learnt this in school so I'm going to give it my best shot. (Don't be surprised if I get this wrong though.)
So, Quadrilaterals A and B are similar. They have the same angles. Therefore, (I'm thinking that) Quadrilateral B is just a scaled-up version of Quadrilateral A.
Here comes my theoretical part:
If one side of Quadrilateral B is 5 times longer than the same side of Quadrilateral A...
(Quadrilateral A is 3cm, and Quadrilateral B is 15cm).
... then the area of the entire Quadrilateral B should just be 5 times bigger than Quadrilateral A.
Therefore, (I'm guessing), Quadrilateral B has an area of 25cm²
Elizabeth has 214 gallons of milk in her refrigerator, and she drinks 23 of the quantity. How much milk does Elizabeth drink?
Answer:
9 days
Step-by-step explanation:
We know
Elizabeth has 214 gallons of milk; she drinks 23 of the quantity each day.
We take
214 / 23 = 9 days
So, she can drink in 9 days
Plz, help me with this question!
Answer:
O A. 8
Step-by-step explanation:
the line is 180, so subtract 140 to get 5x. 5x = 40 so divide by 5
180 - 140 = 5x
40 = 5x
/5 /5
8 = x
Answer: X=8
Step-by-step explanation:
it is a 180 degree angle total.
180=5x+140
subtract 140 from both sides
40=5x
divide by 5 on both sides
8=x
The school store is selling shirts at cost for $5.50 and Jackets for $12. The volleyball coach spent $208 to buy a total of 26 shirts and jackets. How many shirts did they buy?
Answer:
16 shirts.
Step-by-step explanation:
You can make a system of equations
x + y = 26
5.50x + 12y = 208
You can solve this in many ways, however chose to graph using desmos. I got that x = 16, and y = 10.
What is Y =- 2 on a graph?
The graph of y is a straight line parallel to the x−axis through the point (0,-2)
Now, According to the question:
What is slope and example?
Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The given equation is Y = -2
y = -2 is a line in which all points have the y-value -2. The line has a slope of 0 (horizontal line) since the y-value does not change for any value of x.
The point-intercept form for the equation of a line is:
y = mx + b
We can write y = -2
As y = 0x - 2;
slope = 0, y-intercept = -2
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please help i need help asap i have class in 2 hours pls
The value of x, given the angles next to the triangle, can be found to be 38 °
How to find the value of x ?To find the value of x, you first need to find the value of the other angles in the triangle.
Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:
= 180 - 134
= 46 °
The angle to the bottom right is:
= 180 - 84
= 96 °
The angles in a triangle add up to 180 ° so the value of x would be:
= 180 - 46 - 96
= 38 °
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How do you solve this?
Answer: 140^3
Step-by-step explanation:
The 3 is an exponent. To solve this, you basiclly have to multiply the three numbers and add a 3 exponent.
what is the x and y intercept of line, plz write as an ordered pair and plz give step by step explanation
Answer:
y-intercept: (0, 1)
x-intercept: (1, 0)
an x-intercept is when a line crosses the x-axis, and a y-intercept is when a line crosses the y axis.
Can you help me with this
Answer: (-4, -6)(9, 2):
y=8/13x - 46/13 (Point slope form: y + 6 = 8/13 *(x+4)
If the height of the triangle given below is 35 cm, what then is its area? (Round your final answer to the tenths place, if necessary).
Answer:
I need the width in order to solve it. . .
Formula - To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.
Was there a width?
Hello can someone please help me with this
1. The best geometric model for the rail road is C. Line
2. Two straight lines cannot go through any two points. It is false.
3. The length of the cake is A. 5.5 inches.
4. The vertical angles are AHC and GHE.
How to illustrate the information?The best geometric model for a set of railroad tracks would likely be a line, as it represents the linear path that the tracks follow. A point would not be appropriate as it does not represent the length or direction of the tracks, and a plane would not be necessary as the tracks are linear and exist in a three-dimensional space.
It should be noted that two straight lines cannot go through any two points. Only one line can. The length of the cake will be:
= 6.0 - 0.5
= 5.5
It should be noted that vertical angles are equal. This was Illustrated as AHC and GHE.
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What is the value for the lower quartile of the set?
Answer:
I believe its 4
Step-by-step explanation:
Help me please and Thank you!