Answer:
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
is the required polynomial with degree 3 and p ( 7 ) = 0
Step-by-step explanation:
Given:
p ( 7 ) = 0
To Find:
p ( x ) = ?
Solution:
Given p ( 7 ) = 0 that means substituting 7 in the polynomial function will get the value of the polynomial as 0.
Therefore zero's of the polynomial is seven i.e 7
Degree : Highest raise to power in the polynomial is the degree of the polynomial
We have the identity,
[tex](a -b)^{3} = a^{3}-3a^{2}b +3ab^{2} - b^{3}[/tex]
Take a = x
b = 7
Substitute in the identity we get
[tex](x -7)^{3} = x^{3}-3x^{2}(7) +3x(7)^{2} - 7^{3}\\(x -7)^{3} = x^{3}-21x^{2} +147x - 343[/tex]
Which is the required Polynomial function in degree 3 and if we substitute 7 in the polynomial function will get the value of the polynomial function zero.
p ( 7 ) = 7³ - 21×7² + 147×7 - 7³
p ( 7 ) = 0
[tex]p (x) = x^{3} - 21x^{2}+ 147x - 343[/tex]
A polynomial function with degree 3 and P(7)=0 can be written as p(x) = a(x - 7)(x - r2)(x - r3), where r2 and r3 can be any real number and a is any non-zero real number.
Explanation:The student has asked for a polynomial function with a degree of 3 such that P(7) equals 0. By definition, a polynomial function of degree n with given roots can be written as:
p(x) = a(x - r1)(x - r2)... (x - rn)
Since we have been given that P(7)=0 , we can choose 7 as one root, but the other roots can be chosen arbitrarily. So, we can create a polynomial function like below:
p(x) = a(x - 7)(x - r2)(x - r3)
Where r2 and r3 can be any real number and a is any non-zero real number. For example, if we choose r2=1, r3=2 and a=1. The function would be:
p(x) = 1*(x - 7)(x - 1)(x - 2) = ([tex]x^3 - 10x^2[/tex] + 29x - 14)
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what the range set of blank means
Answer:
The range of a set of data is the difference between the highest and lowest values in the set
Step-by-step explanation:
Answer:
point blank range is the range at which you don’t need to aim high or low to hit your aiming point. Maximum Point Blank Range (MPBR) is simply the farthest end of that distance.
Step-by-step explanation:
The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters, as shown. What is the area of
the top of the lid?
6 cm
Use the formula for the area of a square, A - 52, where A represents the area and s represents the side length.
12 cm²
24 cm²
36 cm²
72 cm²
Answer:
c.)36
Step-by-step explanation:
Answer:
36 cm
Step-by-step explanation:
The area of a square is length times width. Since it is a square all sides are equal so you multiply 6×6.
Formula: A=s^2 or A=s×s
Complete the solution of the equation. Find
the value of y when x equals -8.
7x - 2y = -52
Enter the correct answer,
Answer:
y = -2
Step-by-step explanation:
to do this, you have to plug in -8 for x
7(-8) - 2y = -52
-56 - 2y = -52
+56 +56
-2y = 4
/-2 /-2
y = -2
Sylvia ran 3km 290m in the morning then she ran some more in the evening if she ran a total of 10km how far did Sylvia run in the evening
Answer:
She ran 6.71km in the evening
Step-by-step explanation:
3km 290m = 3.29km
10 - 3.29 = 6.71km
Sylvia ran 6 km 710 m in the evening.
Given that, Sylvia ran a total of 10 km and 3 km 290 m in the morning.
We need to find the number of kilometres she ran in the evening.
What to subtract the two differnt units?When we are dealing with two numbers that are expressed in units, if the units are the same, we can add or subtract normally. However, if the units are different, then we can add or subtract only if the units can be converted into the same units.
Now, 3 km 290 m can be written as 3.29 km
So the distance ran in the evening =10-3.29
=6.71 km
=6 km 710 m
Therefore, Sylvia ran 6 km 710 m in the evening.
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Which of the following is equivalent to 18 -sqrt -25?
[tex]\bf 18-\sqrt{-25}\implies 18-\sqrt{-1\cdot 25}\implies 18-\sqrt{-1}\cdot \sqrt{25}\implies 18-5i[/tex]
Answer: 18-5i
Step-by-step explanation:
Please help I gave extra points please it’s super simple to some of you I just don’t know how to do it :(
Answer:
1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]
2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]
3. The x-intercept of the linear model is [tex]d = x = 12[/tex]
Step-by-step explanation:
Given:
[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]
Where,
[tex]P_{2}[/tex] is the number of phones.
d is the number of days he has worked that week.
This is a linear model type equation.
Can be represented in the slope intercept form which is equal to
[tex]y = mx + c[/tex]
Where,
m = Slope of the line.
c = y-intercept.
Now if we compare the given model by slope intercept formula we get
[tex]m = \frac{-25}{3}\\\\c = 100[/tex]
So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].
and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]
For finding x-intercept put y = 0
Here,[tex]P_{2}(d) = 0[/tex]
[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]
So, the x intercept of the linear model is [tex]d = x = 12[/tex]
radius CS bisects chord AG what is measure CGF?
Answer:
m∠CGF=25°
Step-by-step explanation:
we know that
In a circle, a radius that bisects a chord is perpendicular to the chord
so
CS is perpendicular to AC
The triangle GFC is a right triangle
Remember that the sum of the measures of the interior angles in a triangle must be equal to 180 degrees
m∠CGF+m∠GFC+m∠GCF=180°
we have
m∠GFC=90°
m∠GCF=65°
substitute
m∠CGF+90°+65°=180°
m∠CGF+155°=180°
m∠CGF=180°-155°
m∠CGF=25°
Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the rest . What is the area planted in corn
Answer:
Corn was planted in 24 sq.ft. of the vegetable garden.
Step-by-step explanation:
Length of garden = 9 ft
width of garden = 8 ft
Hence we will first find the total area of garden.
Total area of garden = length × width = [tex]8 \times 9 = 72ft^2[/tex]
He planted 1/2 of the garden with vegetables.
Hence.
Area of Vegetables garden = [tex]\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2[/tex]
He planted tomatoes in 1/3 of the vegetable garden and corn in the rest
Area in which tomatoes was planted = [tex]\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2[/tex]
Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = [tex]36ft^2-12ft^2=24ft^2[/tex]
Hence Area of vegetable garden in which corn was planted is 24 sq.ft.
) Ava walks from her apartment to the train station, which is 25 blocks away. She has walked
15 blocks so far. Ava wants to know what percent of the distance to the train station she
has walked so far.
To find out what percent of the distance Ava has walked so far, we can set up a proportion and solve for x. Ava has walked 60% of the distance to the train station.
Explanation:To find out what percent of the distance Ava has walked so far, we can set up the following proportion:
15/25 = x/100
Where 15 is the distance Ava has walked, 25 is the total distance to the train station, x is the unknown percentage, and 100 represents 100%. To solve for x, we can cross multiply and divide:
15 * 100 = 25 * x
1500 = 25 * x
Dividing both sides by 25, we get:
x = 1500/25
x = 60
Therefore, Ava has walked 60% of the distance to the train station.
Final answer:
To find the percent of the distance Ava has walked so far to the train station, divide the distance she has walked by the total distance and multiply by 100. In this case, Ava has walked 15 blocks out of 25 blocks, so she has walked 60% of the distance.
Explanation:
To find the percent of the distance Ava has walked so far, you can divide the distance she has walked by the total distance to the train station and then multiply by 100.
In this case, Ava has walked 15 blocks out of 25 blocks to the train station. So, the percent of the distance she has walked so far can be calculated as:
Percentage = (15/25) * 100 = 60%
Renee is playing a game online. If she gets a total of 25 points, she will have a new
high score. She currently has -5 points. What is the difference
score of 25 points and the number of points she currently has?
Answer:
20 points
Step-by-step explanation:
key words: difference
Take the amount of points she has and subtract what she has
25-5
The quotient of 5 times a number and 2
Answer:
Let x be the number
5 times a number:
5x
The quotient of the number and 2.
5x / 2
Final answer:
The 'quotient of 5 times a number and 2' can be expressed as '5x/2', where 'x' is the unknown number. Important mathematical concepts, such as order of operations, exponents, and percentages, influence how we calculate and understand such expressions.
Explanation:
The statement 'The quotient of 5 times a number and 2' represents a mathematical expression, where you are asked to first multiply a number by 5 and then divide that product by 2. To elucidate, let us assume the unknown number is represented by 'x'. So we multiply 5 by 'x' to get '5x', and then we divide that by 2 to get the final expression, which is '5x/2'. In this case, we are dealing with division, which is opposite to multiplication, and it's important to follow the correct order of operations when solving mathematical problems.
Which expression shows 56x+40y−48z written as a product of the greatest common factor and one other factor?
A
8(7x+5y−6z)
B
8(7x+5y+6z)
C
8x(7+5y−6z)
D
4(14x+10y−12z)
The expression 56x+40y−48z can be rewritten as a product of the greatest common factor and one other factor, which is 8(7x+5y−6z). Therefore, the correct answer is A.
Explanation:The expression 56x+40y−48z can be factored by identifying the greatest common factor (GCF). In this case, the GCF of 56, 40, and 48 is 8. Therefore, you divide each term in the expression by the GCF which will give you 7x+5y-6z. Hence, the expression can be rewritten as a product of the GCF and one other factor, which is 8(7x+5y−6z). So, the correct answer is A - 8(7x+5y−6z).
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find the answer to this problem 15/16 - -3 / 16
Answer:
The answer would be 18/16 or 1 1/8.
How many roots can a quadratic equation have
Answer:
2 roots, 1 root, or no roots
Step-by-step explanation:
There is a maximum of two roots
If the maximum or minimum is on the x-axis there is 1 repeated root
The roots are imaginary if it does not touch the x-axis
Step-by-step explanation:
It all depends on the discriminants sign.
The quadratic equation:
[tex]ax^2+bx+c=0[/tex]
The discriminant:
[tex]\Delta=b^2-4ac[/tex]
If Δ < 0, then the equation has no real solution
If Δ = 0, then the equation has one solution [tex]x=\dfrac{-b}{2a}[/tex]
If Δ > 0, then the equation has two different solution
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
if 25% of next month's rent is $174.25 what is the total next month's rent
Answer:
$697
Step-by-step explanation:
25% × 4 = 100%
174.25 × 4 = 697
Answer:
174.25
Step-by-step explanation:
174.25 × 4 = 697
697 × 0.25 = 174.25
Answer: 174.25
A computer and printer cost a total of $1028. The cost of the computer is three times the cost of the printer. Find the cost of each item.
Answer:
Printer: $257, Computer: $771
Step-by-step explanation:
First you want to make a part to part diagram. It sounds stupid at first but trust me it works, We assume the both have the same amount. Now we draw 3 boxes for printer because it is 3 times as much. Now we have 4 boxes. divide 1028 by 4 and get 257. That is the amount for each box. You now know the printer is 257 dollars. Now multiply that by 3 to find cost of printer. 257x3=771.
Now you know the computer cost 771 dollars. You can check your work by adding them up. Hope this helped!!!!
Printer | []
Computer| [] [] []
The product of a whole number and a decimal number is a whole number
True or False?
Answer:
true
Step-by-step explanation:
For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH.
Answer:
Option 4 : 19
Step-by-step explanation:
For trapezoid ABCD : AB = 16 and CD = 28
E and F are midpoints of the legs
So, EF = (AB + CD)/2 = (16+28)/2 = 44/2 = 22
GH be the median of ABFE
So, GH = (AB + EF)/2 = (16+22)/2 = 38/2 = 19
Increase 1/2kg by 250g
One kilogram is made of 1000 grams. So, 1/2kg is made of 500 grams. If we add 250 grams, we have 750 grams, or 0.75kg.
To increase 1/2 kg by 250g, add the two values is 750g.
In mathematics, we often encounter situations where we need to perform operations with different units of measurement. In this case, you want to increase 1/2 kg by 250g. The first step is to convert both quantities to a common unit to facilitate the addition.
Step 1: Convert 1/2 kg to grams
We know that 1 kg is equal to 1000 grams (1 kg = 1000g). To find out how many grams are in 1/2 kg, we multiply 1/2 by 1000:
1/2 kg * 1000g/kg = 500g.
So, 1/2 kg is equivalent to 500g.
Step 2: Perform the addition
Now, we have both quantities in the same unit (grams). The addition becomes straightforward:
500g + 250g = 750g.
Thus, when you increase 1/2 kg by 250g, the result is 750 grams.
In summary, to add quantities with different units, it's crucial to convert them into the same unit before performing the operation. Here, we converted kilograms to grams and then added the values to get the final result of 750g.
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Please Help !!!!!!!!!!!!!!!!
Answer:
the first one should be 2 because
if you put 2 it would look like this:
7x + 2 = 7x + 2
and if you answer it or try to simplify
7x + 2 = 7x + 2 or 7x + 2 = 7x + 2
- 2 - 2 -7x -7x
7x = 7x 2 = 2
/7 /7
x = x
and for the second one could be any number but 2
to prove this lets choose 5
and now to solve:
7x + 2 = 7x + 5 or 7x + 2 = 7x + 5
-7x -7x - 2 - 2
2 ≠ 5 7x = 7x + 3
-7x -7x
0 ≠ 3
Antonia participated in a run-a-thon and raised $265 for her school. She received $25 in donations and an additional $8 for every lap she ran. How many laps did Antonia run?
Answer:
30
Step-by-step explanation:
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply f(x)=1/(x+1)(x+2)
Answer:
x=-1 and x=-2
Step-by-step explanation:
Given
[tex]f(x)=\dfrac{1}{(x+1)(x+2)}[/tex]
This function is undefined when the denominator becomes 0. Find values of x for which the denominator is 0:
[tex](x+1)(x+2)=0\\ \\x+1=0\ \text{or}\ x+2=0\\ \\x=-1\ \text{or}\ x=-2[/tex]
Thus, the lines with equations [tex]x=-1[/tex] and [tex]x=-2[/tex] represent vertical asymptotes (see attached graph)
Answer: -1 and -2
Step-by-step explanation:
PLEASE HELP ASAP with questions 12 and 13
Answer:
12. x = 50
13. m∠M = 34°
Step-by-step explanation:
12.
Since the triangles are congruent, the sides' lengths are proportional. We can set up a ratio and solve for x.
Side JG corresponds to Side KM
Side HG corresponds to Side LM
Now, we can set up a ratio, cross multiply, and solve for x. Shown below:
[tex]\frac{35}{70}=\frac{25}{x}\\35x=70*25\\35x=1750\\x=\frac{1750}{35}\\x=50[/tex]
Thus, the value of x is 50
13.
The triangles are similar, so sides are proportional and angles are not related in the same way. Angles are same for both.
We want the value of Angle M, that angle corresponds to Angle G of the left triangle.
It is given that Angle G = 34, so Angle M would be the same degree measure as well.
Hence,
m∠M = 34°
Quick question what’s 2ab+3b+7b+3a•3a•b+4b-8ab•8ab+5a•5a•b-12ab?
Answer:
14b - 10ab + 34a²b - 64a²b²
Step-by-step explanation:
We have to simplify the expression
2ab + 3b + 7b + 3a × 3a × b + 4b - 8ab × 8ab + 5a × 5a × b - 12ab
= 2ab + 3b + 7b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
{Since (3a × 3a × b) = 9a²b, (8ab × 8ab) = 64a²b² and (5a × 5a × b) = 25a²b}
= 2ab + 10b + 9a²b + 4b - 64a²b² + 25a²b - 12ab
= 14b - 10ab + 34a²b - 64a²b² (Answer)
The royal fruit company produces two type of fruit drinks. The first type is 70% pure fruit juice , and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 80% pure fruit juice
Answer:
66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.
Step-by-step explanation:
Let
x ----> pints of pure fruit juice at 70%
y ----> pints of pure fruit juice at 95%
we know that
[tex]x+y=110[/tex] ----> [tex]x=110-y[/tex] ----> equation A
Remember that
[tex]70\%=70/100=0.70[/tex]
[tex]95\%=95/100=0.95[/tex]
[tex]80\%=80/100=0.80[/tex]
so
[tex]0.70x+0.95y=0.80(110)[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.70(110-y)+0.95y=0.80(110)[/tex]
solve for y
[tex]77-0.70y+0.95y=88[/tex]
[tex]0.25y=88-77[/tex]
[tex]0.25y=11[/tex]
[tex]y=44[/tex]
Find the value of x
[tex]x=110-y[/tex] ---> [tex]x=110-44=66[/tex]
therefore
66 pints of 70% pure fruit juice and 44 pints of 95% pure fruit juice must be used.
a group of adults plus a child attend a movie tickets cost $9 for adults and $6 for children the total for the movie is $78 write an equation to find the number of adults in the group
gets brainilist!!!!!!!what is the absoulute value of -4.5 and what is the absoulute value of 1
Answer:
The absolute value of a number is its distance from zero on the number line. For example, -7 is 7 units away from zero, so its absolute value would be 7
|-4|=4
|1|=1
Step-by-step explanation:
the absolute value of - 4.5 = | - 4.5 | = + 4.5
the absolute value of 1 = | 1 | = + 1
Samantha cut 6 3/4 yd of yarn into
3 equal pieces. Explain how she could use mental
math to find the length of each piece.
Answer:
27/12
Step-by-step explanation:
6 3/4=27/4
(27/4)/3
(27/4)(1/3)=27/12
You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
Answer:
The segment area [tex]= 113.09\ unit^2[/tex]
Step-by-step explanation:
Area of the segment = [tex]\frac{(\theta)}{360} \times \pi r^2[/tex],where [tex]\theta[/tex] is the angle.
We can also say that [tex]90\ degrees[/tex] is covered with one segment and we have total [tex]4[/tex] segments (quadrants),so area of the circle divided by [tex]4[/tex] will give us the segement area of the arc.
So area [tex]\frac{\pi r^2 }{4} =\frac{\pi(12)^2}{4} = 113.09\ units^2[/tex]
So the area of the segment [tex]= 113.09 \ units^2[/tex]
Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3. (5 points)
y^2 = -12x
y^2 = -3x
y = negative x^2 divided by 12
y = negative x^2 divided by 3
Answer:
From given option , the equation of parabola is y = negative x² divided by 12
Step-by-step explanation:
Given as for parabola :
The focus is at (0 , - 3)
The directrix equation is y = 3
Now, equation of parabola parallel to y-axis is
( x - h )² = 4 p ( y - k )
where focus is ( h , k+p ) and directrix equation is y = k - p
So, from equation
h = 0 and k + p = - 3
And y = k - p i.e k - p = 3
Now solving ( k + p ) + ( k - p ) = - 3 + 3
or, 2 k = 0 ∴ k = 0
Put the value of k , k + p = - 3
So, 0 + p = - 3 ∴ p = - 3
Now equation of parabola with h = 0 , k = 0 , p = - 3
( x - h )² = 4 p ( y - k )
I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )
Or, x² = - 12 y is the equation of parabola
Hence From given option , the equation of parabola is y = negative x² divided by 12 Answer