The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)
Given,
x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).
Point = (3, 14).
We have to find the polynomial equation;
A polynomial is defined as;-
P(x) = a(x - c₁) (x - c₂)....(x - cₙ)
Here,
a is a constant
c₁, c₂,...cₙ are the zeros of the polynomial
Here,
-5, -3 and 1 are the zeros of the given polynomial
(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.
Then the equation of polynomial be like;
P(x) = a(x + 5) (x + 3) (x - 1)
This polynomial passes through point (3, 14)
That is,
14 = a(3 + 5) (3 + 3) (3 - 1)
14 = a x 8 x 6 x 2
14 = 96a
a = 96/14
a = 6.86
Substitute this in equation of polynomial;
That is,
P(x) = 6.86(x + 5) (x + 3) (x - 1)
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Can somebody help me with question number 4?
nswer:
[tex]\begin{gathered} x\text{ = -4} \\ y\text{ = 3} \end{gathered}[/tex]Explanation:
ere, we want to solve the syastem of linear equations simultaneously by elimination
We have this as:
[tex]\begin{gathered} -4x+\text{ 3y = 25} \\ 6x-5y\text{ = -39} \end{gathered}[/tex]We start by multiplying the first equation by 6 and the second by 4. We have this as:
[tex]\begin{gathered} -24x\text{ + 18y = 150} \\ 24x-20y\text{ = -156} \end{gathered}[/tex]Add both equations as follows:
[tex]\begin{gathered} -2y\text{ = -6} \\ y\text{ = }\frac{-6}{-2}\text{ = 3} \end{gathered}[/tex]To get x, we multiply the first equation by 5 and the second by 3
We have this as:
[tex]\begin{gathered} -20x\text{ + 15y = 125} \\ 18x-15y=-117 \end{gathered}[/tex]We proceed to add both equations:
[tex]\begin{gathered} -2x\text{ =8} \\ x\text{ = }\frac{8}{-2} \\ x\text{ = -4} \end{gathered}[/tex]List the first 6 multiples of 8
Answer: 8, 16, 24, 32, 40, 48
Step-by-step explanation:
because if you add all of those numbers up, that's what you get.
Answer:
8 - 16 - 24 - 32 - 40 - 48
Step-by-step explanation:
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
Mr. Salcedo was driving at a constant speed. He drove 120 3/4 miles in 3 hours. At that speed, how
many miles will he drive in 7 1/2 hour? How many miles will he drive in one hour?
He will cover 301.875 miles in 7.5 hours at a unit speed of 40.25 miles per hour.
What is unit rate?A ratio that compares two amounts of different types of units is called a rate. When a unit rate is expressed as a fraction, the denominator is 1 unit.
Rate = Distance/Time
If Mr.Salcedo was driving at 120 3/4 miles in 3 hours, his unit rate will be calculated as:
Unit rate =[120 3/4]/3
Unit rate = 483/12
Unit rate = 40 1/4 miles/hr
This shows that he drove 40 1/4 miles/hr.
The miles he drove in 7 1/2 hour is expressed as;
Miles driven = 161/4 * 15/2
Miles driven = 301.875 miles
Hence the miles that he will drive in 7.5 hours is 301.875miles and the unit rate is 40.25 miles/hr
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I will give brainliest, like and rating if u solve this right
If f(x) = x³+ 3x² + 4x + 5 and g(x) = 5, then g (f(x)) =_?
What’s the slope of this line?
X
6
9
15
21
у
-5
-7
-11
-15
Slope is [tex]\frac{-2}{3}[/tex] of coordinates (6,5) and (9,-7).
What is slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; however, there is no obvious reason for this. The slope of a curve at a point in differential calculus is defined as the slope of the tangent line at that point as a generalization of this practical definition. The slope can be determined between any two locations when the curve is represented by a series of points in a diagram or list of point coordinates. Maybe when the curve is represented as a continuous function.
Given Data
coordinates - (6,-5) and (9,-7)
slope of the line denoted as m
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
m = [tex]\frac{-7-(-5)}{9-6}[/tex]
m = [tex]\frac{-2}{3}[/tex]
Slope is [tex]\frac{-2}{3}[/tex]
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Which number is equivalent to 3^(4)÷3^(2)
the answer is definitely 9
The width of a rectangle is 15 cm less than the length. The perimeter is
8 cm. Find the rectangle's dimensions.
If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm
The width of a rectangle is 15 cm less than the length
Consider the length of the rectangle as x
The the width of the rectangle = x-15
The perimeter of the rectangle = 150 cm
The perimeter of the rectangle = 2(l+w)
Where l is the length and w is the width
Substitute the values in the equation
2(x+(x-15))=150
2(2x-15)=150
4x-30 = 150
4x = 180
x = 45 cm
The width of the rectangle = x-15
= 45-15
= 30 cm
Hence, If the width of a rectangle is 15 cm less than the length and the perimeter of the rectangle is 150 cm, then the length is 45 cm and width is 30 cm
The complete question is
The width of a rectangle is 15 cm less than the length. The perimeter is
150 cm. Find the rectangle's dimensions.
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Hello, help me please)
olution:
iven;
[tex]\log_52x=3[/tex][tex]\log_52x=3[/tex]Applyin the power property of logarithm given as;
[tex]\log_ba=c\Leftrightarrow a=b^c[/tex]Thus;
[tex]\operatorname{\log}_52x=3\Leftrightarrow2x=5^3[/tex]Simplify further, we have;
[tex]\begin{gathered} 2x=5\times5\operatorname{\times}5 \\ \\ 2x=125 \end{gathered}[/tex]ivide both sides by 2;
[tex]\begin{gathered} \frac{2x}{2}=\frac{125}{2} \\ \\ x=\frac{125}{2} \end{gathered}[/tex]NSWER:
[tex]x=\frac{125}{2}[/tex]if a population has a mean of 30, if 3 points are added to each score how do you calculate the mean for the new distribution
When the population has a mean of 30, if 3 points are added to each score, the mean for the new distribution is 33.
How to illustrate the information?It should be noted that mean simply means the average of a given set of numbers that are given. The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole. A population in research doesn't usually refer to humans.
In this case, the population has a mean of 30 a and 3 points are added to each score.
In this case, the new mean will be the addition of the numbers. This will be illustrated as:
= 30 + 3
= 33
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Annalise buys a pair of sunglasses for 30% off and saves $15. What is the original price of the pair of sunglasses?
*
Answer:
$50
Step-by-step explanation:
We will call x the original price of the sunglasses.
We can create the equation below using the information given.
[tex]x*\frac{30}{100} =15[/tex]
Now solve for x.
[tex]x = 15*\frac{100}{30}[/tex]
[tex]x = \frac{100}{2}[/tex]
[tex]x=50[/tex]
Can you solve this please.
The simplified expression of (x¹² ÷ x⁴). x³ is x¹¹
How to solve expression?The expression can be solved as follows:
(x¹² ÷ x⁴). x³
The law of indices can be used to solve the expression.
Therefore,
[tex]\frac{x^{a} }{x^{b} } = x^{a - b}[/tex] and [tex](x^{a} )^{b} = x^{ab}[/tex] and [tex]x^{a} .x^{b} = x^{a+b}[/tex]
Hence,
(x¹² ÷ x⁴) = x¹² / x⁴ = x¹²⁻⁴ = x⁸
Therefore,
(x⁸). x³ = x⁸⁺³
Finally,
x⁸⁺³ = x¹¹
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Houston wants to play the "Guess your weight" game at the Strawberry Festival. If the guess is not within 10 pounds of his actual weight, Houston wins a prize. Houston weighs 102 pounds.
Write an equation to represent this situation. Use the equation to determine the greatest and least guesses that can be made without Houston winning a prize?
An equation to represent this situation is |x - 102| = 10.
The greatest and least guesses that can be made without Houston winning a prize are 112 pounds and 92 pounds.
Given:
Actual Weight of Houston = 102 pounds
Now, if the guess is not within 10 pounds of his actual weight, Houston wins a prize.
An equation to represent this situation can be written as,
|x - 102| = 10
As we know a modulus function always generates a positive value.
We need the difference between the guessed weight and the actual weight to be exactly 10 pounds so we have applied modulus in the equation.
Now we utilize the above equation to determine the greatest and least guesses that can be made without Houston winning a prize.
The greatest guessed weight will be,
x - 102 = 10 ⇒ x = 102 + 10 ⇒ x = 112 pounds
The least guessed weight will be (the modulus value will be negative in this case)
-x + 102 = 10 ⇒ x = 102 - 10 ⇒ x = 92 pounds
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Nautical flags are used to communicate on
ships. Kimani uses the
scale drawing at the
right to sew a nautical Z flag. The scale from
her flag to the drawing is 20
Each color is
4
of the flag. How many square inches of
each color of fabric does Kimani need?
Answer:
5
Step-by-step explanation:
according to my own understanding since her flag to the drawing is 20. each colour is 4,then u divide 20 by 4. The answer is 5
3/4+6 and 2/4÷1 and 3/5
The answer is a) 27/6 b) 1/2 c) 0.6 = 6/10 = 3/5 and their sum is 5.6
What are the various mathematic operations?The four basic arithmetic operations in Maths, for all real numbers, are:
→ Addition (Finding the Sum; ‘+’)
→ Subtraction (Finding the difference; ‘-’)
→ Multiplication (Finding the product; ‘×’ )
→ Division (Finding the quotient; ‘÷’)
In this given question ;
a) [tex]\frac{3}{4}[/tex] + 6
first take LCM so we will get : [tex]\frac{3+24}{6}[/tex] = [tex]\frac{27}{6}[/tex]
b) [tex]\frac{2}{4}[/tex]÷ 1
this implies [tex]\frac{1}{2}[/tex] ÷ 1 = [tex]\frac{1}{2}[/tex]× 1 = [tex]\frac{1}{2}[/tex]
c) [tex]\frac{3}{5}[/tex] = 0.6
If we were to solve a + b + c we get : 27/6 = 4.5
b= 1/2 = 0.5
so 4.5+ 0.5 + 0.6 = 5.6
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Omar buys eggs and lemons at the store.
He pays a total of $26.10.
He pays a total of $6.30 for the eggs.
• He buys 6 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
Answer:
Each bag of lemons cost $3.30
Step-by-step explanation:
The equation will be
6x = 26.10 - 6.306x=26.10−6.30
Solve for x to get,
6x = 19.86x=19.8
x = 3.3x=3.3
Answer:
$3.30 for each bag of lemons
Step-by-step explanation:
We know that Omar only bought both lemons and eggs. We also know that the total amount of money he spent on groceries is $26.30 and that the eggs are worth $6.30 out of the total.
So, if we can subtract the cost of the eggs from his total cost of groceries to find how much the lemons cost. After that we can divide the cost of all the lemons, which is $19.80, by the number of bags, which is 6, to find how much each bag costs.
(26.10 - 6.30) / 6 = ?
19.8/6 = 3.30
Find the equation (in terms of xx ) of the line through the points (-4,1) and (5,-3)
EXPLANATION
Given two points of a line, we can find the the equation of that line using the steps below:
• Step 1
Determine the slope of the line, using the formula below:
[tex]\text{slope(m)}=\frac{y_2-y_1}{x_2-x_1}[/tex]The points given are (-4, 1) and (5, -3). This implies that the coordinates are
x₁= -4 y₁=1 x₂=5 y₂=-3
Substitute the values into the formula and simplify.
[tex]m=\frac{-3-1}{5+4}=-\frac{4}{9}[/tex]• Step 2
Determine the y-intercept(b) of the line.
Substitute x₁= -4 y₁=1 and m=-4/9 into y=mx + b and solve for intercept(b).
1 = (-4/9)(-4) + b
[tex]1=\frac{16}{9}+b[/tex]Subtract 16/9 from both-side of the equation.
[tex]b=1-\frac{16}{9}[/tex][tex]b=\frac{9-16}{9}=-\frac{7}{9}[/tex]The intercept (b) = -7/9
• Step 3
Form the equation by substituting the value of the slope and intercept into y=mx + b.
Hence, the equation of the line is:
[tex]y=-\frac{4}{9}x-\frac{7}{9}[/tex]
Daniel and his three friends are sharing the cost of a pizza. The pizza costs $13.00. If Daniel has
$5.00, how much will he have left after he pays his share?
Answer: 1.75
Step-by-step explanation:
13/4 = 3.25
5.00-3.25
1.75
Which of the following is LEAST associated with human capital?
a)medical treatment that reduces time off of work due to illness or injury.
b)maintenance of fully automated production facilities
c)a college course in accounting
d)an on-the-job training course in the latest production methods.
Answer:
Hope it helps you
Step-by-step explanation:
(a) medical treatment that reduces time off of work due to illness or injury.
the expression 2x squared minus -x squared is equivalent to
2x² - x²
Factor:
x²(2 - 1)
x²(1)
x²
--------------------------------------------
(3x² + x + 8) + (x² - 9)
Add like terms:
(3x² + x²) + x +(8 - 9)
4x² + x - 1
-----------------------------------------------
-3x² - 7x + 9 - 5x² + 6x - 4
Add like terms:
(-3x² - 5x²) + (-7x + 6x) + (9 - 4)
-8x² - x + 5
To find the solution to |3x + 2|= 4, which two equations must you solve?
Answer:
YOU MUST SOLVE ---> |3x + 2|
Step-by-step explanation:
|3x + 2| = 4
-2 -2
3x = 4
x = 0.75
HOPE this HELPED
Sanjay uses 225 N of force to move a wheelbarrow 18 m at a velocity of 1.8 m/s. What was the amount of power used?
The amount of power used when Sanjay applied a force of 225N to move a wheelbarrow over the given distance at a velocity of 1.8m/s is 405 watts.
What was the amount of power used to move the wheelbarrow?Power is the quantity of energy transferred per unit time. The relationship between force, velocity and power is expressed aa;
P = F × v
Given the data in the question;
Force applied F = 225N = 225kgm/s²Distance moved s = 18mVelocity v = 1.8m/sPower = ?To find the amount of power used, plug the given values into the above formula and solve for P.
P = F × v
P = 225kgm/s² × 1.8m/s
P = 225kgm²/s³ × 1.8
P = 405kgm²/s³
Power P = 405W
Therefore, the amount of power used by Sanjay is 405 watts.
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for each of the points identify the axis or constant where the point is located 8.7 and 2.3 
The given points are located in the 1st quadrant.
How to determine which quadrant?Refer to the attachment.
Since the two points x or abscissa = 8.7 and ordinate or y axis = 2.3 and both the numbers are positive thus they belong to the First quadrant.
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HELP I GIVE BRAINLIEST!!!!!
Drop Down 1
(2 in)(10 ft/1 in) = 20 ft
Drop Down 2
This means the scale factor is 1:2, and thus the new length will be 3 inches.
At the city museum, child admission is $6.00 and adult admission is $9.60. On Sunday, twice as many adult tickets as child tickets were sold, for a total sales of $630.00. How many child tickets were sold that day?
Answer:
25 child tickets and 50 adult tickets
Step-by-step explanation:
Let c be the number of child tickets and a be the number of adult tickets. We have this system of equations:
6.00c + 9.60a = 630.00
a = 2c
Substitute 2c for a in the top equation:
6.00c + 9.60(2c) = 630.00
6.00c + 19.20c = 630.00
25.20c = 630.00
c = 25, a = 50
If 343 is the third proportional of A and B, where a:b= 1:7 then the value of a+b will be
I have been stuck in this problem for 2 hours please help
We need to find the values of "x" and "y" from two triangles that are congruent. If the triangles are congruent it means that the corresponding angles are equal. This means that angle R and angle N are the same, and from the angle sum theorem w know that the interior angles of triangle QPR sum 180, that is mathematically:
[tex](9x-18)+84+\angle R=180[/tex]Since angle N is 3x+y, we replace that in the equation:
[tex](9x-18)+84+(3x+y)=180[/tex]Simplifying we get:
[tex]\begin{gathered} 12x+y+66=180 \\ 12x+y=180-66 \\ 12x+y=114,\text{ (1)} \end{gathered}[/tex]That gives us equation (1), but we need another equation since we have two variables. The other equation we get it from angles L and P, since this two angles must be equal. So we get the following equation:
[tex]4x+17=9x-18[/tex]Solving for "x", we get:
[tex]\begin{gathered} 4x-9x=-18-17 \\ -5x=-35 \\ x=-\frac{35}{-5}=7 \end{gathered}[/tex]The value of "x" is 7. Now we input this value in equation (1), like this:
[tex]\begin{gathered} 12x+y=114 \\ 12(7)+y=114 \\ 84+y=114 \end{gathered}[/tex]Solving for "y", we get:
[tex]\begin{gathered} y=114-84 \\ y=30 \end{gathered}[/tex]therefore, the value of "y" is 30.
Pedro has scores of 81, 80, 82, 88 after four tests. What score must he make on his fifth test to have an average of 76 or greater?
Answer:
he must make sure he gets up to 49 and higher to obtain an average of 76 or greater
Step-by-step explanation:
logically from 49 - 100 :)
(x + a)(x + 2)(3x + 1) = bx³ + cx² + dx - 10
Find the values of a, b, c and d.
Mark operates a small sign-making business. He finds that if he charges x dollars for each sign, he sells 37−x signs per week. What is the smallest number of signs that he can sell to have an income of $300 in one week?
The smallest number of signs that he can sell to have an income of $300 in one week is 12.
The price of one sign is x
Number of signs he sells per week = 37-x
The total earning from selling these is x(37-x) which is given as $300
(37- x) x = 300
37x - x² = 300
x² - 37x + 300 = 0
As per formula to find base in a quadratic equation
[tex]x =\frac{37 - \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 - \sqrt{1369-1200 } }{2} \\x =\frac{37 - \sqrt{169 } }{2} \\x = \frac{37-13}{2}\\ x = \frac{24}{2}\\ x = 12[/tex]
The other base can be
[tex]x =\frac{37 + \sqrt{37^{2}-4 . 1 . 300 } }{2 . 1} \\x =\frac{37 + \sqrt{1369-1200 } }{2} \\x =\frac{37 + \sqrt{169 } }{2} \\x = \frac{37+13}{2}\\ x = \frac{50}{2}\\ x = 25[/tex]
Therefore the smallest number of signs that he can sell to have an income of $300 in one week is 12.
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Round to the place value of the underlined digit 698, 07 to the underline number is six
The place value of the underlined digit (6) is tens of thousands and should be rounded to 70,000.
What is a place value?A place value simply refers to a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousandsIn this scenario, the place value of the underlined digit (6) is tens of thousands and 9 is the next digit to six (6). Therefore, we would add one (1) to the underlined digit (6) and then change all of the other digits to zero (0) as follows:
69,807 = 70,000
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