Answer:
x + 3 is a factor of the polynomial.
Step-by-step explanation:
We have been given that p(x) is a polynomial with integer coefficient.
Also p(-3)=0
Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.
Now, we apply factor theorem.
Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).
Applying this theorem, we can say that (x+3) must be a factor of the polynomial.
Hence, first statement must be true.
Answer: The correct option is (A) (x + 3) is a factor of the polynomial.
Step-by-step explanation: Given that p(x) is a polynomial with integer coefficients and p(-3)=0.
We are to select the true statement from the given options.
Factor Theorem: If q(x) is a polynomial with integer coefficients and q(a) = 0, then (q - a) will be a factor of q(x).
Here, it is given that
p(x) is a polynomial with integer coefficients and p(-3) = 0.
Therefore, by Factor theorem, we can say that (x-(-3)), ie., (x + 3) is a factor of the polynomial p(x).
Thus, (x + 3) is a factor of the polynomial.
Option (A) is CORRECT.
find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ? find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ?
The non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Explanation:An expression is undefined when its denominator is equal to zero. Therefore, we need to find the values of x that make the denominator, 2x-4, equal to zero.
Solve the equation for x: 2x - 4 = 0 2x = 4 x = 2
Therefore, x = 2 is a non-permissible replacement because it makes the denominator zero.
Additionally, the expression also includes x^2 in the numerator. Since any number multiplied by zero is still zero, dividing any non-zero number by zero results in undefined. Therefore, x = 0 is also a non-permissible replacement.
In conclusion, the non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
When segments intersect inside a circle, what is the relationship between the angle of intersection and the intercepted arcs?
Answer:
Angle of intersection is one half of the sum of measurements of intercepted arcs.
Step-by-step explanation:
An inscribed angle is the angle formed by the intersection of two chords having a common endpoint in a circle.
Also, by the angles of Intersecting Chords Theorem,
When two chords intersect inside a circle, then the measure of the angle formed is one half of sum of the measure of the arcs intercepted by the angle and its vertical angle.
Which is the relationship between the angle of intersection and the intercepted arcs.
Three mathematicians are applying for a job. There are five hats, three white, two black. They’re lined up, and a hat is placed on each. The first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. The first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. Assume these are INTELLIGENT mathematicians, and that they will do the logically correct thing at each stage — if something can be deduced, they will figure it out.
After a long pause,the first person, who cannot see any hats, says he knows the color of his hat. What is the color, and how does he know?
Classify the number 0. Check all that apply.
Real
Irrational
Rational
Integer
Whole
Natural
Knowing that you use 275 KWH from 7am-7pm and 265 KWH 7pm-7am, answer the question.
How much have you paid on the NightTImer plan?
NightTimer Plan: If more than 50% of usage is outside of 7pm-7am, then you have to pay the DayTimer rate for all power used between 7am-7pm. $0.06445/KWH
DayTimer: As long as most power used if from 7am-7pm, then you receive a 20% discount on power usage between 7pm-7am.
$0.06831/KWH
Answer: 35.86
Step-by-step explanation:
By applying the DayTimer and NightTimer plans' rules and doing the necessary calculations, the total payment on the NightTimer plan would be $33.26747.
Explanation:The total power used from 7am-7pm is 275 KWH and from 7pm-7am is 265 KWH. In this case, you have used more power during the 7am-7pm period. As such, you qualify for the DayTimer plan's rate. Therefore, you pay $0.06831/KWH for the power used between 7am-7pm, which results in 275 KWH * $0.06831/KWH = $18.78575. However, since most of your power usage is from 7am-7pm, you receive a 20% discount on your night usage. The night rate, therefore, is 20% less than the DayTimer rate, which is $0.06831 * (1 - 20/100) = $0.054648/KWH. Hence, you will pay 265 KWH * $0.054648/KWH = $14.48172 for power used between 7pm-7am. By adding these two amounts together, your total payment on the NightTimer plan would be $18.78575 + $14.48172 = $33.26747.
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what is the answer to n/5- 9= 1/5
If 20% of all manually filed returns contain errors, and 0.05% of all electronically filed returns contain errors, how much more likely is a manual filer to make an error than an electronic filer?
a.
40,000 times more likely
b.
4,000 times more likely
c.
400 times more likely
d.
40 times more likely
Answer:
c. 400 times more likely
Step-by-step explanation:
A surveyor standing 67 meters from the base of the building measures the angle to the top of the building and finds it to be 36 degrees. The surveyor then measures the angle to the top of the radio tower on the building and finds it is 46 degrees. How tall is the radio tower?
my choices are: a. 11.81m , b. 20.7 m, c. 7.66 m, d. 8.81 m
Any advice or assistance is appreciated. ...?
Answer:
Option B is the correct answer.
Step-by-step explanation:
Refer the the figure below of the question given.
The height of radio tower = CD
CD = AD - AC
We have
[tex]tan46=\frac{AD}{AB}\\\\AD=ABtan46=67tan46\\\\tan36=\frac{AC}{AB}\\\\AC=ABtan36=67tan36\\\\CD=67tan46-67tan36=20.70m[/tex]
Option B is the correct answer.
Shape 1 and shape 2 are plotted on a coordinate plane. Which statement about the shapes is true?
Shape 1 is congruent to shape 2, which can be shown using a sequence of dilations and translations.
Shape 1 is not congruent to shape 2 because the shapes do not have the same absolute coordinates.
Shape 1 is congruent to shape 2, which can be shown using a translation.
Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."
Solution:
As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.
Both the shapes are concave polygon.
The base length of two shapes are equal .
→2 × AB = P Q →(approx)
→BC=QR
→2 × CD= RS→→→(approx)
If translation has taken place, all the vertices has been translated by same amount.
So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."
1.) Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52> How old is Mousy?
2.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?
If sec 2A = 1/sin 13A, determine the angle A in degrees.
a. 5°
b. 6°
c. 3°
d. 7°
If a line segment has endpoints A(3x + 5, 3y) and B(x − 1, −y), what are the coordinates of the midpoint of AB ?
(x + 3, 2y)
(2x + 3, y)
(2x + 2, y)
(4x + 4, 2y) ...?
You need to use the midpoint formula of (x1+x2)/2,(y1+y2)/2
put in the actual points will look like this. (3x+5+x-1)/2,(3y-y)/2
now solve to get (4x+4)/2,(2y)/2
finish (2x+2,y)
Final answer:
The coordinates of the midpoint of the line segment with endpoints A(3x + 5, 3y) and B(x - 1, -y) are (2x + 2, y), using the midpoint formula.
Explanation:
To find the coordinates of the midpoint of a line segment with endpoints A and B, you can use the midpoint formula, which is ((x₁ + x₂)/2, (y₁ + y₂)/2). For the given endpoints A(3x + 5, 3y) and B(x - 1, -y), substituting the coordinates into the formula gives us the midpoint coordinates as follows:
x-coordinate of the midpoint = (3x + 5 + x - 1)/2 = (4x + 4)/2 = 2x + 2y-coordinate of the midpoint = (3y - y)/2 = 2y/2 = yHence, the coordinates of the midpoint of AB are (2x + 2, y).
a bag of oranges weighs 5 1/4 pounds. how much do (1 & 1/2) bags weigh
*WRITTEN ANSWER....PLZ HELP, AND TELL ME HOW YOU SOLVED IT! THANK YOU AND HAVE A FANTASTIC DAY!*
Answer:
7 7/8 pounds
Step-by-step explanation:
Given that a bag of oranges weighs 5 1/4 pounds and you want to know how much do 1 1/2 bags weigh, the next proportion must be satisfied:
(5 1/4 pounds)/(1 bag of oranges) = (x pounds)/(1 1/2 bag of oranges)
Isolating x:
x = (5 1/4)*(1 1/2)/1
x = 7 7/8 pounds
a number of apples divided into 12 baskets
On the way home from school, ross wears his 20-pound backpack and carries his 7-ounce lunchbox. how many ounces does he carry in total?
Answer: [tex]327[/tex] [tex]\text{ounce}[/tex]
Step-by-step explanation:
Given: On the way home from school, ross wears his [tex]20[/tex] pound backpack and carries his [tex]7[/tex] ounce lunchbox.
To Find: how many ounces does he carry in total.
Solution:
Weight of Ross's backpack [tex]=20[/tex] [tex]\text{pound}[/tex]
Weight of Ross's lunchbox [tex]=7[/tex] [tex]\text{ounce}[/tex]
Now,
As unit of weight of backpack and lunchbox is different, we need to convert it.
[tex]1[/tex] [tex]\text{pound}[/tex] [tex]=16[/tex] [tex]\text{ounce}[/tex]
Now weight of backpack is[tex]=\text{weight in pound}\times16[/tex]
[tex]20\times16[/tex]
[tex]320[/tex] [tex]\text{ounce}[/tex]
Total ounces carried by Ross [tex]=\text{weight of backpack}+\text{weight of lunchbox}[/tex]
[tex]320+7[/tex] [tex]\text{ounce}[/tex]
Hence Total ounce carried by Ross is [tex]320+7[/tex] [tex]\text{ounce}[/tex]
Write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
We need to write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
Therefore, 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
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Tim wants to model a dollhouse from a real house that measures 60 feet in length by 28 feet in width. He decides to use a scale in which 1/4 inch equals 1 foot. What will the dimensions of his model be?
Length= __________ inches
Width= ___________ inches
Answer:
15
7
Just to simplify the answer above.
Step-by-step explanation:
olivia has $180 to buy presents for her 3 sisters and 2 nephews. she wants to spend $20 more on each sister then she spends on each nephew.
Answer:
she spends 44 dollars per sister, 24 dollars per nephew
Step-by-step explanation:
180=3(20+x)+2x
180=60+3x+2x
120=5x
x=24
x+20=44
Nam has a beginning balance of $815 in her checking account. She writes a check for $210 and has a debit transaction of $525. What is her new balance?
$125
$80
$1550
$120
Which speed is the fastest? A 18 feet in 20 minutes B 90 feet in 2.5 hours C 20 yards in 1.5 hours D 3 2/3 yards in 15 minutes
''90 feet in 2.5 hours'' have fastest speed.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
There are some distances and time.
Now,
For Option A;
⇒ 18 feet in 20 minutes
Since, We know that;
⇒ Speed = Distance / Time
= 18/20
= 0.9 feet per minutes
For Option B;
⇒ 90 feet in 2.5 hours
⇒ 90 feet in 150 minutes
Since, We know that;
⇒ Speed = Distance / Time
= 90/150
= 0.6 feet per minutes
For Option C;
⇒ 20 yards in 1.5 hours
Since, 1 yards = 3 feet
⇒ 60 feet in 90 minutes
Since, We know that;
⇒ Speed = Distance / Time
= 60/90
= 0.67 feet per minutes
For Option D;
⇒ 3 2/3 yards in 15 minutes
Since, 1 yards = 3 feet
⇒ 11 feet in 15 minutes
Since, We know that;
⇒ Speed = Distance / Time
= 11/15
= 0.73 feet per minutes
Hence, Clearly ''90 feet in 2.5 hours'' have fastest speed.
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Final answer:
After converting each option to the same unit of speed, it's clear that Option A with a speed of 0.9 feet per minute is the fastest.
Explanation:
To determine which speed is the fastest, we need to convert each option into the same unit of speed, typically feet per minute or meters per second for consistency. Here, we'll choose feet per minute for simplicity.
Option A: 18 feet in 20 minutes = 0.9 feet/minute
Option B: 90 feet in 2.5 hours (150 minutes) = 0.6 feet/minute
Option C: 20 yards (60 feet) in 1.5 hours (90 minutes) = 0.67 feet/minute
Option D: 3 2/3 yards (11 feet) in 15 minutes = 0.73 feet/minute
Comparing these speeds, Option A is the fastest with 0.9 feet per minute.
A function takes in values of the ____________________ variable, called inputs, and gives back values of
the ____________________ variable, called outputs. A function takes in values of the ____________________ variable, called inputs, and gives back values of
the ____________________ variable, called outputs.
How do I simply this, thanks!
Can fractions still be considered natural, whole, integers, rational, irrational, or real numbers?
An employee receives a weekly salary of $340 and a 6% commission on all sales.
Find the employee's earnings for a week with $660 total sales.
The employee earns a fixed salary of $340 plus a 6% commission on sales. In a week with $660 in sales, his total earnings would be $379.60.
Explanation:The employee's weekly income is a combination of a fixed salary and a percentage of sales. His fixed salary is $340. From his sales, he earns a 6% commission. So for a week with $660 in sales, the commission would be 6/100 * 660, which equals $39.60. Adding this commission to the fixed salary: $340 + $39.6 = $379.60. So, the employee's overall earnings for the week would be $379.60.
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What is the length of the other diagonal DF?
5 cm
16 cm
21 cm
32 cm
Applying the Pythagorean theorem, the length of diagonal DF is: C. 21 cm.
What is the Pythagorean Theorem?The sum of the squares of the two shorter legs of a right triangle equals the square of the length of the longest leg.
Let the point of intersection of the diagonals be O.
Diagonal FD bisects diagonal EG into equal segments EO and OG. EO = OG = 24/2 = 12 cm
Find the lengths of FO and OD using the Pythagorean theorem:
FO = √(20² - 12²) = 16 cm
OD = √(13² - 12²) = 5 cm
Length of diagonal DF = FO + OD = 16 + 5 = 21 cm.
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What is 75% of 90? 67.5 6750 675 6.75
To calculate 75% of 90, convert the percentage to a decimal (0.75) and multiply it with 90, resulting in 67.5.
To find 75% of 90, we can use the concept that 'percent' means 'per hundred'. The calculation involves turning the percentage into a decimal by dividing by 100 and then multiplying by the number in question. Thus, 75% can be written as 0.75 (since 75 divided by 100 equals 0.75).
Therefore, to find 75% of 90, we multiply 90 by 0.75:
0.75 × 90 = 67.5
The correct answer is 67.5, not 6750, 675, or 6.75.
Use the Distributive Property to complete the following statement:
4(x−1)=4x−
1.
–4.
4.
–1.
Which of the following expressions describes the solution set m ≥ -3?
All real numbers that are negative three or greater.
All real numbers that are greater than negative three.
All real numbers that are negative three or less.
All real numbers that are less than negative three.
The correct expression of the solution set will be;
''All real numbers that are greater than negative three.''
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The solution set is,
m ≥ - 3
Now,
Here, The solution set is,
m ≥ - 3
Clearly, a number 'm' is greater than or equal to - 3.
Thus, We can formulate;
The correct expression of the solution will be;
''All real numbers that are greater than negative three.''
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Describe a real world situation that would show a strong negative correlation explain your reasoning
The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium.
True
False ...?
The given statement:
The condition ∑ Fi = 0 is sufficient to assure that a rigid body is in equilibrium is a
TRUE statement.
Step-by-step explanation:According to the condition for the equilibrium of a rigid body, the vector sum of all the forces acting on the body must be zero.
The first condition of equilibrium for a rigid body is as follows:
∑ Fi = 0
where the expression ∑ Fi are the sum of all the forces acting on the body.
Hence, the given statement is a TRUE statement.