The value of the polynomial at the point [tex]x=a[/tex], just replace [tex]x[/tex] with [tex]a[/tex] in the polynomial equation.
Verify the following equation:
[tex]=4x^{2} -7x+5[/tex]
The given solution:
[tex]x=-3[/tex]
[tex]4x^{2} -7x+5[/tex]
Find the equation:
[tex]4x^{2} -7x+5[/tex]
[tex]4(-3x)^{2} -7(-3)+5[/tex]
[tex]=4(9)+21+5[/tex]
[tex]=36+26[/tex]
[tex]=62[/tex]
Therefore,The option E [tex]62[/tex] is the correct answer
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Given LM- MP and L, M, and P are collinear, which of the following is false about the relationship of L, M. and P?
(1) LM = MP (2) M is the midpoint of LP (3) LM +MP=180 (4) M bisects LP
The statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
What are Collinear Points?When two or more points are on a straight line, they are classified as collinear points.
What is the Midpoint of a Segment?The point on a line segment that bisects the segment into two equal parts is referred to as the midpoint of the line segment.
We are given that:
LM = MP, since, points L, M. and P are collinear points, therefore, it implies that point M is the midpoint of segment LP.
It also means that M bisects segment LP since LM = MP, where M is the midpoint of segment LP.
Thus, the statement that is false about the relationship of L, M, and P that are collinear is: 3. LM + MP = 180.
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Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 4 / 5;
The value of x as an int variable is 0
What is a int variable?An int(integer) variable is a variable containing only whole numbers.
Given the expression;
x = - 3 + 4 % 6/ 5
Let's make into proper fraction, we have
x = - 3 + {}4/ 100 × 6/ 5
Multiply through
x = -3 + 6/ 5/ 4/ 100
x = -3 + {6/ 5 ÷ 0. 4}
x = -3 + {3}
expand the bracket
x = -3 + 3
Add like terms
x = 0
Thus, the value of x as an int variable is 0
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Complete question;
Assume that x is an int variable. what value is assigned to x after the following assignment statement is executed? x = -3 + 4 % 6/ 5;
The population of Georgia is growing at a yearly rate of about 1.3%. The current population is
about 9,815,210 people. The population of North Carolina is growing at a yearly rate of about
1.25%. North Carolina's current population is about 9,656,401 people.
a. What is the equation that models Georgia's population growth?
b. What is the equation that models North Carolina's population growth?
c. What do the graphs of the equations look like? Graph the equations on the provided grid.
The equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph).
We are given that:
For Georgia:
Growth rate of population = 1.3 %
Population = 8,815,210
For North Carolina:
Growth rate of population = 1.25 %
Population = 9,656,401
a) The equation that models Georgia's population growth can be found out by using the concept of compound interest as the population will increase in a compounded way.
So, the equation will be:
P = 8,815,210 ( 1 + 1.3 % )ⁿ
P = 8,815,210 ( 1.013 )ⁿ
where P is the population after n years.
b) the equation that models North Carolina's population growth:
P = 9,656,401 ( 1.0125)ⁿ
where P is the population after n years
Therefore, we get that, the equation for population growth in Georgia is P = 8,815,210 ( 1.013 )ⁿ ( red line on the graph) and the equation for population growth in North Carolina is P = 9,656,401 ( 1.0125)ⁿ ( blue line on the graph)
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(5x^4)^2 solve this equation
Compare the two numbers. Use > or < .
√63, 7.5
Compare the two numbers √63, 7.5
[tex]\sqrt{63} =7.93[/tex]
So, √63 > 7.5
What is a square root?
A square root is a factor of a number in mathematics that, when multiplied by itself, equals the original value.Square roots can be taken into account more broadly in any situation where the concept of an object's square is specified.Among other mathematical structures, these include function spaces and square matrices.The term square root is sometimes used to refer to the major square root of a positive number, even though it is merely one of the two square roots of that number.To learn more about square roots, refer:
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help Finding the initial amount and rate of change given a table for a linear function
(a) The table clearly shows distance gets smallers as time passes, so the first choice is correct.
Since we know the rate at which the escalator moves is constant, we know that the average rate of change of the escalator's distance from the first floor is the same across any time interval we choose. Take for instance the average rate of change from [tex]t=6[/tex] to [tex]t=9[/tex]. If [tex]d(t)[/tex] denotes distance at time [tex]t[/tex], then the average rate of change over these 3 seconds, and at every point in time for that matter, is
[tex]\dfrac{d(9) - d(6)}{9 - 6} \dfrac{\rm cm}{\rm s} = \dfrac{890 - 980}{9 - 6} \dfrac{\rm cm}{\rm s} = -30 \dfrac{\rm cm}{\rm s}[/tex]
In other words, the distance from the first floor is decreasing at a rate of 30 cm/s. (negative sign = decreasing)
(b) At the start, when [tex]t=0[/tex], suppose Alan's distance from the first floor was [tex]x[/tex]. For every second that passes, we know the distance from the first floor decreases by 30 cm. This would mean that after [tex]t[/tex] seconds have passed, the distance would have decreased by a total [tex]30t[/tex] cm.
This tells us that Alan's distance from the first floor at any time [tex]t\ge0[/tex] is
[tex]d(t) = x - 30t[/tex]
Using any of the values from the table, we can solve for [tex]x[/tex].
[tex]t=6 \implies d(6) = x - 30\cdot6 \implies 980 = x - 180 \implies x = 1160[/tex]
which places Alan 1160 cm = 11.6 m from the first floor at the start.
m jkm = 77 m nkm = 22 and kn bisects lkm find jkl
The measure of the angle JL is 33 degrees
Bisection of anglesA bisection is a line that divides an angle into two equal portion. Using the addition postulate below:
<JKM = <JKL + <LKN + <NKM
If the line KN bisects <LKM then <LKN = <NKM = 22 degrees
Substitute the given parameters
<JKM = <JKL + <LKN + <NKM
77 = <JKL + 22 + 22
77 = <JKL + 44
<JKL = 77 - 44
<JKL = 33 degrees
Hence the measure of the angle JL is 33 degrees
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Assume you make $10 an hour and work 20 hours a week. In addition, you receive $1,200 a year in income from a trust fund. What is your total annual income
By adding wages and incomes, we conclude that the worker has a total annual income of $ 11,600.
What is the total annual income?
A year comprises a total of 52 weeks and the worker works 20 hours a week at a wage of $ 10 an hour and receive a total of $ 1,200 in income from a trust fund. The total annual income is the sum of wages of the entire year and the income from the trust fund:
x = (52 weeks) · (20 hours / week) · (10 USD / hour) + 1,200 USD
x = 11,600 USD
The worker has a total annual income of $ 11,600.
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what is the exact distance from (-5, 1) to (3, 0)
Answer:
[tex]\sqrt{17} }[/tex]
Step-by-step explanation:
To find the distance between these points in the Cartesian Plane, apply the distance formula (aka pythagorean theorem).
(x1-x2)^2+(y1-y2)^2= d^2 , where d is distance.
(-5-3)^2+(1-0)^2 -> (-8)^2+(1)^2 ->
16+1 -> 17
Find square root of d^2 to find d, which gives you the exact answer of [tex]\sqrt{17}[/tex].
Evaluate each expression for x=0 . 5 x+2
After evaluation each expression for x = 0 then the equation 5 x+2
⇒ 5(0)+2
⇒ 0 + 2
⇒ 2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Which statements have an inverse that is false?
1.If two angles are congruent, then they are vertical angles.
2.If two angles are a linear pair, then they are supplementary.
3.If two angles are acute, then their sum is less than 90.
4.If two angles are complementary, then both angles are acute.
Statement 1 is a false statement.
What are supplementary angle?
Supplementary angles are two angles whose measures add up to 180° . ex 150° and 30°
What are complementary angles?
When the sum of two angles is equal to 90° degrees, they are called complementary angles. For example, 30° and 60° are complementary angles.
What are vertical angles?
Vertical angles are formed when two lines meet each other at a point. A vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180°What are congruent angles?
Two or more angles that are identical to each other.
False - All vertical angles are considered congruent but not all congruent angles are considered vertical angles. Any acute or obtuse angle may also be considered congruent. True - If 2 angles whose measures add to 180°, it means they are supplementary. They form a linear pair.True - Let one angle be 30° and the other angle is 40° , both of which are acute angles, then their sum is 70°, which is less than 90° True - Both angles in a complementary pair will always be acute. For ex: 30° and 60° are complementary angles , but are less than 90°, so they both are acuteThus we can conclude that all vertical angles are congruent but not all congruent angles are considered vertical angles
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Humpback whales are known to weigh as much as 80,000 pounds. The tiny krill they eat weigh only
2
.
1875
×
10
−
3
pound. About how many times greater is the weight of a humpback whale?
Select Choice
The weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
What are factors of a number?A factor is a number that divides the given number without any remainder.
We have,
Weight of a Humpback whale = 80,000 pounds
Weight of tiny krill = 2.1875 x [tex]10^{-3}[/tex] pounds
We need to find what value multiplied with 2.1875 x [tex]10^{-3}[/tex] would give 80,000.
Let the value be M.
M x 2.1875 x [tex]10^{-3}[/tex] = 80,000
M = 80,000 / 2.1875 x [tex]10^{-3}[/tex]
M = 80,000 x / 2.1875 x [tex]10^{-3}[/tex]
M = 3.6571 x [tex]10^{7}[/tex]
Thus the weight of the Humpback whale is 3.6571 x [tex]10^{7}[/tex] times greater than the weight of the tiny krill.
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How to do 0.86 \ 0.004
Since 0.004 is 4/1000, muiltiply the numerator and denominator by 1000.
That is: (0.86×1000)= 860
(0.004×1000) = 4
860/4= 215
Answer:
215
Step-by-step explanation:
0.86 ÷ 0.004 = 215
Suppose x and y vary together such that y = 2 x 8 . suppose x varies from x = 3 to x = 9.5 . over this interval, how much does x change by?
A function assigns the values. The value of x changes by 6.5, and the value of y changes by 13.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that x and y vary together such that y = 2x+8. Also, the of x varies from x = 3 to x = 9.5. Therefore, we can write,
x change by = Maximum value of x - Minimum value of x
= 9.5 - 3
= 6.5
Further, the minimum and the maximum value of y will be when the value of x is minimum and maximum, this is because the function is linear. Therefore, we can write,
Minimum value of y, y = 2(3) - 8 = -2
Maximum value of y, y = 2(9.5) - 8 = 11
y change by = Maximum value of y - Minimum value of y
= 11 - (-2)
= 11 + 2
= 13
Hence, the value of x changes by 6.5, and the value of y changes by 13.
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what is 49/200 equal to explain
Answer: It can not be simplified
Step-by-step explanation:
49 is divisible by 1 and 7
200 is not divisible by 7
Divide. State any restrictions on the variables.
7 x / 4 y³ ÷ 21 x³ / 8 y
The restrictions on the variables x and y be
x = 0 ⇒ 2/0 = ∞
y = 0 ⇒ 2/0 = ∞
What is meant by expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
How to divide the given expression (7x/4y³) ÷ (21x³/8y)?(7x/4y³) × (8y/21x³) = (2/3x² y³)
What are the restrictions on the variables?
Here, x = 0 ⇒ 2/0 = ∞
Similarly, y = 0 ⇒ 2/0 = ∞
So , x, y ≠ 0
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Maria has a square brick patio. She wants to reduce the width by 3 feet and
increase the length by 3 feet.
T
3 ft
3 ft
3 ft
O A. Iw= x(x-3); 40 square feet
3 ft
Let x represent the length of one side of the square patio. Write expressions
for the length and width of the new patio. Then find the area of the new patio
if the original patio measures 8 feet by 8 feet.
Answer:
Length = x + 3 ft
Width = x - 3 ft
Area of new patio = x² - 9 sq ft
If original side length = 8, new area = 55 sq ft
Step-by-step explanation:
The original patio has side length of x
If one side is reduced by 3 we get (x - 3) as the new side
If the side is increased by 3' we get (x + 3) as the new side
Area of new Patio = (x - 3)(x+3) = x² - 9
Original patio is 8 x 8
New patio width = 8 - 3 = 5
New patio length = 8 + 3 = 11
Area = 5 x 11 =55 sq ft
A rental car company charges $71.87 per day to rent a car and $0.09 for every mile driven. Aaliyah wants to rent a car, knowing that: she plans to drive 475 miles. She has at most $320 to spend. Which Inequality can be used to determine d, the maximum number of days Aaliyah can afford to rent for while staying within her budget?
Answer: Yes, she can affort to rent the car.
Step-by-step explanation:
You multiply 0.09 times 475 which equals $42.75. Next you use the remaining amounts that Aaliyah has and divide it by $71.87.
Write a flow proof.
Given: ZX bisects ∠ W Z Y ; XZ bisects ∠Y X W.
Prove: Δ W X Z ≅Δ X Z Y
We can conclude that ΔWXZ ≅ ΔXZY under ASA condition.
What do we mean by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To Prove: ΔWXZ ≅ ΔXZY
ZX = ZX = (Common)∠WZX = ∠YZX = (Equal as ZX bisects ∠WZY)∠ZXW = ∠ZXY = (Equal as XZ bisects ∠WXY)So, ΔWXZ ≅ ΔXZY under ASA consition.
Therefore, ΔWXZ ≅ ΔXZY.
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If you were to graph the inequality below on a number line
42≤−7x
Would you use an open circle, or a closed circle?
Would your arrow go to the left or the right?
The approximate weights of two animals are 5.36 x 104 lbs. and 6.2 x 104 lbs. Find the total weight of the two animals. Write the final answer in scientific notation with the correct number of significant digits.
12 x 104 lbs.
5.9 x 104 lbs.
1.22 x 105 lbs.
1.2 x 105 lbs.
Help plssss answer fast
The total weight of the two animals is 1.2 x 10^5 lbs
How to determine the total weight of the two animals?The given parameters are
Animal 1 = 5.36 x 104 lbs.
Animal 2 = 6.2 x 104 lbs
Rewrite the parameters properly
Animal 1 = 5.36 x 10^4 lbs.
Animal 2 = 6.2 x 10^4 lbs
The total weight of the two animals is calculated as
Total weight = Animal 1 + Animal 2
This gives
Total weight = 5.36 x 10^4 lbs + 6.2 x 10^4 lbs.
Factor out 10^4 lbs
Total weight = (5.36 + 6.2) x 10^4 lbs.
Evaluate the sum
Total weight = 11.56 x 10^4 lbs.
Rewrite as
Total weight = 1.156 x 10^5 lbs.
Approximate
Total weight = 1.2 x 10^5 lbs.
Hence, the total weight of the two animals is 1.2 x 10^5 lbs
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Solve for x.
A. 8
B. 4.8
C. 4
D. 7.2
i don’t know how to do it pls help
Answer:
[tex] - 1 \geqslant x \geqslant 2[/tex]
write each expression in factored form
1. 3m + 9n
Answer: 3(m+3n)
Step-by-step explanation:
3m + 9n=
3*m + 3*3n=3(m+3n)
The formula for calculating the volume of a cone is V=-rh. Solve this formula for h.
that is the solution above
Write these numbers in order of size.
Start with the smallest number.
0.6
2
3
65%
0.606
what is the correct answer to the following solution 5−3y≤−y−15.
Razonar ¿Cuál es el primer paso para resolver la
ecuación 3(3x - 5x) + 2 = -8?
(-1.5) to the 5th power * (3.2) to the 5th power
Answer:
-2548.03968
Step-by-step explanation:
(-1.5)^5*(3.2)^5
Answer:
Step-by-step explanation:
Evaluate the function.
f(x) = x² + 3x - 7
2
Find f(-5)
