[tex]f(x) = \alpha (x - 4) {}^{2} (x - 2) {}^{2} \\ f(x) = \alpha (x {}^{2} - 8x +16 )(x - 4x - 4) \\ f(x) = \alpha (x {}^{4} - 12x {}^{3} + 52x {}^{2} - 96 x + 64) \\ where \: \alpha ∈ \: \real[/tex]
3. Suppose you graph the information in the table. Find the slope of a line drawn through the points.
Answer:
I can't see the information in the table but I can tell you how to do it
Step-by-step explanation:
pick two points on the graph, then do this: (y2-y1)/(x2-x1)
this will help you to find the slope of the line
In a class of 30 children, 60% of the children are girls. How many boys are there in the class?
Answer:12 boys
Step-by-step explanation:100-60=40 40% of 30 is 12
Write in index form using a unit fraction 10 √ 34
Answer:
2.6
i thank
Step-by-step explanation:
Slope intercept form (-6,19) and (3,-2)
Answer:
[tex]y = -\dfrac{7}{3}x +5[/tex]
Step-by-step explanation:
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
[tex]m = \dfrac{-2 - 19}{3 - (-6)}\\\\[/tex]
[tex]\\\\m= \dfrac{-21}{9}[/tex]
[tex]m = -\dfrac{7}{3}[/tex]
So slope-intercept form is
[tex]y = -\dfrac{7}{3}x +b\\\\[/tex]
[tex]-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\[/tex]
or 7 -2 = b
==> b = 5
[tex]y = -\dfrac{7}{3}x +5[/tex]
Lourdes can buy 3-packs of paper for $10.50, or she can buy 4-packs of paper for $13.50. She wants to buy 12 packs of paper. How much more will she spend if she buys only 3-packs of paper? Explain why.
If Lourdes buys 12 packs of paper in terms of 3 packs each she has to pay 0.5 dollars more.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given Lourdes can buy 3-packs of paper for $10.50.
∴ The cost of per pack of paper is = (10.50/3) = $3.5.
In this case, if she can buy 4-packs of paper for $13.50,
The cost per paper pack is = (13.50/4) = $3.375.
To buy 12 packs in terms of 3 packs each Lourdes has to pay,
(3.5×12) dollars.
= 42 dollars.
To buy 12 packs of paper in terms of 4 packs each she has to pay,
(3.375×12) dollars.
= 40.5 dollars.
∴ She has to pay (40.5 - 40) = 0.5 dollars more.
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Simplify each expression.
log (a²-10a+25) + 1/2 log 1/(a-5)³ - log (√a-5)
After simplifying logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression can be written as,
[tex]log_{10}(a^2-10a+25) + \frac{1}{2} log_{10}\frac{1}{(a-5)^3} - log_{10}(\sqrt{a} -5)\\\\[/tex]
apply formulas for log a + log b and log a - log b
[tex]log_{10}(a^2-10a+25) + log_{10}(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}(a^2-10a+25).(\frac{1}{(a-5)^3})^\frac{1}{2} - log_{10}(\sqrt{a} -5)\\\\= > log_{10}\frac{(a^2-10a+25). (\frac{1}{(a-5)^3})}{(\sqrt{a} -5) } \\\\= > log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
Thus, after solving the logarithm equation is : [tex]log_{10} \frac{(a-5)^\frac{1}{2} }{a^\frac{1}{2}-5 } \\[/tex]
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6c4 what is the combination
Answer: 6 CHOOSE 4 can also be denoted as 6C4.
Draw 4 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.
In 15 possible combinations, AB and BA are not considered as different events.
AB and BA considered as a single combination in 15 events.
Step-by-step explanation:
Evaluate each expression for the given value of x
2x for x=3
Value of the expression 2x at x=3 is 6.
By considering the given expression
2x=2(3)=6
A mathematical expression is created when we successfully combine numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
Expression. Equation. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
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Use synthetic division to find the quotient. 2x⁴ - 4 - 7x - 38x²/x - 4
Answer: A binomial (of the form ax+b).
Step-by-step explanation:
2x⁴ - 4 - 7x - 38x²/x-4=ax+b , hope this is correct
two rectangles have the exact same area. the measurements of the first rectangle is 3k by 3.calculate the value of k
The value of k is 6.
Given we have length as 3k and the width as 3 of the first rectangle.
length = k₊3 and width = 6 of the second recatngle
Two rectangles has the same exact area.
area = length × breadth
3k × 3 = (k₊3)6
9k = 6k ₊ 18
3k = 18
k = 18/3
k = 6
hence we get the value of k as 6.
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d)
A-
C
P
f
55°
h9
Q
R
e
k
S
B
e)
The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 4 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after n steps can be shown using the following expression:
25√3 / 2 * (3/4)^n
What does 25√3 / 2 signify in the expression? (Image Shown Below)
O Each step multiplies the area 25√3 / 2.
O The original figure had an area of 25√3 / 2 square units.
O Each step increases the area of the figure by 25√3 / 2 square units.
O After many steps, the figure will have an area of 25√3 / 2 square units.
The original figure had an area of 25√3 / 2 square units option (B) is correct.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
The Sierpinski triangle is a fractal image:
The original figure is an equilateral triangle.
The area remaining in a particular design after n steps can be shown using the following expression:
= 25√3/2 (3/4)ⁿ
Plug n = 0
= 25√3/2 (3/4)⁰
= 25√3/2 square units
The expression 25√3/2 represents the area of the image of the triangle(shown in the first number image)
Thus, the original figure had an area of 25√3 / 2 square units option (B) is correct.
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Solve each trigonometric equation for θ in terms of y .
y=2 cosθ+1
Answer:
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
Step-by-step explanation:
y = 2cosΘ + 1 ( subtract 1 from both sides )
y - 1 = 2cosΘ ( divide both sides by 2 )
[tex]\frac{y-1}{2}[/tex] = cosΘ , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{y-1}{2}[/tex] )
if 251x=100 two, find x
Answer:
X = 102/251
Step-by-step explanation:
251x = 102
/ /
251 251
X= 102/251
5/12 simplified as a fraction
Answer:
Step-by-step explanation:
You can't simplify 5/12 any more. That is the simplest form
Answer:
5/12 is the simplest form already
A typical paper bag at a grocery store cannot hold more than 49 pounds. Let p represent the number of pounds a typical paper bag can hold.
Create an inequality to represent the situation. Move a symbol to the lines to create the inequality.
P___49
Answer: = is it maybe
if not sry
p≤49 is the inequality to represent the situation.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that a typical paper bag at a grocery store cannot hold more than 49 pounds.
Let p represent the number of pounds a typical paper bag can hold.
We have to find the inequality to represent the situation
As grocery store cannot hold more than 49 pounds which means it holds less than or equal to 49.
p≤49
Hence, p≤49 is the inequality to represent the situation.
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Joseph buys a subway pass for $55. Every time he rides the subway, money is deducted from the value of the pass. He rode the subway 5 times and $40 was deducted from the value of the pass. How much was deducted from Joseph's account for each ticket? Write a mathematical expression to represent this situation; then find the answer.
The amount deducted from Joseph's account for each ticket is $8
The mathematical expression representing the situation is:15=55-5x
What is the total amount deducted from the subway pass?
On the premise that Joseph's subway pass was deducted each time he passes through the subway and that $40 was deducted in all for his number of passes, the total cost of $40 can be modeled into an equation as shown below:
amount left after the deductions=55-40
amount left after the deductions=15
15=total amount paid-(number of passes*cost per subway pass)
total amount paid=55
number of passes=5
cost per subway=x
15=55-5x
5x=55-15
5x=40
x=40/5
x=$8
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Angles of Triangles #3: Find the angles below
All the angles in the given diagram are;
∠5 = 81°
∠1 = 128°
∠2 = 52°
∠3 = 47°
∠4 = 133°
How to find Congruent Angles?
We are given different angles. Thus;
52 + ∠5 + 47 = 180
This is because sum of angles on a straight line is 180°. Thus;
99 + ∠5 = 180
∠5 = 180 - 99
∠5 = 81°
∠1 = ∠5 + 47° because of the definition of corresponding angles. Thus;
∠1 = 81° + 47°
∠1 = 128°
∠2 = 52° because they are corresponding angles.
∠3 = 47° because they are corresponding angles.
∠4 = 180 - 47° because sum of angles on a straight line is 180°.
∠4 = 133°
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luis is making a wooden model of a flag for his school project. He found a bargain on square pieces of plywood. If his flag is to be 18 inches by 12 inches,what is a reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood?
NEED SOON
The reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We have been given that the flag is to be 18 inches by 12 inches, then;
The area of the rectangle = length × Width
The area of the rectangle = 18 x 12
= 216
Since the area of flag will be equal to area for the square piece of plywood.
The area of a square of side length l is given by l squared;
A(l) = l²
216 = 14.6²
Hence, the reasonable area for the square piece of plywood he must purchase if he only wants to make one cut in the wood would be 216 sq inches.
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PLEASE ANSWER RIGHT AWAY
4⁰ + 9 x 2 – 5³
show work please im doing a test
The simplified form of the expression is -106
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
4⁰ + 9 x 2 – 5³
Simplifying
4⁰ + 9 x 2 – 5³
First, evaluate the exponents
5³ = 125
4⁰ = 1
Thus, the expression becomes
1 + 9 x 2 – 125
Simplifying further
1 + 18 - 125
= 19 - 125
= -106
Hence, the simplified form of the expression is -106
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The supertanker and the iceberg are headed straight toward each other. The supertanker traveling at a speed of 12 miles per hour, while the iceberg is traveling at 0.5 miles per hour. If the two are exactly 50 miles apart, in how many hour will the hit
If the two are exactly 50 miles apart, it will hit in
T=0.25hours
This is further explained below.
If the two are exactly 50 miles apart, in how many hour will they hit?Generally, the equation for Time is mathematically given as
T=v/d
Therefore
T=(12+0.5)/50
T=0.25hours
In conclusion, If the two are exactly 50 miles apart, it will hit in
T=0.25hours
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Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function.
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0)
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0)
Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
Domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output
Range of a function means all possible outputs or all the numbers that are the result of all the inputs or value of y
Intercept is the point on graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y intercept where the value of x coordinate is zero
the function given is g (x) = -4x +8
The domain of the given function is all real numbers or - infinite < x< infinite
The range of the given function is all real numbers or - infinite < x< infinite
The x intercept of of the given function is where y = 0
so, 0 = -4x + 8
-8 = -4x
x = 2
The x intercept is (2,0)
Hence, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) which is first option
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Step-by-step explanation:
Took test
A group of friends wants to go to the amusement park. They have $183 to spend on
parking and admission. Parking is $8, and tickets cost $25 per person, including tax.
Write and solve an equation which can be used to determine x, the number of people
who can go to the amusement park.
The equation is 25x + 8 = 183
The value of x is 7
How to determine the value of x ?The group of friends have $183 to spend
The cost of parking is $8
The tickets cost $25 per person
The equation can be written as follows
25x + 8 = 183
Collect the like terms
25x= 175
Divide by the coefficient of x which is 25
x= 175/25
x= 7
Hence the value of x is 7 and the equation is written as 25x + 8 = 183
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Find 29- 3f + 2g, when f=4 and g=3
29-3f+2g
=29-3(4)+2(3)
=29-12+6
=23
solve for y
-4=-2+y/2
Answer:
y = -4
Step-by-step explanation:
-4 = -2 + y/2
-2 = y/2
2(-2) = y
y = -4
In the figure below, /BC/= 2cm, /AB/= 3cm and ZACD= 1500, what is the value of sin A? A D 150° с A√3 B √√3 2 2cm 2/3 3cm B DE 2 3
Answer:
E 1/3
Step-by-step explanation:
m<ACB = 30° because of supplementary angles.
Use the Law of Sines
sin C/AB = sin A/BC
sin 30°/3 = sin A/2
sin A = (2 × sin 30°)/3
sin A = (2 × 0.5)/3
sin A = 1/3
Answer: E 1/3
Simplify each number.
6¹/₂ . 12¹/₂
[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 6= 2 x 3
Prime factorization of 12= 3 x 2 x 2
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m} )^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
Applying the laws of indices mentioned above,
∴[tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] = [tex](2 X 3)^{\frac{1}{2} } . (3 X 2^{2}) ^{\frac{1}{2} }[/tex]
= [tex](3^{2} X 2^{3})^{\frac{1}{2} }[/tex]
= [tex]\sqrt{72}[/tex] = 8.48.
Thus, [tex]6^{\frac{1}{2} } .12^{\frac{1}{2} }[/tex] can be simplified into 8.48.
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A glider begins its flight 3/4
mile above the ground. After 45 minutes, it is 3/10
mile above the ground. Find the change in height of the glider. If it continues to descend at this rate, how long does the entire descent last?
The change in height is
mile(s).
The entire descent lasts
hour(s).
Skip to navigation
Answer:Answer One: 3 miles. Answer Two: 105.
Step-by-step explanation:
i need help pls i give brainist
Answer:
0.000027 ÷ 0.000009
= 2.7 x 10^-5 ÷ 9.0 x 10^-6
= (2.7/9) x 10^(-5 - (-6))
= .3 x 10^1
= 3
Step-by-step explanation:
A grain of rice weighs about 0.03 g.
a) Write the mass of a grain of rice in standard form.
In the USA, about 4.3 million tonnes of rice are eaten each year.
b) 1 tonne = 1 million grams
What is the mass, in grams, of rice eaten in the USA each year?
Give your answer in standard form.
a) The mass of a grain of rice in standard form; 0.3×10⁻¹ gram.
b) The mass, in grams, of rice eaten in the USA each year: 4.6×10¹² grams.
What is described as scientific notation?Scientific notation is a handy way to shorten extremely large numbers with positive exponential values and also very small numbers with negative exponential values. To shorten long numbers in scientific notation, employ positive exponents and decimals.For the given question;
a) Weight of the rice grain is 0.03 g.
Shift the point to one decimal of the right and replace it with 10⁻¹ for this.
= 0.3×10⁻¹
Thus, the number in standard form becomes 0.3×10⁻¹ grams.
b) In USA, the rice eaten per year = 4.3 million tonnes.
1 tonne = 1 million grams
And, we know, one million can be written as.
1 million = 10⁶
4.3 million tonnes = 4.6×10⁶ tonnes.
Now, if 1 tonne = 1 million grams.
Then, multiply both side by 4.6×10⁶.
4.6×10⁶ × 1 tonne = 4.6×10⁶×1 million grams.
4.6×10⁶ tonnes = 4.6×10⁶ million grams.
Again convert million as 10⁶.
= 4.6×10⁶×10⁶
= 4.6×10⁶⁺⁶
= 4.6×10¹²
Thus, in USA 4.6×10¹² grams of rice is eaten each year.
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