Answer:
No
Step-by-step explanation:
Lets simplify both expressions:
We will start with Gloria's first expression:
[tex]1/4 (12x + 24) -9x[/tex]
Apply distributive property:
[tex](3x + 6) -9x[/tex]
Combine like terms, we are then left with:
[tex]6-6x[/tex]
Now lets simplify the second expression
[tex]-6(x+1)[/tex]
Apply distributive property
[tex]-6x-6[/tex]
Rearrange:
[tex]-6-6x[/tex]
Now we can see that the two equations are not equal, as the first is 12 greater than the second. Another way we could have tested this was plugging in a value for x and then solving.
Jenny draws the path to walk from her house over to her grandmother's house. She knows that she has to avoid the end of the segment where construction is taking place. If she wants to use equations to identify her path on the coordinate plane, what should her answer look like?
Her answer should look like y = x + 2, x ≤ 2
How to determine the equation?The complete question is added as an attachment
From the attached graph, we have the following points
(x, y) = (2, 4) and (0, 2)
See that the difference between the y and x values is 2 where y > x
So, we have
y - x = 2
Add x to both sides
y = x + 2
The highest value of x in the graph is 2.
So, we have
x ≤ 2
Hence, her answer should look like y = x + 2, x ≤ 2
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Proof : tan10 x tan20 x tan…70 x tan80=1
This follows from the identity
[tex]\cot(x) = \dfrac1{\tan(x)} = \tan(90^\circ - x)[/tex]
The overall product is 1 because
[tex]\tan(10^\circ) \tan(80^\circ) = \cot(80^\circ) \tan(80^\circ) = 1[/tex]
[tex]\tan(20^\circ) \tan(70^\circ) = \cot(70^\circ) \tan(70^\circ) = 1[/tex]
[tex]\tan(30^\circ) \tan(60^\circ) = \cot(60^\circ) \tan(60^\circ) = 1[/tex]
[tex]\tan(40^\circ) \tan(50^\circ) = \cot(50^\circ) \tan(50^\circ) = 1[/tex]
Complete the empty tables below with the correct values
Based on the information provided in the first table, we have the following angle and trigonometric function:
θ = 60°sin60 = √3/2cos60 = 1/2csc60 = 2/√3sec60 = 2cot60 = 1/√3How to complete the table of values?Based on the information provided in the first table, we have the following trigonometric function:
tanθ = √3
θ = tan⁻¹(√3)
θ = 60°.
In radians, we have:
θ = 60 × π/180
θ = 1.0472 radian.
sin60 = √3/2
cos60 = 1/2
csc60 = 2/√3
sec60 = 2
cot60 = 1/√3
Based on the information provided in the second table, we have the following trigonometric function:
θ = 30 × π/180
θ = 0.5236 radian.
sin30 = 1/2
cos30 = √3/2
tan30 = 1/√3
csc30 = 2
sec30 = 2/√3
cot30 = √3
Based on the information provided in the third table, we have the following trigonometric functions:
sinθ = √2/2 tanθ = 1
θ = sin⁻¹(√2/2) θ = tan⁻¹(1)
θ = 45°. θ = 45°.
In radians, we have:
θ = 45 × π/180
θ = 0.7854 radian.
cos45 = √2/2
csc45 = √2
sec45 = √2
cot45 = 1
Based on the information provided in the fourth table, we have the following trigonometric function:
sinθ = 1
θ = sin⁻¹(1)
θ = 90°.
θ = 90 × π/180
θ = 1.5708 radian.
cos90 = 0
tan90 = not defined
csc90 = 1
sec90 = not defined
cot90 = 0
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the accompanying diagram shows a kit that has been secured to skate in the ground with a 20-foot string. the kit is located 12 feet from the ground, directly over point X. what is the distance, in feet, between the skate and point X.
The distance between the skate and point X is 16 feet
Given that the distance between point X and kite is 12 feet
and the distance between stake and kite is 20 feet
We need to find the distance between the stake and point X
Here,
Perpendicular = 12 feet
Hypotenuse = 20 feet
Base = ?
According to Pythagoras Theorem
(Hypotenuse)² = (Perpendicular)²+(Base)²
(20)² = (12)² + (Base)²
∴ (Base)² = 400 - 144
∴ (Base)² = 256
∴ Base = 16 feet
Hence the distance between the Point X and the stake is 16 feet
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compare these heights:
5,2 and 46,5
46.5 is higher than 5.2
Comparison of heightNote that:
The larger the magnitude(value) of the heights given the larger the heights
Units are not added to the values representing each height
By carefully considering the heights given:
5.2 is a lesser value than 46.5
Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2
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What is the solution of the equation. find the value of y when x equals -10. 2x - 9y = -38
Answer:
y =2
Step-by-step explanation:
Substitute -10 for x:
2(-10)-9y = -38
-20-9y = -38
-9y = -18
9y = 18
y = 2
Can someone please explain how to do this? I don’t need the answer I just don’t know how to solve it.
Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.
Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].
Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].
The baker sells all but 3 cakes, so
[tex]P + D = 117[/tex]
After the sale, the baker earns a total of $991, so
[tex]7P + 11D = 991[/tex]
Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.
(The selected answer is actually the correct one.)
A soccer team played 25 games last season. they won 16 games, lost 5 games, and tied the rest.
[tex]\frac{25}{4}[/tex] of the games was a tie.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.To find what fraction of the games was a tie:
Total game played = 25
Win 16 lose 5 total = 21
So, tie matches = 4
The fraction will be 25/4.
Therefore, [tex]\frac{25}{4}[/tex] of the game was a tie.
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Complete question:
A soccer team played 25 games last season they won 16 games, lost 5 games, and tied the rest what fraction of the games was a tie?
I need help in this !! Thank you !!
(a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
Cumulative frequency curve (OGIVE)From the question, we are to determine the median mark
The median mark for a cumulative frequency curve corresponds to the second quartile (Q₂)
Q₂ = 1/2(n+1)th mark
Where n is the total frequency
In the graph,
n = 160
∴ Q₂ = 1/2(160+1)th mark
Q₂ = 80.5th mark
The 80.5th mark is 44
∴ The median mark is 44
(b)
The number of students who scored 54 marks or less = 120 - 0
The number of students who scored 54 marks or less = 120
(c)
The number of students who scored 60 marks or more = 160 - 140
The number of students who scored 60 marks or more = 20
Hence, (a) The median mark is 44
(b) The number of students who scored 54 marks or less is 120
(c) The number of students who scored 60 marks or more is 20
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Aiden evaluated the expression to find the volume of a cylinder. What could be dimensions of the cylinder
The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.
Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.
The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).
Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.
Assuming the units to be cm, we can say that:
The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.
Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.
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The complete question is:
Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?
The height is 12 cm, and the diameter of the base is 8 cm.
The height is 12 cm, and the area of the base is 16 cm².
The height is 16 cm, and the diameter of the base is 6 cm.
The height is 16 cm, and the area of the base is 12 cm².
What is the slope of the line through parentheses two, three parentheses and parentheses -3, four parentheses?
The Slope of the line :
[tex]m=-\frac{1}{5} \approx-0.2[/tex]
What is slope?Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.
Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.
slope = (y₂ - y₁) / (x₂ - x₁)
Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.
P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
we have that:
[tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]
Fill in the blanks in the slope calculation,
[tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]
Reaction: the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]
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780tonnes 650kilograms ÷13
Answer:
60 kilograms
Step-by-step explanation:
LOOK AT PIC!!! PLS HELP
Answer:
C. 21°C
Step-by-step explanation:
Substitute 69.8 for F in the equation, [tex]69.8=\frac{9}{5}C+32[/tex]. This becomes [tex]37.8=\frac{9}{5} C[/tex]. Divide both sides by [tex]\frac{9}{5}[/tex] to get [tex]21=C[/tex].
Answer:
21
Step-by-step explanation:
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I cant figure this out
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the width, hence:
length = x + 2
The area of a rectangle is the product of its length and its width.
Area = length * width
Area = x(x + 2)
120 = x² + 2x
x² + 2x - 120 = 0
x = 10, length = 10 + 2 = 12
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
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the amount of bacteria in a fish tank was 830. After 5 hours, the amount of bacteria is 3202.
Complete the table to determine which of these equations could approximate the amount of bacteria
Answer: 37.92
Step-by-step explanation: We know that 3202 / 5 = 640.4.
We subtract that by 830 to get (830 - 640.4 =) 189.6. Then we do / by five again to get 37.92. That is the answer.
The sum of a positive number and 56 times its reciprocal is equal to its cube. What is the number?
Answer:
2×sqrt(2) = 2.828427125...
Step-by-step explanation:
x = "a positive number"
x + 56/x = x³
x² + 56 = x⁴
x⁴ - x² - 56 = 0
(x² + 7)(x² - 8) = 0
this is true only for
x² = -7
or
x² = 8
x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.
x² = 8 means
x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...
The angle measurements in the diagram are represented by the following expressions.
Answer:
X = 12
<B = 45°
Explanation:
From the diagram above:
Alternate exterior angles are equal. Therefore,
[tex]5x - 15 = 2x + 21 \\ collecting \: liketerms \\ 5x - 2x = 21 \: + 15 \\ 3x = 36 \\ dividing \: bothsides \: by \: 3 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12 [/tex]
For the measure of angle B
2x + 21°
2(12) + 21 = 24 + 21 = 45
Measure of angle B = 45°
The nth term of a sequence is 2n2² - 4n+4 Work out the 8th term of the sequence. 8th term= Submit Answer Skip for Now
The nth term of a sequence exists 2n2² - 4n+4 is 36.
What is PEMDAS' order of operations?The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).
[tex]$2*8*2^{2} - 4*8+4[/tex]
Follow the PEMDAS order of operations
Calculating the exponents, we get 2² = 4
[tex]= 2*8*4 - 4*8+4[/tex]
= 64-32 +4
= 36
Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.
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Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other
equivalent forms. Explain how each form was created. (10 points)
The polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2
How to create the polynomial?The GCF is given as:
GCF = 5z
This means that the polynomial can be represented as:
P(z) = GCF * Another factor
We can make use of the following function
P(z) = 5z * (z - 1)
Expand
P(z) = 5z^2 - 5z
Rewrite as:
P(z) = -5z + 5z^2
Hence, the polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2
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Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f _________.
The differentiation of the stated series expansion of f term-by-term to obtain the corresponding series expansion for the stated derivative of f is [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)Xⁿ⁻¹
What are the steps to arrive at the above solution?f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ
⇒ f'(x) = d/dx [[tex]\sum_{n=0}^{\infty}[/tex](-1)ⁿ 3ⁿXⁿ]
= [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿ d/dx (xⁿ)
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿ(nxⁿ⁻¹)
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿnxⁿ⁻¹
= [tex]\sum_{n=1}^{\infty}[/tex] ((-1)ⁿnxⁿ⁻¹)3ⁿ
= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)xⁿ-1
What is differentiation?In mathematics, differentiation is used to calculate rates of change. In mechanics, for example, velocity is the rate of change of displacement (with regard to time).
The acceleration is the rate of change of velocity (with respect to time).
What is the practical use of Differentiation in real life?They are employed in many fields, including
biologyeconomicsphysicschemistry, and engineering.They can be used to represent:
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Full Question:
Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f.
If f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ
PLEASE HELP IM SUPER STUCK
Answer:
[tex]y = \frac{1}{4} x + 9[/tex]
Step-by-step explanation:
All lines take the form
[tex]y = mx + c[/tex]
Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.
To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:
[tex]y = \frac{1}{4} x + 9[/tex]
What value(s) of x will make x²=81 true?
Answer: 9,-9
Step-by-step explanation:
Answer: 9
Step-by-step explanation:
9x9=81
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
linear equationThis are equations that has a leading degree of 1. GIven the expression as shown below
2.3p – 10.1 = 6.5p – 4 – 0.01p
Collect the like terms
2.3p – 6.5p + 0.01p =– 4 + 10.1
Simplify
-4.19p = 6.1
Hence the equations have the same solution are 2.3p – 6.5p + 0.01p =– 4 + 10.1 and -4.19p = 6.1
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3 + 2 x 7 - 30(^2)
help me
What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
(7, 3)
(3, 7)
(−2, −3)
(−3, −2)
Answer:
(7,3)
Step-by-step explanation:
you can add the equations together to eliminate y and first solve for x
(x-3y = -2) + (x+3y=16) = (2x = 14)
x = 7
then plug x into one of the equations to solve for y
(7) - 3y = -2
9 = 3y
y = 3
the solution is (7,3)
Answer: (7, 3)
Step-by-step explanation:
x - 3y = -2
x + 3y = 16
Here we can add the two equations together to cancel out the y
2x = 14
divide by 2 on both sides to get
x = 7
Now that we have the X value, plug in x value into an equation to get the Y
x - 3y = -2
7 - 3y = -2
-3y = -9
y = 3
So the solution is (7, 3)
Dad is 4 times as old as his son Jim is now. In 10 years, Dad's age will be 20 years more than twice Jim's age. If D = dad's age now and J = Jim's age now, how old is Jim?
Answer:
Jim is 5
Step-by-step explanation:
word problems can be sort of like translation questions
'times' means multiply
'as old as' means equal or =
'will be' means equal or =
'more than' means plus or +
when I saw
"Dad is 4 times as old as his son Jim is now"
I knew needed to make
Jim = x &
Dad = 4x
when I saw
"In 10 years, Dad's age will be 20 years more than twice Jim's age"
I knew
'Dad's age' means 4x
'In 10 years' means 10 +
'will be' means equal sign or =
'20 years more than' means 20 +
'twice Jim's age' means 2x
sentence can be re written
4x+10=20+2x
'if D = dad's age now' means 4x=D (Dad)
'J = Jim's age now' means x = J (Jim)
I solved for x
4x+10=20+2x
2x=10
x=5
then I checked the math
today
x = Jim = J = 5
4x = Dad = D = 20
'in 10 years'
Dad is 20 + 10 = 30
means
does 30 = 20 years more than twice Jim's age?
does 30 = 20 + 2x ?
does 30 = 20 + 2(5)?
does 30 = 20 + 10?
does 30 = 30?
yes!
it checks out!
The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________
The z value for the probability in the standard normal table is 1.29.
In this question,
Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.
The value of probability is 0.80
A standard normal random variable is between -z and +z, So
P(-z < 0 < z) = 0.80
⇒ 2P(0 < z) = 0.80
⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]
⇒ P(0 < z) = 0.40
From the standard normal table, z value for the probability 0.40 is
⇒ z = 1.29
Thus P(0 < 1.29) = 0.40
Hence we can conclude that the z value for the probability in the standard normal table is 1.29.
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Which function represents a reflection of f(x) = 2(0.35)x over the y-axis?
h(x) = 2(0.35)x
h(x) = –2(0.35)x
h(x) = 2(0.35)–x
h(x) = 2(–0.35)–x
The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
How to determine the reflection?The equation is given as:
f(x) = 2(0.35)^x
The reflection of a function over the y-axis is :
f'(x) = f(-x)
So, we have:
f(-x) = 2(0.35)^(-x)
From the list of options, we have
h(x) = 2(0.35)^(-x)
Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)
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ASAP PLEASE I NEED YouR HELP
Subtract − 4 b 2 + 4 b − 4 from 3 b 2 + 2 b − 5 .
Step-by-step explanation:
I assume the question really looks like
-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.
so,
3b² + 2b - 5 - (-4b² + 4b - 4) =
= 3b² + 2b - 5 + 4b² - 4b + 4 =
= 7b² - 2b - 1
What expression is equivalent to (square root)
Answer:
C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]
Step-by-step explanation:
To simplify the expression, you need to:
1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]
-----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
2.) Distribute the exponents
-----> When an exponent is raised to another exponent, they should be multiplied
3.) Create common denominators
4.) Combine the variables
-----> When two variables with exponents are being multiplied, the exponents should be added