No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.
We have 2(12 ÷ 2)2 – 14 + 6
Here according to the BODMAS rule which stands for Brackets Of Division Multiplication Addition Subtraction, we will first solve the brackets.
Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.
12 ÷ 2 = 6
Hence we get
2 X 6 X 2 - 14 + 6
Now we need to multiply.
2 X 6 X 2 = 12 X 2 = 24
Hence we get
24 - 14 + 6
Now we need to add the numbers up.
24 + 6 = 30 hence we get
30 - 14
= 16
Hence Chase's work is not correct.
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find two consecutive numbers whose cubes differ by 217
The two consecutive numbers whose cubes differ by 217 are n=-9 or n=8.
How can the two consecutive numbers be calculated?The concept that will be used here is factorization. Consecutive numbers are those that follow one another continually, from lowest to largest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.
The number can be arranged as
(n+1)^3 -n^3=217
We can simplified this as:
[n^3+3n^2 +3n+1 -n^3]=217
3n^2+3n+1=217
This can be simplified as :
3n^2+3n-216=0
This can be factorized as
(n+9)(n-8)=0
n=-9 or n=8
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Evaluate. −8+(6+4)÷(−2)
−13
negative 13
−4
negative 4
−3
negative 3
−1
The solution of the given expression is -13. The correct option is A.
PEMDAS stands for the sequence of operations for multi-step mathematical expressions. The letters PEMDAS stand for parentheses, exponents, multiplication, division, addition, and subtraction.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given the expression is −8+(6+4)÷(−2). The expression by using the PEMDAS will be solved as below,
E = −8+(6+4)÷(−2)
First, solve the bracket and then division,
E = -8 + ( 10 ) ÷ (−2)
E = -8 - 5
E = -13
Hence, the solution is -13.
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A company is offering a bank account. The value, in dollars, of the account, is represented by the function A(t)=50,000(1.02)^t, where t represents the number of years since the account was first opened. Determine the average rate of change of the account value from t = 0 to t = 5. Express your answer in the nearest cent. PLS HELP!!!
The average rate of change of the account value from t = 0 to t = 5 is the change in the account value divided by the change in time, or (A(5) - A(0))/(5 - 0).
We can substitute the given function into the equation:
A(t) = 50,000(1.02)^t
So,
A(5) = 50,000(1.02)^5
and
A(0) = 50,000(1.02)^0
Now we can substitute these values in the equation of average rate of change:
(A(5) - A(0))/(5 - 0) = (50000(1.02)^5 - 50000(1.02)^0) / (5-0)
This simplifies to
(50000(1.02)^5 - 50000) / 5
Which is approximately equal to 67,622.05
So the average rate of change of the account value from t = 0 to t = 5 is approximately 67,622.05.
4 3/7 ÷ 1/7
What is it?
Answer: 31
Step-by-step explanation:
4 3/7 = 31/7
31 × 7 = 217
7 × 1 = 7
217/7 = 31
What is the value of f(m) = 55?
Answer:
Step-by-step explanation:The exponent of a number shows how many times the number is multiplied by itself.
According to the rules of exponents,
We know that, am ÷ an = am − n
(5m ÷ 5−3) = 55
5m−(−3) = 55
5m + 3 = 55
The bases are the same on both the sides, so their exponents must be equal.
∴ m + 3 = 5
⇒ m = 5 − 3
⇒ m = 2
Find the missing angles measurements. Please show your steps.
If m∠DAC = 65°, m∠DAC and m∠BCA can be classified as alternate interior angles. And m∠BCA = 65°.
What is alternate interior angles of a rectangleAlternate interior angles of a rectangle are congruent, which implies they are equal in measure and are formed by the intersection of the opposite sides of the rectangle.
Considering the diagonal AC from one corner of the rectangle to the opposite corner, the angles formed at the intersection of the non-parallel sides will be congruent
Therefore, the angles m∠DAC and m∠BCA are alternate interior and m∠DAC = m∠BCA, which makes m∠BCA = 65°
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how many inches is a feather
Answer: 4-6 inches
Step-by-step explanation: Hope this helps
Answer:
Feathers are 214 in or less
Step-by-step explanation:
Determine weather the mean value theorem can be applied to f(x)= sqrt(5-x) on (-4,5) find all values of c in (-4,5) such that f’(c)= f(b)-f(a)/b-a if possible
Answer:2.75 (or 11/4, they are equal).
Step-by-step explanation: The graph of f(x) is continuous on the closed interval and differentiable on the open interval. Now we need to find the average slope over the interval, which is [0-3]/[5-(-4)] = -3/9 = -1/3. The goal is to find a place where f'(c) = -1/3, so basically anywhere where the derivative equals -1/3. First we need to find the derivative of the function which can be rewritten as (5-x)^(1/2). Differentiating this using the chain rule gives you -1/(2*sqrt(5-x)). Set this equal to -1/3. The numerator is -1, so really we just need to find where the denominator, 2sqrt(5-x), is equal to 3. Divide by 2 and get sqrt(5-x) = 3/2. Square both sides and get 5-x = 9/4. Subtract 5 and get -x = -2.75, so x = 2.75. This means c = 2.75.
x+2=4(2x + 3)-3
X = ?
Answer:
x= 3x/7 - 10/7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x = -1Step-by-step explanation:
x+2=4(2x + 3)-3
x+2=8x+9
2=8x+9−x
2=7x+9
2-9=7x
-7=7x
-7/-7=7x/-7
-1 = x
x=-1
the variable bwght gives the birthweight of the baby (in ounces). what is the difference in average birthweight between smoking mothers and non- smoking mothers?
The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
When cigs=0, the bwght is 119.77 ounces.
The average birth weight of the baby when the mother is not a smoker is 119.77 ounces.
When cigs=20,
bwght = 119.77 − 0.514(20) = 109.49,
The bwght is 109.49 ounces.
However, as more cigarettes are smoked, the birthweight of the baby decreases at the rate of 0.5138 ounce for every additional cigarette smoked per day.
Obviously, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
So, The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.
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For what values of the variable does each of the following expressions make sense?
sqrt -(6-x) pls help
The value of the equation is A = √ ( -6 + x )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = √ - ( 6 - x ) be equation (1)
On simplifying the equation , we get
Remove the parentheses for addition or subtraction
A = √ ( -6 + x )
when the value of A = 0
√ ( -6 + x ) = 0
Taking squares on both sides of the equation , we get
-6 + x = 0
Adding 6 on both sides of the equation , we get
x = 6
Therefore , the value of x is 6
Hence , the equation is A = √ ( -6 + x )
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Angel read 1 3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1 4 of the book left to read. How much of the book did Angel read at night?
The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.
What is ratio ?
Ratio can be defined as the given value divided by the total value.
The easiest thing to do first is convert all of these fractions to common denominators, and figure out the rest of the problem from there.
So the common denominator between 1/3 and 1/4 is 12, so convert these to fractions to /12 and continue on.
Think of the whole book being 12/12, and Sarah read 4/12 of it in the morning, so we know she has 8/12 left of it. Since we know she still has 3/12 left to read by the end of the day, we can subtract 8/12 - 3/12 to find out how much she read at night, which is 5/12. This makes sense because when we add all the fractions up (4/12 + 3/12 + 5/12) it comes out to 12/12, which is the whole book.
Therefore, The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.
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HELPPPPPPPPP
What is the value of x?
Enter your answer as a decimal in the box.
Check the picture below.
a model of a flagpole has a scale of 1in:12ft. The flagpole is 174 feet tall. How tall is the model flagpole
Answer:12 feet
Step-by-step explanation:
Evaluate 12.3v + 11.7w when v=3 and w=4.
Answer:
83.7
Step-by-step explanation:
Substitute v = 3 and w = 4:
[tex]\displaystyle{12.3 \cdot 3 + 11.7 \cdot 4}\\\\\displaystyle{= 36.9 + 46.8}\\\\\displaystyle{= 83.7}[/tex]
Therefore, the value is 83.7
Select the equivalent expression. (2^-10/4^2)^7
The equivalent expression for the given expression is 1/2⁹⁸.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is (2⁻¹⁰/4²)⁷.
Now, (2⁻¹⁰/(2²)²)⁷
= (2⁻¹⁰/2⁴)⁷
= (1/2¹⁰×2⁴)⁷
= (1/2¹⁰⁺⁴)⁷
= (1/2¹⁴)⁷
= 1/2⁹⁸
Therefore, the equivalent expression for the given expression is 1/2⁹⁸.
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2x is greater than 5 + 2
Answer:
x = greater than or equal to 3.5 x = 3≥
Step-by-step explanation:
any number that is greater than or is 3.5 will make 2x greater than 5 + 2 which equals 7
Caroline has 32 marbles. Caroline gives 3/8 of the marbles to Leon
The two Caroline's marbles are hence blue.
What happens to the denominator when you multiply fractions?Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
Adding a whole number to the numerator multiplies it. No change is made to the denominator. In the simplest possible way, simplify the product. The denominator stays the same since a whole number's denominator is 1, when expressed in fractional form.
3 Caroline's marbles are blue.
In line with the assertion made:
16 marbles total, 1/8 of which are blue belong to Caroline.
16 marbles are included in the total.
Blue portions of them
calculate the proportion of blue marbles in Caroline's collection.
marbles that are blue in number =1/8 * 16 = 2.
The two Caroline's marbles are hence blue.
The complete question is,
Caroline has sixteen marbles. eight of them are blue. what proportion of Caroline's marbles are blue?
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A dartboard has a radius of 9 inches. How much area covers the dartboard in which you can land?
According to the area of circle, the area covers the dartboard in which you can land is 254.34 square inches.
In math the term called area of circle is defined as the process of π multiplied by the square of the radius and area of a circle(A) when the radius 'r' is given is πr² here the value of π is approx. 3.14 or 22/7.
Here we know that the dartboard has a radius of 9 inches.
And the value of area covers the dartboard in which you can land is calculated as,
Where the value of r is 9, then the area is calculated as,
=> A = π(9)²
When we expand the terms, then we get,
=> A = π x 81
Apply the value of π as 3.14, then we get,
=> A = 3.14 x 81
=> A = 254.34
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For value of the variable does this expression make sense?
[tex]\sqrt{\frac{1+3a}{25}[/tex]
Answer: a ≥ -1/3
Step-by-step explanation:
If we want the result of the expression to end up as a real number, the fraction under the square root cannot be negative.
Therefore, we can make an equation like this:
(1+3a) / 25 ≥ 0
Multiply by 25
1 + 3a ≥ 0
Subtract 1
3a ≥ -1
Divide by 3
a ≥ -1/3
WILL MARK BRAINLIEST!! function g is the result of these transformations on the parent sine function: •vertically stretch by a factor of 3 •horizontal shift left pi/2 units • vertical shift down 4 units. Substitute the values of A, C, and D to complete the equation modeling function g
By substituting the values of A, C, and D, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.
From the question, we have the following information;
The vertical distance of the sine function = 3 × The parent function
∴ A = 3
Given that the horizontal shift left = π/2 units (from an online source with a similar question)
The vertical shift down = 4 units
The given function g is g(x) = A·sin(x + C) + D
Where,
A is the amplitude = The maximum displacement from the rest or equilibrium position = 3
C is the horizontal shift = -π/2 (The negative sign is for the shifting to the left)
D is the vertical shift = -4 (The negative sign is for a shift in the downward direction)
Therefore, the equation modelling the function is g(x) = 3·sin(x - π/2) - 4.
--The given question is incomplete; the complete question is
"Enter the correct answer in the box. Function g is the result of these transformations on the parent sine function:
Vertical stretch by a factor of 3.
Horizontal shift left units.
vertical shift down 4 units.
Substitute the values of A, C, and D to complete the equation modelling function g. g(x) = Asin(x + C) + D."--
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Which expression is equal to 3/square root of 7?
In triangle ABC. AD is a median. P and q are the midpoints of AB and AD respectively. If ar (ABC) = 72cm ^ 2 then ar (APQ) =?
The area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
Define the term median of triangle?A line segment from such a vertex here to middle of the other side is what is meant by a median. When the vertex is just an angle in a right triangle and the non-congruent angle about an isoceles triangle, it also functions as an angle bisector.Given that:
AD is ABC's median, ABC will be divided into two distinct triangles by AD.We are aware that a triangle's middle separates that into two triangles with equal areas. Triangle ABC's median is AD, and ABD's median is PQ.Then, area (ΔABD) = area (ΔADC)
And, area (ΔABD) = 1/2 area (ABC) eq.....(i)
Thus, In ΔABD, PQ is the median, as PQ are the mid points on AB and AD respectively.
Then,
ar (APQ) = 1/2 ar(ΔABD)
ar (APQ) = 1/2 × [1/2 ar(ABC)] ....... (Use eq (i))
ar (APQ) = 1/4 ar(ΔABC)
ar (APQ) = 1/4 *72 cm ^ 2
ar (APQ) = 18 cm ^ 2
Thus, the area of the ar (APQ) = 18 cm ^ 2 for the given triangle ABC.
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Maria is 5 feet 3 inches tall. Marla is 4 feet 11 inches tall, Mandy is 5 feet 2 inches tall
and Marilyn is 4 feet 8 inches tall.. What is the average height of these 4 friends? Explain
how you found your answer.
Answer:
the average height is 5 feet 0 inches
Step-by-step explanation:
To find the average height of Maria, Marla, Mandy and Marilyn, we need to add up their individual heights and divide by the number of people in the group.
First, we need to convert all the heights to a common unit of measurement. Since inches are the smallest unit of measurement, we will convert all the heights to inches.
Maria: 5 feet 3 inches = 63 inches
Marla: 4 feet 11 inches = 59 inches
Mandy: 5 feet 2 inches = 62 inches
Marilyn: 4 feet 8 inches = 56 inches
Now we can add up the heights:
63 inches + 59 inches + 62 inches + 56 inches = 240 inches
To find the average, we divide the total height by the number of people:
240 inches / 4 people = 60 inches
So the average height of these four friends is 60 inches or 5 feet, which is the same as 5 feet 0 inches.
Therefore, the average height of these four friends is 5 feet 0 inches.
Which of the sets of equations represent the two lines graphed?
Responses
A y = -x + 2 and y = -x - 4y = -x + 2 and y = -x - 4
B y = x - 2 and y = -x - 4y = x - 2 and y = -x - 4
C y = x + 2 and y = x - 4y = x + 2 and y = x - 4
D y = x + 2 and y = -x - 4y = x + 2 and y = -x - 4
E y = -x + 2 and y = x - 4y = -x + 2 and y = x - 4
The linear equations for the graph is obtained to be option D: y = x + 2 and y = -x - 4.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The graph of two lines are given.
For the first line going from top left corner to bottom right corner, the point of coordinates are (-5, 1) and (-3,-1).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-1 - 1]/[-3 - (-5)]
(-2)/(2)
-1
So, the slope point is obtained as m = -1.
The equation becomes - y =-x + b
To find the value of b substitute the values of x and y in the equation -
-1 = -(-3) + b
-1 = 3 + b
b = -1 - 3
b = -4
So, the value for b is -4.
Now, the equation becomes -
y = -x - 4
Now, for the second line going from bottom left corner to top right corner, the point of coordinates are (-1, 1) and (-3,-1).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-1 - 1]/[-3 - (-1)]
(-2)/(-2)
1
So, the slope point is obtained as m = 1.
The equation becomes - y = x + b
To find the value of b substitute the values of x and y in the equation -
-1 = (-3) + b
-1 = -3 + b
b = -1 + 3
b = 2
So, the value for b is 2.
Now, the equation becomes -
y = x + 2
Therefore, the two equations are y = -x - 4 and y = x + 2.
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I need help with this question o can’t seem to solve this one.
Each can hold 330 milliliters of sparkling water. Layla buys 6-pack of sparkling water. Which sentence about the amount of sparkling water Layla buys is true?
A) Layla bought 20mL less than 2 L
B) Layla bought 120mL less than 2 L
C) Layla bought 20mL less than 20 L
D) Layla bought 120mL less than 20 L
I need help solving this and can you show me by step by step how to solve and thank you
For the given situation sentence represents amount of the sparkling water bought by Layla is given by :
Option A). Layla bought 20milliliters less sparkling water than 2 liters.
Sparkling water in each pack is equal to 330 milliliters
Number of packs of sparkling water bought by Layla is equal to 6 packs
Amount of sparkling water in 6 packs = 330 milliliters
⇒ Amount of sparkling water in 6 packs = ( 330 × 6 ) milliliters
⇒ Amount of sparkling water in 6 packs = ( 1980 ) milliliters
1 liter = 1000milliliters
⇒ 2 liter = 2000milliliters
1980 is less than 2 liters
Difference between 1980milliliters and 2 liters
2000 - 1980 = 20milliliters
Therefore, sentence which represents the given situation of sparkling water bought by Layla is option A) Sparkling water bought by Layla is 20ml less than 2L.
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Please answer this question within 10 min! Information in the picture.
The area of triangle A(F) D is 42.44 units²
How to find the area of the triangle?
The formula to calculate the area of a triangle with base b and height h is given by:
Area = 1/2(bh)
In ΔA(F) D, the base is (F)D and A(F) is the height
Using trigonometric ratio:
sin 30° = A(F) /AD (opposite/hypotenuse)
0.5 = A(F) /14
A(F) = 7 units
(F)D = √(14²-7²) = 7√3 units (Pythagoras theorem)
Area of ΔA(F) D = 1/2 × (F) D × A(F)
Area of ΔA(F) D = 1/2 × 7√3 × 7
Area of ΔA(F) D = (49√3)/2
Area of ΔA(F) D = 42.44 units²
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Choose the expression that is equivalent to fraction with 5 raised to the negative tenth power in the numerator and 5 raised to the fourth power times 5 raised to the zero power in the denominator.
negative 1 divided by 5 raised to the fourteenth power
−514
1 divided by 5 raised to the fourteenth power
514
The equivalent expression is 1 divided by 5 raised to the fourteenth power 5^14. Option B
What are index forms?The index form of a number is described as the number written as an exponential expression, or even a single number that is raised to another number.
This exponent, or index form, of an exponential expression tells us the number of multiple times to multiply the base by itself to simply the expression.
Other names for index forms are scientific notation or standard forms.
From the information given, we have that;
5 raised to the negative tenth power in the numerator = 5⁻¹⁰ 5 raised to the fourth power times 5 raised to the zero power in the denominator = 5⁴ × 5⁰This is represented as;
5⁻¹⁰/5⁴ × 5⁰
Any number raised to zero = 1
5⁻¹⁰/5⁴
subtract the exponents
5⁻¹⁰⁻⁴
5⁻¹⁴
Hence, the value is 5⁻¹⁴
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5 5/7 divided by 1 3/5 times 4 2/3
Answer:
50/3
Step-by-step explanation:
5 5/7 divided by 1 3/5 times 4 2/3
5 5/7 = 40/7
1 3/5 = 8/5
4 2/3 = 14/3
40/7 divided by 8/5 = 40/7 times 5/8 = 200/56
200/56 times 14/3 = 2800/168 = 400/24 = 100/6 = 50/3
So, the answer is 50/3
Find the values of x and y.
Answer: (30, 5)
Step-by-step explanation:
Since the 3 red angles are equal, then they are all 60 degrees, which shows that the triangle is equilateral. Therefore, 8y = 40, so y = 5
Also, since BD = BC, triangle BDC is isosceles. We know that angle BDC = 180 - 60 = 120, so 2x = 60 and x = 30
(x, y) = (30, 5)