The required intermediate step is (x-5)² = 25 for the equation -5x² - 50x = -250.
Completing the square is a method used to rewrite the equation in the form (x+a)²=b. The intermediate step involves adding and subtracting the square of half of the coefficient of x in the equation.
To complete the square for the equation -5x² - 50x = -250:
First, we'll add and subtract (1/2 * 50)² = 625/4 on both sides of the equation:
-5x² - 50x + 625/4 = -250 + 625/4
Next, we'll factor out the x term on the left side of the equation:
-5x² - 50x + 625/4 = -250 + 625/4
-5(x² - 10x) + 625/4 = -250 + 625/4
-5(x² - 10x + 25) + 625/4 = -250 + 625/4
-5(x - 5)² + 625/4 = -250 + 625/4
The intermediate step is in the form of (x-5)² = (625/20 + 250)/5
So, the intermediate step is (x-5)² = 25
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a^4 + 1 + 1/a^4 ???????????????????????????
By solving the equation, a^4 + 1 + 1/a^4 this we get [tex]\frac{a^{8} + a^{4} + 1 }{a^{4} }[/tex]
How is the calculation found?Equations are considered to be equivalent when they have the same roots or solutions in an algebraic problem.
When the same number or expression is added to or removed from both sides of an equation, the equation is said to be similar.
A non-zero equation can be made equal by multiplying or dividing both sides by the same value.
What are the three guidelines for resolving equations?To solve linear equations, utilize the steps that are provided below. Remove parentheses from each side of the equation and combine similar phrases 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.
Given,
[tex]a^{4} + 1 + \frac{1}{a^{4} }[/tex]
Taking [tex]a^{4}[/tex] as LCM,
⇒ [tex]\frac{a^{8} + a^{4} + 1 }{a^{4} }[/tex]
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8.
There are 2,916 books in the library. There are 243 students in the 8th grade. If all
the books are checked out, how many books will each 8th grade student get?
A.13
B12
C.11
D.14
Answer:
B. 12
Step-by-step explanation:
you’ll have to divide
2916/243 = 12
Answer: B. 12
Step-by-step explanation: 2,916 ÷ 243= 12
(a) A company manufactures 15-inch laptops and 17-inch laptops. It takes 3 hours to manufacture a 15-inch laptop and 5 hours to manufacture a 17-inch laptop. Each 15-inch laptop has 256 GB of memory and each 17-inch laptop has 512 GB of memory. The company has 480 hours available and parts for 43,520 GB of memory. The company makes a profit of $2000 on each 15-inch laptop and $3000 on each 17-inch laptop.
Answer:
We can start by using the information provided to calculate how many laptops of each size the company can manufacture within the 480 hours available:
15-inch laptops: 480 hours / 3 hours per laptop = 160 laptops
17-inch laptops: 480 hours / 5 hours per laptop = 96 laptops
With the 480 hours available and the number of laptops that can be manufactured, we can calculate the total amount of memory that can be used:
15-inch laptops: 160 laptops x 256 GB per laptop = 40,960 GB
17-inch laptops: 96 laptops x 512 GB per laptop = 49,152 GB
Since the company has 43,520 GB of memory available, it can manufacture:
15-inch laptops: 43,520 GB / 256 GB per laptop = 170 laptops
17-inch laptops: 43,520 GB / 512 GB per laptop = 85 laptops
The company can manufacture 170 15-inch laptops and 85 17-inch laptops.
Now, we can calculate the profit that the company can make:
15-inch laptops: 170 laptops x $2000 per laptop = $340,000
17-inch laptops: 85 laptops x $3000 per laptop = $255,000
So, the company can make a total profit of $595,000 from the 170 15-inch laptops and 85 17-inch laptops.
The company can manufacture 170 15-inch laptops and 85 17-inch laptops, and make a total profit of $595,000.
Step-by-step explanation:
4y^2+4(2y^2-8)=
How to combine like terms
Answer:
12y² - 32
Step-by-step explanation:
4y² + 4(2y² - 8) = 4y² + 8y² - 32 = 12y² - 32
Round the underlined digit to its nearest place value: 84.68=
Answer:
84.68
Rounded to the nearest 0.01 or
the Hundredths Place.
Step-by-step explanation:
84.68_
You rounded to the nearest hundredths place. The 8 in the hundredths place rounds down to 8, or stays the same, because the digit to the right in the thousandths place is _.
84.68
When the digit to the right is less than 5 we round toward 0.
84.68 was rounded down toward zero to 84.68
The points (5, 7) and (3, 3) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y = 2x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 7 ) and (x₂, y₂ ) = (3, 3 )
m = [tex]\frac{3-7}{3-5}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2 , then
y = 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 3 ) , then
3 = 2(3) + c = 6 + c ( subtract 6 from both sides )
- 3 = c
y = 2x - 3 ← equation of line
The terminal ray of angle A passes through the point (- 6,4)
Enter your answer as an exact answer, in simplified form, in the box.
angle A is drawn in standard position.
What is the value of sec(A) ?
The value of sec(A) is 2/√(13) in simplified form, in the standard position.
What is the point of intersection?
When the lines intersect, the point of intersection is the only point that the two graphs have in common, so the coordinates of that point are the solution for the two variables used in the equations.
The terminal ray of an angle in standard position passes through the point (x,y) in the coordinate plane, where x and y are the coordinates of the point of intersection of the terminal ray with the x-axis and y-axis respectively.
Given that the terminal ray of angle A passes through the point (-6,4)
The coordinates of the point of intersection of the terminal ray with the x-axis are (-6,0) and y-axis are (0,4)
Using the distance formula
The distance from the origin to the point (-6,4) is √((-6-0)^2 + (4-0)^2) = √(6^2 + 4^2) = √(36 + 16) = √(52) = 2*√(13)
Now we can use these coordinates to find the value of sec(A) which is defined as sec(A) = 1/cos(A) = distance of point from x-axis/distance from origin.
sec(A) = 4/2*√(13) = 2/√(13)
hence, the value of sec(A) is 2/√(13) in simplified form, in the standard position.
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Distance from television camera to base of stadium(pic included)
The line of sight distance from the television camera to the base of the stadium is approximately 1778 m
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are Given the following information;
Television camara at 13°
Altitude = 400
Since the formed angle is a 90° angle then we have;
90-13= 77
The trigonometric function that relates Hyp angle and Adj is Cos then
Cos ∅ = Adj /Hyp
where
angle = 77
adj=400
Hyp= The distance from camara to the stadium
then
Cos 77 = 400/Hyp
Hyp = 1778
Hence, the line of the sight is approximately 1778 m
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please help please..
Answer:
first option
Step-by-step explanation:
integers are like whole numbers but can also be negative
Answer:
A
Step-by-step explanation:
5. A food company designs a cylindrical can that will be used for beans. The net of the cylinder is shown.
What is the approximate surface area of the cylindrical can, using 3.14 for π? Round to the nearest hundredth if necessary. PLEASE HELP ME DUE I BEG THANK U
Answer:
Should be 87.92 inches
Step-by-step explanation:
First calculate the circumference of the circle - this is the length of the rectangle. The rest should be straight forward.
C = 2πr
= 2 * 3.14 * 2
= 12.56
A(circle) = πr^2
= 3.14 * (2)^2
= 12.56
A(rectangle) = lw
= 12.56 * 5
= 62.82
SA = area of rectangle + area of circle + area of circle
= 62.82 + 12.56 + 12.56
= 87.92
Give three solutions to the equation y=3x−4
Answer: (0,-4) (4/3,0) (1,-1)
Step-by-step explanation: equation y=3x-4
here we will use when x=0
y = 3(0) -4
y = -4
when y = 0
0 = 3x -4
3x = 4
x = 4/3
when x=1
y = 3(1) -4
y = -1
A two-digit number is 3 times the sum of its digits. The number is also 45 less than the number formed by reversing the digits of the original
number. What is the original number?
The original number is 27
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the 10's digit
let y be the units digit
Given: A two digit number is 3 times the sum of it's digits.
=> 10x + y = 3(x+y)
10x + y = 3x + 3y
10x - 3x = 3y - y
7x = 2y......(1)
Given: The number is also 45 less than the number formed by reversing the digits and the original number.
=> 10x + y = 10y - x - 45
10x - x = 10y - y - 45
9x = 9y - 45
divide both sides by 9
x = y - 5............(2)
replace x with (y-5) in the equation 1
7(y-5) = 2y
7y - 35 = 2y
7y - 2y = 35
5y = 35
y = 35/5
y = 7 is the units digit (original number)
and
x = 7 - 5
x = 2 is the 10's digit
Thus, the original number is 27
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Determine whether you would use a one-dimensional, two-dimensional, or three-dimensional
measurement to answer each of the following questions (you do not have to answer the questions.)
Explain your choice in each case.
a. You are planning to paint all of the walls in your kitchen. How much paint will you need?
b. A box measuring 3 inches by 6 inches by 9 inches is to be wrapped in brown paper. How much
paper will be needed?
c. After the box of part b is wrapped, it is to be tied with string. How much string will be needed?
Therefore , the solution of the given problem of dimensional comes out to be volume of given dimension is 162 inch cube
What exactly is the dimension?a three-dimensional figure is one with measurements in one or more directions, particularly height, length, or breadth. Two-dimensional When two variables are connected. Similar to how we are asked to locate a space ,Then, it depends on two variables: length and width.
Here,
Given dimensions :
=> length = 3 inch , width = 6 inches and height = 9 inches.
=> Volume = l*b*h
=> Volume = 3* 6* 9
=> Volume = 162 inch cube
Therefore , the solution of the given problem of dimensional comes out to be volume of given dimension is 162 inch cube
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A zoo's annual budget for animal care is $83,595. The director calculates that 1/6
of that is spent on educational programs for zookeepers. What is the cost for
zookeeper education?
So the cost for zookeeper education is $13,932.5
What is a fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).
To calculate the cost for zookeeper education, we need to multiply the total budget for animal care by 1/6.
83,595 x 1/6 = 13,932.5
So the cost for zookeeper education is $13,932.5.
Explanation:
1/6 of the budget, which is expressed as a fraction, is the same as dividing the budget by 6.
So we can use the formula 83,595 / 6 = 13,932.5, the result is the cost for zookeeper education.
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Which statement is true about the points shown on the number line?
Option B is a correct representation of the given number line, -3.8 < 1.5, and is located to the left of 1.5.
What is a number line?A number line is a visual depiction of numbers on a straight line drawn either horizontally or vertically. It is simple for humans to compare numbers and carry out simple arithmetic operations on them when they are written down on a number line. A number line is thought to begin at zero (0). Left of zero, there are only negative numbers, and right of zero, there are only positive numbers.
Given a number line and two points marked on it,
-3.8 and 1.5
we find from the number line that -3.8 lie left to 1.5,
and the negative numbers are always less than the positive numbers,
so -3.8 is less than 1.5,
-3.8 < 1.5, and lie left to 1.5.
Hence, option B is correct.
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Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving at a constant rate of 50 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.
function notation in slope-intercept form: f(x) =
reasonable domain:
≤ x ≤
The function that models the distance they drive as a function of time is; 120 = 50t + 20
The required domain is;. 0 ≤ t ≤2
How to find the domain of the function?The formula for calculating distance travelled is expressed as:
Distance = Speed × time
The parameters are;
Total distance = 120 miles
Distance already travelled = 20miles
They are driving at a constant rate of 50mi/hr. Thus, the distance travelled at the time "t", during this period will be 50t.
The equation of a line in slope intercept form is;
y = mx + c
Thus,
The required function that models the distance is expressed as;
120 = 50t + 20
To find the domain, we need to get the value of t as shown;
120 = 20 + 50t
120 - 20 = 50t
100 = 50t
t = 100/50
t = 2sec
Hence the required domain must be within the range of 0 and 2.
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34 points for 3 questions!!!
Answer:
1) Linear, negative slope: -4/3 2) Slope: 3 3) Slope: -6, y-int: +2
Step-by-step explanation:
1. Slope = rise/run = [tex]\frac{3-(-1)}{-2-1} = -\frac{4}{3}[/tex]
2. Slope = rise/run (just pick 2) = [tex]\frac{1-(-2)}{1-0} = 3[/tex]
3. The breakdown is pretty simply just follow the slope formula y=mx + b thus m = slope = -6 and b= y-int = +2
. a person who is 6 feet tall is standing 90 feet from the base of a tree, and the tree casts a 100 foot shadow. the person's shadow is 10 feet in length. what is the height of the tree?
Height of the tree = 60 feet
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given,
Height of the person = 6 feet
Length of the shadow of person = 10 feet
Length of the shadow of the tree = 100 feet
Tree and person at distance of 90 feet
let 'h' be the height of the tree
Triangles made by Tree, the person and the shadows are similar
the following proportion counts
h : 6 = 100 : 10
h = (6×100)/10
h = 60 feet
the tree is 60 feet high.
Hence, 60 feet is the height of the tree.
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Help me please I’m stuck no links or random questions
Answer:
No
Step-by-step explanation:
It misses a decent amount of the data. When you plot the line y=10x there are about 8 points that are over the line and none below so it is not a good fit for the data
Which phrase best describes f(x), graphed on the coordinate plane below?
On a coordinate plane, a curve goes through two cycles. The first part of the curve approaches x = negative 6, has a maximum at (negative 4, 3), and has a minimum at (negative 2, negative 2). The second part of the curve has a maximum at (1.5, 2.5), has a minimum at (4, negative 3), and approaches x = 6.
f(x) is an odd function. Therefore, option A is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The first part of the curve approaches x= -6, has a maximum at (-4, 3), and has a minimum at (-2, -2). The second part of the curve has a maximum at (1.5, 2.5), has a minimum at (4, -3), and approaches x=6.
The graph of an odd function consists of symmetry that is rotational with respect to the origin that means that the graph remains unchanged post the 180-degree rotation about the origin.
Therefore, option A is the correct answer.
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What is the perform indicated operation for 1 1/7×2 4/5
Answer: 16/5 or 3.2 or 3 and 1/5
Step-by-step explanation:
What is the following product?
√√4x² √√4x²
O 4x²
O 16x4
O2 14x4
O
16x4
Answer: 4[tex]x^{2}[/tex]
Is The answer.
The solution is, The correct answer is option B). 7x² -12x√14 + 72
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
we know that,
Identity
(a - b)² = a² - 2ab + b²
Find the product
It is given that ( x√7 - 3√8)(x√7 - 3√8)
(x√7 - 3√8)(x√7 - 3√8) = (x√7 - 3√8)²
(x√7 - 3√8)² = (x√7)² - 2*x√7*3√8 +(3√8)²
= 7x² - 6x√56 + 72
= 7x² - 6x*2√14 + 72
= 7x² - 12x√14 + 72
Therefore the correct answer is option B). 7x² - 12x√14 + 72
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Complete question:
What is the following product?
( x√7 - 3√8)(x√7 - 3√8)
To create an entry code, you must first choose 3 letters and then, 3 single-digit numbers. How many different entry codes can you create?
The number of entry codes will be 720.
What are permutation and combination?The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations.
When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.
Given that you must first choose 3 letters and then, 3 single-digit numbers.
The number of arrangements will be calculated as,
Codes = 6!
Codes = ( 6 x 5 x 4 x 3 x 2 x 1 )
Codes = 720
Hence, the combination of the code will be 720.
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if line ST is congruent to line SV, TU=w+10, and UV=2w what is the value of w
If line ST exists congruent to line SV, TU=w+10, and UV=2w then the value of w exists 10.
What does congruent line mean?If two line segments are congruent to one another and are the same length, then they are said to be equal. The angles they make with an axis or location in the plane may or may not be the same.
Congruence between two line segments indicates that their lengths are equal. Two shapes are said to be congruent if they correspond throughout if you take one up and place it on the other (they will match up perfectly and you will not be able to see the one on the bottom).
If line ST exists congruent to line SV, TU = w + 10, and UV = 2w.
TU = UV
substitute the values of TU and UV in the above equation, we get
w + 10 = 2w
simplifying the equation, we get
w = 2w - 10
-w = -10
Divide both sides by -1
[tex]$\frac{-w}{-1}=\frac{-10}{-1}$$[/tex]
w = 10
Therefore, the values of w exists 10.
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Read the excerpt from "Healthy Eating."
But no one can ignore the damage being wrought by all this bad eating. More than one out of three adults in the United States -- 37.5 percent -- are obese, according to the Centers for Disease Control and Prevention. Some of the leading causes of death -- heart disease, stroke and type 2 diabetes -- are directly linked to obesity. And childhood obesity has tripled in the last 30 years. With more than a third of kids between 6 and 19 considered obese, the CDC reports, they are at substantially more risk for developing cardiovascular disease, diabetes, bone and joint conditions, and cancer.
PLS HELP.
Which statement best describes the author's argument in this part of the article?
Eating a poor diet can have harmful effects on people's health.
Eating healthier foods is not as easy as some might think.
Children should be required to maintain a healthy diet.
Eating habits have changed significantly in recent years.
Answer:
A
Step-by-step explanation:
Eating a poor diet can have harmful effects on people's health.
Answer:
A. Eating a poor diet can have harmful effects on people's health.
Step-by-step explanation:
right on edge
zoe is using a 72 foot ladder to reach the top of a 60 foot building, what is the distance from the bottom of the ladder to the base of the building?
The distance from the bottom of the ladder to the base of the building is 39.6ft.
What is the Pythagorean theorem in plain English?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
This is a question about the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
We can call the distance from the bottom of the ladder to the base of the building as x, and the distance between the ladder base and the building as the ladder's height = h.
By using Pythagorean theorem: x^2 + h^2 = 72^2 , the distance from the bottom of the ladder to the base of the building is x = √(72^2 - 60^2) = √(5184 - 3600) = √1584 = 39.6 ft.
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ouise stops at the gift store to buy a souvenir of the Statue of Liberty. The original height of the tatue Is 151 feet. If a scale factor of 1 inch = 20 feet is used to design the souvenir, what is the weight of the replica?
The height of the Statue of Liberty replica at the gift store is 7.55 inches
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Scaling is used to increase or decrease the size of a figure by a scale factor.
The scale factor is 1 inch = 20 feet. If the height of the statue is 151 feet, hence:
Height of the replica = 151 feet * 1 inch per 20 feet = 7.55 inches
The height of the replica is 7.55 inches
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Q2: Determine whether the graphs of each pair of equations are parall
perpendicular or neither.
1. y = 3x + 4
y = 3x + 7
3. y = 2x-5
y = 5x -5
5. y = 3/5x - 3
5y = 3x - 10
7. y = 7x + 2
x + 7y=8
2. y = -4x+1
4y = x + 3
4. y=-1/3x + 2
y = 3x - 5
6. y = 4
4y = 6
8. y = 5/6x - 6
x + 5y = 4
Answer:
x+5y = 4 i think its the answer but I'm not sure
Brent has a piece of lumber 8 feet long that he needs to split into -foot pieces. How many -foot pieces will he be able to cut from 8 feet? Select the equation that correctly models the situation.
A.
B.
C.
D.
need help quick
Answer: he could have 8 pieces
Step-by-step explanation:
well you have 8 feet and if you need to get as many feet cut out well just do 8 divided by 1 and that is 8 and theres your qoutiont
Two square boards are made of the same material and their diagonals measure 40 cm and 45 cm, respectively. If the smaller costs N1 920 to make, what should be the other cost?
2430 should be the other cost, if the smaller cost N1 920.
What are the different kinds of quadrilaterals?The answer of what square is equal to multiplied by
40×40×2`=800
45×45×2=1012.5
(1012.5÷800)×1920=2430
A quadrilateral is a polygon with the following characteristics.
Four vertices and four sides enclosing four angles
The total of a quadrilateral’s internal angles equals 360 degrees.
The sum of interior angles may alternatively be calculated using the polygon formula, which is (n -2) 180, where n is the number of sides of the polygon.
Parallelograms include the shapes square, rectangle, and rhombus.
A square is both a rectangle and a rhombus.
A rectangle or rhombus is not a square.
A trapezium is a parallelogram.
A trapezium is not the same as a parallelogram.
Kite does not form a parallelogram.
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