Answer:
(x - 7)² = x² - 14x + 49Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-7)^2=x^2-2(x)(7)+7^2=x^2-14x+49\\\\\bold{METHOD\ 2:}\\\\\text{We know:}\ a^2=a\cdot a\\\\(x-7)^2=(x-7)(x-7)\\\\\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(x)(x)+(x)(-7)+(-7)(x)+(-7)(-7)\\\\=x^2-7x-7x+49\qquad\text{combine like terms}\\\\=x^2-14x+49[/tex]
Please answer this correctly is the answer
2:29am
3:29am
1:35am
6:29am
Answer:
2:29 AM
Step-by-step explanation:
By the time the planes reaches California, the time, in Mountain time, is 14:89 AM or 3:29 AM. From the mountains to the Pacific, the time goes back by 1 hour. 3:29 - 1 hour is 2:29 AM.
michael mixes 60 ounces of red paint with 15 ounces of blue paint to get a shade of purple.what is the ratio of red paint to blue paint expressed in lowest terms?
Answer: 4:1
Step-by-step explanation:
Red paint = 60 ounces
Blue paint = 15 ounces
Ratio = 60/15 = 4/1 = 4:1 to the lowest term.
1. What is 15% of 60?
15%×60=
=15×60/100
=900/100
=9
Answer:
9
Step-by-step explanation:
15/100 = 60/x
Cross Multiply...
100x = 15*60
100x = 900
x = 900/100
x = 9
Are all right triangles similar?Are all equilateral triangles similar?
Answer:
Yes to both.
Step-by-step explanation:
Similar means the same shape but the sizes may be different.
Right angles are similar and so are equilateral triangle.
Right triangles are not necessarily similar unless they have the same hypotenuse and an acute angle. All equilateral triangles are similar because they have equal angles and sides. This discussion relates to the nature of mathematical truths, which are absolute in their systems, compared to observational truths that rely on variable sensory evidence.
Not all right triangles are similar because they can have different ratios between their sides despite having a right angle. However, if two right triangles have the same length of their hypotenuse and an acute angle correspondingly, they are indeed similar according to a mathematical corollary.
In contrast, all equilateral triangles are similar because they all have equal angles (60 degrees each) and their side lengths are also in the same ratio, which is 1:1:1, making them the same shape, although they can be different sizes.
This connects to the larger questions about mathematical truths. For instance, the statement that the three interior angles of a triangle are equivalent to two right angles is a mathematical truth that is similar to definitional truths, such as 'green is a color,' since both are based on definitions and logical deductions in their respective systems.
However, mathematical truths differ from observational truths like 'there is beer in the refrigerator' because observational truths are subject to sensory evidence which can change, whereas mathematical truths are absolute within the context of their axiomatic systems.
When considering questions that lead to insights into forms, mathematical questions are often better suited over observational ones as they transcend physical reality and provoke a more abstract level of reasoning.
A restaurant bill comes to $28.35 find the total coast if the tax is 6.25% and 20% tip is left on the amount before tax
Answer:
The total cost of the bill = $36.146
Step-by-step explanation:
Here, the total amount of the bill = $28.35
Now, the amount of tip = 20%
So, calculating 20% on the bill amount, we get
[tex]\frac{20}{100} \times 28.35 = 5.67[/tex]
or, the amount of 20% tip = $5.67
So, the total bill amount after 20% tip = Bill Amount + Tip
= $28.35 + $5.67 = $34.02
Now, the tax is calculated on the amount of bill $34.02.
[tex]\frac{6.25}{100} \times 34.02 = 2.126[/tex]
or, the amount of tax on the bill = $2.126
So, the total bill amount after 6.25% tax = Bill Amount + Tax
= $34.02 + $2.126 = $36.146
Hence, the total cost of the bill = $36.146.
A student answered three questions on a 40-percent test incorrectly. What percent did the student answer correctly
Answer:
The percentage of questions correctly answered by the student was 92.5%
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of questions incorrectly answered by the student = 3
Number of questions on the test = 40
2. What percentage did the student answer correctly?
Number of questions correctly answered by the student = Number of questions on the test - Number of questions incorrectly answered by the student
Replacing with the real values:
Number of questions correctly answered by the student = 40 - 3
Number of questions correctly answered by the student = 37
Now, let's calculate the percentage:
Percentage = Number of questions correctly answered by the student /Number of questions on the test * 100
Percentage = 37 /40 * 100
Percentage = 0.925 * 100
Percentage = 92.5%
what method can you use to calculate 40÷7 fast?
Answer:
Usally the fastest method to calculating a problem is to do it in your head. With enough practice your brain will be faster then most tools, ganing efficiency with practice.
Answer:
Step-by-step explanation:
In your head:
5 * 7 = 35 so its 5 point something with remainder 5.
7*7 = 49 so its 5.7 approximately.
Find the square root of (3√5-3)³
Answer: 76.36753237
Step-by-step explanation:
If you have trouble, you can always use Desmos Scientific calculator and get your answer straight away.
Duke went to the convenience store to buy a frozen pizza and some
toothpaste, and while he was in the checkout line, he also threw a ballpoint
pen and a banana into his shopping basket. Which two products were
impulse purchases?
A. The frozen pizza and the banana
O
O
B. The ballpoint pen and the toothpaste
C. The ballpoint pen and the banana
O
O
D. The frozen pizza and the toothpaste
Answer:
ballpoint pen and banana
Step-by-step explanation:
hello! could anyone help me on this one khan acadamy question. it is soooooooo hard for me to understand this lesson.
-1 / 4 = -0.25
1 / 3 = .3
-0.25 / .3 = -0.833333333.
Answer:
-3/4
Step-by-step explanation:
What is y - 2 = -3(x – 7) written in standard form?
Choose 1 answer:
A-y - 2 = -3x + 21
B-y=-3x + 23
C-3x + y - 23 = 0
D-3x + y = 23
Answer:
It's D
Step-by-step explanation:
-3+y=23
To write the equation in standard form, distribute and rearrange the terms. The equation is 3x + y = 23.
Explanation:To write the equation y - 2 = -3(x - 7) in standard form, we need to expand the expression and rearrange the terms. Starting with the given equation, we can distribute the -3 to the terms inside the parentheses: y - 2 = -3x + 21. Next, we can move the -3x term to the left side of the equation by adding 3x to both sides: 3x + y - 2 = 21. Finally, we can move the constant term (-2) to the right side of the equation by adding 2 to both sides: 3x + y = 23. Therefore, the equation in standard form is 3x + y = 23 (Option D).
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Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If nor more than 62 people will attend, how many tables seating four people each will she need?
Answer:16
I think this is the answer
What is the product of 4.23 and 1.2
Answer:
its 5.08
Step-by-step explanation:
slope = –8, (1,4) in slope intercept form
Answer:
y= -8x-12
Step-by-step explanation:
y-4= -8(x-1)
-8x+8
+4= +4
y= -8x+12
Answer:
The correct answer on E2020 Is y=-8x(1,4)+y+8x+(1,4)
Hope this helps you!
(p.s:Please mark me as brainlyest!)
Step-by-step explanation:
I just took the test
Which is the simplified version of 7x+12+3x=-6(x-7)+9x ?
Answer:
x=30/7
Step-by-step explanation:
7x+12+3x=-6(x-7)+9x
10x+12=-6x+42+9x
10x+12=3x+42
10x-3x+12=42
7x+12=42
7x=42-12
7x=30
x=30/7
BIG IDEAS MATH
Writing Expressions > Section Exercises 3.2 > Exercise 27
Write the phrase as an expression. Then evaluate when y = 20.
3 less than the quotient of a number y and 4
Expression:
When y=20, the value of the expression is
Basic
Write the phrase an expression. The evaluate when y=20
3 less than the quotient of a number y and 4.
Answer:
The required expression is [tex]\frac{y}{4}-3[/tex].
The value of the expression when y=20 is 2.
Step-by-step explanation:
Consider the provided phase.
3 less than the quotient of a number y and 4
The quotient of a number y and 4 can be written as: [tex]\frac{y}{4}[/tex]
Now 3 less than the quotient of a number y and 4 can be written as:
[tex]\frac{y}{4}-3[/tex]
Hence, the required expression is [tex]\frac{y}{4}-3[/tex].
Now evaluate when y=20.
Substitute y=20 in above expression.
[tex]\frac{20}{4}-3[/tex]
[tex]5-3[/tex]
[tex]2[/tex]
Hence, the value of the expression when y=20 is 2.
A triangle has two angles measuring 69 and 77. Determine the measure of the third angle b
Answer:
[tex]m\angle B=34\°[/tex]
Step-by-step explanation:
Given measures of 2 angles of a triangle :
m∠A = 69°
m∠C = 79°
Find m∠B.
We know that sum of angles of a triangle =180°
So, we have
[tex]m\angle A+m\angle B+m\angle C=180\°[/tex]
Substituting the vales of m∠A = 69° and m∠C = 79°
[tex]69\°+m\angle B+77\°=180\°[/tex]
Adding like terms.
[tex]m\angle B+146\°=180\°[/tex]
Subtracting both sides by 146°.
[tex]m\angle B+146\°-146\°=180\°-146\°[/tex]
∴ [tex]m\angle B=34\°[/tex] (Answer)
Julie has 42 sheets of paper. She gives 17 sheets of paper to karo. How many sheets of paper does julie have now explained please help me
Answer:
25
Step-by-step explanation:
Subtract 17 from 42.
Answer:
42-17=25
Step-by-step explanation:
just subtract 17 from 42
Create a 3rd degree
polynomial and divide it by x-2. Show all steps. WILL MARK BRAINLEST!
Step-by-step explanation:
Monomial = x^2, 1 term
Binomial = x^2 + x, 2 terms
Trinomial = x^2 + x + 3, three terms
Binomial is more than 3 terms
Let's do a 3rd degree polynomial like:
[tex] {x}^{3} + 2x^{2} + 4x + 8[/tex]
Now let's put parenthesis around (x^3 + 2x^2) and (4x + 8)Let's treat both of these as seperate for now. In the first part, you can see an x^2 can be factored out of itFor example:[tex] {x}^{2} (x + 2)[/tex]
As you can see, if you do the distributive property, it equals the original.Now let's factor the second part, the 4x + 8. This can be factored by a 4.
[tex]4(x + 2)[/tex]
Your new equation is:
[tex] \frac{( {x}^{2} + 4)(x + 2)}{x - 2} [/tex]
x^2 + 4 can be factored again down to (x + 2)(x + 2)
YOUR FINAL EQUATION IS:
[tex] \frac{(x + 2)(x + 2)(x + 2)}{x - 2} [/tex]
Two customers went to a post office to buy postcards and large envelopes. Each postcard
costs the same amount, and each large envelope costs the same amount.
The first customer paid $12 for 14 postcards and 5 large envelopes.
The second customer paid $24.80 for 10 postcards and 15 large envelopes.
•
What was the cost in dollars of each large envelope?
A $1.42 c $1.15
B $0.35 D $0.63
The right answer is Option A.
Step-by-step explanation:
Let,
x be the postcards
y be the large envelops
According to given statement;
14x+5y=12 Eqn 1
10x+15y=24.80 Eqn 2
Multiplying Eqn 1 by 3;
[tex]3(14x+5y=12)\\42x+15y=36\ \ \ Eqn \ 3[/tex]
Subtracting Eqn 2 from Eqn 3;
[tex](42x+15y)-(10x+15y)=36-24.80\\42x+15y-10x-15y=11.20\\32x=11.20\\[/tex]
Dividing both sides by 32
[tex]\frac{32x}{32}=\frac{11.20}{32}\\x=0.35[/tex]
Putting x=0.35 in Eqn 1;
[tex]14(0.35)+5y=12\\4.90+5y=12\\5y=12-4.90\\5y=7.10[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{7.10}{5}\\y=1.42[/tex]
Therefore, one large envelope costs $1.42
The right answer is Option A.
Keywords: linear equations, subtraction
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Answer: A. $1.42
Step-by-step explanation: I did it on the test and got it right!
A freight train travels 1445 miles in 25 hours. What is the train's average rate of speed?
Final answer:
The average speed of the freight train is found by dividing the distance traveled, 1445 miles, by the time taken, 25 hours, resulting in an average speed of 57.8 mph.
Explanation:
To calculate the average speed of the freight train, we divide the total distance traveled by the time it took to cover that distance. The train travels 1445 miles in 25 hours.
The formula for average speed is:
average speed = total distance / total time
Therefore, the average speed of the train is:
average speed = 1445 miles / 25 hours = 57.8 miles per hour (mph)
find c in the pic below
Answer:
A
Step-by-step explanation:
To find the angle inside the triangle (to the right side of 90 degree angle), we first have to find the adjacent angle (below it).
Angle 122 and that adjacent angle is same (parallel lines cut by transversal -- they are corresponding angles).
So that angle is 122.
The inside triangle angle (what we want) is adjacent to 122, so we can write:
Angle + 122 = 180 [straight angle/straight line is 180 degrees]
Solving for that angle, we have:
Angle = 180 - 122 = 58
Now, looking at the triangle, Side C is "opposite" of 58° and side "20" is the side that is "hypotenuse" [side opposite of 90 degree angle is hypotenuse).
Which trig ratio relates "opposite" and "hypotenuse"??
Yes, it is SIN. Thus we can write:
[tex]Sin(58)=\frac{Opposite}{Hypotenuse}=\frac{C}{20}[/tex]
We can now solve for C:
[tex]Sin(58)=\frac{C}{20}\\C=20*Sin(58)\\C=16.96[/tex]
Correct answer is A
Algebraic Woru
An algebraic word problem can be presented in either a real-life or
require you to set up and solve an equation or inequality to arrive at the
require you to translate words into an expression, equation, or inequate
1. Kyle has three times as much money in his savings account as
Hayden. Hayden has twice as much money in his savings account
as Jeremy. Combined Kyle, Hayden, and Jeremy have a total of
$612. How much money does Kyle have in his account?
(A) $68 Khles Hot money = 3
(B) $136
(C) $204
(D) $306
(E) $408
The right answer is Option D.
Step-by-step explanation:
Let,
Kyle's money = x
Hayden's money = y
Jeremy's money = z
According to statements;
Kyle has three times as much money in his savings account as Hayden.
x = 3y Eqn 1
Hayden has twice as much money in his savings account as Jeremy.
z = 2y Eqn 2
Combined Kyle, Hayden, and Jeremy have a total of $612.
x+y+z=612 Eqn 3
Putting value of x and z from Eqn 1 and 2 in Eqn 3
[tex]3y+y+2y=612\\6y=612[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{612}{6}\\y=102[/tex]
Putting in Eqn 1;
[tex]x=3(102)\\x=306[/tex]
Kyle has $306 in his account.
The right answer is Option D.
Keywords: Linear equations, division
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1/2 / 3 equals x / 4
Answer:
x=2/3
Step-by-step explanation:
(1/2)/3=x/4
(1/2)(1/3)=x/4
1/6=x/4
cross product,
6*x=1*4
6x=4
x=4/6=2/3
x=2/3
Of all the students who participate in the school music programs in the district, 394 students play a wind instrument. If 2/5 of the students play a wind instrument, how many students in the district participate in the school music program
Answer:
985 students in the district participate in the school music program.
Step-by-step explanation:
2/5=0.4
394/0.4=985
Susie wants to write equations in the form y=mx + b for the lines passing through
point R that are parallel and perpendicular to line s. First she finds the slope of lines
and line v to be and the slope of line t to be 3. Point R is located at (2, 2). Which
step could be used to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point R (2,2) in y=mx+b and then solve for b for each equation.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Substitute the slope and the coordinates of point R (2,2) in y=mx+b and then solve for b for each equation.
Jonah plants flower in garden. He plants 2 flowers in each row and 5 rows. DrAw an array to figure out how many flowers he has planted
if john can buy 8 liters of soft drinks at the store for $6.40 how much does it cost to buy 12 liters
Answer:
$9.60
Step-by-step explanation:
first figure out cost for 1 liter.
6.40 / 8 = 0.80
1 liter = $0.80
12 * 0.80 = 9.60
12 liter = $9.60
prove the identity with steps. sin (x-y)/cos x sin y = tan x cot y -1
Step-by-step explanation:
sin(x−y) / (cos x sin y)
Use angle sum/difference formula:
(sin x cos y − sin y cos x) / (cos x sin y)
Divide:
(sin x cos y) / (cos x sin y) − 1
Rearrange:
(sin x / cos x) (cos y / sin y) − 1
Simplify:
tan x cot y − 1
Reduce each fraction:
144 over 168
144/168
reduce the fraction by dividing by 4
144/4= 36
168/4= 42
36/42 - reduce by dividing by 6
36/6= 6
42/6= 7
answer:
6/7