Answer:
a. (x² + y²)² = (x² - y²)² + (2xy)²
b. The conjecture works in all cases.
c. Sides of 119, 120, and 169
Step-by-step explanation:
a. Equation that models this conjecture
x² + y² = sum of squares
x² - y² = difference of square
2xy = twice the product of the integers
If these are the sides of a right triangle then
(x² + y²)² = (x² - y²)² + (2xy)²
b. Test the conjecture
(i) Try x = 2, y = 1
(2² + 1²)² = (2² - 1²)² + (2×2×1)²
5² = 3² + 4²
25 = 9 + 16
(ii) Try x = 3, y = 1
(3² + 1²)² = (3² - 1²)² + (2×3×1)²
10² = 8² + 6²
100 = 64 + 36
(iii) Try x = 3, y = 2
(3² + 2²)² = (3² - 2²)² + (2×3×2)²
13² = 5² + 12²
169 = 25 + 144
The conjecture appears to work in all cases.
c. A possible triangle
We must have one side greater than 100. That means,
x² > 100 or x >1 0.
Let x = 12
One side = 12² + y²
The second side = 12² - y²
The third side must have 2xy > 100
24y > 100
y > 4.2
Try y = 5
(12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²
169² = 119² + 120²
So, one right triangle could have sides of 119, 120, and 169.
Furthermore, these sides have no common factors.
Check:
169² = 119² + 120²
28561 = 14161 + 14400
28561 = 28561
4) Find the value of x in the given diagram. (3 points)
88°
142°
136°
105°
136°
xº
Answer:
113
Step-by-step explanation:
The given shape has 6 angles so it's a hexagon and the sum of interior angles in a hexagon is = 720
To find the the value of x we need to add all given values up and subtract it from 720:
88 + 142 + 105 + 136 + 136 + x = 720
607 + x = 720 subtract 607 from both sides
x = 113
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 10 minutes. Air traffic control approved a new flight plan that will allow her to arrive three times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination. y equals one third times x plus 10 y = 3x + 10 y equals one third times x minus 10 y = 3x − 10
Answer:
a. y equals one third times x plus 10
= y = 1/3(x) + 10
Step-by-step explanation:
Let us represent:
Let the original final plan = x
Let the current flight plan = y
The initial time of departure = 4.00pm
Her flight was then delayed for 10 minutes
We are told in the question that:
The current flight plan allows her arrive at her destination three times faster.
This means y= (1/3)x
y = x/3
Hence the equation generated =
y = x/3 +10
y = 1/3(x) + 10
Answer:
y = 1/3x + 10
Step-by-step explanation:
The rectangle below has been enlarged by a scale of 3.5.
original rectangle: length: 8 units width: 6 units
What is the area of the enlarged rectangle?
A. 48 square units
B. 168 square units
C. 336 square units
D. 588 square units
answer:
The answer is d
Step-by-step explanation:
Answer:
your answer is 588 square units
Step-by-step explanation:
i got it right on the test
15. What is the value of x?
x°
(x + 10)°
(3x - 5)°
X =
Answer:
35
Step-by-step explanation:
x + 10 + 3x - 5 + x = 180
5x + 5 = 180
5x = 175
x = 35
NEED HELP ASAP PLS!
Answer:
5x² + 5x + 9
Step-by-step explanation:
(3x + 4) + ((5x² - 1) + (2x + 6))
Remove parenthesis
3x + 4 + 5x² - 1 + 2x + 6
Group like terms
5x² + 3x + 2x + 4 - 1 + 6
Subtract 1 from 4
5x² + 3x + 2x + 3 + 6
Add 3 and 6
5x² + 3x + 2x + 9
Combine like terms
5x² + 5x + 9
Answer: 5x² + 5x + 9
Write an algebraic expression for 11 times the quantity 16 less than a number d
Answer:
d - 11*16
Step-by-step explanation:
Algebraic Expressions
We use algebraic expressions to model real-world situations and we must pay close attention to the writing of the problem to do it properly and accurately.
Let's build the expression in small steps:
11 times the quantity 16 = 11*16
That amount less than a number d. It suggests a subtraction:
d - 11*16
you had $22 to spend on three pretzels. After buying them you had $15.70.How much did each pretzel cost?
Answer: $2.10
Step-by-step explanation: 22-15.70= 6.3
This means you spent $6.30 on pretzels. Divide 6.30 by 3 to find out how much each pretzel costs. You would get 2.1 (which is written as $2.10 in money).
Which expression is a trinomial of degree 1?
6 + x – y
3x – y
Answer:
=> 6 + x – y
Step-by-step explanation:
=> The trinomial of degree 1 = 6 + x – y
You poured some 6% alcohol solution and some 8% alcohol solution into a mixing container. Now you have 600 grams of 7.4% alcohol solution. Write and solve a system of equations to find how many grams of 6% solution and how many grams of 8% solution you poured into the mixing container.
You mixed ___ grams of 6% solution with ____grams of 8% solution.
Answer:
180 grams of 6%420 grams of 8%Step-by-step explanation:
Let s and e represent the grams of 6% and 8% solution, respectively. The given relations can be described by ...
s + e = 600 . . . . . you have 600 grams of mixture
0.06s +0.08e = 0.074(600) . . . . grams of alcohol in the mixture
__
The first equation can give an expression for s that substitutes nicely into the second equation:
s = 600 -e
0.06(600 -e) +0.08e = 0.074(600) . . . . substitute for s
0.02e = 0.014(600) . . . . . . subtract 0.06(600)
e = 420 . . . . . . . divide by 0.02
s = 600 -420 = 180
You mixed 180 grams of 6% solution with 420 grams of 8% solution.
Answer: 180 grams of 6% solution with 420 grams of 8% solution.
Step-by-step explanation:
Let x and y be the weight (in grams) of 6% and 8% alcohol solution. Since the total weight is 600 grams, therefore,
[tex]$$\Rightarrow x+y=600 \ldots \text { (1) }[/tex]
Using the statement given, we can write the following equation:
[tex]\Rightarrow 6 x+8 y=(7.4)(600)\\ \Rightarrow 6 x+8 y=4440 \text {... (2) }[/tex]
Substitute the value of y from equation (1) into equation (2), we'll get:
[tex]\begin{gathered}\Rightarrow 6 x+8(600-x)=4440 \\\Rightarrow 6 x+4800-8 x=4440 \\\Rightarrow 2 x=360 \\\Rightarrow x=180\end{gathered}[/tex]
Therefore,
[tex]\Rightarrow y=600-180=420[/tex]
Therefore, you mixed 180 grams of 6% solution with 420 grams of 8% solution.
Assessment timer and count
Assessment items
Item 3
A lamp is on sale, and its price is reduced from $80 to $50.
What is the percent of decrease?
Answer:
37.5 percent
Step-by-step explanation:
Finding percent is simple. You want to find percent of the price drop so you subtract 50 from 80 and get 30. Once you get 30 you divide by 80 (your original price). Once you do this you will get 0.375. Multiply this by 100 to get your percent.
Which is a factor of x2 8x – 48? (x – 6) (x 4) (x – 16) (x 12)
Answer: D
Step-by-step explanation:
Solve this please and send
Answer:
Where is the question mate ????
Answer:
question please .........
A jacket's original price is $65.00. It is on sale for 40% off. You have to pay 5% sales tax. What is the final price for the jacket?
Explain good pls
Answer:
$40.95
Step-by-step explanation:
Original price = $65.00
If the jacket is on sale for 40% off, then it is now 60% of the original price.
60% = 60/100 = 0.6
⇒ 60% of $65.00 = 0.6 × 65
= $39
If we have to pay 5% sales tax, then this means that the final price will be 105% of the sale price.
105% = 105/100 = 1.05
⇒ 105% of $39 = 1.05 × 39
= $40.95
Discount:-
[tex]\\ \rm\rightarrowtail 0.40(65)=26\$[/tex]
Now
Price after discount=65-26=39$So
Sales tax is 5%
Total price=39+0.05(39)=40.95$
Write three steps that will result in 4 (x+2)?
Answer:
1. 3x + 5 + x + 3
2. 4x + 8
3. 4(x + 2)
Step-by-step explanation:
1. Write out the problem, break it down.
2. Combine like terms.
3. Factor.
Answer: fist you could Write out the problem and then , break it down.
2. Combine it like terms.
3. And then the Factor.
A group of friends was eating in a restaurant the bill is $415.28 and they paid 18% tip, what was the total?
Answer:
$490.03
Step-by-step explanation:
($415.28)(0.18) = $74.75
$415.28 + $74.75 = $490.03
will give brainliest
Answer:
1. A, 2. A , good luck!!!
Step-by-step explanation:
anyone know this? pleaseee
Answer:
x-4/3
Step-by-step explanation:
the unknown number is the number they think of, you can't read their mind. but you know you have to subtract by 4 and divide by 3.
100 BRAINLY POINTS!!!
A scatter plot shows a negative linear relationship between the time spent reviewing a writing assignment and
the number of spelling mistakes on it. The following statements describe possible relationships between the
variables.
I. As the review time decreases, the number of spelling mistakes increases.
II. As the review time increases, the number of spelling mistakes increases.
III. As the review time decreases, the number of spelling mistakes decreases.
IV. As the review time increases, the number of spelling mistakes decreases.
Which of these statements are correct?
A. Only IV
B. Only III
C. II And III
D. I And IV
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
PLEASE CUH I NEED HELP
Negative slope
Means sample equation in slope intercept form is
y=-mxSo if you spot 2 mistakes on observing 1 min
then slope is 2
y=-2xPut one by one
(1,-2)(2,-4)Direct variation
Hence
Option 1 and 4 are correctAnswer:
D) I and IV
Step-by-step explanation:
The variable along the x-axis is the independent variable.
The variable along the y-axis is the dependent variable.
It would be fair to determine that the time spent reviewing a writing assignment is dependent upon the number of spelling mistakes, as the more mistakes an assignment has, the longer it should take to review, however we cannot say this for certain, therefore we cannot assign the dependent and independent variables.
If the scatter plot shows a negative linear relationship, then as the x-values increase, the y-values decrease.
Statements I and IV suggest a negative linear relationship only, depending on which variable is dependent and independent.
(FYI Statements II and III describe positive linear relationships)
Statement I
x-axis (independent variable) = number of spelling mistakes
y-axis (dependent variable) = review time
Statement IV
x-axis (independent variable) = review time
y-axis (dependent variable) = number of spelling mistakes
Therefore, as we cannot be sure which is the dependent variable and which is the independent variable, the solution is D.
What is the slope of a line that is perpendicular to the line
y=−4/5x + 7
Answer:Thats Just Notes To Right Down.
Step-by-step explanation:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 45 4 5 . The equation of a perpendicular line to y=4x5+7 y = 4 x 5 + 7 must have a slope that is the negative reciprocal of the original slope.
please help will give brainliest to the correct answer
Answer:
Step-by-step explanation:
One way to answer this problem is to notice as x goes up 1, y will go up 2. The relationship is linear. No exponential function is going to do that. The jump will not be so easily described.
So what's the answer?
The exact description is D. It is just what I wrote in more general terms.
Homework Jim Thompson! Part 1
Problem 1
Answers:
Choice A) CylinderChoice C) Rectangular prismChoice D) Rectangular pyramidReason:
Refer the diagram below to see how rectangular cross sections are possible. The cross sections are marked in red.
For the rectangular prism, we could have a vertical or horizontal plane. For the cylinder, only a vertical cross section is possible. On the flip side, a rectangular pyramid can only have horizontal rectangular cross sections (which are similar to the base).
========================================================
Problem 2
Answer: Approximately 73,280.62908 square feet
Explanation:
Calculate the area of the trapezoid. Ignore the small triangle for now.
A = h*(b1+b2)/2
A = 354*(266+158)/2
A = 75,048
Now calculate the area of the triangle we ignored earlier
Before we do this, we'll need to use the pythagorean theorem to find the missing horizontal piece
a^2 + b^2 = c^2
b = sqrt(c^2 - a^2)
b = sqrt(97^2 - 40^2)
b = 88.368546 which is approximate.
Now we can find the area of the small triangle
Area = base*height/2 = 88.368546*40/2 = 1,767.37092
This is to be subtracted from the area of the trapezoid we found earlier.
75,048 - 1,767.37092 = 73,280.62908
Round the result however you need to.
You are standing on a dock that is 8 feet above the surface of a lake. You jump in the lake and touch the bottom, which is 10 feet below the surface of the water. What is the total distance that you have traveled?
Water flows through a pipe at a rate of 5 pints per minute. Express this rate of flow in liters per hour. Round your answer to the nearest whole number. please help!!!
Answer:
142 l/hr
Step-by-step explanation:
Answer:142
Step-by-step explanation:
add [7x] ^2-8, [2x] ^2+1 and 5-x^2. and ^ means power and if you spam i will report you
Answer:
52x2−2
Step-by-step explanation:
=49x2+−8+4x2+1+5+−x2
Combine Like Terms:
=49x2+−8+4x2+1+5+−x2
=(49x2+4x2+−x2)+(−8+1+5)
=52x2+−2
True or false: When describing range, you should start with the smallest y-value, au
work your way to the largest.
Answer:
true
Step-by-step explanation:
hope this helped!
p.s it would be cool if you gave me brainliest.
Answer:
True
Step-by-step explanation:
To find the range first order the data from the least to greatest. Then subtract the smallest value from the largest value in the set.
What is the area of triangle ABC?
Answer: C
Step-by-step explanation:
Can anybody help me please with question 1 please and thank you .I would really appreciate it so much.
Answer:
Given
Step-by-step explanation:
At the beginning it says "Given: AB = CB" so they just gave you that information.
What is the length of the radius?
Answer:
h is 9 inches
Step-by-step explanation:
the volume of the cone is 2π[tex]r^{2}[/tex](h)(1/3）just substitution, easy
75π=2π[tex]r^{2}[/tex](h)(1/3）
Solution:
Given:
[tex]\bullet \ \ \text{Volume of party hat} = 75\pi \text{ inches}^{3}[/tex]
[tex]\bullet \ \ \text{Radius of party hat:}\ 5 \ \text{inches}[/tex]
Recall that the formula to find the volume of a cone is πr²h/3. Now, let's use the formula to find the height.
[tex]\bullet \rightarrow \text{Volume of cone:} \ \dfrac{ \pi r^{2} h}{3}[/tex]
[tex]\bullet \rightarrow \text{Volume of party hat} =\dfrac{ \pi r^{2} h}{3} = 75\pi \text{ inches}^{3}[/tex]
[tex]\bullet \rightarrow \dfrac{ (\pi )( 5^{2})( h)}{3} = 75\pi \text{ inches}^{3}[/tex]
[tex]\bullet \rightarrow (\pi )( 5^{2})( h)} = 75\pi \times 3[/tex]
[tex]\bullet \rightarrow { (\pi )( 25)( h)}= 225\pi[/tex]
[tex]\bullet \rightarrow \dfrac{{ (\pi )( 25)( h)}}{25} = \dfrac{225\pi}{25}[/tex]
[tex]\bullet \rightarrow { (\pi )( h)}= 9\pi[/tex]
[tex]\bullet \rightarrow \dfrac{{ (\pi )( h)}}{\pi } =\dfrac{ 9\pi}{\pi }[/tex]
[tex]\bullet \rightarrow \boxed{\bold{h= 9 \ \text{inches}}}[/tex]
Thus, the height of the party hat is 9 inches.
What is the last digit when you multiply by 10?
5
1
0
Answer:
0 is the last digit. Hope this helps
Can you answer the question on the picture
Answer:
[tex]\huge\boxed{\sf 6x^2-x+16}[/tex]
Step-by-step explanation:
[tex]= (2x-3)(3x+4)\\\\Expand\\\\= 2x(3x+4)-3(3x+4)\\\\Distribute\\\\= 6x^2+8x-9x+16\\\\= 6x^2-x+16\\\\\rule[225]{225}{2}[/tex]
Answer:
6x²-x-12
Step-by-step explanation:
(2x-3)(3x+4)
2x(3x+4) -3(3x+4)
6x²+8x-9x-12
6x²-x-12