Answers
Answer:
Leg₂ ≈ 6.481 or √42
Step-by-step explanation:
a² + b² = c²
(√7)² + b² = (7)²
7 + b² = 49
b² = 42
b = √42
b ≈ 6.481
Related Questions
Worksheet 1.3
Part 1: Write a math expression for each problem (model the problem).
1)
Lumpy drove for h hours at 50 mph. How far did he drive?
Answers
Answer:
50h milesStep-by-step explanation:
For us to write a math expression for the problem, we will use the formula for calculating speed.
Speed is the change of distance of a body with respect to time.
Mathematically, Speed = Distance/Time
Distance = Speed * Time
If Lumpy drove for h hours at 50 mph, then Lumpy speed = 50mph and time = h hours.
Substituting the given parameters into the formula to get the distance;
Distance = 50mph * h hours
Distance = 50h miles
Hence the math expression that modeled how far Lumpy drive is 50h miles
Solve the following simultaneous equations :
1. x + 2y = 1, 3x - y = 17
Answers
Answer: x= 5 and y= -2
Step-by-step explanation:
Which of the following statements is not true concerning the equation x2−c=0 for c>0? A. The left-hand side of this equation is called a difference of two squares. B. This equation is not considered to be a quadratic equation because it is not of the form ax2+bx+c=0. C. A quadratic equation in this form can always be solved by factoring. D. A quadratic equation in this form can always be solved using the square root property.
Answers
Answer:
The correct option is;
B. This equation is not considered to be a quadratic equation because it is not in the form a·x² + b·x + c = 0
Step-by-step explanation:
A. The given equation, x² - c = 0, can be presented in the form of the difference of two squares as follows;
(x + √c)·(x - √c) = 0
B. The equation x² - c = 0, is a quadratic equation because it is a polynomial equation of degree 2
C. The equation x² - c = 0 can always be factored as (x + √c)·(x - √c) = 0
D. Where c > 0, the equation x² - c = 0 can by the square root property as follows;
x² - c = 0
x² = c
x = √c
Domain And Range. Need Help
Answers
Answer:
The first option.
Step-by-step explanation:
Domain is anything less than or equal to 2, but anything greater than or equal to -4
Range is anything greater than or equal to -4, but also less than or equal to 4
Gasoline at a particular gas station cost $2.78 per gallon if Cory buys $18 of gas how many gallons did he buy?
Answers
Answer:
6.47 gal
Step-by-step explanation:
cost of gas per gallon = $2.78
rate of change is cost of gas per gallon as cost to buy gas changes with the change in quantity of gallon.
Total cost for x gallons = cost of gas per gallon*x = 2.78x
Given that total money paid by him is $18
2.78x = 18
x = 18/2.78 = 6.47
Answer:
6.47 gallons
Step-by-step explanation:
18 divided by 2.78 = 6.47
Write the equation for a line in standard form (Ax+By+C) that is perpendicular to y = 3x -
2 and passes through the point (6,4).
Answers
Answer:
x+3y-6=0
Step-by-step explanation:
given eqn is y=3x-2 which is 3x-y-2=0
the eqn of line perpendicular to given eqn is -x+3y+k=0
it passes through (6,4)
-6+3*4+k=0
or,. -6+12+k=0
or, k= -6
therefore, the eqn of line perpendicular to given eqn is x+3y-6=0
Given f (x) = x2 + 7, evaluate f (4).
Answers
Answer:
f(4) = 23
Step-by-step explanation:
[tex] f(x) = x^2 + 7[/tex]
Plug x = 4
[tex] f(4) = 4^2 + 7[/tex]
[tex] f(4) = 16 + 7[/tex]
[tex] f(4) = 23[/tex]
Answer: f(4) = 23
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(4).
We find f(4) by plugging 4 in for x, everywhere that x appears in the function.
So we have f(4) = (4)² + 7.
(4)² is 16 so we have 16 + 7 which is 23.
So f(4) is 23.
y = 3x – 5. Find the value of y when x = 1
Answers
Y= (3*1) - 5
Y= 3 - 5
Y= -2
Hope this helps
First, rewrite the equation by substituting x for 1:
y = 3(1) - 5
Then, solve:
y = 3(1) - 5
y = 3 - 5
y = -2
Given x=-3, y=6, and z=-4
-15+(-x)+y=
Answers
Answer:
-6
Step-by-step explanation:
We are given x=- 3 , y= 6 and z= -4.
We are also given the expression:
-15 + (-x) +y
Substitute -3 in for x and 6 in for y.
-15 + (- -3) + 6
2 negative signs creates a positive sign
-15 + (+3) +6
-15 + 3+ 6
Add -15 and 3.
(-15+3) +6
-12 +6
Add -12 and 6.
-6
-15+(-x)+y evaluated at x= -3 and y=6 is equal to -6.
Match the property name with the appropriate equation. Use each once.
19. Opposite of a Difference
A. -[(-r) + 2p] =-(-r) - 2p
20. Opposite of a Sum
B. 160 - (3d + 2)(0) = 160 - 0
21. Opposite of an Opposite
C. 5(2 - x) = 10 - 5x
22. Multiplication by 0
D. -(4r + 3s) + t = (-1)(4r + 3s) + t
23. Multiplication by -1
E. -(8 - 3m) = 3m - 8
24. Distributive Property
F. [-19 - 2w)] = 9 - 2w
Answers
Answer:
19. Opposite of a Difference ↔ E. -(8 - 3·m) = 3·m - 8
20. Opposite of a sum ↔ A. -[(-r) + 2p] = -(-r) - 2p
21. Opposite of an Opposite ↔ F. -1[ -1(9 - 2w)] = 9 - 2w
22. Multiplication by 0 ↔ B. 160 - (3d + 2)(0) = 160 - 0
23. Multiplication by ↔ D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t
21. Distributive property ↔ C. 5(2 - x) = 10 - 5x
Step-by-step explanation:
19. Opposite of a difference is the difference of the opposites
20. Opposite of a sum is the sum if the opposites
21. Opposite of an opposite is the original number
22. Multiplication by 0- The result of multiplication by 0 is 0
23. Multiplication by -1 results in the change in sign of a number
24. Distributive property - Multiplying the sum or difference of two numbers by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.
A map of Nevada in the shape of a trapezoid is shown. The length of one base is 483 miles, the length of the other base is 207 miles, and the length of a side is 405 miles. The length of the altitude is 320 miles. Hien would like to estimate the area of Nevada using a trapezoid. She uses the dimensions shown as approximations. What is the approximate area of Nevada? sq. mi
Answers
Hey there! I'm happy to help!
To find the area of a trapezoid, you add the lengths of the two bases, divide by two, and then multiply by the height.
We add our two bases.
483+207=690
We divide by 2.
690/2=345
We multiply by the height.
345(320)=110,400
Therefore, Hien can estimate that the area of Nevada is 110,400 square miles.
Have a wonderful day! :D
The formula for area of a trapezoid is [tex](b_{1} + b_{2})*\frac{1}{2} h=A[/tex]
b=base
h=height AKA altitude.
A=area.
Base 1 is 483.
Base 2 is 405.
483+405=888
888×320 (h) = 284160
284160 × [tex]\frac{1}{2}[/tex] = 142080
The approximate area of Nevada is 142080 square miles.
♡ Hope this helps! ♡
❀ 0ranges ❀
The diagram shows a solid formed by joining a hemisphere, of radius rcm, to a cylinder, of radius rcm and height hcm. The total height of the solid is 18 cm and the surface area is 205pie cm? Find the value of r and the value of h cm
Answers
Answer:
Step-by-step explanation:
The total surface area of the sphere = 2πr²
Total surface area of the cylinder = 2πr²+2πrh
Total surface area of the solid = 4πr²+2πrh
r is the radius of the sphere and the cylinder
h is the height of the cylinder
Total surface area of the solid = 2πr(r+h)
If the total height of the solid is 18 cm, then r+h = 18cm
Given the Total surface area of the solid = 205π cm
205π = 2πr(r+h)
205π = 2πr(18)
205π = 36πr
205 = 36r
Divide both sides by 36
205/36 = 36r/36
r = 5.69cm
Since r+h = 18cm
5.69+h = 18
h = 18-5.69
h = 12.31cm
There is a quadrilateral MNPQ in which side MN is congruent to side PQ and side NP is parallel to side MQ. The diagonal MP and the diagonal NQ intersect each other at point R. If MP = 6x − 5, QR = 3x + 1, and RN = 6, what is QN?
Answers
Answer: QN = 12
Step-by-step explanation: This quadrilateral is a paralelogram because its 2 opposite sides (NP and MQ) are parallel and the other 2 (MN and PQ) are congruent.
In paralelogram, diagonals bisect each other, which means QR = RN.
If QR = RN:
QR = 6
Then,
QN = QR + RN
QN = 6 + 6
QN = 12
The diagonal QN of quadrilateral MNPQ is QN = 12.
I cant find whats wrong
Answers
Dena bought 4 stuffed animals and 7 toy trains for $75. At the same prices, Nico bought 6 stuffed animals and 5 toy trains for $74. What is the price of a stuffed animal?
Answers
Answer:
$6.50
Step-by-step explanation:
Create a system of equations, where s represents the price of a stuffed animal and t represents the price of a toy train:
4s + 7t = 75
6s + 5t = 74
Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2:
12s + 21t = 225
-12s - 10t = -148
11t = 77
t = 7
Plug 7 in as t to find s:
4s + 7t = 75
4s + 7(7) = 75
4s + 49 = 75
4s = 26
s = 6.5
= $6.50 for a stuffed animal
Solve the equation
(If possible please show work)
Answers
2 - 4n = 2 - (12 - 8n) distribute the 4
2 - 4n = 2 - 12 - 8n parentheses don’t matter anymore
2 - 4n = -10 - 8n subtract 12 from 2
2 = -10 - 4n add 4n to both sides
12 = -4n add 10 to both sides
-3=n divide both sides by -4
Hope this helps!!:)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{n = 1}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2 - 4n = 2 - 4(3 - 2n)} [/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{ 2 - 4n = 2 - 12 + 8n}[/tex]
Move 8n to left hand side and change it's sign
⇒[tex] \sf{2 - 4n - 8n = 2 - 12}[/tex]
Collect like terms
⇒[tex] \sf{2 - 12n = 2 - 12}[/tex]
Move 2 to right hand side and change it's sign
⇒[tex] \sf{ - 12n = 2 - 12 - 2}[/tex]
Calculate
⇒[tex] \sf{ - 12n = - 12}[/tex]
Divide both sides of the equation by -12
⇒[tex] \sf{ \frac{ - 12n}{ - 12} = \frac{ - 12}{ - 12} }[/tex]
Calculate
⇒[tex] \sf{n = 1}[/tex]
Hope I helped!
Best regards!!
Find the component form of the vector that translates P(−3, 6)
to P′(−4, 8).
Answers
Answer:
Component form of the vector will be (-1, 2).
Step-by-step explanation:
When [tex]P(x_1, y_1)[/tex] translates to [tex]P'(x_2,y_2)[/tex] vector V formed after the translation will be,
V = [tex]<(x_2-x_1), (y_2-y_1)>[/tex]
If we draw this vector on a graph,
Vector will start from origin and the terminal point will be at [tex][(x_2-x_1), (y_2-y_1)][/tex]
Therefore, component form of the vector that translates from P(-3, 6) and P'(-4, 8) will be,
V = [tex]<(-4+3),(8-6)>[/tex]
V = [tex]<(-1,2)>[/tex]
Translation involves changing the position of a point
The vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
The points are given as:
[tex]\mathbf{P = (-3,6)}[/tex]
[tex]\mathbf{P' = (-4,8)}[/tex]
The translation rule is calculated as:
[tex]\mathbf{(x,y) = P' - P}[/tex]
So, we have:
[tex]\mathbf{(x,y) = (-4,8) - (-3,6)}[/tex]
Combine
[tex]\mathbf{(x,y) = (-4+3,8-6)}[/tex]
[tex]\mathbf{(x,y) = (-1,2)}[/tex]
Express as vectors
[tex]\mathbf{<x,y> = <-1,2>}[/tex]
Hence, the vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]
Read more about translations at:
https://brainly.com/question/12463306
Choose the correct expressions using the fewest number of bases possible that are equivalent to the current expression. (Select all that apply); (Hint: There are 2 correct choices) Question 2 options: 53+2 53×52 53×2 55
Answers
Answer:
[tex]\huge \boxed{\mathrm{5^{3+2} \ \ \ \ 5^5 }}[/tex]
Step-by-step explanation:
5³ × 25
25 can be written as a base of 5.
5³ × 5²
We need expressions with fewest number of bases possible.
Apply exponent rule : [tex]a^b \times a^c = a^{b+c}[/tex]
[tex]5^{3+2}[/tex]
Add exponents.
[tex]5^5[/tex]
Answer:
The answer is easy its 53 times 2 and 52 times 2
Step-by-step explanation:
evaluate g(x)=3x when x= -2,0, and 5
Answers
Answer:
-6, 0, 15
Step-by-step explanation:
You just replace x with the given number.
g(-2)= 3(-2)
=-6
g(0)=3(0)
=0
g(5)=3(5)
=15
The required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been the given expression:
g(x) = 3x
To determine the evaluated values of g(x) = 3x when x= -2, 0, and 5
We have to substitute x with the given number.
⇒ g(x) = 3x
Substitute the value of x = -2 in the g(x) = 3x
⇒ g(-2) = 3(-2)
⇒ g(-2) = -6
Substitute the value of x = 0 in the g(x) = 3x
⇒ g(0) = 3(0)
⇒ g(0) = 0
Substitute the value of x = 5 in the g(x) = 3x
⇒ g(5) = 3(5)
⇒ g(5) = 15
Hence, the required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.
Learn more about the algebraic expression here :
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A phone company offers two monthly plans. Plan A costs 8 plus an additional 0.16 for each minute of calls. Plan B costs 20 plus an additional 0.14 for each minute of calls.
Answers
Answer:
Total time when cost are equal = 600 minutes
Total cost = 104
Step-by-step explanation:
Given:
Plan A = costs 8 plus an additional 0.16 for each minute
Plan B = costs 20 plus an additional 0.14 for each minute
Find:
Total time when cost are equal
Computation:
Assume total time = x minutes
Plan A = 8 + 0.16x
Plan B = 20 + 0.14x
Plan A = Plan B
8 + 0.16x = 20 + 0.14x
0.02x = 12
x = 600 minutes
Total time when cost are equal = 600 minutes
Total cost = 8 + 0.16x
Total cost = 8 + 0.16(600)
Total cost = 104
change .
0.9kg into grams
Answers
Answer:
900 grams.
Step-by-step explanation:
1 kg = 1000 grams.
0.9 kg = 1000 * 0.9
= 900 grams.
Answer:
900 grams is the answer
A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet." How many cows does she have? How many chickens does she have? (Note: chickens have 2 feet and cows have 4 feet.)
Answers
Answer:
Step-by-step explanation:
yo
The number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet.
Let x be the number of cows and y be the number of chickens.
2x + 2y = 162 (there are 162 eyes)
4x + 2y = 270 (there are 270 feet)
From the first equation take the value of x and plug it into the equation second.
2y = 162 - 2x
y = 81 - x
4x + 2(81 - x) = 270
4x + 162 - 2x = 270
2x = 108
x = 54
y = 27
Thus, the number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.
Learn more about the linear equation here:
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write the sets of all possible factors and the sets of common factors of the pairs of numbers, then find their H.C.F. could you show step by step.
a. 8,12
b. 12,18
c. 16,24
d. 20,30
e. 24, 36
Answers
Answer:
a= 1,2,4 b= 1,2,3,6 c=1,2,4 d=1,2,5,10 e=1,2,3,4,6,12 H.C.F of all the pairs= 2
Step-by-step explanation:
Factors of:
a. 8=1,2,4,8
12=1,2,3,4,6,12.
common factor=1,2,4
b. 12=1,2,3,4,6,12
18=1,2,3,6,9,18
common factor=1,2,3,6
c. 16=1,2,4,16
24=1,2,3,4,6,8,12,24
common factor=1,2,4
d. 20=1,2,4,5,10,20
30=1,2,3,5,6,10,15,30
common factor=1,2,5,10
e. 24=1,2,3,4,6,8,12,24
36=1,2,3,4,6,9,12,18,36
common factor=1,2,3,4,6,12
HIGHEST COMMON FACTOR (H.C.F)=
The factor common to the whole pairs
which is 1 and 2
therefore 1 multiplied by 2 which is equal to 2
(and in Mathematics means multiplication)
in a mixture of 60 litres, the ratio of milk to water is 2:1. if this ratio is to be 1:2, then find the quantity of water to be further added.
Answers
Answer: 20 liters
Step-by-step explanation:
The mixture is 60 liters. The ratio is 2 : 1 (2 parts to one part)
60 ÷ (2 + 1) = one part
60 ÷ 3 = 20
Therefore, the ratio of 2 : 1 means 2(20) liters milk to 1(20) liters water
If we change it to a ratio of 1 : 2, then we have 1(20) liters milk to 2(20) liters water.
2:1 ratio has 20 liters water
1:2 ratio has 40 liters water
The amount of water added is 40 - 20 = 20 liters
Find the complex number solutions to the quadratic f(x)=2x^2-6x+17
Answers
Answer:
im pretty sure the answer is b. im not 100% though
Step-by-step explanation:
ax+ by = c
solve for y
Answers
Answer:
[tex]\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]
Step-by-step explanation:
[tex]ax+by=c\\\\ax-ax+by=c-ax\\\\by=c-ax\\\\\frac{by=c-ax}{b}\\\\\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]
Hope this helps.
A single carton of juice costs $4.20. A special offer pack of 3 cartons costs $9.45. Ali bought a special offer pack instead of 3 single cartons. Calculate his percentage saving
Answers
1 cartons of juice = $4.20
3 single cartons = 4.20 * 3 = $12.60
1 pack = $9.45
He saved 12.60 - 9.45 = $3.15
So, he saved $3.15, compared to the total ($12.60)
To calculate the percentage, we will do a proportion:
3.15 (money saved) : 12.60 (total of 3 single cartons) = x (how much percentage) : 100 (total)
3.15 : 12.6 = x : 100
To calculate x, we will moltiplicate the ends (where we have known numbers) than divide all per 12.6
So
x = (3.15 * 100) / 12.60 = 315 / 12.6 = 25
So the percentage saving is 25%
Can you please help me 4(x+4)=4x+16 justify solutions of an equation one variable
Answers
Answer:
any x value would work
Step-by-step explanation:
4(x+4)
4*x=4x
4*4=16
4x+16=4(x+4)
please help me on this
Answers
Answer: The coordinate of L is 4.
Step-by-step explanation:
Let's say you were to plot the point on a number line and find the distance between P and G.
P is -6 on the number and G is 18 on the number so to find the distance between them we will need to find the different between the number and find its absolute value.
-6- 18 = -24 and the absolute value of -24 is 24.
In other words to get from -6 to 18 on the number line you need to move 24 units to the right.
Now to answer the question, we know that the distance between the two numbers is 24 and and it says that L is 1/6 of the distance.
We can represent that by the equation,
L = [tex]\frac{1}{6} * 24[/tex]
L = 4
The area of a square field is 841m.A rectangular field whose length is twice it's breath has its perimeter equal to square field.Find the area of square field
Answers
Given: The area of a square field is 841 sq.m
Since side of square = √Area
So, side of square field = [tex]\sqrt{841} =29[/tex]
Thus , side of square field = 29 m
Perimeter of square = 4( side) = 4(29) = 116 m
Let x be the breadth of rectangle then 2x be the length
Perimeter of rectangle = 2 (length+breadth) = 2(2x+x)= 2(3x)=6x
As per question, perimeter of rectangle= Perimeter of square
[tex]\Rightarrow\ 6x=116\\\\\Rightarrow\ x=\dfrac{116}{6}=\dfrac{58}{3}\ m[/tex]
Length : [tex]2x =2\dfrac{58}{3}=\dfrac{116}{3}\ m[/tex]
Area of rectangle = length x breadth
[tex]=\dfrac{116}{3}\times\dfrac{58}{3}=\dfrac{6728}{9}\\\\=747\dfrac{5}{9}\ m^2[/tex]
Area of rectangle = [tex]747\dfrac{5}{9}\ m^2[/tex]