let a,b be the two numbers. we know that a2-b2=5 and a*b=6
using the formula we are given
[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]
Answer:
13
Step-by-step explanation:
Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,
[tex](x^2-y^2)=5[/tex]......................(1)
[tex]xy=6[/tex]..........(2)
We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :
[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]
Using equation (1) and (2) in above equation, we get :
[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]
[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]
[tex]x^2+y^2=13[/tex]
So, the sum of squares of two numbers is 13. Hence, this is the required solution.
A box contains 8 books. It is 1/6 full. If the box were completely full, how many books would be in the box? A) 14 books B) 48 books C) 16 books D) 24 books
Let x equal the number of books in the box.
x* 1/6 = 8
Multiply each side by 6
x=48 books
The correct answer is B) 48 books.
To determine how many books a completely full box would hold, we need to consider the information given:
The box contains 8 books and it is 1/6 full. To find out how many books would be in the box if it were completely full, we need to set up a proportion:
[tex]\(\frac{8}{\frac{1}{6}} = \frac{8 imes 6}{1} = 48\)[/tex]
This means the box can hold 48 books when full.
So, the correct answer is:
B) 48 books
Find [tex]f^-1 ( x ) when f ( x ) = \frac{3x}{x-2}[/tex]
[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]
let y = f(x), then rearrange making x the subject
y = [tex]\frac{3x}{x-2}[/tex] ( multiply both sides by (x - 2 ))
y(x - 2 ) = 3x (distribute )
xy - 2y = 3x ( subtract 3x and add 2y to both sides )
xy - 3x = 2y (factor out x on left side )
x(y - 3 ) = 2y ( divide both sides by (y - 3) )
x = [tex]\frac{2y}{y-3}[/tex]
change y to x for inverse function
[tex]f^{-1}[/tex](x) = [tex]\frac{2x}{x-3}[/tex]
I don't know how to solve.. please show work
3x^3 +7x^2 +x -2
This is a cubic form. I am assuming this should be factored.
With cubics like this it's worthwhile trying to find one root by simply guessing. My guess that worked out is x=-2
To verify:
3(-2)^3+7(-2)^2+(-2)-2 = 0 -> so -2 is a root and we get the first factor: (x+2)
Next we divide the cubic by the factor (x+2). I let you do the division. Here is the result
(3x^3 +7x^2 +x -2):(x+2) = (3 x^2 + x - 1)
(3 x^2 + x - 1) is a quadratic form and you can use the quadratic formula to get the two other roots. I got [tex]\frac{-1\pm \sqrt{13}}{6}[/tex].
So the entire cubic is now factored as follows:
[tex](x+2) \cdot (x+ \frac{-1+ \sqrt{13}}{6}) \cdot (x+ \frac{-1- \sqrt{13}}{6})[/tex]
What is the value of x?
A.)62°
B.) 46°
C.) 56°
D.) 134°
The sum of the interior angles in a triangle is 180°. To find the value of x, you must subtract 47 and 71 from 180.
180-47-71=x
x=62
The answer is A. 62°
Connor drives an an eighteen-wheeler. It cost Conner $456 to fill the truck up with diesel fuel. If diesel fuel cost $3 a gallon, how many gallons of fuel were bought? A) 148 gallons B) 152 gallons C) 156 gallons D) 164 gallons
First to answer this take note of how much he spends and how much it cost,
456 is the total cost and it is 3 a gallon
To figure how many gallons he got divide 456 by 3
456/3=152
Which statements are biconditional? Check all that apply.
All triangles and rectangles are polygons.
Sam bakes cookies or he bakes bread.
If it is fashionable, then this store sells it.
If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.
Victoria will play outside if and only if the weather is nice.
Biconditionals are statements that work both ways.
Some examples:
If it rains, I go out, and if I go out, it must be raining.
This can be stated concisely in mathematical terms as
I go out IF AND ONLY IF it rains.
So looking at the given statements, only the last two work both ways, namely:
If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.
Victoria will play outside if and only if the weather is nice.
Answer:
D&EStep-by-step explanation:
Free Brainliest! **PLEASE HELP**
Use the equation to find the length of the missing leg measure.
a^2 + 16^2 = 20^2
1. Evaluate Powers: A^2 + 256 = 400
2. Undo addition: a^2 = 144
3. Undo The square: a= 144 ( Square root )
What is the length of the missing leg measure?
a = ________ units
Answer:
a = 12 units
Step-by-step explanation:
Equation given is [tex]a^2 + 16^2 = 20^2[/tex]
First we have to evaluate the powers.
[tex]16^{2}[/tex] = [tex]16*16[/tex]=[tex]256[/tex]
[tex]20^{2}[/tex] = [tex]20*20[/tex]=[tex]400[/tex]
So we can now write the equation again as:
[tex]a^2 +256 =400[/tex]
Now we have to undo the addition,
[tex]a^2=400-256 [/tex]
[tex]a^2=144 [/tex]
Now we have to find the square root of [tex]a^2[/tex] to get the value of [tex]a[/tex]
[tex]\sqrt{a^{2}} = \sqrt{144}[/tex]
[tex]a=12[/tex] or [tex]a=-12[/tex]
But the length of a leg cannot be a negative value, so we can take the +12.
a = 12 units
Answer:
a = 12 units
Step-by-step explanation:
When rolling a fair number cube with numbers 1 through 6, what is the probability of rolling a number greater than 2?
A.) 1/2
B.) 1/4
C.) 2/3
D.) 5/6
You are asking for the proportion of numbers 1–6 that are greater than 2. The ones greater than 2 are 3, 4, 5, 6. There are 4 of them, out of the 6 possible numbers. Since the cube is fair, all numbers have equal probability. This means the probability of an outcome greater than 2 is
... 4/6 = 2/3
The appropriat choice is ...
... C.) 2/3
Please help, will mark brainliest.
I have attached the problem, and the answers are as follows:
A ) 2x - h - 4
B) 2x - 3h - 4
C) 4x + 2h - 3
D ) 4x + h - 3
f(x+h)-f(x) / h
f(x) = 2x^2-3x-4
Replace X with (x+h):
2(x+h)^2 - 3(x+h) -4
Simplify:
2x^2 + 4hx +2h^2 -3x -3h -4
Now you have:
(2x^2 + 4hx +2h^2 -3x -3h -4 - 2x^2-3x-4) / h
Simplify to get 4x +2h-3
The answer is C.
Only need help on 8!!!
Answer:
Marked-down price: $19.99
Step-by-step explanation:
The markdown amount is ...
$29.99×33 1/3% = $10.00 . . . . . 9.99667 rounded up
The marked-down price is the original price less the markdown:
$29.99 - 10.00 = $19.99
_____
You will recognize that 33 1/3% = 1/3, so that the calculation is ...
[tex]\text{markdown}\,=\dfrac{\$29.99}{3}=\$9.99\overline{6}\approx\$10.00[/tex]
A golf instructor ordered 21 cartons of golf balls. Each carton contained 15 golf balls. And equal number of golf balls were given to each of his six classes and the rest were put in his golf bag. How many golf balls to the instructor put in his golf bag?
10 1/2 golf balls to get it
Multiply and simplify: 10x(6x2 + 7x + 9) 60x3 + 160x 60x3 + 70x2 + 90x 60x2 + 70x + 90 6x2 + 17x + 9
Multiply each term in the parentheses by 10x. (This is the Distributive Law).:-
10x*6x^2 +10x*7x + 10x*9
= 60x^3 + 70x^2 + 90x
12600 x to the power of 2 + 37887 x + 40829
What percent of 80 is 50? Show your work.
50*2= 100
So 50 is one half of One hundred and if we use 100 divided by 2 to get 50 then we need to do 80 / 2 which will give us 40.
!!!! I need help with numbers 1 and 9 please !!!!!
(1)
given [tex]\frac{j}{6}[/tex] = [tex]\frac{9}{10}[/tex] ( cross- multiply )
10j = 54 ( divide both sides by 10 )
j = [tex]\frac{54}{10}[/tex] = [tex]\frac{27}{5}[/tex] ← in simplest form
(9)
let h be the hours worked daily , then
3h = 20 [tex]\frac{2}{3}[/tex] = [tex]\frac{62}{3}[/tex] ( divide both sides by 3 )
h = [tex]\frac{62}{3}[/tex] ÷ 3
= [tex]\frac{62}{3}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{62}{9}[/tex] = 6 [tex]\frac{8}{9}[/tex]
She worked 6 [tex]\frac{8}{9}[/tex] hours each day
Graph the following lines and write the equation in slope-intercept form. y intercept of −3 and an x intercept of −4.5.
Hello!
To find the equation of the line with a y-intercept of (0, -3) and a x-intercept of (-4.5, 0), we need to use the slope formula.
The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
With that, we substitute the given ordered pairs into the formula, and solve.
[tex]\frac{0 - (-3)}{-4.5 - 0} = \frac{3}{-4.5} =\frac{3}{-\frac{9}{2} } = -\frac{2}{3}[/tex]
The slope of this line is -2/3 or -0.667 repeated (doesn't specify).
Therefore, the equation of the line is y = -2/3x - 3. (I also included the graph!) :-)
Find b and c so that y=-14x^2+bc+c has vertex (-9,8)
b = - 252 and c = - 1126
the equation of a parabola in vertex form is
y a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = - 14(x + 9)² + 8 ← equation in vertex form
expand and compare coefficients
y = - 14(x² + 18x + 81 ) + 8 = - 14x² - 252x - 1134 + 8
compare to y = - 14x² + bx + c
b = - 252 and c = - 1126
The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival. She only spent her money on ride tickets and admission into the festival. The price of admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation to calculate the cost for anyone who only pays for festival admission and rides
(c) Explain your answer to Part B. PLEASE HELP ITS DUE TODAY!!!
X= amount of rides
Y=total price (33.50)
Equation: 0.75(18) + X = 33.50
13.50+ X=33.50
-13.50 -13.50
X=20.00
Admission=20.00
Answer:
Part a) [tex]x=18\ tickets[/tex], [tex]y=\$33.50[/tex]
Part b) [tex]y=0.75x+20[/tex]
Step-by-step explanation:
Let
x------> the number of ride tickets.
k-----> constant that represent the cost for festival admission
y----> the total cost
we know that
[tex]y=0.75x+k[/tex]
we have that
[tex]x=18\ tickets[/tex]
[tex]y=\$33.50[/tex]
substitute the values
[tex]33.50=0.75(18)+k[/tex]
solve for k
[tex]k=33.50-0.75(18)[/tex]
[tex]k=\$20[/tex]
The linear equation to calculate the cost for anyone who only pays for festival admission and rides is equal to
[tex]y=0.75x+20[/tex]
What percentage increase is this?
17.50 to 25.00
The percentage increased by 42.86%.
To calculate the percentage increase:
First: work out the difference (increase) between the two numbers you are comparing.
Increase = New Number - Original Number
Then: divide the increase by the original number and multiply the answer by 100.
% increase = Increase ÷ Original Number × 100.
If your answer is a negative number then this is a percentage decrease.
mary has 81 coins that have a total value of $5.40. if all of the coins are nickels and dimes how many of each does mary have
54 nickels and 27 dimes
1 dime = 10 cents = $0.1
1 nickel = 5 cents = $0.05
setting up 2 equations
let n = amount of nickels and d = amount of dimes, then
n + d = 81 → (1)
0.05n + 0.1d = 5.4 → (2)
multiply (2 ) by 10
0.5n + d = 54 → (3)
subtract (3) from (1) to eliminate d
0.5n = 27 ( divide both sides by 0.5 )
n = [tex]\frac{27}{0.5}[/tex] = 54
substitute n = 54 in (1)
54 + d = 81 ( subtract 54 from both sides )
d = 27
Mary has 54 nickels and 27 dimes
help please 4, 5, 6.......
4. Supplementary angles together make a straight line (two right angles). So BOE is supplementary to BOC
Answer: ∠BOE
5. Distance and midpoint between (4,-2), (6,8)
[tex]d = \sqrt{ (6-4)^2 + (8 - -2)^2} = \sqrt{2^2+10^2}=\sqrt{104}=2 \sqrt{26}[/tex]
midpoint
[tex]\left(\dfrac{4 + 6}{2}, \dfrac{-2 + 8}{2} \right) = (5, 3)[/tex]
Answer: distance 2√26, midpoint (5, 3)
6.That's a rectangle oriented parallel to the axes, width parallel to the x axis of 7 - -3 = 10 and length along y of 1 - - 4 = 5, so an area of 10(5)=50
Answer: 50
Please, Help!
If 108 people attend a concert and tickets for adults cost $3.75 while tickets for children cost $1.5 and total receipts for the concert was $252, how many of each went to the concert?
Answer:
adults = 40
children = 68
Step-by-step explanation:
Let the children=c
Let the adults = a
Equations
a + c = 108 (1)
3.75a + 1.5c = 252 (2)
Multiply (1) by 1.5
1.5a + 1.5c = 162 (3)
Subtract (3) from (2)
3.75a + 1.5c = 252
1.5 a + 1.5c = 162 Subtract
2.25a = 90 Divide by 2.25
a = 90/2.25
a = 40
Find the number of children
a + c = 108
40 + c = 108
c = 108 - 40
c = 68
Check
LHS
3.75 * 40 + 1.50 * 68
150 + 102
252 Which checks with the right hand side.
How many feet is 84 inches
Answer:
7 ft.
Step-by-step explanation:
1 ft./12 in. = x/84
Cross multiply:
1 × 84 = 84
x · 12 = 12x
12x = 84
12x/12 = 84/12
12x/12 = x
84/12 = 7
Ans. x = 7
Hope this helps! :)
There are 7 feet in 84 inches.
Given that we need to determine that how many feet in 84 inches.
To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.
There are 12 inches in a foot.
Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:
84 inches ÷ 12 inches/foot = 7 feet
So, 84 inches is equal to 7 feet.
Hence there are 7 feet in 84 inches.
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Convert y = 2x + 10 from slope intercept form to function notation.
Please help with explanation
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = 2x + 10 is in this form
To express in functional notation replace y by f(x), thus
f(x) = 2x + 10
Megan pours sand into a bucket at a constant rate. The graph shows the total weight of the bucket and the sand over time. After 10 seconds, the total weight is 35 ounces.
What is an equation of the line parallel to the line on the graph that passes through (3, 35)?
Answer:
B. y = 2x + 29
Step-by-step explanation:
The given graph has a slope of 2 (a rise of 10 for a run of 5), so the last two chioices are not viable. Clearly a parallel line through the given point will have a positve y-intercept, so the first choice is not viable.
The appropriate choice is the second one:
... B. y = 2x + 29
Hence the line parallel to this is y = 2x + 29.
Hence, option B is correct.
What is line?A straight group of points that stretch in opposing directions is what is known as a line. It is endless in both directions and lacks any ends. It is not thick. It only has one dimension.
In the given graph,
The line is passing through (0, 15) and (10, 35).
Therefore the slope of this lien is,
m = (35-15)/(10-0)
= 2
Now the parallel line to this line will have same slope.
Which passes through (3, 35),
Hence the line be ,
y - 35 = 2(x - 3)
y - 35 = 2x - 6
y = 2x + 29
Hence the line is y = 2x + 29.
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Triangle ABC is similar to triangle XYZ by the AA Similarity Postulate. Also, m∠A = 73° and m∠C = 43°. What is m∠Y?
∠Y = 64°
since the triangles are similar
∠Y = ∠C
∠C = 180° - (73 + 43 )° = 64° = ∠Y
Which of the following is not a solution of 10 > x – 7y? A. (–3, 10) B. (0, 7) C. (12, 0) D. (2, 10)
Answer:
C. (12, 0)
Step-by-step explanation:
Try the choices:
A. 10 > -3 -7·10 . . . true
B. 10 > 0 -7·7 . . . . true
C. 10 > 12 -7·0 . . . false . . . this is your answer
D. 10 > 2 -7·10 . . . true
The option that is not a solution of the inequality 10 > x - 7y is C. (12, 0), as substituting these values into the inequality gives 10 > 12, which is false.
To find out which option is not a solution of the inequality 10 > x
- 7y, we need to substitute the values of x and y from each given pair into the inequality and check if it holds true.
The only option that does not satisfy the inequality is C. (12, 0), because 10 is not greater than 12.
Alejandra gets paid 9 dollars per hour she works. If h is the total number of hours Alejandra works, which expression could be used to find the total pay, in dollars, that she receives?
your answer would be 9h
Can someone help me with this?
Which angles are corresponding angles? Select all that apply.
∠1 and ∠3
∠6 and ∠8
∠2 and ∠8
∠5 and ∠7
∠2 and ∠7
∠3 and ∠6
If you were to think of this diagram as a map of intersecting roads, corresponding angles are the ones on the same corner:
NW corner: ∠1 and ∠3
NE corner: ∠5 and ∠7
SE corner: ∠6 and ∠8
SW corner: ∠2 and ∠4
The choices in bold font above are the only pairs of corresponding angles that are in your answer list:
∠1 and ∠3∠5 and ∠7∠6 and ∠8Answer:
∠1 and ∠3 , ∠6 and ∠8 , ∠5 and ∠7 are corresponding angles
Step-by-step explanation:
Corresponding Angles are angles which occupy same relative position at intersection when a line intersects two lines.
In pair of corresponding angles, one angle is interior angle and other one is exterior angle.
Option 1:
∠1 is exterior angle and ∠3 is interior angle. Also Both are at relatively same position.
Thus they are Corresponding angles.
Option 2:
∠6 is interior angle and ∠8 is exterior angle. Also Both are at relatively same position.
Thus they are Corresponding angles.
Option 3:
∠2 and ∠8 both are exterior angle.
Thus they are not Corresponding angles.
Option 4:
∠5 is interior angle and ∠7 is exterior angle. Also Both are at relatively same position.
Thus they are Corresponding angles.
Option 5:
∠2 and ∠7 both are exterior angles.
Thus they are not corresponding angles.
Option 6:
∠3 and ∠6 both are interior angles.
Thus they are not corresponding angles.
A bag contains 4 Green Marbles and 5 white marbles suppose a marble is randomly selected what are the odds in favor of picking a white marble
The odds in favor of picking a white marble from a bag with 4 green and 5 white marbles are 5 to 4.
This is calculated by comparing the number of white marbles to the number of green marbles.
Explanation:To determine the odds in favor of picking a white marble from a bag containing 4 green marbles and 5 white marbles, we need to calculate the ratio of the number of successful outcomes (picking a white marble) to the number of unsuccessful outcomes (not picking a white marble).
In this case, the successful outcomes are the 5 white marbles, and the unsuccessful outcomes are the non-white marbles, i.e., the 4 green marbles.
The odds in favor are therefore 5 to 4, or simply, 5:4.
Here's how to calculate odds using a probability example:
The probability of drawing a white marble on the first try isSo, the odds in favor of picking a white marble are 5 to 4.
X+5/x^2+x-12
What are the restrictions for x
x ≠ - 4, 3
the denominator of the fraction cannot equal zero as this would make the fraction undefined. Equating the denominator to zero and solving gives the values that x cannot be
solve x² + x - 12 = 0
(x + 4)(x - 3) = 0
equate each factor to zero abd solve for x
x + 4 = 0 ⇒ x = - 4
x - 3 = 0 ⇒ x = 3
restrictions on x are : x ≠ - 4, 3