[tex]s=(\frac{1}{2} p)(l)[/tex]
Flip equation:
[tex]\frac{1}{2} lp=s[/tex]
Divide both sides by p/2:
[tex]\frac{1/2lp}{p/2} =\frac{s}{p/2}[/tex]
[tex]l=\frac{2s}{p}[/tex]
6. Find the equation for a parabola with vertex (5,-8) containing the point (1,1).
Answer:
[tex]y=\frac{9}{16}(x-5)^2-8[/tex]
Step-by-step explanation:
The equation in vertex form is [tex]y=a(x-5)^2-8[/tex].
Substituting in the coordinates [tex](1,1)[/tex] to solve for [tex]a[/tex],
[tex]1=a(1-5)^2-8 \\ \\ 1=16a-8 \\ \\ 9=16a \\ \\ a=9/16[/tex]
So, the equation is [tex]y=\frac{9}{16}(x-5)^2-8[/tex].
What is the value of |−13|?
Answer:
+ 13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
when you see the absolute value and the number is negative or positive it is just the whole number inside
ind the radius of a circle that has a circumference of 16.
r = 4
r = 8
r = 12
r = 16
8 units is the radius of the circle with a circumference of 16π.
What is the radius of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
C = 2 × π × r
Where r is radius and π is constant pi ( π = 3.14 )
Given the data in the question;
Circumference C = 16πRadius r = ?To find the radius of the circle, plug the given value into the circumference formula and solve for r.
C = 2 × π × r
16π = 2π × r
r = 16π / 2π
r = 16/2
Radius r = 8
Therefore, the radius of the circle is 8.
Option B is the correct answer.
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Hey, could someone help me out on this?
Ruby went on a walk that was 10/3 miles long. She stopped to have lunch when she walked 12/25 of her way. How far, in miles, did ruby walk before lunch? Give your answer as a fraction in its simplest form
Fraction - The distance she walked before lunch 214 / 75 miles
What is Fraction ?
A fraction, which also represents a portion of a whole, is a mathematical symbol for any number of equal parts. A fraction, such as one-half, eight-fifths, and three-quarters, indicates the number of components of a specific size when used in conversational English.
Given that,
The distance Ruby has to walk = 10/3miles
The distance left to complete before stopping = 12/25miles
The distance Ruby has to walk before lunch = 10/3 - 12/25
= 250 - 36 / 75
= 214 / 75miles
Hence, she walked 214 / 75 miles before lunch
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The sum of an integer and 2 times the next consecutive integer is -13. Find the value of the greater integer.
Answer:x+x+1=13
2x+1=13
2x=13−1
2x=12
x=
2
12
x=6
x+1=6+1=7
Step-by-step explanation:yes
Is the relationship between the number of tickets sold and the number of hours proportional? If so, how many tickets were sold in 8 hours?
hours.
1) 3
2) 5
3) 9
Tickets sold
1) 240
2) 400
3) 720
suppose that a large mixing tank initially holds 400 gallons of water in which 80 pounds of salt have been dissolved. pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. determine a differential equation for the amount of salt a(t) in the tank at time
The differential equation for the amount of salt A(t) in the tank at the time (dA / dT) / (A / 100) = 0, A(0) = 30
It is Given that a large tank holds 400 gallons of water, in which 80 ponds of salt have been dissolved, given that pure water is pumped into the tank at a rate of 8 gallons/min. here we have to find the differential equation for the amount of salt in the tank at the time when the solution is well stirred. we have to multiply both 400 gallons of water and pumped water at the rate of 8 gallons/min.
dA / dT = Rin - Rout
Rin = 0
Rout = A(t) / 400 * 8
= A / 50
So,
dA / dt = Rin - Rout
dA / dt = 0 - A /50
After solving the differential equation we get
A(0) = 30
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PLEASE HELP ! :)
1. G(X)=1/4x+1
what is g(-16)?
g(-16)=
In many cases, when we evaluate functions, we just have to replace x with a given value and simplify the expression.
Solving the Question[tex]g(x)=\dfrac{1}{4}x+1[/tex]
⇒ To solve for g(-16), plug in -16 as x:
[tex]g(x)=\dfrac{1}{4}(-16)+1\\\\g(x)=-4+1\\\\g(x)=-3[/tex]
Answerg(-16) = -3
PLS HELP WILL GIVE 20 POINTS AND BRAINLIEST!! ASAP!!!!
Answer:
[tex]\frac{36}{49}[/tex]
Step-by-step explanation:
the pattern identified in the sequence is to add 1/49 after each step in the sequence.
When you add 1/49 to 34/49 you get 35/49, which can be simplified to 5/7.
To get the next value in the sequence just add 1/49 to 35/49, which equals 36/49.
this answer can not be simplified further.
help past due!
Multiply the polynomials (5a² + 2a − 7) and (3a² − a + 1). Simplify
the answer.
Answer:
C
Step-by-step explanation:
Use the distributive property to solve.
(5a²+2a-7)(3a²-a+1)
=15a⁴-5a³+5a²+6a³-2a²+2a-21a²+7a-7
=15a⁴+a³-18a²+9a-7
< A and < B are supplementary angles. If m m < B= (2x+30), then find the measure of < A.
Answer:
m<A = 50°
Step-by-step explanation:
supplementary angles add up to 180°
m<B = 2x + 30
we don't know m<A, so we'll say the value of it is x
2x + 30 + x = 180°
3x + 30 = 180
3x = 150
x = 50
plug this value back in for x
m<B = 2(50) + 30 = 130
m<B = 130°
m<A = x = 50
m<A = 50°
to prove these are supplementary angles, 130 + 50 = 180
David, Eva and Farooq share a sum of money.
1/6
David gets
- of the money and Eva gets -
1
4
- of the money.
Farooq gets the rest of the money.
David gets £2.50
Work out how much money Farooq gets.
Answer:
Farooq gets £8.75
Step-by-step explanation:
Let's represent the amounts obtained by David, Eva and Farooq as D, E and F to make things simpler. Let M be the total amount of money shared
D = 2.50 and represents 1/6 of the total amount of money(M)
So
M/6 = 2.50
Multiply both sides by 6 => M = 2.50 x 6 = £15
Eva gets 1/4th of this so E = 15 x 1/4 = £3.75
David gets £2.50
Together they get £2.50 + £3.75 = £6.25
The balance goes to Farook so F = 15 - 6.25 = £8.75
Which choice is the value of three over five raised to the second power?
three over twenty-five
three over ten
nine over twenty-five
six over seven
The value of three over five raised to the second power is nine over twenty-five.
How can the operation be performed?From the question , we were given that three over five raised to the second power which can be interpreted as (3/5)^2 then we can find the square of the given value so that we can arise at the answer.
In this case , (3/5)^2 = 9/25 which implies that the value of the (3/5)^2 is been found and to calculate the value of (3/5)^2, we will need to find the square of 3 which is the numerator as well as the square of 5 which is the denominator.
Therefore, the third option is correct.
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Tyrell bought n number of shares for s dollars and paid a 3% commission. He sold
the stock for d dollars and paid a flat fee of $15. Which expression below models
Tyrell’s net proceeds algebraically?
The expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15) .
In the question ,
it is given that ,
Tyrell bought n shares for s dollars
So the price Tyrell paid for shares = $ ns .
Tyrell also paid 3% commission ,
so the total cost price Tyrell paid for shares = price of share + commission
total cost price = ns + 3% of ns
= ns + 0.03ns ....as 3% = 0.03
= 1.03ns ...(i)
Tyrell sold the stocks for d dollars .
Tyrell also paid the flat fee of $15 .
So, the selling price for stocks = d-15 ......(ii)
The Tyrell's Net Proceeds can be calculated using the formula
Net Proceeds = Selling Price - Cost price
Substituting the values of selling price and cost price from (i) and (ii) ,
we get ,
Net Proceeds = (d-15)-(1.03ns)
= d-15-1.03ns
= d-(1.03ns + 15)
Therefore , the expression that models Tyrell's net proceeds algebraically is d-(1.03ns + 15) .
The given question is incomplete , the complete question is
Tyrell bought n number of shares for s dollars and paid a 3% commission. He sold the stock for d dollars and paid a flat fee of $15. Write an expression to model Tyrell’s net proceeds algebraically.
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Picture attached below, and it's not a rectangle. It's a pentagonsolve a and b
a)
The perimeter is given by
[tex]2x+3+4x+5+3x+15+40[/tex]b)
Then we simplify by summing similar terms we obtain that the expression of the perimeter is
[tex](2x+4x+3x)+(3+5+15+40)[/tex][tex]9x+63[/tex]
Given mn, find the value of x.
(8x-7)°
(9x-28)°
Answer: top: x= -15 bottom: x= -37
Step-by-step explanation: First you need to get x by itself so for example on the top one you would do 8-8 to get x alone and then you would also do -7- 8 because whatever you do to one side you have to do to the other.
Hope this helped!!!
In Exercises 3 and 4, plot the points in a coordinate plane. Then determine whether
AB and CD are congruent.
3. A(-7, 1), B(-4, 1), C(3, -5), D(3, -2)
4. A(1, -1), B(1, 1), C(3, -4), D(5,-4)
AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
What is congruency?If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence. In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.So, all coordinates are shown on the graph as follows:
(Refer to the image attached below)
Now, we can see that in the 4th quadrant, two triangles are formed that are ABE and CDE.
We can see that:Then, we can conclude that:
AB ≅ CD (Angle in front of them is similar so, the sides are also similar)Therefore, AB is congruent to CD as an angle in front of them is congruent so, the sides are also congruent.
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In the equation
2H₂ + 102 →→ 2H₂O
if you change the 2H₂ to 3H2 molecules and balance the equation, which statement is correct?
If you change the 2H₂ to 3H₂ molecules and balance the equation the equation will produce three molecules of water.
The provided chemical equation is,
2H₂ + O₂ → 2H₂O.
Changing 2H₂ with 3H₂
The chemical equation becomes,
3H₂ + O₂ → 2H₂O.
By doing this, the equation has become completely imbalanced,
So first we will balance it,
3H₂ +3/2O₂ → 3H₂O
Now, there will be 3 molecules of water formed.
As we observe the reaction more closely, we can see that the number of atoms of all the elements are equal on both the sides of the reaction.
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A football team lost 14 yards on their first play then lost another 7 yards on the next play. What integer represents the total change in yards for the two plays?
Answer:
- 21
Step-by-step explanation:
They lost 14 yards, then lost and additional 7 more. You would simply add and make it a negative number due to the key word " lost ".
The equation would look like this: -14 + ( -7 ).
Another way to solve this equation is to multiply. ( + ) x ( - ) = -.
Your equation will the look this this: -14 - 7.
Now you just solve.
Thus, your answer should be - 21.
Hopes the helps!
Have a great day.
Answer: -21
Step-by-step explanation:
.A football team will lose an additional 7 yards if they lost 14 on their first play.
. Since the first play resulted in a loss of 14 yards, the integers that reflect the overall change in yards for the two plays are negative.
.In the second play, we score 14 points but lose 7 yards, which is a loss of 7 points.
.Negative 14 + Negative 7 = Negative 21, which is the overall change in yards.
. Hence, the answer would be -21 yards.
. -21 would be the correct integer that will represent the the total change in yards for the two plays.
one out of every 9 light bulbs is defective. What constant of proportionality relates defective bulbs to total bulbs?
the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
We are given that 1 bulb out of every 9 bulbs is defective.
So, this means that if there is a total of 9 bulbs, then 1 bulb in it will be defective.
Let us assume:
Total bulbs = 9
So, this implies that:
Defective bulbs = 1
Constant of proportionality = Defective bulbs / Total bulbs.
Substituting the values in this, we get that:
Constant of proportionality = 1 / 9
Therefore, we get that, the constant of proportionality that relates defective bulbs to total bulbs is 1 / 9.
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The area of the compound shape below is 92 cm². Find the value of x.
Answer:
Step-by-step explanation:
Solve for x. 1/4+1/2+x=−3/4 Enter your answer as a fraction in simplest form in the box.
Answer:
yes!! finally a question i can solve:
so,
Step-by-step explanation:
Exact Form:
x = − 3/2
Decimal Form:
x = −1.5
Mixed Number Form:
x = -1 1/2
A basketball player attempts 15 baskets in a game. He makes 9 out of the attempted baskets.
Which describes the number of the baskets the player made to the number of baskets the player attempted?
The ratio is 3:5 .
The problem we are dealing with is related to the term ratio, where the ratio is characterized as the comparison of two quantities of the same units that shows how much of one amount is present within the other amount. Ratios can be classified into two sorts. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio indicates how two distinct entities or groups are related. whereas, the part-to-whole proportion indicates the relationship between a particular group to an entirety.The situation we are given is that the player attempted 15 baskets in a game and out of 9 was the number of times he made the attempted baskets.We just need to find the ratio of the number of baskets made to the number of baskets attempted,
= 9:15
Here we divide each by 3
= 9/3: 15/3
=3:5
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HELP PLEASE!! I’ll give
The square root x^4= x^2
Find the sum of AP 35+29+23+....... as far as the 15th term
Answer: The answer is y=6x.
Write the slope-intercept form of the equation of each line given the slope and y-intercept. Slope = 3/5, y-intercept = 0
Answer:y=3/5x
Step-by-step explanation:
just plug 3/5 in and you don’t need to add the 0
All of the following represent three multiplied by six except:
03x6
03-6
O3(6)
3:6
Help please
Answer:
Except the last one 3:6 because its not multiplied by six but divided. Therefore the correct answer is the last one
Step-by-step explanation:
hope it helps
If 2y+ 5x = 5 and 4y - x = 21, then what is the value of x + y ?
The value of equation (x + y) will be 1.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The equation are;
2y + 5x = 5 ... (i)
4y - x = 21 ... (ii)
Now, Solve both the equation and find the value of x and y as;
Multiply by 2 in equation (i) we get;
4y + 10x = 10
Subtract above equation by (ii);
4y + 10x - (4y - x) = 21 - 11
11x = 11
x = 1
And, 2y + 5x = 5
Substitute x = 1;
2y + 5x = 5
2y + 5 = 5
2y = 0
y = 0
So, x + y = 1 + 0 = 1
Thus, The value of (x + y) will be 1.
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Given that [tex]\alpha , \beta[/tex], roots of [tex]4x^{2} - x + 1 = 0[/tex], without finding the value of [tex]\alpha , \beta[/tex] ; evaluate
a. [tex]\beta x^{2} +\alpha x^{2} -\alpha \beta[/tex]
b. [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]
Considering the product and the sum of the roots of the quadratic function, the numeric value of the expressions are given as follows:
1. [tex]\beta x^2 + \alpha x^2 - \alpha\beta = \frac{1}{4}(x^2 - 1)[/tex]
2. [tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{7}{4}[/tex]
What are the product and the sum of the roots of the quadratic function?A quadratic function is defined according to the following rule:
y = ax² + bx + c.
In which a and b are the coefficients of the equation.
Supposing that the equation has roots [tex]\alpha[/tex] and [tex]\beta[/tex], the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex][tex]\alpha + \beta = -\frac{b}{a}[/tex]In this problem, the equation is:
4x² - x + 1.
Hence the coefficients are:
a = 4, b = -1, c = 1.
Then the product and the sum of the roots of the quadratic function are given as follows:
[tex]\alpha\beta = \frac{1}{4}[/tex][tex]\alpha + \beta = \frac{1}{4}[/tex]Then the numeric values for the expressions can be found as follows:
[tex]\beta x^2 + \alpha x^2 - \alpha\beta = x^2(\alpha + \beta) - \alpha\beta = \frac{1}{4}x^2 - \frac{1}{4} = \frac{1}{4}(x^2 - 1)[/tex]
For the second expression:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = 4(\alpha^2 + \beta^2)[/tex]
The sum of the squares of the roots is:
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta[/tex]
Hence:
[tex]\alpha^2 + \beta^2 = \frac{1}{16} - \frac{1}{2} = -\frac{7}{16}[/tex]
Then:
[tex]\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = -\frac{28}{16} = -\frac{7}{4}[/tex]
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