Buckets of cement needed is 5 and sand needed is 20
Solution:
Given that Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1 : 4 : 6
cement : sand : gravel = 1 : 4 : 6
Let the cement needed be "1x"
Let the sand needed be "4x"
Let the gravel needed be "6x"
Given that 20 buckets of sand used
4x = 20
x = 5
Thus buckets of cement needed = 1x = 1(5) = 5
Buckets of sand needed = 4x = 4(5) = 20
5 buckets of cement and 20 buckets of sand are needed
How would I graph these equations in a system? : 2r + b = $8.40, and 3r + b = $9.35. If you need specifics, I can tell you the whole story problem. I will mark the best answer as Brainliest.
Answer:
The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown
Step-by-step explanation:
Given as :
The two line equation are
2 r + b = $8.40 .........A and
3 r + b = $9.35 .........B
Now, Solving equations A and B
i.e (3 r + b) - (2 r + b) = $9.35 - $8.40
Or, (3 r - 2 r) + (b - b) = 0.95
or, r + 0 = 0.95
∴ r = $0.95
Now, put the value og r into eq A
∵ 2 r + b = $8.40
So, 2× $0.95 + b = $8.40
Or, $1.9 + b = $8.40
Or, b = $8.40 - $1.9
∴ b = $6.5
So, The value of r = $0.95 and b = $6.5
Now, for plotting the equation on graph
let put r on x axis
and put b on y-axis
Hence, The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown . Answer
A point is reflected across the x-axis the new point is (-7.5, 6) what is the difference between the two points
Answer:
The y-coordinate of the original point is negative and the y-coordiinate of the new point is positive.
The transformation is:
[tex](-7.5, 6)[/tex] → [tex](-7.5, -6)[/tex]
Step-by-step explanation:
For this exercise it is important to remember the definition of "Reflection".
A Reflection is a transformation that consists in folding an figure over a line called "Line of reflection",
In tranformations, the original figure is called "Pre-image" and the figure obtained after the transdformation is called "Image".
Given a point [tex](x,y)[/tex], if this is reflected across the x-axis, the x-coordinate of the point does not change, but the sign of the y-coordinate is transformed into its opposite. Then:
[tex](x,y)[/tex] → [tex](x,-y)[/tex]
So, given the new point:
[tex](-7.5, 6)[/tex]
You can determine that the original point is:
[tex](-7.5, -6)[/tex]
Simpify pls help
(x^7)^2
Answer:
x^14
Step-by-step explanation:
(x^7)^2=x^7×2
=x^14
While on a ski vacation, a group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week. The sales tax on each rental is 16%.
The group has $2,500 available to spend on ski and snowboard rentals. What is the greatest number of pairs of skis and snowboards the group can rent if the ratio of pairs of skis to snowboards is 7:3?
Answer:
The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.
Step-by-step explanation:
Given:
A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.
The sales tax on each rental is 16%.
The group has $2,500 available to spend on ski and snowboard rentals.
If the ratio of pairs of skis to snowboards is 7:3.
Now, to find the greatest number of pairs of skis and snowboards rentals.
So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]
And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]
So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:
[tex]318.50 + 330 = 648.50.[/tex]
Now, to get the rental amount after sales tax:
648.50 + 16% of $648.50.
[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]
[tex]=648.50+103.76[/tex]
[tex]=\$752.26.[/tex]
The total rental amount after sales tax = $752.26.
As the group has available $2,500.
So, the sets according to the given ratio:
[tex]2500\div 752.26 = 3.32.[/tex]
[tex]=3\ sets.[/tex]
Thus, there are 3 sets of the ratio 7:3.
So, the rental price according to sets are:
The rent of Skis:
[tex]7\times 3 = 21[/tex]
[tex]21\times 45.50= 955.50[/tex]
The rent of snowboards:
[tex]3\times 3 = 9[/tex]
[tex]9\times 110 = 990[/tex]
So. the total rental amount of skis and snowboards according to sets are:
[tex]955.50 + 990 = 1,945.50[/tex]
Now, the amount of rent after sales tax:
$1945.50 + 16% of $1945.50.
[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]
[tex]=1945.50+311.28=\$2256.78.[/tex]
Thus, the total cost = $2256.78.
Now, to get the greatest number of pairs of skis to snowboards that can be rent:
[tex]2,500 - 2,256.78 = 243.22[/tex]
The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.
Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.
Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.
any 10th grader solve it
for 50 points
Answer:
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex] is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.
Step-by-step explanation:
Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.
First term of given arithmetic progression is A
and common difference is D
ie., [tex]a_{1}=A[/tex] and common difference=D
The nth term can be written as
[tex]a_{n}=A+(n-1)D[/tex]
pth term of given arithmetic progression is a
[tex]a_{p}=A+(p-1)D=a[/tex]
qth term of given arithmetic progression is b
[tex]a_{q}=A+(q-1)D=b[/tex] and
rth term of given arithmetic progression is c
[tex]a_{r}=A+(r-1)D=c[/tex]
We have to prove that
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0[/tex]
Now to prove LHS=RHS
Now take LHS
[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)[/tex]
[tex]=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)[/tex]
[tex]=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)[/tex]
[tex]=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}[/tex]
[tex]=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}[/tex]
[tex]=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}[/tex]
[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]
[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]
[tex]\neq 0[/tex]
ie., [tex]RHS\neq 0[/tex]
Therefore [tex]LHS\neq RHS[/tex]
ie.,[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]
Hence proved
A dress costs p dollars. An 8% sales tax must be added to the cost of the dress. Martha wants to multiply the cost of the dress by 0.08 to find the tax and then add it to the cost of the dress. Esther thinks that the cost of the dress should be multiplied by 1.08. The expressions for the two methods are shown below.
Martha: p+0.08p
Esther: 1.08p
Are the two expressions equivalent? Explain.
What does this mean in terms of the methods outlined by Martha and Esther?
Answer:
Yes, both expressions for the two method are equivalent.
Step-by-step explanation:
Let the cost of the dress be p as given.
Marta want to evaluate the tax which is proportional to the cost.
8% sales tax will correspond to (8/100)*p=0.08p
Then she will add 0.08 p to p to obtain 0.08p+p= p(0.08+1)= 1.08p
On the other hand, Esther thinks that the cost of the dress, p, should be multiplied by 1.08 to obtain 1.08p at once!
Thus both expressions are equivalent. Only that Martha is wanting to pay much attention to the details , while Esther is a quick one :-)!
If f(x) = x2 + 7, what is the value of f(4)?
Answer:
18
Step-by-step explanation:
18x9/0-12.6 x 14 x 13.2 = 18
f(x)=x2+7
f(4)=4*2+7
4*2=8
8+7=15
Find an equation of the line satisfying the given conditions. Write the equation in standard form. Horizontal; through ( 3,6)
Answer:
Step-by-step explanation:
A horizontal line has the equation "y = " something, while a vertical line has the equation "x = " something. If our line is horizontal through (3, 6), it will be horizontal through the y coordinate (and vertical through the x coordinate). Our equation is y = 6
(The vertical equation through this point would be x = 3, just so you understand what I meant above.)
write two division equations for each multiplication equation.
a. 15 x 2/5=6
b. 6 x 4/3=8
c. 16 x 7/8=14
Two division equations were found for each given multiplication equation. The division equations are the inverse of the multiplication equations, essentially reversing the operation.
Explanation:The goal is to find two division equations that correspond to each given multiplication equation. Basically, we are undoing or reversing the multiplication operation.
a. 15 x 2/5 = 6
First Division Equation: 6 ÷ 15 = 2/5Second Division Equation: 6 ÷ 2/5 = 15b. 6 x 4/3 = 8
First Division Equation: 8 ÷ 6 = 4/3Second Division Equation: 8 ÷ 4/3 = 6c. 16 x 7/8 = 14
First Division Equation: 14 ÷ 16 = 7/8Second Division Equation: 14 ÷ 7/8 = 16Learn more about Division and Multiplication Equations here:https://brainly.com/question/32871453
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what is 1/3 + 3/6 =
Answer:
5/6
Step-by-step explanation:
1/3+3/6=2/6+3/6=5/6
Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday. Which sentence
could be used to find h, the number of hours remaining for Kendra to work this week?
A. 5.5 +5.25 = h + 20
B. 5.5 +5.25 = h x 20
c. h= 20 - (5.5 +5.25)
D. h-5.5+5.25 = 20. E. h= 20 - 5.5 +5.25
Answer:
Step-by-step explanation:
she works 20 hrs each week....so far, she has worked 5.25 hrs and 5.5 hrs
h = hours remaining
so we are basically taking the total hrs and subtracting the combined hrs she has worked
h = 20 - (5.5 + 5.25) <== ur equation
The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).
What is the expression?
An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Kendra works 20 hours each week. So far this week, she has worked 5.5 hours on Tuesday and 5.25 hours on Thursday.
Let h be the number of hours remaining for Kendra to work this week.
The sentence that could be used to find h, the number of hours remaining for Kendra to work this week is;
A number of hours remaining for Kendra to work this week = Total number of hours - working on Tuesday - working on Thursday.
h = 20 - 5.5 - 5.25
h = 20 - (5.5 + 5.25)
Hence, the sentence that could be used to find h, the number of hours remaining for Kendra to work this week is h = 20 - (5.5 + 5.25).
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HELPPP In the two squares shown above, m
=0.9. Which of the following is a correct statement about the two squares?
OA. There is not enough information to determine whether the squares are congruent.
OB. The squares are congruent.
OC. The squares are not congruent
Answer:
OA there is not enough information
Step-by-step explanation:
only the angles are congruent in both squares
Answer:
OA there is not enough information to determine whether the squares are congruent.
Step-by-step explanation:
If 32x+1 - 3x+5, what is the value of x?
оооо
Answer:
x = [tex]\frac{4}{35}[/tex]
Step-by-step explanation:
Given
32x + 1 = - 3x + 5 ( add 3x to both sides )
35x + 1 = 5 ( subtract 1 from both sides )
35x = 4 ( divide both sides by 35 )
x = [tex]\frac{4}{35}[/tex]
Answer:
[tex]x = \frac{ - 6}{29} [/tex]
Step-by-step explanation:
[tex]32x + 1 - 3x + 5[/tex]
Collect like terms
[tex]32x - 3x + 1 + 5[/tex]
[tex] 29x + 6[/tex]
For simplifying, equate the expression to zero. Thus,
[tex]29x + 6 = 0[/tex]
Add -6 to both sides of the equation
[tex]29x + 6 - 6 = 0 - 6[/tex]
[tex]29x = - 6[/tex]
Divide through by 29
[tex] \frac{29x}{29} = \frac{ - 6}{29} [/tex]
[tex]x = \frac{ - 6}{29} [/tex]
A movie theater sells 180 adult tickets and 60 children tickets to a movie. As part of a special promotion one ticket will be chosen at random and the winner will receive a prize. What is the probability the winner will be a child.
Answer:
25%
Step-by-step explanation:
180+60=240
60/240=0.25
0.25*100
25%
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What are the coefficients in
W - 8x + 20y + 6z
The coefficients in the expression W - 8x + 20y + 6z are -8 for x, 20 for y, and 6 for z. W is not considered a variable with a coefficient but would implicitly have a coefficient of 1.
Explanation:The coefficients in the expression W - 8x + 20y + 6z are the numerical factors that are multiplied by the variables. In this case:
The coefficient for x is -8.The coefficient for y is 20.The coefficient for z is 6.Coefficients are important as they determine the rate at which the value of the expression changes with respect to changes in the variable values.
Note that W in this expression is not preceded by a coefficient, and if it is supposed to have a coefficient, it is implicitly 1.
However, as the question does not consider W as a variable with a coefficient, we exclude it from the list of coefficients.
A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost? Verify your answer using mathematical reasoning and language.
Answer:
$162÷24=$6.75
$6.75-per each
five pairs of socks-$6.75x5=$33.75
Final answer:
To determine the cost of five pairs of socks when the coach spent $162 for 24 pairs, we find the cost per pair ($6.75) and multiply it by 5, resulting in $33.75 for five pairs.
Explanation:
The student's question is, "A soccer coach spent 162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost?" To solve this, we start by determining the cost per pair of socks. We divide the total cost by the number of pairs to get the price for each pair:
Cost per pair = Total cost / Number of pairs
= $162 / 24 pairs
= $6.75 per pair
Now, to find the cost for five pairs of socks, we multiply the cost per pair by the number of pairs desired:
Cost for five pairs = Cost per pair x 5
= $6.75 x 5
= $33.75
Therefore, five pairs of socks cost $33.75.
Fei yeng"s dog eats 8 ounces of dog food each day.Fri yen bought a 28 pound bag of dog food. How many 8 ounce serving are in a 28 pound of dog food
A triangle has sides with lengths of 8 inches 10 inches and 11 inches is it a right triangle?
Answer:
yes it is!
Step-by-step explanation:
if you add 8+10=18
11+10+21
8+11=19
if the numbers do not repeat or add up to one of the numbers you've got as an option it is a right triangle.
An ant is on the top of a tree 23 meters tall directly above her home which is 0.3meters below the ground
Using ants on a stretching ruler to illustrate Hubble's Law shows how objects further away move faster relative to an observer, much like galaxies in the universe, while highlighting the organization and communication in ant colonies.
Explanation:The scenario described involves ants on various points of a stretchable ruler, illustrating a concept similar to Hubble's Law in cosmology. One ant measures how the distance to the other ants increases as the ruler stretches, showing that ants further away appear to move faster relative to the observing ant. This phenomenon occurs not because the ants are moving of their own volition, but because the ruler itself is stretching, much like space-time expands in the universe.
Furthermore, ants in a colony communicate using pheromones, and their large groups, called colonies, are highly organized with different roles such as workers, soldiers, and a queen. The example of ants traveling on a ruler and cooperating in a colony also demonstrates principles of coordination, communication, and perception from a relative standpoint.
Lie is rolling a random number cube. The cube had six sides, and each side is labeled with a different number 1 through 6. What is the probability that he will roll a 5 and then a 3 in two rolls?
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
We will find the probability of rolling a 5 and then probability of rolling a 3 and then multiply the numbers to get the probability that he will roll a 5 and then a 3 in two rolls.
There are 6 total possibilities (1 through 6).
There are one 5s, so the probability of rolling a 5 would be:
P(roll 5) = 1/6
Also, there is one 3, so rolling a 3 would have the same probability.
P(roll 3) = 1/6
Hence,
Probability of rolling a 5 and then a 3 is:
P(5,3) = 1/6 * 1/6 = 1/36
How many 1 4 cup servings are in 3 8 cups of pudding? (in simplest fraction form) A) 1 6 B) 2 3 C) 3 2 D) 3 8
Answer: is c 3/2
Step-by-step explanation:
The answer is option C) 3/2.
To find out how many 1/4 cup servings are in 3/8 cups of pudding, we can use the formula:
First, let's convert 3 8/10 cups to an improper fraction.
To do this, we multiply the whole number (3) by the denominator (10) and add the numerator (8) to get the numerator of the improper fraction. The denominator remains the same.
(3/8) ÷ (1/4) = (3/8) × (4/1) = 12/8 = 3/2
Therefore, there are 3/2 or 1 1/2 servings of 1/4 cup in 3/8 cups of pudding.
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A circle with a radius of 9cm sits inside of a circle with a radius of 11cm. What is the area of the shaded region? Round your answer to the nearest hundredth. PLEASE HELP DUE TOMORROW
Answer:
[tex]A=125.66\ cm^2[/tex]
Step-by-step explanation:
The complete question is
The area of the shaded region is the area inside the larger circle and outside the smaller circle
so
To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle
Remember that
The area of the circle is
[tex]A=\pi r^{2}[/tex]
therefore
The area of the shaded region is
[tex]A=\pi [r_1^2-r_2^2][/tex]
where
[tex]r_1=11\ cm[/tex] ---> radius of the larger circle
[tex]r_2=9\ cm[/tex] ---> radius of the smaller circle
assume
[tex]\pi =3.1416[/tex]
substitute
[tex]A=3.1416 [11^2-9^2][/tex]
[tex]A=3.1416 [40][/tex]
[tex]A=125.66\ cm^2[/tex]
Please answer if you know the solution. Thx
Answer:
the first blank is 10
and the second blank is 5
Step-by-step explanation:
plz help me out asap
Answer:
Table C represents an exponential function.
sara can run 49 yards in 7 seconds. At that rate, how many feet can she run in 3 minutes?
Answer:
3780 feet
Step-by-step explanation:
49/7*60*3(be careful that it is 3 minutes,not seconds)
=1260
Now,we have to convert yards into feet.
1260 yards = 3780 feet
Because feet is three times yard.
Hope this answer helps! ;)
Answer:
Distance ran by Sara in 3 minutes is 3780 feet.
Step-by-step explanation:
We know that,
1 yard = 3 feet
So, 49 yards = 49 × 3 feet = 147 feet
Now, it is given that Sara can run 49 yards in 7 seconds. So, we can say that, Sara can run 147 feet in 7 seconds
So, distance ran by Sara in 7 seconds = 49 yards = 147 feet
Now, distance ran by Sara in 1 second = (147 ÷ 7) feet = 21 feet
Now, 1 min = 60 sec, then 3 min = 3 × 60 sec = 180 sec
So, distance ran by Sara in 3 min or 180 sec = 21 × 180 = 3780 feet
∴ distance ran by Sara in 3 minutes is 3780 feet.
What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m?
[A] 8π m³
[B] 16π m³
[C] 64π m³
[D] 256π m³
Answer:
C. 64 pie m^3
Answer: 64[tex]\pi[/tex][tex]m^{3}[/tex]
Step-by-step explanation:
The volume of cylinder is given as
V = [tex]\pi[/tex][tex]r^{2}[/tex]h
r = 4m
h = 4m
Substituting into the formula , we have
V = [tex]\pi[/tex] x [tex]4^{2}[/tex] x 4
V = [tex]\pi[/tex] x 16 x 4
V = [tex]\pi[/tex] x 64
Therefore : V = 64[tex]\pi[/tex][tex]m^{3}[/tex]
Complete the recursive formula of the arithmetic sequence
a(1) =
a(n)= a(n-1)+
Answer:
The recursive formula of the arithmetic sequence
[tex]a_{1}=First term of the arithmetic sequence[/tex]
[tex]a_{n}= a_{n-1}+common difference(d)[/tex].
Step-by-step explanation:
A recursive formula is used to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference.
To find the recursive formula of the arithmetic sequence
[tex]a_{1}=First term of the arithmetic sequence[/tex]
[tex]a_{n}= a_{n-1}+common difference(d)[/tex]
What are the x- and y-coordinates of point P on the
directed line segment from A to B such that Pis the
length of the line segment from A to B?
(2, -1)
(4, -3)
(-1,2)
(3,-2)
Answer:
answer b
Step-by-step explanation:
The coordinates of p are (3, -2). Option D is correct.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
From the graph, the coordinates of A = (9,-8) and the coordinates of B =(-6, 7) p divides the line segmentin 2/3 thus,
We can use the section formula to find the coordinates of the point P that divides the line segment AB into the ratio 2:3.
The section formula states that if a line segment AB is divided by a point P into two line segments, with lengths in the ratio m:n, then the coordinates of P are:
[tex][Px = (nA_x + mB_x)/(m+n), \\Py = (nA_y + mB_y)/(m+n)][/tex]
In this case, we want to divide the line segment AB into the ratio 2:3, so we have m:n = 2:3. This means that m = 2 and n = 3.
Substituting the given values, we get:
[tex]P_x = (3*9 + 2(-6))/(2+3) = 3\\Py = (3*(-8) + 2*7)/(2+3) = -2[/tex]
Therefore, the coordinates of P are (3, -2).
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The equation a company uses to
calculate pay checks is p = 12h +0.25s
where h is the number of hours worked
and s is total sales. What is the equation
solved for s?
The equation solved for s is s = 4p - 48h
Solution:
Given that equation a company uses to calculate pay checks is p = 12h +0.25s
Therefore the given equation is:
p = 12h + 0.25s
Where "h" is the number of hours worked
"s" is the total sales
To find: equation for "s"
Let us solve the given equation for "s"
p = 12h + 0.25s
Now move 12h from R.H.S to L.H.S
p - 12h = 0.25s
Now move from 0.25 from R.H.S to L.H.S
[tex]s = \frac{p-12h}{0.25}\\\\s = \frac{p}{0.25} -\frac{12h}{0.25}[/tex]
We know that, [tex]0.25 = \frac{1}{4}[/tex]
[tex]s = \frac{p}{\frac{1}{4}} -\frac{12h}{\frac{1}{4}}\\\\s = p \times \frac{4}{1} - 12h \times \frac{4}{1}\\\\s = 4p - 48h[/tex]
Thus the equation for s is s = 4p - 48h
Solve equation by completing the square round to the nearest hundredth if necessary
X2-4x-=5
Answer:
x=-1 and x=5
Step-by-step explanation:
we have
[tex]x^{2} -4x=5[/tex]
Solve it by completing the square method
We take the coefficient of x that is -4, divide it by 2 and then square it
so
[tex]-\frac{4}{2}=-2[/tex]
square it
[tex](-2)^2 = 4[/tex]
Adds 4 both sides
[tex]x^{2} -4x+4=5+4[/tex]
Combine like terms right side
[tex]x^{2} -4x+4=9[/tex]
Rewrite as perfect squares
[tex](x-2)^{2}=9[/tex]
take square root both sides
[tex]x-2=\pm3[/tex]
[tex]x=2\pm3[/tex]
therefore
[tex]x=2+3=5[/tex]
[tex]x=2-3=-1[/tex]