Answer:
Step-by-step explanation:
3p. = 2m - 5q
-2m. = -3p - 5q
Divide through by -2
m. = (3p + 5q) \2
The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.
Given equation 3p = 2m - 5q
3p + 5q = 2m
(3p + 5q) / 2 =m
Hence, m = (3p+5q) / 2
To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.
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5(x+2)-3(x-2)+7x
PLEASE HELP ME RMS IS KILLING ME HOLY COW
Answer:
9x + 16
Step-by-step explanation:
Let's simplify step-by-step.
5(x+2)−3(x−2)+7x
Distribute:
=(5)(x)+(5)(2)+(−3)(x)+(−3)(−2)+7x
=5x+10+−3x+6+7x
Combine Like Terms:
=5x+10+−3x+6+7x
=(5x+−3x+7x)+(10+6)
=9x+16
Please give me brainiest!
olumide plays the piano and guitar.for every 5 min of piano practice,he spends 8 min practicing guitar.how many minutes will olumide practice piano if he spends 64 minutes practicing guitar?
Answer:
Olumide will practice 40 minutes of playing the piano
Step-by-step explanation:
Olumide practices piano and guitar in the ratio of 5:8
64 minutes of guitar playing means that Olumide has had 8 individual practicing sessions of guitar (64 / 8 = 8), so he has also had 8 practicing sessions of piano.
5 x 8 = 40 minutes of piano practice
10. A life insurance company found that
among its last 200 claims, there were six
dozen smokers. What is the ratio of smokers
to nonsmokers in this group of claimants?
Write in lowest terms.
for homework .
if a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 17 feet, what angle does the ramp make with the ground? round to 2 decimal places.
The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
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A triangle with two sides that measure 5 cm and
8 cm with an included angle of 39º.
Answer:
the other 2 sides equal 70.5 ...but I am not for sure because you did not give me enough information (like a picture)
20-foot extension ladder set base six feet from house How far up will ladder reach?
The top of the 20-foot ladder used for painting will be 19 feet up from the base of the house
How to determine how high up the house the ladder will goinformation given in the question
Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder
he sets the base of the ladder six feet from the house
adjacent = 6 feet from the house
opposite = how far up will the top of the ladder reach = ?
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = adjacent² + opposite²
substituting the values into the equation
let x be thow far up will the top of the ladder reach
20² = 6² + x²
400 = 36 + x²
400 - 36 = x²
x² = 364
x = √364
x = 19.08
The ladder Brain borrowed will go 19 feet high
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complete question
Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?
after euclid high school's last basketball game, it was determined that 1/4 of the team's points were scored by alexa and 2/7 were scored by brittany. chelsea scored 15 points. none of the other 7 team members scored more than 2 points. what was the total number of points scored by the other 7 team members?
The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.
What is defined as the term two variable equation?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers as well as the coefficients of x and y, i.e., a and b, respectively, really aren't equal to zero, then it is said to be a linear function in two variables.For the given question.
Let 't' be the total points scored.
Alexa = 1/4 t.
Brittany = 2/7 t
Chelsea = 15
Let 'x' be the points scored by remaining 7 team.
Thus, the two variable equation becomes.
1/4 t + 2/7 t + 15 + x = t .....eq 1
Where, x ≤ 14 ( for 7 terams)
Simplifying eq 1.
15 + x = 13/ 28 t
28x + 28 = 13 t
Now, t must be divisible by 28.
Let t = 28 u, u ≥ 0 and divisible by 28.
Thus,
x + 15 = 13u.
Then, u = 2( t = 56) has been the only candidates for which x = 11.
Thus, the total number of points scored by the other 7 team members is 11.
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
can 2 parabolas have the same vertex but different directions of opening?
Answer:
Step-by-step explanation:
Yes, of course!
A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!
how do u solve these simultaneous equations
y=3x+5
y=4x^2+x
The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).
What is the solution to the simultaneous equations?It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.
Given: y = 3x + 5 and y = 4x² + x.
Therefore, since y = y; it follows that the equation which holds true is;
3x + 5 = 4x² + x
4x² - 2x - 5 = 0.
Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;
x = 1.4 OR x = -0.9.
Therefore, the corresponding values of y are;
y = 3(1.4) + 5 = 9.2
OR
y = 3(-0.9) + 5 = 2.3
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1: A is directly proportional to B.
When A = 12, B = 3
Direc
(a) Find a formula for A in terms of B.
(b) Find the value of A when B = 5
(c) Find the value of B when A= 36
Answer:
a)A=4B
b)A=20
c)B=9
If it is directly proportional it means that A=kB.
you can substitute the numbers to find k.
12=k3
k=4
so the formula is A=kB.
For part b and c it is just substitution
Please help, I am timed and I have no clue what to do here!
Answer:
Step-by-step explanation:
Re-order terms so constants are on the left
Then divide both sides by the same factor its -2
then Simplify answer is 1
$12000 into an investment account for 5 years. The investment earns 6% interest per
annum, compounding quarterly.
What is the interest rate per quarter?
Answer:
We may use the logarithm formula,
N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.
EV is end value, SV is start value.
EV is 20000, SV is 12000, interest is 5.6% semi annual
(1+r) is obtained as,
Step-by-step explanation:
3409.1 in exponential form
3409.1 In exponential form is 3.4091 * 10^3
What is exponential form?Writing a number in exponential form is a way of writing numbers using base and exponents
Scientific notations is among the ways numbers appears in exponential forms
using scientific notation we have
= 3409.1
converting to fractions
= 34091 / 10
applying the scientific notation
= 3.4091 / 10 * 10000
eliminating the fraction by dividing by 10
= 3.4091 * 1000
applying exponential notation
= 3.4091 * 10^3
rewriting gives
= 3.4091 E+3
In scientific notation 10^3 is E+3 and it is called kilo and can be represented as k
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determine whether the lines are parallel, intersect, coincide y = x-7, y = -x + 3
The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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a hamburger regularly cost $6.00 each additional topping cost $0.59. on Monday the cost of hamburger only is half off
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A burger consistently cost $6.00 each extra fixing cost $0.59.
Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,
c = 0.59t + 6
On Monday the expense of the burger just is half off. Then the equation is given as,
c = 0.50(0.59t + 6)
c = 0.295t + 3
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
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an ant walks along a straight path. After traveling for 1 meter it stops, turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a distance of half a meter. Again, the ant turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a quarter of a meter. The ant continues in this manner indefinitely.
a) How many turns will the ant have made after covering a distance of 63/32 meters?
b)How far will the ant "eventually" travel?
The description of the motion of the ant which is a geometric series is as follows;
a) After covering 63/32 meters, the ant will have made 6 turns
b) The distance the ant will eventually travel is 2 meters
What is a geometric series?Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.
The distances traveled by the ant is a geometric progression of the form;
aₙ = a·rⁿ⁻¹The sum of the distance is given by the sum of the geometric progression as follow;
[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]
Where;
aₙ = The distance traveled in the nth turn
Sₙ = The sum of the distances
a = The first term = 1 meter
r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5
a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;
[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]
31.5 = 32 × (1 - 0.5ⁿ)
32 × 0.5ⁿ = 32 - 31.5 = 0.5
0.5ⁿ = 0.5 ÷ 32
n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6
After covering a distance of 63/62 meters, the ant will have made 6 turnsb) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;
[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]
Which gives;
[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]
The distance the ant eventually travels is 2 meters
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Multiply (0.000302)(1000)
Answer:
0.302
Step-by-step explanation:
Answer: 0.302
Step-by-step explanation:
48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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ksiodhhhwdaaaaaaaaaaoidjooaaaaaaaaaaaaaaaaaaa
Answer:
vyfyxfrr6c*"8&"; hxh6 byhd,tf7zg5gzyfe55eE4E45w522
Step-by-step explanation:
6dyxg9yyfz6t bztrfr 4.Sabina the tortoise is an 56,123 way of Policy for recharge of the angles and tricks of Policy in order for me and I have a wonderful experience and a
1. A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree.
a. If there are 8 appetizers and 11 entrees, how many different Special Dinners
are there?
b. If there are 12 appetizers and 7 entrees, how many different Special Dinners
are there?
a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
Given that,
In a typical Chinese restaurant, the Special Dinner is frequently offered, allowing the customer to select one appetizer and one entrée.
We have to find
a) How many unique special dinners are there if there are 8 appetizers and 11 entrees.
b) How many unique special dinners are there if there are 12 appetizers and 7 entrees.
We solve
a) We just multiply
8×11=88
b) 12×7=84
Therefore, a) 88 unique special dinners are there if there are 8 appetizers and 11 entrees.
b) 84 unique special dinners are there if there are 12 appetizers and 7 entrees.
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Round to the nearest hundredth. 44.242
Answer:
44.24
Step-by-step explanation:
The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5
Answer:
44.24
Step-by-step explanation:
hopes this helps please mark brainliest
find the intervals of increase and decrease of 3/512(x-4)^2(x-8)(x-10)(x^2+16)
The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval (4, −∞).
What is an increasing and decreasing functions?
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
We have,
[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]
[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 4, 4i, −4i, 10, 8
∴ f′(x) = 0
x = 4,
Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)
In interval (−∞, 4), f′(x) < 0
Hence, the given function (f) is strictly decreasing in interval (−∞, 4)
In interval (4, −∞), f′(x) > 0
Hence, the given function (f) is strictly increasing in interval (4, −∞)
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Find the highest common factor (HCF) of 72 and 90
Answer:
Step-by-step explanation:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
The six frequent factors between 72 and 90 are 1, 2, 3, 6, 9, and 18.
Consequently, 18 is the number that links 72 and 90 most frequently.
What is the answer to this problem?
Answer:
$22,000 at 5%, $10,000 at 11%
Step-by-step explanation:
Let x be the amount invested at 5%.
[tex].05x = .11(32000 - x)[/tex]
[tex].05x = 3520 - .11x[/tex]
[tex].16x = 3520[/tex]
[tex]x = 22000[/tex]
$22,000 at 5%, $10,000 at 11%
Please help me with this question
Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86
Let d represent:
I do not drink bottled water.
Lett represent:
I eat pizza.
What is the symbolic representation of the following statement?
I do not eat pizza or I do not drink bottled water
I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.
What is meant by symbolic representation?Traditionally, symbolic representation is defined as the representation of a principal, such as a nation, through a symbol, such as a flag, that evokes specific meanings and emotions about the nation. The use of physical or psychological processes to represent an object (either another object or an idea) in a symbolic form is referred to as symbolic representation (Carlson, Sroufe, & Egeland, 2004). A written character or mark that is used to represent something; a letter, figure, or sign that is traditionally used to represent some object, process, etc. (Oxford English Dictionary). Figures denoting the planets, signs of the zodiac, and so on are examples of something visible that represents something else that is invisible by association or convention. Synonyms include symbol, symbolization, and symbolization.To learn more about symbolic representation, refer to:
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a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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Tim and Jessica plan to rent a camper van for a vacation. The van costs $183 per day.
The rental includes 120 miles for free and then charges $0.39 per mile.
The total price Tim and Jessica paid to rent the camper van is $598.74. Write an
equation that models the cost of the van rental in terms of miles traveled, m.
Create an equation
The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .
What is the equation that represents the cost?The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
The general form of linear equations is: y = a + bx
Where:
a = intercept
b = slope
The form of the equation that models the cost is:
Total cost = cost of renting the van + [cost per mile x (m - 120 miles)
$598.74 = $183 + [$0.39 x (m - 120)
$598.74 = $183 + $0.39m - 46.80
$598.74 = 136.20 + $0.39m
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