Let the initial savings at first be = x
Given ratio is [tex]\frac{5}{4}[/tex] and after donating $40 to charity, the ratio becomes [tex]\frac{13}{10}[/tex]
Hence, the relation becomes:
[tex]\frac{5x-40}{4x-40}=\frac{13}{10}[/tex]
[tex]10(5x-40)=13(4x-40)[/tex]
= [tex]50x-400=52x-520[/tex]
[tex]-2x=-120[/tex] or
[tex]2x=120[/tex]
[tex]x=60[/tex]
So , Dave's saving at first was 5x = 5*60 = $300
and Sam's saving at first was 4x = 4*60= $240
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
Answer:
8x + 10y = $830
Step-by-step explanation:
8x + 10y = total revenue
if the total revenue is 830 then you can equate the above formula to 830 to give
8x + 10y = $830
Answer:
The required equation is [tex]8x+10y = 830[/tex].
Step-by-step explanation:
Consider the provided information.
As it is given that variable x represents the number of cars that paid to park and variable y represents the number of trucks that paid to park.
The cost of parking a car is $8 per day, the expression to represent the cost of parking x cars per day is 8x.
The cost of parking a truck $10 per day, the expression to represent the cost of parking y trucks per day is 10y.
The total revenue for the day was $830.
Thus, the equation represent the number of cars and trucks that paid to park that day is:
[tex]8x+10y = 830[/tex]
Hence, the required equation is [tex]8x+10y = 830[/tex].
Jerome finds that (3x6) ÷ 2 and 18÷2 are equal explain why this is true
Answer:
because 3x6=18 so it will be the same problem
Step-by-step explanation:
If lines joined each given point on the graph to the origin, which points would be on lines that represent a unit rate greater than the one represented in the table?
Answer:
The first three, (2, 8), (3, 9) and (4, 10).
Step-by-step explanation:
The unit rate, or rate of change, is another term for the slope.
The formula for slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
The slope in the table would be given by
m = (22-11)/(10-5) = 11/5 = 2.2.
For the slope of the line that goes through (2, 8) and (0, 0), we have
m = (8-0)/(2-0) = 8/2 = 4. This is greater than 2.2.
For the slope of the line that goes through (3, 9) and (0, 0), we have
m = (9-0)/(3-0) = 9/3 = 3. This is greater than 2.2.
For the slope of the line that goes through (4, 10) and (0, 0), we have
m = (10-0)/(4-0)/ = 10/4 = 2.5. This is greater than 2.2.
For the slope of the line that goes through (5, 8) and (0, 0), we have
m = (8-0)/(5-0) = 8/5 = 1.6. This is not greater than 2.2.
For the slope of the line that goes through (6, 7) and (0, 0), we have
m = (7-0)/(6-0) = 7/6 = 1.16. this is not greater than 2.2.
For the slope of the line that goes through (7, 6) and (0, 0), we have
m = (6-0)/(7-0) = 6/7 = 0.86. This is not greater than 2.2.
which ecpression is equivalent to sqrt 8x^7y^8?
[tex]Domain:\ x\geq0\ \wedge\ y\in\mathbb{R}[/tex]
[tex]\sqrt{8x^7y^8}=\sqrt8\cdot\sqrt{x^7}\cdot\sqrt{y^8}=\sqrt{4\cdot2}\cdot\sqrt{x^6\cdot x}\cdot\sqrt{y^{4\cdot2}}\\\\=\sqrt4\cdot\sqrt2\cdot\sqrt{x^6}\cdot\sqrt{x}\cdot\sqrt{(y^4)^2}=2\sqrt2\cdot\sqrt{x^{3\cdot2}}\cdot\sqrt{x}\cdot y^4\\\\=2y^4\sqrt2\cdot\sqrt{(x^3)^2}\cdot\sqrt{x}=2y^4\sqrt{2x}\cdot x^3\\\\=\boxed{2x^3y^4\sqrt{2x}}[/tex]
[tex]Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]
Answer:
c is correct
Step-by-step explanation:
edge 2020
Please factorise these using identies
7. (x-7)(x-7)
8. (3x-5y)(3x-5y)
9. (x-15)(x+3)
10.(7m+6n)(7m+6n)
11. (2x+1)(2x+1)
12. (7x+2)(7x+2)
13. (p-18)(p+4)
Notice how 7,8,10,11, and 12 are all perfect squares. A good way to tell if a trinomial can be factored into a perfect square is if the square root of the coefficient of your variable multiplied by the square root of the constant (number with no variable) multiplied by 2 equals the middle term's coefficient.
For example, take 4x^2+16x+16. Taking the square root of 4 gives us 2. Taking the square root of 16 gives us 4. So, 2*2*4=16, which is our middle term, thus proving that this trinomial is indeed a perfect square.
Evaluate 3/2+(-k)+(-2) where k is -5/2
Answer:
2
Step-by-step explanation:
3/2 + (-k) + (-2) =
= 3/2 + [-(-5/2)] - 2
= 3/2 + 5/2 - 2
= 8/2 - 2
= 4 - 2
= 2
If it is 40 degrees Celsius, what is the temperature in Fahrenheit?
A. 40 degrees
B. 104 degrees
C. 54 degrees
D. 102 degrees
Answer:
104 = B
Step-by-step explanation:
A quick way to do this is to use this formula
F = 2*C + 30C = 40F = 2*40 + 30 F = 80 + 30F = 110Since this is an estimate, you are only guided to whether your answer is correct or not. Here's the actual formula
F = (9/5) * 40 + 32F = 360/5 + 32F = 72 + 32F = 104Write an exponential function to model the situation.A population of 300 animals decreased at an annual rate of 22%
Answer:
[tex] y = 300(0.78)^x [/tex]
Step-by-step explanation:
x is the number of years. y is the population after x years.
Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.
year zero: y = 300
year 1: y = 300 * 0.78 = 300 * (0.78)^1
year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2
year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3
year x: y = 300(0.78)^x
Margarito opened a savings account with a $500 deposit and a simple interest rate of 5.6%. If there were no deposits or withdrawals, how much total money is in the account after 8 ½ years ?
Hey there!
Simple interest is based on only the original deposit of money, which in this case is $500.
To find 5.6% of 500, we can multiply it by the decimal that represents that part of a whole: 0.056.
[tex]500 \times 0.056 = 28[/tex]
The question asks for how much money is in the account after 8 1/2 years. This means we multiply the interest for 1 year (28) by 8 1/2.
[tex]28 \times 8.5 = 238[/tex]
Lastly, we add the interest to the original deposit.
[tex]500 + 238 = 738[/tex]
The answer is $738.
Hope this helps!
Marco wants to save his money to buy a new computer for school. He has $300 in his bank account. Marco has a part-time job that pays $75 per week. He plans to put all the money he earns each week into his bank account. Which of the following functions accurately models the amount of money Marco will have saved after x weeks?
Probability On a nearby pond, black and white ducks are swimming in groups of three. Use the table to find the experimental probability of two white ducks and one black duck swimming together. Tails up represents white ducks and heads up represents black ducks.
Answer:
There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trial
Step-by-step explanation:
Answer:
7/20
Step-by-step explanation:
I came across the question
-11 , -15, -19 is an arithmetic sequence
Find the nth term of the sequence
Answer:-47
Step-by-step explanation:
1# 11+4=15
2# 15+4=19
3# 19+4=23
4# 23+4=27
5# 27+4=31
6# 31+4=35
7# 35+4=39
8# 39+4=43
9# 43+4=47
REMEBER its negative not positive.
Is this relation a function?why or why not?[(-5,7),(-2,1),(0,3),(4,7)]
Answer:
No, every relation is not a function.
Step-by-step explanation:
Every function is a relation because there are two points (x,y) somehow related to each other.
But every relation is not a function
The given ordered pairs are the function
Since, we are getting different value of y for ecah x.
The condition for function is we should get different value of y for each x.
A sprinter can run 120 meters in 10 seconds. what is his average speed
Answer:
12 Meters Per Second
Step-by-step explanation:
Average Speed = Distance divided by time
Average Speed = 120 Meters / 10 Seconds
Average Speed = 12 Meters Per Second
if sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.
What is Speed?Speed is defined as the rate of change of position of an object in any direction
Given that A sprinter can run 120 meters in 10 seconds.
Average Speed = Distance divided by time
Speed = Distance/ Time
The distance is 120 meters and times is 10 seconds.
Speed=120/10
=12 meters per second
Hence, if sprinter can run 120 meters in 10 seconds then 12 meters per second is the average speed.
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Let $x$ be a value such that $8x^2 + 7x - 1 = 0$ and $24x^2+53x-7 = 0.$ What is the value of $x$? Express your answer as a simplified common fraction.
[tex]8x^2+7x-1=0\ \wedge\ 24x^2+53x-7=0\\\\\text{The equation:}\\\\24x^2+53x-7=8x^2+7x-1\qquad\text{subtract}\ 8x^2\ \text{and}\ 7x\ \text{from both sides}\\\\16x^2+46x-7=-1\qquad\text{add 1 to both sides}\\\\16x^2+46x-6=0\qquad\text{divide both sides by 2}\\\\8x^2+23x-3=0\\\\8x^2+24x-x-3=0\\\\8x(x+3)-1(x+3)=0\\\\(x+3)(8x-1)=0\iff x+3=0\ \vee\ 8x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\8x-1=0\qquad\text{add 1 to both sides}\\8x=1\qquad\text{divide both sides by 8}\\\boxed{x=\dfrac{1}{8}}[/tex]
The values for x in the given equations, 8x^2 + 7x - 1 = 0 and 24x^2 + 53x - 7 = 0 are x = 1/4, x = -1/2, x = 1/8, and x = -7/6 respectively when the quadratic formula is applied.
Explanation:To find the value of x for each equation, you will need to use the quadratic formula (x = [-b ± sqrt(b^2 - 4ac)] / (2a)). The quadratic formula is used in algebra to solve quadratic equations (polynomials of degree 2). The formula provides solutions for the variable x in terms of the coefficients of the equation, denoted as a, b, and c.
For the first equation, 8x^2 + 7x - 1 = 0, a = 8, b = 7, and c = -1. Plugging these values into the quadratic formula, the solutions come out to be x = 1/4 or x = -1/2.
Similarly, for the second equation, 24x^2 + 53x - 7 = 0, a = 24, b = 53, and c = -7. The solutions for x in this case come out to be x = 1/8 or x = -7/6.
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Find the midpoint and distance on a number line between 6, -15
The midpoint between the numbers 6 and -15 on a number line is -4.5. The distance between 6 and -15 on the number line is 21.
Explanation:The midpoint on a number line between two points is found by adding the two points together and then dividing by 2. So, for points 6 and -15, the midpoint would be (6-15)/2 = -9/2 = -4.5. This means the midpoint between 6 and -15 on the number line is -4.5.
The distance between two points on a number line is found by subtracting the smaller number from the larger number and taking the absolute value. So, the distance between 6 and -15 is |6 - (-15)| = |-9| = 21. Therefore, the distance between 6 and -15 on the number line is 21.
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Help me find the value of h please
Answer:
-2
Step-by-step explanation:
Answer:
h = 1
Step-by-step explanation:
If in a function, you replace x with x - h, you translate the function horizontally h units. The black function is f(x) = |x|. The blue function is the black function translated 1 unit to the right. That means h is 1.
Black function: f(x) = |x|
Blue function: f(x) = |x - 1|
h = 1
The perimeter of a rectangle is 276 centimeter. It's length is 5 times its width find it dimension
Answer:
A) 2 * Length + 2 * Width = 276
B) L = 5W then multiplying equation B) by -2 we get
-2L +10W = 0 then we add this to A)
A) 2L + 2W = 276 and get
12W = 276
Width = 23
Length = 115
Step-by-step explanation:
The value of y is directly proportional to the value of x. If y = 288 when x = 32. What is the value of y when x = 25?
Algebra 1
Answer:
y = 225
Step-by-step explanation:
since y and x are directly proportional the equation relating them is
y = kx ← k is the constant of proportionality
to find k use the given condition y = 288 when x = 32
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{288}{32}[/tex] = 9
y = 9x ← is the equation of proportionality
when x = 25, then
y = 9 × 25 = 225
What are the intercepts to graph the equation -4x - 3y = 36?
Answer:
The x intercept = -9
The y intercept = -12
Step-by-step explanation:
To find the x intercept, set y = 0 and solve for x
-4x - 3y = 36
-4x -0 = 36
Divide by -4
-4x/-4 = 36/-4
x = -9
The x intercept = -9
To find the y intercept, set x = 0 and solve for y
-4x - 3y = 36
0 -3y = 36
Divide by -3
-3y/-3 = 36/-3
x = -12
The y intercept = -12
Answer:
x = -9
y = -12
Step-by-step explanation: Substitute 0 for x & y to get your points.
-4x - 3y = 36
-4(0) - 3y = 36
0 - 3y = 36
-3y = 36
-3y -3y
y = -12
-4x - 3y = 36
-4x - 3(0) = 36
-4x - 0 = 36
-4x = 36
-4 -4
x = -9
Remember, a negative divided by a positive is a negativeAnything times 0, is the number itself. Like for example, 0 times 46 = the number itself, which is 46.Hope this helps you!!! :)
Jerry hears 5 case ever 2 3/8 hours Jerry hears a constant rate how many case does Jerry hear per hour
Answer:
The rate of cases is [tex]\frac{40}{19}[/tex] per hour
Step-by-step explanation:
we are given
Total number of cases =5
total time is
[tex]=2\frac{3}{8}[/tex] hour
we can simplify it
total time is
[tex]=\frac{2\times 8+3}{8}[/tex] hour
[tex]=\frac{19}{8}[/tex] hour
we can use formula
rate of cases = ( total number of cases)/( total time)
now, we can plug values
Rate of cases is
[tex]=\frac{5}{\frac{19}{8} }[/tex]
[tex]=\frac{40}{19}[/tex]
Answer: -Jerry hears [tex]2\frac{2}{19}[/tex] per hour.
Step-by-step explanation:
Since time is given in mixed fraction [tex]2\frac{3}{8}[/tex] , thus first convert it into improper fraction
Time=[tex]\frac{19}{8}[/tex] hours
The total number of cases Jerry hears in =5 cases
⇒The number of cases Jerry hears in 1 hour
[tex]=\frac{5}{\frac{19}{8}}\\\\=\frac{5\times8}{19}\\\\=\frac{40}{19}=2\frac{2}{19}[/tex] cases per hour.
Thus, Jerry hears [tex]2\frac{2}{19}[/tex] cases per hour .
25 Points!!! Help plzz!! Will give Brainliest!!!
Answer:
Option C : ASA
Step-by-step explanation:
Side WS Lies between ∠W and ∠S
Side NT lies between ∠N and ∠T
Hence the theorem which supports the congruency of the two triangles
is ASA
Angle - Side - Angle
what is the area if a regular hexagon if the distance from a midpoint of a side to the midpoint of the opposite side is 10
Answer:
50√3 or 86.6
Step-by-step explanation:
Divide the hexagon into six equilateral triangles as in Figure 1 below.
Then draw a line from the midpoint of one side to the midpoint of the opposite side.
The height (h) of each triangle will be 5.
To find the area of the whole triangle, we first need to find the length of the base (see Figure 2).
If the base length (b) is 2s, we have the relation
5/s = tan60°
5/s = √3 Multiply each side by s
5 = s√3 Divide each side by √3
s = 5/√3 Rationalize
s = (5√3)/3
b = 2s
b = (10√3)/3
The area (A) of the triangle is
A = ½bh
A = ½ × (10√3)/3 × 5
A = (25√3)/3
There are six equilateral triangles in the hexagon, so
Total area = 6A
Total area = 6 × (25√3)/3
Total area = 50√3
Total area ≈ 86.6
Provide an example of an integer that is not a whole number
Answer:
-5
Step-by-step explanation:
The integers are ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers. All whole numbers are integers (and all natural numbers are integers), but not all integers are whole numbers or natural numbers. For example, -5 is an integer but not a whole number or a natural number.
An example of an integer that is not a whole number is -1, as whole numbers are non-negative and -1 is negative.
The set of integers includes all the positive whole numbers, zero, and their opposites, which are the negative whole numbers. Whole numbers are defined as non-negative integers (0, 1, 2, 3, ...). Therefore, any negative integer like -1, -2, -3, and so forth, while being an integer, is not considered a whole number.
Cal es el volumen de un cono que tiene una altura 10 pulgadas y un radio de 6 pulgadas
Answer:
≈ 376.99 pulgadas
Step-by-step explanation:
El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.
La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener El volumen de un cono con una altura de 10 pulgadas y un radio de 6 pulgadas es de aproximadamente 376.99 pulgadas en cubos.
La fórmula para el volumen de un cono es π (r ^ 2) (h / 3). Puedes sustituir r con 6 yh con 10 para obtener aproximadamente 376.99
Find the missing side Lengths (70 POINTS!)
Answer:
The sides are as follows: [tex]x=18,\,\,\,y=9\sqrt{3}[/tex]
Step-by-step explanation:
Starting with the side y, we can use the tan to solve for y:
[tex]\tan 30^\circ = \frac{9}{y}\implies y = \frac{9}{\tan 30^\circ}={9}\sqrt{3}[/tex]
The side x can be determined using sin:
[tex]\sin 30^\circ = \frac{9}{x}\implies x = \frac{9}{\sin 30^\circ}= 18[/tex]
So, the sides as as follows: [tex]x=18,\,\,\,y=9\sqrt{3}[/tex]
(you can also verify this result is correct using the Pythagorean theorem)
Answer:
x=18
y=[tex]\sqrt 18[/tex]
Step-by-step explanation:
Evaluate the following without using the calculator
[tex] \cos(30) \sin( \frac{\pi}{4} ) + \frac{ \sec(60) }{3} [/tex]
[tex]\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}[/tex]
A school district transported a total of 409 students and teachers to a zoo in buses and vans.
-Each bus transported a total of 55 students and teachers.
-Each van transported a total of 12 students and teachers.
-There were 5 more buses than vans.
What is the total number of students and teachers who rode to the zoo in buses? What is the total number of students and teachers who rode to the zoo in vans?
Answer:
Step-by-step explanation:
Let x be the number of buses and y be the number of vans.
We know that there are 5 more buses than vans, therefore, we can set up:
[tex]x=y+5[/tex]
Since a bus transports 55 people and a van transports 12 people, therefore, we can set up:
[tex]55x+12y = 409\\[/tex]
Now lets solve the above two equations together by substitution
[tex]55(y+5)+12y = 409\\\\55y+275+12y=409\\\\67y+275=409\\\\67y=409-275\\\\67y=134\\\\y=2,x=2+5=7[/tex]
Total number of students and teachers who rode to the zoo in buses[tex]=55*7=385[/tex]
Total number of students and teachers who rode to the zoo in vans[tex]=12*2=24[/tex]
Someone help me on this question.
Let's go:
6x + 7 + 12x - 3 = 112
18x + 4 = 112
18x = 112 - 4
18x = 108
x = 6
mADB = 6.6 + 7 = 43°
I hope I helped you.
Answer:
43°
Step-by-step explanation:
Since we know that ∠ADC, which is the sum of ∠ADB and ∠BDC, is 112, we can solve for x:
112 = 6x + 7 + 12x - 3
112 = 18x +4
112 - 4 = 18x → 108 = 18x
108/18 = x → 6 = x.
Now, we can substitute 6 for x in the equation for ∠ADB to get the answer:
6(6) + 7 ⇒ 36 + 7 ⇒ 43°.
Hope this helps! Have a nice day!
a bookstore has 780,000 and sales revenue in 2005 $190,000 2011 assuming a constant annual rate of decrease what is the predicted sales revenue for 2017
Answer5,90,000
Step-by-step explanation:
780,000 subtract 190,000 = 590,000
after every 6 years
i'm not sure if its correct. please let me know