First one.
y = -2x + 3
5x - (-2x + 3) = 11
y = -2x + 3
5x + 2x - 3 = 11
//
7x = 14
x = 2
y = - 2(2) + 3 = - 4 + 3 = - 1.
One x, one solution.
Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $24.80. The oil change for the other car required 7 quarts of oil and cost $29.30. How much is the labor fee and how much is each quart of oil?
The labor fee is $13.55 and each quart of oil is $2.25
Step-by-step explanation:
Let,
x be the amount of each quart of oil
y be the amount of labor fee
According to given statement;
5x+y=24.80 Eqn 1
7x+y=29.30 Eqn 2
Subtracting Eqn 1 from Eqn 2
[tex](7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{4.50}{2}\\x=2.25[/tex]
Putting x=2.25 in Eqn 1
[tex]5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55[/tex]
The labor fee is $13.55 and each quart of oil is $2.25
Keywords: linear equation, subtraction
Learn more about subtraction at:
brainly.com/question/116715brainly.com/question/11680012#LearnwithBrainly
4/5 is greater than less then or equal to 1/2
Greater Than!
First make the denominator (the bottom number) the same for both fractions. So you can multiply the 1/2 by 5 and the 4/5 by 2.
This will make them 5/10 and 8/10.
Then, you see that 8/10 (4/5) is greater than 5/10 (1/2)
Hope that’s makes sense! :)
The fraction 4/5 is greater than 1/2. This conclusion can be reached by converting the fractions to decimal form, where 4/5 becomes 0.8 and 1/2 becomes 0.5, highlighting that 0.8 is indeed greater than 0.5.
Explanation:The question is whether the fractional value of 4/5 is greater than, less than, or equal to 1/2. To compare these fractions, it may be helpful to first convert them to decimal form, as this is often easier to understand than comparing fractions directly. 4/5 as a decimal is 0.8 and 1/2 as a decimal is 0.5. Hence, 0.8 is greater than 0.5. Therefore, 4/5 is greater than 1/2.
Learn more about Comparing Fractions here:https://brainly.com/question/34222181
#SPJ2
A total of $30,000 is invested in two corporate bonds that pay 5.5% and 6.25% simple interest. the investor wants an annual interest income of %1800 from the investments. what is the most that can be invested in the 5,5% bond?
Answer:
$10,000
Step-by-step explanation:
Let x represent the amount invested in the 5.5% bond.
For an annual income of $1800, we want ...
(5.5%)x + (6.25%)(30,000-x) = 1800
(-0.75%)x + 1875 = 1800
-0.0075x = -75 . . . . . . . . . subtract 1875
x = 10,000 . . . . . . . . . . . . . divide by -0.0075
At most $10,000 should be invested at 5.5% to obtain at least $1800 in interest.
How do we solve for “p”, when
P= 75 + 45h
Answer:
See below.
Step-by-step explanation:
The equation is already solved for p.
p = 75 + 45h
Final answer:
To solve for the fluid density 'p', use the hydrostatic pressure formula P = pgh. By rearranging the formula to p = P / (gh) and inputting the known values for P (atmospheric pressure) and h (height of the water column), the density can be calculated.
Explanation:
To solve for density 'p' when given the equation P = 75 + 45h, where P represents atmospheric pressure and h is the height of a column of fluid, we need to incorporate the concept of hydrostatic pressure. The formula for hydrostatic pressure is P = pgh, where 'p' is the fluid density, 'g' is the acceleration due to gravity, and 'h' is the height of the fluid column. If we know the value of 'P' and the value of 'h', we can isolate 'p' by rearranging the equation to p = P / (gh). This calculation assumes that 'g', the acceleration due to gravity, is a known constant.
Let's assume 'P' is given as 1.00 atm (standard atmospheric pressure) for a water column which is the fluid we're working with. The density 'p' of water that creates this pressure can be calculated by inserting the known values into the expression for 'h'. For instance, if 'h' is 10 meters, the equation would be p = 1.00 atm / (9.81 m/s² × 10 m). To get 'p' in appropriate units, we would convert atm to pascals, and the result will provide the density in kg/m³.
Hey yall It's been a while Wassup but da question is : What term best describes 3x+5 . If u dont know da answer dont waste my time typin junk dat dont make sense
This graph shows how the length of Karen's essay depends on the number of hours she spends writing this week.
What is the constant of variation?
Type your answer as a decimal.
pages per hour.
Answer: [tex]0.8[/tex] pages per hour.
Step-by-step explanation:
For this exercise it is important to know that, by definition, Direct variation equations have the following form:
[tex]y=kx[/tex]
Where "k" is the constant of variation.
Therefore, it is a straight line that passes through the origin.
In this case, given the graph attached in the exercise, you can follow these steps in order to find the constant of variation:
Step 1: You need to choose any point on the line. Let's choose the point (5,4).
Step 2: Now you must ubstitute the coordinates of that point into [tex]y=kx[/tex]. Then:
[tex]4=k(5)[/tex]
Step 3: Finally, you must solve for the Constant of variation "k", in order to find its value. Therefore, you get that this is:
[tex]k=\frac{4}{5}\\\\k=0.8[/tex]
Greatest to least 1/2 1/5 3/8
Answer:
1/5 3/8 1/2
Step-by-step explanation:
- V17 is the geometric mean between 7 and what other number?
Answer:
[tex]\large\boxed{x=\dfrac{17}{7}}[/tex]
Step-by-step explanation:
[tex]\text{A geometric mean of}\ x\ \text{and}\ y:\\\\\sqrt{xy}\\\\\text{Let}\ x-\text{the number}.\\\\\text{Substitute:}\\\\\sqrt{17}=\sqrt{(7)(x)}\iff17=7x\qquad\text{divide both sides by 7}\\\\\dfrac{17}{7}=\dfrac{7x}{7}\to x=\dfrac{17}{7}[/tex]
4 times the quotient of 3 and 4
Answer:
3
Step-by-step explanation:
You would start by dividing
3 by 4. Then multiply 3/4 and 4. The 4s would cancel out leaving you with 3. 3/ 4×4=3
hope this helps
Final answer:
To answer the student's question, first find the quotient of 3 and 4, which is ¾, and then multiply that result by 4 to get the final answer of 3.
Explanation:
The student is asking for the result of multiplying 4 with the quotient of 3 and 4. To solve this, first calculate the quotient of 3 and 4, which is ¾. Then, multiply this result by 4.
Step 1: Quotient of 3 and 4 = 3 ÷ 4 = ¾
Step 2: Multiply the quotient by 4 = ¾ × 4
When you calculate step 2, you get:
¾ × 4 = (3 × 4) / 4 = 3
So, 4 times the quotient of 3 and 4 is 3.
when Elena 's car moves forward such that each tire make one full rotation ,the car has traveled 72 inches .how many full rotations will the tire need to make for Elena's car to travel 10 yards
I will mark free Brainlyest and free point if answered correctly.
How good is Pizza to you? And what is 8/2?
Answer:
Pizza is pretty good tbh. Also the answer is 4.
Answer:
Pizza is great
Step-by-step explanation:
And 8/2 is 4. Pls mark brainliest thx! :)
what is the answer of 1/4+1/5+1/6=
15/60+12/60+10/60= 37/60
When 238 is divided by the natural number n, the quotient is 3 more than n, and there is no remainder. What is n?
Answer:
n = 14
Step-by-step explanation:
Write the equation in algebraic (numbers and symbols) form
[tex]\frac{238}{n}[/tex] = n + 3 Rearrange the equation
[tex]n\frac{238}{n}[/tex] = n(n + 3) Multiply both sides by 'n'
238 = n(n + 3) On the left, multiplying and dividing by 'n' cancels out
238 = n² + 3n Distributed right side
0 = n² + 3n - 238 Rearranged to standard form for quadratic equations
Remember standard form for quadratic equations is: ax² + bx + c = 0
State the variables a, b and c:
a = 1; b = 3; c = -238
When a quadratic equation is in standard form, you can use the quadratic formula to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)
[tex]n = \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex] (ignore the Â, it's a formatting error)
[tex]n = \frac{-(3)±\sqrt{(3)^{2}-4(1)(-238)}}{2(1)}[/tex] Substitute the values for 'a', 'b' and 'c' from the equation
[tex]n = \frac{-3±\sqrt{9-(-952)}}{2}[/tex] In the root, two negatives make a positive
[tex]n = \frac{-3±\sqrt{9+952}}{2}[/tex] Add inside the root
[tex]n = \frac{-3±\sqrt{961}}{2}[/tex] Find the square root of 961
[tex]n = \frac{-3±{31}{2}[/tex] Split the equation at the ±
Split for adding:
[tex]n = \frac{-3+31}{2}[/tex] Simplify
n = 14
Split for subtracting:
[tex]n = \frac{-3-31}{2}[/tex] Simplify
n = -17
You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.
The problem says 'n' is a natural number. Natural numbers are all non-partial numbers count up from 1. (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.
Therefore, 'n' is 14.
In testing the effectiveness of an energy drink on the performance of athletes, 50 athletes were given water and 50 athletes
were given a new energy drink, Yellow Bull. After drinking, each athlete was asked to perform a one-mile run, a 100 yard sprint
and 20 pull-ups.
A) conclusion
B)hypothesis
C)dependent variable
D)independent variable
The correct answer is C; Dependent variable.
Further explanation:
Researchers are very interested in the dependent variable. This variable is what is being tested and measured during the research in progress. In this case, it is the new energy drink.
The researchers are looking for an effect to occur while changing the independent variable of the case study. There are three main different types of variables used in research studies, they are;
IndependentDependentControlWith the athletes doing exercises after consuming the test product, they are seeing if the product does give more energy than if they hadn't of consumed the energy drink.
Learn more about dependent variables at https://brainly.com/question/383055
#LearnwithBrainly
what fractions are less than and greater than 1/2
Answer:
Less than: 1/4, 1/8, 1/16,...
Greater than: 5/8, 3/4, 1,...
Hope this helps :)
For which values of A, B, and C will Ax + By = C be a vertical line through the point (8, 6)
Answer:
Step-by-step explanation:
a vertical line has an undefined slope....(8,6).....its equation is x = 8 because no matter what y is, x will always be 8.
but u need it in standard form Ax + By = C
so it is written as : x + 0y = 8 <===
A = 1
B = 0
C = 8
Ax + By = C will be a vertical line passing through point (8,6) for values of A = 1 , B = 0 and C = 8.
What is a vertical line ?
In a coordinate plane, a line parallel to the Y-axis is called vertical Line. Any point in this line will have the same value for the x-coordinate.
We know that the x-axis has lines that run vertical then if you have a point use your x-ordinate.
The equation of a vertical line is :
x = C
here : C is the value of the x- coordinates the line passes through.
In the given question we have to find out the values of A , B and C for which Ax + By = C be a vertical line passing through point (8,6).
Here , the coordinate of point (x , y) is (8 , 6).
So , the equation of vertical line will be x = 8.
So , if we compare it with the general form of line , Ax + By = C, then we get :
8A + By = 8
So , values of A , B and C :
A = 1, B = 0, C = 8
Therefore , Ax + By = C will be a vertical line through point (8,6) for values of A = 1 , B = 0 and C = 8.
Learn more about vertical lines here :
https://brainly.com/question/16583313
#SPJ2
25. Belle had the choice of taking out a 4-year car loan at
8.5% simple interest or a 5-year car loan at 7.75%
simple interest. If she borrows $15,000, how much
interest would she pay for each loan? Which option
will require less interest?
Answer:
the first loan is cheaper
Step-by-step explanation:
convert percent values to decimals
8.5/100=.085
7.75/100=.0775
find the value for the first loan
1550*.085*4=527
find the value for the first loan
1550*.0775*5=600.625
compare
Belle would pay $5100 in interest for the 4-year loan at 8.5% and $5812.50 for the 5-year loan at 7.75%. Therefore, less interest would be paid with the 4-year loan.
Explanation:To calculate the simple interest, we use the formula I = P*R*T, where P is the principal amount, R is the interest rate, and T is the time in years.
For the 4-year loan at 8.5%, interest would be: I = $15,000 * 8.5/100 * 4 = $5100
For the 5-year loan at 7.75%, interest would be: I = $15,000 * 7.75/100 * 5 = $5,812.50.
So, the 4-year loan at 8.5% will require less interest payment.
Learn more about Simple Interest here:https://brainly.com/question/40405117
#SPJ2
Please help me with these answers!!!
Answer:
Step-by-step explanation:
5) D 2000/200 = 10
6) C 90/9 = 10
7) B 80/8 = 10
8) A) 10 times 2 =10*2 = 20
what is 9/20 times 4/5 in simplest form ?
Answer:
0.36 or [tex]\frac{9}{25}[/tex]
Step-by-step explanation:
9/20=.45
4/5=.8
Answer: .36
Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must Seth attend in order for it to benefit his father to buy the pass?
Answer:
In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.
Step-by-step explanation:
Given:
Cost of movie pass = $40
Cost per matinees with pass = $1.00
Cost per matinees without pass = $3.50
To Find:
Number of times must Seth attend in order for it to benefit his father to buy the pass = ?
Solution:
Let x be the number of times he wants to visit
To profit his father
The number of visits without pass = the number of visits with passin the cost of $3.50
Then, without pass if he visits for x times then the cost will be = 3.50x
Also with pass, the number of times he can visit the pass = [tex]\frac{40}{3.50}[/tex]
then
[tex]\frac{350 x}{3.50} = \frac{40}{3.50}[/tex]
[tex]3.50x = 40[/tex]
[tex]x = \frac{40}{3.50}[/tex]
x = 11.42
x = 11 (approx)
Show how to use unit multipliers to convert 4 hours to seconds.
Answer:
4 hours = 14400 seconds.
Step-by-step explanation:
i) In 1 hour there are 60 minutes
ii) in 1 minute there are 60 seconds
iii) therefore 1 hour = 60 minutes
= 60 [tex]\times[/tex] 60 seconds
= 3600 seconds
iv) therefore to convert 4 hours to seconds we have to multiply the number of hours by 3600 seconds
therefore 4 hours = 4 [tex]\times[/tex] 3600 seconds = 14400 seconds.
Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A
enter the ratios in reduced form:
Answer:
see explanation
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{20}{29}[/tex]
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{21}{29}[/tex]
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{20}{21}[/tex]
The functions sin, cos, and tan for a given angle in a right triangle are defined in terms of ratios of the side lengths. They are respectively the ratios of the opposite side to the hypotenuse, the adjacent side to the hypotenuse, and the opposite side to the adjacent side.
Explanation:In a right triangle, sin(A) is defined as the ratio of the side opposite to angle A (opposite side) to the hypotenuse, cos(A) as the ratio of the adjacent side to the hypotenuse, and tan(A) as the ratio of the opposite side to the adjacent side.
Suppose the lengths of the sides of the given right triangle are a, b, and c (where c is the length of the hypotenuse).
Then, sin(A) = a/c, cos(A) = b/c, and tan(A) = a/b. These ratios must be put in reduced form by simplifying the fractions if necessary.
Learn more about Trigonometric Ratios here:https://brainly.com/question/31675053
#SPJ11
Read the pic boiiiiiiiiiiiiiiiii
Answer:
a is the answer or 320 ft
Step-by-step explanation:
95*65=6175 ft^ for area
95+95+65+65=320 ft
Alex wants to buy 4 pounds of peaches.They cost $1.20 per pound.How much will Alex need to spend for the peaches?
Write the equation of a line that contains (2,-4) and that is perpendicular to y=2/3x+2
Answer:
y = - [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{2}{3}[/tex] x + 2 ← is in slope- intercept form
with slope m = [tex]\frac{2}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex], thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 4) into the partial equation
- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1
y = - [tex]\frac{3}{2}[/tex] x - 1 ← equation of perpendicular line
what is 1 1/2 divided by 3/4
The answer to this one would be 2.
Answer: 2
Step-by-step explanation:
1 1/2 divided 3/4
First make all a fraction
3/2 divided 3/4
3/2*4/3 inverted
2
sahil is putting together supply kits and has 36 packs of x pencil, 12 packs of y crayons, and 24 erasers. Write an expression to show the total number of items.
Answer:
36x + 12y + 24 = T
Step-by-step explanation:
If Sahil has 36 packs of x pencils, then x would equal the number of pencils in each pack. Same thing goes for y. 12 packs of y pencils and y will be the number of crayons in each pack.
36(x) = Total number of pencils.
12(y) = Total number of crayons.
24 = The numbers of erasers which is given.
36x + 12y + 24 = Total numbers of items.
the sum of the 5th term of the 7th term of an ap is 52 and the 10th term is 46 find the AP
Answer:
The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................
Step-by-step explanation:
From the question;
Sum of fifth term and 7th term is 52 That is; 5th term + 7th term = 5210th term is 46We are required to find the AP;
We need to know that in an AP ;nth term = a + (n-1) d , where a is the first term and d is the common difference
Therefore, In this case;5th term = a + 4d
7th term = a + 6d
Therefore;5th term + 7th term = 2a + 10d = 52 ..........eqn 1
10th term = a + 9d
Thus, a + 9d = 46 ............. eqn 2We can solve eqn 1 and eqn 2 simultaneously to get the value of a and d2a + 10d = 52
a + 9d = 46
Multiplying the second equation by 2, we get;
2a + 10d = 52
2a + 18d = 92
Eliminating a by subtracting the two equations; we get;
-8d = -40
d = 5
Solving for a
a + 9d = 46
a = 46 - 9d
= 46 - 9(5)
= 46 - 45
a = 1
Thus, the first term, a= 1 and the common difference, d= 5
Therefore;
First term = a = 1
Second term = a + d = 1 + 5 = 6
Third term = a + 2d = 1 + 2(5) = 11
Fourth term = a + 3d = 1 + 3(5) =16
Fifth term = a + 4d = 1 + 4(5) = 21
Sixth term = 1 + 5d = 1 + 5(5) = 26
Seventh term = 1 + 6d = 1 + 6(5) = 31
Thus,
The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................
What is (4x+5y)(2x+3y)
Answer:
8
x
2
+
22
x
y
+
15
y
2
Step-by-step explanation:
yeet
Answer:
Step-by-step explanation:
YOU WILL BRAINLIST ALSO 47 POINTS!!!
1. It takes 1 banana and 3 scoops of ice cream to make a banana split. If an ice cream shop scooped 42 scoops of ice cream into banana splits, how many bananas did they use? [Type your answer as a number.]
a0 bananas ___
2. At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
a0 minutes __
3. A zoo has 3 mammals for every 5 reptiles. If the zoo has 72 mammals, how many reptiles does it have? [Type your answer as a number.] __
Answer:
Please Mark Brainliest!
Step-by-step explanation:
i think it would be 14 bananas if u take 3 divided by 42
hope that is right.
he rides for 7 min and waits in line for 20 min, if he was to wait in line for 60 min then he would ride for 21 min, if you divide 20/60 then you'll get 3. Multiply the 7 with that 3 and you'll get "21".
120