Answer:
a = -0.6b + 0.2c
Step-by-step explanation:
Simplifying
5a + 3b = c
Solving
5a + 3b = c
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-3b' to each side of the equation.
5a + 3b + -3b = -3b + c
Combine like terms: 3b + -3b = 0
5a + 0 = -3b + c
5a = -3b + c
Divide each side by '5'.
a = -0.6b + 0.2c
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.40 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
$ 80.22
Step-by-step explanation
Assumed 20% tip is on the discounted meal.The cost of the meal is $78.65
The cost of the meal after discount (15%)is 78.65(1−0.15)≈$ 66.85
Tip (20%) is : 66.85⋅0.2$13.37
Total cost of the meal is
66.85+13.37≈$80.22 [Ans]
find the slope of (-9,17) and (1,-13)
Answer:
-3
Step-by-step explanation:
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
Slope
[tex] = \frac{17 - ( - 13)}{ - 9 - 1} [/tex]
[tex] = \frac{17 + 13}{ - 10} [/tex]
[tex] = \frac{30}{ - 10} [/tex]
= -3
17. Which is written in scientific notation correctly?
A
-44.4 x 102
B
4
-0.4 x 10-2
4 x 10-2
D
0.44 X 102
Answer:
Step-by-step explanation:
Please help me I really need this done
Answer:
the one on the top right
Step-by-step explanation:
it multiplies by 6 and shows 3/4 of the all the columns shaded in
Solve each quadratic inequality then test their interval of the inequality.
1. x² - x - 20 > 0
2. x² - 2x - 11 < 0
3. x²+ 9x + 14 > 0
4. r² - 10r + 16 > 0
Answer:
Step-by-step explanation:
1) x² -x - 20 > 0
x² - 5x + 4x - 20 > 0
x( x - 5) + 4(x - 5) > 0
(x - 5)(x + 4) > 0
x - 5 > 0 ; x + 4> 0
x > 5 ; x < -4
3) x² + 9x + 14 > 0
x² + 7x + 2x + 14 > 0
x(x + 7) + 2(x + 7) > 0
(x + 7) (x + 2) > 0
x < - 7 and x > -2
4) r² - 10r + 16 > 0
r² - 8r -2r + 16 > 0
r(r - 8) - 2(r - 8) > 0
(r - 8)(r - 2) > 0
r < 2 ; r > 8
Lamar bought 4 CDs that were each the same price. Including sales tax, he paid a total of $62.40. Each CD had a tax of 0.70. What was the price of each CD before tax?
gerald pays $90 for 6 baseball lessons. what is the cost per lesson
Answer:
$15
Step-by-step explanation:
90/6=15
answer please
a real answer!!!!!!!!
Answer:
its the first one and the third one
Step-by-step explanation:
What type of protein allows cells to communicate with each other
Answer:
Receptor proteins
Step-by-step explanation:
Simplify: |15 − 12|4 − ∣∣−21 + 98∣∣
Step-by-step explanation:
[tex] = \frac{ |15 - 12| }{4} - | \frac{ - 21 + 9}{8} | [/tex]
[tex] = \frac{ |3| }{4} - \frac{ | - 12| }{ |8| } [/tex]
[tex] = \frac{3}{4} - \frac{12}{8} [/tex]
[tex] = \frac{3}{4} - \frac{6}{4} [/tex]
[tex] = - \frac{3}{4} [/tex]
Option → B
The simplified value of the Expression [tex]\(\left| \frac{(15 - 12)}{4} \right| \times \left| \frac{(-21 + 9)}{8} \right|\)[/tex] in fractional form is 9/8.
To simplify the expression: [tex]\(\left| \frac{(15 - 12)}{4} \right| \times \left| \frac{(-21 + 9)}{8} \right|\)[/tex]
Step 1: Perform the calculations inside the absolute value signs:
[tex]\(\left| \frac{3}{4} \right| \times \left| \frac{-12}{8} \right|\)[/tex]
Step 2: Simplify the fractions inside the absolute value signs:
[tex]\(\left| \dfrac{3}{4} \right| \times \left| \dfrac{-3}{2} \right|\)[/tex]
Step 3: Evaluate the absolute values of the fractions:
[tex]\(\left| \dfrac{3}{4} \right| = \dfrac{3}{4}\)[/tex]
This is because the absolute value of any positive number is itself
[tex]\(\left| \dfrac{-3}{2} \right| = \dfrac{3}{2}[/tex]
and, the absolute value of a negative number is the positive version of that number.
Step 4: Multiply the absolute values:
= 3/4 x 3/2
Step 5: Multiply the fractions:
= 9/8
So, the simplified expression is 9/8.
Learn more about Absolute value here:
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Amy will rent a car for the weekend. She can choose one of two plans. The first plan has no initial fee but costs $0.90 per mile driven. The second plan has an initial fee of $75 and costs an additional $0.80 per mile driven. How many miles would Amy need to drive for the two plans to cost the same?
Answer:
Our two formulas for each plan:
50 (base fee) + .80x (cost per mile) = y (total cost)
.90x (cost per mile) = y (total cost)
We want to find how many miles we have to drive, so solve for x. We're going to plug in y (from equation 2) into the value for y. This is the substitution method.
50+.80x=y
Plugin: 50+.80x = .90x
Add .90x to each side, subtract 50 from each side: .80x -.90x = -50
Simplify: -.10x = -50
Divide: x = -50/-.10 (two negatives make a positive)
x = 500
So this tells us that she has to drive 500 miles to make the plans equal. Let's verify this by plugging in the value we found for x.
499 miles, plan 2 is cheaper.
50 + .80(499) = 449.20
.90(499) = 449.1
500 miles, they are equal
50 + .80(500) = 450
.90(500) = 450
501 miles, plan 1 is cheaper
50 + .80(501) = 450.8
.90(501) = 450.9
Not my work.
Answer:
750mi
Step-by-step explanation:
x = how many miles
75+0.8x=0.9x
Move all terms containing x to the left side of the equation.
75−0.1x=0
Subtract 75 from both sides of the equation.
−0.1x=−75
Divide each term in −0.1x=−75 by −0.1 and simplify.
x=750
PLEASE HELP ME WITH NUMBER 42
Answer:
Y < X
Z > X
ZY = X
Explanation
-2 < -1
1 < -1
1-2 = -1
Write an equation of a line that is perpendicular to y = 3x + 4
Answer:
[tex]y = - \frac{1}{3} x + 2[/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
y= 3x +4
Since the given equation is already in the slope-intercept form, we can easily identify the slope of this line by looking at the coefficient of x.
slope= 3
The product of the slopes of perpendicular lines is -1. Let the slope of the perpendicular line be m.
m(3)= -1
Divide both sides by 3:
m= -⅓
y= -⅓x +c
Since the question does not specify the points the perpendicular line passes through, c can be any integer.
Thus, the equation of the perpendicular line could be y= -⅓x +2.
Kirk has $60 in a savings account. The interest rate is 10%, compounded annually.
To the nearest cent, how much will he have in 3 years?
Answer:
1,800
Step-by-step explanation:
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-8=-16+m
pls show work! ty
Answer:
m = 8
Step-by-step explanation:
-8 = -16 + m
Switch sides.
-16 + m = -8
Add 16 to both sides.
m = 8
Evaluate the expression: 3/5+2^2−2/5(8−6)÷3
Answer:
Exact value: 13/3
Mixed number form: 4 1/3
Step-by-step explanation:
Answer:
B. 4 1/3
Step-by-step explanation:
just did this on T4L
PLS HELP MEEE
Determine which lines, if any, are parallel. Choices may be repeated and some might not be used at all.
Answer:
Step-by-step explanation:
The sum of 2 and b is less than or equal to 26
PLEASE HELP :C
2+b <= 26
solving for b,
b<=24
3. Determine the measure of angle 1 in the figure.
What is the value of x?
(Not multiple choice)
Answer:
x= 82°
Step-by-step explanation:
According to the angle sum property, sum of all angle in a triangle is 180°
45°+53°+x= 180°
98°+x= 180°
x= 180-98
x= 82°
Question Write an equation of the line passing through the point A(3, −1) that is parallel to the line y = 1/3x+10.
Answer:
y= 1/3x - 2
Step-by-step explanation:
Clayton is setting tables at the restaurant where she works. She starts with a pile of 85
napkins, and she places 6 napkins on every table she sets. After Clayton sets all the tables,
there are 25 napkins left. How many tables are there?
Write and solve an equation to find the answer.
Answer:
10 tables is the answer
Step-by-step explanation:
I did IXL and got it correct
you earn $48 for washing 6 cars. How much money do you earn for washing 3 cars
Answer: $24
Step-by-step explanation: 3 is half of 6 and if you gain $48 for washing 6 cars then half it half of 6 is 3 and half of $48 is $24
The numbers 0 and 1 have special properties that are shared by no other numbers for each of the following , decide whether the property is true for 0,1 both or neither
Question
688 + 7888 + 688 - 688 =
Answer:
8,576
Step-by-step explanation:
Add first.
688 + 7888 + 688 - 688
9264 - 688
= 8576
688 + 7.888 + 688 - 688 = ?
= 688 + 7.888 + 0
= 688 + 7.888
= 8.576✔
In the diagram below, AB is parallel to CD. What is the value of x?
Answer:
1
Step-by-step explanation:
To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only three sides will need to be fenced. There is 120 ft of fencing material. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house? What dimensions will maximize the area of the enclosure?
Answer:
Let the length parallel to the house be y
let each of the other two equal sides be x
2x + y = 120
y = 120 - 2x
Area = xy
= x(120 - 2x) or -2x^2 + 120x
b) you want the vertex.
x of the vertex is -120/(-4) = 30
when x = 30
y = 60
Maximum area = xy = 1800 ft^2
The quadratic function that represents the area of the rectangular enclosure is -2x² + 120x and x = 30 and y = 60 will make the area maximize.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's suppose the length parallel to the house is y
And the remaining side is x then,
Perimeter = x + x + y
2x + y = 120
y = 120 - 2x
The area of the rectangle = xy
Area = x(120 - 2x)
⇒ -2x² + 120x
To find the maximum first derivate of the function area with respect to x compare with zero.
d/dx(-2x² + 120x) = 0 ⇒ -4x + 120 = 0
x = 30 so y = 120 - 2(30) = 60
Hence "The quadratic function that represents the area of the rectangular enclosure is -2x² + 120x and x = 30 and y = 60 will make the area maximize".
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Pls I need help!!!! Will mark Brainiest!!!
Answer:
2×10^3 ans2000
Step-by-step explanation:
2.5×10^3 is 2.5×1000=2500
5000000/2500=2000
In scientific notation that would be 2×10^3
[tex]12\times 12\times 11[/tex]
What are the domain and range of the function f(x) = 2^x+1?
Answer:
Domain: (-∞, ∞)
Range: (0,∞)
Step-by-step explanation:
Exponential functions are curves which approach a horizontal asymptote usually at y=0 or the x-axis unless a value has been added to it. If it has, the curve shifts. This function has addition on the exponent but not to the whole function so it does not change the asymptote. Its y - values remain between 0 and ∞. This is the range, the set of y values.
However, the range of exponentials can change based on the leading coefficient. If it is negative the graph flips upside down and its range goes to -∞. This doesn't have it either.
The addition to 1 on the exponent shifts the function to the left but doesn't change the range.
In exponential functions, the x values are usually not affected and all are included in the function. Even though it shifts, the domain doesn't change either. Its domain is (-∞, ∞).
Domain: (-∞, ∞)
Range: (0,∞)
