Answer:
52/21
Step-by-step explanation:
Translate the word equation into an algebraic equation as follows:
Let the number be X
two-and-a-half of a number --> (2 1/2) X
2 1/2 = (2 x 2 + 1) = 5/2
So two-and-a-half of a number --> (9/2)X = 9X/2
three-quarters of the same number --> (3/4)X --> 3X/4
two and half of a number added to three quarters of the same number becomes 9X/2 + 3X/4
gives you 13 --> = 13
So we get the equation:
9X/2 + 3X/4 = 13
Multiply both sides by 4 to get rid of the denominators
4.(9X/2) + 4(3X/4) = 4 x 13 = 52
36X/2 + 12X/4 = 52
==> 18X + 3X = 52
==> 21X = 52
==> X = 52/21
Ethan works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 25% of his total sales for the week. How much would Ethan make in a week in which he made $1250 in sales? How much would Ethan make in a week if he made xx dollars in sales?
Ethan makes in a week = $812.5
Given :
Total sales for the week = $1250
a guaranteed salary = $500
paid a commission on top of his base salary (Percentage commission) = 25%
Time and work problem:
Work Done = Time Taken × Rate of Work
Rate of Work = 1 / Time Taken
Time Taken = 1 / Rate of Work
If a piece of work is done in x number of days, then the work done in one day = 1/x
Total Wok Done = Number of Days × Efficiency
Efficiency and Time are inversely proportional to each other
X:y is the ratio of the number of men who are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x
Solution :
Amount of commission earned = 25% of $1250
= 25/100 × $1,250
= 0.25 × 1250
= $312.5
Total earnings = Base salary + Amount of commission earned
= $500 + $312.5
= $812.5
Ethan makes in a week = $812.5
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Find the measure of the missing angles.
121°
20°
e
d
f
Answer: e=20° d=121° f=39°
Answer:
f=39°
e=20°
d=121°
Step-by-step explanation:
d=121°(vertically opposite angles are equal)
e=20°(vertically opposite angles are equal)
f=180°-(d+e)
=180-141
=39°
Pls show steps on how u got the answer and thank u
Answer:
A=3
Step-by-step explanation:
-7a+28=7
subtract 28 from both sides to eliminate it from the first side
-7a=-21
Two negatives equals a positive
7a=21
divide both sides by 7
a=3
What is the surface area of a pyramid with the measurements being 4 4 7
the base of s is the triangular region with vertices (0, 0), (2, 0), and (0, 2). cross-sections perpendicular to the x-axis are squares.
I assume you want the volume of the shape with the given cross sections. In the [tex]x,y[/tex]-plane, the base is set
[tex]\left\{(x,y) ~:~ 0\le x\le 2 \text{ and } 0 \le y \le 2-x\right\}[/tex]
Each cross section is a square plate with side length [tex]2-x[/tex] (the vertical distance between the [tex]x[/tex]-axis and the line [tex]y=2-x[/tex]) and thickness [tex]\Delta x[/tex], hence volume [tex](2-x)^2\,\Delta x[/tex].
As [tex]\Delta x\to0[/tex] and the number of cross sections grows to infinity, the total volume of the plates converges to volume of the solid [tex]S[/tex], given by the definite integral
[tex]\displaystyle \int_0^2 (2-x)^2 \, dx = \int_0^2 x^2 \, dx = \frac{2^3-0^3}3 = \boxed{\frac83}[/tex]
(where we make the substitution [tex]2-x\mapsto x[/tex])
I don't get this, I would be happy if someone helped me.
Answer:
Step-by-step explanation:
(5/8 + 6/8)/(-4/6 - 5/6)
(11/8)/(-9/6)
(11/8)*(-6/9)
= -66/72 = -11/12
Answer:
11/12
Step-by-step explanation:
5/8 + 3/4 = 1 3/8
-2/3 - 5/6 = 1 1/2
1 3/8 divided by 1 1/2 = 11/12
3 and 1/4 divided by 2 and 1/6
Answer:
{3 1/4} / {2 1/6} =
1.5
Step-by-step explanation:
Answer:
Exact Form:
3/2
Decimal Form:
1.5
Mixed Number Form:
1 1/2
find the volume of the parallelepiped with one vertex at (5,4,4), and adjacent vertices at (0,−1,5), (4,10,5), and (11,7,11).
The volume of the parallelepiped is 299³ units.
What is parallelepiped?A parallelepiped is a three-dimensional character formed by six parallelograms in geometry (the term rhomboid is also sometimes used with this meaning). It is analogous to a parallelogram in the same way that a cube is analogous to a square. In Euclidean geometry, the 4 concepts—parallelepiped and cube in three dimensions, parallelogram as well as square in two-dimension —are defined, but only parallelograms and parallelepipeds exist in the context of more general affine geometry, in which angles are not differentiated.So,
The volume of parallelopiped can be calculated using the steps below.
PQ = Q - Vertex = (-5, -5, 1)PR = R - Vertex = (-1, 6, 1)PS = S - Vertex = (6, 3, 7)Now, the volume of parallelopiped is increasing:
[tex]v=\left|\begin{array}{lll}-5 & -5 & 1 \\-1 & 6 & 1 \\6 & 3 & 7\end{array}\right|[/tex]
The matrix's determinant is:
⇒ -5(42 - 3) +5(-7 -6) +1(-3 - 36)
⇒ -5(39) +5(-13) +1(-39)
⇒ -195 -65 -39
⇒ |-299| = 299
Therefore, the volume of the parallelepiped is 299³ units.
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2. Question
A car averages 32 mpg. Gas costs $1.97 per gallon. How much
would it cost to pay for the gas if this car made a trip of 866 miles?
O$37.51
O$13.73
0 $55.20
O$53.31
show
your
Work ↓
The cost for 866 miles will be $53.31.
How to calculate the cost?The car car averages 32 mpg and gas costs $1.97 per gallon.
Therefore,. the cost for 866 miles will be:
= 866/32 × $1.97
= 27.0625 × $1.97
= $53.31
The cost is $53.31.
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Find parametric equations that describe the intersection of the cone z=x^2+y^2 and the plane =2z
Answer:
hhrhrthrtht
Step-by-step explanation:
hlllppppp! brainliest to first
y = -2x + 18
y = 8
Solution for the above system?
brainliest to first!!!!!!!hlpppppp!!!!!!!!!!!
Answer:
x =5
Step-by-step explanation:
8 = -2x + 18 Subtract 18 from both sides
-10 = -2x Divide both sides by -2
5 = x
If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?
Answer:
0.05
Step-by-step explanation:
Answer:
10 cents
Step-by-step explanation:
Well the bat and baseball is 1.10 simply subtract 1.00 from 1.10 and you have your answer!
Have an AMAZING day! :)
I NEED HELP FAST PLEASE‼️‼️
SIMPLIFY TO SIMPLEST FORM‼️
Answer:
1/2
Step-by-step explanation:
-put 3/8 and 3/4 side-by-side.
-keep 3/8
-change the division sign to a multiplucation sign
-flip 3/4 to 4/3
-multiply
Find the distance between A (4, 6) and B (9, 7). Write your answer as a radical and as a decimal rounded to the nearest
tenth.
The distance between the two points is ___ or about ___
Answer: the distance between the two points is √26 or about 5.1
Step-by-step explanation:
A(4,6) B(9,7)
[tex]\boxed {L_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} }\\\\L_{AB}=\sqrt{(9-4)^2+(7-6)^2} \\\\L{ab}=\sqrt{5^2+1^2}\\\\ L_{AB}=\sqrt{25+1} \\\\L_{AB}=\sqrt{26} \\\\L_{AB}\approx5.1[/tex]
The distance between A (4, 6) and B (9, 7) is √26 or 5.1.
How to find the distance between two points?Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So the distance between A (4, 6) and B (9, 7) will be
[tex]d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }[/tex]
d = √26 = 5.099
Rounded to nearest tenth ⇒ 5.1 units.
Hence "The distance between A (4, 6) and B (9, 7) is √26 or 5.1".
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Wayne ate Takis everyday for n days. He ate 28 bags total.
Write an expression for how many bags of Takis Wayne ate each day.
I NEED AN ANSWER SOON!!!!
The expression for no. of bags of Takis Wayne ate each day is given by, b = 28/n.
What is an expression?Expresssion are mathemaical ways of writing staments.There are many types of mathematical expressions some of them are :- Algebraic expressions, Logarithmic expressions, Trigonometric expressions and many more.
Here the no. of days is represented by 'n' and total no. of bags of akis he ate is 28.
Assuming Wayne ate 'b' bags of Takis everyday.
∴ No. of bags of Takis each day multiplied by no. of days is equal to total no. of bags of Takis he ate which is numerical form is,
b×n = 28.
So, The expression for no. of bags of Takis Wayne ate each day is ,
b = 28/n.
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What is the 4th term in the following expression?
-2 - 5x -7 - 9x
The value of the expression is -65.
How to compute the expression?It should be noted that the function given is illustrated as:
-2 - 5x -7 - 9x
In this case, you've to put the value of x as 4.
This will be:
= -2 - 5x -7 - 9x
= -2 - 5(4) - 7 - 9(4)
= -2 - 20 - 7 - 36
= -65
Therefore, the value of the expression is -65.
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In right triangle abc with m/C=90°, m/B=75°, and AB = 12 cm. Find the area
of triangle ABC. No trig
The area of the Triangle ABC will be 18 cm²
In the question, It is given that ∠B = 75° and ΔABC is Right angeled at ∠C = 90° and AB = 12CM.
We know that the Area of Δ is defined by : [tex](\frac{1}{2} *b*h)[/tex]
In the picture below, we have base and height BC and AC respectively.
We don't have the values for AC and BC. So to find the values of Base & Height we will use Trigonometric Ratios.
We know Sin(∠) = Perpendicular/Hyoptenuse and,
Tan(∠) = Perpenciular/Base. Putting values into the respective ratios and taking ∠B = 75°, we get
=> [tex]Sin(B) = \frac{AC}{BC} = > Sin(75) = \frac{AC}{12}[/tex]
=> [tex]AC = 0.96 * 12 = > AC = 11.59[/tex]
Similarly, [tex]Tan(B) = \frac{AC}{BC} = > Tan(75) = \frac{11.59}{BC}[/tex]
=> [tex]BC = \frac{11.59}{3.73} = > BC = 3.10[/tex]
Now, we have AC = 11.59cm and BC = 3.10cm putting these values in the Area of the Triangle we get :
Area = [tex]\frac{1}{2} *b*h[/tex] => Area = [tex]\frac{1}{2}[/tex] * BC * AC
Area = [tex]\frac{1}{2}[/tex] * 3.10 * 11.59 => Area = 18
Hence, we get the Area of Δ ABC = 18cm²
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Answer:
18
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
x=17/99
Step-by-step explanation:
Lets break this problem down ^^
Let x= 0.171717...
100x = 17.1717...
100x=17.1717.. - x=0.171717...
99x=17
x= 17/99
Hope this helps!! ^^
if the discounted price is 14 how much money dose one section represent
The price of one section represent $2.
We will use the tape diagram to represent the sale price and regular price of the item.
We know that percentage is used to represent the fractions of a whole number.
Here, the regular price is the whole number, and the discount and discounted price represent the fractions.
The coupon she used is 30%, which means 30% off the regular price is the discounted price. We know that 30% + 70% = 100%. This means Mia paid 70% of the regular price for the backpack.
Refer to the attached image for the tape diagram.
By looking at the tape diagram attached, it is clear that 7 sections are used to show the discounted price.
If the discounted price is $14,
The price of one section = $14/7 = $2
Therefore, the price of one section is $2.
⇒The regular price = 10 × price of one section = 10 × $2 = $20.
So, Peter needs to pay $20 to buy a similar backpack.
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Disclaimer:
The given question is incomplete.
Assume the following as the complete question.
Mia told Peter that her new backpack only cost $14 because she used a 30% off coupon when she bought it. Peter wants to buy a similar backpack. How much will it cost if he does not have a 30% off coupon?
An ice cream store recorded the flavors of its recent cone sales.
chocolate 10
cookie dough 6
mocha 20
vanilla 8
Considering this data, how many of the next 99 cones sold would you expect to have mocha ice cream?
The inverse of f(x)=9x^2
Given function:
f(x) = 9x²Let the inverse is y = f⁻¹(x).
Swap x and y in the given function and solve for y:
x = 9y²y² = x/9y = √(x/9)y = √x / 3The inverse of the given function is:
f⁻¹(x) = √x / 3Answer:
f-¹(x) = √(x)/3
Step-by-step explanation:
Now we have to,
→ find the inverse of f(x)=9x²
Then the inverse function will be,
→ f(x) = 9x²
→ y = 9x²
→ 9y² = x
→ y² = x/9
→ y = √(x/9)
→ [ y = √(x)/3 ]
Hence, the inverse is √(x)/3.
explain the process of finding the mean of a data set in your own words.
Answer:i hope this helps
Step-by-step explanation:add all the terms together and divide by the amount of terms given
What is the value of the expression 3 -4?
Answer:
-1
Step-by-step explanation:
3 - 4 = -1
When dealing with subtraction, you must be very careful with the order you place your numbers in. Let alone, subtraction is important in real-world situations, so just something to help. :)
______________________________
Wrapping up:
➲ Hope this helps.
➲ Notify me of any concerns, and I will address those concerns.
➲ Have a good day.
can anyone help with
4x + 6 + 2x = 18
Answer:
x=2
Step-by-step explanation:
[tex]4x+2x+6=18 < - Start-by-grouping-the-like-terms![/tex]
[tex]6x+6=18 < - Then-add-the-similar-elements![/tex]
[tex]6x+6-6=18-6 < - Subtract-6-from-both-sides-and-simplify.[/tex]
[tex]6x=12[/tex]
[tex]\frac{6x}{6}=\frac{12}{6} < - Divide-both-sides-by-6-to-further-simplify![/tex]
[tex]x=2[/tex]
________________________________________________________
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Suppose that both of the events you have just analyzed are partly responsible for the decrease in the price of hamburgers. Based on your analysis of the explanations offered by the two groups of students, how would you figure out which of the possible causes was the dominant cause of the decrease in the price of hamburgers?.
If there is an increase in the equilibrium quantity of hamburgers, the supply shift in the market must have been greater than the demand shift.
Assuming that all demand-shift factors remain constant, the hamburger demand curve illustrates the relationship between hamburger price and quantity required by consumers. The factors influencing how many hamburgers consumers desire to purchase at a particular price are known as demand determinants.
If the price of hamburgers increases, the demand curve will move from the previous price to the new price. However, if any of the demand-shift variables change, such as the cost of hot dogs, the cost of hamburger buns, or the income of hamburger consumers, the demand curve will alter.
Demand is where the demand curve is located. Demanded quantity is the volume that customers want to purchase.
The position of the supply curve is referred to as supply. The quantity of supplies you desire to sell is referred to as the quantity supply.
In this instance, an increase in supply will result in a fall in the equilibrium price and a movement all along the demand curve. The quantity demanded changes, while the demand curve does not.
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(1 point) Find an equation for the linear function g(x) which is perpendicular to the line 5x−2y=6 and intersects the line 5x−2y=6 at x=8.
g(x)=
Answer: y=-0.4x+20.2
Step-by-step explanation:
[tex]5x-2y=6\\5x-2y+2y=6+2y\\5x=6+2y\\5x-6=6+2y-6\\5x-6=2y[/tex]
Divide both parts of the equation by 2:
[tex]\displaystyle\\\frac{5x-6}{2}=y\\\\\frac{5}{2} x-3=y[/tex]
Coordinates of the intersection point of the equations:
[tex]\displaystyle\\y=\frac{5}{2}x-3 \ and\ x=8\ are:[/tex]
[tex]\displaystyle\\x=8\\Hence,\\y=\frac{5}{2} (8)-3\\\\y=\frac{5*8}{2} -3\\\\y=\frac{5*4*2}{2}-3\\\\y=5*4-3 \\\\y=20-3\\\\y=17\\Thus, (8,17)[/tex]
[tex]\displaystyle\\The\ slope\ \perp=-\frac{1}{\frac{5}{2} } \\\\The\ slope\ \perp=-\frac{2}{5}[/tex]
[tex]\displaystyle\\-\frac{2}{5} =\frac{y-17}{x-8}[/tex]
Multiply both parts of the equation by (x-8):
[tex]\displaystyle\\-\frac{2}{5}(x-8)=y-17\\\\-\frac{2}{5} x+\frac{2*8}{5} =y-17\\\\-\frac{2}{5}x+\frac{16}{5} =y-17\\\\ -0.4x+3.2=y-17\\\\ -0.4x+3.2+17=y-17+17\\\\-0.4x+20.2=y[/tex]-
The radius of a cone can be found using the formula , where stands for the volume of the cone and stands for the height. If r=3, h=6, and pi is 3.14 , find the volume (V). Round the answer to the nearest hundredths place.
The volume of the cone with radius 3 and height of the cone 6 is 56.52.
Any shape's volume in geometry is the area it takes up in a three-dimensional space. As a result, the space occupied by a cone in three dimensions is known as its volume.
The formula for the radius of a cone is given as:
r = √( 3 × V / π × h)
Where h is the height of the cone, V is the volume of the cone.
Now, squaring the above equation.
(r)² = [ √( 3 × V / π × h) ]²
r² = [ √ (3 × V) / √ ( π × h ) ]²
3V = π × r² × h
V = π × r² × h / 3
We have,
r = 3, h = 6, and π = 3.14
V = ( 3.14 × (3)² × 6 / 3 )
V = 3.14 × 3 × 6
V = 56.52
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3x + 4y = -23
2y - x = -19
What is the solution (x, y) to the system of equations
above?
A) (-5,-2)
B) (3, -8)
C) (4, -6)
D) (9,-6)
=======================================================
Explanation:
I'll use the substitution method.
Let's solve the second equation for x.
2y - x = -19
-x = -19-2y
x = 19+2y
Then plug that into the first equation
3x + 4y = -23
3( x ) + 4y = -23
3(19+2y)+4y = -23
3*19 + 3*2y + 4y = -23
57+6y+4y = -23
57+10y = -23
10y = -23-57
10y = -80
y = -80/10
y = -8
Use this y value to find x.
x = 19+2y
x = 19+2(-8)
x = 19-16
x = 3
---------------------------
Summary:
We found that x = 3 and y = -8
The ordered pair solution is therefore (x,y) = (3, -8)
Technically you could have stopped once reaching y = -8, since choice B is the only one that fits the description. But it helps to have practice.
Answer:
answer is B
Step-by-step explanation:
picture is upside down.
math work please help <3
Using translation concepts, it is found that:
a.
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.b.
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Quadratic functionThe quadratic function has vertex at (-4,-6), hence:
y = a(x + 4)² - 6
When x = -6, y = 0, hence we use it to find a as follows:
0 = 4a - 6
a = 1.5.
Hence the function is:
y = 1.5(x + 4)² - 6.
When it is reflected over the x-axis, we have that:
y -> -y.
Hence:
y = -1.5(x + 4)² + 6.
When it is moved up 3 units, we have that y -> y + 3, hence:
y = -1.5(x + 4)² + 9.
The function is defined for all real values, assuming values from negative infinity to 9, hence:
The equation is: y = -1.5(x + 4)² + 9.The domain is all real values.The range is y ≤ 9.Square root functionThe parent square root function is given by:
[tex]y = \sqrt{x}[/tex]
From the graph, it is found that:
The function was reflected over the x-axis, hence y -> -y.The function was shifted one unit to right, hence x -> x - 1.The function was shifted two units up, hence y -> y + 2.Hence the rule is:
[tex]y = -\sqrt{x - 1} + 2[/tex]
The translations given by the item are:
6 units left, hence x -> x + 6.8 units up, hence y -> y + 8.Thus:
[tex]y = -\sqrt{x + 5} + 10[/tex]
Then the function will be defined for values of -5 and greater, assuming values of 10 and less, hence:
The rule is [tex]y = -\sqrt{x + 5} + 10[/tex].The domain is x ≥ -5.The range is y ≤ 10.More can be learned about translation concepts at https://brainly.com/question/4521517
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2. Cassie finishes softball practice at 3:52 p.m. after practicing for 30 minutes. What time did Cassie's
practice start?
Answer:
3:22!
Step-by-step explanation:
Answer:
3:22 p.m.
Step-by-step explanation:
30 minutes before 3:52 p.m.
think of hours and minutes separately for now
3hours
52 minutes
if you are trying to find the time 30 minutes before 3:52 subtract 30 from 52 then put your hours and minutes side by side with a colon (:) in between
3:22
Add a.m. if its after midnight and p.m. if it's after noon