Answer:
What do mean by equals 16?
Step-by-step explanation:
1/2x+8=16
1/2x=16-8
1/2x=8
x=8:1/2
x=8*2
x=16
Hope this helps! <3
For two-week. John and Amanda had the following transaction occurred to their checking account a deposit of 1644 and 50 Cent Shake written for 190 45 $7.50 and a debit card transaction for $30 14514 59 another one for $7.20 and $21.30 what is the ending balance for this time frame
Answer:
$1,337.91
Step-by-step explanation:
Hello, my dear friend, I am sure the question you are intending should be corrected as follows:
For two weeks, John and Amanda had the following transactions occur to their checking account: a deposit of $1,644.50; checks written for $190, $45, and $7.50; and debit card transactions for $30, $5.59, $7.20, and $21.30. What is the ending balance for this time frame?
If this is the case, then see the operation for the transactions below:
1,644.5−190-45-7.5-30-5.59-7.2-21.3=1,337.91
Please note that Deposits are positive in your account while written checks and debit card charges are negative.
PLS HELP ASAP
Which equation represents a proportional relationship?
y=32x
y=−2x
y = 4x + 3
y=2(x+1)
The proportional relationship:
y = ax for a > 0.
Therefore your answer is:
y = 32xWater is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the rate of 2 cm3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 8 cm deep? Show all work and include units in your answer. Give an exact answer showing all work and include units in your answer
Answer:
[tex]-\frac{1}{2\pi}[/tex] cm³/min
Step-by-step explanation:
Let h = height of water and r = radius of its surface
[tex]V = \frac{ 1}{ 3}\pi r^{2}h[/tex]
At all times,
[tex]\frac{r }{h } = \frac{4 }{16 } = \frac{ 1}{4 }[/tex]
So, [tex]r = \frac{h }{4 }[/tex]
[tex]V = \frac{ 1}{ 3}\pi (\frac{h }{ 4})^{2}h[/tex]
[tex]V = \frac{ 1}{ 48}\pi h^{3}[/tex]
[tex]\frac{\text{d}V}{\text{d}h} = \frac{ 1}{ 16}\pi h^{2}[/tex]
We want [tex]\frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t} = \frac{\text{d}V}{\text{d}h} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}V}{\text{d}t}[/tex] = -2 cm³/min
[tex]-2 = \frac{ 1}{ 16}\pi h^{2} \frac{\text{d}h}{\text{d}t}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{2}{\frac{ 1}{ 16}\pi h^{2} }[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi h^{2}}[/tex]
When h = 8 cm
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi\times8^{2}}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{64\pi}[/tex]
[tex]\frac{\text{d}h}{\text{d}t} = -\frac{1}{2\pi}[/tex] cm³/min
The depth of the water is decreasing at a rate of [tex]\frac{1}{2\pi}[/tex] cm³/min
.
Determine the next three terms in the following sequence: 2, 3, 5, 8, ____, ____, ____,... a. 13, 19, 26 b. 12, 17, 23 c. 12, 16, 20 d. 13, 17, 23 Please select the best answer from the choices provided A B C D
Answer:
B. 12,17,23
Step-by-step explanation:
2,3,5,8, _,_,_
2,3 is increased by 1
3,5 is increased by 2
5,8 is increased by 3. theres our pattern, each time it increases it follows the next number so the next 3 numbers it would be increased by is. 4,5,6.
Now knowing it is 4,5,6 we need to add, start adding.
8+4=12. Which answers have 12 in them? B and C.
We know 12 is the next number, now we add 5 to that.
12+5=17.
B has 17 but C doesn't, so that tells you its most likely going to be B. To make sure add 6 to 17.
17+6=23. Its true that it is B, as B is 12.17.23.
The next three terms in the sequence are 13, 21, and 34.
Explanation:The given sequence is 2, 3, 5, 8.
To find the next three terms in the sequence, we need to determine the pattern.
By observing the sequence, we can see that each term is obtained by adding the two previous terms.
For example,
3 = 2 + 1,
5 = 3 + 2, and
8 = 5 + 3.
Using this pattern, the next term would be obtained by adding 8 + 5, -
8 + 5 = 13
The two terms after that would be
13 + 8 = 21 and
21 + 13 = 34.
Therefore, the next three terms in the sequence are 13, 21, and 34.
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Ms. Blankenship had $80 to purchase school supplies for her class. She bought 32 glue sticks and 32 boxes of crayons. Each glue stick cost $1.40, and each box of crayons cost $0.59. How much money did Ms. Blankenship have left after these purchases?
Answer:
$16.32
Step-by-step explanation:
1. Ms. Blankenship bought 32 glue sticks each for $1.40, then she spent
[tex]\$1.40\cdot 32=\$44.80[/tex]
for all sticks.
2. Ms. Blankenship bought 32 boxes each for $0.59, then she spent
[tex]\$0.59\cdot 32=\$18.88[/tex]
for all boxes.
3. Together 32 glue sticks and 32 boxes cost
[tex]\$44.80+\$18.88=\$63.68.[/tex]
4. If Ms. Blankenship had $80, then she had left
[tex]\$80-\$63.68=\$16.32.[/tex]
Algebra 2. Help!
Which grows faster as x increases, x3 or 3x? Explain.
As x increases, x^3 grows faster than 3x.
As x increases, the growth rate of x^3 (x cubed) is faster than that of 3x. This can be explained by comparing their respective derivatives.
The derivative of x^3 with respect to x is 3x^2, while the derivative of 3x is simply 3.
The derivative represents the rate of change, or the slope of the function at a given point. In the case of x^3, its derivative 3x^2 grows at a faster rate than the derivative of 3x, which is a constant (3).
This means that as x increases, the rate of change of x^3 (3x^2) increases faster compared to the rate of change of 3x (which is constant at 3). In other words, x^3 exhibits exponential growth, while 3x exhibits linear growth. So, as x increases, x^3 grows faster than 3x.
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What is the total number of unique triangles with side lengths of 4 centimeters. 5 centimeters, and 10 centimeters that can be drawn
There are 0 unique triangles that can be drawn with the side lengths 4 cm, 5 cm, and 10 cm
How to determine the total number of unique triangles that can be drawn
From the question, we have the following parameters that can be used in our computation:
Side lengths = 4 cm, 5 cm, and 10 cm
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, we have
4 + 5 > 10 --- false
4 + 10 > 5 --- true
5 + 10 > 4 --- true
Since one of the conditions is false, no triangles can be formed using the side lengths
a student phototcopies a drawing without realizing tht the copier is set to enlarge the image by 15%. if the height of the actual drawing is 4.25 inches, approximately how tall is the phototcopied drawing?
If an image is being enlarged by 15% you would take the base number multiply it by the percent in decimal form and add the result to the base number.
4.25*0.15=0.6275
0.6375+4.25=4.8875
Answer: 4.8875
To find out the height of the photocopied drawing, we first calculate 15% of the original height (4.25 inches) and add this to the original height. The photocopied drawing is approximately 4.89 inches tall.
Explanation:The student photocopied a drawing with the copier set to enlarge the image by 15%. If the original drawing is 4.25 inches tall, the enlarged photocopied drawing would be larger by 15% of 4.25 inches.
Firstly, to find 15% of 4.25 inches, you multiply 4.25 by 0.15 (the decimal equivalent of 15%), which equals 0.6375 inches.
Adding this to the original height of the drawing, we get 4.25 inches + 0.6375 inches = 4.8875 inches, which is approximately 4.89 inches when rounded to two decimal places.
So, the photocopied drawing is approximately 4.89 inches tall.
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Which is true about an equilateral triangle?
Answer: all angle measures are equal
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:think as it as coordinates on a graph. Time=x Amount=y. So if the time is 0 and the amount is 60 you would graph a point on (0,60)
Step-by-step explanation:
What decimal is represented by this expanded form?
5×10,000+3×1,000+2×10+8×1+ 6×1/100+4×1/1,000
Answer:
53028.064 I think
Step-by-step explanation:
Which steps should be used to compare the fractions 2/9 and 5/6
Answer: you need to get a common denominator.. once you have a common denominator, you can compare numerators to see what is larger..
Step-by-step explanation:
to get the common denominator, you would first see what this would be.. in this case 18, as that's the lowest. then, you would multiply each fraction by 2/2 for first and 3/3 for second, which are just funky looking ones. therefore, D is the correct answer.
Answer:It is C
Step-by-step explanation:In the question it says to COMPARE the fraction.
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Solve using elimination
5x-4y=-21
-2x+4y=18
Answer:
x=-1, y=4
Step-by-step explanation:
When we solve by elimination, we are getting rid of one variable, in this case y. We will add the two equations together.
5x-4y=-21
-2x+4y=18
---------------
3x = -3
Divide each side by 3
3x/3 =-3/3
x =-1
Now we need to calculate y
-2x +4y = 18
Substitute x=-1
-2(-1)+4y = 18
2+4y =18
Subtract 2 from each side
4y = 18-2
4y=16
Divide each side by 4
4y=16/4
y =4
What is 4:2 the same as
Answer:
4:2 is the same as:
2:1
8:4
or anything that is proportional to 4:2
Step-by-step explanation:
A proportion is anything that corresponds in size or amount to something else.
Answer:
2:1
Step-by-step explanation:
just reduce the ratio b and divivd bith sides by 2
show that the points p(7,12) and q(-3,-12) and r (14,5) lie on a circle with center c(2,0)
If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]
OP = OQ = OR, therefore the points P, Q and R lie on one circle.
PRE CALC PLEASE HELP!!!
Topic: Rational Functions
If f(x)=2x^3-bx^2+cx+12, Were b and c integers, list all possible rational roots of f(x)
Answer: [tex]\bold{\pm \{1, 2, 3, 4, 6, 12, \dfrac{1}{2}, \dfrac{3}{2}\}}[/tex]
Step-by-step explanation:
Q P
f(x) = 2x³ - bx² + cx + 12
Possible rational roots are all of the factors of P divided by all of the factors of Q, including both positive and negative signs.
[tex]\quad \pm \dfrac{\text{factors of P}}{\text{factors of Q}}\\\\=\pm \dfrac{\text{factors of 12}}{\text{factors of 2}}\\\\=\pm \dfrac{1,2,3,4,6,12}{1,2}\\\\=\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm \dfrac{1}{2}, \pm \dfrac{3}{2}\\[/tex]
Use the drop-down menus to identify the values of the parabola
Answer:
What drop down menues??????????????????????
Step-by-step explanation:
Answer:
options?
Step-by-step explanation:
Selling price is $70.00. Rate of the sales tax is 60%. That is the sales tax?
The sales tax would be $42.00, making the total cost $112.00.
To calculate the sales tax on an item, one must first convert the sales tax rate from a percentage to a decimal. Converting 60% to a decimal by dividing by 100 gives us 0.60.
Then, multiply this decimal by the selling price to find the amount of sales tax.
Amount of sales tax = price x rate of sales tax
So for a selling price of $70.00, the sales tax would be calculated as follows:
= $70.00 x 0.60 = $42.00
The sales tax on a $70.00 item at a rate of 60% is $42.00.
To find the total cost, one must add this tax to the original selling price.
Total cost = selling price + sales tax
Total cost = $70.00 + $42.00
Total cost = $112.00
Thus, the total amount paid including sales tax would be $112.00.
The percent change of 40;50
Answer:
25%
Step-by-step explanation:
Change = Final - initial
% Change =(Final - Initial)/Initial × 100%
% Change = (50 - 40)/40 × 100%
% Change = 10/40 × 100%
% Change = 25%
Answer:
25%
Step-by-step explanation:
1) Find the difference of the two numbers, do (Largest Number)-(Smallest Number).
2) Use your difference as a fraction. Use the difference over the initial value.
3) Create a proportion
10/40 = x/100
4) Cross multiply, 10*100 = 200, 40*p = 40p
5) Simplify expression 1,000=40p
6) Solve, 1,000/40 = 25
7) Put it as a fraction, 25/100
8) Make it a percent 25%
a used automobile dealership recently reduced the price of a used compact car by 10 % if the price of the car before discount was $33500 find the discount and the new price
Answer: The new price is $3350.
Answer:
$3350; $30 150
Step-by-step explanation:
Original price = $33 500
Discount = 33 500 × 10 %
Discount = 33 500 × 0.10
Discount = $3350
New price = Original price - Discount
New price = 33 500 - 3350
New price = $30 150
write an equation of a line that passes through (3,0) and (6,-3) in slope intercept and point slope form
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, 0) and (6, -3). Substitute:
[tex]m=\dfrac{-3-0}{6-3}=\dfrac{-3}{3}=-1[/tex]
The point-slope form:
[tex]y-(-3)=-1(x-6)\\\\\boxed{y+3=-(x-6)}[/tex]
or
[tex]y-0=-1(x-3)\\\\\boxed{y=-(x-3)}[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
From the second point-slope form we have slope-intercept form:
[tex]y=-(x-3)\\\\y=-x-(-3)\\\\\boxed{y=-x+3}[/tex]
What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?
answers:
4x - y = 13
4x + y = 13
4x + y = -13
Answer:
The equation of this line would be 4x + y = 13
Step-by-step explanation:
In order to find this equation we must first find the slope of the original line. To do this, we solve the original equation for y.
4x + y - 2 = 0
4x + y = 2
y = -4x + 2
The original slope (the coefficient of x) is -4, which means the new slope will also be -4 because parallel lines have the same slope. Now, we can use this slope along with the point in point-slope form to find the equation of the line. Just plug in the numbers and solve for the coefficient.
y - y1 = m(x - x1)
y + 3 = -4(x - 4)
y + 3 = -4x + 16
4x + y + 3 = 16
4x + y = 13
pleasee answer the question in the picture
Answer:
a (5,2)
Step-by-step explanation:
To get to the smiley face, we move 5 units in the x direction from the origin, then we move 2 units up in the y direction (x,y) so the point is at (5,
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-3=-1/5(x+2);(-2,7)
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the line
[tex]y-3=-\dfrac{1}{5}(x+2)\to m=-\dfrac{1}{5}[/tex]
If m₁ and m₂ are the slopes of the perpendicular lines, then
[tex]m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
Therefore the slope of ouer line is
[tex]m=-\dfrac{1}{-\frac{1}{5}}=5[/tex]
We have the point (-2, 7). Put the coordinates to the equation of a line in the point-slope form:
[tex]y-7=5(x-(-2))[/tex]
[tex]y-7=5(x+2)[/tex] use the distributive property
[tex]y-7=(5)(x)+(5)(2)[/tex]
[tex]y-7=5x+10[/tex] add 7 to both sides
[tex]\boxed{y=5x+17}[/tex]
the sum of two numbers is 53. their difference is 17. Find the numbers.
Answer: the two numbers is 35 and 18
Step-by-step explanation: 35+18=53 35-18=17
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Final answer:
The two numbers are 35 and 18. We found these by solving the simultaneous equations x + y = 53 and x - y = 17, representing their sum and difference.
Explanation:
Finding Two Numbers Given Their Sum and Difference
Let's denote the two unknown numbers as x and y. According to the conditions given:
x + y = 53 (Equation 1: The sum of the two numbers)
x - y = 17 (Equation 2: The difference of the two numbers)
We can solve these two simultaneous equations to find the values of x and y.
Add the two equations:
(x + y) + (x - y) = 53 + 17
2x = 70
x = 35
Substitute x in Equation 1:
35 + y = 53
y = 53 - 35
y = 18
Therefore, the two numbers are 35 and 18.
five more then -8 times a number is 29. What is the number? Let the mystery number be represented by n.
Answer:
The mystery number is -3
Step-by-step explanation:
five more then -8 times a number is 29.
-8n +5 = 29
Subtract 5 from both sides
-8n +5-5 = 29-5
-8n = 24
Divide by -8 on each side
-8n/-8 = 24/-8
n= -3
The mystery number is -3
The mystery number in the equation is -3, determined by solving the algebraic equation 5 + (-8 × n) = 29.
The equation given in the problem statement translates to the mathematical expression 5 + (-8 × n) = 29, where n is the mystery number. To find the value of n, we can perform the following steps:
Subtract 5 from both sides to get -8n = 24.
Divide both sides by -8 to isolate n, giving us n = 24 / -8.
Calculate the result to find that n = -3.
Therefore, the mystery number is -3.
What is the eighth term in the arithmetic sequence defined by the explicit formula an=2n+7? Enter your answer in the box.
Answer:
The 8th term is 23
Step-by-step explanation:
If we are given the formula for the sequence
an=2n+7,
then to find the 8th term we substitute n=8 into the formula.
a8 = 2(8) +7
a8 = 16+7
a8 = 23
The 8th term is 23
How do you convert a fraction to a decimal? Say, [tex]\frac{2}{5}[/tex] ?
Answer:
you divide the top number by the bottom number
Step-by-step explanation:
2/5 = 0.4
please help me, PLEASE!!!!!!
Tell wheather the sequence is arithmetic. If it is , what is the common difference? -12,-7,-2,3.......
A yes ;5
B yes ;8
C yes :3
D no
Answer:
C
Step-by-step explanation:
To find whether it is a arithmetic or geometric sequence it is easiest to try to subtract term a2 from a1, seeing if d or r is positive. If that does not heed an answer try dividing a2 by a1 to see if it is a geometric sequence.
The terms go as follows just in case (They would normally be in subscripts)-
a1= -12
a2= -7
a3= -2
a4= 3
Answer: Yes; 5 (choice A)
We add 5 to each term to get the next
-12+5 = -7
-7+5 = -2
-2+5 = 3
and so on. The nth term formula is
an = -12 + 5(n-1)
If you were to plug in n = 1, 2, 3, ... then it should generate the terms shown
Question 1(Multiple Choice Worth 1 points) (02.06 MC) Charles wants to determine which car is the fastest. The actual speed of four cars is shown below: Car A B C D Speed (in km/h) 60.34 60.32 60.33 60.35 If the speedometer can only measure to the nearest tenth of a second, which car will have a different measurement?
Answer:
Car D will have a different measurement because the 60.35 would round up to be 60.31 where all the other would round down and remain at 60.30
Step-by-step explanation: