Answer:
Step-by-step explanation:
Value of the car at the end of the first year = £9680
Depreciation = 12 %
Original price = £ x
If we reduce 12% of original price from x, we will get £9680
x - 12% of x = £ 9680
[tex]x-\frac{12}{100}x=9680\\\\\\\frac{88}{100}x=9680\\\\x=9680*\frac{100}{88}\\\\x = 11000[/tex]
Original price = £ 11000
Kristina wants to buy a flute that costs 240 . She has saved 20 each week for 3 weeks . How many more weeks does Kristina need to save money if she continues to save 20 each week
The ratio of the cost of a shirt to the cost of a jacket is 2:5. If the jacket cost $240 more than the shirt,
find the cost of the shirt and the cost of the jacket.
Given:
The ratio of the cost of a shirt to the cost of a jacket is 2:5.
The jacket cost $240 more than the shirt.
To find:
The cost of the shirt and the cost of the jacket.
Solution:
Let x be the cost of the shirt.
The jacket cost $240 more than the shirt. So, the cost of Jacket is (x+240).
The ratio of the cost of a shirt to the cost of a jacket is 2:5. So,
[tex]\dfrac{x}{x+240}=\dfrac{2}{5}[/tex]
[tex]5x=2(x+240)[/tex]
[tex]5x=2x+480[/tex]
Subtract 2x from both sides.
[tex]5x-2x=480[/tex]
[tex]3x=480[/tex]
Divide both sides by 3.
[tex]x=\dfrac{480}{3}[/tex]
[tex]x=160[/tex]
So, the cost of shirt is $160.
Now, the cost of jacket is:
[tex]160+240=400[/tex]
Therefore, the cost of shirt is $160 and the cost of jacket is $400.
Find the slope of
(6,-3)(-2,-3)
Answer:
0
Step-by-step explanation:
We can find the slope by using the slope function
m = (y2-y1)/(x2-x1)
= (-3 - -3)/(-2 - 6)
= (-3+3)/(-2-6)
= 0/-8
= 0
To calculate the slope use the gradient formula.
[tex] \bf \Large \: m \: = \: \frac{y_2 \: - \: y_ 1}{x_2 \: - \: x_ 1} \\ [/tex]
[tex] \bf \large\longrightarrow \: y_2 \: = \: - 3[/tex]
[tex]\bf \large\longrightarrow \: y_1 \: = \: - 3[/tex]
[tex]\bf \large\longrightarrow \: x_1 \: = \: 6[/tex]
[tex]\bf \large\longrightarrow \: x_2 \: = \: - 2[/tex]
Substuting the values[tex]\bf \Large \: m \: = \: \frac{( - 3 )\: - \: (- 3)}{ (- 2) \: - \: 6} \\ [/tex]
[tex]\bf \Large \: m \: = \: \frac{ \: 0 }{ - 8 \: \: } \\ [/tex]
[tex]\bf \Large \: m \: = \: \cancel\frac{ \: 0 }{ - 8 \: \: } \: ^{0} \\ [/tex]
[tex]\bf \Large \: m \: = \: 0[/tex]
Hence , the slope is 0A boat travels 84 miles in 4 hours. How should you calculate the unit rate of miles to hours
Answer:
The boat is going 21 MPH
Step-by-step explanation:
If the boat is going 84 miles in 4 hours, and you want to find the unit rate, divide 84 by 4.
84/4 = 21
Hope this helps!
solve the triangle. Round decimal places to the nearest place
Which inequality is represented by the graph?
Y>-2/3x+1
Y<-2/3x+1
Y<-3/2x+1
Y>-3/2x+1
Answer:
Last option, y > -3/2x+1
That's the answer you're looking for
Nigel makes the claim that x=6 is the solution to the equation 4(5x−12)−7x=5x. His work to support his claim follows. Given: 4(5x−12)−7x=5x Step 1: 20x−48−7x=5x Step 2: 20x−7x−48=5x Step 3: 13x−48=5x Step 4: 13x−13x−48=5x−13x Step 5: 0−48=−8x Step 6: 6=x Which of the following justifications can be used to justify and support Nigel's work? Select all justifications that are correct.
Step 1 is justified by the Distributive Property. , Step 1 is justified by the Distributive Property. , ,
Step 4 is justified by the Symmetric Property. , Step 4 is justified by the Symmetric Property. , ,
Step 5 is justified by the Property of Additive Inverses. , Step 5 is justified by the Property of Additive Inverses. , ,
Step 2 is justified by the Commutative Property. , Step 2 is justified by the Commutative Property. , ,
Step 6 is justified by the Associative Property.
Answer:
Step 1 is justified by the Distributive Property.
Step 4 is justified by the Symmetric Property
Step-by-step explanation:
Given the equation solved by Nigel expressed as
4(5x−12)−7x=5x.
First, we need to expand the bracket using the distributive property
4(5x−12)−7x=5x.
4(5x)-4(12) -7x = 5x
20x - 48 - 7x = 5x
Hence Step 1 is justified by the Distributive Property.
Next is to collect the like terms;
20x - 7x - 48 = 5x
Take the difference
13x - 48 = 5x
Next is to subtract 13x from both sides according to the symmetric property
13x - 48 - 13x = 5x - 13x
Hence Step 4 is justified by the Symmetric Property
The resulting equation will be
0-48 = -8x
Divide both sides by -8
-48/-8 = -8x/-8
6 = x
Hence the correct justifications are Step 1 is justified by the Distributive Property AND Step 4 is justified by the Symmetric Property
Find the area of the shaded region.
Answer:
pi × 18cm^2
Or approximately,
56.52cm^2 (using 3.14 for pi)
or
56.5487cm^2 (using pi button on calculator)
Step-by-step explanation:
Area of a circle is pi times [radius squared].
All circles are 360°.
Problem can be solved by finding area of whole circle, and then using ratios.
Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2
80° / 360° = Area[shaded] / (pi × 81cm^2)
pi × 18cm^2 = Area[shaded]
((If you read my answer before the edit, I am sorry. I made a calculator error.))
HURRY!!!!! HELP PLEASE!!!! NO SPAM!!!!!!!!!There are two identical oil tanks. The level of oil in Tank A is 6 ft and is drained at the rate of 0.5 ft/min. Tank B contains 10 ft of oil and is drained at the rate of 1 ft/min. After how many minutes will the level of oil in the two tanks be the same?
Answer:
8 munutes
Step-by-step explanation:
let :
x is the final level for both tanks (in ft) and
t is the time (in minutes)
the equation :
x = 6 - 0.5 t (eq.1)
x = 10 - 1t (eq.2)
eq. 1 = eq. 2
=>
6-0.5t = 10-1t
1t - 0.5t = 10-6
0.5t = 4
t = 4/0.5 = 8
t = 8 minutes
Answer: 8 minutes
Step-by-step explanation:
Write an equation for the level of oil in each tank.
Let t = the number of minutes.
Tank A: y = 6 − 0.5t
Tank B: y = 10 − 1t
Solve the system by using a table of values
When t = 8 minutes, the level in both tanks will be at 2 feet.
Christian has 1/2 of a foot of tape. His friend gives him 3/10 of a foot of tape. How much tape does Christian have now?
Answer:
4/5 foot
Step-by-step explanation:
Add the lengths together
1/2 +3/10
Get a common denominator
1/2 *5/5 + 3/10
5/10 + 3/10
8/10
Simplify the fraction by dividing the top and bottom by 2
4/5
[tex]\rm \implies \: Total \: \: length \: \: of \: \: tape \: = \: \frac{1}{2} \: + \: \frac{3}{10} \\ [/tex]
Now , we take LCM of denominators.LCM of 2 and 10 is 10.[tex]\bf \large \rightarrow \: \: \frac{5 \: + \: 3}{10} \: = \: \frac{8}{10} \\ [/tex]
Now , simplifying the fraction in simplest form.
[tex]\bf \large \rightarrow \: \: \cancel\frac{8 \: \: ^{4} }{10 \: \: ^{5} } \: = \frac{4}{5} \\ [/tex]
Christian have 4/5 foot of tape have now.
factories 2x^3+ 7x^2+ 7x +2 emergency pls
hope it helps you...............
Answer:
the answer is (x+1)(x+2)(2x+1)
If necessary, write in simplest radical form
Answer:
2*sqrt(5)
Step-by-step explanation:
By using Pythagoras theorem, we have
4^2+2^2=(the third side)^2
16+4=(the third side)^2
Third side=sqrt(20)=2*sqrt(5)
Describe the solution to the inequality. r < –3
Answer:
98
Step-by-step explanation:
if measure of three angles of a quadrilateral are 65 degree 95 degree and 45 degree then find the measure of the fourth angle?
Answer:
155 degrees
Step-by-step explanation:
Hi there!
The sum of the interior angles of a quadrilateral is always 360 degrees. To find the measure of the fourth angle, subtract 65, 95 and 45 from 360:
360-65-95-45
= 155
Therefore, the measure of the fourth angle is 155 degrees.
I hope this helps!
Answer:
155 degrees
Step-by-step explanation:
A quadrilateral has a total internal angle sum of 360 so we can set up an equation where x is the fourth angle
360=65+95+45+x
360=205+x
x=155
Determine the intercepts of the line.
Answer:
y-intercept = -55
x-intercept =25
Step-by-step explanation:
I know how to do this
What is the measure of ABC in the figure below?
1.) Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.
2.) Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation.
3.) Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation
9514 1404 393
Answer:
x = x+10 = x+1x+1 = x+1Step-by-step explanation:
1. There will be no solution if the equation is a contradiction. Usually, it is something that can be reduced to 0 = 1.
If we choose to make our equation ...
x = x +1
Subtracting x from both sides of the equation gives ...
0 = 1
There is no value of the variable that will make this be true.
__
2. Something that reduces to x = c will have one solution. One such equation is ...
0 = x+1
x = -1 . . . . subtract 1 from both sides
__
3. Something that reduces to x = x will have an infinite number of solutions.
One such equation is ...
x+1 = x+1
Subtracting 1 from both sides gives ...
x = x . . . . true for all values of x
which of the statement is true
Answer:
c
Step-by-step explanation:
Profit = 4.5 (240)-1080 = 0
the maximum profit would occur when u sell all 350 tickets,
profit = 4.5(350)-1080 = 495 (not a nor b)
Answer:
The statement that is true is C
Rewrite the expression in the form x^n:
x^-10/3
---------
x^3
Answer:
x^ (-19/3)
Step-by-step explanation:
x ^ (-10/3) ÷ x^3
We know a^b ÷ a^c = a^(b-c)
x ^ (-10/3) ÷ x^3 = x^(-10/3 - 3) = x^(-10/3 - 9/3) = x^ (-19/3)
Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
Answer:
580
Step-by-step explanation:
Assuming that the answer should be in terms of z scores, we can calculate the z score as
z = (observed value - mean)/(standard deviation)
For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is
z = (86-71)/20 = 0.75
Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have
0.75 = (observed score - 550)/40
multiply both sides by 40 to remove a denominator
0.75 * 40 = observed score - 550
add 550 to both sides to isolate the observed score
0.75 * 40 + 550 = observed score = 580
2cos5xcos3x+sinx=cos8x
It looks like your equation (it's not an identity) is
2 cos(5x) cos(3x) + sin(x) = cos(8x)
Recall that
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
==> 2 cos(x) cos(y) = cos(x + y) + cos(x - y)
so that
2 cos(5x) cos(3x) = cos(8x) + cos(2x)
Then the equation simplifies to
cos(8x) + cos(2x) + sin(x) = cos(8x)
cos(2x) + sin(x) = 0
Also recall that
cos(2x) = 1 - 2 sin²(x)
so the equation is quadratic in sin(x) and can be factorized:
1 - 2 sin²(x) + sin(x) = 0
2 sin²(x) - sin(x) - 1 = 0
(2 sin(x) + 1) (sin(x) - 1) = 0
Solve for x :
2 sin(x) + 1 = 0 or sin(x) - 1 = 0
sin(x) = -1/2 or sin(x) = 1
[x = arcsin(-1/2) + 2nπ or x = π - arcsin(-1/2) + 2nπ] or x = arcsin(1) + 2nπ
(where n is any integer)
x = -π/6 + 2nπ or x = -5π/6 + 2nπ or x = π/2 + 2nπ
If a semi-circle was rotated about the y-axis, like the one shown below, what would be the resulting three-dimensional shape?
Pyramid
Cylinder
Sphere
Cone
Answer:
Step-by-step explanation:
This rotation would create a sphere.
If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere.
What is a semi-circle?A semicircle is a half-circle formed by a one-dimensional locus of points.
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.
If a semi-circle is rotated about the y-axis of the graph, then the resulting three-dimensional shape will be a sphere. This is because of the fact that when the semi-circle will be rotated about the y-axis then all the points will be at equal distance in all the directions from the centre.
Learn more about Sphere:
https://brainly.com/question/11374994
2/3 (9-12n)
plz tell me fast its urgent
no spam or i will report
Answer:
6 -8n
Step-by-step explanation:
2/3 (9-12n)
Distribute
2/3 *9 - 2/3 *12n
6 -8n
A set of prime number between 5 and 15 . express it in listing and set builder methods.
Answer:
Step-by-step explanation:
{7,11,13}
Which is the best estimate for the percent equivalent of StartFraction 7 Over 15 EndFraction? 21% 22% 46% 47%
Answer:
47%
Step-by-step explanation:
StartFraction 7 Over 15 EndFraction = 7/15
Equivalent Percentage
7/15 × 100
= 0.4666666666666 × 100
= 46.666666666666%
Approximate to the nearest whole percentage
= 47%
The answer is 47%
Answer:7
Step-by-step explanation:
see attached photo, please help asap, it is due in 30 minutes !!!
Answer:
Answer is 3.398
Step-by-step explanation:
Solve by putting into calculator.
A bag contains 4 purple beads and 3 green beads. A bead is drawn and then replaced before drawing the second bead. Find the probability both beads drawn are green.
A) 16/49
B) 6/7
C) 6/49
D) 9/49
Answer:
9/49
Step-by-step explanation:
4 purple beads and 3 green beads= 7 beads
P( green) = green = total = 3/7
Replace the bead
4 purple beads and 3 green beads= 7 beads
P( green) = green = total = 3/7
P( green , replace, green) = 3/7 * 3/7 = 9/49
Find the number in which 9 has greater value.
0.5689
5.6890
56.89
569.80
Answer:
569.80Step-by-step explanation:
Among all the choices, the digit 9 has the greatest value in number 569.80. For the reason that 9 got ones value - which are greatest than other.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
graph the equation y=5/7x
Answer:
Step-by-step explanation:
8x square + 1 + 3square - 2
Answer:
8x^2-1+3^2
Step-by-step explanation:
