Given:
The cost of a laptop increased by 25% between 2015 and 2019.
In 2019, the laptop cost £1000.
To find:
The cost of the laptop in 2015.
Solution:
Let x be the cost of the laptop in 2015.
The cost of a laptop increased by 25% between 2015 and 2019. So, the cost of the laptop in 2019 is
Cost of laptop in 2019 = [tex]x+\dfrac{25}{100}x[/tex]
= [tex]x+0.25x[/tex]
= [tex]1.25x[/tex]
In 2019, the laptop cost £1000.
[tex]1.25x=1000[/tex]
[tex]x=\dfrac{1000}{1.25}[/tex]
[tex]x=800[/tex]
Therefore, the cost of the laptop in 2015 is £800.
State the solutions for the quadratic equation graphed below.
(6x-3)(4x-1) standard form
Answer:
6x+3
Step-by-step explanation:
24x-6x-12x+3
6x+3
-4x = 7y + 13
Find the slope of the line
Answer:
-4/7
Step-by-step explanation:
The first step of this problem would be changing the format of the equation so that it fits into slope-intercept form.
-4x = 7y + 13
-4x -7y = 13 (subtract 7y from both sides)
-7y = 4x + 13 (add 4x to both sides)
7y = -4x -13 (divide both sides by -1)
y = -4/7x - 13/7 (divide both sides by 7)
Now that it is in slope-intercept form, finding the slope is simple as long as you know what to look for.
Remember that y is simply a variable, just because it is at the beginning of the equation does not mean -4/7x - 13/7 is the answer. The question is asking specifically for the slope of the line. Slope in this equation is m. If y = mx + b, then m = -4/7.
The slope of the line is -4/7.
I need help please.
Answer I think D, I would never choose b :
Step-by-step explanation:
Use the sequence {0.3, 0.03, 0.003, 0.003, ... } to answer the question.
What is the explicit rule that describes the sequence?
1 an = 0.3(0.01)(n-1)
2 an = 0.3(0.001)(n-1)
3 an = 0.3(10)(n-1)
4 an = 0.3(0.1)(n-1)
Answer:
2 an ? Im pretty sure hope it helped
Answer:
an = 0.3(0.1)^(n - 1)
Step-by-step explanation:
so it's number 4 ;)
c=3
c2 + 5
..............
Answer:
3x2+5=11
Step-by-step explanation:
The ratio of math teachers to choir teachers is 3:2 respectively. There are 12 math teachers. How many math and choir teachers are there all together?
Answer:
Hi liddywiddy, sorry you had to wait so long
There are 20 teachers in all
Step-by-step explanation:
the ratio 3:2 is now 12:x
12 / 3 = 4
so the multiplier is 4
now:
4x2 = 8
Next we add them: 12+ 8 = 20
Answer:
20 teachers in all
Step-by-step explanation:
12 / 3 = 4,
4 * 2 = 8,
so 12 + 8 = 20
Jimmy and Kima are going on a trip. They will drive for three days. The first day they will drive 182 miles. The second day they will drive 439 miles. The third day they will drive 217 miles.
Which expression is the closest estimate of how many miles Jimmy and Kima will drive on their trip?
options.
150 + 400 + 200
200 + 400 + 200
200 + 450 + 200
200 + 500 + 200
Answer:
200 + 400 + 200
This is because you always round up past 50 and down under 50 so.
182->200
439->400
217->200
3m² – 17m + 10 factoring polynomials
This is midpoints geometry I need help soon.
Answer:
x=4.5
Step-by-step explanation:
PR=28
PQ= 2x+5
Require
Find X
What is 600 minus 258?
Answer:
342
Step-by-step explanation:
Answer:
342
Step-by-step explanation:
600 - 258 = 342
Note:
Please mark as Brainliest! <3
Hello, happy Friday, I am just here with some geometry questions.
Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!
Please explain how you got it.
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
By the Triangle Proportionality Theorem:
[tex]\displaystyle \frac{x}{12}=\frac{x+1}{15}[/tex]
By cross-multiplication:
[tex]\displaystyle 12(x+1)=15(x)[/tex]
Distribute:
[tex]12x+12=15x[/tex]
Subtract 12x from both sides:
[tex]12=3x[/tex]
Hence:
[tex]x=4[/tex]
Answer:
4
Step-by-step explanation:
The first thing you should notice is that the triangles (the smaller one and the larger one) are similar due to angle-angle similarity (the top angle equals itself, and because the bases are parallel lines cut by a transversal, the base angle of the bigger triangle is equal to the corresponding base of the smaller triangle.
Similar triangles' corresponding sides have equal ratios to one another. That means we can set up an equation: side of smaller triangle ÷ corresponding side of larger triangle = other side of smaller triangle ÷ corresponding side of larger triangle. We plug the values given to us and can change this equation to:[tex]\frac{x}{x + 12} = \frac{x + 1}{x + 16}[/tex] **
We now multiply both sides of the above equation by [tex](x + 12)(x + 16)[/tex] to get: [tex]x(x + 16) = (x + 1)(x + 12)[/tex]
[tex]x^{2} + 16x = x^{2} + 13x + 12[/tex]
[tex]3x = 12[/tex]
[tex]x = 4[/tex]
That means our answer, for the value of x, is 4
** Make sure you don't say [tex]\frac{x}{12} = \frac{x + 1}{15}[/tex], because those aren't the sides of the larger square.
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
20, 10, 5, ...
Answer:
geometric, with a common ratio of 1/2
Step-by-step explanation:
The sequence is geometric because you get successive trems by multiplying the previous term by a certain constant, the 'common ratio'. (If you got each successive term by adding or subtracting the same constant number each time, that would be an arithmetic sequence.)
In this case, it looks like you get each successive term when you multiply the previous term by 1/2.
Thus, the common ratio is 1/2.
6x - 8y = 12 and 5x + 8y = -1 Solve using elimination
Answer:
Step-by-step explanation:
6x-8y=12
5x+8y=-1
add them
11x=11
x=1
y=-3/4
Answer:
(1,-3/4)
Step-by-step explanation:
Luckily, y is already opposites, so it should be easier:
6x-8y=12
5x+8y=-1
Combine; This should end up with y eliminated -
11x = 11
x = 1
Now we can plug 1 in for x in one of the equations to find y. I'm going to use the second one.
5(1) +8y = -1
5+8y=-1
8y=-6
y=-6/8 (you can simplify)
The point at which the lines intersect is (1,-3/4)
Henry has 96 marbles. he is packing containers with 8 marbles in each container. how many containers, c, does Henry need to pack all the marbles?
A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7. What
should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated?
-3x-7--56
-7x+10y - 1
Answer:
-3
Step-by-step explanation:
7(-3x-7y-56)
-21x-49y-392
-3(-7x+10y-1)
21x-30y+3
because the eq. multiplied by 7 is negative, the second eq mus be positive in order to eliminate the x variable. this is why we multiply by a (-). by multiplying the second eq by 3, both eq. will result in a coefficient of 21. one positive one negative allowing the x variable to be eliminated from the problem.
The line passes through (6,6) and (-2,2)
Step-by-step explanation:
y-y1=m(x-x1)
m=y2-y1/x2-x1
Which of these IS a Pythagorean triple? 11,60,62 6,8,15 5,11,12 18,80,82
Answer:
18,80,82
Step-by-step explanation:
82^2= 6724
18^2+ 80^2= 6724
The square of the largest number is equal to the sum of the squares of the two smaller numbers.
Three rides at the Fun Park cost $10.50. How
many rides can you get on with $38.50?
Answer:
With $38.50 you can get on 11 rides.
Step-by-step explanation:
10.50 ÷ 3 = 3.50 per ride.
38.50 ÷ 3.50 = 11 rides.
Equation R: y = -2x + 10
Equation S: y = 3x - 20
What is the solution ( , )
Step-by-step explanation:
3x -20= -2x +10
or,5x=30
or,X=30/5
or,X=6
Y= -2×6 + 10
= -2
therefore solution is (6, -2)
Need help ASAP
questions in the pics i have sent
Answer:
Step-by-step explanation:
Picture 1
In right triangle ABC,
Side AB is the opposite side of angle C.
Picture 2
In triangle MKL,
tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{KL}{KM}[/tex]
= [tex]\frac{15}{8}[/tex]
Option (1) is the answer.
Picture 3
In ΔXYZ,
sin(∠Z) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{XY}{XZ}[/tex]
For the length of XY we will apply Pythagoras theorem in ΔXYZ,
XZ² = XY² + YZ²
XY² = XZ² - YZ²
= (40)² - (32)²
XY = √576
= 24
sin(Z) = [tex]\frac{24}{40}[/tex]
sin(Z) = [tex]\frac{3}{5}[/tex]
Picture 4
In right triangle DEF,
Cos(D) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{EF}{DF}[/tex]
= [tex]\frac{75}{72}[/tex]
= [tex]\frac{25}{24}[/tex]
Picture 5
In ΔABC,
tan(63°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(63°) = [tex]\frac{BC}{AB}[/tex]
AB = [tex]\frac{BC}{\text{tan}(63)}[/tex]
AB = [tex]\frac{8}{\text{tan}(63)}[/tex]
AB = 4.0762 ≈ 4 m
Option (3) will be the answer.
UNDERSTAND
There are eight cups of ice cream in a large container of Berry
Blast ice cream. Each scoop of ice cream is 1/2 of a cup. How
many scoops of ice cream are in an entire container of Berry Blast
ice cream?
The area of the triangle below is 33.62 square feet. What is the length of the base?
Answer:
4.1
Step-by-step explanation:
is this table proportional?
explain
Answer:
yes because the hours to distance is moving at a constant rate and if you were to graph it, it would also go through the origin
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
This table is not proportional because the outputs do not get their answer using the same equation. The first to inputs and outputs ([tex]\frac{1}{2}[/tex] and [tex]\frac{1}{4}[/tex]; 1 and [tex]\frac{1}{2}[/tex]) are proportional. You multiply the input (distance) by [tex]\frac{1}{2}[/tex] to get the output (hours). The final option of input and output ([tex]2\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex]) is not proportional.
Hope it helps!
List three factors that must be considered when designing and building a house? Describe how each factor can influence the design and the building of the house.
I will be giving brainiest to correct and best explained answer! :)
Step-by-step explanation:
I would say the area its getting built. imagine wanting to build a house but you can't dig the sewer (if thats the spelling) pipes bc the area you want doesn't have any water or something like that. definitely money. without it, you can't do anything, you can't buy materials or even hire people to help you because you cannot tell me that you can build a house on your own. Another I would say is Labor cause like I said, if you ain't got nobody to help you, you're probably going to take a few years or more. so if you want to build a house in an area where there is a few architects and designers, you're just going to have to suck it up and get what you get.
120 coins what is the ratio if 2/6 is nickels and 2/6 are dimes and the rest is quarters. What is the ratio of nickels to dimes to quarters?
Hi there!
If the nickels and dimes ratioe are both 2:6, then the quarter is also 2:6.
The total of of all together is also 6:6 and 6:6 is also 120 coins.
120 divide by 3 different kinds of coins are 40.
This means that there are 40 of 1 coin out of 3 different kinds of coins. What I really mean is that each coins all have 40 each...
Therefore, the ratios of nickels to dimes and to quarters are 40:40:40...
What is the slope of X= -15
Answer:
Step-by-step explanation:
Since x = -15 is a vertical line, their is no y- intercept and the slope is undefined
Pls answer this is a khan academy question
Answer:
Oak tree - linearBirch tree - exponentialStep-by-step explanation:
The first table represents a linear function
For each 3 years, the rise of branches is ~12The second table represents an exponential function
For each years time, the branches increase ~4 times(8x²-4x+1)+(-3x²+x+5)
Answer:
[tex]5x^{2} -3x+6[/tex]
Step-by-step explanation:
Please help on my last question asap
Answer:
A is the answer
Step-by-step explanation: