Answer:
Step-by-step explanation:
Given a general quadratic formula given as ax²bx+c = 0
To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;
Step 1:
Bringing c to the other side
ax²+bx = -c
Dividing through by coefficient of x² which is 'a' will give:
x²+(b/a)x = -c/a
- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:
x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a + b²/4a²
- Taking the square root of both sides
√(x+b/2a)² = ±√-c/a + b²/√4a²
x+b/2a = ±√(-4ac+b²)/√4a²
x+b/2a =±√b²-4ac/2a
- Taking b/2a to the other side
x = -b/2a±√√b²-4ac/2a
Taking the LCM:
x = {-b±√b²-4ac}/2a
This gives the vertex form with how it is used to Solve a quadratic equation.
Find a value of 3a+4b when a=17 and b=9. Then use the formula v=u+at when the initial velocity is 3 m/s, the acceleration is 1.5m/s squared and the time is 7 seconds.
Final answer:
The value of 3a+4b is 87 when a=17 and b=9. Using the kinematics equation v=u+at, the final velocity is calculated as 13.5 m/s given the initial conditions provided.
Explanation:
To find the value of 3a+4b when a=17 and b=9, we substitute the given values into the expression:
3(17) + 4(9) = 51 + 36 = 87.
Thus, the value of 3a+4b is 87.
The next part of the question involves using the kinematics equation v = u + at to find the final velocity v. We are given an initial velocity u = 3 m/s, an acceleration a = 1.5 m/s2, and a time t = 7 seconds. Plugging the values into the formula gives us:
v = 3 m/s + (1.5 m/s2)(7 s) = 3 m/s + 10.5 m/s = 13.5 m/s.
The final velocity after 7 seconds is therefore 13.5 m/s.
Consider this sphere with a diameter of 5 m.
What can be concluded about the sphere? Check all
that apply,
The sphere has a radius of 10 cm.
The diameter measure is substituted into the
formula to find the volume.
5 m
The radius is half the diameter.
The formula to apply is y=- Bh
The volume of the sphere is two-thirds the volume
of a cylinder with the same radius and height.
9514 1404 393
Answer:
The radius is half the diameter.The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.Step-by-step explanation:
Regardless of the diameter, the radius is half the diameter. For this sphere, it is 5/2 m = 2.5 m.
__
The height of the sphere is equal to its diameter, so is 2r. The volume of a cylinder with radius r and height 2r is ...
V = πr²h = πr²(2r) = 2πr³
The volume of a sphere with radius r is ...
V = 4/3πr³
Then the ratio of sphere volume to cylinder volume is ...
(4/3πr³)/(2πr³) = (4/3)/2 = 2/3
The sphere volume is 2/3 that of a cylinder with the same radius and height.
A soccer field is 100 yards long and 60 yards wide. If a coach asks players to run from one corner to the corner diagonally across from it, how far will they run? Round to the nearest tenth of a yard.
A:12.6 yards
B:6.3 yards
C:80 yards
D:116.6 yards
What is the volume of this cone?
Answer:
133.97 cubic yard
Step-by-step explanation:
For Cone
radius (r) = 4yd
height (h) = 8yd
Volume of the Cone
= π r^2 * h/3
= 3.14 * 4*4 *8/3 yd
= 133.97 cubic yard
You rent an apartment that costs $1200 per month during the first year, but the rent is set to go up 10.5% per year. What would be the rent of the apartment during the 7th year of living in the apartment?
The rent of the apartment during the 7th year of living in the apartment is $2414.
Given that, principal = $1200, rate of interest =10.5% and time period = 7 years.
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
[tex]A=1200(1+\frac{10.5}{100} )^7[/tex]
[tex]A=1200(1+0.105)^7[/tex]
[tex]A=1200(1.105)^7[/tex]
[tex]A=1200\times2.0116[/tex]
[tex]A=2413.88[/tex]
A ≈ $2414
Therefore, the rent of the apartment during the 7th year of living in the apartment is $2414.
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Final answer:
To calculate the 7th year rent after a 10.5% annual increase starting from an initial rent of $1200, use the formula for compound interest. The rent amounts to approximately $2277.60 for the 7th year.
Explanation:
Calculating Future Rent Increase
To calculate the rent of the apartment during the 7th year after a consistent annual increase, we need to apply the percentage increase formula within a compound interest framework:
Rentₙ = Rent₀ × (1 + rate)ⁿ
Where Rentₙ is the rent after n years, Rent₀ is the initial rent, rate is the annual increase rate in decimal form, and n is the number of years.
For an initial rent of $1200 with a 10.5% increase per year:
Rent for the 7th year will be calculated as follows:
Rent₀ = $1200
rate = 10.5% or 0.105 in decimal form
n = 6 (since we are starting from year 1 to year 7)
Using the formula:
Rent₇ = $1200 × (1 + 0.105)⁶
Upon calculation, the rent for the 7th year is approximately:
Rent₇ = $1200 × (1.105)⁶ ≈ $1200 × 1.898 = $2277.60
Thus, the rent of the apartment during the 7th year of living there would be approximately $2277.60
Don has two jobs for job 1 he earns 7.55 an hour. For job 2 he earns 8.45 an hour last week he worked at the first job for 10 hours and the second job for 15 hours. What were his average earnings per hour
Answer:
for the first job is $75.05 and for the second job is $126.75
The average earning of Don is obtained as 8.09.
How to calculate the average?In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.
The total value can be calculated by multiplying the average to the number of data.
The time spent on first job is 10 hours and on second is 15 hours.
Now, the average earning per hour can be calculated as below,
(Earning for first job + Earning for second job) ÷ 25
⇒ (10 × 7.55 + 15 × 8.45) ÷ 25
⇒ 8.09
Hence, the average earnings per hour is given as 8.09.
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I NEED HELP ASAP ITS DUE IN 10 mins PLEASE
ILL MARK YOU AS BRAINLIST
Step-by-step explanation:
Simple
x - 7 = 0
x = 7
x + 8 = 0
x = - 8
Option no 1 is the correct answer
What is the data point that is the farthest from other data points when the box plot is NOT symmetrical?
A. Median
B. Outliner
C. Greatest Point
need an answer ASAP
Answer: B. Outlier
Step-by-step explanation:
An outlier is an extremely large or extremely small data value in a data set such that it appears far from the other data points when we plot data points on scatter plot or box plot.
Thus, the data point that is the farthest from other data points when the box plot is NOT symmetrical is Outlier.
Its presence affects the value of mean directly. So when a data set have outliers , we prefer Median(Mid value of a data set) as the best measure of central tendency because existence of outliers does not effect Median .
Hence, the correct option is B. Outlier.
find the measure of an angle between 0 and 360 coterminal with 510
Answer:
150 degrees
Step-by-step explanation:
HOPE THIS HELPED!
The measure of an angle between 0° and 360° coterminal with 510° is 150°. The difference between coterminal angles yields 360°.
Which angles are said to be coterminal?The angles that share a common terminal side are said to be coterminal angles. So, the difference between those angles is 360°.
Calculating the measure of the required angle:The given coterminal angle is 510°.
So, the reference angle = 510° - 360° = 150°
Thus, the angle is required as a measure of 150°.
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A.complementary
B.supplementary
C.congruent.
D.vertical.
Answer:
B.supplementary
Step-by-step explanation:
Angle ABC and Angle CBD are supplementary angles, which means they add up to 180 degrees
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth.
Answer:
38.47 square units
Step-by-step explanation:
All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.
The square has a side that measures 5.5 units.
The perimeter of a square is given as:
P = 4L
where L = length of side of the square
Therefore, the perimeter of the square is:
P = 4 * 5.5 = 22 units.
This means that the circumference of the circle is 22 units.
The circumference of a circle is given as:
C = 2πR
and the area of a circle is given as:
[tex]A = \pi R^2[/tex]
where R = radius
Therefore:
22 = 2πR
=> R = 22 / (2 * 3.14)
R = 22 / (6.28)
R = 3.50 units
The area is therefore:
[tex]A = \pi * 3.50^2[/tex]
A = 38.47 square units
The area of the circle is 38.47 square units.
The area of the circle is approximately 15.64 square units, calculated using the perimeter of the square and circle formulas.
To find the area of the circle with a circumference equal to the perimeter of the square, we'll first calculate the perimeter of the square using its side length. Then, we'll use the circumference formula to find the radius of the circle. Finally, we'll use the area formula for a circle to find the area.
Step 1:
Calculate the perimeter of the square.
Perimeter of square = 4 * side length = [tex]\(4 \times 5.5 = 22\)[/tex] units.
Step 2:
Set up the equation for the circumference of the circle.
Circumference of circle =[tex]\(2\pi \times\)[/tex] radius = Perimeter of square.
Step 3:
Solve for the radius.
[tex]\[2\pi \times \text{radius} = 22\][/tex]
[tex]\[\text{radius} = \frac{22}{2\pi}\][/tex]
Step 4:
Use the radius to find the area of the circle.
Area of circle = [tex]\(\pi \times \text{radius}^2\)[/tex]
Step 5:
Substitute the value of the radius and calculate.
[tex]\[Area = 3.14 \times \left(\frac{22}{2\pi}\right)^2\][/tex]
[tex]\[Area \approx 15.64\][/tex]
The area of the circle with a circumference equal to the perimeter of the square is approximately [tex]\(15.64\)[/tex] square units.
scale factor is 6/5 is the dilation an enlargement, reduction or congruence transformation? *
Answer:
Enlargement transformation
Step-by-step explanation:
A dilation is a transformation which produces an image of the same shape as the original, but may/may not be of the same size. A dilation could be an enlargement, reduction or a congruence.
The following rule applies(given the scale factor k)
If k > 1, there is an enlargement. If 0 < k < 1, there is a reduction. If k = 1, there is a congruence.therefore, since k=6/5=1.2>1, there is an enlargement transformation
Final answer:
When the scale factor is 6/5, it indicates that each dimension of the original figure is increased to achieve the new figure's dimensions, marking this transformation as an enlargement because the scale factor is greater than 1.
Explanation:
If a scale factor is 6/5, this means every dimension in the original figure is multiplied by 6/5 to get the dimensions of the new figure. Since the scale factor is greater than 1, each dimension of the original figure is increased to get the dimensions of the new figure. Therefore, this type of dilation is an enlargement, not a reduction or congruence transformation. An enlargement increases the size of an object while keeping its shape the same. In contrast, a reduction would mean the scale factor is less than 1, and a congruence transformation, which includes transformations like translation, rotation, and reflection, does not change the size at all.
answer for brainliest
Answer:
The slope of the equation is -3
The y-intercept of the equation is (0,-1)
Step-by-step explanation:
For slope: [tex]\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}[/tex]
[tex]m=-3[/tex]
For y-intercept: [tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]
[tex]\mathrm{Solve\:}\:y=-3\cdot \:0-1:\quad y=-1[/tex]
[tex]\mathrm{Apply\:rule}\:0\cdot \:a=0\\y=-0-1\\\\\mathrm{Subtract\:the\:numbers:}\:-0-1=-1\\y=-1\\[/tex]
what is the five-number summary for this data set? 3, 8, 14, 19, 22, 29, 33, 37, 43, 49
Assume the numbers in each answer choice are listed in this order: min, Q1, median, Q3, max
Answer: 3, 14, 25.5, 37, 49
Step-by-step explanation: Apex said so
which geometric figure contains exactly two perpendicular lines
Answer:
Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.
Step-by-step explanation:
Answer:
a right triangle
Step-by-step explanation:
What is the measure of angle f?
Answer:
∠ f = 37°
Step-by-step explanation:
f and 37 are vertical angles and congruent, so
∠ f = 37°
Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. She wants to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers. How many stickers can Kayla put in each bag?
Answer:
Kayla can put 9 stickers in each bag.
she can distribute it into bags of 9 stickers each of the same colour.
Step-by-step explanation:
Given;
yellow stickers = 36
red stickers = 27
blue stickers = 18
For her to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers without remainder.
We need to find the highest common factor of the number of the three colours.
36 = 4×9
27 = 3×9
18 = 2×9
We can see that they are all divisible by 9
Therefore, she can distribute it into bags of 9 stickers each
Final answer:
The greatest common divisor of 36, 27, and 18 is 9, so Kayla can put 9 stickers of the same color in each bag.
Explanation:
Kayla wants to distribute her stickers into bags, with each bag containing the same number of stickers of only one color. To find out how many stickers she can put in each bag, we need to find the greatest common divisor (GCD) of the numbers of stickers she has for each color. Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. The GCD of 36, 27, and 18 is 9. Therefore, Kayla can put 9 stickers in each bag.
Step-by-Step Solution
Identify the quantity of each color of stickers: yellow (36), red (27), blue (18).
Calculate the GCD of the three quantities: GCD(36, 27, 18) = 9.
Distribute the stickers into bags with 9 stickers of the same color per bag.
Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. What will the value of the boat be x years after she purchased it?
We have been given that Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. We are asked to find the value of the boat x years after Sandra purchased it.
We will use exponential decay formula to solve our given problem.
An exponential decay function is in form [tex]y=a(1-r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Decay rate in decimal form,
x = Time.
Let us convert 7% into decimal form.
[tex]7\%=\frac{7}{100}=0.07[/tex]
Initial value of car is $28,800, so our function will be:
[tex]y=$28,800(1-0.07)^x[/tex]
[tex]y=$28,800(0.93)^x[/tex]
Therefore, the value of boat after x years would be [tex]y=$28,800(0.93)^x[/tex].
An equation that equals 19
Answer:
There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:
5x = 95.....................................Divide both sides b 5x = 19.......................................There's one for you :)
1 + x - 5 = 15............................Combine like termsx - 4 = 15..................................Add 4 to both sides
x = 19
A pathway made of slate tiles measures 513 yards long. A tile measuring 2 feet is added to the end of the pathway. What is the total length of the pathway now? 513 ft 1023 ft 18 ft 22 ft
Answer:
The total length of the pathway now is 1,541 ft
Step-by-step explanation:
To calculate the length of the pathway now, what we need to do is to have a consistency in units.
Thus, we need to convert the 513 yards to ft
Mathematically 1 yard = 3 feet
Thus 513 yards will be = 513 * 3 = 1,539 ft
Thus the total length of the pathway now will be 1539 ft + 2 ft = 1541 ft
Answer: the answer is 1 5 3 ft
Step-by-step explanation:
Solve the system of equations 3x + y = 3 and 7x + 2y = 1.
1 Solve for the variable y in the first equation: y = 3 - 3x
2. Substitute the value for y into the second equation: 7x + 2(3 - 3x) = 1
3. Solve for x
Answer: -5
Step-by-step explanation:
Answer:
-5 is right
Step-by-step explanation:
Does anyone know the answer to this?
Answer: The height of the monitor is 12 inches.
Step-by-step explanation:
First, you need to acknowledge the Pythagorean Theorum,
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
You already have the c and the b , so you just have to plug them in to find a!
This is what it looks like when you substitute:
a² + 16² = 20²
Then, simplify.
a² + 256 = 400
Now, to isolate the variable, you have to move 256 to the other side. This, of course, means it changes from a positive to a negative number.
a² = 400 - 256
a² = 144
Now, you have to remove the square root from a. But, don’t forget, what you do to one side, you have to do to the other side. So, your equation will now look like this:
√a² = √144
The square root of a squared is obviously just a! And the square root of 144 is 12. Therefore, we now know that:
a = 12
So, the height of the monitor was 12 inches.
What’s the area of this figure?
Awnser:
14.5 cm
Step-by-step explanation:
1*7=7, 5*3=15/2=7.5
Answer:
14.5 cm^2
Step-by-step explanation:
We can find the area by adding the area of the long rectangle and the triangle
The rectangle is 1 cm by 7 cm
A = 1*7 = 7 cm^2
The triangle is 5 cm by (7-4) =3 cm
A = 1/2 (5*3)
A = 7.5 cm^2
The total area is
7+7.5 = 14.5 cm^2
Please help with this problem
Answer:
i dont know
Step-by-step explanation:
In a train yard, there are 6 flatcars, 7 boxcars, and 3 livestock cars. A train is made up of 9 cars.
Which would you use to find the number of ways the train could be made up?
Answer:
The answer is A on edge
Step-by-step explanation:
The number of ways the train could be made up are 4,151,347,200.
What is permutation?A permutation of a set is an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Now the given cars are 6 flatcars, 7 boxcars, and 3 livestock cars.
So the total number of cars, n = 6 + 7 + 3
= 16
Now, a train is made up of 9 cars,
Therefore, r = 9
Hence the required number of ways the train could be made is nPr
nPr = n!/(n-r)!
nPr = 16!/(16-9)!
nPr = 16!/7!
nPr = 16*15*14*13*12*11*10*9*8
nPr = 4,151,347,200
Hence,the number of ways the train could be made up are 4,151,347,200.
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how many days until 20 november from 19 october
answer: 334 days googled it
Which function has a vertex at (2, –9)? f(x) = –(x – 3)2 f(x) = (x + 8)2 f(x) = (x – 5)(x + 1) f(x) = –(x – 1)(x – 5
Answer:
c
Step-by-step explanation:
The function that has a vertex at (2, -9) is;
C: f(x) = (x - 5)(x + 1)
How to find the vertex of a Function?The formula for x-coordinate of a vertex is;
x = -b/2a
The correct function is Option C with f(x) = (x - 5)(x + 1).
We will expand to get;
f(x) = x² -5x + x - 5
f(x) = x² - 4x - 5
Putting 2 for x gives;
f(2) = 2² - 4(2) - 5
f(2) = -9
Also, x = -b/2a = -(-4)/(2*1) = 2
Thus, it is proved that option C has it's vertex at 2, -9
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Find the slope of the line that passes through (57, -27) and (-19, -34)
Answer:
10.86
Step-by-step explanation:
m = Y2 - Y1 / X2 - X1 = -19 -57 / -34 +27 = -76 / -7 = 10.86
Answer:
y=7/76x-129/4
Step-by-step explanation:
I'm going to assume you want this in slope intercept form.
The equation of a line is equal to y = mx+b
Where m is the slope and b is the y-intercept.
The slope of a line is a measure of how steep the line is.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
y2-y1/x2-x1
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (57,-27), point #1, so the x and y numbers given will be called x1 and y1, and the second point will be x2 and y2.
So we just plug in the numbers, and find the slope to be 7/76.
What about b(the y-intercept), I can already hear you typing. Well, to do that, you plug in the coordinates of the points given and solve for b.
And there you have it:
y=7/76x-129/4 is the equation of the line.
Suppose the system of linear equations has no solution. Which is NOT a possible value of the constant for the second equation?
6x + 9y = 15
2x + 3y = __
A) 5
B) 10
C) 15
D) 20
Answer:
A) 5
Step-by-step explanation:
The coefficients of the second equation are 1/3 of those of the first equation. If the constant of the second equation is also 1/3 of the constant of the first equation, then the equations are dependent, and will have an infinite number of solutions.
The constant must be something other than 1/3·15 = 5 to make the equations inconsistent, having no solutions.
Easy Question
Topic: Volume
Use the other attachment to help u find the formula
Answer:
see below
Step-by-step explanation:
V = l*w*h for the rectangular tank
V = 70* 40*40
=112000 cm^3 = 1mL
The water is 84000
Make this a fraction
84000/112000 = 3/4
The water fills 3/4 of the tank
1-3/4 = 1/4
It is 1/4 from the top
Find the volume of the treasure chest
V = 12*10*8 =960
Tower
V = pi r^2
3.14 * 10^2 *10
=3140
Water + chest + tower
84000+960+3140 =88100
This is less than 112000 so the water will not overflow
Answer:
a) 10 cm
b) Will not overflow
Step-by-step explanation:
8400 = base area × height
84000 = 70 × 40 × h
h = 30
From the top: 40 - 30 = 10cm
b) Capacity of the tank:
70 × 40 × 40
112,000 cm³
Combined volume of the two vessels:
(12 × 10 × 8) + (3.14 × 10² × 10)
960 + 3140
4,100 cm³
4100 = 70 × 40 × rise
rise = 1.464285715 cm
Since 1.464285715 < 10
It will not overflow