The equation 2x² - 7x - 30 = 0 has two solutions: x = -5/2 and x = 6 and both solutions are real.
What is the number and type of solutions of the quadratic equation?Given the equation in the question:
2x² - 7x - 30 = 0
We can use the quadratic formula to to determine the number and type of solutions :
x = (-b±√(b² - 4ac)) / (2a)
2x² - 7x - 30 = 0
a = 2
b = -7
c = -30
Plugging in these values, we get:
x = (-b±√(b² - 4ac)) / (2a)
x = (-(-7) ± √((-7)² - ( 4 × 2 × -30))) / (2×2)
x = (7 ± √( 49 - ( -240))) / (4)
x = (7 ± √( 49 + 240)) / (4)
x = (7 ± √( 289)) / (4)
x = (7 ± 17) / 4
x = (7 - 17) / 4 and x = (7 + 17) / 4
x = -5/2 and x = 6
Therefore, the two solutions are x = -5/2 and x = 6.
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Question 4
A is at -6 and B is at 9. Find the point, T, so that T is three-fifths of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
1
2 3 4 5 6 7 8 9 10
The location of point T on the number line is 3
Calculating the location of point TFrom the question, we have the following parameters that can be used in our computation:
A = -6
B = 9
T = three-fifths of the distance from A to B.
Using the above as a guide, we have the following:
T = A + 3/5 *(B - A)
Substitute the known values in the above equation, so, we have the following representation
T = -6 + 3/5 *(9 + 6)
Evaluate
T = 3
Hence, the location is 3
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can you please help me with the answer?
The dimension is gioven as 69.26 feet
How to solve for the dimensionxy = 1836
This is the area
The cost of fence = 2x + 2y
cost of interior fencing
2x + 4y
C = 20.40(C1) + 12.00(C2)
We have to put the vakues in the formula above
C = 20.40(2x + 2y) + 12.00(2x + 4y)
= 40.80x + 40.80y + 24.00x + 48.00y
= 64.80x + 88.80y
from xy = 1836
y = 1836 / x
We have to put the value in C
C = 64.80x + 88.80(1836/x)
= 64.80x + 164236.80/x
Take the deriveative with respect to x
64.80 - 164236.80/x^2 = 0
x = √(164236.80/64.80)
= 69.26 feet
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
Just Need the blanks filled in PLEASE HELP
The Equation based on the function will be: t = (1/0.07) * ln(P/1,500,000)
How to explain the functionInitially, the exponential expression is extracted and formulated as follows:
It should be noted that to obtain e^(0.07t) = P/1,500,000
Secondly, in order to determine the value of t, take the natural logarithm of both sides of the equation such that:
Take ln(e^(0.07t)) = ln(P/1500000)
It can now be represented by 0.07t = ln(P/1500000)
Finally, on dividing both components of the term through 0.07, it results in the isolation of t where:
Equation: t = (1/0.07) * ln(P/1,500,000)
In conclusion, this function's inverse describes the number of years, since the year 1990, for a determined population figure, P - its formation being previously outlined above.
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Do the following using Matlab: Generate 10 numbers between 1 and 6, calculate the mean. Generate 100 numbers between 1 and 6. calculate the mean. Generate 1000 numbers between 1 and 6, calculate the mean. There is a command in Matlab to generate numbers. Do not include the numbers when you submit the project. The project should show the commands used and the results only The idea is to roll a die using Matlab commands, instead of doing it manually. Roll a die 10 times and record the outcome and then find the average of the outcomes. Then compare the means for the cases of 10, 100 & 1000. On page 2 of lecture 10, we found that the mean of rolling a die to be 3.5. Therefore, your answer will be close to 3.5 every time you repeat the experiment for larger numbers.
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
We have,
To generate numbers between 1 and 6 in Matlab, we can use the "randi" command.
To generate 10 numbers, we can use:
```matlab
numbers10 = randi([1, 6], [1, 10]);
mean10 = mean(numbers10);
disp(mean10);
```
To generate 100 numbers, we can use:
```matlab
numbers100 = randi([1, 6], [1, 100]);
mean100 = mean(numbers100);
disp(mean100);
```
To generate 1000 numbers, we can use:
```matlab
numbers1000 = randi([1, 6], [1, 1000]);
mean1000 = mean(numbers1000);
disp(mean1000);
```
After running these commands, we will get the means for generating 10, 100, and 1000 numbers between 1 and 6.
As mentioned in the question, the mean of rolling a die is 3.5.
Therefore,
We can see that the means we got from Matlab are close to 3.5 for larger numbers of rolls.
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How many cubic meters of dirt are there in a pile conical shape 9m in diameter and 4m high
The Volume of Cone is 84.8 m³.
We have,
d = 9 m
r= 4.5 m
H = 4 m
So, Volume of Cone
= 1/3 πr²h
= 1/3 (3.14) (4.5)² (4)
= 1/3 (3.14) (20.25) (4)
= 84.8 m³
Thus, the volume is 84.8 m³.
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A foam cube, 5 in. in width has a mass of 62 g. What is the volume and density
The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.
Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.
So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.
MARK ME BRAINLEISTWhich linear equation shows a proportional relationship?
y = 2x
y equals one third times x plus 2
y equals negative two fifths times x minus 1
y = 1
A linear equation which shows a proportional relationship include the following: A. y = 2x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4
Constant of proportionality, k = 2.
Therefore, the required linear equation is given by;
y = kx
y = 2x
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Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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A student is using wooden blocks to build two towers of different heights. All of the blocks are the same size and have a height of 3/4inch. The short tower is 5 blocks high and the tall tower is 9 blocks high. What is the difference in height, in inches, between the short tower and the tall tower?
The difference in height of short and tall tower is 3 inch.
We have,
length of each block = 3/4 inch
So, the length of 5 block
= 5 x 3/4
= 15/4 inch
and, the length of 9 blocks
= 9 x 3/4
= 27/4 inch
So, the difference in height of short and tall tower is
= 27/4 - 15/4
= 12/4
= 3 inch
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Rachel works at a lemonade stand at the park on Monday she used 1 2/5 bags of lemons on Tuesday she use 1 1/4 times as many lemons as on Monday how many bags of lemons does Rachel have use on Tuesday
Answer:
1.75 Bags of Lemons
Step-by-step explanation:
1 2/5 = 1.4
1 1/4 = 1.25
1.4 * 1.25 = 1.75 Bags of Lemons
What is the sum of 3.0 x 4.1 x 5.5
Answer: 67.65
Step-by-step explanation:
Multiply 3.0*4.1 and you get 12.3
Then take that sum and multiply it by the 5.5
So 12.3*5.5=67.65
Find the measure of the exterior angle 1
WILL mark as brainliest if you get correct
Answer: C: 144
Step-by-step explanation:
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
thats the meaure of the exterior angle!
Answer:144
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
(a) The equation of a straight line, 4, is given as y=-²x = ³
(i) State the gradient of the line, l₁.
(ii)The point A (b, 4) lies on the line l₁. Determine the value of b.
(iii) A line, 12, passing through the point (0,-5), is perpendicular to l₁. Find the equation of the straight line l2.
Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.
The null hypothesis and the alterative hypothesis are [tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220.
The standardized test statistic is 1.725.
We have,
[tex]\mu[/tex] > 1220,
α = 0.03
[tex]\sigma[/tex] = 202.17
X = 1249.88
n= 300
a) According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:
[tex]H_0[/tex] : [tex]\mu[/tex] > 1220
[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220
b) The standardized test statistic is
=| [tex](\mu[/tex] - X) / ([tex]\sigma[/tex] / √n)|
= |( 1220 - 1249.88) / (202.17/√300)|
= |(-29.88)/ 17.320|
= |-1.725|
= 1.725
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Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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please help me!!!!!!
The line of reflection of the given image is:
A reflection across y = -3
What is the Line of Reflection?A line of reflection is a line that lies between two identical mirror images, so the distance of any point of one figure from the line will equal the distance of the same point of the mirror image (flipped figure).
The definition above tells us that if we are given two images, such as mirror images of each other, the line of reflection can be determined by calculating the midpoint from any two points of the figures.
Looking at the given image, the center point of the mirror images is seen as y = -3
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Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)−7sin(θ)−4=0
Select all that apply:
0.4
3.61
1.66
5.81
1.4
3.07
Answer:
3.615.81Step-by-step explanation:
You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].
GraphA graph of the left-side expression shows it has a value of 0 at ...
θ ≈ 3.61 or 5.81.
CheckUsing a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)
Algebraic solutionWe can let x = sin(θ). Then the equation is ...
4x² -7x -4 = 0
x² -7/4x = 1
(x -7/8)² = 1 +(7/8)² = 113/64
x = (7 ±√113)/8
The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...
{π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians
Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is
inconsistent.
2x-4y= -4
3x+3y= 2
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. The solution is.
(Simplify your answers.)
OB. There are infinitely many solutions. The solution can be written as {(x,y) |x=y is any real number).
(Simplify your answer. Type an expression using y as the variable.)
OC. The system is inconsistent.
Inc
solve the inequality and graph the solution on the line provided.
5x - 15 < 10
Answer: x < 5, see attached for the graph.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
5x - 15 < 10
Add 15 to both sides of the equation:
5x < 25
Divide both sides of the equation by 5:
x < 5
For the graph, we will use an open circle because this is only less than (<), not less than and equal to.
Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.
apllo traveld 48 leauges in 3 day then he tripled his rate how long would it take him to travel 336 leagues at this new speed
Add and simplify 12ft. 8in. + 16ft. 11in.
Answer:
Step-by-step explanation:
29 ft
7 in
14. A clothing store has a cost of producing t-shirts at $4.50 per unit. The store also has a
monthly rent charge of $500. The store sells each t-shirt for $12.00 each.
Write an equation to model the store's profits each month:
Answer:
there gonna have to buy 120 to pay the rent
I am unsure about how to do this problem, pictured below.
The time taken to reach a population of 500 is gotten from 500=50e^0.55t
What is the exponential growth?
Exponential growth is a process that increases quantity over time as in the bacterial culture here.
We know that from the question, we have;
P(t)=Poe^rt
P(t) = population at time t
Po= Initial population
r = growth rate
t = time taken
Then we have that;
150 = 50e^2r
3=e^2r
ln3 = 2r
r = ln3/2
r = 0.55
If the rate of growth is 0.55, then to reach a population of 500;
500=50e^0.55t
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NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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In circle R, find arc length of arc GH
The length of the arc GH is 13.3 cm
What is length of an arc?The length of an arc is the distance that runs through the curved line of the circle making up the arc.
The length of an arc is expressed as;
l = tetha/360 × 2πr
tetha = R
R = 360-( 170+80)
R = 360-250
R = 110°
l = 110/360 × 2 × 3.14 × 6.4
l = 4787.2/369
l = 13.3 cm (1.dp)
therefore the length of the arc GH is 13.3 cm
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Please help asap need it please
Answer:
Step-by-step explanation:
i think that you times the numbers
The applet has eight pairs of triangles. Each group member should choose 1–2 pairs of triangles. Use them to help you answer the following questions.
Which pair(s) of triangles do you have?
Can each pair be composed into a rectangle? A parallelogram?
I don't have access to the applet you are referring to. Can you please provide more information or context about the applet so I can better assist you?
A group of student athletes were asked which organized sport they participate in. Each athlete participates in exactly 1 sport. The results are shown in this frequency table. How many baseball and basketball players are there? Enter your answer in the box. players
14
6
9
8
12
10
12 baseball and 9 basketball players are there. The frequency of a value in the data is its occurrence.
One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table. The frequency of a value in the data is its occurrence. We can immediately see how frequently each value appears in a table. 12 baseball and 9 basketball players are there.
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2. Tell if the number shown is written in scientific notation. If it is, write correct, if incorrect
explain why and correct the mistake.
A. 0.5045 x 10
B. 2.804 x 10"
C. 12.04 x 10
The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.
What is Scientific notation?Scientific notation can be described as the way of writing very large as well as very small numbers.
It should be noted that the number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.
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