Given:
A quadratic equation is
[tex]-6=x^2+4x-1[/tex]
To find:
The standard form of the given equation and find the value of c.
Solution:
The standard form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex] ...(i)
We have,
[tex]-6=x^2+4x-1[/tex]
It can be rewritten as
[tex]0=x^2+4x-1+6[/tex]
[tex]0=x^2+4x+5[/tex]
[tex]x^2+4x+5=0[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]c=5[/tex]
Therefore, the value of c is equal to 5 and the correct option is C.
Answer:
the answer is c
Step-by-step explanation:
Loc can mow his entire lawn in 20 minutes; Loc's roommate Reza needs 30 minutes to mow the entire lawn. If Loc starts mowing at 1:00, mows for five minutes and then Reza starts to help with his own mower, at what time will they finish mowing the lawn
Loc and Reza together will finish the entire mowing process on the lawn at 1:14 p.m.
Calculation of total mowing time takenLoc mow the total area in 20 mins.
So, his pace is 1 lawn / 20 minutes or 1/20th of a lawn each minute.
Reza's pace is 1 lawn / 30 minutes, or 1/30th of a lawn each minute because he can mow the grass in that amount of time.
Reza joins Loc after he has been mowing for 5 minutes. He can mow 1/20th of the grass in these 5 minutes, which is 5/20th of the lawn =1/4th lawn
There is currently just
1-1/4=3/4 of the lawn left to complete.
We may construct the following equation by assuming that they mow together for x mins:
1/20x + 1/30x = 3/4 [amount done by Loc + Reza = total amount]
⇒(3x+2x)/60x = 3/4
⇒5x/60 = 3/4
⇒x/12= 3/4
⇒4x=36
⇒x= 9 mins
So, when they collaborate, they can complete the lawn in 9 minutes.
Hence, Loc mows alone for 9+5 mins = 14 mins
Therefore, it is concluded that starting at 1 p.m they finish the mowing at 1:14 p.m.
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Solve the system of equations 2x-2y=-14 and 3x-y=-1 by combining the equations.
The solution to the system of equations is x = 3 and y = 10
How to solve the equations?The system is given as:
2x-2y=-14
3x-y=-1
Multiply (1) by 1 and (2) by 2
So, we have:
1(2x-2y=-14)
2(3x-y=-1 )
This gives
2x - 2y=-14
6x - 2y=-2
Subtract the equations
-4x = -12
Divide by -4
x = 3
Substitute x = 3 in 3x-y=-1
3(3)-y=-1
Evaluate
9 - y = -1
Solve for y
y = 10
Hence, the solution to the system of equations is x = 3 and y = 10
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9. Two hexagons are similar in shape. The larger hexagon has an area of
7350 mm². Find the area of the smaller hexagon.
22,509.3 mm²
12,862.5 mm²
4,214.3 mm²
2,400 mm²
Answer:
2400 mm^2.
Step-by-step explanation:
The ratio of their areas = ratio of the squares of their sides.
So x / 7350 = 40^2 / 70^2 where x is area of smaller hexagon.
x = 7350 * 40^2 / 70^2
= 2400 mm^2.
The area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
The areas of two similar figures are in the ratio which is equal to the square of the ratio of their corresponding sides.
If we have two figures A and B, and they are similar, then we can say that:
(Area of A)/(Area of B) = {(Side of A)/(Side of B)}².
In the question, we are informed that the two hexagons are similar in shape.
We are asked to find the area of the smaller hexagon, given the larger hexagon has an area of 7350 mm².
As the two hexagons are similar, we can show that:
(Area of the smaller hexagon)/(Area of the larger hexagon) = {(Side of the smaller hexagon)/(Side of the larger hexagon)}².
The side of the smaller hexagon is given to be 40mm, whereas the corresponding side of the larger hexagon is given to be 70 mm.
Thus, we can show that:
(Area of the smaller hexagon)/7350 = {40/70}²,
or, Area of the smaller hexagon = (16/49)*7350 = 16*150 mm² = 2400 mm².
Thus, the area of the smaller hexagon is found to be 2,400 mm², given the two hexagons are similar. Hence, 4th option is the right choice.
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Suppose a normal distribution has a mean of 50 and a standard deviation of
3. What is P(x≤44)?
Answer:
.0228
Step-by-step explanation:
44 is two standard deviations below the mean z-score = -2
look up z-score = -2 in z-score table
= .0228 or 2.28 %
Answer:
0.025
Step-by-step explanation:
Select the correct answer. A linear function on a coordinate plane passes through (minus 5, minus 3), (0, minus 4), and (5, minus 5) Which equation describes the line graphed above? A. y = − 4 x − 5 B. y = − 1 5 x − 4 C. y = − 5 x − 4 D. y = − 4 x − 1 5
The linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
Linear functionLinear function are functions that has a leading degree of 1. The equation of a linear function is expressed as y = mx + b
where
m is the slope
b is the intercept
Given the coordinates (-5, -3) and (0, -4)
Slope = -4+3/0+5
Slope = -1/5
The y-intercept of the line will be -4
Determine the equation
y = -1/5x-4
Hence the linear function on a coordinate plane passes through (-5, -3) and (0, -4) is y = -1/5x-4
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15. Juan has a fair six-sided die, if Juan rolls the die
twice in a row, what is the probability that the die
will show a 3 both times?
Answer:
1/36
Step-by-step explanation:
The probability for showing a three the first time is 1/6, and then again is another 1/6, multiply and you get 1/36
heloo need help with this integration
Use the given function to find the [tex]y[/tex]-coordinate of [tex]A[/tex].
[tex]x=2 \implies y = 10+8\cdot2+2^2-2^3 = 22[/tex]
Find the equation of the line through the origin and [tex]A[/tex]. This line has slope
[tex]\mathrm{slope} = \dfrac{22-0}{2-0} = 11[/tex]
and passes through (0, 0), so its equation is
[tex]y - 0 = 11 (x-0) \implies y = 11x[/tex]
Then the area of the shaded region is given by the definite integral
[tex]\displaystyle \int_0^2 (y - 11x) \, dx = \int_0^2 (10 + 7x + x^2 - x^3) \, dx \\\\ ~~~~~~~~ = \left(10x + \frac72 x^2 + \frac13 x^3 - \frac14 x^4\right)\bigg|_0^2 \\\\ ~~~~~~~~ = 10\cdot2+\frac72\cdot2^2+\frac13\cdot2^3-\frac14\cdot2^4 = \boxed{\frac{98}3}[/tex]
The sides of a triangle are 3 1 2 cm , 4 2 5 cm and 5 1 4 cm respectively. what is its perimeter?
Answer:
1251 cm
Step-by-step explanation:
Perimeter is just adding the side lengths together.
WILL MAKE BRAINLIEST!! Solve for x
Answer:
5
Step-by-step explanation:
6x+4=34
6x=30
x=5
hope this helps <3
If 0° < θ < 90° or 180° < θ < 270°, explain why sin 2θ is always positive.
Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, [tex]\sin{2\theta}[/tex] is always positive.
What is the trigonometric identity for sin 2θ?It is given by:
[tex]\sin{2\theta} = 2\sin{\theta}\cos{\theta}[/tex]
In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and [tex]\sin{2\theta}[/tex] is always positive.
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Annette the shoe salesperson has two job offers. The Comfort over Style Shoe Emporium has offered her a $52,000 salary plus $3.25 for every pair of shoes she sells. The Heels for Fashion Slaves Boutique has offered a $37,000 salary plus $4.75 for every pair of shoes she sells. Over what range of shoe sales will Annette make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job?
Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:
C(x) = 52000 + 3.25xH(x) = 37000 + 4.75xHe will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:
C(x) > H(x)
52000 + 3.25x > 37000 + 4.75x
1.5x < 15000
x < 15000/1.5
x < 10000
The range is x < 10000.
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a cube with volume 343 cubic inches is inscribed in a sphere so that each vertex of the cub touches the sphere. what is the lenght of the radius in inches of the sphere
The length of the radius of the sphere is 9.26 inches.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.
Volume of cube=343 cubic inches
Side of cube=[tex]\sqrt[3]{343}[/tex] = 7 inches
The radius of the sphere is equal to half the diagonal length of the cube since the cube is inscribed inside the sphere, whose diameter is the cube's diagonal length. Utilizing the distance formula, we can determine the cube's diagonal length.
[tex]d=\sqrt{7^{2}+7^{2}+7^{2} } \\=\sqrt{7*7^{2} } \\=7\sqrt{7}[/tex]
To determine the radius of the sphere, divide the value by two.
Radius of sphere=[tex]\frac{7\sqrt{7} }{2}[/tex] = 9.26 inches
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A rectangular park is 70 meters wide and 120 meters long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
Answer:
1 m by 189 m
Step-by-step explanation:
The perimeter is 2(70+120)=380.
The area is (70)(120)=8400.
If we let the park have a width of 1 meter and a length of 189 meters, then the area will be 189 square meters, which is smaller than 8400 square meters, as required.
I enter the mall with dollars. I spend dollars at American Eagle, which is more than the amount I spent at Banana Republic. I also spent less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores
The correct answer is 64 - 3 a.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.I spent a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic ( b ).
a = b + 4. Therefore: b = a - 4
Also I spent 15 less at American Eagle than I spent in Cole Haan ( c ).
a = c - 15, or: c = a + 15.
75 - a - ( a - 4 ) - ( a + 15 ) = 75 - a - a + 4 - a - 15 =
= 64 - 3 a
Therefore, I have 64 - 3a dollars left after shopping at these three stores. Now we just have to know how much dollars I spent at American Eagle and we will have the amount in dollars.
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The complete question is -
I enter the mall with $75 dollars. I spend a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic. I also spent 15 less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores?
determine the slope of the line!!!!!
Answer: -3/2
Step-by-step explanation:
we could use the two points (2,3) and (0,4) from the graph
y2-y1/x2-x1
= 0-3/4-2
= -3/2
Express sin S as a fraction in simplest terms. R S
Answer:
[tex]\sf Sin \ S = \dfrac{2}{9}[/tex]
Step-by-step explanation:
Trigonometry ratios:[tex]\sf \boxed{\bf Sin \ S = \dfrac{opposite \ side \ of \ \angle S}{hypotenuse}}[/tex]
[tex]\sf = \dfrac{RQ}{SQ}\\\\= \dfrac{2}{9}[/tex]
Sumaya's smoothie store is planning to sell an extra-large size. the extra-large size will have three times the volume of the small size (the small size is (8,4) ). it will cost twice as much as the small size.
which coordinate pair represents the volume and cost of the extra-large size?
The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).
A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.
The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)
Since the volume of the extra-large size will have three times the volume of the small size, hence:
Volume of extra-large size = 8 * 3 = 24
The cost of an extra large is twice as much as the small size, hence:
Cost of extra large = 4 * 2 = 8
A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).
Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.
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Find equation of the line passing through the point (-1,0) and parallel to the line y=-1/2x + 3/7
Answer:
Step-by-step explanation:
A parallel line will have the same slope, m, as the reference line given by the form y=mx+b. b is the y-intercept, the value of y when x=0.
The reference line of y = -(1/2)x + (3/7) has a slope of -(1/2).
The parallel line will have the same slope, so we can write:
y - -(1/2)x + b
We need a value of b that forces the line to go through point (-1,0). Enter that point in the equation and solve for b:
y - -(1/2)x + b
0 - -(1/2)(-1) + b
b = -(1/2)
The equation of the line parallel to y = -(1/2)x + (3/7) and going through (-1,0) is
y=-(1/2)x - (1/2)
If (x + 1)(x-3) = 5, then which of the following statements is true?
Ox+1=0 orx-3=0
Ox+1=5 orx-3=5
Ox-4-0 orx+2=0
Answer:
(x-4)=0 or (x+2)=0 is correct
Step-by-step explanation:
(x+1)(x-3)=5
x^2 -3x +x -3=5
x^2-2x-8=0
x^24x+2x-8=0
(x+2)(x-4)=0
so,
(x-4)=0 or (x+2)=0
The solutions to the expression are:
x - 4 = 0 or x + 2 = 0.
Option C is the correct answer.
We have,
To determine which of the following statements is true:
(x + 1) = 0 or (x - 3) = 0
(x + 1) = 5 or (x - 3) = 5
(x - 4) = 0 or (x + 2) = 0
We can solve the given equation (x + 1)(x - 3) = 5 by expanding the equation and setting it equal to 0:
(x + 1)(x - 3) - 5 = 0
Expanding the equation:
x² - 3x + x - 3 - 5 = 0
x² - 2x - 8 = 0
Now we can factor the quadratic equation:
(x - 4)(x + 2) = 0
From this factorization, we find two possible solutions:
x - 4 = 0 --> x = 4
x + 2 = 0 --> x = -2
Therefore,
The correct statement is:
(x - 4) = 0 or (x + 2) = 0
i.e
x - 4 = 0 or x + 2 = 0.
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i’m a bit confused here
A quadrilateral has congruent side lengths. 2 opposite angles have measures of 100 degrees. The other 2 opposite angles have measures of 70 degrees and (5 x) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Angles of a quadrilateral add to 360 degrees, so
[tex]100+100+70+5x=360\\\\270+5x=360\\\\5x=90\\\\x=18[/tex]
Which theorem correctly justifies why the lines m and n are parallel when cut by a transversal k
The theorem which justifies that two lines are parallel when cut by a transversal k is converse of the alternate interior angles theorem.
Given that two lines m and n are parallel.
We have to find the theorem which justifies that the lines m and n are parallel when cut by a transversal k.
Parallel lines are those lines which do not meet each other at any point on the surface.
If we know that the alternte interior angles are equal,then m and n become parallel to each other.
So the converse of the alternate interior angles theorem correctly justifies that the lines are parallel if cut by a transversal k.
Hence to justify that two lines are parallel if they are cut by a transversal k, we have to use converse of the alternate interior angles theorem.
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Question is incomplete as it should include the following options:
1) converse of the corresponding angles theorem,
2) converse of the alternate interior angles theorem.
3) converse of the same side interior angles theorem,
4) converse of the alternate exterior angles theorem.
Need help understanding how to find the answer to problem
Answer:
3.Tan(45)=n/2
1=n/2
n=2
Cos(45)=2/m
1/√2=2/m
m=2√2
5.Sin(60)=x/14
√3/2=x/14
14√3/2=x
x=7√3
Cos(60)=y/14
1/2=y/14
y=7
Each of the following is an example of quantitative data, except Group of answer choices weight in ounces income in dollars political affiliation age in years
The correct option is C. political affiliation.
An example of quantitative data are-
weight in ouncesage in yearsincome in dollarsWhat is quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data. In most cases, the data is accompanied with measuring units, such as metres in the case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.
Types of Quantitative Data are-
Counter: A measure of entities. For instance, the quantity of users who have downloaded a specific app from the App Store.Measurement of physical objects: Calculating the dimensions of any physical object is called measurement. The HR executive, for instance, meticulously measures the size of each cubicle given to the new hires.Sensory calculation: Mechanism to automatically "sense" the parameters being monitored in order to generate a continuous source of data. A digital camera, for instance, transforms electromagnetic signals into a string of numerical data.Data projection: Algorithms and other mathematical analysis techniques can be used to project future data. For instance, after conducting a thorough investigation, a marketer will forecast a rise in sales following the introduction of a new product.To know more about quantitative data, here
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The complete question is-
8. Each of the following is an example of quantitative data, except ______.
A. weight in ounces
B. income in dollars
C. political affiliation
D. age in years
A comet is estimated to be about 960,000,000 km from Earth. Write this distance in scientific notation. [?] × 10 km Enter 13
Answer:
[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8
Step-by-step explanation:
The answer is written above.
Hope this helps!
Answer:
9.6 * 10^8 km.
Step-by-step explanation:
960,000,000
= 9.6 * 10^8 km.
The value of the exponent = number of digits after the 9, which = 8.
An isosceles triangle has two equal sides. If two of the sides are 5 inches and 2 inches, what is the perimeter of the triangle
Step-by-step explanation:
12 inches
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a rotation is a transformation where an object
Rotation is a transformation where an object is rotated about a fixed point.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation, reflection and rotation are rigid transformations because they preserve the shape and size of the figure.
Rotation is a transformation where an object is rotated about a fixed point.
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Select the correct answer. what is this expression in simplified form? v12 . 4v3 options a.7 b.4v15 c.6 d.24
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Christopher decides that another road to be named Saturn Avenue is needed that will go past
the cleaners and be perpendicular to Sunshine Avenue. Determine the slope of the equation
of the line that represents Saturn Avenue. [Show your work. Draw and label Saturn Avenue
on the coordinate plane. (Optional)
Slope of the equation of the line that represents Saturn Avenue: slope =
y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. This can be obtained by using the formula for finding the equation of the line.
Find the equation of the line:
Equation of a line can be determined using the formula,
y = mx + c
where m is the slope of the line and c is the y - intercept.
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
Here in this question draw the line passing through cleaners and perpendicular to Planet Drive.
The point where x = 0 is (0, 4)
This means that y - intercept is 4
By considering two points on the line we can find the slope of the equation,
Consider the points (8, 4) and (16, 4)
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
m = (4 - 4)/(16 - 8) = 0/8 = 0
So we got that,
y - intercept of the line = 4 slope of the line = 0Putting in the equation of line we get,
y = mx + c
⇒ y = (0)x + 4 ⇒ y = 4
Hence y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. Determine the equation of the line that represents Saturn Avenue. Show your work. Draw and label Saturn Avenue on the coordinate plane.
A motorcycle's wheel has 30 spokes on it. what is the angle between each of the spokes?
Answer:
The circle is a round shape that has a total angle of 360 degrees. If a circle is divided into 6 equal parts, the measure of the angles between spokes is 12 degrees.
Step-by-step explanation:
to find the angle
360/30=12
the angle is 12 degrees
I hope this helps and have a good day!