The quadratic equation is,
[tex]y=-3x^2-4x+c[/tex]The value of coefficients of square term, x term and constant terms are,
a = -3
b = -4
and c = c.
For two real roots,
[tex]b^2-4ac>0[/tex]Dubstitute the values in the equation to obtain the value of c.
[tex]\begin{gathered} (-4)^2-4\cdot(-3)\cdot(c)>0 \\ 16+12c-16>0-16 \\ \frac{12c}{12}>\frac{-16}{12} \\ c>-1.333 \end{gathered}[/tex]So value of c should be greater than -1.333, and from from the options it can be observed that value more than -1.333 is only c = -1.
So answer is c = -1.
07ess inWhich statement concerning the equation x2 + 2 = x is true?0 Its discriminant is 0, so it has one real solution.O Its discriminant is – 7, so it has two complex solutions.Its discriminant is -7, so its solutions are negative.-Its discriminant is 0, so it has no solution.
The given quadratic equation is;
[tex]x^2+2=x[/tex]This can be written properly as;
[tex]x^2-x+2=0[/tex]The discriminant is used to test for nature of roots of a quadratic equation and it is given by the equation;
[tex]D=b^2-4ac[/tex]From the given quadratic equation;
[tex]\begin{gathered} x^2-x+2=0 \\ a=1;b=-1,c=2 \end{gathered}[/tex]Thus, the discriminant will be;
[tex]\begin{gathered} D=b^2-4ac \\ D=(-1)^2-4(1)(2) \\ D=1-8 \\ D=-7 \end{gathered}[/tex]Since the discrimiant has a value(-7) less than zero(0), thus it has two(2) complex roots.
Hence, the correct option is option B
8-1.2.41 Graph the equation and find the y-intercept AY 10- y = 5x - 2 - o Use the graphing tool to graph the equation 6- Click to enlarge graph 2- -10 8 -5 4 2 2 4 6 10 -2- -6- -8-
From the equation of the line, the y-intercept is the point (0, -2) and its slope is m = 5
To graph this line, first, we need to find the point (0, -2), and then we need to find another point of the line, we can do that with the help of the slope, as follows:
(0+1, -2+5) = (1, 3)
Next, we have to connect these two points
Enter the degree of the polynomial below.5x^5 + 8x^2 + 2x - 3x^9 - 8x^4 - 4x^5A. 8B. 9C. 6D. 5
By definition, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients.
In this case, the monomial with the highest degree is
[tex]-3x^9[/tex]Then, the degree of the polynomial is 9 and the correct answer is B. 9.
0.7 mg of a medication has been ordered. The recommended maximum dosage of the drug is 0.35 mg, and the minimum recommended dosage is 0.175 mg is the dosage ordered within the allowable limits?
The ordered quantity, 0.7 mg, is outside the recommended dosage permissible range.
What is the range?
The range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest. The range in a piece of data is the distinction between the highest and lowest value.
It is given the maximum, and minimum dosage of medicine is 0.35 and 0.175 mg, respectively.
So, permissible range=[0.175,0.35]
0.7 mg of medicine is ordered.
Note that 0.7>0.175.
Also, 0.7>0.35
That means 0.7 does not lie in the permissible range.
So, the ordered quantity, 0.7 mg, is outside the recommended dosage range.
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Consider the function f(x) =−5x−8 how do you find the following? B) The average rate of change between the points (a,f(a)) and (b,f(b)) . c) The average rate of change between the points (x,f(x)) and (x+h, f(x+h)).
The rate of change between a and b is -5, and between x and x + h is also -5.
How to find the rates of change?
For a function f(x) the formula for the rate of change on an interval [a, b] is:
( f(b) - f(a))/(b - a)
so if the function is f(x) = -5x - 8, the average rate of change will be:
( -5b - 8 + 5b + 8)/(b - a) = 5*(a - b)/(b - a) = -5
c) Now we want to use the interval [x, x + h], we will get:
( -5*(x + h) - 8 + 5*x + 8)/(x + h - x)
= (-5h)/h = -5
Again, the rate is -5
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9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer10. Refer to problem 9. If each woman filled the order for 30 dresses by herself, how manymore days would it take Alberta Emery?AnswerSteung can
We know rate and time are inverses of each other.
Let's take the inverse of each time to find their rates.
Alberta Emery
It takes her 3 days to sew a dress. So, her rate is 1/3
Allison Taylor
It takes her 2 days to sew a dress. So, her rate is 1/2
Their combined rate (when working together) is '1/3 + 1/2'
We know
rate x time = job completed
We can use the combined rate (just found) and jobs = 30 dress, to find the time it will take both of them working together to sew 30 dresses.
The equation is,
[tex](\frac{1}{3}+\frac{1}{2}_{})t=30[/tex]Solving for "t", we get,
[tex]\begin{gathered} (\frac{1}{3}+\frac{1}{2}_{})t=30 \\ (\frac{2}{6}+\frac{3}{6})t=30 \\ \frac{5}{6}t=30 \\ t=\frac{30}{\frac{5}{6}} \\ t=30\times\frac{6}{5} \\ t=\frac{180}{5} \\ t=36 \end{gathered}[/tex]So, it will take them 36 days to sew 30 dresses if they work together.
The function g(c)=75-3.5c represents the amount of money remaining on a gift card after purchasing c number of ice cream cones how much does an ice cream cone cost
The price of an ice cream, as calculated with the help of given function is 3.5
What is function in mathematics?
A function is a relationship between a set of inputs and a set of permitted outputs, and it has the property that every input is connected with exactly one output. If every element in set A has one end and only one image in set B, then the mapping from set A to set B is merely a function. Choose any two non-empty sets for A & B.
In order to get price of 1 ice cream, we will first calculate the amount left after purchasing 2 ice creams and the amount left after purchasing 1 ice cream with the help of given function. then we will do subtraction to get the answer.
The amount left after purchasing 2 ice creams:
given function is: g(c)=75-3.5c
putting c = 2
g(2) = 75 - 3.5(2)
g(2) = 68
So, the amount left after purchasing 2 ice creams.
The amount left after purchasing 1 ice cream1:
given function is: g(c)=75-3.5c
putting c = 1
g(2) = 75 - 3.5(1)
g(2) = 71.5
So, the amount left after purchasing 1 ice cream.
Subtracting the amount left after purchasing 2 ice cream from the amount left after purchasing 1 ice cream.
71.5 - 68
= 3.5
Hence, the price of an ice cream is 3.5.
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how would solve for 2x – 17y = 13 for y
SOLUTIONS
To solve for y in 2x – 17y = 13
[tex]2x-17y=13[/tex]Make y the subject of formular
[tex]\begin{gathered} 2x-17y=13 \\ 2x-13=17y \end{gathered}[/tex]divide both side by 17
[tex]\begin{gathered} \frac{2x-13}{17}=\frac{17y}{17} \\ y=\frac{2x-13}{17} \end{gathered}[/tex]Therefore the value of y is
[tex]y=\frac{2x-13}{17}[/tex]Rectangular prism has a length of 8½ inches, a
width of 4.25 inches and a height of 3 %. What is the volume in cubic
inches? Round to the nearest hundreths. (V = Bh or V = lwh
Volume of rectangular prism with length 8.5 inch , width 4.25 and
height 3 inch is :
108.38 cubic inches
What is the volume of rectangular prism?A rectangular prism is a 3-dimensional solid shape with six faces, all of which are rectangles. Right rectangular prisms and non-right (oblique) rectangular prisms are the two types of rectangular prisms.To calculate the volume of a rectangular prism, multiply its three dimensions: length, width, and height. Volume is measured in cubic units.
Volume = l x w x h
Here given,
l = 8 .5 inch
w = 4.25 inch
h = 3 inch
To find volume ,
Volume = l x w x h
= 8.5 x 4.25 x 3
= 108.375 cubic inches
= 108 .38 cubic inches
So the volume of rectangular prism is 108 .38 cubic inches .
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Line u has a slope of -2/9. Line v is perpendicular to u. What is the slope of line v?
Answer: Say you have a line with a slope of -4. What is the slope of the line perpendicular to it? First, take the negative of the slope of your line -(-4) = 4 Second, take the inverse of that number. 4 is a whole number so its denominator is 1. The inverse of 4/1 is 1/4.
Step-by-step explanation:
helpful please math
Given data:
The given graph.
The range is the value of y, for which the given function is defined.
[tex]R=\lbrack0,\text{ }\infty)[/tex]Thus, the range of the given graph is [0, ∞).
if 5 lb of oranges cost $11.55 how many would it cost for 12 lb of oranges
To solve this problem we can apply the rule of three, in our case
[tex]\begin{gathered} 5\rightarrow11.55 \\ 12\rightarrow x \end{gathered}[/tex]Then, 12 lb of oranges will cost
[tex]\frac{(12)(11.55)}{5}=\frac{138.6}{5}=27.72.[/tex]Therefore, 12 lb of orange will cost $27.72.
Which expression equals 15.51
Let x is the number multiplied by 2.2 gives 15.51
So:
[tex]\begin{gathered} x\times2.2=15.51 \\ x=\frac{15.51}{2.2} \\ x=7.05 \end{gathered}[/tex]Hence option D is correct.
which is an equivalent ratii to 6/7
Let:
[tex]\begin{gathered} k=constant_{\text{ }}of_{\text{ }}proportionality \\ k\in\N \end{gathered}[/tex][tex]\begin{gathered} 6\colon7=\frac{6}{7} \\ let \\ k=2 \\ \frac{6}{7}\equiv\frac{k}{k}\times\frac{6}{7}=\frac{2}{2}\times\frac{6}{7}=\frac{12}{14} \\ so\colon \\ \frac{6}{7}\equiv\frac{12}{14} \end{gathered}[/tex][tex]\begin{gathered} 9\colon5=\frac{9}{5} \\ let \\ k=3 \\ \frac{9}{5}\equiv\frac{k}{k}\times\frac{9}{5}=\frac{3}{3}\times\frac{9}{5}=\frac{27}{15} \\ so\colon \\ \frac{9}{5}\equiv\frac{27}{15} \end{gathered}[/tex]Drag numbers to the line to complete the solution to the equation.
HELP PLEASEE
When solving the quadratic equation x² + 4x + 3 = 0 we get:
x = -1 and x = -3 .
What is completing the squares?In mathematics, completing the square is a method for converting a quadratic expression of the form ax² + bx + c to the vertex form ,a(x + m)² + n.
The most common application of this method is to solve a quadratic equation by rearranging the expression obtained after completing the square: a(x + m)² + n, so that the left side is a perfect square trinomial.Here given an equation,
x² + 4x + 3 = 0
(x² + 4x +4) + (-4 + 3) =0
(x² + 4x + 4 ) = 1
(x + 2)² = 1
x + 2 = ±√1
x + 2 = ± 1
x + 1 = 0
x + 3 = 0
x = -1
x = -3
The answers are underlined.
By solving the equation x² + 4x + 3 = 0 we get x = -1 and x = -3.
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Approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.)
A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Our function starts increasing, and approximately at x = 2, it starts decreasing, which means this is a relative maximum point, and this is also the greatest possible value for our function, therefore, this is also an absolute maximum. There are no further critical points.
Marcus needs a grade higher than 88 on his quiz for an A. Which inequality represents this?
this is:
grade = g, so
[tex]g>88[/tex]Q = p^2 - r / t for p
The equation solved for the variable p is p = √Qt + r
What is subject of formula?A subject of formula can simply be defined as the variable in an equation or given expression that is being worked out.
The subject is mostly made to stand on its own on one end of the equality sign.
It is also described as the variable mathematical written in terms of other variables found in an equation or expression.
Given the expression;
Q = p^2 - r / t
To solve for , we take the following steps
cross multiply
p^2 - r = Qt
Now, collect the variable 'r' over the equality sign, we have;
p² = Qt + r
Now, to make 'p' stand alone, find the square root of both sides
√p² = √Qt + r
p = √Qt + r
Hence, the expression is p = √Qt + r
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PLEASSEEE HELPP
Find the coordinates of the image of point A(3, –9) after a rotation of 90 degrees clockwise about the origin.
(–3, 9)
(9, 3)
(–9, –3)
(3, 9)
Answer:
B
explanation
I just did it on a paper
Answer:
See below
Step-by-step explanation:
(x,y) which is (3, -9) will change to ( y, -x ) = ( -9,-3)
A gardener plants three different sapling at East Green Central Park. The number of magnolia saplings he planted was 3 less than crab apples saplings. The Kwanzan cherry sapling planted amounted to twice the number of magnolia. Is 35 saplings were planned in all, how many Kwanzan cherry sapling he planted?
16 number of Kwanzan cherry saplings he planted.
Let the gardener plant the no of Crab apple saplings was x
Since the no of magnolia in saplings he planted was 3 less than crab apple saplings.
Therefore, the no. of magnolia Saplings planted was x-3
Also, the Kwanzan Cherry sapling planted amounted to twice the number of magnolia.
Therefore, the Kwanzan Cherry sapling was. planted by him 2(x-3)
Conditionally,
x+(x-3)+2(x-3) = 35
= x+x-3 +2x-6 = 35
4x = 44
x = 11
Hence the no. of kwanzan Cherry sapling. he planted was
=2(11-3).
2x8 = 16
What is sampling?Sampling means choosing a group from which you will collect data in your research. For example, if you are researching the opinions of students at your university, you can study a sample of 100 students. In statistics, sampling allows testing a hypothesis about the characteristics of a population. There are two types of sampling methods: Probability sampling involves random selection that allows strong statistical inferences to be made about the entire group.Non-probability sampling involves non-random selection based on convenience or other criteria that allow you to easily collect data.To learn more about sampling, refer;
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Find the value of h(0). include proper units. what does this output represent?
Answer:
you will suffer inpain with hell
A process for which its result is well defined is called a/an _____________.experimentprocesssample spaceevent
In any experiment, all the possible out comes are well defined. So,
A process for which its result is well defined is called a/an experiment.
Answer: Experiment
Which of the following equation(s) are equivalent to y − 4 = 2/3(x − 1)?
A y= 2/3x - 10/3
B y= 2/3x - 3 1/3
C y= 2/3x + 3
D y= 2/3 + 10/3
Answer:
D) y = 2/3x + 10/3Step-by-step explanation:
GivenEquation of the line in point-slope form:
y - 4 = 2/3(x - 1)Convert the equation into slope-intercept form of y = mx + b:
y - 4 = 2/3(x - 1)y - 4 = 2/3x - 2/3y = 2.3x + 4 - 2/3y = 2/3x + (12 - 2)/3y = 2/3x + 10/3Correct choice is D
Answer:
[tex]\textsf{D.} \quad y=\dfrac{2}{3}x+\dfrac{10}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]y-4=\dfrac{2}{3}(x-1)[/tex]
Distribute the parentheses on the right side of the equation:
[tex]\implies y-4=\dfrac{2}{3}x-\dfrac{2}{3}[/tex]
Add 4 to both sides:
[tex]\implies y-4+4=\dfrac{2}{3}x-\dfrac{2}{3}+4[/tex]
[tex]\implies y=\dfrac{2}{3}x-\dfrac{2}{3}+4[/tex]
Rewrite 4 as 12/3:
[tex]\implies y=\dfrac{2}{3}x-\dfrac{2}{3}+\dfrac{12}{3}[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{12}{3}-\dfrac{2}{3}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{12-2}{3}[/tex]
[tex]\implies y=\dfrac{2}{3}x+\dfrac{10}{3}[/tex]
Therefore, the equation that is equivalent to the given equation is:
[tex]\boxed{y=\dfrac{2}{3}x+\dfrac{10}{3}}[/tex]
find the slipe of 3,9 and 1,12
The slope of the line that passes through 3, 9 and 1, 12 is -3/2
How to calculate the slope of the line?From the question, the points are given as
3, 9 and 1, 12
Rewrite the above points properly
So, we have the following ordered pairs
(3, 9) and (1, 12)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (3, 9) and (1, 12)
Substitute the known values in the above equation
So, we have the following equation
Slope = (12 - 9)/(1 - 3)
Evaluate
Slope = -3/2
Hence, the slope of the line is -3/2
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I need help with this practice problem with that is from trigonometry prep book
Answer:
[tex]cos(\alpha-\beta)=-0.9691[/tex]Explanation: The diagram of the alpha and the beta angles is as follows:
the angles are as follows:
[tex]\begin{gathered} \arctan (-\frac{12}{5})=-67.38^{\circ}\Rightarrow\alpha=180+(-67.38^{\circ})=112.62^{\circ} \\ \alpha=112.62^{\circ} \\ \arccos (\frac{3}{5})\Rightarrow arc\cos (0.6)=53.1^{\circ} \\ \beta=360^{\circ}-53.1^{\circ}=306.9^{\circ} \\ \beta=306.9^{\circ} \\ \therefore\Rightarrow \\ cos(\alpha-\beta)=\cos (112.62^{\circ}-306.9^{\circ}) \\ \cos (-194.28^{\circ})=-0.9691 \end{gathered}[/tex]Therefore the answer is:
[tex]cos(\alpha-\beta)=-0.9691[/tex]1+1 pls help me im 4
Answer:
2
Step-by-step explanation:
because i say so and i am older
Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 10 hours longer to clearthe land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round your answer to thenearest tenth.)
To answer this question we will set and solve a system of equations.
Let A be the time (in hours) that it would take Company A to clear the parcel of land alone, and B be the time (in hours) that it would take Company B to clear the parcel of land alone.
Since working together, the two companies can clear the parcel of land in 8 hours, and wirking alone, it would take Company A 10 hours longer than Company B, then we can set the following system of equations:
[tex]\begin{gathered} \frac{1}{A}*8+\frac{1}{B}*8=1, \\ A=B+10. \end{gathered}[/tex]Substituting the second equation in the first one we get:
[tex]\frac{8}{B+10}+\frac{8}{B}=1.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} \frac{8B}{(B+10)B}+\frac{8(B+10)}{(B+10)B}=1, \\ \frac{16B+80}{(B+10)B}=1. \end{gathered}[/tex]Multiplying the above result by (B+10)B we get:
[tex]\begin{gathered} \frac{16B+80}{(B+10)B}*(B+10)B=1*(B+10)B, \\ 16B+80=(B+10)B. \end{gathered}[/tex]Simplifying the above result we get:
[tex]16B+80=B^2+10B.[/tex]Subtracting 16B+80 from the above result we get:
[tex]\begin{gathered} 16B+80-(16B+80)=B^2+10B-(16B+80), \\ 0=B^2-6B-80. \end{gathered}[/tex]Using the quadratic formula we get:
[tex]\begin{gathered} B=\frac{6\pm\sqrt{(-6)^2-4*1(-80)}}{2*1}=\frac{6\pm\sqrt{36+320}}{2} \\ =\frac{6\pm\sqrt{4*89}}{2}=3\pm\sqrt{89}. \end{gathered}[/tex]Since a negative value of B has no real meaning, we get that:
[tex]B=3+\sqrt{89}\approx12.4.[/tex]Answer: 12.4 hours.
Please help i dont have as much time
Answer:
Step-by-step explanation
answer is f(x)=6x
help me please
thank you
Answer:
Domain: A, [tex][2, \infty)[/tex]
Range: A, [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A 6 inch by 10 inch rectangle is dilated by afactor of 3. What is the area of the dilatedrectangle?
Given;
There are given that the 6 inches by 10-inch rectangle.
Explanation:
dilated by a factor of three means that the two dimensions needed for the area are multiplied by 3.
So,
The width of the rectangular is:
[tex]width=6\times3=18[/tex]And,
The length of the rectangular is:
[tex]10\times3=30[/tex]Then,
The area of dilated rectangular is:
[tex]\begin{gathered} Area\text{ of dilated rectanular=}width\times\text{length} \\ =18\times30 \\ =540inch^2 \end{gathered}[/tex]Final answer:
Hence, the area of the dilated rectangle is 540 inch^2.
