Answers
We have:
vertex = (-1, 16)vertical intercept = (0, 14)x-intercepts = (-3,83, 0), (.1,83, 0).How to find the vertex of the parabola?
For a parabola like:
[tex]y = a*x^2 + b*x + c[/tex]
The vertex is at:
[tex]x = -b/2a[/tex]
In this case, we have:
[tex]y = -2x^2 -4x + 14[/tex]
So the vertex is at:
[tex]x = 4/2*(-2) = -1[/tex]
To get the y-value, we need to evaluate in x = -1.
[tex]y = -2*(-1)^2 - 4*(-1) + 14 = -2 + 4 + 14 = 16[/tex]
So the vertex is (-1, 16)
How to find the y-intercept?To do that we just evaluate in x = 0.
[tex]y = -2*0^2 -4*0 + 14 = 14[/tex]
The vertical intercept is (0, 14).
How to get the x-intercepts?Using Bhaskara's formula we get:
[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*(-2)*14} }{2*-2} \\\\x = \frac{4 \pm 11.31 }{-4}[/tex]
So the two roots are:
x = (4 + 11.31)/(-4) = -3.83
x = (4 - 11.31)/(-4) = 1.83
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Related Questions
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d? A. 4 km B. 9 km C. 48 km D. 16 k
Answers
The approximate distance in km between her house and her job is 9 km.
What is the approximate distance?The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.
The scale of the map = 8cm : 12km
Distance between the house and the job = (12 x 6) / 8 = 9m
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Which criterion can be used to prove abc and adc are congruent? triangles, abc and acd, are plotted on a grid that share a common side ac. angles cad and acb are marked congruent. angles cab and acd are marked congruent. a. sss b. aaa c. sas d. asa
Answers
The correct answer is option D which is ASA ( Angle - Side - Angle).
What is congruency?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In triangles ABC and ADC,
Angles BCA and DAC are congruent (from the diagram);
Angles BAC and DCA are congruent (from the diagram);
AC is congruent AC (by reflexive property).
So, the triangles ABC and CDA are congruent with the ASA postulate.
ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Therefore the correct answer is option D which is ASA ( Angle - Side - Angle).
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Given: NQ is the bisector of ZMNP and ZNMQ
ZNPQ
Prove: Δ MNQ =ΔΡΝΟ
M
N
Q
P
Answers
1) [tex]\overline{NQ}[/tex] is the bisector of [tex]\angle MNP[/tex] and [tex]\angle NMQ \cong \angle NPQ[/tex] (given)
2) [tex]\angle MNQ \cong \angle QNP[/tex] (a bisector splits an angle into two congruent angles)
3) [tex]\overline{NQ} \cong \overline{NQ}[/tex] (reflexive property)
4) [tex]\triangle MNQ \cong \triangle PNQ[/tex] (AAS)
Help asap I need help really bad
Answers
Sorry for the weird symbol typing lol.
Answer: it's answer A
Step-by-step explanation:
It's because the line move toward the greater side and the point where the line starts it a solid circle which then the answer is x is greater than or equal to 0 (x≥0)
and remember that when the circle is solid which means that the middle of the circle is black is should be always 'equal' when the middle of the circle isn't fully black that means you just have to put your answer like ">" just that.
the atomic mass unit is presently based on assigning an exact integral mass (in amu) to an isotope of an hydrogen oxygen sodium carbon helium
a. hydrogen
b. oxygen
c. sodium
d. carbon
e. helium
Answers
Answer:
The reference atomic mass is carbon-12 when calculating atomic masses.
Step-by-step explanation:
The one-twelfth mass of an atom of carbon-12 is known as an atomic mass unit.
Because no other nuclide has a mass that is exactly a whole number in this scale except for carbon-12.
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Which inequality is equivalent to 3+4/x>_x+2/x
Answers
Answer:
the right answer is the first one
2x+2 over x >0
What are the solution(s) to the quadratic equation 9x² = 4?
0 x =
and x =
0 x =
I
69
4
and x = -
2
0 x = ² and x = -²
2
Ono real solution
Answers
Answer:
x= 2/3, -2/3
Step-by-step explanation:
9x² = 4
To solve this quadratic, divide each side by 9
x^2 = 4/9
Take the square root of each side
sqrt(x^2) = sqrt(4/9)
x = ±2/3
Answer:
x = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
9x² = 4 ( divide both sides by 9 )
x² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
x = - [tex]\frac{2}{3}[/tex] , x = [tex]\frac{2}{3}[/tex]
387 kilograms = x grams
Answer:
a. 387,000g
b. 38,700g
c. 387g
d. 3.87g
Answers
Answer:
a
Step-by-step explanation:
I kilogram is 1000 grams
The answer is letter A (just multiply the given by 1,000)
One root of f (x) = x cubed 10 x squared minus 25 x minus 250 is x = –10. what are all the roots of the function? use the remainder theorem.
Answers
Answer:
x= -10 , x= -5 , x=5
Step-by-step explanation:
we are given function as
x^3+10x^2-25x-250
We are given one of zero is x=-10
we can find all possible factors of 250
so, we will check zeros at x=-5 and x=5
At x=-5:
we can plug x=-5
At x=5:
we can plug x=5
So, other zeros are
x=-5 and x=5
All zeros are
x=-10 , x=-5 , x=5
Use the drawing tools to sketch the graph of a rational function with a domain of { x | x ∈ R , x ≠ - 5 , 4 } . Include one removable discontinuity and one nonremovable discontinuity. Label each discontinuity using the text tool.
Answers
If [tex]f(x)[/tex] has a removable discontinuity at [tex]x=a[/tex], then the limit
[tex]\displaystyle \lim_{x\to a} \frac{f(x)}{x-a}[/tex]
exists and is finite.
A non-removable discontinuity at [tex]x=b[/tex] would entail a non-finite limit,
[tex]\displaystyle \lim_{x\to b} \frac{f(x)}{x-b} = \pm\infty[/tex]
or the limit does not exist (which could be due to the limits from either side of [tex]x=b[/tex] not matching or existing).
For a rational function, we want
[tex]f(x) = \dfrac{p(x)}{q(x)}[/tex]
where [tex]p[/tex] and [tex]q[/tex] are polynomials in [tex]x[/tex]. To get a removable discontinuity at [tex]x=a[/tex], both [tex]p[/tex] and [tex]q[/tex] must be divisible by [tex]x-a[/tex], and the limit of their quotient after removing these factors still exists. That is,
[tex]\displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \frac{p(x)}{q(x)} = \lim_{x\to a} \frac{(x-a)p^*(x)}{(x-a)q^*(x)} = \lim_{x\to a} \frac{p^*(x)}{q^*(x)} = \frac{p^*(a)}{q^*(a)}[/tex]
On the flip side, we get a non-removable discontinuity [tex]x=b[/tex] if [tex]p[/tex] is not divisible by [tex]x-b[/tex], in which case
[tex]\displaystyle \lim_{x\to b} f(x) = \lim_{x\to b} \frac{p(x)}{q(x)} = \lim_{x\to b} \frac{p(x)}{(x-b)q^*(x)} = \frac{p(b)}{0\times q^*(b)}[/tex]
and this is undefined.
Suppose [tex]f(x)[/tex] has a non-removable discontinuity at [tex]x=-5[/tex] and a removable one at [tex]x=4[/tex]. Then one such function could be
[tex]f(x) = \dfrac{x-4}{(x-4)(x+5)} = \dfrac{x-4}{x^2+x-20}[/tex]
A segment that intersects a circle in two points is called a ________________.
Answers
I need help with Algebra every single time
Please help
Answers
Answer:
perimeter = 12 z + 3
Explanation:
The perimeter of a shape is the sum of all the sides.
Therefore, we add all the sides' lengths together:
perimeter = (4z - 2)+(3z + 3)+(z + 5)+(4z- 3)
= 12 z + 3
my father is 4 times old as me. after 5 years my father will be 3 times old how old is my father now
Answers
Answer:
Step-by-step explanation:
Which solid is a Platonic solid?
Please hurry!!!
Answers
Answer:
The five Platonic solids (regular polyhedra) are the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. In other words the second one.
what value of x makes this equation true , use numerals instead of words.
-2x+3=-15
Answers
Answer:
x = 9
Step-by-step explanation:
-2x + 3 = -15
-2x = -18
x = 9
Answer:
9Step-by-step explanation:
what value of x makes this equation true , use numerals instead of words.
-2x+3=-15
-2x + 3 = -15
-2x = -15 - 3
-2x = -18
x = -18 : (-2)
x = 9
--------------------
check
-2 * 9 + 3 = -15
-18 + 3 = -15
-15 = -15
the answer is good
What type of polynomial is P(x)=x^3-1?
Answers
According to no. of terms it's binomial since it has two terms , according to the power it's cubic function since the power of X is 3
PLEASE GIVE BRAINLIEST
Base area = 18 ft²
Volume=
11 ft
7
Answers
Answer:
nhddhdbndbd
Step-by-step explanation:
jh h benrheoek
Use the graph of the exponential growth function
f(x) = a(2x) to determine which statement is true.
f(0) = 2 when a = One-half.
f(0) = 3 when a = 3.
f(1) = 9 when a = 9.
Answers
By direct evaluation of the exponential function f(x) = a · 2ˣ we conclude that the proposition "f(0) = 3 when a = 3" is the only true. (Correct choice: B)
How to analyze an exponential function
Herein we should analyze an exponential function of the form f(x) = a · 2ˣ and find what proposition is true by direct evaluation:
x = 0
2 = a · 2⁰
a = 2
x = 0
3 = a · 2⁰
a = 3
x = 1
9 = a · 2
a = 9/2
By direct evaluation of the exponential function f(x) = a · 2ˣ we conclude that the proposition "f(0) = 3 when a = 3" is the only true. (Correct choice: B)
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Suppose f(x)=x^2 and g(x)=5x^2. Which steamy best compares the graph of g(x) with the graph of f(x)?
Answers
By understanding and applying the concepts of dilation and quadratic functions, the function g(x) is a vertically dilated version of f(x) by a factor of 5.
How to compare the graphs of two functions
In this questions we know two quadratic equations of the form y = a · x². f(x) is known as the canonical function as a = 1 and g(x) is the consequence of dilating f(x) vertically by a factor of 5. Now we proceed to present graphically between the two functions.
In a nutshell, the function g(x) is a vertically dilated version of f(x) by a factor of 5.
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Write the sentence as an equation.
253 equals the product of 232 and k
Type a slash ( / ) if you want to use a division sign.
Answers
The solution to a given word problem by writing it as an equation is k = 253/232
Expressing word problems in mathematical forms:The process of expressing word problems in mathematical forms takes a logical and chronological approach while taking the variables and arithmetic operations given into consideration.
From the given information, to express the word problem in mathematical form, we have:
253 = 232 × k253 = 232kMaking k the subject of the equation, we have:
k = 253/232
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Could someone help me on this?
Answers
which of the following sets of inequalities
Answers
Inequalities help us to compare two unequal expressions. The correct options are 2 and 3.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The inequality for the red portion is,
slope, m = (-2/-4) = 1/2
y-intercept is 2.
y ≤ (1/2)x + 2
The inequality for the blue portion is,
slope, m = (5-0)/(3-0.5) = 2
y-intercept is -1.
y > 2x - 1
Hence, the correct options are 2 and 3.
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The average of 7, 20, and X is 20. what is the value of X?
Answers
Answer:
33
Step-by-step explanation:
do it in reverse
there are 3 numbers
average is 20
that means total is 20 times 3 which is
60
7+20+x=60
27+x=60
x=60-27=
33
Answer:
x = 33
Step-by-step explanation:
we find the "average" of a data set by adding all of the numbers in the data set together, and then dividing by the number of numbers/values present
for example,
the average of 2 and 20
2 + 20 = 22
(there are two numbers, so we divide by 2)
22 / 2 = 11
so, this example has an average of 11
we can apply the same logic to a variable:
we know that
[tex]\frac{20+7+x}{3}[/tex] = 20
We can now solve for x:
[tex]\frac{20+7+x}{3}[/tex] = 20
· 3 ·3 {multiply both sides by 3}
20 + 7 + x = 60 {combine like terms}
27 + x = 60 {subtract 27 from both sides to isolate x}
x = 33
{check answer:
7 + 20 + 33 = 60
60 / 3 = 20 (divided by 3 because we have 3 numbers) }
so, the value of x is 33
(x = 33)
hope this helps!!
3n-5p+2n=10 solve for n
Answers
Answer:
n=3p
Isolate the variable by dividing each side by factors that don't contain the variable.
3n - 5p + 2n = 10
5n - 5p = 10
5n = 10 + 5p
n = 2 + p
I need help with this please
Answers
2534+? but its not that clear cant understand it
The bar graph shows the number of customers at a nail salon each day for one week. What percent of the customers came on Friday or Saturday? Round your answer to the nearest hundredth of a percent. * I NEED ANSWER*
Answers
Answer:
Friday = 11.43%Saturday = 17.14%Friday & Saturday = 28.57%Step-by-step explanation:
Total number of customers
⇒ 15 + 5 + 10 + 14 + 8 + 12 + 6 = 70
Percentage of customers who came on Friday
[tex]\begin{aligned}\implies \sf Percentage & = \sf \dfrac{Friday\:customers}{Total\:number\:of\:customers} \times 100\\\\& = \sf \dfrac{8}{70} \times 100\\\\& = \sf 11.43\%\:\:(nearest\:hundredth)\end{aligned}[/tex]
Percentage of customers who came on Saturday
[tex]\begin{aligned}\implies \sf Percentage & = \sf \dfrac{Saturday\:customers}{Total\:number\:of\:customers} \times 100\\\\& = \sf \dfrac{12}{70} \times 100\\\\& = \sf 17.14\%\:\:(nearest\:hundredth)\end{aligned}[/tex]
Percentage of customers who came on Friday and Saturday
[tex]\begin{aligned}\implies \sf Percentage & = \sf \dfrac{Fri\:and\:Sat\:customers}{Total\:number\:of\:customers} \times 100\\\\& = \sf \dfrac{8+12}{70} \times 100\\\\& = \sf 28.57\%\:\:(nearest\:hundredth)\end{aligned}[/tex]
28.57 is the answer, and its rounded to the nearest hundredth
A number written in scientific notation has a ________ that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
Answers
A number written in scientific notation has a Negative Exponent that indicates the digits used in the number and is always written with 1 digit to the left of the decimal place.
The coefficient is always a number larger than or equal to one and less than ten in scientific notation. There is an integer exponent. When using scientific notation to write integers bigger than ten
The exponent is positive and equals the number of spaces to the left of the original decimal point. When expressed in scientific notation, a negative exponent. The exponent's value is equal to how many places to the right the decimal has been pushed.As a result, when a number is smaller than 1, it will have a negative exponent in scientific notation.
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1. What is the binomial expansion of (x + 3)5?
Answers
Answer:
5x + 15
Step-by-step explanation:
To expand the binomial, you need to multiply each term inside the parentheses by 5.
(x + 3)5
= (x * 5) + (3 * 5)
= 5x + 15
Order these fractions from smallest to lowest
1[tex]\frac{1}{2} \frac{7}{12} \frac{2}{17}[/tex]
Answers
Answer: [tex]\frac{1}{2} \frac{2}{17} \frac{7}{12}[/tex]
Step-by-step explanation:
What term does the formula sin A/a = sin B/b represent?
Answers
Answer:
Law of sines
Explanation:
The law of sines states that the ratios of the sines of angles and their opposite sides are equal for all angles inside a triangle.
Step-by-step explanation:
hope you can understand