Part of the graph of a quadratic function is graphed below. Between which two integers will the graph again cross the x-axis?
Answers
From the coefficients of the quadratic equation and the vertex of the parabola, it was found that the graph again crosses the x-axis in x=7.
Quadratic Function
The standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving the quadratic function, you should find the discriminant: Δ=b²-4ac and then use this variable in the formula: [tex]\frac{-b \pm \sqrt{\Delta} }{2a}[/tex] .
The given equation is a quadratic function because have a degree equal to 2. Therefore, the graph is represented by a parabola. The vertex of the parabola is given by the coordinates(xv= -b/2a, yv= -Δ/4a).
From the given figure, it is possible to see that:
the graph crosses the x-axis in x= -1 the graph crosses the y-axis in y=2. xv=3 and yv=7For x= -1, you have y=0, then:
ax²+bx+c=0 -> x=-1
a (-1)²-b+c=0
a*1-b+c=0
a-b+c=0 (1)
For y= 2, you have x=0, then:
ax²+bx+c=0
a*0²+b*0+c=2
0+0+c=2
c=2 (2)
As, a-b+c=0 (1) and c=2 (2), you have:
a-b+c=0
a-b+2=0
a-b=-2 (3)
Now, you should use the information about the xv.
[tex]x_v=\frac{-b}{2a} =3[/tex]
-b=6a
b=-6a
From equation 3, you will find the coefficient a .
a-b=-2 (3)
a-(-6a)= -2
a +6a =-2
7a= -2
a=-2/7
If a= -2/7, from equation 3 you can find the coefficient b.
b=-6a = -6* (-2/7)=12/7
Thus, the quadratic equation of the plot is: ax²+bx+c
[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex]
Now, you should find the roots for the found equation :[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex].
[tex]x_{1,\:2}=\frac{-12\pm \sqrt{12^2-4\left(-2\right)\cdot \:14}}{2\left(-2\right)}[/tex]
[tex]x_1=\frac{-12+16}{2\left(-2\right)}=-1,\:x_2=\frac{-12-16}{2\left(-2\right)}=7[/tex]
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Related Questions
⦁ The function p (w) = 230(1.1)w represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period. 10 points
⦁ During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
⦁ Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
⦁ When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
you will get 10 points
Answers
The increasing exponential functions are described as follows:
f(t) = a(1 + r)^t.
In which the parameters are listed as follows:
a is the initial value.r is the growth rate.For the old factory, the function is of:
p (w) = 230(1.1)^w.
Hence:
During week 0, 230 items are produced.The growth rate is of 10%.For the new factory, from the graph given at the end of the answer, the parameters are given as follows:
a = 190, which is the intercept.b = 1.1578, as 220/190 = 1.1578.Hence the function is:
pn(w) = 190(1.1578)^w.
The new factory overtakes the old factory when:
pn(w) > p(w)
190(1.1578)^w > 230(1.1)^w
(1.1578/1.1)^w > 230/190
wlog(1.1578/1.1) > log(230/190)
w > log(230/190)/log(1.1578/1.1)
w > 3.73 weeks.
Missing InformationThe graph for the second factory is given by the image presented at the end of the answer.
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(sec(t)-cos(t))/sin(t)
Answers
The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)
How to simplify trigonometric ratios?There are different trigonometric ratios such as;
sin x
tan x
cos x
sec x
cosec x
cot x
Now, we want to simplify the trigonometric expression;
(sec(t) - cos(t))/sin(t)
We know that;
sec (t) can be written as 1/cos t
Thus;
(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t
= (1/(sint cos t) - cos t/ sin t
= (1 - cos²t)/(sin t cos t)
= sin²t/(sin t cos t)
= sin t/cos t
= tan t
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Find the perimeter of \triangle PQR△PQR. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answers
154.5
Step-by-step explanation:
left triangle and right triangle has the same degree.
M to Q 107/2 = P to R 53.5
O to N 110/2 = R to Q 55
Find X
M to N 92/2 = P to Q 46
Perimeter- 53.5+ 55+ 46= 154.5
Complete the function table. Function: t = 5d − 2
Answers
The table for the linear equation is summarized below:
d t
3 13
4 18
5 23
6 28
How to complete a table related to a linear function
In this problem we have a two-column table associated to a linear function, the first column of the table represent a set of values of the domain (d) of the function and the second column of the table is for the set of values of the range (t) of the same. We need to fill the second column of the table with the values associated with the range:
d = 3
t = 5 · 3 - 2
t = 15 - 2
t = 13
d = 4
t = 5 · 4 - 2
t = 20 - 2
t = 18
d = 5
t = 5 · 5 - 2
t = 25 - 2
t = 23
d = 6
t = 5 · 6 - 2
t = 30 - 2
t = 28
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Ray buys a computer game for $38. He uses a coupon to receive 15% off the price of the game. After the coupon is deducted, he must pay 6% sales tax. What is the tota cost of the game, to the nearest cent? A $28.00 C. $34.58 D. $36.56
Answers
Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85
Answers
Answer:
665-09
Step-by-step explanation:
Which equation represents this sentence?
Half the difference of a number and 5 is−2.
Responses
12(5−x)=−2
1 half left parenthesis 5 minus x right parenthesis equals negative 2
12x−5=−2
1 half x minus 5 equals negative 2
12(x−5)=−2
1 half left parenthesis x minus 5 right parenthesis equals negative 2
5−12x=−2
Answers
The equation which represents the sentence given; Half the difference of a number and 5 is−2 is; 1/2(x - 5) = -2; 1 half left parenthesis x minus 5 right parenthesis equals negative 2.
Word phrases from Algebraic expressions.It follows from the task content that the expression which best represents the given algebraic expression is to be determined.
First, the difference of a number, x and t is represented as; (x - 5).
Hence, the word phrase; Half the difference of a number and 5; is best represented algebraically as; 1/2(x - 5).
Ultimately, the whole word phrase; Half the difference of a number and 5 is -2 can best be represented as; 1/2(x - 5) = -2.
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What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answers
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
Barney just bought stock in Purple Dinosaur Industries. He paid a total of $7,380. The price of the stock is $12 for one share. How many shares did he buy?
Answers
The number of shares he buy is $615.
Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.
We want to find the number of shares Barney buys.
The total amount barney should pay is $7380.
The price of the stock for one share is $12.
The total number of shares barney buy is 7380/12=615.
Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.
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how many cards must be selected from the standard 52 deck to guarantee that at least 3 cards of the same suit are chosen
Answers
Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
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Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52?
0.23 × 52
23% of $52 is $
11.96
.
An easy way to check your answer is to use the friendly
50%
and divide 52 by
2
to get
13
.
Am i right???
Answers
Answer:
yeah i think so
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find the 23% of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
The similar expression is,
→ 0.23 × 52
→ $11.96
Hence, answer is $11.96.
(b) Work out the value of (2.3 × 10³) × (5.9 × 105)
Give your answer in standard form.
Answers
Answer: 1424850
Step-by-step explanation:
2.3 x 10³ = 2300
5.9 x 105 = 619.5
2300 x 619.5 = 1424850
Pls thank and rate <3 (and branliest if ok with u :)))
Direct and Inverse Variations
Answers
The value of y is 24 when x is 7.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
There are direct variations
y= 24 when x=2
We need to find value of y when x =7
This can be found by forming an equation.
Let the value of unknown y be a
2/24=7/a
Apply cross multiplication
2a=24(7)
2a=168
We need to divide by 2 on both sides
a=24
Hence the value of y is 24 when x is 7.
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8x + 24 I was solutions
Answers
Step-by-step explanation:
8x + 24 is a simplified expression.
It is not an equation, so it can't be solved.
There are two terms in 8x + 24, 8x and 24.
The two terms are unlike terms, so they cannot be combined together.
The radius of a circle is 15 inches. What is
the circumference of the circle? Write
your answer using T.
Answers
Answer:
C = 30pi inches
Step-by-step explanation:
The radius is 15 inches (said so in the question)
The diameter is 30 inches (The diameter is twice the radius)
The circumference is
C = pi•d
C = pi•30
C = 30pi
The circumference is 30pi inches.
Suppose that A and B are points on the number line.
If AB=5 and B lies at 12, where could A be located?
If there is more than one location, separate them with commas.
:0
Location(s) of A :
0.0....
X
Answers
Answer:
locations of A are 7, 17
Step-by-step explanation:
since B is positioned at 12 and AB = 5 , then
A = 12 - 5 or 12 + 5 = 7 , 17
How do you write 5 11/16 and 7 24/25 as a decimal?
Answers
Answer:
5 11/16 as a decimal = 5.6875
7 24/25 as a decimal is 7.96
Step-by-step explanation:
Answer:
5 11/16 = 5.6875
7 24/25 = 7.97
Step-by-step explanation:
you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)
And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)
Graph the points of the given function with the x-values x=−4 , x = 0, and x = 5. f(x)=−2x+4−−−−√
Answers
The graph is attached and the table of value of the graph is as follows
x y
-4 12
0 4
5 -6
How to get the table of valuesThe function y = −2x + 4 is a linear function and will have a straight line graph
The table of values is gotten form the equation y = −2x + 4
solving for x = -4,
y = −2 * -4 + 4 = 12
solving for x = 0
y = −2 * 0 + 4 = 4
solving for x = 5,
y = −2 * 5 + 4 = -6
x y
-4 12
0 4
5 -6
The graph is plotted by finding the points in the table in the Cartesian plane and joining the points together
Other values are solved for in similar step
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Answer:Here is your answer
Step-by-step explanation:
mary invests £12000 in a savings account.
the account pays 1.5% compound intrest per year.
y is inversely proportional to x.
when y=7, x=9
a) work out an equation connecting y and x.
b) work out the value of y when x=21.
pls show step by step working out.
Answers
Using a proportional relationship, it is found that:
a) The equation is: y = 63/x.
b) When x = 21, the numeric value is of y = 3.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables are inversely proportional, we have a inverse proportional relationship, in which the output variable y is obtained by the division of k by the input variable x, as follows:
y = k/x.
For this function, when y = 7, x = 9, hence the constant is obtained as follows:
7 = k/9
k = 9 x 7
k = 63.
Hence the equation is:
y = 63/x.
The numeric value of the function when x = 21 is given as follows:
y = 63/21 = 3.
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Solve for x:-
[tex]\sf -10 + x + 4 - 5 = 7x - 5[/tex]
Answers
Answer:
x = -1
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ -10 + x + 4 - 5 = 7x - 5
Then the value of x will be,
→ -10 + x + 4 - 5 = 7x - 5
→ -11 + x = 7x - 5
→ 7x - x = -11 + 5
→ 6x = -6
→ x = -6/6
→ [ x = -1 ]
Hence, the value of x is -1.
PLEASE HELP!
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
Show all your working.
Answers
Answer:
£3,774
Step-by-step explanation:
629 students at a school each pay £6 to go on a school trip. How much money do they pay in total?
629 * £6 = £3,774
Answer:
no of students= 629
amount paid each =£6
amount paid by all the students =no of students × amount paid each
:: 629
× 6
£3774
Find the initial population size
Answers
The numeric values for the population function are given as follows:
Initial population: 49 individuals.Population after eight years: 292 individuals.How to find the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.
The function giving the population after t years is defined as follows:
[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]
The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:
[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]
After eight years, the population is given by the numeric value at t = 8, hence:
[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]
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Colin buys a car for £45500. It depreciates at a rate of 6% per year. How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
The answer is 33,710 euros.
Step-by-step explanation:
Start by multiplying 45,550 by 6%. This will give 2,730. over the next three years the price decreases, so multiply 2,730 by 3, which is 8,190. Finally, subtract 45,550 by 8,190 to get 33,710.
PLS HELP !! ITS DUE tommorow!!
Answers
In the given square, the values of f and g are equal that is 4√3cm.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.So, the values of f and g are:
From the given diagram we know that ABCD is a square.So, all sides are the same.The area of ABCD is 48cm².
Now, calculate for sides as follows:The formula for the area of the square: A = s²Then,
A = s²48 = s²s = √48s = √2×2×2×2×3s = 2×2√3s = 4√3Since f and g are 2 sides of the square, their values are 4√3cm.
Therefore, in the given square, the values of f and g are equal that is 4√3cm.
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Describe the transformation of
f(x) = -2|x + 1 + 5
Shift Up__units.
Shift Down__units.
Shift Right__units.
Shift Left__units.
Compress by a factor of__
Stretch by a factor of__
Reflect over__axis.
Answers
The transformation of the equation f(x) = -2|x + 1| + 5 is
Shift Left 1 units
Shift Up 5 units
Compress by a factor of 2
Reflect over x axis
Interpretation of the transformationsTransformation involves movements of image or object usually described in a cartesian plane
starting from |x| at the origin
|x + 1| is a shift to the left 1 unit
|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units
2|x + 1| + 5 is a vertical compression by a factor of 2
-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over
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sally purchases some apples and oranges for $5.25. oranges cost 51 cents each and apples costs 42 cents each. sally purchased 11 pieces of fruit in total. how many oranges did sally purchase? g
Answers
Sally purchased 7 pieces of orange .
Conversion applied :
1 dollar = 100 cents
Cost of 1 piece of orange = 51 cents
Cost of 1 piece of apple = 42 cents
Let pieces of orange purchased be x .
⇒ pieces of apples purchased = 11 - x .
The following linear equation becomes ,
51 x + 42 ( 11 - x ) = 5.25 * 100
Solving linear equation in 1 variable given above ,
9 x = 63
x = 7
⇒ no. of oranges purchased = 7
Therefore Sally purchased 7 pieces of orange .
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In the triangle below, with right angle G, suppose that m/F= (3x-14)° and mZH=(5x-16)°.
Find the degree measure of each angle in the triangle.
Answers
The degree measure of each angle in the triangle is
∠H = 59°
∠F = 39°
Angle sum property of triangle says that sum of all the triangle is always equal to 180°
∠G is given to us as 90°
So by applying the property we an say that
90 + (3x - 14) + (5x - 16) = 180
8x = 180 - 90 + 14 + 16
8x = 120
x = 15
∠H = 5x - 16
∠H = 5*15 - 16
∠H = 75 - 16
∠H = 59°
∠F = 3x - 14
∠F = 3*15 - 14
∠F = 45 - 14
∠F = 39°
Therefore ∠H = 59° and ∠F = 39°
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Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
Answers
The time it takes to paint the whole bookcase is 50 minutes.
How to calculate the value?From the information, Wilson paints 40% of a bookcase in 20 minutes.
Let the time taken to paint the whole bookcase be x. This will be illustrated as:
20/x = 40/100
Cross multiply
40x = 100 × 20
40x = 2000.
Divide
x = 2000 / 40
x = 50
The time taken is 50 minutes.
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its easy but im lazy please helppppp
Answers
y=1/58x
because in 3 hours its 174 miles.
let y=miles
x=time
so 174y=3x
divide by 3 on both sides
58y=x
isolate y by dividing by 58 on both sides
therefore you get the answer
Replace the star astrict (*) with a digit that allows you to reduce the fraction. If there are two * in the same fraction, replace them with the same digit. Find all possible values of * in each fraction. This is the one that I got stumped in...
12*/23* This is a fraction. Fill it in. Remember, you have to fill it in, so it can get reduced.
Please answer by 3:00PM Pacific time Sunday november 6th 2022
Answers
The star asterisk in the fraction 12*/23* is being replaced by all the possible values as outlined
1 to be 11/21
2 to be 61/116
4 to be 62/117
5 to be 25/47
6 to be 63/118
8 to be 64/119
0 to be 12/23
What are fractions?In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a chunk or section taken from a whole, which can be any number, and can represent any amount.
The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.
The asterisk value is replaced with digit in each case, and the fraction formed is reduced to their equivalent forms as below
12*/23* * replaced by 1 and reduced to be 11/21
12*/23* * replaced by 2 and reduced to be 61/116
12*/23* * replaced by 4 and reduced to be 62/117
12*/23* * replaced by 5 and reduced to be 25/47
12*/23* * replaced by 6 and reduced to be 63/118
12*/23* * replaced by 8 and reduced to be 64/119
12*/23* * replaced by 0 and reduced to be 12/23
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