The required inequality for number of outfit is n ≤ 6.3 and Christopher can purchase 6 biking outfits.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Given that,
Maximum amount that Christopher can spend = $780.
The price of new bicycle = $446.45.
Also, Christopher buys 2 bicycle reflectors for $16.82 each.
And a pair of bike gloves for $24.60.
Let Christopher buys n outfits.
The price of 1 outfit is $43.70.
The price of n outfits = $43.70n
Since, Price of 1 bicycle reflectors = $16.82
Price of 2 reflectors = $16.82 x 2 = $33.64
The inequality to determine the number of outfits can be written as,
43.70n + 446.45 + 24.60 + 33.64 ≤ 780.
43.70n + 504.69 ≤ 780.
43.70n ≤ 780 - 504.69
43.70n ≤ 275.31
n ≤ 6.3
The maximum number of outfit Christopher can purchase is 6.
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100 POINTS AND BRAINLIEST
For what values of c does the quadratic equation -x^2+4x+c=0
1. Have no real roots?
2. Have two roots with the same sign?
3. Have one negative root and one root equal to 0?
4. Have two roots with opposite sides?
Answer:its c
Step-by-step explanation:
Answer:
1. c < -4
2. -4 < c < 0
3. c = 0
4. c > 0
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]
Given quadratic equation:
[tex]-x^2+4x+c=0[/tex]
Question 1If the quadratic equation has no real roots, then the discriminant is less than zero:
[tex]\implies b^2-4ac < 0[/tex]
[tex]\implies (4)^2-4(-1)(c) < 0[/tex]
[tex]\implies 16+4c < 0[/tex]
[tex]\implies 4c < -16[/tex]
[tex]\implies c < -4[/tex]
Question 2If the quadratic equation has two real roots, then the discriminant is greater than zero:
[tex]\implies b^2-4ac > 0[/tex]
[tex]\implies (4)^2-4(-1)(c) > 0[/tex]
[tex]\implies 16+4c > 0[/tex]
[tex]\implies 4c > -16[/tex]
[tex]\implies c > -4[/tex]
Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root. If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.
Therefore, for the two roots to have the same sign, -4 < c < 0.
Question 3If c = 0 then:
[tex]\implies -x^2+4x=0[/tex]
[tex]\implies -x(x+4)=0[/tex]
[tex]\implies x(x+4)=0[/tex]
Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.
Question 4Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.
Therefore, for the equation to have two roots with opposite signs, c > 0.
NEED HELP ASAP!!!
I am 20 years older than twice my daughter's age. How old is my daughter? ( 1. 17 years ago, I was half the age I am now. How old am I? - Part of 2.)
The daughter's age is 7 years old.
What is the equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.
Let the age of the parent be x,
He/she was half of the age 17 years back, then,
x/2 = x-17
x = 34
Therefore, parent's present age is 34 years.
He is 20 years older than twice his daughter's age,
Let his daughter's age be y,
2y+20 = 34
2y = 14
y = 7
Hence, his daughter's age is 7 years old.
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Kinda urgent
Will mark brainliest
:)
The function rule for the transformation of the graph f(x) = 2x
reflection over the x - axis (x, y) → (x, -y)
f(x) = -2xvertical compression of a factor of 1/4
g(x) = -x/2How to find the required transformationConsidering the given function f(x) = 2x that requires reflection and vertical compression
The transformation rule for reflection over the x - axis
(x, y) → (x, -y)
comparing to the equation y = f(x) = 2x
-y = -2x
hence f(x) = -2x
vertical compression involves multiplying by 1/4
= 1/4 * f(x)
= 1/4 - 2x
= -x/2
Hence g(x) = -x/2
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A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.
The linear function that models the problem of movie theater sells popcorn is
y = 2.50x + 3.50 How to model the required equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = cost of the bucket = $3.50
m = cost of refills = $2.50
y = 2.50x + 3.50
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Andrew decided so joys a tenner clench. Below is a chart that displays how many games of lenis he has played and the meatal cost of playing those panes. In this scenario, C ( y ) represents the total cost for playing games.
The linear function that represents the situation is of:
C(y) = 13y + 145.
The intercept is of:
C(0) = 145, meaning that the flat fee to pay the game is of $145.
What is the linear function?The slope-intercept representation of a linear function is given by the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the rate of change of the function.b is the y-intercept of the function, representing the initial value of the function.Two points of the function, from the table, are given as follows:
(8, 249) and (13,314).
The slope is given by the change in y of the two points divided by the change in x, hence:
m = (314 - 249)/(13 - 8) = 13.
Hence:
C(y) = 13y + b
When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:
249 = 13(8) + b
b = 249 - 13 x 8
b = 145.
Meaning that the flat fee to pay the game is of $145.
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NEED AN ANSWER PLEASE HELP!!
Answer:
5.12
Step-by-step explanation:
If u times 1.6 and 3.2 you get 5.12 also i got it correct on my test
. Lin's family has completed 60% of a trip. They have traveled 30 miles
How many miles is the trip?
A 50 miles
B. 48 miles
C. 30 miles
D. 18 miles
Answer: A 50 miles
Step-by-step explanation:
Its A becuase 60%=0.6 and 0.6 times 50 is 30 which means 60 percent of 50 is 30.
Multiply. 2u*3u^2 please help me
Answer: 6u^3
Step-by-step explanation:
You have to add the exponents when you multiply them.
But before that, you can multiply the coefficients of 2 and 3 so you get 6.
Now you have u and u^2 left.
u = u^1
u^2 = u^2
1+2 =3
(9√-81)(-10√64) is the answer -6480i? im confused
[tex]i=\sqrt{-1}[/tex]
Solving the Question[tex](9\sqrt{-81})(-10\sqrt{64})[/tex]
⇒ Take out i from the first square root:
[tex]= (9i\sqrt{81})(-10\sqrt{64})[/tex]
⇒ Evaluate the square roots:
[tex]= (9i\times9)(-10\sqrt{64})\\= (9i\times9)(-10\times 8)[/tex]
⇒ Multiply:
[tex]= (81i)(-10\times 8)\\= (81i)(-80)\\= -6480i[/tex]
Answer-6480i
please find the gradient
Answer:
-2
Step-by-step explanation:
use the formula
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
What is the solution to the system?
-4x - 2y = 8
y = x2 - 3
Will give points for answer
Answer:
Step-by-step explanation:
to find x;
-4x - 2 -1 =8
-4x + 3 = 8
+4 + 3 = +4
x + 3 = 12
-3 + -3
x = 10
to find y;
y = x2 - 3
y = (10)2 - 3
y = 20 - 3
y = 17
Your friend bought a new pair of shoes. He said the regular price was $75 but he got a 40% discount from the sales clerk. What is the sale price of the shoes
Answer:
40% off of 75 is 45$
Step-by-step explanation:
Divide the number by 100 (move the decimal place two places to the left).Multiply this new number by the percentage you want to take off.Subtract the number from step 2 from the original number. This is your percent off number.Need help asap! thanks
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of the given expression is 1479.40
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Sum of [tex]2(\frac{4}{3})^n[/tex] from n = 0 to n = 6.
This can be written as,
= [tex]2(4/3)^0 + 2(4/3)^1 + 2(4/3)^2 + 2(4/3)^3 + 2(4/3)^4 + 2(4/3)^5 + 2(4/3)^6[/tex]
= 2 x 1 + 8/3 + 2 x 16/9 + 2 x 64/27 + 2 x 256/81 + 2 x 1024/243 +
2 x 4096/729
= 2 + 2.67 + 3.56 + 4.74 + 6.32 + 8.43 + 1458
= 1479.40
Thus,
The value of the given expression is 1479.40
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Write the expression as a single logarithm.
7log6z - 1/2log6x +3log6y
The value of the logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
As per the given logarithm,
7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex]
Since,[tex]alog_{b}c = log_{b}c^\frac{1}{a}[/tex]
Thus,
7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex] =d [tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]dddd
Since,[tex]log_{a}b+log_{a}c=log_{a}bc[/tex]
Therefore,
[tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]= [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].
Hence "The value of the given logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex]".
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Reagan is running toward school twice as fast as her brother. If her brother is running at 2meterspersecond, how much time will it take Reagan to run 28meters?
Write your answer as a whole number.
The time taken by the Reagan to cover the distance of 28 meters will be 7 seconds.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.
Given that Reagan is running toward school twice as fast as her brother. If her brother is running at 2 meters per second.
The time taken to cover the distance of 28 meters will be calculated as,
R = 2B
Brother's speed = 2 m / s
Reagan's speed = 2 x 2 = 4 m/s
The time will be,
T = Distance / Speed
T = 28 / 4
T = 7 seconds
Therefore, the time taken by Reagan to cover the distance of 28 meters will be 7 seconds.
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Pythagoras theorem
How do i find the n
Answer:
n = 44
Step-by-step explanation:
the 'dashes ' through the 2 legs of the triangle indicate they are congruent.
then n = 44 mm
due to road works and a diversion on the m1, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes how long did it take anjam?
The minutes when Anjam travel from Sheffield at 10.15am and arrived in Watford 3.55pm in minutes is 320 minutes.
How to calculate the time?It is important to note that the question is simply about the calculation of the time involved. Based on this situation, it should be noted that:
60 minutes = 1 hour.
Given that due to road works and a diversion, Anjam's drive from Sheffield to Watford took a lot longer than planned. He left Sheffield at 10.15am and arrived in Watford 3.55pm in minutes.
The time for the journey will be:
= 3.35pm - 10.15am
= 5.20 hours.
We will change this to minutes:
= (5 × 60) + 20
= 320 minutes
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Write an equation of the line that passes through the pair of points. (5/12, −1), (−3/4, 1/6)
Answer:
[tex]y=-x-\frac{7}{12}[/tex]
Hope this helps!
How do I write a two-column proof for this problem?
Given: Isosceles △ABC with legs AB and AC, BD ⊥DC and CE⊥BE
Prove: BD ≅ CE
BD ≅ CE is proved and is shown below.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are two triangles as shown in the figure.
Triangles ΔMPN and ΔSTU are congruent. We can write -
2x - y = 13
2x - 50 = 24
Now -
2x - 50 = 24
2x = 74
x = 3The measurements of [x] and [y] are 37 and 61 respectively.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.
In △BDC and △CEB, we can write -
∠D = ∠E = 90°
BC = BC {Common}
∠B = ∠C {Angles opposite to equal sides are equal}
By SAS criteria △BDC ≅ △CEB.
So, we can write -
BD ≅ CE
Therefore, BD ≅ CE is proved and is shown above.
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Find the x-intercept of the line 14x–11y= – 1.
Answer:
x- intercept = - [tex]\frac{1}{14}[/tex]
Step-by-step explanation:
to find the x- intercept, that is where the line crosses the x- axis, let y = 0 in the equation and solve for x
14x - 11(0) = - 1
14x = - 1 ( divide both sides by 14 )
x = - [tex]\frac{1}{14}[/tex] is the x- intercept
30 POINTS!!!!!! HELP ASAP! At cruising speed a car burns fuel at a rate of 2.5 kilograms per hour the mass of the car including the fuel when it reaches cruising speed is 1,550 kg and the mass of the car when the fuel tank is empty is 1,520 kg. the domain of the function f(t) is best described as
The domain of the function f(t) is best described as 608 ≤ t ≤ 620
How to determine the domain of the function?From the question, we have the following parameters that can be used in our computation:
Rate = 2.5 kilograms per hour
Mass of the car (including the fuel) = 1550 kg
Mass of the car (not including the fuel) = 1520 kg
Calculate the times using the rate and the masses above
So, we have the following representations
Time 1 = 1550/2.5
Time 1 = 620
Time 2 = 1520/2.5
Time 2 = 608
Express as an interval
608 ≤ t ≤ 620
Hence, the domain is 608 ≤ t ≤ 620
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Write an expression to represent: 4 less than the quotient of x and 5.
x/5 - 4 represents 4 less than the quotient of x and 5.
Im stuck on this ones i dont know how to get the answers
The measurements of [x] and [y] are 37 and 61 respectively.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given are two triangles as shown in the figure.
Triangles ΔMPN and ΔSTU are congruent. We can write -
2x - y = 13
2x - 50 = 24
Now -
2x - 50 = 24
2x = 74
x = 37
then -
2 x 37 - y = 13
74 - 13 = y
y = 61
Therefore, the measurements of [x] and [y] are 37 and 61 respectively.
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4. Solve the quadratic equation 4x² + 7 = 25.
use the formula 「x= [-b±✓(b²-4ac)]/2a」a= 4, b= 0, c= -18x= [-0±✓(0²-4(4)(-18))]/2(4)x= 2.1213... , x= -2.1213...
7 ÷ (-9 - -8)³ how do I solve this? What’s the answer
Answer: -7
Step-by-step explanation:
7 ÷ (-9 - -8)³
(-9 - -8)³ = -1
7 ÷ -1 = -7
Answer:
-7
Step-by-step explanation:
We have to solve this according to the B O D M A S theorem.
That is:
B ⇒ Brackets
O ⇒ Of
D ⇒ Division
M ⇒ Multiplication
A ⇒ Addition
S ⇒ Subtraction
Also, we know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( + )
( + ) × ( - ) = ( - )
Let us solve it now.
7 ÷ ( - 9 - ( - 8 ) )³
7 ÷ ( - 9 + 8 )³
7 ÷ ( - 1 )³
7 ÷ ( - 1 )
- 7
in the figure pictured below DF=3 BF =14 GF =8 find the lengths of:
A. cf
B. ef
C. ag
The lengths of CF, EF and A.F are 6 units, 28 units and 16 units, respectively
How to determine the lengths of these sides?From the question, the given parameters to solve the question are represented as
DF = 3
BF = 14
GF = 8
The point F in the triangle is the centroid of the triangle
This means that the point F divides the lines that passes through it in the ratio 1 : 2 or 2 : 1 (as the case may be)
The claim above also means that
CF = 2 * DF
EF = 2 * BF
A.F = 2 * GF
Substitute the known values in the above equation, so, we have the following representation
CF = 2 * 3 = 6
EF = 2 * 14 = 28
A.F = 2 * 8 = 16
Hence, the lengths are 6 units, 28 units and 16 units
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Simplify quantity x squared plus 5 x plus 4 end quantity over quantity x plus 4 (5 points) x − 1 x + 1 x2 + 1 x2 − 1
Answer:
Step-by-step explanation:
there is no oblique asymptote
Does anyone know how to do this pls
Haha ITS MATHXL
Anyways, constant rate of +90 and currently has 1560.
Say y will be the amount of students, and x is how many years later.
y=90x+1560
So for a), the answer is y=90x+1560
For b), plug in 3 for x, since 2017 is 3 years after 2014.
y=90(3)+1560
y=270+1560
y=1830
Amount of students in 2017: 1830
For c), plug in 2010 for y.
2010=90x+1560
Subtract 1560 both sides
450=90x
Divide both sides by 90
x=5
Answers
a) y=90x+1560
b) 1830
c) 5 Years Later, or 2019
Hope this helps!
75 − 3.5y − 4y = 4y + 6 for y. please show how you got
Answer:
y=6
Step-by-step explanation:
75-3.5y-4y=4y+6
Combine like terms on each side
75-7.5y=4y+6
Add 7.5y to both sides since it is the inverse of subtraction
75-7.5y=4y+6
+7.5y. +7.5y
75=11.5y+6
Isolate y on one side by subtracting 6 from both sides
75=11.5y+6
-6. -6
69=11.5y
Divide both sides by 11.5
69=11.5y
/11.5. /11.5
6=y
hopes this helps please mark brainliest
Please help this is URGENT
TQ/VQ=TV/VR is true for the given triangle. Option B is correct
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Two pairs of corresponding angles are equal
Three pairs of corresponding sides are proportional
Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
From these we can say that the sides TV is proportional to Rs and TQ is proportional to VQ
Hence, TQ/VQ=TV/VR is true for the given triangle. Option B is correct
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