Claire and jane did an examination together. jane scored 9 more marks than claire and her marks were 60% of the sum of their scores. what are the scores of each student?

I'm going to assume you meant to say

[tex]\displaystyle \lim_{x\to-4} \frac{x+4}{x^2-16}[/tex]

Factorize the denominator to reveal a removable discontinuity in the limand:

[tex]\dfrac{x+4}{x^2-16} = \dfrac{x+4}{(x+4)(x-4)}[/tex]

In the limit, we're considering values of x *near* -4, and not x = -4 itself. So we can cancel the factors of x + 4 and we're left with

[tex]\displaystyle \lim_{x\to-4} \frac{x+4}{x^2-16} = \lim_{x\to-4} \frac1{x-4} = \frac1{-4-4} = \boxed{-\frac18}[/tex]

Answer: b/5

Step-by-step explanation:

They divide the total by 5 to get the cost each person has to pay

Using the cosine rule, the equation to use to solve for x is: x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41)) ≈ 3.1 cm.

The cosine rule is given as, c = √(a² + b² − 2ab × cos(C))

Given the following:

Plug in the values:

x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41))

x ≈ 3.1 cm

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Answer:

Step-by-step explanation:

truth to the power 6 15 raised to the power x

The statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

= 6 + 4i

Multiplied by 3:

= 18 + 12i

If we plot on the coordinate plane there will be no rotation the scalar has changed by multiplying with a real number.

Thus, the statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.

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Answer:

80%

Step-by-step explanation:

I'm assuming you meant express 4/5 as a percent and not 4/5%. So simply evaluate 4/5 to get 0.80. Now multiply this value by 100 to get the percentage which gives you 80%

Answer:

c.

Step-by-step explanation:

Assuming we are not restricting the domain of f, the inverse isn't a function

[tex] \frac{1}{ {x}^{2} } - 7[/tex]

[tex]y = \frac{1}{ {x}^{2} } - 7[/tex]

[tex]x = \frac{1}{ {y}^{2} } - 7[/tex]

[tex]x + 7 = \frac{1}{ {y}^{2} } [/tex]

[tex] {y}^{2} = \frac{1}{x + 7} [/tex]

[tex]y = \sqrt{ \frac{1}{x + 7} } [/tex]

Since square root are Positve or negative, the function will not be a function.

The correct answer is c.

Answer:

Step-by-step explanation:

1)   = f(x - a) + b

Coordinate change

(x, y) → (x + a, y + b)

2) RFy(x, y) = f(-x)

Coordinate change

(x, y) → (-x, y)

3) RFx(x, y) = -f(x)

Coordinate change

(x, y) → (-y, x)

4) RCCW90(x, y) = f⁻¹(-x)

Coordinate change

(x, y) → (-y, x)

5) RCCW180(x, y) = -(f(-x))

Coordinate change

(x, y) → (-x, -y)

6) A 270 degrees counterclockwise rotation gives;

RCCW270(x, y) = -(f⁻¹(x))

Coordinate change

(x, y) → (y, -x)

Step-by-step explanation:

1) Horizontal translation a units right = f(x - a)

The vertical translation b units up = f(x) + b

Therefore, we get;  = f(x - a) + b

The coordinate change

(x, y) → (x + a, y + b)

2) A reflection across the y-axis = RFy(x, y) = f(-x)

The coordinate change

(x, y) → (-x, y)

3) A reflection across the x-axis gives RFx(x, y) → (x, -y)

Therefore, in function notation, we get;

RFx(x, y) = -f(x)

4) A 90 degrees rotation counterclockwise, we get RotCCW90(x, y) → (-y, x)

In function notation RotCCW90(x, y) = INVf(-x) = f⁻¹(-x)

5) A 180 degrees counterclockwise rotation about the origin gives;

(x, y) → (-x, -y)

Therefore, we get;

In function notation RotCCW180(x, y)  = -(f(-x))

6) A 270 degrees counterclockwise rotation gives RotCCW270(x, y) → (y, -x)

In function notation RotCCW270(x, y) = -(f⁻¹(x))

Answer:

[tex] \sqrt{30} [/tex]

Step-by-step explanation:

altitude rule

10 / x = x / 3

x^2 = 30

x = sqrt(30)

Answer:

3.31 x 10^4

Step-by-step explanation:

3.111 x 10^4 is 31110

2 x 10^3 is 2000

31110 + 2000 = 33100 or 3.31 x 10^4

Answer:

b) 3.31 × 10⁴

Explanation:

[tex]\sf \rightarrow \left(3.11\cdot 10^4\right)+ \left(2\cdot 10^3\right)[/tex]

remove parenthesis

[tex]\rightarrow \sf 3.11\cdot \:10^4+2\cdot \:10^3[/tex]

simplify

[tex]\rightarrow \sf 31100+2000[/tex]

add the numbers

[tex]\sf \rightarrow 33100[/tex]

convert to scientific form

[tex]\sf \rightarrow 3.31 \ x \ 10^4[/tex]

The measure of the unknown angle are; a) x = 89 degrees, b) p = 92 degrees.

For a regular polygon of any number of sides, the sum of its exterior angle is 360°.

We already know that a 4-sided polygon's angles add up to 360 degrees.

So to find the value of x:

69 + 118 + 84 + x = 360

x = 360 - (69 + 118 + 84)

x = 89 degrees

b)

For a 4-sided polygon, we also know that the outside angles add up to 360 degrees.

So to find the value of p:

100 + 62 + 106 + p = 360

p = 360 - (100 + 62 + 106)

p = 92 degrees

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The average rate of change of a (continuous) function f(x) over an interval [a, b] is given by the so-called difference quotient,

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Here we have f(x) = x² + 8x + 12 and the interval is [-10, -2], so the ARoC of f(x) on this interval is

[tex]\dfrac{f(-2) - f(-10)}{-2 - (-10)} = \dfrac{0 - 32}8 = \boxed{-4}[/tex]

Answer:

[tex]LM = 35cm[/tex] and [tex]m \angle H = 98^o[/tex]

Step-by-step explanation:

For this problem, it is critical to understand what the opening statement means.

[tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex] means that each pair of corresponding sides between shapes are congruent (they have equal length), and each pair of corresponding angles between shapes are congruent (they have equal measure -- or same number of degrees when measured with a protractor).

So, it's important to be able to determine which pairs are the corresponding parts.  When the congruence is given like [tex]Quadrilateral GHJK \cong quadrilateral LMNP[/tex]  the letters are in a particular order.  That order explains the order in which the shape is drawn out, and they put them in the same order for both shapes to mean that those are the letters that correspond with each other.

So, the first letter of each are a corresponding pair, the second letter of each are a corresponding pair, ... etc

In other words, point G and L correspond, point H and K correspond, etc.

To find the corresponding sides, the sides for these shapes are defined by a two adjacent letters (two letters next to each other in the name, or ... as it wraps around the end of the name... the first and last letter).

[tex]\overline{GH} \cong \overline{LM}\\ \overline{HJ} \cong \overline{MN} \\\overline{JK} \cong \overline{NP}\\\overline{KG} \cong \overline{PL}[/tex]

While all of that is true, we only have a few sides with any information in them.  Notice that side GH in the first shape, and sides PL & LM in the second shape are the only sides with anything written.  So, we just need to determine which sides correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent sides above, we see that  [tex]\overline{GH} \cong \overline{LM}[/tex]

Since the sides (line segments) are congruent, their lengths are equal

[tex]GH = LM[/tex]

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "x"

[tex]GH = LM\\(4x+3)=(6x-13)[/tex]

[tex](4x+3)+13=(6x-13)+13\\4x+16=6x[/tex]

[tex](4x+16)-4x=(6x)-4x\\16=2x[/tex]

divide both sides by 2

[tex]\frac{16}{2}=\frac{2x}{2}\\8=x[/tex]

So, to find the length, LM, we just need to look back at the expression for LM:

[tex]LM = 6x-13\\LM = 6(8)-13\\LM = 48-13\\LM = 35[/tex]

remembering that the lengths are measured in centimeters (as indicated on the diagram): [tex]LM = 35cm[/tex]

To find the corresponding angles, the angles for these shapes are defined by a single letter, so since the points correspond in order, the names of the shapes tell which angles are congruent.

[tex]\angle G \cong \angle L\\\angle H \cong \angle M\\\angle J \cong \angle N\\\angle K \cong \angle P[/tex]

While all of that is true, we only have a few angles with any information in them.  Notice that ∠H in the first shape, and ∠L & ∠M in the second shape are the only angles with anything written.  So, we just need to determine which angles correspond (and thus, are congruent), so that we know how to move forward.  Looking at the list of congruent angles above, we see that  

[tex]\angle H \cong \angle M[/tex]

Since the angles are congruent, their measures are equal

[tex]m\angle H = m\angle M[/tex]

...so we can substitute the expressions for each angle into the equation and solve for the unknown value "y"

[tex]m\angle H = m\angle M\\(9y+17)=(11y-1)[/tex]

subtract 1 from both sides

[tex](9y+17)+1=(11y-1)+1\\9y+18=11y[/tex]

subtract 9y from both sides

[tex]\\(9y+18)-9y=(11y)-9y\\18=2y[/tex]

divide both sides by 2

[tex]\frac{18}{2}=\frac{2y}{2}\\9=y[/tex]

So, to find angle H, we just need to look back at the expression for the measure of angle H:

[tex]m\angle H = 9y+17\\m\angle H = 9(9)+17\\m\angle H = 81+17\\m\angle H = 98[/tex]

remembering that the angle is measured in degrees (as indicated on the diagram): [tex]m \angle H = 98^o[/tex]

Answer:

32ounces

Step-by-step explanation:

24/3=8pounds

8pounds=8x16=128ounces

but each 8 pounds is split into quarters so

8/4=2pounds=32ounces

Answer:

Money made by tickets=

2753 x $5 = $13765

We have to subtract the cost of the concert from the money made by tickets to get our profit. Therefore,

$13765 - $8000 = $5765

A function assigns the values. The inverse of the function is y = (x+5)/2.

A function assigns the value of each element of one set to the other specific element of another set.

To find the inverse of the function, the function is needed to be solved for x, and then replace x with y and vice versa. Therefore, the inverse of the function will be,

f(x) = y = 2x - 5

y = 2x - 5

y + 5 = 2x

x = (y+5)/2

y = (x+5)/2

Hence, the inverse of the function is y = (x+5)/2.

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Answer:

a. 73:100

b. 27:73

Step-by-step explanation:

total: 100

number remaining: 27

number taken: 100 - 27 = 73

a. taken:total = 73:100

b. remaining:taken = 27:73

#a

total milk cartons used=100-27=73

So the ratio is

#b

It's already mentioned in question

The probability that the selected customer purchased a Brand 1 model is 0.14.

Given that probability a customer would purchase the Brand 1 model TV was 70% while the rest of the customers purchased the Brand 2 model. and 20% of the Brand 1 customers purchased an extended warranty while 40% of Brand 2 customers purchased an extended warranty.

The probability that a customer would purchase Brand 1 model TV P(A)=0.70.

The probability that a customer purchases the extended warranty given that the customer purchased the Brand 1 model TV is

P(B|A)=0.20

P(A and B)÷P(A)=0.20

P(A and B)÷0.70=0.20

P(A and B)=0.14

Hence, the probability that the selected customer purchases a Brand 1 model and an extended warranty is 0.14.

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The correct answer is option b which is the exponential grows at the same rate as the quadratic.

The complete question is given below with the graph attached:-

An exponential function and a quadratic function are graphed below. Which of the following is true of the growth rate of the functions over the interval

a. The exponential grows at half the rate of the quadratic.

b.The exponential grows at the same rate as the quadratic.

c.The exponential grows at twice the rate of the quadratic.

d.The exponential grows at four times the rate of the quadratic.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2 and a quadratic finction, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval

a ≤ x ≤ b

is given by

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval

0 ≤ x ≤ 1

is given by

[tex]\dfrac{f(1)-f(0)}{1-0}= \dfrac{2-1}{1}=1[/tex]

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval

0 ≤ x ≤ 1

is given by

[tex]\dfrac{g(1)-g(0)}{1-0}=\dfrac{1-0}{1}=1[/tex]

Therefore, the exponential grows at the same rate as the quadratic in the interval .

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The infusion time for the IV solution that will be prescribed 480 mins.

The time taken by the saline to be dripped in the infusion is called as the infusion time.

To calculate the infusion time the formula for IV drip rate is used which is;

Drip rate = volume/time × Drop factor

Drip rate = 5gtt/min

Volume = 120mL

Drop factor= 20 gtt/mL

Time = ?

From the formula above, make time the subject of the formula. That is,

Time = vol × drop factor/drip rate

Time = 120 × 20/5

Time= 120 x 4

Time= 480 mins

Therefore, the infusion time for the IV solution that was prescribed = 480 mins

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: f(0) = -3 [/tex]

[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]

[tex]\qquad \tt \rightarrow \: f(4) = 1 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

F(x) represents the value of y on curve for given value of x

[tex] \textsf{\large First -} [/tex]

[tex]\qquad \tt \rightarrow \: f(0) =( 0) {}^{2} - 3[/tex]

[ since 0 < 2 ]

[tex]\qquad \tt \rightarrow \: f(0) = 0 {}^{} - 3[/tex]

[tex]\qquad \tt \rightarrow \: f(0) = - 3[/tex]

[tex] \textsf{\large Second} [/tex]

[tex]\qquad \tt \rightarrow \: f(2) = (2) {}^{2} - 3[/tex]

[ since 2 = 2 ]

[tex]\qquad \tt \rightarrow \: f(2) = 4{}^{} - 3[/tex]

[tex]\qquad \tt \rightarrow \: f(2) = 1[/tex]

[tex] \textsf{\large Third -} [/tex]

[tex]\qquad \tt \rightarrow \: f(4) = - 4 + 5[/tex]

[ since 4 > 2 ]

[tex]\qquad \tt \rightarrow \: f(4) = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

The perimeter of a rectangle is P = 2(L + W) where

Given that P = 16 m,

P = 2(L + W)

16 = 2(L + W)

16/2 = L + W

L + W = 8

So, W = 8 - L

The area of the rectangle, A = LW where

Since W = 8 - L, substituting W into the equation for A, we have

A = LW

A = L(8 - L)

A = 8L - L²

So, the area A of the rectangle as a function of the length, L of one of its sides is A = 8L - L²

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Answer:

John = 41 years

Sam = 32 years

Step-by-step explanation:

The recursive formula is  [tex]a_n= a_{n-1} -5[/tex].

A set of numbers is an arithmetic progression (AP) or an arithmetic sequence such that the difference between successive words is unchanged.

Given:

A(n)=(-1)+(n-1)(-5)

A(n) = -1 - 5n + 5

A(n) = 4-5n

n=1

A(1)= 4-5= -1

n=2,

A(2) = -6

n=3

A(3)= -11

Hence, the recursive formula is [tex]a_n= a_{n-1} -5[/tex].

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15

5x-2y=9......(1)

6x+ky=4......(2)

slope of eqn i= -5/-2

=5/2

slope of eqn ii = -6/k

since the line are perpendicular

5/2 * -6/k = -1

-30= -2k

k=15

Answer:

96Km

Step-by-step explanation:

l wrote 90/60 because the speed is given in hours.

so I had to deal with hours only not hours and minutes.

that's why I wrote 90/60 .

you can also choose to divide.

I mean to change the minutes to hours so that the formula can work.

good day.

The number of people that speak only spanish = 6

We are given;

Total number of people surveyed = 50

31 speak French 2 speak French, German and Spanish.

4 speak French and Spanish but not German.

7 speak German and Spanish.

8 do not speak any of the languages.

All 10 people who speak German speak at least one other language.

Thus;

From the Venn diagram;

Number of people that speak only French and German = 10 - 5 - 2 - 0 = 3

Number that speak only spanish = 50 - 22 - 3 - 2 - 4 - 5 = 6

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