Karen and Aisha share £18 in
the ratio 11 : 4. Work out how
much money Aisha gets.​

Answer:

Step-by-step explanation: Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

p*(x)-((2*x^2-9*x+7)*(x-2))=0

STEP

1

:

Equation at the end of step 1

px - (((2x2 - 9x) + 7) • (x - 2)) = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 2x2-9x+7

The first term is, 2x2 its coefficient is 2 .

The middle term is, -9x its coefficient is -9 .

The last term, "the constant", is +7

Step-1 : Multiply the coefficient of the first term by the constant 2 • 7 = 14

Step-2 : Find two factors of 14 whose sum equals the coefficient of the middle term, which is -9 .

-14 + -1 = -15

-7 + -2 = -9 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -2

2x2 - 7x - 2x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (2x-7)

Add up the last 2 terms, pulling out common factors :

1 • (2x-7)

Step-5 : Add up the four terms of step 4 :

(x-1) • (2x-7)

Which is the desired factorization

Equation at the end of step

2

:

px - (2x - 7) • (x - 1) • (x - 2) = 0

STEP

3

:

Equation at the end of step 3

px - 2x3 + 13x2 - 25x + 14 = 0

STEP

4

:

Solving a Single Variable Equation:

4.1 Solve px-2x3+13x2-25x+14 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Supplement : Solving Quadratic Equation Directly

Solving 2x2-9x+7 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

5.1 Find the Vertex of y = 2x2-9x+7

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 2 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.2500

Plugging into the parabola formula 2.2500 for x we can calculate the y -coordinate :

y = 2.0 * 2.25 * 2.25 - 9.0 * 2.25 + 7.0

or y = -3.125

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = 2x2-9x+7

Axis of Symmetry (dashed) {x}={ 2.25}

Vertex at {x,y} = { 2.25,-3.12}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 1.00, 0.00}

Root 2 at {x,y} = { 3.50, 0.00}

3 Solving 2x2-9x+7 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 2

B = -9

C = 7

Accordingly, B2 - 4AC =

81 - 56 =

25

Applying the quadratic formula :

9 ± √ 25

x = —————

4

Can √ 25 be simplified ?

Yes! The prime factorization of 25 is

5•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 25 = √ 5•5 =

± 5 • √ 1 =

± 5

So now we are looking at:

x = ( 9 ± 5) / 4

Two real solutions:

x =(9+√25)/4=(9+5)/4= 3.500

or:

x =(9-√25)/4=(9-5)/4= 1.000

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

\(Solution,\\Let~a=10in.,~b=24in.~and~c=26in.\\Semiperimeter(s) = \frac{a+b+c}{2}= \frac{10+24+26}{2} = 30in.\\Now,\\Area~of~triangle = \sqrt{s(s-a)(s-b)(s-c)} \\~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{30(30-10)(30-24)(30-26)} \\~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{30(20)(6)(4)} = \sqrt{14400}=120sq.inches\)

The inequality shown by a number line which describes that 12 is to the right of -2 is; 12 > -2.

It follows from the task content that the inequality which represents the number line as described in the task content is to be determined

On this note, it follows that since, numbers are arranged from left to right in increasing order on the number line, then;

Since 12 is to the right of -2, the inequality which represents the situation is; 12 > -2.

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a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

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Answer:

4/6 is more than 5/12

Step-by-step explanation:

First, set the denominators of the fractions equal to eachother to make it easier to compare.  mulitiply 6 and 4 by 2 so that the denominator now equals 12, and you have the new fractions 5/12 and 8/12.  Since 8/12 is more than 5/12, 4/6 is more than 5/12.  

Answer:

5/12 is greater than 4/6

Step-by-step explanation:

using the butterfly method, multiplying 12 x 4 = 48

and 6x5=30  48 is more than  30

48 Stands for 5/12

30 stands for 4/6

Answer:

Multiplication property of equality because we need to multiply both sides by 5 to get rid of the denominator, so we get w = 50.

Hope this helps and brainliest please

Answer:

You would use the multiplication property of equality and by using that you get W=50.

Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

So the greatest common factor 44 and 220 is 44.

Step-by-step explanation:

Answer:

10605

Step-by-step explanation:

Answer:

As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.

Step-by-step explanation:

Here n= 20

Sample mean GPA = x`= 2.84

Standard mean GPA = u= 2.55

Standard deviation = s=  0.45.

Level of Significance.= ∝ = 0.01

The hypothesis are formulated as

H0: u1=u2   i.e the GPA of night students is same as the mean GPA of day students

against the claim

Ha: u1≠u2

i.e the GPA of night students is different from the mea GPA of day students

For two tailed test  the critical value is  z ≥ z∝/2= ± 2.58

The test statistic

Z= x`-u/s/√n

z= 2.84-2.55/0.45/√20

z= 0.1441

As the calculated value of z does not lie in the critical region the null hypothesis is accepted that the GPA mean of the night students is the same as the GPA mean of the day students.

\(\pink{\bigstar}\) The measure if ∠x \(\large\leadsto\boxed{\tt\purple{43^{\circ}}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• To Find:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

The given angles are made by a straight line. We know that the total angle made by a straight line is 180°.

Therefore, all the angles should sum upto 180°.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Working:-

➪ \(\sf (x + 31^{\circ}) + (x + 20^{\circ}) + (x) = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x + 31^{\circ} + x + 20^{\circ} + x = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x + 51^{\circ} = 180^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x = 180^{\circ} - 51^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf 3x = 129^{\circ}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ \(\sf x = \dfrac{129}{3}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ \(\large{\bold\red{x = 43^{\circ}}}\)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, the measure of the ∠x is 43°.

Step-by-step explanation:

\(we \: know \: that \: sum \: of \: angles \: in \: a \: line \: = 180 \\ so \\ x + 31 + x + 20 + x = 180 \\ 3x + 51 = 180 \\ 3x = 180 - 51 \\ 3x = 129 \\ x = \frac{129}{3} \\ x = 43degree \\ thank \: you\)

It depends on the number of variables, if the inequality has one variable, then it is graphed on a number line.

The type of diagram that we need to use depends on the number of variables that we have.

That is the main reason, for example:

x > 2

Is graphed on a number line.

y > 3x + 4

is graphed on a coordinate plane.

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Using the concept of a statistical question, this question is not one example of those, as it cannot be answered collecting data that vary.

It is a question that can be answered collecting data that vary, for example, the number of Buffalo Bills fans in a sample of 1000 people.

In this problem, the number of days in June is a fixed amount(30), hence it is not a statistical question.

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Answer:

(2−1)(3+2)

Step-by-step explanation:

Rewrite in product form

2x(3x+2) - 1(3x+2)

(2x-1) (3x+2)

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

The answer is the first option - leaf.

Answer:

the answer is stem.

Step-by-step explanation:

i know this because i am on the same question and there are only two answers so if the other answer was wrong it means this one has to be right.

The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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Answer:

0.85

Step-by-step explanation:

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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Answer:

37 million

Step-by-step explanation:

The completed contingency table that summarizes the classification of students by weight and gender is attached below.

a. For a randomly selected student, describe the following in words

W1 is an event in which a randomly selected student is obese.

P(W1) is the probability that a randomly selected student is obese.

b. The following probabilities: (Round the answers to 4 decimal places)

i. P(W2) = (42 + 55) / 173 = 0.574

ii. P(G1) = (76 + 76) / 173 = 0.500

iii. P(W1 and G2) = (76) / 173 = 0.440

iv. P(W3 or G2) = (30 + 22 + 76 + 76) / 173 = 0.884

v. P(W3 | G2) = (22) / (22 + 76) = 0.214

c. For the following:

i. W3 and G1 are not mutually exclusive. This is because there are students who are both obese and male. For example, the value in the cell (W1, G1) is 76.

ii. W3 and G1 are not independent. This is because the probability of being obese is different for male students than it is for female students. For example, the probability of being obese is 0.440 for male students, but it is only 0.130 for female students.

iii. W3 and W2 are not mutually exclusive. This is because there are students who are both underweight and normal. For example, the value in the cell (W2, W3) is 30.

iv. W3 and W2 are not independent. This is because the probability of being underweight is different for normal students than it is for obese students. For example, the probability of being underweight is 0.300 for normal students, but it is only 0.154 for obese students.

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Answer:

LxWxH

Step-by-step explanation:

The angles inside a trapezoid add up to equal 360 degrees

X = 360-90-90-75 = 105 degrees.

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

Answer: D.

hope this helps

Answer:

we can't see the graph

Step-by-step explanation:

gdhdhd

The limit of xlnx when x is tending towards zero is zero.

What is limit in mathematics?

In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.

Given limit is:

\(\lim_{x \to 0} x lnX\)

Considering f = x, and g = ln x

The limit of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the limit f/g equals it.

The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as

\(\frac{lnx}{1/x}\)

We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as

The limits

\(\lim_{x \to 0^+} lnx= - \infty\), and

\(\lim_{x \to 0^+} \frac{1}{x}\)

The limits  \(\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}\) exists as:

\(\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0\)

Hence the answer is 0.

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