ABCD is a trapezium.
AB = P
AD = q
DC: AB= 3:2
D
a
A
Р
B
C
a) Write vector DC in terms of p.
E

b) Work out vector BC in terms of p and q.
Give your answer in its simplest form.

Answer:

y = 12x + 86

Step-by-step explanation:

y = mx + b

slope is 12 so m = 12

Using (-6,14) then

14 = 12(-6) + b

14 = -72 + b

b = 72 + 14 = 86

The simplified form is [tex]5x^{3} y^{9}[/tex].

Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.

The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.

Factoring the number,

[tex]125=5^{3}[/tex]

[tex]\sqrt[3]{5^{3} x^{6} y^{9} }[/tex]

Applying radical rule,

[tex]\sqrt[3]{5^{3} } =5^{9}[/tex]

[tex]5x^{3} y^{9}[/tex]

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Answer:

a)18 points

Step-by-step explanation:

a)

[tex]p = 3(w) + d[/tex]

therefore

[tex]p = 3(5 \: wins ) + 3 \: draws [/tex]

find the product of 5 and 3

[tex]p = 15 + 3[/tex]

[tex]p = 18[/tex]

B) how many games lost

[tex]3x + 14 = 50[/tex]

[tex]3x + 14 - 14 = 50 - 14[/tex]

[tex]3x = 36[/tex]

[tex] \frac{3x}{3} = \frac{36}{3} [/tex]

[tex]x = 12 \: games \: won| [/tex]total Games= Games won + games drawn + games lost

[tex]35 = 12 + 14 + x[/tex]

[tex]35 - 26 = 26 - 26 + x[/tex]

[tex] \times = 18 \: games \: lost[/tex]

Answer:

The values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

Step-by-step explanation:

In this question we need to solve the given equation that is 5x² - 9x - 10 to obtain the value of x using the complex solution method.

Now, the given equation is 5x² - 9x - 10 in which we need to apply the quadratic formula to find the solution;

So, the quadratic formula is => -b ± √(b² - 4ac) / 2a

Now, on comparing the equation 5x² - 9x - 10 we get the values;

a = 5

b = -9

c = -10

Further, on substituting the values given above in the quadratic formula to obtain the value of x.

=> -(-9) ± √((-9)² - 4(5×(-10)) / 2×5

=> 9 ± √(81 +200) / 10

=> 9 ± √(281) / 10

After simplifying the above equation we obtained the value of x that is;

=> x = 9 ± √(281) / 10

Now, the final values of x from the above condition are;

=> x = 9 + √(281) / 10  

and

=> x = 9 - √(281) / 10

It can be further represented in the decimal form;

=> x = 2.57630546...

and

=> x =  −0.77630546...

Thus, the values of x for the equation 5x² - 9x - 10 is x = 9 ± √(281) / 10.  

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Step-by-step explanation:

what is it you need help in?

The arrow is in -7 on the number line since 3 + (-10) = -7.

A number line is a pictorial representation of numbers on a straight line.

It is a horizontal line that has equally spread number increments.

We have,

3 + (-10)

This can be written as:

= 3 - 10

= -7

We can draw a number line to represent graphically:

                         <↓-------(subtracting 10)-------------->

< ---------(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8------------->

Thus the equation can be represented graphically with an arrow in -7 on the number line since 3 + (-10) = -7.

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Answer:

+ x = 116/9

- x = 40

* x = -2/3 and x = 59/3

/ x =  -2/3

Step-by-step explanation:

Since it's unclear what operations here are all of them, plus, minus, multiply and divide. If you need Steps, let me know.

Answer:

=====================

Given inequality:

Simplify and collect like terms:

Answer:

[tex]\frac{1}{y^9}[/tex]

Step-by-step explanation:

Exponent rule → [tex]a^{-b}=\frac{1}{a^b}[/tex]

Using exponent rule → [tex]y^{-9}=\frac{1}{y^9}[/tex]

Final result → [tex]=\frac{1}{y^9}[/tex]

Answer:

34

Step-by-step explanation:

I really don't know I just wanted to answer for points

She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

To make the recipe,

3/4 quart of lemonade and 3 cups of cranberry juice

The ratio of cranberry juice to a quart of lemonade

⇒ 3/(3/4) = 4

To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.

So,

4 = cranberry juice / 1(2/5)

(5/7) × cranberry juice = 4

Cranberry juice = 28/5 ⇒ 5 (3/5).

Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".

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Answer:

3150mm

Step-by-step explanation:

1cm is 10mm you convert it then times it together l x b x h will equal 3150

If the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

Given that the concentration of hydrogen ions in household dish detergent is 10⁻¹² .

We are told to find the pH level of household dish detergent.

pH is basically a measure of how acidic/basic water is. The range of pH ranges from 0 - 14, with 7 being neutral.

We have to find the negative value of log value of concentration level to find pH of the solution.

pH=-log ([tex]10^{-12}[/tex])

pH=-(-12)log (10)          [We know that [tex]log a^{b}[/tex]=b log a]

pH=12*1

pH=12

Hence if the concentration of hydrogen ions in household dish detergent is 10⁻¹² , then the calculated pH level of household dish detergent is 12.

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After rotating a parallelogram 270° counterclockwise points of D will be (2,7).

There are 4 types of translation they are, translation, rotation, and dilation.

We know when we rotate a shape 270° counter-clockwise the coordinates (x,y) becomes (y, -x) that is we switch x and y and make x negative.

Given a parallelogram with points C(-4,6), D(-7,2), E(6,6) and F(3,2).

Assuming point D when rotated 270° becomes D'.

∴ The points of D will switch which is (2,-7) and then we will make x negative.

So, D' becomes (2,7).

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The solution for the inequality | x | + 9 ≤ 7 is (option d) x ≤ -2 and x > -16

You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if either side is multiplied or divided by a negative number. Therefore, the answer is x > 1.

Given,

The expression:   | x | + 9 ≤ 7

If | x | ≤ a ⇒ -a ≤ x ≤ a

Then,

-7 ≤ | x | + 9 ≤ 7

⇒ -7 - 9 ≤ x ≤ 7 - 9

⇒ -16 ≤ x ≤ -2

That is x ≤ -2 and x > -16.

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After solving the equation 1.1+ln x²=6, the value of x is equal to  [tex]\sqrt{e^{4.9}}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We have been asked to find x in 1.1+ln x²=6

⇒ 1.1+ln x²=6

⇒ ln x² = 6 - 1.1

⇒ ln x² = 4.9

⇒ x² = [tex]e^{4.9}[/tex]

⇒ x  =  [tex]\sqrt{e^{4.9}}[/tex]

Thus,  x =  [tex]\sqrt{e^{4.9}}[/tex] in 1.1+ln x²=6

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Using linear functions, we have that:

a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.

b) The slope represent the hourly pay for each job.

c) The intercepts represent the fixed salary for each job.

d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.

e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.

A linear function is modeled by the following rule:

y = mx + b

In which:

For this problem, the two functions are given as follows:

The functions are graphed at the end of the answer.

Hence:

a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.

b) The slope represent the hourly pay for each job.

c) The intercepts represent the fixed salary for each job.

The pay will be equal when:

A(h) = B(h)

Hence:

75 + 14h = 17h

3h = 75

h = 25.

d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.

For 40 hours, the payments are given as follows:

Hence:

e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.

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Answer:

[tex] \sf \fbox{46.296 British Pounds}[/tex]

Step-by-step explanation:

1 shower job requires 3 hours of work,

plumber will fix only 1 shower that means he will work for 3 hours,

Charges of 1 hour = 25$

Charges of 3 hour = 25× 3 = 75$

The currency that plumber accept is British pound (£),

1 British pound (£) = 1.62 dollar ($)

x British pound = 75 dollar

[tex] \frac{1}{x} = \frac{1.62}{75} [/tex]

taking reciprocal both the side,

[tex] \frac{x \cancel £}{1\cancel£} = \frac{75 \: \cancel\$ }{1.62 \:\cancel \$} [/tex]

[tex]x = 46.296[/tex]

Jamar need to pay 46.296 British Pounds to plumber for the shower job.

The two units that were cancelled was Dollar & Pound.

It is required to cancel units because, mathematical operation does not work for different units. For e.g. If I have given two measurement one is volume(cm³) & another is length(cm) so I cannot add them.

[tex] \sf Volume + Length = Not \: possible [/tex]

Same thing happens with division Operation of two different units, the magnitude gets cancelled but unit still remains there.

[tex]\sf \small \pink{Thanks }\: \green{for} \: \blue{joining} \: \orange{brainly } \: \red{community}![/tex]

Answer:

45

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{Guide to follow:}[/tex]

[tex]\large\text{The word \boxed{\rm{difference}} means subtraction/subtract.}[/tex]

[tex]\large\text{The word \boxed{\rm{product}} means addition/add.}[/tex]

[tex]\large\text{The word \boxed{\rm{quotient}} means division/divide.}[/tex]

[tex]\large\text{The word \boxed{\rm{product}} means multiplication/multiply.}[/tex]

[tex]\large\text{Also guide to follow:}[/tex]

[tex]\large\text{2 negatives gives you a positive}[/tex]

[tex]\large\text{2 positives gives you a positive as well}[/tex]

[tex]\large\text{1 negative \& 1 positive gives you a negative}[/tex]

[tex]\large\text{1 positive \& 1 negative gives you a negative as well}[/tex]

[tex]\large\textsf{So, in this particular question we're doing multiplication because the}\\\large\textsf{key term in the word phrase is \boxed{\textsf{product}}. }[/tex]

[tex]\large\text{Now, that we have that information out of the way we can answer}\\\large\text{your given question.}[/tex]

[tex]\large\text{The product of }\large\text{-15 and -3 is translated to \boxed{\rm{-}\large\text{15 }\times\ -\large\text{3}}}[/tex]

[tex]\large\text{Equation: }\rm{-15\times-3}[/tex]

[tex]\large\text{Simplify the equation we have gathered above and you should have}\\\large\text{pverall answer.}[/tex]

[tex]\large\text{We have received was 45}[/tex]

[tex]\huge\text{Therefore, your answer should be \boxed{\mathsf{45}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex] \sf \: x=0.4[/tex]

Step-by-step explanation:

-0.5x-3.69=x-1.9-2.39

Step 1: Simplify both sides of the equation.

−0.5x−3.69=x−1.9−2.39

−0.5x+−3.69=x+−1.9+−2.39

−0.5x−3.69=(x)+(−1.9+−2.39)(Combine Like Terms)

−0.5x−3.69=x+−4.29

−0.5x−3.69=x−4.29

Step 2: Subtract x from both sides.

−0.5x−3.69−x=x−4.29−x

−1.5x−3.69=−4.29

Step 3: Add 3.69 to both sides.

−1.5x−3.69+3.69=−4.29+3.69

−1.5x=−0.6

Step 4: Divide both sides by -1.5.

−1.5x/−1.5 = −0.6/−1.5

x=0.4

The value of x will be 0.4.

In mathematics, an equation is a connection of two expressions that is expressed as an equality on all sides of the corresponding sign.  A statement that uses the equal sign to show that both of the expressions possess the same value is called an equation. Mathematical equations are made up of figures, an equal sign, and an optional variable in the position of an unknowable value.

-0.5x-3.69=x-1.9-2.39

-0.5x - x = -1.9 - 2.39+3.69

Simplifying the given equation:

-1.5 x = - 0.6

x = 0.6 / 1.5

x = 0.4

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The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.

What are the characteristics of a linear function?

What are the properties of equation?

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Following is domain and range for given function -

A)The function's range is -5≤ a≤50.

The function's range is -50≤c≤150.

B) The information we got from equation of the function is used to determine domain and range.

Given,

The whole amount spent is $750.

As a result, our equation is

ca = 750

calculating c,

c = 750 / a

The function's domain and range are:

a ≤ 5

Each prize now needs to be under 50.

= 50 ≤ c

Using the formula, ac = 750

A's maximum value is 75.

we can say that domain is

5 ≤ a ≤ 50

Finally, by substituting a = 5 we can see that the maximum for c is 150.

This gives range for c as -

50 ≤ c ≤ 150

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Answer:

x = 13

Step-by-step explanation:

In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set

While multiplying two integer numbers, the rule is simple.

If both the integers have the same sign, then the result is positive.

If the integers have different signs, then the result is negative.

For example,

(+2) x (+3) = +6

(+3) x (-4) = – 12

The major Properties of Integers are:

Closure Property

Associative Property

Commutative Property

Distributive Property

Additive Inverse Property

Multiplicative Inverse Property

Identity Property

According to the distributive property of integers, if a, b and c are integers, then:

a x (b + c) = a x b + a x c

Example: Prove that: 3 x (5 + 1) = 3 x 5 + 3 x 1

LHS = 3 x (5 + 1) = 3 x 6 = 18

RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18

Since, LHS = RHS

Hence, proved.

1) (a-b)+c

a= 0.5 , b= 2, c= -1

 (0.5- 2)+-1

=-1.5-1

=-2.5

2) a= 3 . b=-4, c=-2

(3-(-4)+-2

= (3 +4)+2

= 9

3) a= -8, b= 5, c= 3

 (-8+5)+3

=-3+3

= 0.

-(a-b)-c

1) a=0.5 , b= 2, c=-1

 -(o.5-2)-(-1)

=-0.5+2+1

= 2.5

2) a= 3, b= -4, c=-2

-(3-(-4)-(-2)

-(3+4)+2

-3-4+2

= -5

3) a= -8, b=5 ,c=3

-(-8-5)-3

=(8+5)-3

= 13-3

= 10.

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The Solution for equation 2 ln x=4 is 7.4088.

2 ln x=4

( [tex]x^{2}[/tex]) = [tex]e^{4}[/tex]

[tex]x^{2}[/tex] = 54.598

x = √54.598

x = 7.4088

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Two expressions joined by the equals symbol ("=") form an equation. The "left hand side" and "right hand side" of the equation are the expressions on either side of the equals sign. The right side of an equation is frequently considered to be zero.

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A. 525.34

B. 12.086

C. 7.294

D. 31.52

Hope it helps ^^

Using the mean absolute deviation concept, it is found that:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

Hence, for a mean of 50 and a mean absolute deviation of 10, with 6 pennies, we want data-sets with these following characteristics:

Hence:

1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).

2.  Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).

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Answer: Letter C

Step-by-step explanation:

just look at the problem a little closely

The solution of the equation  x² - 24 x + 144 = 0  is  x = 12 .

It is a quadratic equation , it will have 2 roots .

Using factorisation ,

x²-24 x+144=0

( [tex]x^{2}[/tex] - 12 x - 12 x + 144 ) = 0

x ( x - 12 ) - 12 ( x - 12 ) = 0

( x - 12 ) * ( x - 12 ) = 0

x = 12

Both roots are same and are equal to 12 .

Hence , the solution of the equation x² - 24 x + 144 = 0 is 12 .

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