Given parallelogram LMNO with diagonals intersecting at point P. If MP = 2x + 5 and OP = 3x − 4, find OP.


−9

9

23

31

In the formula V = (1/3)πr²h , (A)V/3πr² is the expression equal to h.

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

Here given that,

V= (1/3)πr²h

V/3πr² = (1/3)πr²h/3πr²         (divided both sided with 3πr²)

V/3πr² = h or h = V/3πr²

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Answer:

90

Step-by-step explanation:

You can find the answer by dividing 9 by .10

9 / .10 = 90

To check your answer, you can multiply 90 by .10

90 x .10 = 9

The probability that she makes no more than 20 of them is 0.394

We use Binomial Distribution in solving this question.

The discrete probability distribution known as the binomial distribution only offers two outcomes for an experiment: success or failure.

Sum of independent Bernoulli trials is binomial distribution; a random Variable x is said to be following binomial distribution if it's density is given as

P(X=x) = (nCx) px (1−p)n−x    where x=0,1,2…n

Let x denotes the number of throws that makes a free throw so here

x follows Binomial distribution with n=28 and p=0.603

Thus, we calculate

P(X≤20) =∑_(k=0)^1▒1= (28Ck)0.603k (1−0.603)28−k =0.3144

=0.394

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Answer:

£41.20

Step-by-step explanation:

Pack of 10 x 8 = 80

(I got the 8 from 84)

80 divided by 2 = 40

then all you need are 4 pencils = 1.20

40 + 1.20 = 41.20

Hope this makes sense aha, if it doesn't just contact me :) xx

Answer:

-0.625

Step-by-step explanation:

A fraction is the numerator (top) divided by the denominator (bottom).  In this case it is -5 divided by 8.  Put that into a calculator and you will get -0.625.

 The result of the evaluation of the series described by 1/2, 3/2, 5/2, . . . . . . . , 15/2 is:

∑ = 28

A series is the summation of a set of numbers or sequences.

The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

The equation for this type of problem is:

∑ = n(a1 + an)/2

 Our values are:

1/2, 3/2, 5/2, . . . . . . , 15/2

∑ = 7(1/2 + 15/2)/2

∑ = 7(8)/2

∑ = 28

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The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.

The given expression is [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex].

We need to find the equivalent expression for the given expression.

Equivalent expressions are expressions that work the same even when they seem different. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Now, [tex]((\frac{2}{3} )^{4}\times(\frac{2}{3} )^{3})^{2}[/tex] using [tex]a^{m} \times a^{n}=a^{m+n}[/tex].

We get, [tex]((\frac{2}{3} )^{4+3})^{2}=((\frac{2}{3} )^{7})^{2}[/tex]

Using the exponents rule [tex](a^{m} )^{n}=a^{m\times n}[/tex]

=[tex]=(\frac{2}{3} )^{7\times 2}=(\frac{2}{3} )^{14}[/tex]

The equivalent expression for the given expression is [tex](\frac{2}{3} )^{14}[/tex]. Therefore, option C is the correct answer.

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Answer:

Answer: Option 3

Step-by-step explanation:

like radicals are radicals that have the same root number and the same 'radicand' (number or expression under the square root)

The fish population will be the same as on January 1, 2002 on January 1, 2017 and all the fish in the lake will have died by 2019

The function is given as:

F(t) = 1000(30 + 15t - t^2)

Start by calculating F(0) --- population in 2002

So, we have:

F(0) = 1000(30 + 15(0) - 0^2)

F(0) = 30000

Substitute 30000 for F(t) in F(t) = 1000(30 + 15t - t^2)

1000(30 + 15t - t^2) = 30000

Divide by 1000

30 + 15t - t^2 = 30

Simplify

t^2 - 15t = 0

Divide through by t

t - 15 = 0

Solve

t = 15

This means that

Year = 2002 + 15

Year = 2017

Hence, the fish population will be the same as on January 1, 2002 on January 1, 2017

This means  that F(t)= 0

So, we have:

1000(30 + 15t - t^2) = 0

Divide by 1000

30 + 15t - t^2 = 0

Rewrite as

t^2 - 15t - 30 = 0

Using a graphing calculator, we have

t = 17 (approximated)

This means that

Year = 2002 + 17

Year = 2019

Hence, all the fish in the lake will have died by 2019

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the length of the stringer for the staircase of 6 steps is 199.74 cm.

The sum of the squares of the two sides (a and b) equals to the square of the hypotenuse (c). In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

According to the question,

Each step is 28 cm long that is the length of one step of the staircase. And 18 cm high which is the height of the step at 90-degree angle thus forming a right-angle triangle and the stringer acts as a hypotenuse. Therefore, we can use Pythagoras theorem to find the length of the stringer of one step.

Length=a=28 inch

Breadth=b=18 inch

Applying the Pythagoras theorem, we get

28²+18²= (length of the stringer)²

28²+18²= = 1108  

Now, √1108 = 33.29

to find the length of 6 steps multiply 33.29 with 6

33.29*6 = 199.74

Therefore, the length of the stringer for the staircase of 6 steps is 199.74 cm.

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Answer:

199.7 cm

Step-by-step explanation:

The equation of the line in standard form with slope equal to 2/3 and y -intercept (0 , 5) is 2x - 3y = -15.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the slope-intercept form, plug in the values of the slope and the point to set up the equation.

y = mx + b

where m = 2/3 and y-intercept, b = 5

y = 2/3 x + 5

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y = 2/3 x + 5

2/3 x - y = -5

Multiply both sides by 3 to have integer coefficients.

3(2/3 x - y) = -5(3)

2x - 3y = -15

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The sum of the polynomial is equal to -10x^3 + 2x^2 + 7x + 8.

In mathematics, polynomials refers to an algebraic equation which have more than two terms, the terms are usually same variable but the exponents tends to increase the number of terms.

An algebraic equation with the highest power as two is generally called parabolic equation/ When the power goes above two they are called polynomial.

addition of polynomials is achieved by adding like terms together. the like terms as in the question include similar alphabet and same exponents

( -4x^3 + 10x^2 + 6 ) - ( 6x^3 + 8x^2 - 7x - 2 )

terms with x^3: -4 - 6 = -10

terms with x^2: 10 - 8 = 2

terms with x:  0 - ( - 7 ) = 0 + 7 = 7

constant terms : 6 - ( - 2 ) = 6 + 2 = 8

constant terms refers to terms that does not have x

writing the equation together with their terms gives -10x^3 + 2x^2 + 7x + 8. Hence we can conclude that addition of polynomials involves addition performed considering the terms by adding like term.

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Answer: p=14, r=48

Step-by-step explanation:

x^8 • x^6 = x^p

x^(8+6) = x^p

8+6=p

p=14

(x^8)^6 = x^r

x^(8*6)=x^r

8*6=r

r=48

Answer:

98.5%

Step-by-step explanation:

1000 cubic centimeters = 1 litre

(3 decimal spaces to the left)

985 cubic centimeters = .985 liters (almost 1 litre)

.985 = 98.5% (2 decimal spaces to the right)

Answer: x = 3

Step-by-step explanation:

From the diagram above , the area of a triangle especially a right angled triangle

A = 1/2 X b X h where b is the base and h is the height.
Now,

h = x + 3

b = x + 1

Now , substitute for those values in the formula provided vide

A = 1/2 x (x+ 3)( x + 1 ) and equated it to 12

= (x+3)(x+1)

—————. = 12

2

Now, multiply both side a by 2 to make it a linear equation or better put , cross multiply

= (x+3)(x+1) = 2 x 12

= (x+3)(x+1) = 24

Then open the bracket by multiplication

= x2 + x + 3x + 3 = 24

= x2 + 4x + 3 = 24

= x2 + 4x + 3 - 24 = 0

By solving this quadratically,

= x2 + 7x - 3x - 21 = 0 ,

( x2 + 7x) - ( 3x - 21 ) = 0

x( x + 7 ) - 3( x + 7 ) = 0

Therefore

( x+ 7 )( x - 3 ) = 0

Solving this gives

x = -7 or x = 3

Therefore x = 3 since x can’t be negative, x can’t be = -7

The following set of numbers, 10, 12, and 23, cannot be the measures of the sides of a triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 10, b = 12, and c = 23

a + b > c     10 + 12 > 23     22 > 23     False

a + c > b     10 + 23 > 12     33 > 12     True

b + c > a     12 + 23 > 10     35 > 10     True

If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.

Hence, the set of numbers 10, 12, and 23 can not be the measure of the sides of a triangle.

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All the three equations represent the same function as they equal x² + 6x - 16.

It should be noted that the function that Corey wrote is:

y = (x + 8)(x - 2)

y = x² - 2x + 8x - 16

y = x² + 6x - 16

Kimberly wrote y = x² + 6x - 16

Joshua wrote (x + 3)² - 25

= (x + 3)(x + 3) - 25

= x² + 3x + 3x + 9 - 25

= x² + 6x - 16

In conclusion, the three equations represent the same function as they equal x² + 6x - 16.

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Answer:

0

Step-by-step explanation:

Substitute x for 1 and solve.

2(1) -2

2-2

0

Answer:

0 I belive

Step-by-step explanation:

f(x) =2x-2

f(1)= 2(1)-2

2-2

f(1)= 0

The effect of repeating the phrase “piano moan” in the poem is A. It sets a sad, mournful tone.

It should be noted that in literature, the feeling and emotions of the author is illustrated in the tone.

In this case, the repetition of the words were I

important to show the emotions of the author.

Therefore, the effect of repeating the phrase “piano moan” in the poem is that it sets a sad, mournful tone.

In conclusion, the correct option is A.

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Answer:

just fix the cilcle more it have it looing for the answer

Step-by-step explanation:

that all i got i wish i can help u more

If Max is building a set of shelves and he buys a board that is 4 yards long and he wants to cut as many pieces of board that are 3/4 yards long as he can, then the no of pieces he can cut is 5 and he will have 0.25 yards of board left over.

3/4 is a fraction which can be represented as,

3/4 = 0.75

The number of pieces of board that Max can cut that is 4 yards long can be determined by the division of the length of the board by the length of the cut pieces. Therefore,

number of pieces cut = length of the board ÷ length of a cut piece

number of pieces cut = 4 ÷ 0.75

number of pieces cut = 5.33, that is round off to 5

Thus he can cut 5 pieces of 3/4 yards.

As 5 × 3/4 = 3.75 yards

The remaining yards of the board can be calculated by subtraction.

Board leftover = 4 - 3.75 = 0.25 yards

Hence, Max can cut 5 pieces of 3/4 yards and will have 0.25 yards of the board left over.

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(a) 2.1°C per minute

(b) 1.9°C per minute

(a)

(b)

Answer:

Step-by-step explanat

36=10x-4

40=10x

10x=40

x=40/10

x=4

As per latent heat, size of 11.61 BTUH is required to complete the whole action.

Let's assume the ice was at 32° F. So, 144 BTU/lb is required as latent heat. To melt ice and make it 32°F water required BTU is:

10 × 144 = 1440 BTU ( m× l = H where m is the mass and l is the latent heat )

To, convert 10°F ice to 32°F ice required heat is,

10×0.5035× ( 32° - 10°) = 110.77 BTU ( H = msΔt, m= mass, s = specific heat of ice, and Δ t = difference in temperature which is, 32° - 10° = 22°)

Now, to convert 32°F water to 212°F water required heat is:

10×1×180 = 1800 BTU ( SPECIFIC HEAT OF WATER IS 1 and Δt = 212-32 = 180°F )

To covert 212°F water to 212°F steam the required heat is,

10 × 970 = 9700

Now, to convert 212°F steam to 400°F steam, the required heat is ;

10 × .47 × 188 = 883.6 BTU ( The specific heat if steam is .47, Δt = 188°F )

Now total heat is, 883.6 BTU +9700 BTU + 1800 BTU + 110.77 BTU + 1440 BTU = 13934 BTU

Required power to convert it within 20 min. or 1200 sec is,

13934/1200 = 11.61 BTUH.

We can now say that, if 10 pounds of ice starts at ten degrees and is changed to steam at 400 degrees in twenty minutes, 11.61 BTUH is required.

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Answer:

n=3

Step-by-step explanation:

2:6=1:3

divide by 2 on both the 2 and the six and 2/2=1 and 6/2=3 so n=3

Answer:

1:3

Step-by-step explanation:

So, what you need to do is figure out the common factor of 2 and 6

which then the answer comes out to 3, so your answer would be 1:3 ratio.

Brainliest thx

Answer: a₁=31    a₁₁=-9

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.[/tex]

Subtract equation (2) from equation (1):

[tex]3d=-12[/tex]

Divide both parts of the equation by 3:

[tex]d=-4[/tex]

Thus,

[tex]a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9[/tex]

Answer:

a = 43

d = -6

[tex]\sf a_{11} = -17[/tex]

Step-by-step explanation:

Arithmetic sequence:

 Use the formula to find the nth term:

    [tex]\sf \boxed{\bf a_n= a+(n-1)d}[/tex]

Here, a is the first term, n is the number of terms and d is the common difference.

[tex]\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)[/tex]

        [tex]\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\[/tex]

Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.

     (ii)       a + 6d = 7

     (i)        a + 4d = 19

                -    -     = -    

                       2d = -12

                          d = -12/2

                          [tex]\sf \boxed{\bf d = -6}[/tex]

Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)

  a + 4*(-6) = 19

  a - 24      = 19

               a = 19 + 24

               [tex]\sf \boxed{\bf a = 43}[/tex]

[tex]\sf a_{11} = a + 10d[/tex]

      = 43 + 10*(-6)

      = 43 - 60

[tex]\sf \boxed{\bf a_{11} = -17 }[/tex]