Sophia finished 32 pages of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?

The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

Let p represents the paycheck.

William  paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.

He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund

If we put the parts together, the equation we get is;

p = $50 +$100 +$100 +$100

The equation can be summarized as;

p = $50 + 3($100 )

Now we can easily find how much was William  paid;

p = $50 + 3($100)

p = $50 +$300

p = $350

Hence William was paid $350.

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Based on the length of the subway sandwich, the length of the larger pieces is 11 feet.

Assume that the length of the shorter pieces is x.

The length of the larger pieces is therefore 5 + x.

The relevant equation to find the length is:

52 = x + x + x + x +x + 5 + x + 5 + x

52 = 7x + 10

x = (52 - 10) / 7

= 6 foot

The length of the larger pieces is:

= 5 + x

= 5 + 6

= 11 foot

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Answer:

B

Step-by-step explanation:

5x + 4y >= 2

4y >= -5x + 2

y >= -5/4x + 1/2

Since the equation is >=, everything on or above the line y = -5/4x + 1/2 should be shaded.

Answer:

Step-by-step explanation:

See the attached file below it will help to understand this problem and it will improve your grade and score.

The value of x from the given diagram is 64 degrees

A line is defined as the shortest distance between two points. From the given diagram, we have that the line AB bisects FAB, hence;

<FAB = <CAB = 58 degrees

Also since the sum of angles on a straight line is 180 degrees, hence;

58 + 58 + x = 180

116 + x = 180

x = 180 - 116

x = 64 degrees

Hence the value of x from the given diagram is 64 degrees

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Answer: 1²⁷/₂₈

Step-by-step explanation:

[tex]\displaystyle\\\frac{5}{7}+\frac{1}{2}+\frac{3}{4} =\\\\\frac{5*4+1*14+3*7}{28} =\\\\\frac{20+14+21}{28} =\\\\\frac{55}{28} =\\\\1\frac{27}{28}[/tex]

After dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 )​, we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.

We are given an expression:

( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 )​

We need to perform division of the algebraic expression:

                                  5 x² - 7 x + 4

             3 x² + x + 1 √15 x⁴ - 16 x³ + 10 x² + 8 x - 17

                                   15 x⁴ + 5 x³ + 5 x²

                                   ______________________

                                             - 21 x³ + 5 x² + 8 x - 17

                                             - 21 x³ - 7 x² - 7 x

                                   ______________________

                                                       12 x²  + 15 x - 17

                                                       12 x²  + 4 x + 4

                                   ______________________

                                                                   11 x - 21

                                   ______________________

Therefore, after dividing ( 15 x⁴ - 16 x³ + 10 x² + 8 x - 17 ) ÷ ( 3 x² + x + 1 )​, we get the quotient as 5 x² - 7 x + 4 and the remainder as 11 x - 21.

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Question :

(-2+1)exponent2+5(12/3)-9=

Answer:

The answer is : 12 po

Answer:

2/9

Step-by-step explanation:

To multiply fractions you just multiply the numerators with the numerators and the denominators with the denominators

1/4 * 2/3 = 2/12 which simplifies to 1/6

1/6 * 4/3 = 4/18 which simplifies to 2/9

:D

Delila is correct as she multiplying three negative numbers and determines that the solution will be negative.

As given in the question,

Let the three negative numbers be -x , -y , and -z.

Delia is multiplying three negative numbers

Multiply First two numbers

(-x) (-y) = + x y  as (-)(-) = +

Multiply by third numbers

(+x y) (-z) = -x y z   as ( +)(-) = -

Therefore, Delila is correct as she multiplies three negative numbers and determines that the solution will be negative.

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Answer:

Yes, she is correct.

The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

Slope of the line:

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given,

The point (9,10) that cuts off the least area from the first quadrant

Here we need to find the slope and y intercept of the line.

A line is passing through a point (9,10) cuts off least area in first quadrant.

The equation of the line passing through point (9,10) and has slope m can be expressed as,

=> y - 10 = m (x - 9)

=> y = m(x - 9) + 10

=> y - mx = - 9m + 10

Divide the terms by - 9m + 10, then we get,

=> (y/- 9m+10) - (mx/ - 9m+10) = 1

=> (mx/9m+10) - (y/9m+10) = 1

It can be rewritten as,

[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]

We know that,

The equation of straight line in intercept form is

=> x/a + y/b = 1

So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:

a = 9m-10/m

b =  10 - 9m

The area of the triangle made by the line in first quadrant can be expressed as,

=> A = 1/2 x (9m-10/m) x (10 - 9m)

=> A = -1/2 (9m-10)²/m-----------------------(1)

Differentiate the equation (1) with respect to m.

[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]

when we simplify it,

=> dA/dm = -(9m-10)/2m² [9m-10]

Let dA/dm = 0, then

=> 0 = -1/2m² (9m-10)(9m-10)

=> 0 = 1/m² (10-9m)(9m-10)

=> 0 = (10 - 9m) (9m -10)

Therefore, the value of m is,

=> 10 - 9m = 0

=> -9m = -10

=> m = 10/9

And

=> 9m - 10 =0

=> 9m = 10

=> m = 10/9

The line will be in first quadrant and forms a triangle with axes if the slope is negative.

Substitute m = -10/9

Then, b = 10-9m

Then,

=> y = 10 - 6(-10/9)

=> y = 10 + 20/3

=> y = 50/3

So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

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Answer:

234

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

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

here [ a, b ] = [3, 6 ] , then

f(b) = f(6) = [tex]3^{6}[/tex] + 17 = 729 + 17 = 746

f(a) = f(3) = 3³ + 17 = 27 + 17 = 44 , then

average rate of change = [tex]\frac{746-44}{6-3}[/tex] = [tex]\frac{702}{3}[/tex] = 234

Answer:

Solution

12-6b6+4b-3b4, find Polynomial in descending order

Solution:

The Given Polynomial =12-6b6+4b-3b4

Descending order is basically when its terms are arranged in order from largest degree to smallest degree

Descending order of polynomial =-6x6-3x4+4x+12

Step-by-step explanation:

Answer:

Option a 340 cm²

Area= bxh

20x17=340 cm²

Answer: a, 9x10^9, largest number 900000000

Answer: greatest is A.

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

x is a variable, so to do g(2) you have to write g(x), but substitute 2 in place of x:

g(2) = 4*2² + 2*2 - 24 = 16 + 4 - 24 = -4

Answer:

19

Step-by-step explanation:

5w+3°=98°

5w=98°-3°

5w=95°

therefore w=95/5=19

The probability of choosing a red marble is 1/6.

Probability is the chance of occurring a certain event out of total possible events that can order in a given situation.

According to the given question an urn contains 19 red marbles, 29 blue marbles, and 43 yellow marbles.

So there are total of ( 19 + 29 + 43 ) = 85 marbles.

∴ No. of sample space N(s) = 85.

No. of red marble N(red) = 19.

One marble is to be chosen from the urn without looking the probability of choosing a red marble P(red) is N(red)/N(s) which is

P(red) = 19/85

P(red) = 1/5.

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The solution of the given equation are (1/2 , 17/2) and (-3 , 12)

The two equation that we have been given are :

    y = 9 – x            (1)

    y = 2x² + 4x + 6       (2)

We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get

       9 – x = 2x² + 4x + 6

        3 = 2x² + 5x

2x² + 5x – 3 = 0

Now to find the factors of the value x we will use quadratic formula.

   x = (-b±√b² – 4ac)/2a

   x = [ -5 ± √25 + 24 ]/4

   x = [ -5 ± 7 ]/4

x = (-5 + 7)/4              and                 x = (-5 – 7)/4

x = 1/2     and    x= -3

putting the required value of x in equation (1) we get

y = 9 – 1/2            and             y = 9 – (-3)

y = 17/2      and    y = 12

Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)

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Answer: Left 10 Units

Step-by-step explanation: hope this helps

A function assigns the values. The output(y) of the function y=20x + 38 if the input is -9 is -142.

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

Given the function y=20x+38, therefore, if the input of the function is -9, then the output can be calculated by substituting the value of x as -9. Therefore, we can write the function as,

y = 20x + 38

y = 20(-9) + 38

y = -180 + 38

y = -142

Hence, the output(y) of the function y=20x + 38 if the input is -9 is -142.

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Answer:

The absolute value inequality will be |x| ≥ -2.

Step-by-step explanation:

The width of the rectangle is determined as: B. 16 m.

The perimeter of a rectangle = 2(l + w)

Given the parameters:

Perimeter of rectangle = 88 meters

Width of the rectangle = w meters

Length = 2w - 4 meters

Plug in the values into the perimeter formula of a rectangle

2(2w - 4 + w) = 88

2(3w - 4) = 88

6w - 8 = 88

6w = 88 + 8

6w = 96

6w/6 = 96/6

w = 16

Thus, the width of the rectangle is determined as: B. 16 m.

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The correct option is C. x² + (x – 2)² = 100.

The equation which depicts x, the side length of the greater square is  x² + (x – 2)² = 100.

In geometry, a square is a plane figure with 4 equal sides as well as 4 right (90°) angles. A square is a subset of a rectangle (an equilateral rectangle) and a subset of a parallelogram (an equilateral & equiangular one).

Now, as per the question;

This is given by relation shown by expression;

x² + (x-2)² = 100

Therefore, the equation which represents x, the side length of the greater square is x² + (x-2)² = 100.

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The complete question is-

A group of students is given a 10 by 10 grid to cut into individual unit squares. The challenge is to create two squares using all of the unit squares. Their teacher states that after the two new squares are formed, one should have a side length two units greater than the other.

Which equation represents x, the side length of the greater square?

A. x² + (x – 2)² = 10

B. x² + 2x² = 10

C. x² + (x – 2)² = 100

D. x² + 2x² = 100

∠AOM ≅ ∠BOM  because they are both congruent to the same angle, not because they are vertical angles.

From the image of the angles attached, we are given that;

∠AOM ≅ ∠DON

Now, from the vertical angle theorem, we can say that;

∠AOM ≅ ∠CON

Similarly, by vertical angles theorem, we can also say that;

∠BOM ≅ ∠DON

From transitive property of congruence, we can equally say that since ∠AOM and ∠BOM are equal to the same angle, then;

∠AOM ≅ ∠BOM

From transitive property of congruence, we can equally say that since ∠CON and ∠BOM are equal to the same angle, then;

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Answer: ∠AOM≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.

Step-by-step explanation:

cause I did the mastery test

Answer:

h(-6) = 1

Step-by-step explanation:

Hello!

Substitute -6 for x in the equation.

h(-6) is 1.

If the boy is riding a bicycle and gets stuck or got accident by a car, 440ml of IV fluid will be administered.

To avoid further injury, place the victim on the ground very gently and slowly without handling vigorously. In one direction, tilt the sufferer. Dress loosely around the waist, chest, and neck. So that the tongue can fall forward and allow blood and vomit to drain out, tilt your head back and slightly downward. When you come across an accident victim, the first thing you need to determine is whether the victim's body has sustained any physical wounds. Depending on how severe the collision was, you might not be able to see any inside injuries, but you will see a few exterior ones.

In a car accident, spine injuries and head trauma are common. Therefore, be aware that rough handling of the sufferer will result in additional injuries while opting to assist the victim in moving to a safer location on the road. Therefore, request any onlookers to carefully assist in moving the sufferer to a location near the road where it will be safer.

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In step 1 mistake has been made because negative multiplication gives a positive result but is written negative.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given that,

−4(6−y) + 4 = −4

By using distribution property

-24 + 4y + 4 = -4

But in the question +4y is written as -4y which is wrong.

Hence In step 1 negative multiplication gives a positive result but is written negative so in step 1 mistake has been made".

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The given question is not complete.

Consider this solution to a problem.

Problem: −4(6−y)+4=−4

Step 1: −24−4y+4=−4

Step 2: −20−4y=−4

Step 3: −4y=16

Step 4: y=−4

In the first response box, enter the number of the step where the mistake is made.

The linear combination of u and v = <3,-27>=5U+4V.

A linear combination of two or more vectors is the vector formed by multiplying two or more vectors (with distinct directions) by scalar values. The above equation demonstrates that the vector is produced by adding two vectors to three vectors.

The term "linear" has two independent meanings: geometric and algebraic. Because linear combinations essentially linear in the both senses, the expression is accurate.

Let u= <3,3> and v= <-3,3>

<3,-27> = x< 3,3> + y<-3,3> = <3x - 3y, 3x + 3y>

3x - 3y = 3 => x - y = 1

3x + 3y = -27 => x + y = -9

Adding both, we get

2x = -8 => x = -4

y = -5

So <3,-27> = -4< 3, 3 > + (-5) < -3 , 3 >

The linear combination of u and v = <3,-27>=5U+4V.

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I understand that the question you are looking for is:

A sum of scalar multiples of two vectors (such as au + bv, where a and b are scalars) is called a linear combination of the vectors.

Let u= <3,3> and v= <-3,3>. Express <3,-27> as a linear combination of u and v.