7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings

Answer:

x = 12

Step-by-step explanation: You start off with this

3x + 2

Then since AC is 38 you make it

3x+2=38

Then you do -2 getting rid of the 2 and doing 38 - 2 which is 36

you now have:

3x = 36

then you do 3x divided by 3 on both sides

you do 36 divided by 3 then you get

x = 12

The distance from B to AC can be constructed as

The distance from G to EF can be constructed as

The distance from Q to SR can be constructed as

What is the distance of a line from a point?

A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.

For the first figure,

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First, break down the problem.  

Someone can skate 3 miles in 9 minutes.

What is their speed?  How far would they go if they did that speed for 1 minute?

To find speed given time and distance, divide distance by time.

3/9 = 1/3

Speed is 1/3 mile per minute

if they travel one minute, they will travel 1/3 of a mile

hope this helps :)

Step-by-step explanation:

they are parabolas.

their line of symmetry is exactly in the middle between their x-intercepts (when y = 0).

these x-intercepts we get from the factors : y can only be 0, when at least one of the factors is 0.

y = (x + 14)(x + 16)

means y = 0, when x = -14 or x = -16.

so, the line of symmetry is

x = -15

y = (x - 12)(x - 18)

y = 0, when x = 12 or x = 18

line of symmetry is

x = 15

y = (x + 13)(x - 17)

x = -13 or x = 17

line of symmetry

x = 2 (again, the middle between -13 and +17)

y = (x - 10)(x + 20)

x = 10 or x = -20

line of symmetry

x = -5

Answer:

x = 4, 2

Step-by-step explanation:

The total amount of sugar which contains in 4 grams of sugar = 304 grams.

Amount of sugar fast food smoothie has = 76 gram

amount of sugar a teaspoon of sugar contains = 4 gram

Thus the total amount of sugar which contains in 4 grams of sugar = 4 × 76

this implies  the total amount of sugar which contains in 4 grams of sugar  = 304 grams

In this question we used the unitary method where we multiplied a quantity with a known quantity to find the value of an unknown quantity.

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The area of the shape is 32  square yards

The given consist of one rectangle and a right triangle

The area of the figure = The area of the rectangle + The area of the right triangle

The area of the rectangle = The length × The width

The length of the rectangle = 6 yards

The width of the rectangle = 4 yards

The area of the rectangle = 6×4

= 24 square yards

The area of the triangle = (1/2)bh

The base of the triangle = 9 - 5 = 4 yards

The height = 4 yards

The area = (1/2)× 4 × 4

= 8 square yards

The area of the figure = 24 + 8

= 32 square yards

Hence, the area of the shape is 32  square yards

The complete question is:

What is the area of the shape below?

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Answer:

2.5 - 2(-3-0.5) + 2(n) > 10.75

Step-by-step explanation:

Step 1: two and 5 tenths is 2.5

Step 2: 2 times the quantity of the difference of negative three and one half is 2(-3-1/2)

Step 3:  two times a number is at least ten and three quarters = 2(n) > 10.75

Combine: 2.5 - 2(-3-0.5) + 2(n) > 10.75

In tech internship

Slope of the line m is $11.50, y intercept is 0 and the point slope form is  y = 11.50x + 0

In Amusement park attendant

The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100

In tech internship

Schedule = part time (20 hours/week)

The wage = $11.50/hour

The slope intercept form

y = 11.50x

Slope of the line m = $11.50

y intercept = 0

y = 11.50x + 0

In Amusement park attendant

Schedule- full time (40hours/week)

Wage - 9/hour+ 100 bonus

The slope of the line = $9

y intercept = 100

The equation is

y = 9x + 100

Hence,

In tech internship

Slope of the line m is $11.50, y intercept is 0 and the point slope form is  y = 11.50x + 0

In Amusement park attendant

The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100

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Answer:

Step-by-step explanation:

NOSEEEEEE

The solutions of the given quadratic equation are

[tex]x = 3 \ or \ x = -\frac{1}{4}[/tex]

What is quadratic equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

The given quadratic equation is

[tex]4x^2 - 11x - 3[/tex]

Now,

[tex]4x^2 - 11x - 3 = 0\\\\(2x)^2 - 2 \times 2x \times \frac{11}{4} + (\frac{11}{4})^2 - (\frac{11}{4})^2 -3 = 0\\\\(2x - \frac{11}{4})^2 = \frac{121}{16} + 3\\\\(2x - \frac{11}{4})^2 = \frac{121+48}{16}\\\\(2x - \frac{11}{4})^2 = \frac{169}{16}\\\\2x - \frac{11}{4} = \sqrt{\frac{169}{16}}\\\\2x - \frac{11}{4} = \pm\frac{13}{4}\\\\2x - \frac{11}{4} = \frac{13}{4} \ or \ 2x - \frac{11}{4} = -\frac{13}{4}\\\\2x = \frac{13}{4} + \frac{11}{4} \ or \ 2x = \frac{11}{4} - \frac{13}{4}\\\\[/tex]

[tex]2x = 6 \ or \ 2x = -\frac{1}{2}\\x = 3 \ or \ x = -\frac{1}{4}[/tex]

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Answer:

x=y/3 + 2/3

Step-by-step explanation:

Is this what you wanted?

The sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

We will use the method of percentage to solve the given question.

We are given:

A basketball backboard set that sold for $79 is discounted by 15%.

We need to find the sale price after the discount is given.

We will subtract the discount from the marked price.

Let us solve this;

Sale price = marked price - discount

Sale price =  $79 - $79 * 15%

Sale price =  $79 - $79 * 15 / 100

Sale price =  $79 - $11.85

Sale price = $67.15

So, the sale price will be $67.15.

Thus, the sale price of a basketball backboard set that sold for $79 is discounted by 15% is $67.15.

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The value of x and y which is on midsegment of the triangle is 1 and 11.

What is midsegment?

 A triangle's midsegment is the section of the triangle's shape that connects the midpoints of its two sides. a section of a line connecting the midpoints of two triangle's sides. There are three possible midsegments in a triangle. The section of a line between the midpoints of two triangle sides is known as a midsegment. Due to the fact that triangles have three sides, they also have three midsegments. A line drawn by joining the midpoints of any two of a triangle's sides is known as the midsegment.

let us assume triangle as ABC and DE is the midsegment .

Where  DE=2x+1 and BC = 8x-2 .

According to the midsegment theorem ,

=> DE = 1/2 BC

=> 2x+1 = 1/2(8x-2)

=> 2x+1=4x-1

=> 2x=2

=> x=1

Now AB divided intp AD=3z and DB=z+22

Then, AD=DB

=> 3z = z+22

=> 2z = 22

=> z = 11.

Hence the value of x=1 and z= 11.

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Answer:

Food desert census tracts typically have fewer populations than all other census tracts, a higher percentage of unoccupied or abandoned dwellings, and residents who are less likely to have a college degree, make less money, or be employed.

The amount of money paid by each of the 4 persons will be $33.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.

Total cost = $105.73 x 1.06 x 120

Total cost = $134.48

Amount for each person,

A = $134.48 / 4

Amount = $33.62

Therefore, the amount of money paid by each of the 4 persons will be $33.6.

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6 school-supply kits can be put together in 30 minutes.

What do you mean by the Unitary method?

By using the unitary technique, we may determine the value of a single unit and, using that value, get the value of the necessary number of units.

According to the questions,

By applying the unitary method,

40 school supply kits can be put together in 8 minutes.

∴1 school supply kit can be prepared in (8/40) minutes

∴30 school supply kits can be prepared in (30/5) minutes

Hence,

6 school-supply kits can be put together in 30 minutes.

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By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.

We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.

We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:

sin(a) = (opposite cathetus)/(hypotenuse)

Replacing what we know we will get:

sin(36°) = x/15ft

Solving this for x we get:

x = sin(36°)*15ft = 8.82ft

The height of the kite is 8.82 feet.

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There  are no prime numbers between7,608 and 7,620

A prime number is a whole number greater than 1 whose only factors are 1 and itself

The numbers between 7608 and 7620 are:

7609,7610,7611,7612,7613,7614,7615,7616,7617,7618,7619

Here we have to check these numbers are prime number or not

Prime factorization

7609=7×1087

7610=2×5×761

7611=3×43×59

7612=2×2×11×173

7613=23×331

7614=2×3×3×3×3×47

7615=5×1523

7616=2×2×2×2×2×2×7×17

7617=3×2539

7618=2×13×293

7619=19×401

Hence, proved that there are no prime numbers between7608 and 7620

Answer:

$210 in bank

Step-by-step explanation:

Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?​

70% = 0.7

300 * 0.7 = $210 in bank

The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

From the graph:

vertex:

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

here vertex = (-2,2)

Axis of symmetry:

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.

x = -2.

Parabola:

It is clearly visible that the parabola is facing downward so it is a downward parabola.

Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

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Answer:

1-10.

Step-by-step explanation:

Find the degree of the equation to determine if linear.

Linear

The remainder is 360.

When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

Given a cubic polynomial, x³+8x²+11x-20

The zero of the linear polynomial.

Substitute it in the given polynomial.

As a result, we get the remainder.

x - 5 = 0

x = 5

Substitute 5 to x³ + 8x² + 11x - 20:

5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360

Hence, The remainder is 360.

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i came back home now....

The probability is 8/9.

From the question, we have

probability = (1/3)*(1/3)*(1/3) = 1/27 chance (all of them lie)

probability = (2/3)*(2/3)*(2/3) = 8/27 chance (all of them true).

Since, they all say it's heads.

Thus, the probability of it being heads = (8/27)/ ((8/27)+(1/27)) = 8/9.

Probability:

Chance is referred to as probability. This branch of mathematics studies the probability of a random event. The value is between 0 and 1. Probability is a concept that mathematics has adopted to predict the likelihood of particular events. Probability is just the measure of how likely something is to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will be able to comprehend the possible results for a random experiment. How likely something is to occur can be determined using probability. It might be challenging to predict many things with complete certainty. We can only predict whether an event will occur or how likely it is using it, not if it will actually occur.

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Given the equation x² + y² + 4x - 8y + 11 = 0, the center of the circle is (-2, 4).

The standard form of the equation of circle is given by

(x - h)² + (y - k)² = r²

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x² + y² + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h² + k² - r².

If the equation of the circle in general form is x² + y² + 4x - 8y + 11 = 0, then the coefficients are:

D = 4

E = -8

F = 11

If D = -2h and D = 4, then

4 = -2h

h = -2

If E = -2k and E = -8, then

-8 = -2k

k = 4

Hence, the center of the circle is (h, k) = (-2, 4).

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The values of a, b and c from the given polynomial are a = -1 , b = 2 and, c= -35.

We are given the expression:-

[tex]x^2+2x-35[/tex]

We know that, the general form of a quadratic expression is :-

[tex]ax^2+bx+c[/tex]

We can rewrite the given expression as:-

[tex]-1x^2+2x+(-35)[/tex]

Comparing it with the given equation, we get:-

a = -1 , b = 2 , c= -35

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

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Answer:

b. y + 5 = -2(x + 3) or

    y = - 2x - 11

Step-by-step explanation:

Point-slope equation:

Convert this to slope-intercept form:

Correct choice is b.