A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.

Answer:

Step-by-step explanation:

The answer for this can be an inequality or an interval notation or a graph

* Subtraction of (1) in both sides of the inequality

* Let's call part A: [tex]X+1\geq 3[/tex]

* Let's call part B: [tex]\frac{4}{3} X < -8[/tex]

* Solve part A first:

Do the subtraction of (1) on both sides of the inequality.

X ≥ 3 −1

X ≥ 2

Subtract

* Solve part B now:

Multiply  for 3/4 both sides of the inequality  to eliminate the [tex]\frac{4}{3}[/tex]

[tex]\frac{4}{3} X (\frac{3}{4} < -8 (\frac{3}{4})[/tex])

X < -24/4

X < -6

Answer

Inequality Form:

x < −6 or x ≥ 2

Interval Notation:

( − ∞,−6)∪[2,∞)

In Graph:

See the attach

Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.

Whole number:

Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.

Given,

Here we have the following expression:

(A) (4- 2i) (4 - 2i)

(B) (3 + 2i) (3 - 2i)

(C) (-6+ i)(3- i)

(D) (-4+3i)(4-3i)

Now, we need to find the whole number product.

In order to find the solution we have to perform the multiplication on the given expression,

First expression will gives the following,

(A) (4 - 2i) (4 - 2i)

When we apply the (a-b)² formula in it then we get,

=> 4²+ (2i)² - (2 x 4 x 2i)

=> 16 - 4 - 16i

=> 12 - 16i

Which is not a whole number product.

Second expression,

(B) (3 + 2i) (3 - 2i)

Apply the (a + b)(a - b) formula in it,

Then we get,

=> 3² - (2i)²

=> 9 + 4

=> 13

Therefore, this one is the whole number product.

Third expression,

(C) (-6 + i) (3 - i)

When we perform the multiplication on it, then we get,

=> -18 + 6i +3i -i²

=> -18 + 9i + 1

=> -17 + 9i

his one is not a whole number product.

Final expression,

(D) (-4 + 3i) (4 - 3i)

When we perform the multiplication on it, then we get,

=> -16 + 12i + 12i - (3i)²

=> -16 + 24i + 9

=> -7 + 24i

This one is also no the whole number product.

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Answer:

Slope = 0.75

Step-by-step explanation:

Slope Formula: y2-y1/x2-x1

4-1/5-1=3/4=0.75

The factorization of the expression  [tex]x^3+3x^2+9x+27[/tex] is  [tex](x+3)(x^2+9)[/tex].

What is factorization?

  The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.

Here the given polynomial expression is ,

=> [tex]x^3+3x^2+9x+27[/tex]

=> [tex]x^2(x+3)+9(x+3)[/tex]

=> [tex](x+3)(x^2+9)[/tex]

Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].

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Answer:

y = 1.2·x

x = 1;  y = 1.2·1 = 1.2

x = 2;  y = 1.2·2 = 2.4

x = 3;  y = 1.2·3 = 3.6

Answer:

value of x are 2 and 3 which make the inequality true

At the end of 6 months she will have $410 when calculated using simple interest.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Main Body:

Principle =$400

Rate = 5%

Time = 6 months = 1/2 years

Simple interest = P*R*T/100

S.I. = 400*5*(1/2)/100

S.I. = 10

Hence total amount is 400+ 10= $410.

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Max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.

Two or more expressions with an Equal sign is called as Equation.

Given,

When Max was a puppy, he weighted [tex]5\frac{1}{2}[/tex] pounds

At his 1-year check-up with the vet, Max weighted 15.8 pounds

We need to find the weight did Max gain between the time he was a puppy and his 1-year check-up.

To find this we need to find the difference when Max was a puppy and after one year check up.

Difference is nothing but subtracting one value from another value.

Let us convert mixed fraction  [tex]5\frac{1}{2}[/tex] pounds to improper.

[tex]5\frac{1}{2}[/tex] =11/2=5.5

Now subtract 15.8-5.5

10.3 pounds.

Hence, max gain 10.3 pounds of weight between the time he was a puppy and his 1-year check-up.

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The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.

The relation between two unequal expressions is defined as inequality.

The given inequalities are 3x + 6 < 15 and  2x - 5 >7.

Solve the first inequality:

3x + 6 <15

3x < 15 -6

3x < 9

x < 3

Solve the second inequality:

2x - 5 > 7

2x > 7 + 5

2x > 12

x > 6

Hence, the solution to the compound inequality is x < 3 and x >6.

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Answer:

Pedro can buy 4 pounds of pears and 3 pounds of apples.

Step-by-step explanation:

Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.

$2×3lb + $3×4lb=$18

78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.

What is the linear equation?

A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that the total number of meals is 169.

Assume that,

a = number of meals eaten in a restaurant

b = number of meals eaten in a car

c = number of meals eaten at home

a + b + c = 169 .....(i)

Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.

Thus b + c = a + 13 .....(ii)

Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.

a = 20 + c .....(iii)

Subtract equation (ii) from (i)

a + b + c - b - c = 169 - a - 13

2a = 156

Divide both sides by 2

a = 78

Substitute a = 78 in equation (iii)

78 = 20 +c

c = 58

Putting c =58  and a =78  in equation (ii)

b + 58 = 78 + 13

b = 33

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Question:

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.

Answer:

50 miles per hour

Step-by-step explanation:

80 km         1 mi        

---------- x ------------ = 50 mi/hr

  1 hr         1.6 km

a) The coefficients are the costs of the respective shirts.

b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)

c) 3 solutions are:

(0, 25), (30, 0), (25, 4)

Here we know that:

And we have the linear equation:

10x + 12y = 300

The first coefficient is the one in the term "10x"

The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.

The second coefficient is on the term "12y"

And 12 means the cost in dollars of each long-sleeved shirt.

b) The graph of the linear equation can be seen on the image at the end.

The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.

The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.

c) 3 possible solutions can be seen on the graph, some examples are:

(0, 25), (30, 0), (25, 4)

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The volume is the amount of space thus the volume of the given prism will be 204.7 cm³ thus option (B) is correct.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

The volume of the given prism will be the area of the front triangle with a length of 12 cm.

The form triangle has been attached below,

The length x will be,

x = √(6² - 3.5²) = 4.87 cm.

The area of from triangle = (1/2) × 7 × 4.87

A = 17.06 cm²

The volume of the prism = A × length (12 cm)

Volume = 17.06 × 12 = 204.68 cm².

Hence "The volume is the amount of space thus the volume of the given prism will be 204.7 cm³".

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The complete question has been attached below ;

Using mathematical operations of addition and subtraction, Rodrigo needs to buy additional 2⁷/₂₄ pounds of vegetables.

The basic mathematical operations are addition, subtraction, division, and multiplication.

These mathematical operations can be used to determine the results of mathematical expressions.

The total pounds of vegetables required for a stew = 3 pounds

Available pounds of vegetables:

Onions = 3/8 pounds

Tomatoes = 1/3 pounds

The total available pounds = 17/24 pounds

Additional pounds required = 3 - 17/24 pounds

= 2⁷/₂₄ pounds

Thus, based on addition and subtraction, Rodrigo needs additional 2⁷/₂₄ pounds of vegetables.

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Complete steps to find domain of function is describe below.

Domain is defined as the all input values which satisfy the function or can say all inputs any function have.

suppose we have a function f(x) = 6x^2 + 5x - 4

For domain solve it for x

⇒ 6x^2 + 5x - 4

⇒ 6x^2+ 8x - 3x - 4

⇒ 2x(3x + 4)· -1(3x + 4)

⇒ (3x + 4) (2x - 1)

values of x are positive for quadratic  equation,

⇒ (3x + 4) (2x - 1)≥0

⇒ x ≥ 1/2  or  x ≥ -4/3

These  are the domain of function.

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The spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.

We are given;

Kenneth is making a cake for the first time.

His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try.

He uses a small spoon to remove the extra sugar.

He needs to remove 12 spoonfuls.

We need to find the quantity of sugar his spoon hold.

First, let us find the extra amount of sugar;

Extra sugar = 295 - 280 = 15 grams.

We will find each spoon by using the unitary method;

Since 12 spoonfuls hold 15 grams.

So, 1 spoonful holds 15 / 12 grams = 1.25 grams = 1250 milligrams.

So, 1 spoonful holds 1250 milligrams of sugar.

Thus, the spoon holds 1250 milligrams of sugar if Kenneth needs to remove 12 spoonfuls.

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By using property of triangle and trapezium, it is obtained that

a) value of x is 35°

b) Third option is correct

What is a triangle and trapezium?

Triangle is a three sided two dimensional figure.

Trapezium is a quadrilateral whose one pair of opposite side is parallel and another pair of opposite side is non parallel

Here property of triangle is used

[tex]m \angle D = (2x)^{\circ}, \ m\angle E = (2x - 4)^{\circ}, m \angle F = (x +9)^{\circ}[/tex]

[tex]m \angle D + m\angle E + m \angle F = 180\\2x + 2x - 4 + x + 9 = 180\\5x + 5 = 180\\5x = 180 - 5\\5x = 175\\x = \frac{175}{5}\\x = 35^{\circ}[/tex]

In the second question, if the trapezoid is rotated 90° clockwise, then (x, y ) will change to (y, -x) and new coordinate of A is (1, 5)

Third option is correct

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The amount that would be credited,  given the partial payments and the terms, would be $6, 060.61. The balance due would be $19, 939.39.

The terms 2/10 and 1/15 mean that if the buyer pays their bill in 10 days, they get a 2% discount. If they pay in 15 days, they get a 1% discount.

Pete paid on the:

= 27 - 15

= 12 days

This means that the 1 % discount would apply on the $6, 000. The credited amount would be:

= 6, 000 / (1 - 1%)

= $6, 060.61

The balance due would be:

= 26, 000 - 6, 060.61.

= $19,939.39

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The resulting value of the the expression 6769 x 925 by first rounding each number so that it has only 1 nonzero digit is 63,000

Round off

Round off refers a number is made simpler by keeping its value intact but closer to the next number. And it is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given,

Here we need to estimate  6769 x 925 by first rounding each number so that it has only 1 nonzero digit.

Here we have to take individual terms to round off then we get,

By rounding 6799 so that it has only one non-zero digit is rounding it to nearest thousand.

6769 rounds to nearest thousand as 7000 as hundreds digit 7 > 5.

Similarly, by rounding 925 so that it has only one non-zero digit is rounding it to nearest hundred.

925 rounds to nearest hundred as 900 as tens digit 2 < 5.

Now, the estimated value after rounding each number so that it has only one non-zero digit is

=> 7000 x 900

=> 63000.

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2/3 is the unit rate of the relationship

A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e.  $5 for one orange.

On a linear graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:

Slope = y2-y1 / x2-x1  

Thus, we can any two convenient points on the graph and use it calculate the slope as shown in the attached image:

Slope = y2-y1 / x2-x1

Slope = 6-2 / 9-3 = 4/6 = 2/3

Therefore, the unit rate for this relationship is 2/3. The 2nd option is the answer

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The expected value of the proposition is -$1007.41

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Suppose a basketball player has made 215 out of 322 free throws.

This means that p = 215/322 = 0.6677

2 free throws:

This means that

Probability of making two free throws.

This is P(X = 2).

P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]

P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629

Expected value:

If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.

Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.

E = 0.29629*24 - 31.70371*32 = -1007.41

Hence, The expected value of the proposition is -$1007.41

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The equation of the line perpendicular to the given line is, y = 3x + 1.

What is slope of the line?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

Consider, the given equation of line

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

We have to find the equation of line passes through the point (-2, -5) and perpendicular to the given line.

Here, the point is (-2, 5).

First to find the slope of the line.

Since, the slope of the line, perpendicular to the given line is negative reciprocal of the slope of given line.

Here, the slope of given line is, -1/3.

So, the slope of perpendicular line is [tex]-(\frac{1}{(-\frac{1}{3}) }) = 3[/tex]

Therefore, the slope of the line is 3.

Now to find the equation of the line.

Consider, the point - slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (-2, -5) , m = 3[/tex]

⇒

[tex]y-(-5)=3(x-(-2))\\y+5=3(x+2)\\y+5=3x+6\\y=3x+6-5\\y=3x+1[/tex]

Hence, the equation of line in slope - intercept form, is y = 3x + 1.

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Answer: 10 squares

Step-by-step explanation:

The answer for the area is 10 squares but I’m not sure that’s what they’re asking for.

Answer:

See below

Step-by-step explanation:

Eight minus unknown quantity 'x' equals two.

Answer:

Step-by-step explanation:

90

The two numbers that are compatible are 0.25 and 8. The property which helps to calculate it is commutative property.

What is the commutative property?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution.

Given numerical expression is (0.25 x 12.3) x 8.

First remove the parenthesis from the numerical expression:

(0.25 x 12.3) x 8 = 0.25 x 12.3 x 8

Now apply commutative property:

(0.25 x 12.3) x 8 = (0.25 x 8) x 12.3

(0.25 x 12.3) x 8 = 2.00 x 12.3

(0.25 x 12.3) x 8 = 24.6

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