Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify. The product of 7 and the square of a number.

The number of cloves of garlic you will plant is 288

Given,

There are two groups of garlic bulbs.

Ratio of garlic bulbs = Planting : Cooking = 6 : 1

The number of garlic bulbs used for cooking = 6

The number of cloves in a garlic bulb = 8

We have to find the number of cloves of garlic used for planting:

Here,

Ratio = 6 : 1

1 in ratio represents 6 bulbs of garlic

So, 6 will be, 6 × 6 = 36

That is, the number of garlic bulbs used for planting is 36.

Now,

Number of cloves of garlic used for cooking = 6 × 8 = 48 cloves

Number of cloves of garlic used for planting = 36 × 8 = 288 cloves.

That is, the number of cloves of garlic you will plant is 288.

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Answer:

-4.1 < -√20

Step-by-step explanation:

-√20 = -4.472135954 (-4.47)

-4.4 < -4.47 (-√20)

The rule of signs in binomial factors given a trinomial in the form :

Note that b and c can be positive or negative.

And the factor may be :

First thing to do is to check the sign of c.

If it is positive, the signs of m and n can be both positive or both negative.

Since positive multiplied by positive is positive and

negative multiplied by negative is also positive.

If the sign of c is negative, one of the factors must be negative and the other must be positive, because negative multiplied by positive is negative.

After considering the sign of c, next to check is the sign of b.

Case 1 :

If b and c are both positive, we know that the factors can be both negative or both positive.

And since the sign of b is positive, we must follow the sign of it which is positive.

So both m and n are positive

For example :

The factor will be :

which are both positive.

Case 2 :

If b is negative and c is positive, we will follow the sign of b. m and n will be both negative.

For example :

The factors are :

which are both negative

Case 3 :

Now the third case is tricky.

If c is negative, we know that one of m and n is negative and the other one is positive.

The sign of the larger number between m and n will follow the sign of b.

For example :

c is negative, so one factor must be negative and the other must be positive. The sign of b is negative, so the larger factor must be negative also.

The factor will be :

3 is larger than 2, so the negative sign of b will proceed to the factor 3.

The average balance in the bank account is $1,125.64.

So, the average balance of the account will be:

Fill in the values and solve as follows:

Therefore, the average balance in the bank account is $1,125.64.

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The position of the given term is mathematically given as

n = 24

This is further explained below.

A function that goes from one set to another gives each element of the first set precisely one element of the second set.

This particular set, X, is referred to as the function's domain, and this particular set, Y, is referred to as the function's codomain.

Generally, the equation for Function the is mathematically given as

f(n) = 2.5 n - 16

Considering that the total is 52, we need to locate the letter "n." (position). Now let's get the answer for "n":

52=(2n-2)+2

52=2n-2+2

52 = 2n-4

n = (52-4)/2

n = 24

In conclusion, the position of the given term.

n = 24

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After evaluating for the function f, the value of f(-3) = -12, f(-2) = -2, f(-1) = 4, f(0) = −10

A function is a specific type of relationship that maps inputs to precisely one output. Consider a function as a machine for useful insight. The domain of the function, which describes the types of input that the machine will accept, states that it will produce one and only one output for each input.

A function's fundamental notation is of the form f( x), where x is the input variable and f is the function's name. "F of X" should be read as this. Any time you see this notation, f(x) generally refers to a function's output, though these letters are subject to change.

We have given the function f, to evaluate f(-3), f(-2), f(-1), and f(0)

[tex]f(x)= \begin{cases}-2 x^2+6 & \text { if } x \leq-1 \\ 7 x-10 & \text { if } x > -1\end{cases}[/tex]

f(-3) = -2x² + 6                    (as x < -1)

⇒ -2(-3)² + 6

⇒ -12

f(-2) = -2x² + 6                    (as x < -1)

⇒ -2(-2)² + 6

⇒ -2

f(-1) = -2x² + 6                    (as x < -1)

⇒ -2(-1)² + 6

⇒ 4

f(0) = 7x - 10                      (as x > -1)      

⇒ 7(0) - 10  

⇒ −10

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The value of c would be -32 to get the slope of 8.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given equation is cx + 4y = 12. Convert the equation into the general form of the equation.

cx + 4y = 12

4y = -cx + 12

y = (-c / 4)x + ( 12 / 4 )

y = ( -c / 4) x + 3

The slope of the equation is ( -c / 4 ) which is to be equal to 8.

( -c / 4 ) = 8

c = -32

Therefore, the value of c would be -32 to get the slope of 8.

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Answer:

for my question u commented on u can just talk about u or anyone for a reference

Step-by-step explanation:

Answer:

Step-by-step explanation:

- 36

The generalize term of the pattern is aₙ = 16 (1 / 2)ⁿ⁻¹

The pattern follows a geometric sequence.

The pattern follows a geometric progression.

Therefore, using geometric sequence formula,

where

Hence,

a = 16

The common ratio is the amount between each number in a geometric sequence. In other words,  it is the ratio between two consecutive numbers in the sequence

r = 8 / 16 = 4 / 8 = 2 / 4 = 1 / 2

The generalize pattern of the sequence is as follows:

aₙ = 16 (1 / 2)ⁿ⁻¹

Hence,

aₙ = 16 (1 / 2)ⁿ⁻¹

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Answer:

Rosa

Step-by-step explanation:

5/7 fraction  = 0.71

4/6 fraction  = 2/3 = 0.6

The first 4 sequence of Arithmetic progression is 42, 37, 32,  27.

Let n =1

[tex]a_{n} = 42-5(n-1)\\a_{1} = 42-5 (1-1)\\a_{1} = 42[/tex]

Let n=2

[tex]a_{n} = 42-5(n-1)\\a_{2} = 42-5 (2-1)\\a_{2} = 42-5\\a_{2} = 37[/tex]

let n= 3

[tex]a_{n} = 42-5(n-1)\\a_{3} = 42-5 (3-1)\\a_{3} = 42-10\\a_{3} = 32[/tex]

Let n= 4

[tex]a_{n} = 42-5(n-1)\\a_{4} = 42-5 (4-1)\\a_{4} = 42-15\\a_{4} = 27[/tex]

An arithmetic sequence is a list of numbers with a specified pattern. If you take some number in sequence, subtract it from the previous one, and the result is always the same or constant, it is an arithmetic sequence.

An arithmetic sequence is defined in two ways. It is "a sequence in which the differences between any two consecutive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to the previous term. The following is an arithmetic sequence because each term is obtained by  a fixed number when added to its previous term.

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Answer:5

Expand 0.6/0.12

by multiplying both numerator and the denominator by 100.

60/12

Divide 60 by 12 to get 5.

5

Answer:

55

Step-by-step explanation:

6.6/12 = 55

Considering the definition of perpendicular line, the equation of the straight line passing through the point (0,-1) which is perpendicular to the line y=3/4x-3 is y= -4/3x -1.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 3/4x - 3. The line has a slope of  3/4.

If you multiply the slopes of two perpendicular lines, you get –1, you get:

3/4× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (3/4)

slope perpendicular line= -4/3

The perpendicular line has a form of: y= -4/3x + b

The line passes through the point (0, -1). Replacing in the expression for perpendicular line:

-1= -4/3×0 + b

-1= 0 + b

-1= b

Finally, the equation of the perpendicular line is y= -4/3x -1 .

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Answer:

y = -7

Step-by-step explanation:

If y = 10 when x = 20, then we can find the difference when we do y + 1 = x + 1, which is 11 = 21. Therefore, the difference between x and y is 10. So, we need to do 3-10, which gives us -7.

The equation of the line for the bike path is :

y = -5x - 15.

Here :

Equation for the Lorne Lane line is y = -4/5x.

slope of the Eqe is -4/5

slope of the bike path perpendicular to Lorne Lane is -5/4

from the Graph point p is (-4, -10)

so

Equation of the line is y = -5x -15;

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Answer:

y=-5x-15

Step-by-step explanation:

What is Asymptote?

The term asymptote means approaching a value or curve arbitrary closely. A line or curve that is asymptotic to given curve is called asymptotic.  

Given,

The function f(x) = 16(1.87)x

Now, We know that

If the value of b < 1, it is a decay while if the value of b > 1, then it is growth. Given the exponential equation below;

f(x) = 16(1.87)x

Since, b = 1.87 which is greater than 1, hence it is a growth. Find the graph attached.  

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Answer: -16

Step-by-step explanation:

IF THE EQUATION HAS EQUAL ROOTS IT MEANS

[tex] {b}^{2} - 4ac = 0[/tex]

THAT IS THE RULE.

WHERE b is the coefficient of x

a si the coefficient of

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

and c is the constant number.

IF QE CHECK IN THE GIVEN EQUATION WE WILL FIND THAT a=2

b= -(b-4)

c= -4(b+2)

[tex]( - (b - 4))^{2} - 4(2)( - 4(b + 2)) = 0 \\ (4 - b ) ^{2} - 8( - 4b - 8) = 0 \\ (4 - b )(4 -b ) + 32b + 64 = 0 \\ 16 - 4b - 4b + {b }^{2} + 32b + 64 = 0 \\ {b }^{2} + 24b + 80 = 0 \\ (b + 20)(b + 4) = 0 \\ b + 20 = 0 \\ \\ \\ orb \\ \\ b + 4 = 0 \\ b = -2 0 \\ \\ \\ or \\ b = - 4[/tex]

ATTACHED IS THE SOLUTION

The value of the function (b²)²(b²)² from the given quadratic equation is 390,625.

The solution of a quadratic function is determined from either formula method or completing the square method.

The equation for the formula method of solving a quadratic function is given as;

[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]

where;

The given quadratic function;

3x² - 5x - 3 = 0

from the equation above we can infer the following;

a = 3

b = -5

c = -3

The obtain the value of the function [ (b²)²(b²)²], we will substitute the value of b from the above quadratic equation into the given function as shown below.

(b²)²(b²)² = (-5²)²(-5²)² = (-5)⁸ = 390,625

Thus, the value of the function (b²)²(b²)² is determined by applying the formula method of solving a quadratic function.

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Answer: 8690

Step-by-step explanation:

Divide $43450 by the number of months there are in a year (which is 12) and you get the answer

Answer:

x = 100° , y = 75° , z = 135°

Step-by-step explanation:

x and 80° are a linear pair and sum to 180° , that is

x + 80° = 180° ( subtract 80° from both sides )

x = 100°

y and 105° are a linear pair and sum to 180° , then

y + 105° = 180° ( subtract 105° from both sides )

y = 75°

the sum of the interior angles of a polygon is

sum = 180° ( n - 2 ) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the interior angles and equate to 540°

z + x + 90° + 110° + 105° = 540°

z + 100° + 90° + 110° + 105° = 540°

z + 405° = 540° ( subtract 405° from both sides )

z = 135°

Answer:

Brand a price is less than Brand b.

Step-by-step explanation:

given-

two brands of canned dog food are on sale. assume that the cans are the same size. brand a costs $13.60 for eight cans and brand b costs $8.75 for five cans

first-brand a costs $13.60 for eight cans

second- brand b costs $8.75 for five cans

solve first

for 8 cans-->$13.60

then,1 can -->$13.60/8

               =>$1.7

in similar manner we solve for second

for 5 cans-->$8.75

then,1 can -->$8.75/5

               =>$1.75

Brand a price is less than Brand b.

Unit pricing helps consumers compare the prices of packaged goods when those goods aren't sold in equal quantities. It's unit pricing that allows, for example, a shopper to tell at a glance which is the better buy: a 20-pound bag of dog food that sells for $13.95 or a 15-pound bag that sells for $10.69.

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As a result, in the parallelogram before, x = 4, Angle E = 104 degrees, and Angle EFH = 32 degrees.

1. Opposing sides are congruent sides. ...

2. Opposing angles are congruent angles. ...

3. Interior angles that follow one another on the same side are supplementary. ...

4.Each of a parallelogram's diagonals divides it into two congruent triangles. ...

5. The diagonals of a parallelogram split in half.

As a result,

EH and FG's sides are parallel and equal.

so 3x=12

x=4

to determine Angle E

FGH Triangle

Angles FHG + HFG + G add up to 180.

(The total of a triangle's angles is 180)

FHG angle=180-44+104

                 =32

Angles EFH = FHG (alternate interior angles)

                    =32

Angle HFG = Angle EHF (alternate interior angles)

                   =44

Angle E=Angle HGF( opposite angles are equal in a parallelogram)

            =104

Therefore the value of x in the given quadrilateral is 4 , the angle E is 104 degree and the value of Angle EFH is 32 degree.

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Using proportions, it is found that the percent of decrease in Darnel's daily water consumption was of 0%.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.

One example of application of proportions is for percentage problems, and for the case in this problem, the percent decrease is given by the change divided by the initial amount and multiplied by 100%.

For this problem, we have that:

Hence the percent decrease is found applying the following proportion:

0/100 x 100% = 0%.

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after simplifying the expression - 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p), we get the result as 27 - 17 / 4 p.

We are given the expression:

- 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p)

We need to simplify and solve the expression.

First we will solve the brackets.

- 15 / 4 p + 9 + 16 - 2 / 4 p

Now we will combine the like terms, so, we get that:

= 27 - 17 / 4 p

Therefore, after simplifying the expression - 3 / 4 (5 p - 12) + 2 (8 - 1 / 4 p), we get the result as 27 - 17 / 4 p.

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Answer:

its all real numbers i took the quiz before

Step-by-step explanation:

The standard deviation for the test is 8, the mean score is 79.

The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Given that,

On a science test, a score of 91 falls exactly 1.5 standard deviations above the mean.

μ + 1.5σ = 91

If the standard deviation for the test is 8

σ = 8

μ + 1.5σ = 91

μ + 1.5(8) = 91

μ + 12 = 91

μ = 91-12

μ = 79

Therefore, the mean score is 79.

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Answer:

5: 13

6: 7

7: 26

8: 18

9: x=11 , y=3

Step-by-step explanation:

5:

9x + 2 = 119

9x = 117

x = 13

6:

12x - 8 + 104 = 180

12x - 8 = 76

12x = 84

x = 7

7:

5x + 7 = 8x - 71

3x = 78

x = 26

8:

7x - 61 = 4x - 7

3x = 54

x = 18

9:

9x + 25 = 13x - 19

4x = 44

x = 11

13(11) - 19 + 17y - 5 = 180

143 - 24 + 17y = 180

119 + 17y = 180

17y = 61

y = 3

The curve that matches the graph of:

y = 2x^2 + x

Is the orange curve.

Here we want to see which one of the graphed curves matches the graph of the quadratic equation:

y = 2x^2 + x

To check that, we can evaluate this curve in some values of x and find some points.

For example, if x = 0 then:

y = 2*0^2 + 0 = 0

So we have the point (0, 0).

Now, if x = 1 then:

y = 2*1^2 + 1 = 2 + 1 = 3

So we have the point (1,3).

So now we just need to see which of the curves passes through the points (0, 0) and (1, 3), and that one will be the orange curve.

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