Use trigonometric identities to transform the left side of the equation into the right side (0 < < /2).

Answer:

y = 1/4x

Step-by-step explanation:

The slope changes from 4 to 1/4

so,

y = 1/4x + b

Then, plug in (4,1) into the equation

1 = 1/4(4) + b

1 = 1 + b

b = 0

y = 1/4x + 0

y = 1/4x

Answer:

x=40

Step-by-step explanation:

2−3=77

2−3+3=77+3

2=77+3

2x=80

2x/2=80/2

x=80/2

x=40

Answer:

4^5

Step-by-step explanation:

8×4³+2×4⁴

4×2×4^3+2×4^4

4^4×2+2×4^4

4^4(2+2)

4^4×4

4^5

So answer is 4^5

Answer:

he raked 10 bags each hour

30/3 = 10

Answer:

2 1/3, 2 1/4, 2 3/7

Step-by-step explanation:

Mixed Fractions

Mixed fractions are made of an integer part followed by a proper fraction.

Some examples of mixed fractions are:

3 1/2, -4 5/8, 2 2/3

Between two consecutive integers a and a+1, there are infinitely many fractions. The centered number is a 1/2. Any number with its improper fraction part less than 1/2 is closer to a than to a+1.

In our problem, Jayne bought between 2 and 3 pounds of granola. We need to provide a mixed number that is closer to 2 pounds than to 3 pounds.

We can select any number with integer part 2 and a proper fraction less than 1/2.

Examples could be :

2 1/3, 2 1/4, 2 3/7

All of them are less than 2.5

Answer:

1. 0.18333333333

2.  1.5

3. 0.55555556

4. 2.75

5. 0.81818181818

6. 4.1111111111

Have a nice day, brainliest Please? :)

Answer:

Step-by-step explanation:

assume the equation is (7x-4)/y=10

10y= 7x-4 didvide both sides by 10

y= (7/10)*x - (2/5)

m=7/10

b=-2/5

The equation for 7x - 4/y =10 in the form y = mx + b . The equation in the form

[tex]\(y = mx + b\) is: \[y = \frac{4}{7x - 10}\][/tex]

To rewrite the equation in the form  we need to  [tex]\(y = mx + b\),[/tex]  isolate the term involving y on one side of the equation. Here's the step-by-step process:

Step 1: Add  [tex]\(\frac{4}{y}\)[/tex]  to both sides of the equation to isolate the 7x term on the left side:

[tex]\[7x = 10 + \frac{4}{y}\][/tex]

Step 2: Get rid of the fraction by multiplying both sides of the equation by y:

[tex]\[7xy = 10y + 4\][/tex]

Step 3: Now, we want to express  y alone on one side. To do this, subtract 10y  from both sides:

[tex]\[7xy = 10y + 4\][/tex]

Step 4: Factor out y on the left side:

[tex]\[y(7x - 10) = 4\][/tex]

Step 5: Finally, divide both sides by to solve for  [tex]\((7x - 10)\)[/tex]

[tex]\[y = \frac{4}{7x - 10}\][/tex]

Now, the equation is in the form where [tex]\(y = mx + b\), \(m\)[/tex] is the coefficient of x and b is the constant term. In this case,[tex]\(m = \frac{4}{7x - 10}\) and \(b\)[/tex]  is equal to 0.

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Answer:

$60

Step-by-step explanation:

just is

Answer:

191.016 in²

Step-by-step explanation:

Let the volume of the cube be V = lwh where l = length of box, w = width of box and h = height of box.

Now l = 3w.

So, V = lwh = (3w)wh = 3w²h

h = V/3w²

Since the rectangular box is open at the top, its total surface area is A = lw + 2lh + 2wh

substituting l = 3w, we have

= (3w)w + 2h(l + w)

= 3w + 2h(3w + w)

= 3w² + 2h(4w)

= 3w² + 8wh

substituting h = V/3w²

= 3w² + 8w(V/3w²)

A = 3w² + 8V/3w

Differentiating A with respect to w and equating it to zero, we have

dA/dw = d[3w² + 8V/3w]dw

dA/dw = d3w²/dw + d(8V/3w)/dw

dA/dw = 6w - 8V/3w²

dA/dw = 0

6w - 8V/3w² = 0

6w = 8V/3w²

6w³ = 8V/3

w³ = 8V/(3 × 6)

w³ = 4V/9

w = ∛(4V/9)

substituting V = 220 in³, we find the minimum value for the width

w = ∛(4 × 220 in³/9)

w = ∛97.7778

w = 4.607 in

To determine if this is a minimum value of width which gives minimum area, we take the second derivative of A. So,

d²A/dw² = d(6w - 8V/3w²)/dw

= 6 + 16V/3w³

substituting w³ = 4V/9, we have

d²A/dw² = 6 + 16V/3(4V/9)

= 6 + (16 × 9)/(3 × 4)

= 6 + 4 × 3

= 6 + 12

= 18

Since d²A/dw² = 18 > 0 , w = ∛(4V/9) = 4.607 in gives a minimum for the surface area.

So, we calculate this area by substituting w = 4.608 in. So,

A = 3w² + 8V/3w

= 3 × (4.607 in)² + (8 × 220 in³)/(3 × 4.607 in)

= 63.6733 in² + 1,760 in³/13.821 in

= 63.6733 in² + 127.3424 in²

= 191.0157 in²

≅ 191.016 in² to three decimal places.

Answer:

b

Step-by-step explanation:

2*22 = 44

44-25 = 19

Answer:

k = -5

Step-by-step explanation:

The variable is k

9k + 1 = -9 + 7k

-7k        -1

2k = -10

2k/2  -10/2

k = -5

:)

Answer:

78/16=

39/8=

19.5/4= 4.80805

16 is 20.51% of the number 78.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x percent of 78 is 16.

So, x% of 78 = 16

x/100 (78)= 16

78x = 1600

x= 1600/78

x = 20.51%

Hence, 20.51 percent of 78 is 16.

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Answer:

first one is 4

second is   2

Step-by-step explanation:

let me know if you need to  show work

Answer:

first one is 4, 2nd one is 2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

12 ounces

Step-by-step explanation:

48÷4 = 12 ounces

Answer:

x=35

Step-by-step explanation:

70+75is 145

and a triangle is equal to 180 degrees

so 180-145 gives you 35 :)

Answer:

r =1

Step-by-step explanation:

The radius of unit circle is 1

Answer:

1

Step-by-step explanation:

Answer:

7x3=21 ... i think

Step-by-step explanation:

the factor of 35 is 1,5,7 and 35 but 7 is the largest prime number like the factors of 15 is 1,3,5 and 15 but 3 is the smallest prime number according to the question the answer is 7x3+21

Answer:

Corresponding

congruent interior

equation 9x+8=4x+18

angle measure 26

Explanation:

9x+8=4x+18

-4x   = -4x

5x+8=18

-8    = -8

5x=10

x=10/5

x=2

---

so... now plug in 9(2)+8 = 18+8=26degrees

to confirm the angle should be the same for the next one

4x+18=26

solve for x

26-18=4x

8=4x

8/4=x

2=x

Answer:

no

Step-by-step explanation:

Answer:

Yes, if you are referring to proportionality in general. No if you are referring to a direct proportionality.

Step-by-step explanation:

y = -2x is negatively proportional so it is not directly proportional because y or one quantity decreases when x or another quantity increases. In a directly proportional relationship, as one quantity increases another quantity must increase at the same rate, in other words both must increase thus be positive. When something is proportional it has a constant ratio, and relation.

Direct proportionality or variation is represented by y ∝ x, where ∝ is the symbol used to represent proportionality.

y = kx where k is the constant of proportionality.

Where k = y/x.

Answer:

smaller value is 1.2

larger value is 6

Step-by-step explanation:

[tex]f(x)=\frac{3}{1+x^{2} }[/tex]

when x=a=0, one has

[tex]f(0)=\frac{3}{1+0^{2} } \\f(0)=3[/tex]

now, when x=b=2, one has

[tex]f(2)=\frac{3}{1+2^{2} } \\f(2)=\frac{3}{5}[/tex]

Therefore, the absolute minumun is

[tex]m=\frac{3}{5}[/tex]

and the absolute maximun is

[tex]M=3[/tex]

The approximation to the integral is

[tex]\frac{3}{5}(2-0)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2-0)[/tex]

hence

[tex]\frac{3}{5}(2)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2)\\\frac{6}{5} \leq \int\limits^2_0 {f(x)} \, dx \leq 6\\1.2 \leq \int\limits^2_0 {f(x)} \, dx \leq 6[/tex]

 [tex]\boldsymbol{4}[/tex] employees were hired by the company.

Amount of total budget [tex]=\$1,900[/tex]

Amount paid to an employee per hour [tex]=\$11[/tex]

Number of hours for which an employee worked per week [tex]=40[/tex]

So,

Total amount paid to an employee [tex]=11\times 40[/tex]

                                                          [tex]=\$440[/tex]

Number of employees hired [tex]=4.3[/tex]

                                               [tex]\approx 4[/tex]

So, [tex]\boldsymbol{4}[/tex] employees were hired by the company.

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Ignoring overhead, you can hire 4 employees.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

You have a budget of $1,900 per week for employees.

Employees are paid $11 per hour and work 40 hours per week.

That means,

11 x 40 = $440 per week.

The number of employees = 1900/440

= 4.3

≈ 4

Therefore, 4 number of employees.

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Answer:

1.5 miles

Step-by-step explanation:

Answer: Choice A)  All points with an x-value of 3 are located in Quadrant I.

We can show it is false through the use of a counter example. For instance, the point (3, -5) is not in quadrant 1, but rather in quadrant 4.

We would need to say "all points with x value 3 and positive y value" to ensure the point is in quadrant 1.

The false statement:

All points with an x-value of 3 are located in Quadrant I.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

From the given choices:

Let the statement is true.

All points with an x-value of 3 are located in Quadrant I.

Let the coordinate point (3, -7)

This point lies in the fourth quadrant.

Which is contradiction.

Therefore, the statement is false.

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Answer:

5,10

Step-by-step explanation:

10 is 5 more than 5 therefore

5+10=15

Answer:

5,2,2,2,2,2

Step-by-step explanation:

2+2+2+2+2=10

10+5=15

Given:

Number of girls = 20

Number of boys = 30

The president must be a girl and the vice president a boy

To find:

Number of ways to choose a president, vice president, and secretary.

Solution:

The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.

Total number of ways = Selecting 2 boys and 1 girl +  Selecting 1 boy and 2 girls

[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]

[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]

[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]

[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]

[tex]=8700+3800[/tex]

[tex]=12500[/tex]

Therefore, the required number of ways is 12500.

Answer:

domain is x is an element of all real numbers, or {xer}, and the range is {3.5}

Step-by-step explanation:

since x stretches the whole way it is all real numbers, and y only touches one point on the graph so it has to be a single point

Answer:

75 degrees

Step-by-step explanation:

Isosceles triangle with 3rd angle being 30 degrees:

2x + 30 = 180

2x = 150

X = 75

Answer:

no

Step-by-step explanation:

because there is supposed to be a decimal point for example 5.18 there needs to be a period

Answer:

what do you mean there is not decimal in the number you could make it a decimal tho

it would be 5.18 as a decimal

Step-by-step explanation: