7th grade question

easy question

[tex]

\cot(a-b)=\frac{\frac{1}{(x+1)(x-1)}+1}{\frac{1}{x-1}+\frac{1}{x+1}} \\ \\ =\frac{1-1+x^2}{2} \\ \\ =\frac{x^2}{2} \\ \\ \therefore 2\cot(A-B)=x^2[/tex]

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\cot \theta=\dfrac{1}{\tan \theta}$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

[tex]\begin{aligned}\implies 2\cot (\alpha - \beta) & =\dfrac{2}{\tan (\alpha - \beta)}\\\\ & =\dfrac{2}{\dfrac{ \tan \alpha - \tan \beta}{1+\tan \alpha \tan \beta}}\\\\ & =\dfrac{2(1+\tan \alpha \tan \beta)}{ \tan \alpha - \tan \beta}\\\\ & =\dfrac{2(1+(x+1)(x-1))}{ (x+1) - (x-1)}\\\\& = \dfrac{2(1+(x^2-x+x-1))}{x+1-x+1}\\\\& = \dfrac{2(1+(x^2-1))}{2}\\\\& = \dfrac{2x^2}{2}\\\\& = x^2\end{aligned}[/tex]

Hence verifying that 2cot(α - β) = x².

Answer:

$6.79

Step-by-step explanation:

You add the cost of the first two then subtract that by the total she spent to get the answer

$10.79 + $8.72 = $19.51

$26.30 - $19.51 = $6.79

Answer:

OA

Step-by-step explanation:

the federal government only manages the things about the country , that's why there are different types of government becuz each one of them has responsibilities

The required milliliters should be​ administered is 0.875 milliliter .

Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units. The definition of length is interrelated with volume.

Given:

A​ patient's order is 70 milligrams of a drug.

Available in stock is 80 milligrams in 1 milliliter of liquid.

According to given question we have

80 milligrams = 1 milliliter

70  milligrams =1*70/80 milliliter

70  milligrams = 0.875 milliliter

Therefore, the required milliliters should be​ administered is 0.875 milliliter .

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The number of times Maria drove the car on day 4 is 9 times.

A line graph is a graph that connects different data points on a graph using a straight line. A line graph is made up of a x-axis and a y-axis. In the line graph given, the number of days is on the x-axis and the number of times the car was driven is on the y-axis. A line graph is used to show quantitative data. Line graphs are used to visualise data.

In order to determine the number of times Maria drove the car on day 4, locate where day 4 is on the x-axis. Then trace 4 upward toward a data point. When the data point is located, trace it to the y-axis. When day 4 is traced to the y-axis, the value gotten is 9.

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Answer:

soln

given,

1dozen=rs 80

therefore,cost of 18 dozen pencils =80 × 18

=1440 Rs

Answer:

270cm2

Step-by-step explanation:

you have to split the figure into 2.

the triangle above is = 1/2 x20cmx13cm=130cm2

the rectangle is = 20cmx7cm=140cm2

total area=140cm2+130cm2

               =270cm2

Answer:

3x^2

Step-by-step explanation:

Explained in image.

The interest rate 2% per year

The time period is 7 years

The initial investment is $600

The current investment is $84

The interest rate can be calculated as follows

84/600 × 7

= 84/4200

= 0.02

The interest rate is

= 0.02 × 100

= 2%

Hence the interest rate is 2%

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The profit per bag for the bags sold at 3$ each is $1.5 per bag.

The total cost will be:

= $300000 + (1 × $600000)

= $900,000

The revenue will be:

= $3 × 600000

= $1,800,000

Therefore, the profit per bag will be:

= ($1800000 - $900000) / 600000

= $900000/600000

= $1.5

The profit is $1.5.

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Step-by-step explanation:

X=48 becase 42+90=132

180-132= 48

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

because you can't  count before 42 so eight

When you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

It should be noted that in subtraction when you reduce the first number, you will get a value that's lesser by 1.

In this case, if we have 20 - 5 = 15, then 19 - 5 = 14. We can see that 14 and 15 is a difference of 1.

Therefore, when you subtract two numbers, if you reduce the first number in the subtraction by one, the result is one less. This is true.

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< TSU = 4y + 11 = 23 degrees

What does angle relationship mean?

We talk of angle relationships because we are comparing position, measurement, and congruence between two or more angles. For example, when two lines or line segments intersect, they form two pairs of vertical angles

we have to find m < TSU if SU bisects < TSV, m < TSU = 4y + 11, m < USV = 6y + 5

SU bisects < TSV

=>    < TSU = < USV

4y + 11 = 6y + 5

-2y = -6

y = 3

< TSU = 4y + 11 = 23 degrees   ( put the value of y=3)

∠USV = 6y + 5 = 23 degrees      ( put the value of y=3)

Hence ,< TSU = 4y + 11 = 23 degrees

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Step-by-step explanation:

10+290=x is the answer

x=290-10

x=280#

The required verbal form of the expression is two more than 25 times of a number.

Given that,
An expression is given we have to determine the verbal expression of the given algebraic expression.

The algebraic expression consists of constant and variable. eg x, y, z etc.

Here,m
Given expression = 25x + 2
Where x is any variable number 25 times and further added 2.
So.
The verbal expression can be given as
two more than 25 times of a number.

Thus, the required verbal form of the expression is two more than 25 times of a number.

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The y-intercept is where the graph crosses the y-axis and is not necessarily where the maximum is. For instance, consider the graph of [tex]y=x^2 +2x+4[/tex].

The distance from the Earth to the moon, in the scale model, is d. 0.25 m

As per the known fact, ratio of measurement in real is equal to the ratio of measurement on scale. Further, ratio will be calculated in this case as -

Distance from Earth to Sun in real : Distance from Earth to Moon in real = Distance from Earth to Sun on scale : Distance from Earth to Moon on scale

Keep the values in mentioned relation to find the distance from Earth to Moon.

1.5×10⁸:3.8×10⁵ = 100:distance from Earth to Moon on scale

Distance from Earth to Moon on scale = 100×3.8×10⁵/1.5×10⁸

Distance from Earth to Moon on scale = 0.25 m

Therefore, the correct option for distance is d. 0.25 m.

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The two consecutive whole numbers that it lies between are 28 and 29.

The consecutive numbers are those number which follow each other continuously in the order from smallest to largest numbers.

Let the two consecutive numbers be x and x + 1

x + x + 1 = 57

Combine like terms;

2x + 1 = 57

Now Subtract 1 from both sides;

2x = 57- 1

2x = 56

Divide both sides by 2

x = 56/2

x = 28

Thus, x + 1 = 28 + 1 = 29

The two consecutive whole numbers that it lies between are 28 and 29.

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Answer: 3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

If the last digit in the fractional part of 3.691 is less than 5, then simply remove the last the digit of the fractional part.

Answer: It is impossible to find the square root of negative one, or the square root of any negative number because no number times itself can equal a negative number.

Step-by-step explanation:

Answer:

It is impossible to find the square root of negative one, or the square root of any negative number, because no number times itself can equal a negative number.

Step-by-step explanation:

The square root of a negative number does not exist among the set of Real Numbers.

When problems with negatives under a square root first appeared, mathematicians thought that a solution did not exist. They saw equations such as x2 + 1 = 0, and wondered what the solution n3 really meant.

Answer:

See below

Step-by-step explanation:

Avg shots made =  (45/60) x   = (3/4 ) x = .75 x

Applying addition of integers, the final results of the expressions are given as follows:

a) -6.

b) -6.

c) 35.

d) -1.

To add two integers, we have to keep in mind their signals, if they are the same or different, as follows:

Hence, for item a, we have that:

For item b, the solution is found as follows:

For item c, the solution is found as follows:

For item d, the solution is found as follows:

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The number of students in the 9th grade is 250.

Based on the information, the percentage of those who brought their good from home will be:

= 100 - 24%

= 76%

Therefore, 76% of x = 190

0.76x = 190

x = 190/0.76

x = 250

Therefore, the number of students in the 9th grade is 250.

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u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹

We are given that:

log 4 ^ u - log 8 ^ v = 1

This can also be written in another way using the logarithm properties. We get that:

u log 4 - v log 8 = 1

Subtract v log 8 from both the sides:

u log 4 = 1 + v log 8

v log 8 = u log 4 - 1

v = ( u log 4 - 1 ) / log 8

v = u log (- 4 ) - ( log 8) ⁻¹

Therefore, we get that, u in terms of v will be represented with the logarithm function as v = u log (- 4 ) - ( log 8) ⁻¹

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The volume of D10W solution required to be diluted to make 850 mL of D8W solution is 680 mL.

The dilution formula can be presented as follows;

[tex]C_1 \cdot V_1 = C_2 \cdot V_2[/tex]

Where;

[tex]C_1 = Initial \: concentration = D10W [/tex]

[tex]V_1 = Initial \: volume [/tex]

[tex]C_2 = Final \: concentration = D8W[/tex]

[tex]V_2= Final \: volume = 850 \: mL [/tex]

Which gives;

[tex]V_1 = C_2 \cdot V_2/C_1[/tex]

V1 = 8×850/10 = 680

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Answer:

y = x + 3

y = -x + 11

Step-by-step explanation:

When the slopes are parallel they are the same.  When slopes are negative, the slope is the negative reciprocal.

Parallel:  The slope is 1.  This is the coefficient of the x in the equation given.  If you do not see a number before the x like in  y = x + 1, then number is 1.

Use this form:

y =mx + b  Us the slope of 1 to put in for m.  Use 4 for x and  7 for y

7 =(1)4 + b  Solve for b.

7 = 4 + b  Subtract 4 from both sides.

3 = b

The equation for the parallel line is

y = x + 3.

Perpendicular:

y = mx + b This time the slope is -1 Still use 4 for x and 7 for y

7 = (-1)4 + b

7 =-4 + b add 4 to both sides

11 = b

The equation would be y = -x + 11