Work out the equation of the line which has a gradient of 1/2 and passes through the point (2, -5)

Answer:

The given equation is expansion of (a-b)² = a²-2ab+b²

[tex]\sqrt{81-18\sqrt{7}+7} \\ \sqrt{ {9}^{2} -2 \times 9 \times \sqrt{7}+ { \sqrt{7} }^{2} } \\ \sqrt{ {(9 - \sqrt{7})}^{2} } \\ {(9 - \sqrt{7})}[/tex]

hope that help.

Answer:

[tex]9-\sqrt{7}[/tex]

Step-by-step explanation:

Given expression:  [tex]\sqrt{81-18\sqrt{7}+7}[/tex]

To simplify the given expression, use the "A minus B Whole Square" identity.

A minus B Whole Square identity

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Comparing  [tex]81-18\sqrt{7}+7[/tex]  to the right side of the identity:

Therefore:

[tex](9-\sqrt{7})^2=81-18\sqrt{7}+7[/tex]

Finally:

[tex]\sqrt{81-18\sqrt{7}+7}=\sqrt{(9-\sqrt{7})^2}=9-\sqrt{7}[/tex]

Answer:

D.

Step-by-step explanation:

sin 67 = b / 2.4

b = 2.4 sin 67

= 2.2

cos 67 = a / 2.4

a = 2.4 cos 67

= 0.9

M < A = 90-67 = 23 degrees.

Answer:

The age group that recorded the highest number of children is 7.

Step-by-step explanation:

We can clearly can see from the graph, that the 7 year old age group has 5 children, which is more than the rest of the age groups.

Hope this helps:) Goodluck!

Answer:

use ali result to estimate the probability of him winning the next solitaire game

Answer:

10

Step-by-step explanation:

Answer:

The answer would be ~30~ because 2*2^3 = 2^4= 16 then 3*6=18 then 16+18-4=30

Hope this helps

Have a great day/night

Answer ~

whenever we see an expression in the form of [tex]x^{n}[/tex] we have to multiply x to itself " n " times !

here in the question ,

we're given with the expression ( - 6³ )

so ,

[tex] - 6 {}^{3} = - 6 \times - 6 \times - 6 \\ \dashrightarrow \: - 216[/tex]

hope helpful ~

Answer:

Increasing then decresing

Step-by-step explanation:

the graph is going up then down so therefore it is increasing then decresing.

Answer:

The left side of the parabola is increasing to the maximum, shown on the graph to be (3,6). Then, the right side is decreasing from the max point. The parabola opens down, which means it increases, then decreases.

Step-by-step explanation:

Always decreasing would mean it took a more linear shape, which this parabola is not doing. It is also not always increasing, because some x,y points are graphed on that curve which go from the center (0,0) to (3,6) back down to (6,0).

Answer:

A. 2(x+3)(x^2+1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The given expression is

Taking out the common factor.

The complete factor form of given expression is . Therefore the correct option is A.

A large standard deviation means the view of the people is very dispersed and not near the mean or not similar.

Standard deviation is a very important terminology in Statistics which help to study dispersion of data from the mean

A lower value of standard deviation means the data is accumulated near the mean while a higher value means the data is dispersed in the entire range.

It is given in the question that

A researcher conducts a written survey to determine the opinion of subjects regarding their opinion of the favorability of a certain hospital.

The standard deviation value for the sample is large

A large standard deviation means the view of the people is very dispersed and not near the mean or not same.

There will be difference in the opinion as they deviate from the central value.

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Answer:

here's your answer....

The price of one senior citizen ticket is $7 and the price of one child ticket is $8.

s + 13c = 111 equation 1

12s + 9c = 156 equation 2

Where:

Multiply equation 1 by 12

12s + 156c = 1332 equation 3

Subtract equation 2 from equation 3

1176 = 157c

c = $8

Substitute for c in equation 1:

s + 13(8) = 111

s = 111 - 104

s = $7

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Answer: B) 16 cubic meters

Step-by-step explanation:

To find the volume of a rectangular prism like this sandbox, multiply the length, height, and width together. 2*2*4 = 16.

Answer:

the answer would be 16 cubic meter because l*w*t which is because l*w*t which is 4*2*2

Answer:

[tex]x=13[/tex]

Step-by-step explanation:

Step 1: Isolate the square root on the left hand side

 Radical already isolated

  √x-4 = x-10

Step 2: Eliminate the radical on the left hand side

Raise both sides to the second power

    (√x-4)2 = (x-10)2

    After squaring

    x-4 = x2-20x+100

Step 3: Solve the quadratic equation

    Rearranged equation

    x2  - 21x  + 104 = 0

    This equation has two rational roots:

      {x1, x2}={13, 8}

Step 4: Check that the first solution is correct

    Original equation

    √x-4 = x-10

    Plug in 13 for  x

     √(13)-4 = (13)-10

     Simplify

     √9 = 3

     Solution checks !!

    Solution is:

     x = 13

Step 5: Check that the second solution is correct

    Original equation

    √x-4 = x-10

    Plug in 8 for  x

     √(8)-4 = (8)-10

     Simplify

     √4 = -2

     Solution does not check

     2 ≠ -2

One solution was found :

     x = 13

Answer:

[tex]\sqrt{64} < \sqrt{72} < \sqrt{81}[/tex]

Step-by-step explanation:

The closest perfect squares to 72 would be 81 and 64. Therefore, the square root of 72 must be between 8 and 9.

Answer:

188 cubic yards

Step-by-step explanation:

there are two ways to solve for this problem the first is to use the given numbers to find the missing one, then seperate the two cuboids and solve for their volumes independently, and finally add

the second way is too make one complete rectangular prism and simply find out the volume of the missing side and subtract that from the whole

Using Elimination Method:

[tex]2x + 9y = 11 \\ 3x + 8y = 18 \\ 3(2x + 9y = 11) =( 6x + 27y = 33 )\\ - 2(3x + 8y = 18) = ( - 6x- 16y = - 36) \\ 11y = - 3 \\ y = \frac{ - 3}{11} \\ 2x + 9( \frac{ - 3}{11} ) = 11 \\ 2x - 9( \frac{3}{11} ) = 11 \\ 2x - \frac{27}{11} = 11 \\ 2x = 11 + \frac{27}{11} \\ 2x = \frac{121 + 27}{11} \\ 2x = \frac{148}{11} \\ 2x \div 2 = \frac{148}{11} \div 2 \\ x = \frac{74}{11} \\ x = \frac{ - 3}{11} \\ y = \frac{74}{11} [/tex]

An exponential function follows the form a^x, where a is a constant. Other answers incorrectly say it depend on the exponent but that is no true because this is a constant raised to x NOT x raised to a number.

You ask for rate of change in other words derivative

You may recall that the derivative of a^x is a^x*ln(a).

Answer:

y = a × b^x

b > 1

2 × 2 × 2 × 2

Assume all values are greater than 1

This function is a representation of exponential growth.

Answer:

It depends. If the negative number is greater than the positive, the answer is true. Otherwise, false.

Answer:

B.3x+8=66

Step-by-step explanation:

i think ito po Ang answer hehehe

Part A

x = some unknown number

x+8 = add on 8 to the number

3(x+8) = triple the previous result

Therefore, one equation to set up is 3(x+8) = 66

This is the same as 3x+24 = 66 because 3(x+8) = 3x+3*8 = 3x+24. Use the distributive property to multiply that outer 3 to each term inside.

C)  3x+24 = 66

D)   3(x+8) = 66

============================================================

Part B

Let's solve for x. I'll show the steps for each equation mentioned. When you write out the steps, you probably only need to pick one equation to solve.

3(x+8) = 66

x+8 = 66/3

x+8 = 22

x = 22-8

x = 14

Or

3x+24 = 66

3x = 66-24

3x = 42

x = 42/3

x = 14

Either way, we get the same x value. To confirm this answer, replace x with 14 in either equation and simplify fully. You should get 66 on both sides.

Answer:

d = 105° , e = 32° , f = 43°

Step-by-step explanation:

d and 105° are vertically opposite angles and are congruent , then

d = 105°

e and 32° are vertically opposite angles and are congruent , then

e = 32°

105° , e and f lie on a straight line and sum to 180° , that is

105° + e + f = 180°

105° + 32° + f = 180°

137° + f = 180° ( subtract 137° from both sides )

f = 43°

Answer:

d= 105° f= 43° e= 32°

Step-by-step explanation:

angle d = 105° ( vertically opposite angles are equal)

f°+d°+32°= 180 (angles on a straight line)

f+105+32= 180

f+137=180

f= 180-137= 43°

f= 43°

angle .d+f+e = 180° (angles on a straight line)

105+43+e = 180°

148+ e = 180°

e = 180-148

e = 32°

therefore,

d= 105° f= 43° e= 32°

Answer:

This might not be the best answer but here goes:

A perfect square has to be a number that is expressed by 2 of the same integer multiplied by each other.

To check if a number is a perfect square, you find the square root of it. 64006 does not have a whole square root, meaning it is not a perfect square number. Its square root is:

252.9940711... (very close but not quite whole)

1. A perfect square number always has its square root to be a whole number. But, the square root of 64006 is is 252.99407... (not whole), so it is not a perfect square.

2. A perfect square number can only be written as the product of 2 odd numbers or 2 even numbers. But, 64006 can be written as 32003 x 2 -> NOT a perfect square.

Apply Pythagorean theorem

Answer:

C

Step-by-step explanation:

A linear equation consists of  Ax+By=C

That is the only one without that kinda format

Answer:

The Answer Is C

Step-by-step explanation:

The provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

We have:

[tex]= \rm log_3(\sqrt[5]{x} . y)[/tex]

As we know:

log(mn) = logm + logn

logmⁿ = nlogm

[tex]= \rm log_3({x^{\dfrac{1}{5}}} . y)\\\\= \rm log_3({x^{\dfrac{1}{5}}} )+log_3 (y)\\\\= \rm \dfrac{1}{5}log_3({x^{}} )+log_3 (y)\\\\[/tex]

Thus, the provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.

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Answer:

A, B, C, D

Step-by-step explanation:

They All add up to 360

Answer:

B and D

Step-by-step explanation:

figures which can be circumscribed by a circle are called cyclic quadrilaterals.

the opposite angles of a cyclic quadrilateral sum to 180°

A

∠ B + ∠ D = 82° + 56° = 138° ≠ 180° ← not cyclic

B

∠ B + ∠ D = 103° + 77° = 180° and ∠ A + ∠ C = 90° + 90° = 180° ← cyclic

C

∠ B + ∠ D = 112° + 90° = 202° ≠ 180° ← not cyclic

D

∠ B + ∠ D = 90° + 90° = 180° and ∠ A + ∠ C = 90° + 90° = 180°← cyclic

Then B and D can be circumscribed by a circle

Answer: Y= 1/3x - 2

Step-by-step explanation:

We will see that there are 156,000 different combinations, so the correct option is C.

First, we need to find the selections, here we have:

Now we need to find the number of options for each of these selections.

We assumed that the number can be any integer from 0 to 9.

The total number of possibilities is equal to the product between the numbers of options, we will have:

P = 26*25*24*10 = 156,000

So, the correct option is C.

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Answer:

There are several different ways to get the x-intercept and y-intercept of an equation.  The way that I usually do it is setting one of the variables to zero and finding what the other variable is equal to.  For example, if we set x to 0 that means that we are finding the y-intercept as the value of x is 0 which is the y-axis.  This is also how it works when setting y to 0.  First lets find the x intercept by setting y to 0.

[tex]3x - 2y = 6[/tex]

[tex]3x - 2(0) = 6[/tex]

[tex]\frac{3x}{3} = \frac{6}{3}[/tex]

[tex]x = 2[/tex]

We now know that the x-intercept is 2 and now we need to determine what the y-intercept is.  Now we can just set the x to 0 and find the y-intercept.

[tex]3x - 2y = 6[/tex]

[tex]3(0) - 2y = 6[/tex]

[tex]\frac{-2y}{-2} = \frac{6}{-2}[/tex]

[tex]y =- 3[/tex]

Therefore, we know that our x-intercept is (2, 0) and our y-intercept is (0, -3) because the first spot in the coordinate pair is the x-value and the second one is the y-value.

Hope this helps

Answer:

Step-by-step explanation:

30 square unit is the area of the triangle DEF.

The properties of the triangle are:

We can use the coordinates of the three vertices of the triangle to find the length of its base and height, and then use the formula for the area of a triangle.

The base of the triangle is the line segment from point E to point F, which has a length:

|EF| = √[(4-4)^2 + (7-(-5))^2] = √(0^2 + 12^2) = 12

The height of the triangle is the perpendicular distance from point D to the line containing the base, which is the horizontal line y = -5.

Therefore, the height of the triangle is the vertical distance from point D to the line y = -5, which is 5 units.

The area of the triangle is then:

Area = (1/2) x (base) x (height)

= (1/2) x 12 x 5

= 30 square units.

Therefore, the area of triangle DEF is 30 square units.

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