I don’t know what to do for this

Answer:

See below for proof of identity.

Step-by-step explanation:

Since both terms of [tex]\sin^3\theta+\cos^3\theta[/tex] are perfect cubes, we can use the formula [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex] where [tex]a=\sin\theta[/tex] and [tex]b=\cos\theta[/tex]:

[tex]\displaystyle \frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\\\\\frac{(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)}{\sin\theta+\cos\theta}\\ \\\frac{(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)}{\sin\theta+\cos\theta}\\\\1-\sin\theta\cos\theta[/tex]

Thus, the identity is proven.

Answer:

C

Step-by-step explanation:

In 3 options, the coefficient of x on both sides is the same. Hence, they will all have no solution. The only one which has exactly one solution is :

No, there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.

Two figures are congruent if their vertices can be mapped into one another by appropriate rigid transformation or a combination of rigid transformations. Examples of the transformation are; reflection, dilation, rotation and translation.

Comparing the two figures, it would be observed that they are not congruent. Since there is not a rigid transformation or a combination of rigid transformations that will map ABCD to WXYZ.

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Answer:not congruent.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

|-20| = 20 the positive value of -20

20 is not < 20 so A is false

All the rest are true
(B) |9| = 9

(C) |-20| = 20 > 9

(D) |9| = 9, |20| = 20 and 9 < 20

Answer:

Hypotenuse = 17

Step-by-step explanation:

if: a = 8, b = 15 c = hypotenuse:

[tex]c=\sqrt{a^{2}+b^{2} }[/tex]

[tex]c = \sqrt{(8)^{2} +(15)^{2} } =\sqrt{64+225}=\sqrt{289} =17[/tex]

Hope this helps

Answer:

Jeff, 4.5 hours; Julia 9 hours.

Step-by-step explanation:

To solve the problem, we need to write two equations using the given information.

So, writing the first equation we have:

We know that Jeff can weed the garden twice as fas as his sister Julia, so:

Also, from the statement we know that they can weed the garden in 3 hours, so, writing the second equation we have:

Then, we need to substitute the first equation into the second equation in order to isolate Julia's rate, so, solving we have:

We have that Julia could weed the garden by herself in 9 hours.

So, calculating how long will it take to Jeff, we have:

We have that Jeff could weed the same garden by himself in 4.5 hours.

hope this helps!

a)    Line parallel to the line 3x+5y=-10 is -6x-10y=9

b)    Line parallel to the line 2y-4x=5 and which goes through the point

       (3,7) is y= 2x-1.

c)      Line perpendicular to the line 8x+6y=-1 and which goes through the

        point (-2,1) is 4y= 3x+ 10

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.

a) Equation parallel to 3x+5y=-10 is

    -6x-10y=9

So, it satisfies:  [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

b)given equation into the form of y=mx+c,

     2y-4x=5

we can find the gradient of the line.

  2y= 5+4x

  y= [tex]\frac{5}{2}[/tex] + 2x

Hence, the gradient is 2.

As, Parallel lines have the same gradient

Thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=3, y=7,

7= 2(3) +c

7= 6 +c

c=6-7

c= -1

So, equation of line be: y= 2x-1.

c) Given: 8x+6y=-1

     6y= -1-8x

     y= [tex]\frac{-1}{6} -\frac{4}{3}x[/tex]

Hence, m= [tex]-\frac{4}{3}[/tex]

We know, if two lines are perpendicular have m and m' as slope then,

m*m'=-1

[tex]\frac{-4}{3} *m'=-1[/tex]

 m'= [tex]\frac{3}{4}[/tex]

Now, y= [tex]\frac{3}{4}[/tex] x +c

Put x= -1 and y=1

then, 1= [tex]\frac{3}{4}[/tex] (-2) + c

         c= [tex]\frac{5}{3}[/tex]

So,  y= [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{2}[/tex]

     4y= 3x+ 10

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Answer:

[tex] \sqrt{ - 100} = 10i = 0 + 10i[/tex]

Answer:

Step-by-step explanation:

Questions:

To find:

Solutions:

First, do switch sides.

[tex]\Longrightarrow:\sf{3.1-12.5\left|1-0.8x\right|=5.6}[/tex]

Multiply by 10 from both sides.

[tex]\Longrightarrow: \sf{3.1*10-12.5|1-0.8x|*10=5.6*10}[/tex]

Solve.

31-125|1-0.8x|=56

Subtract by 31 from both sides.

[tex]\Longrightarrow: \sf{31-125\left|1-0.8x\right|-31=56-31}[/tex]

Solve.

[tex]\Longrightarrow: \sf{-125\left|1-0.8x\right|=25}[/tex]

Divide by -125 from both sides.

Solve.

[tex]\Longrightarrow: \sf{\dfrac{-125\left|1-0.8x\right|}{-125}=\dfrac{25}{-125}=\boxed{\sf{No\ solutions.}}}[/tex]

I hope this helps, let me know if you have any questions.

There are no solutions.

Answer:

35

Step-by-step explanation:

Answer:

The answer is 405

Step-by-step explanation:

FIrst you would do 27 times 30 which is 810 then you would divided by 2 which in turn gives you 405

Hope this helped!

The functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum

The functions are given as:

A quadratic function can be represented as:

y = ax² + bx + c

y = a(x - h)² + k

In both cases, when a < 0; the function has a maximum.

This means that all three functions have a maximum.

Next, we determine the axis of symmetry:

Using the above forms, we have:

f(x) = -x² + 4x + 2

Axis of symmetry, x = -4/(2 * -1)

x = 2

g(x) = -(x + 2)² - 5

Axis of symmetry, x = -2

h(x) = -2(x − 1)(x − 3)

Expand

h(x) = -2x² - 8x + 8

Axis of symmetry, x = -8/(2 * -2)

x = 2

This means that f(x) and h(x) have an axis of symmetry of x = 2

Hence, the functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum

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Answer:

16

(14-6)×2=16 So initially Emma had 16 books.

Step-by-step explanation:

2x + 18

x = 18÷2

x=9

hence the answer is 9

Answer:

it would be a

Step-by-step explanation:

8x4=32

The base of the given triangle is calculated as: 16 ft

The formula that is used to calculate the area of a triangle is expressed as:

Area of triangle= ½ × base × height

We are given that:

Area = 32 ft²

Height = 4 ft

Thus:

32 = ½ × base × 4

32 = 2 * base

base = 32/2

base = 16 ft

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Answer:

x= -64°, y= -63°, z=-57°

Step-by-step explanation:

→Solution,

Here,

60°=(-y-3)°[The opposite sides of a parallelogram are equal]

⇒y= -60°-3°

⇒y= -63°

⇒60°+(-2x-8)°=180°[Sum of co-interior angles is 180°]

⇒52°-2x=180°

⇒52°-180°=2x

⇒x= -128°/2

⇒x= -64°

⇒60°+(-2z+6)°=180°[Sum of co-interior angles is 180°]

⇒66°-2z=180°

⇒66°-180°=2z

⇒z= -114°/2

⇒z= -57°

Answer:

a=646.84   c=113.04

Step-by-step explanation:

Answer: C

Step-by-step explanation:

Because there are two pairs of opposite parallel sides, it is a parallelogram.

Since the diagonals intersect at a right angle, the parallelogram is also a rhombus.

Answer:

2) x=5

4) 6y-3

Step-by-step explanation:

2) 2x-3=7

Add 3 on both sides (-3+3 cancel each other out and 7+3 is 10)

Now your equation is 2x=10

Divide 2 from both sides

2x/2 cancel each other and 10/2 is. Therefore, x=5

4) 3(2y-1)

3 times 2y is 6y

3 times -1 is -3 (negative times positive is negative)

Equation: 6y-3

Answer:

(-2, -1)

Step-by-step explanation:

The easiest way to approach this problem is to think of each quadrant as being 90 degrees. As you can see, each quadrant has a 90 degree angle.

If we were to move 2 quadrants (or 180 degrees) clockwise, we would end up in the third quadrant (- , -)

Because we are moving clockwise on the graph, the shape would also turn clockwise. 180 degrees is the halfway point, so the shape will appear to be upside down.

If you're a visual learner, I'd recommend finding a website with an online graph (something like desmos or geogebra) that would allow you to actually graph the points and change their position with commands.

Hope this helps :)

Answer: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Step-by-step explanation:

First, we can ensure that 12 is the median by putting it in the middle and putting the same amount of numbers to its left and right side. To make the values have a mean of 12, the easy why to do it is to subtrate one as you move to the left and add one as you move to the right, that way they will cancel each other out and keep the mean at 12. The answer has a total of 11 values, has more than 3 values that are different, and has a mean and median of 12.

7+8+9+10+11+12+13+14+15+16+17=132

132/11=12

There are 5 values to each side of 12, making 12 the median.

The value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given that;

First, we square both sides

√( 1 + (25/144) ) = 1 + (x/12)

(√( 1 + (25/144) ))² = (1 + (x/12))²

1 + (25/144) = 1 + ( x²/144)

Collect like terms

1 - 1 + (25/144) = ( x²/144)

25/144 = x²/144

We cross multiply

25 × 144 = x² × 144

Multiply each sides by 1/144

x² = 25

x = √25

x = 5

Therefore, the value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

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Answer:

First option

Step-by-step explanation:

The result of first expression:

7(6+z) multiply 7 with inside the parenthesis

7(6+z) = 42 + 7z

the result of second expression:

since we need to do multiplying first,

7*6 = 42 and 7*z = 7z

then we add them

42 + 7z this is the same result we found for the first equation

Answer:

b

Step-by-step explanation:

the answer is b if values are plugged in to function

Answer:

y = -(x - 2)² - 4

Step-by-step explanation:

The vertex form an equation is given as :

Substitute any point in the table to find a :

Hence, the final equation :

Answer:

Keen

Step-by-step explanation:

Favorite shoe brand = Keen

Answer:

Nike

Step-by-step explanation:

Nike shoes are great and comfy

Answer:

18

Step-by-step explanation:

[tex]184 \times 3 = 59 \div 2 = \times \frac{?}{?} [/tex]