Simplify 7 to the 6th power ⋅ 7 to the fifth power.

49 to the 11th power
49 to the 35th power
7 to the 11th power
7 to the 35th power

Answer:

Let s be the son’s current age and d be the daughter’s current age. The system of equations is:

s - 10 = 2(d - 10)

s = 3 + d

Since s is already set to an equation, we can use the substitution method for s in the other equation:

s = 3 + d

s - 10 = 2(d - 10)

3 + d - 10 = 2(d - 10)

Simplify and solve for d:

3 + d - 10 = 2(d - 10)

-7 + d = 2d - 20

-7 = d - 20

13 = d

The daughter is 13 years old. To solve for the son’s age, we will plug in the solution for d into one of the equations. The second one is simpler so we will use that:

s = 3 + d

s = 3 + 13

s = 16

The son is 16 years old. Let us use the other equation to check our solutions:

s - 10 = 2(d - 10)

16 - 10 = 2(13 - 10)

6 = 2(3)

6 = 6

It checks out. The son is 16 years old, and the daughter is 13 years old.

The present age of the daughter and son are 14 and 10 years respectively.

Let the age of the daughter be x

Let the age of the son be y

If the daughter's age is 4 years more than the son's age now, then,

x = y + 4 ............. 1

If Eight years ago, the daughters' age was thrice the son's age, then;

Daughter = x - 8

Son  = y - 8

Hence, x - 8 =3(y - 8).................. 2

Substitute equation 1 into 2 to have:

x - 8 =3(y - 8).

y + 4 - 8 = 3(y - 8)

y - 4 = 3y - 24

y - 3y = -20

-2y = -20

y = 10

Recall that x = y + 4

x = 10 + 4

x = 14

Hence the present age of the daughter and son are 14 and 10 years respectively.

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Answer:

Step-by-step explanation:

Notice that

• π/2 = π/3 + π/6

• π/6 = π/3 - π/6

Recall the angle sum identities for sine:

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

By adding these together, we get

sin(x + y) + sin(x - y) = 2 sin(x) cos(y)

==>   sin(x) cos(y) = 1/2 (sin(x + y) + sin(x - y))

Now take x = π/3 and y = π/6 :

sin(π/3) cos(π/6) = 1/2 (sin(π/2) + sin(π/6))

So the blank should be filled with cos.

Answer:

Step-by-step explanation:

Answer:

The first one.

Step-by-step explanation:

Graph lines as if the inequalities were equal signs.

X = -3 is a vertical line at x = -3, because it's less than we shade to the left. All numbers less than -3 are to the left. The line is dashed because there is no equal to. Only less than. The line is not included in the solution set.

y = -x - 1 is a line with a y-intercept of -1 and a slope of -1. All values that are less that y are below the line. Because it's less than or equal to the line is solid.

Answer:

A

Step-by-step explanation:

The vertical line  is dotted at -3 and shaded to the left

x < -3

This gives us two choices left

A and C

The other line has a y intercept at -1 and is solid and shaded to the left

It is of the form

y ≤ mx+1  

We know the slope is negative since is goes down from left to right

The only Choice is A

Answer:

Yes, both stores will be congruent

Step-by-step explanation:

The given coordinates of the vertices of the home improvement store are;

(-x₁, y₁), (-x₂, y₂), (-x₃, y₃) and (-x₄, y₄)

The coordinates of the vertices of the clothing store are;

(x₁, y₁), (x₂, y₂), (x₃, y₃) and (x₄, y₄)

Therefore, the coordinates of the vertices of the home improvement store, corresponds to the coordinates of the vertices of the image of the reflection of the clothing store across the sidewalk (which is the y-axis)

A reflection of (x, y) across the y-axis gives (-x, y)

Given that a reflection is a rigid transformation, the dimensions (lengths and angles between corresponding sides) of the home improvement store and the clothing store are equal, therefore, the home improvement store will be congruent to the clothing store.

Answer:  yes, because the home improvement store is a reflection of the clothing store.

Step-by-step explanation:

Imagine math!!!

Step-by-step explanation:

Hey there!

Please see attached picture for your answer!

Hope it helps!

Answer is in the attachment.

note:

make a slight change in question 1;

Answer:

= -2i + 3

Step-by-step explanation:

3+i/2-i * 4+i/2+i

Group like terms

= i/2 + i/2 - 4i + i + 3

Combine the fractions i/2 + i/2: i

= i - 4i + i + 3

Add similar elements: i - 4i + i = -2i

= -2i + 3

Not enough information to solve..... Please make your question more clear

Answer:

252 ways

Step-by-step explanation:

The missing details are:

[tex]n = 10[/tex] --- total restaurants

[tex]r = 5[/tex] --- restaurants to visit

Required

The number of ways to perform the visitation

The question is an illustration of combination;

So, we have:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives:

[tex]^{10}C_5 = \frac{10!}{(10 - 5)!*5!}[/tex]

[tex]^{10}C_5 = \frac{10!}{5!*5!}[/tex]

Expand

[tex]^{10}C_5 = \frac{10*9*8*7*6*5!}{5!*5*4*3*2*1}[/tex]

Cancel out 5!

[tex]^{10}C_5 = \frac{10*9*8*7*6}{5*4*3*2*1}[/tex]

[tex]^{10}C_5 = \frac{30240}{120}[/tex]

[tex]^{10}C_5 = 252[/tex]

Answer:

Cost of Turkey per pound is $ 1.25 and Ham is $ 1.65.  

Step-by-step explanation:

Cindy:

cost of 12.3 pound Turkey and 11.7 pound Ham = $ 34.68

Samantha:

cost of 10.7 pound Turkey and 9.5 pound Ham = $ 29.05

Let the cost of one pound of Turkey is T and one pound of Ham is H.

So,

12.3 T + 11.7 H = 34.68 ..... (1)

10.7 T + 9.5 H = 29.05 ......(2)

Solve both these equations, we get

T = $ 1.25 and H =  $ 1.65

Step-by-step explanation:

sec²x + cosec²x = sec²x.cosec²x

1/cos²x + 1/sin²x = 1/cos²x.1/sin²x

or, (sin²x+cos²x)/sin²x.cos²x = 1/(sin²x.cos²x)

or, 1/(sin²x.cos²x) = 1/(sin²x.cos²x)

Hence,

sec²x + cosec²x = sec²x.cosec²x proved!!

Answer: y and x

Step-by-step explanation:

Answer:

For the First Question:

x = 61

y = 61

For the Second Question:

x = 12

y  = 7

Step-by-step explanation:

Second question:

96 = 11y + 19

11y = 77

y = 7

96 = 8x

x = 12

Step-by-step explanation:

hope it helps you........

Answer:

[tex]\sqrt{14^2 + 1^2} = \sqrt{197} = 14.03566885[/tex]

Step-by-step explanation:

Answer:

4 = x

Step-by-step explanation:

f(x) =2x

Let f(x) = 8

8 =2x

Divide each side by 2

8/2 = 2x/2

4 = x

Answer:

4

Step-by-step explanation:

f(x) = 2x

When f(x) = 8, x = 8/2 = 4.

Hope this helped,

~cloud

Answer:

(7, 13/3)

Step-by-step explanation:

Given the expressions

y = 1/3x + 2 and the second line y = 4/3x - 5

Equating both expressions

1/3x + 2 = 4/3x - 5

1/3x - 4/3x = -5 - 2

-3/3x = -7

-x = -7

x = 7

Substitute x = 7 into any of the equations

Using y = 1/3 x + 2

y = 1/3(7) + 2

y = 7/3 + 2

y = (7+6)/3

y = 13/3

Hence the solution to the system of the equation is (7, 13/3)

Answer:

(7,13/3) is your answer, otherwise known as answer choice B.

Step-by-step explanation:

Answer:

(-3,-6) and (-3,2)

Step-by-step explanation:

A line with an undefined slope is vertical. In this case it must have x coordinates equal to -3

Answer:

option 1

Step-by-step explanation:

y ≤ x - 2

-4 ≤ 2-0

-4 ≤ 2  Satisfies the inequality

y ≥ - x - 4

-4 ≥ - 2- 4

-4 ≥ - 6  (2 , -4) satisfies the inequality

Answer:

6x+8+4x+2=180

so!! 10x+10=180

10x=170

x=17

Answer:

[tex]x=17[/tex]

Step-by-step explanation:

The two angles labelled [tex]6x+8[/tex] and [tex]4x+2[/tex] are co-interior angles. When two parallel lines are cut by a traversal, co-interior angles are supplementary, meaning they add up to 180 degrees. Therefore, if line L is parallel to line M, [tex]6x+8[/tex] and [tex]4x+2[/tex] must be supplementary:

[tex]6x+8+4x+2=180[/tex]

Combine like terms:

[tex]10x+10=180[/tex]

Subtract 10 from both sides:

[tex]10x=170[/tex]

Divide both sides by 10:

[tex]x=\frac{170}{10}=\boxed{17}[/tex]

Answer:

I don't know how to do please let me I will try solve the question

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{3}{5}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{3}{5})²}[/tex]

[tex]Sin\theta_{1}=\sqrt{1-(\frac{9}{25})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{16}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*2*2}}{\sqrt{5*5}}[/tex]

[tex]Sin\theta_{1}=\frac{4}{5}[/tex]

Since

In IVquadrant sin angle is negative

[tex]\bold{Sin\theta_{1}=-\frac{4}{5}}[/tex]

Answer:

[tex]\sin(\theta_1)=-\frac{4}{5}[/tex]

Step-by-step explanation:

We'll use the Pythagorean Identity [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex] to solve this problem.

Subtract [tex]\cos^2(\theta)[/tex] from both sides to isolate [tex]\sin^2(\theta)[/tex]:

[tex]\sin^2(\theta)=1-\cos^2(\theta)[/tex]

Substitute [tex]\cos(\theta)=\frac{3}{5}[/tex] as given in the problem:

[tex]\sin^2(\theta_1)=1-(\frac{3}{5}^2)[/tex]

Simplify:

[tex]\sin^2\theta_1=1-\frac{9}{25}[/tex]

Combine like terms:

[tex]\sin^2\theta_1=\frac{16}{25}[/tex]

For [tex]a^2=b[/tex], we have two solutions [tex]a=\pm \sqrt{b}[/tex]:

[tex]\sin\theta_1=\pm \sqrt{\frac{16}{25}},\\\begin{cases}\sin \theta_1=\frac{4}{5},\\\sin \theta_1=\boxed{-\frac{4}{5}}\end{cases}[/tex]

Since the sine of all angles in quadrant four return a negative output, [tex]\frac{4}{5}[/tex] is extraneous and our answer is [tex]\boxed{\sin(\theta_1)=-\frac{4}{5}}[/tex]

Answer:

1

Step-by-step explanation:

The given equation of the function is y = -a·(x - h)² + 1

The positive constants of the equation = a, and h

The points the function crosses the x-axis = 2, and 4

Where the function crosses the x-axis, y = 0, and x = 2, and 4, therefore, when x = 2, we have;

y = 0 = -a·(2 - h)² + 1

When x = 4, we have;

0 = -a·(4 - h)² + 1

-a·(2 - h)² + 1 = -a·(4 - h)² + 1

-a·(2 - h)² = -a·(4 - h)²

(2 - h)² = (4 - h)²

±(2 - h) = +#±(4 - h)

When

(2 - h) is negative, and (4 - h) is positive, but the same magnitude, we have';

-(2 - h) = +(4 - h)

2·h = 4 + 2 = 6

h = 3

0 = -a·(4 - h)² + 1 = -a·(4 - 3)² + 1 = -a + 1

Therefore, a = 1

Answer:

y = + 1/2x -3

Step-by-step explanation:

x - 2y = 6

slope intercept form: y = mx + b

In order to put the given equation in slope intercept form we will need to isolate ( we can do this by solving algebraically ) y as seen in the equation shown above.

x - 2y = 6

Solve for y

Subtract x from both sides

x - x - 2y = 6 - x

-2y = 6 - x

Divide both sides by -2

-2y/-2 = (6 - x)/-2

y = -3 + 1/2x

* Swap -3 and 1/2x *

The equation in slope intercept form would be y = 1/2x - 3

Answer:

y = + x/2 +( - 3)

Step-by-step explanation:

make y the subject of the formula by placing x on the opposite side of y, which is right in this case, then divide every by negative two, then you'll get the answer that I've written.

Answer:

(12xy-6x -12y)

12xy-18xy

6xy

Answer:

- xy - x + 2y

Step-by-step explanation:

5x - 13xy + 14y + 12xy - 6x - 12y ← collect like terms

= (- 13xy + 12xy) + (5x - 6x) + (14y - 12y)

= - xy - x + 2y

Answer:

bka bla bla bla sorry I newbie

The sum of the interior angles of the 12-sided object without measuring the sides is 1800 degrees.

A polygon is a shape with 4 or more sides. Hence a 12-sided figure will be regarded as a polygon.

I will let them understand that the formula for calculating the sum of the interior angle of a regular polygon is expressed using the formula;

S = (n-2)*180 where:

n is the number of sides

Since we are considering a 12-sided object, then n = 12

The next thing is to tell them to substitute n = 12 into the formula given above as shown;

S = (12-2)*180

S = 10 * 180

S = 1800

This shows that the sum of the interior angles of the 12-sided object without measuring the sides is 1800 degrees.

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