What is the solution​

Answer:

The equation that represents the new path is y=(1/2)x-2

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=-2x-7

so

the slope m is equal to

m=-2

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=-2 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=1/2

step 3

With m=1/2 and the point (-2,-3) find the equation of the line

y-y1=m(x-x1)

substitute

y+3=(1/2)(x+2)

y=(1/2)x+1-3

y=(1/2)x-2 -----> equation that represent the new path

Answer:

Y= 1/2x-2

Step-by-step explanation:

Apex

Hope this helps Have a nice day

To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance. Using the given angle of depression of 27° and height of 365 feet, we can calculate that the bear is approximately 632 feet from the base of the waterfall.

To find the distance from the bear to the base of the waterfall, we can use the tangent function, which relates the angle of depression to the distance.

In this case, we have an angle of depression of 27° and a height of 365 feet.

Let's denote the distance we're trying to find as x.

The tangent of the angle of depression is equal to the opposite side (365 feet) divided by the adjacent side (x).

So we can set up the equation tan(27°) = 365/x and solve for x.

Rearranging the equation, we have x = 365/tan(27°). Plugging in the values and using a calculator, we find that x is approximately 632 feet.

The bear is approximately 717 feet away from the base of the waterfall.

To find out how far the bear is from the base of the waterfall, use trigonometry, specifically the tangent of the angle of depression. Tangent relates the opposite side and the adjacent side in a right triangle.
1. Given Information:
  - Height of the waterfall (opposite side), h = 365 feet.
  - Angle of depression, [tex]\( \theta = 27\textdegree[/tex].
2. Formulate the Tangent Function:
  The tangent of an angle in a right triangle is given by [tex]\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)[/tex].
  So in our case, [tex]\( \tan(27\textdegree) = \frac{365}{d} \)[/tex].
3. Solving for d (the distance from the base of the waterfall to the bear):  
  Rearranging for d:  
  [tex]\[ d = \frac{365}{\tan(27\textdegree)} \][/tex]
4. Calculate the Value:
  Using a calculator to find [tex]tan(27\textdegree)[/tex] which is approximately 0.5095.  
  [tex]\[ d = \frac{365}{0.5095} \approx 716.5 \text{ feet} \][/tex]
5. Round to the Nearest Foot:  
  [tex]\[ d \approx 717 \text{ feet} \][/tex]
So, the distance between the bear and base of the waterfall is approximately 717 feet.

Answer:

vertex = (2, 1)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 2)² + 1 ← is in vertex form

with vertex = (h, k) = (2, 1 )

If you know Heron's formula, this is easy.

[tex]\text{area}=\sqrt{s(s-6)(s-10)(s-14)}=15\sqrt3[/tex]

where [tex]s=\dfrac{6+10+14}2=15[/tex] is the semiperimeter of the triangle.

The area is also equal to half the product of the base and height of the triangle, which happen to be

[tex]15\sqrt3=\dfrac{14x}2\implies x=\dfrac{15\sqrt3}7\approx3.711[/tex]

so the answer is B.

Answer:

The perfect square of 3*4 is 9*16

Step-by-step explanation:

A perfect square is a number that can be expressed as the product of two equal integers.

For example 64 is a perfect square because if we multiply 8 two times we will get 64.

Thus the given expression is 3 * 4.

To find perfect square we square the numbers:

3² = 3*3 = 9

4² = 4*4 = 16

Thus the perfect square of 3*4 is 9*16 ....

Answer:

[tex]9x^8[/tex]

Step-by-step explanation:

We need to find perfect square of the root [tex]3x^{4}[/tex]

To find the perfect square, we need to square the root  [tex]3x^{4}[/tex]

[tex](3x^{4})^2[/tex]

Now let's use  exponent power rule and simplify.

[tex](a^{m})^n = a^{mn}[/tex]

= [tex]3^2x^{4*2} = 9x^8[/tex]

Therefore, [tex]9x^8[/tex] is perfect square of the root [tex]3x^4.[/tex]

Answer:

f(x)=-3x+4

Step-by-step explanation:

We need to solve for y.

9x+3y=12

Subtract 9x on both sides.

3y=-9x+12

Divided both sides by 3.

y=-3x+4

Replace y with f(x).

f(x)=-3x+4

Answer:

[tex]f(x)=-3x+4[/tex]

Step-by-step explanation:

the function represented by [tex]9x + 3y = 12[/tex]

To write the given equation in f(x), we need to solve for y

Lets solve the given equation for y

[tex]9x + 3y = 12[/tex]

Subtract 9x from both sides

[tex]3y =-9x+12[/tex]

Now divide whole equation by 3, divide each term by 3

[tex]y =-3x+4[/tex]

To write it as a function , finally we replace y with f(x)

[tex]f(x)=-3x+4[/tex]

its given if already with all the dashes and circle thingys so it's A I'm quite sure

Reflexive property and transitive property.

The answer is option D.

In algebra, the reflexive assets of equality state that a number is continually the same as itself. Reflexive belongings of equality. If a is various, then. a = a.

In math, if A=B and B=C, then A=C. So, if A=5 for instance, then B and C should both also be five with the aid of the transitive property. That is actually—a foundational property of—math because numbers are constant and both facets of the equals signal need to be equal, by definition.

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Answer

2(10 - √10)  or 13.68 to the nearest hundredth.

Step-by-step explanation:

(√5 + √2)^2 + (√8 - √5)^2

= 5 + 2 + 2√5√2 + (8 + 5 - 2√8√5)

= 7 + 2√10 + 13 - 2√40

= 20  + 2√10 - 2√40

=  20 + 2√10 - 4√10

= 20 - 2√10

= 2(10 - √10).

Answer:

U' = (-4,-5)

V' = (-6,-2)

Step-by-step explanation:

Vertex U has coordinates

U = (-4,5)

Vertex V has coordinates

V = (-6,2)

When a quadrilateral is reflected across x- axis the sign of x coordinate remains same and sign of y coordinate changes.

So, U= (-4,5)

then U' is:

U' = (-4,-5)

V = (-6,2)

then V' is

V' = (-6,-2)

Answer:

(-4, -5) and V' is at (-6, -2)

Answer:

Arranging  the sum and differences in increasing order of their values.

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

Step-by-step explanation:

Population of United States: 3.16 X 10^8

Population of Brazil : 1.96 X 10^8

Population of Germany: 8 X 10^7

a) the difference of  the populations  of Germany and  Brazil

Difference of  the populations  of Germany and  Brazil =  1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8

b) the sum of the  populations of  the United States  and Brazil

Sum of the  populations of  the United States  and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8

c) the difference of  the populations  of Brazil and the  United States

Difference of  the populations  of Brazil and the  United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8

d) the sum of the  populations of  Brazil and  Germany

Sum of the  populations of  Brazil and  Germany:  1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8

Arranging  the sum and differences in increasing order of their values.

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

Answer:

A

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y )

Hence

F(- 2, - 1 ) → F'(- 2, 1 )

G(2, 2 ) → G'( 2, - 2 )

H(4, - 3 ) → H'(4, 3 )

Answer:

Step-by-step explanation:

[tex]25x^2-16=5^2x^2-4^2=(5x)^2-4^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(5x-4)(5x+4)[/tex]

The correct product which is equivalent to 25x² - 16 is,

⇒ (5x + 4) (5x - 4)

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 25x² - 16

Now, We can simplify as;

⇒ 25x² - 16

⇒ (5x)² - 4²

⇒ (5x + 4) (5x - 4)

Thus, The correct product which is equivalent to 25x² - 16 is,

⇒ (5x + 4) (5x - 4)

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Answer:

17(21) - 14(20) = 357 - 280 = 77 ft²

The correct answer is I.

Answer:

5x^3 +2x -1

Step-by-step explanation:

f(x)=5x^3-2 and g(x) = 2x+1

(f+g)(x) = 5x^3-2 + 2x+1

Combine like terms

           = 5x^3 +2x -1

Answer:

I found the image of this problem. Its side measure is 13.  The octagon can form 8 triangles. Its apothem can serve as the height of the triangle. We need to get the area of the triangle and multiply it by 8. We then deduct the area of the square from the total area.

Area of a triangle = (height * base) / 2

A = (15.69 * 13) / 2

A = 203.97 / 2  

A = 101.985 sq. units

101.985 x 8 = 815.88 sq. units

Area of the square = s²

A = 13²

A = 169 sq. unit

Area of the shaded region: 815.88 sq. unit - 169 sq. unit = 646.88 sq. unit

Step-by-step explanation:

Answer:

456+56+54+4+4

Step-by-step explanation:

65+465+5+56

sorry, for the 4 items i got it wrong.

5 items: 1 dog bone, 3 water bowls, 1 collar

2 items: 1 box of dog food, 1 collar

The value of x from the given algebraic expression Ax + By = −C would be x = (-C - By)/ A.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

In order to solve x, if we isolate the x variable from the rest of the other variables.

Given algebric expression;

Ax + By = -C

1. Subtract By from the right side

Ax + By -By = -C -By

Ax = -C - By

2. Divide A

x = (-C - By)/ A

Hence, The value of x from the given algebraic expression Ax + By = −C would be x = (-C - By)/ A.

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Answer:

Option 90°

Step-by-step explanation:

AB is the perpendicular bisector of XY

The result of intersection will give 4 right angles

So,the measure of the angle of intersection when AB is the perpendicular bisector of XY = 90°

See the attached figure.

Answer:

1 31/36 is your answer

Step-by-step explanation:

Find common denominators. Note that what you do to the denominator, you must do to the numerator;

(-7/18)(2/2) = (-14/36)

(-9/4)(9/9) = (-81/36)

Combine the terms:

(-14/36) - (-81/36)

Note that two negative signs directly next to each other equals a positive sign.

(-14/36) + 81/36

-14/36 + 81/36

(-14 + 81)/36

Combine like terms. Solve the parenthesis:

(67)/36

Change to a mixed fraction:

(67/36) = 1 31/36

1 31/36 is your answer.

~

Answer:

y-intercept of y=4x-3 is -3

Step-by-step explanation:

The given equation is:

y = 4x -3

The equation is in slope-intercept form.

The standard equation of slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept

So, comparing the given equation with the standard equation the y-intercept is -3

y-intercept of y=4x-3 is -3

Answer:

Step-by-step explanation:

The y intercept of any equation that is a function is the y value taken on when x = 0

So in this case it is y = - 3 because 4*0 = 0. All that is left for y is y = -3.

The point of interception is (0.-3). The way to confirm many answers is to graph the point.

Answer:

y - 1 = (1/3)(x + 1)

Step-by-step explanation:

Look carefully at (0, -3) and (2, 3).  As we move from the first to the second, x increases by 2 (from 0 to 2) and y increases by 6 (from -3 to 3).  Therefore, the slope of this line is m  = rise / run, or m = 6/2, or m = 1/3.  Both lines have the same slope, 1/3, because they are parallel.

Now let's apply the point-slope form of the equation of a straight line.  Here the point in question is (-1, 1) and the slope is 1/3.  Therefore, we have:

y - 1 = (1/3)(x + 1)

Answer:

Step-by-step explanation:

Answer:

m = 50

Step-by-step explanation:

Simplify:

9 + m/5 = 19

9 + 1/5m = 19

1/5m + 9 = 19

Subtract 9 from both sides:

1/5m + 9 - 9 = 19 - 9

1/5m = 10

Multiply both sides by 5:

5 ⋅ ( 1/5m ) = ( 5 ) ⋅ (10)

Answer:

Step-by-step explanation:

[tex]y=-3x-9\qquad(1)\\\\y=\dfrac{1}{3}x-39\qquad(2)\\\\\text{Substitute (1) to (2)}\\\\-3x-9=\dfrac{1}{3}x-39\qquad\text{multiply both sides by 3}\\\\-9x-27=x-117\qquad\text{add 27 to both sides}\\\\-9x=x-90\qquad\text{subtract}\ x\ \text{from both sides}\\\\-10x=-90\qquad\text{divide both sides by (-10)}\\\\x=9[/tex]

[tex]\text{Put the value of x to (1):}\\\\y=-3(9)-9\\\\y=-27-9\\\\y=-36[/tex]

Answer:

It is A

Step-by-step explanation:

Answer:

(2/3)n(n+1)(2n+1)

Step-by-step explanation:

First you have to find the general term formula which is here (2k)^2 which is equal to 4k^2. Sum(k=1 to n) of 4k^2=4•n(n+1)(2n+1)/6

simplified to (2/3)n(n+1)(2n+1)

[tex]\large\boxed{9\,\text{boys and}\,12\,\text{girls}}[/tex]

In this question, we're trying to find how many boys and girls are in the class.

Lets get some important information that will help us to answer the question:

Important information:

With the information above, we can solve the question.

To make this easier, we could turn the fractions into percents.

[tex]3/7 = 0.42857\,\, \text{or}\,\, 0.43 = 43\%\,\, \text{This is for boys}\\\\4/7 = 0.571428\,\, \text{or}\,\, 0.57 = 57\%\,\, \text{This is for girls}[/tex]

Now, we could just multiply 21 by the right decimal in order to get the right amount of boys and girls in Mrs. Clark's classroom.

[tex]21 *0.43=9\,\,\text{boys}\\\\21*0.53=12\,\,\text{girls}[/tex]

When you solve, you would figure out that there are 9 boys and 12 girls in Mrs. Clark's class.

Answer:

see below

Step-by-step explanation:

Take the 4 lb container.  Pour out rice and fill the 3 lbs container.  What is left in the 4 lb container is 1 lb  (4-3 =1)

Empty the 3 lbs container and put the 1lbs into it

Now measure rice into the 4 lbs container

We  have 1lbs ( in the 3lbs container)

and 4 lbs ( in the 4 lbs container)

for a total of 5 bs

Answer:

Option A. ∠ECB=25°

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

∠ECB=(1/2)[arc DB-arc EB]

substitute the given values

(x+10)°=(1/2)[146°-(6x+6)°]

solve for x

2x+20=140-6x

2x+6x=140-20

8x=120

x=15

Find the measure of angle ECB

∠ECB=x+10=15+10=25°

Answer:

25

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The correct option is A.

According to the given statement:

Average of 20 numbers= 0.

So we have avg = sum/20.

That implies sum = 0.

Hence at the most, there can be 19 positive numbers.  

(Such that if the sum of these 19 positive numbers is x, 20th number will be -x)....

Answer:

D. The minimum y-value of g(x) approaches -3

Step-by-step explanation:

Form a table for values of x with corresponding values for f(x) and g(x)

x                   f(x)=3x²-3                                         g(x)=2^x -3                          

-3                   =3(-3²)-3=24                                       2⁻³ -3 = -2.88

-2                    =3(-2²)-3=9                                        2⁻² -3 = -2.75

-1                     =3(-1²)-3=0                                         2⁻¹-3 = -2.5

0                      =3(0²)-3= -3                                        2⁰ -3 = -2

1                       =3(1²)-3=0                                           2¹ -3 = -1

2                      =3(2²)-3=9                                          2²- 3 = 1

3                     =3(3²)-3=24                                          2³ -3= 5

From the table above, you can see the minimum value of y in g(x)  -2.88 approaches -3