At a point on the ground 60 Ft
from the base of a tree, the distance
to the top of the tree is 4 ft more
than 2 times the height of the tree.
Find the height of the tree in ft.​

Answer:

The line will be going 'uphill' from left to right

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

y=mx+b

where m is the slope

b is the y-intercept

If the coefficient of the x-term is positive

then

the slope is positive

therefore

If the values of x increases, the values of y increases

If the values of x decreases, the values of y decreases

The line will be going 'uphill' from left to right

Answer: the line slants up

Step-by-step explanation:

X being positive will cause a “ rise “ in the positive x,y plane.

The answer can be stated as "The solution to a system of two linear equations in two variables corresponds to the intersection of straight lines represented by them."

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

A system of linear equation in two variables can be written as,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂= 0

In order to find their solution these equations are solved either by substitution or elimination.

A linear equation in two variable represents a straight line.

Thus, the solution to these equations are the coordinates of the intersection point of these two lines.

Hence, the solution to a system of linear equation in two variables indicate the coordinate of their intersection.

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Answer:

the values of x, y and z are: x=8, y = -5 and z = -7

Step-by-step explanation:

2x+6y+4z=−42       eq(1)

4x+3y+8z=−39       eq(2)

4x+3y+2z=3          eq(3)

We would solve the above equations using elimination method.

Subtracting eq(3) from eq(2)

4x+3y+8z=−39      

4x+3y+2z=3

-   -     -       -

_____________

0+0+6z = -42

z = -42/6

z = -7

Multiplying eq(1) with 2 and subtracting with eq(2)

4x + 12y +8z = -84

4x +3y +8z = -39

-    -      -        +

_______________

0+9y+0=-45

9y = -45

y = -45/9

y = -5

Putting value of y and z in eq(1)

2x + 6y +4z = -42

2x + 6(-5) +4(-7) = -42

2x -30 -28 = -42

2x -58 = -42

2x = -42 +58

2x = 16

x = 16/2

x= 8

So, the values of x, y and z are: x=8, y = -5 and z = -7

Find the volume of a cylinder, we need to follow the formula:

Volume = πr2h

Following the formula, we substitute for:

π×82×10

π=3.14, so we multiply it:

= 640π

= 2010.6192982975 feet3

Answer:

Here's what I get.

Step-by-step explanation:

[tex]x = 7\frac{1}{2} \div \frac{3}{4}[/tex]

1. Convert the mixed number to an improper fraction

[tex]x = \dfrac{15}{2} \div \dfrac{3}{4}[/tex]

2. Invert the proper fraction and change division to multiplication

[tex]x = \dfrac{15}{2} \times \dfrac{4}{3}[/tex]

3. Multiply numerators and denominators

[tex]x = \dfrac{60}{6}[/tex]

4. Divide the numerator and the denominator

[tex]x = 10[/tex]

The quotient is what you get after you invert the denominator in Step 2 and then multiply the two fractions in Step 3.

Here I'm assuming 7 1/2 / 3/4 is  [tex]7\frac{1}{2} / \frac{3}{4}[/tex]

So let's solve, this first convert the mixed fraction into an improper fraction that is its ideal form to solve an equation

[tex]7\frac{1}{2} = \frac{15}{2}[/tex]

therefore,

= [tex]\frac{15}{2} /\frac{3}{4}[/tex]

= [tex]\frac{15}{2} * \frac{4}{3}[/tex]

= 5 * 2

= 10

A mixed fraction is a combination of a whole number and proper fraction.

Improper fractions and proper fractions are the types of fraction numbers (A fraction number which is written in the form of a/b i.e., " [tex]\frac{a}{b}[/tex] " in which a is called as numerator and b is denominator). A fraction is called improper fraction when its numerator is greater than its denominator and for proper fraction, it's vice versa.

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5 sqrt 3i is the correct answer

Answer: b) √108

c√18.√6

e)√3.√36

Step-by-step explanation:

We know that, for example, √4 = √2² = 2

As the index of the number inside the root maches the index of the root, we can remove it from the root.

And the inverse process is also correct, so 2 can be written as

√2² = √4, this way:

6√3 = √3.√6² = √3.√36 = √108

a) √54 ≠ √108

b) √108 = √108 ok

c) √18.√6 = √108 ok

d) √3.√6 = √18 ≠ √108

e) √3.√36 = √108 ok

f) 108 ≠ √108

Answer:

Dist = 45 m/h * x h

Step-by-step explanation:

We know a speed is a measure of distance over time:  speed = dist / time

In this case, we are looking for a distance expressed in terms of time.

So, we only need to modify the formula a bit: dist = speed * time

We don't know the time (which will be a variable), but we know their speed.  So, the formula becomes:

Dist = 45 m/h * x h

Enter the number of hours in the formula and that will give you an approximation of the distance traveled within that time (approximation since our result will be rely on an average).

Answer:

5/6

Step-by-step explanation:

Dividing fractions:

Step 1: Rewrite the first fraction as it is.

Step 2: Replace the division sign with a multiplication sign.

Step 3: Flip the second fraction.

Step 4: Multiply the fractions and reduce the product if necessary.

Let's use the rule of dividing fractions on your problem.

Step 1: Rewrite the first fraction as it is.

[tex] \dfrac{5}{8} [/tex]

Step 2: Replace the division sign with a multiplication sign.

[tex] \dfrac{5}{8} \times [/tex]

Step 3: Flip the second fraction.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} [/tex]

Step 4: Multiply the fractions and reduce the product if necessary.

To multiply fractions, multiply the numerators together, and multiply the denominators together.

[tex] \dfrac{5}{8} \times \dfrac{4}{3} = \dfrac{5 \times 4}{8 \times 3} = \dfrac{20}{24} [/tex]

We notice that the greatest common factor of 20 and 24 is 4, so we divide both the numerator and denominator by 4 to reduce the fraction.

[tex] = \dfrac{4 \times 5}{4 \times 6} = \dfrac{5}{6} [/tex]

Answer:

The volume of the cylinder is 150.72 cm³ ⇒ last answer

The volume of the cone is 314 cm³ ⇒ 1st answer

The volume of the pyramid is 160 cm³ ⇒ 2nd answer

The volume of the pyramid is 48 cm³ ⇒ 3rd answer

Step-by-step explanation:

* Lets revise the volumes of some shapes

- The volume of the cylinder of radius r and height h is:

 V = π r² h

- The volume of the cone of radius r and height h is:

 V = 1/3 π r² h

- The volume of the pyramid is:

 V = 1/3 × its base area × its height

* Lets solve the problem

# A cylinder with radius 4 cm and height 3 cm

∵ V = π r² h

∵ π = 3.14

∵ r = 4 cm , h = 3 cm

∴ v = 3.14 (4)² (3) = 150.72 cm³

* The volume of the cylinder is 150.72 cm³

# A cone with radius 5 cm and height 12 cm

∵ V = 1/3 π r² h

∵ π = 3.14

∵ r = 5 cm , h = 12 cm

∴ V = 1/3 (3.14) (5)² (12) = 314 cm³

* The volume of the cone is 314 cm³

# A pyramid with base area 16 cm² and height 30 cm

∵  V = 1/3 × its base area × its height

∵ The area of the base is 16 cm²

∵ The height = 30 cm

∴ V = 1/3 (16) (30) = 160 cm³

* The volume of the pyramid is 160 cm³

# A pyramid with square base of length 3 cm and height 16 cm

∵  V = 1/3 × its base area × its height

∵ The area of the square = s²

∵ The area of the base = 3² = 9 cm²

∵ The height = 16 cm

∴ V = 1/3 (9) (16) = 48 cm³

* The volume of the pyramid is 48 cm³

a right cylinder with radius 4 cm

and height 3 cm = 150.72 cu cm

a pyramid with base area

16 sq cm and height 30 cm = 160 cu cm

a pyramid with a square base of

length 3 cm and height 16 cm  = 48 cu cm

a cone with radius 5 cm and

height 12 cm = 314 cu cm

Answer: Bottom Graph

Step-by-step explanation: An easy way to eliminate answers is to plug in 0 for x and see if the y-intercept is accurate. If we plug in 0 for x we get -1, which is the y-int for the bottom graph, but not the top graph, therefore the bottom graph is correct.

The graph of (x + 1)^(1/3) - 2 is option B.

A function is a mathematical expression, rule, or law that specifies the relationship between one variable (the dependent variable) and another variable (the independent variable).

Function given in the question = (x + 1)^(1/3) - 2

Initial function for this is f(x) = x^(1/3)

The changes done in the question is f(x + 1) - 2

Hence the graph of  x^(1/3) will go one unit to the left on the X-axis and two units down on the Y-axis.

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Answer:

m<5 = 45 deg

Step-by-step explanation:

Since lines g and h are parallel, you have a transversal cutting parallel lines. Then, corresponding angles are congruent.

Angles 1 and 5 are corresponding angles, so they are congruent, and their measures are equal.

m<5 = m<1 = 45 deg.

Angles 5 and 8 are vertical angles, so they are congruent, and their measures are equal.

m<8 = m<5 = 45 deg

Answer: m<5 = 45 deg

Answer:

4x^2 - 12x + 9

Step-by-step explanation:

Please use " ^ " to denote exponentiation:  4x^2 - 12x + 9.

This 4x^2 - 12x + 9 factors into (2x - 3)^2, and is thus a perfect square trinomial.

The polynomial [tex]4x^2-12x + 9[/tex] is a perfect square trinomial. It has a binomial factor (2x - 3).

The product of a binomial by itself gives the perfect square trinomial.

A trinomial is a polynomial that has only three terms and A binomial is a polynomial that has only two terms.

A. Trinomial  [tex]4x^2-12x+9[/tex]

⇒ [tex](2x)^2-2(2x)(3)+(3)^2[/tex]

This is in the form of [tex]a^2-2ab+b^2[/tex] . So, we can write [tex](a - b)^2[/tex]

⇒ [tex](2x - 3)^2[/tex] or (2x - 3)(2x - 3)

Thus, this is a perfect square trinomial.

B. Trinomial [tex]16x^2+24x-9[/tex]

⇒ [tex](4x)^2+2(4x)(3)-(3)^2[/tex]

Since it cannot split into a binomial square, this trinomial is not a perfect square trinomial.

C. Trinomial [tex]4a^2-10a+25[/tex]

⇒ (2a)^2-2(5a)+(5)^2

This cannot be split into a binomial square, this is not a perfect square trinomial.

D. Trinomial [tex]36b^2-24b-16[/tex]

⇒ [tex](6b)^2-2(6b)(2)-(4)^2[/tex]

So, this is not a perfect square trinomial.

Therefore, the trinomial at option A is a perfect square trinomial.

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Answer:

19.25 tons = 38500 lbs

Step-by-step explanation:

We are to convert the following given amount of tons in pounds.

We know that, 1 ton = 2000 pounds. So using the ration method, we can convert 19.25 tons into pounds.

[tex]\frac{1 ton}{19.25 tons} =\frac{2000 lbs}{x}[/tex]

[tex] x = 2 0 0 0 \times 1 9 . 2 5 [/tex]

[tex] x = 3 8 5 0 0 lbs[/tex]

Therefore, 19.25 tons = 38500 lbs.

Answer: [tex]38,500\ lbs[/tex]

Step-by-step explanation:

In order to answer the question, it is necessary to make the corresponding conversion from 19.29 tons (t) to pounds (lbs).

Then, for this conversion it is important to remember that:

[tex]1\ t=2,000\ lbs[/tex]

Finally, knowing this, you can make the conversion:

[tex](19.25\ t)(\frac{2,000\ lbs}{1\ t})=38,500\ lbs[/tex]

Therefore, you get this result:

[tex]19.25\ t=38,500\ lbs[/tex]

[tex]m^{24}n^{18}[/tex]

We can distribute the terms using the distributive property first. [tex](m^4)^6 * (n^3)^6[/tex]

Then, use the power of a power property to multiply the powers. [tex]m^{4*6} * n^{3*6} = m^{24}n^{18}[/tex]

Answer:

The correct option is B) zero x = -2.

Step-by-step explanation:

Consider the provided graph y = x + 2

The zeros of a function are the point on which graph intersects the x axis or we can say the value of x when y = 0.

Substitute y = 0 in the provided equation.

0 = x + 2

x = -2

The coordinate is (-2,0). Also the zero of the graph is at x = -2 because it follows the definition of zeros.

Now substitute x = 0 in the provided equation.

y = 0 + 2

y = 2

The coordinate is (0,2).

Now, draw a line passing through the point (-2,0) and (0,2).

The required line is shown in figure 1.

Now consider the provided options only option A and B have the same graph.

But the correct option is B as the zero of the option B is x = -2.

Hence, the correct option is B) zero x = -2.

Explanation of graphing y=x+2 and finding its zero. Find the correct graph and x-intercept.

Graph: First, graph the equation y = x + 2. This is a straight line with a slope of 1 (rise of 1, run of 1) and y-intercept at 2.

Zero of the function: To find the zero of the function (where y = 0), set x + 2 = 0 and solve for x. In this case, x = -2.

Answer:

Number One

Step-by-step explanation:

This is because a natural number is a positive integer so it can't be 2,3,or 4 so the only other option is 1!!

Answer:

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]  and Width [tex]16.5\ ft[/tex]

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y ---> the width of the rectangular garden

Aw ----> the area of the walkway

we know that

[tex]x=y+9[/tex] ----> equation A

[tex]Aw=(x+8)(y+8)-xy[/tex]

[tex]Aw=400\ ft^{2}[/tex]

so

[tex]400=(x+8)(y+8)-xy\\400=xy+8x+8y+64-xy[/tex]

[tex]400=8x+8y+64[/tex] ----> equation B

Substitute equation A in equation B

[tex]400=8(y+9)+8y+64[/tex]

[tex]400=8y+72+8y+64[/tex]

[tex]400=16y+136[/tex]

[tex]16y=400-136[/tex]

[tex]y=16.5\ ft[/tex]

Find the value of x

[tex]x=16.5+9=25.5\ ft[/tex]

therefore

The dimensions of the garden are

Length [tex]25.5\ ft[/tex]

Width [tex]16.5\ ft[/tex]

Answer:

C

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = 2x + 3 + x² - 8 ← collect like terms

               = x² + 2x - 5 ← in standard form → C

Answer:

Third option

Step-by-step explanation:

By observing the diagram we can see that the diameter of circular base is 6 inches. The diameter will be sued to find the radius.

r = 6/2 = 3 inches

We can also see from the diagram that lateral height denoted by l is 5 in.

We know that the formula for surface area of a cone is given by:

[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\ of\ r\ and \l\\SA = \pi (3)(5)+\pi (3)^2[/tex]

Comparing it with the options we get that the third option is correct ..

Answer:

The correct answer is third option

 π(3)(5) + π3²

Step-by-step explanation:

Points to remember

Surface area of cone = πrl + πr²

Where r is the radius of the cone and l is the slant height of cone

To find the correct answer

Here r = 6/2 = 3 in

l = 5 in

Surface area =  πrl + πr²

 =  π(3)(5) + π3²

The correct answer is third option

 π(3)(5) + π3²

Answer:

f^-1 (x) = 2x+20

Step-by-step explanation:

f(x) = 1/2x – 10

To find the inverse, replace f(x) with y

y = 1/2 x -10

Exchange x and y

x = 1/2 y- 10

Solve for y

Add 10 to each side

x+10 = 1/2 y-10+10

x+10 = 1/2 y

Multiply by 2

2(x+10) = 1/2y *2

2x+20 = y

The inverse is

f^-1 (x) = 2x+20

Answer:

x=2

Step-by-step explanation:

y = x^2 -4x-8

This is in the form y = ax^2 + bx +c

The axis of symmetry, h is found by h=-b/2a

We know a = 1, b=-4

h = -(-4)/ (2*1)

  =4/2

  =2

The axis of symmetry is x=2

Final answer:

To calculate the area of triangle ABC with sides measuring 8, 11, and 15 units, Heron's formula is used. The semiperimeter s is 17 units, which leads to an area of the square root of 1836 or approximately 42.8 square units.

Explanation:

To find the area of triangle ABC with sides a = 8, b = 11, and c = 15, we can use Heron's formula, which is a method of finding the area of a triangle when you know the lengths of all three sides. The formula states that the area of a triangle is the square root of s(s-a)(s-b)(s-c) where s is the semiperimeter of the triangle, or half of the triangle's perimeter. First, we calculate the semiperimeter: s = (a + b + c) / 2. Then, we substitute the values of a, b, and c into the formula to find the area.

The semiperimeter s is (8 + 11 + 15) / 2 which equals 17. Using Heron's formula, the area is the square root of 17(17-8)(17-11)(17-15). Therefore, the area of triangle ABC is equal to the square root of 17  imes 9  imes 6  imes 2, which simplifies to the square root of 1836, resulting in an area of 42.8 square units.

Answer:

The answer to this problem is 22.

Step-by-step explanation:

To solve this problem, we simply need to plug in the values given for a and b into the expression given and simplify.

We are given that a=3 and b=4, thus, these are the numbers we will plug in before we simplify.

2a^2 + b =

2(3)^2 + 4

Next, we should follow the rules of PEMDAS.  This tells us that we should solve the parentheses first, but since there are no parentheses, we can move onto exponents.

If we simplify, we get:

2(9) + 4

Next, we should perform the multiplication.

18 + 4

Finally, we can add together the remaining terms.

18 + 4 = 22

Therefore, your answer is 22.

Hope this helps!

2[tex]a^{2} + b[/tex]

First you must substitute a and b for the corresponding values:

a = 3

b = 4

so...

2*[tex]3^{2}[/tex] + 4

Now you must evaluate using the rules of PEMDAS (Parentheses, Exponent, Multiply, Divide, Add, Subtract)

There are no parentheses so skip that step and go on to the next one, exponent, which is [tex]3^{2}[/tex]

[tex]3^{2}[/tex] = 3*3

9

^^^Replace [tex]3^{2}[/tex] with 9

2 * 9 + 4

The next step is multiply 2 and 9

2*9 = 18

^^^Replace 2*9 with 18

18 + 4

Now add 18 and 4 together

22

Hope this helped!

~Just a girl in love with Shawn Mendes

Final answer:

To find the sum of one gross, a quarter of a dozen, and two scores, you add 144 (one gross), 3 (a quarter of a dozen), and 40 (two scores) to get a total of 187.

Explanation:

The sum of one gross, a quarter of a dozen, and two scores can be calculated as follows:

One gross = 144

A quarter of a dozen = 3

Two scores = 40

Therefore, the sum = 144 + 3 + 40 = 187

Answer: 187

Step-by-step explanation:

First, we need to define what these words mean numerically.

      One gross = 144

      A quarter of a dozen = 12/4 = 3

      Two scores = 2 * 20 = 40

Now, we can find the sum of one gross, a quarter of a dozen, and two scores. Sum means addition.

      144 + 3 + 40 = 187

Answer:

BD=AD-AB=6-4=2

Step-by-step explanation:

You have a line segment AD that measures 6 units

AB is part of it and it is 4 units

There is only one part left of AD and it is BD so you just find what's left of 6 if 4 is already spoken for.

For this case we have that the radius of the large circle is given by AD = 6, while the radius of the small circle is given by AB = 4. We want to know the length BD, that is, the difference of the radius of the big circle and the small one.

[tex]BD = AD-AB = 6-4 = 2[/tex]

So, [tex]BD = 2[/tex]

Answer:

[tex]BD = 2[/tex]

To identify geometric figures in a diagram, know the definitions and characteristics of each shape like a circle, triangle, and rectangle. By recognizing these characteristics, you can determine which shapes are in the diagram.

In order to identify which geometric figures are drawn in a diagram, you need to know the basic definitions and characteristics of geometric shapes. For instance, a circle is a figure in which all points are equidistant from a single point in the center. A triangle is a figure formed by three straight lines. A rectangle has four sides and all the angles are right angles. A square is a special type of rectangle where all four sides are equal. By identifying these various characteristics, you can determine which geometric shapes are represented in the diagram.

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1. Only constraint 2 would be met if 18 pairs of leather boots and 36 pairs of running  shoes were ordered.

2. Only constraint 1 would be met if 12 pairs of leather boots and 36 pairs of running shoes were ordered.

Data and Calculations:

Total pairs of shoes required = 48 pairs

Running shoes required (r) = 2 of leather boots

Leather boots required (b)= 1/2 of running shoes

Constraint 1:

The total pairs of different shoes required:

Running shoes = 32r

Leather boots = 16b

Total pairs = 32r + 16b = 48

Constraint 2:

Ratio equation:

Running shoes = 2r

Leather boots = b

Equation = 2r + b = 48

Thus, Constraint 2 satisfies the first order, while Constraint 1 satisfies the second order. The two constraints do not satisfy the two orders.

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Amanda needs 48 pairs of shoes total, with twice as many running shoes as leather boots. Constraint 1 is x + y = 48, and constraint 2 is y = 2x. An order of 18 boots and 36 running shoes meets only constraint 2, while 12 boots and 36 running shoes meet both constraints.

Amanda needs to order a total of 48 pairs of shoes, with twice as many pairs of running shoes as leather boots. To set up the equations, let x represent the number of pairs of leather boots and y represent the number of pairs of running shoes.

Constraint 1:

The total number of pairs of shoes:

x + y = 48

Constraint 2:

The ratio of the number of running shoes to leather boots:

y = 2x

To check which constraints are met by given orders:

1. For 18 pairs of leather boots (x = 18) and 36 pairs of running shoes (y = 36):

Using constraint 1: 18 + 36 = 54. This does not meet constraint 1.

Using constraint 2: 36 = 2(18). This meets constraint 2.

2. For 12 pairs of leather boots (x = 12) and 36 pairs of running shoes (y = 36):

Using constraint 1: 12 + 36 = 48. This meets constraint 1.

Using constraint 2: 36 = 2(12). This meets constraint 2.

Answer:

Option A is correct i.e 2R2+R3 -> R3

Step-by-step explanation:

The given matrix is:

[tex]\left[\begin{array}{ccc}-4&1&2&4\\0&-1&3&1\\3&2&4&5\end{array}\right][/tex]

If we perform the operation 2R2 + R3 we get the result given i.e

[tex]\left[\begin{array}{cccc}-4&1&2&4\\0&-1&3&1\\3&0&10&7\end{array}\right][/tex]

The operations performed are:

2R2 i.e. we multiply the row 2 with 2

we get 0  -2  6  2

now add it with row 3

0  -2   6   2

3   2   4   5

___________

3  0   10    7

So, Option A is correct i.e 2R2+R3 -> R3

Answer:

The answer is 6

Step-by-step explanation:

[tex]\bf 8n^2-4n+2=5n\implies 8n^2-4n-5n+2=0\implies 8n^2-9n+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{8}n^2\stackrel{\stackrel{b}{\downarrow }}{-9}n\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{\underline{two solutions}}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-9)^2-4(8)(2)\implies 81-64\implies 17[/tex]

Answer:

2 real distinct roots.

Step-by-step explanation:

8n^2 - 4n + 2 = 5n

Rearranging to standard form:

8n^2 - 9n + 2 = 0

The discriminant = b^2 - 4ac

= (-9)^2 - 4 * 8 * 2

= 17.

So there will be 2 real distinct roots.