Graph the equations to find the solution(s) to the system.

y = x - 1
y = 1/3(x + 2)(x - 4)

Answer:

30 ft

Step-by-step explanation:

Let the height of the tree be x ft. There are two right triangles:

1. Tree and its shadow are two legs of the first triangle;

2. Man and his shadow are two legs of the second triangle.

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. This means these two triangle are similar. Similar triangles have proportional sides' lengths. Hence,

[tex]\dfrac{\text{tree}}{\text{tree shadow}}=\dfrac{\text{man}}{\text{man's shadow}}\\ \\\dfrac{x}{24}=\dfrac{5}{4}\\ \\4\cdot x=5\cdot 24\\ \\x=\dfrac{5\cdot 24}{4}=5\cdot 6=30\ ft[/tex]

Answer:

30 feet

Step-by-step explanation:

We are given that a tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet.

We are to find the height of the tree.

Using their proportions to compare the height of each object to the length of the shadow.

[tex]\frac{h}{24} =\frac{5}{4}[/tex]

[tex]h=\frac{5\times24}{4}[/tex]

[tex]h=30[/tex]

Therefore, the height of the tree is proportion comparing the height of each object to the length of the shadow 30 feet.

If the angle of depression is 28° the complementary angle in the triangle is 62°. With this you can use soh-cah-toa to find the x value.

cos62 = 350/x; multiply both sides by x

cos62 x = 350; divide both sides by cos62

x = 350 / cos62

x = 745.519

x = 746 ft

Hope this helps you!

Answer:

x=30

Step-by-step explanation:

53+97+x=180

150+x=180

x=30

The sum of all the angles of a triangle is 180 degrees.

Add all the angles together and set it equal to 180, then solve for x

53 + 97 + x = 180

(150-150) + x = 180 -150

x = 30

Hope this helped!

Answer:

$248.03

Step-by-step explanation:

The formula you use for this is as follows:

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

where A(t) is the amount after the compounding is done, P is the initial amount invested, r is the interest rate in decimal form, n is the number of times the compounding is done per year, and t is the time in years.  Using that information and filling in our equation gives us this:

[tex]A(t)=75(1+\frac{.08}{12})^{(12)(15)}[/tex]

which simplifies down to

[tex]A(t)=75(1+.0066667)^{180}[/tex]

which simplifies further to

[tex]A(t)=75(3.307118585)[/tex]

which multiplies to $248.0338938.  Round to the nearest cent to get your answer.

The amount of money is $248.02.

Principal amount = P=75

Interest rate = r = 8% = 0.08

Number of years = t = 15

Number of times compounded in a year = n = 12

A = Amount after t years.

After 15 years there will be:

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\\ A=75\left(1+\frac{0.08}{12}\right)^{\left(12\cdot15\right)}\\ A=248.019110806\\ A \approx 248.02[/tex]

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Answer:

b

Step-by-step explanation:

24*pi=75.4

circumference is found when diameter is multiplied by pi

The diameter is 12 inches.

Option A is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

The diameter of the circle is 2r.

The equation of a circle is also written as,

(x - h)² + (y - k)² = r²

Where r is the radius and (h, k) is the center of the circle.

We have,

Circumference of the circle = 75.4 in

This means,

2πr = 75.4

r = 75.4/(2 x 3.14)

r = 75.4 / 6.28

r = 12 in

Diameter of the circle.

= 2r

= 2 x 12

= 24 in

Thus,

The diameter is 12 inches.

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Answer:

  y = 60°

Step-by-step explanation:

The measure of angle y is half the measure of the subtended arc, so is ...

  y = 120°/2 = 60°

Answer:

x=0,3π/2,π

Step-by-step explanation:

Given

sin^2  x+sin⁡x=0

sin x is a common factor

so,

sin⁡x (sin⁡x+1)=0

We can put both factors one by one equal to zero

sin⁡x=0

x=  sin^(-1)⁡0

sin⁡x  is zero at 0 and π

x=0,π

sin⁡x+1=0

sin⁡x= -1

x=  sin^(-1)⁡(-1)

sin is -1 for 3π/2

So,

x=3π/2

So,

x=0,3π/2,π

Answer:

Part 1) The measure of arc EHL is [tex]108\°[/tex]

Part 2) The measure of angle LVE is [tex]54\°[/tex]

Step-by-step explanation:

step 1

Let

x-----> the measure of arc EHL

y----> the measure of arc EVL

we know that

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

so

[tex]m<EYL=\frac{1}{2}(y-x)[/tex]

we have

[tex]m<EYL=72\°[/tex]

substitute

[tex]72\°=\frac{1}{2}(y-x)[/tex]

[tex]144\°=(y-x)[/tex]

[tex]y=144\°+x[/tex] ------> equation A

Remember that

[tex]x+y=360\°[/tex] -----> equation B ( complete circle)

substitute equation A in equation B and solve for x

[tex]x+(144\°+x)=360\°[/tex]

[tex]2x=360\°-144\°[/tex]

[tex]x=216\°/2=108\°[/tex]

Find the value of y

[tex]y=144\°+x[/tex]

[tex]y=144\°+108\°=252\°[/tex]

therefore

The measure of arc EHL is [tex]108\°[/tex]

The measure of arc EVL is [tex]252\°[/tex]

step 2

Find the measure of angle LVE

we know that

The inscribed angle measures half that of the arc comprising

Let

x-----> the measure of arc EHL

[tex]m<LVE=\frac{1}{2}(x)[/tex]

we have

[tex]x=108\°[/tex]

substitute

[tex]m<LVE=\frac{1}{2}(108\°)=54\°[/tex]

Answer:

6.(6) and 13.(3) liters.

Step-by-step explanation (this way is not the shortest one):

1. the basic rule is: the mas/volume of pure substance after and before combination is the same.

2. There is 4 liters of pure substance in 20*0.2 acid solution (20*0.2=4);

3. if 'x' is the volume of pure substance in 10%-solution; and if 'y' is the volume of pure substance in 20%-solution, then their sum of volumes is 4. It means, x+y=4 - this is the 1-st equation for system.

4. the volume of 10%-solution is x/0.1=10x; the volume of 20%-solution is y/0.25=4y; their sum is 20 litres. It means, 10x+4y=20 - this is the 2-d equation of the system.

5. to calculate the volumes of the pure substance:

[tex]\left \{ {{x+y=4} \atop {10x+4y=20}} \right.  \ =>\ \left \{ {{x=\frac{2}{3} } \atop {y=\frac{10}{3} }} \right.[/tex]

6. to calculate the volume of 10%-solution: 2/3 *10=20/3≈6.(6) litres;

to calculate the volume of 25%-solution: 10/3 *4=40/3≈13.(3) litres.

Answer:

  14.9 cm

Step-by-step explanation:

The side of interest is opposite an angle that is not marked. You find the value of that angle by making use of the fact that the sum of angles of a triangle is 180°.

  C = 180° -150° -12° = 18°

Now, fill in the available information in the given formula for the Law of Sines and solve for c:

  sin(B)/b = sin(C)/c

  sin(12°)/(10 cm) = sin(18°)/c

Cross multiply:

  c·sin(12°) = (10 cm)·sin(18°)

Divide by the coefficient of c:

  c = (10 cm)·sin(18°)/sin(12°) ≈ 14.9 cm

x and y  are supplementary angles

x - y = 27

x + y = 180

--------------------- We add the equations:

2x   / = 207

2x = 207

x = 207/2

Final answer:

To find the angle measure, set up the equation 2x - (180 - x) = 27, simplify to 3x = 207, and solve to find that x = 69 degrees.

Explanation:

The question asks to find the measure of an angle where the difference between twice the angle's measure and its supplement is 27. To solve this, let's designate the measure of the angle as x. Since the angle's supplement will be 180° - x, we can set up the equation 2x - (180° - x) = 27. Simplifying this equation, we get 2x - 180° + x = 27, which simplifies further to 3x = 207°. Dividing both sides of the equation by 3, we find that x = 69°. Therefore, the measure of the angle is 69 degrees.

the shape of the above image is conical

The shape is a cone.

The right answer is Nine.

Answer:

The answer is 9.

Step-by-step explanation:

If you substitute a and b with the numbers given, the equation you'll have to solve is: 2(5)+2-3.

2(5)=10 and 2-3=-1

Once you subtract 10-1, the answer would be 9.

Answer:

300

Step-by-step explanation:

The vertex of quadratic ax^2 +bx+c is on the line x=-b/(2a). This unit cost function defines a parabola opening upward, so its vertex is its minimum. The location of the vertex is ...

x = -(-660)/(2·1.1) = 660/2.2 = 300

300 cars must be made to minimize the unit cost.

_____

Note:

The unit cost at that production level will be $8357.

Explanation:

"Percent" literally means "per hundred" or "divided by 100". The percent symbol (%) is a shorthand way to write /100 ("divided by 100," or "hundredths"). So, hundredths and percent are essentially the same thing.

Given a "hundredths decimal", move the decimal point 2 places to the right and add a % symbol. (Moving the decimal point multiplies the number by 100; adding the % symbol divides it by 100, so the end result is the same value written in a different form.)

Example:

  19% = 19/100 = 0.19 . . . . (nineteen percent = nineteen hundredths)

and in the other direction, ...

  0.53 = 53/100 = 53% . . . . (fifty-three hundredths = fifty-three percent)

Answer:

"Percent" literally means "per hundred" or "divided by 100". The percent symbol (%) is a shorthand way to write /100 ("divided by 100," or "hundredths"). So, hundredths and percent are essentially the same thing. Given a "hundredths decimal", move the decimal point 2 places to the right and add a % symbol.

Answer:

Option B is correct.

Step-by-step explanation:

The slope for public sales:

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]

here x₁ = 2 , x₂= 5 , y₁=24, y₂= 60

[tex]m= \frac{60-24}{5-2}\\ m= \frac{36}{3}\\ m=12[/tex]

The slope for Wholesale sales:

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]

here x₁ = 18 , x₂= 35 , y₁=162, y₂= 315

[tex]m= \frac{315-162}{35-18}\\ m= \frac{153}{17}\\ m=9[/tex]

Now, comparing slopes of wholesales sale and Public sales

9:12

0r

3:4

3:4 can be written as 3/4.

So, Option B The slope of wholesale table is 3/4 times of the slope of the Public table is correct.

Answer:

b

Step-by-step explanation:

took quiz on edge

Answer: Your answer would be 59.5

Answer:

The letters in the word glacier can be arranged in 5040 different ways

Step-by-step explanation:

As there are 7 letters in the word glacier, that means that the number of ways would be 7!

This can also be written as

[tex]7*6*5*4*3*2*1=5040[/tex]

The letters in the word glacier can be arranged in 5040 different ways.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

A permutation of a set exists, loosely articulating, an arrangement of its members into a sequence or linear order, or if the set exists already contained, a rearrangement of its elements.

Given,

As there are 7 letters in the word glacier, that means that the number of ways would be 7!

This can also be written as

7*6*5*4*3*2*1 = 5040

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Answer:

The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (7 ) , and a range of (8 )

Step-by-step explanation:

The data distribution is a normal skewed right with a range of (8) and a mode of (7).

Mode is the most frequently used number.

From the dot plot, it is observed that on the data 7th player took 6 attempts. Which is the greatest. The mode of the data distribution is 7.

The range of the data is the difference between the maximum and the minimum value.

Range = 9-1

Range=8

From the dot plot, it is observed that the maximum value is toward the right. So that it is right-skewed.

Hence, the data distribution is a normal skewed right) with a range of (8) and a mode of (7).

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Answer:

  AB = 4

Step-by-step explanation:

Since point P bisects AB, we have ...

  AP = PB

  y/2 = y - 2

  0 = y/2 - 2 . . . . subtract y/2

  0 = y - 4 . . . . . . multiply by 2

  4 = y . . . . . . . . . add 4

Now, we can find AB:

  AB = 2(AP) = 2(1/2y) = y

  AB = 4

Answer:

-8x(2x - 9)

Step-by-step explanation:

-16x² + 72x

GCF = 8x

8x(16x² / 8x, -7x/8x)

-8x(2x - 9)

hope this helps!!

The answer would be -8x(2x-9)

Answer:

There is few equation that has a solution of all real numbers like this picture

,

a and b are matrices

Answer:

x^3 +9x^2 +27x +27

Step-by-step explanation:

The expansion of a power of a binomial looks like ...

  (a +b)^n = nC0·a^n·b^0 + nC1·a^(n-1)·b^1 + nC2·a^(n-2)·b^2 + ... + nC(n-1)·a^1·b^(n-1) + nCn·a^0·b^n

Of course, nCk = n!/(k!·(n-k)!) and a^0 = b^0 = 1. The list of coefficients nCk corresponds to a row of Pascal's triangle (see attached).

For n=3, this is ...

  (a +b)^3 = a^3 +3a^2b +3ab^2 +b^3

You have a=x and b=3, so the expansion is ...

  (x +3)^3 = x^3 +3·x^2·3 +3·x·3^2 +3^3

  = x^3 +9x^2 +27x +27

The net represents a square pyramid is a net with a square base and 4 triangular sides.

A square pyramid is a pyramid with a square base in geometry. A right square pyramid is one with the tip perpendicular to the square's centre.

There will be five surfaces in the pyramid the base is square and the remaining four will be triangular.

Hence net represents a square pyramid is a net with a square base and 4 triangular sides.

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To find the number of hours, divide the total distance by the speed.

Hours = 76 km / 14 km per hour

Hours = 4.529

Round the answer as needed.

Answer:

[tex]x=21,y=25[/tex]

Step-by-step explanation:

The given equation is:

[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(2+i)^2-(3-4i)^2[/tex]

Apply difference of two squares on the RHS.

[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=[(2+i)+(3-4i)][(2+i)-(3-4i)[/tex]

Simplify the RHS.

[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(5-3i)(5i-1)[/tex]

Expand the RHS

[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(10+28i)[/tex]

Cross multiply to get:

[tex](5-3i)(x+iy)=(10+28i)(4-5i)[/tex]

Expand both sides

[tex](5x+3y)+(5y-3x)i=180+62i[/tex]

Comparing the complex parts, we obtain:

[tex]5y-3x=62...(1)[/tex]

Comparing the real number parts we get;

[tex]5x+3y=180...(2)[/tex]

Solving equations (1) and (2) simultaneously; we get:

[tex]x=21,y=25[/tex]

Answer:

D) 155°

Step-by-step explanation:

The marked vertical angles are equal in measure, so ...

5x = 3x+10

2x = 10

x = 5

5x = 25 . . . . measure of angle AEB

Angle AED is the supplement of angle AEB, so is ...

180° -25° = 155°

Answer:

By doubling each day

Step-by-step explanation:

Jay is increasing  daily a fixed amount of pennies to his collection.  That's an arithmetic series, because to obtain the next term you have to do an addition.

To get a geometric series or progression you have to find the next term through multiplication.

So, if he wants to convert his series into a geometric series, he'd have to double his contribution to his collection each day (as an example).

X=-5

Y=-2

Explanation: