How can you identify the number of solutions of linear equations?

Khalil uses the method of similar triangles to find the distance across the river, [tex]\overline{PR}[/tex]

Reasons:

The distances between the formed the sight-lines are;

[tex]\overline{RB}[/tex] = 185 feet

[tex]\overline{OC}[/tex] = 275 feet

The distance between the point close to the river and the next point further from the river [tex]\overline{RO}[/tex] = 150 feet

In triangles ΔPRB and ΔPOC, we have;

∠PRE = ∠POC = 90° Given

∠PER ≅ ∠PCO By corresponding angle formed between two parallel lines and a common transversal.

∴ ΔPRE is similar to ΔPOC by Angle-Angle, AA, similarity theorem

Which gives;

[tex]\displaystyle \frac{\overline {PR}}{\overline {PO}} = \mathbf{\frac{\overline {RE}}{\overline {OC}}}[/tex]

Let x represent the distance across the river, we have;

[tex]\overline{PR}[/tex] = x

[tex]\overline{PO}[/tex] = 150 + x

Which gives;

[tex]\displaystyle \frac{x}{150 + x} = \frac{185}{275}[/tex]

275·x = 185 × (150 + x) = 27,750 + 185·x

275·x - 185·x = 27,750

90·x = 27,750

[tex]\displaystyle x = \frac{27,750}{90} = \mathbf{308.\overline 3}[/tex]

Therefore, the distance across the river, x = [tex]\mathbf{\overline{PR}}[/tex] = [tex]\underline{308.\overline 3 \ feet}[/tex]

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Using proportions, it is found that:

In this question, 42 out of 75 customers voted for the cheddar flavor, hence:

[tex]p = \frac{42}{75}[/tex]

That is, the fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]

The percentage is:

[tex]\frac{42}{75} \times 100\% = 56\%[/tex]

56% of customers voted for cheddar flavor.

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Answer:

23.2 miles

Step-by-step explanation:

You just need to multiply de number of inches by the number of miles that values 1 in. Therefore

4 multiplied by 5.8 = 23.2

Answer:

The actual distance to the airport is 23.2 miles.

Step-by-step explanation:

1 inch = 4 miles

5.8 · 4 = 23.2

Since the distance to the Airport is 5.8 inches, you will multiply it by 4. You do this because 1 inch = 4 miles.

Answer:

I need help with this too!!!

Step-by-step explanation:

Answer:

what does it mean?

Step-by-step explanation:

I do not understand.

Answer:

6311000

Step-by-step explanation:

The first thing we do is calculate the total amount of people in both states. 6.89 x10 raised to the 6th power is equal to 6890000. Then we multiply 5.79 by 10 to the fifth power, which equals to 579000. Then we subtract the numbers, and get 6311000. They want you to answer in standard notation, which is the regular way of writing numbers such as 10, instead of 10^1.

The difference in population

[tex] = (6.89 \times {10}^{6} ) - (5.79 \times {10}^{5} ) \\ = (6.89 \times 10 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 \times {10}^{5} ) - (5.79 \times {10}^{5} ) \\ = (68.9 - 5.79) \times {10}^{5} \\ = 63.11 \times {10}^{5} [/tex]

Answer:

[tex]63.11 \times {10}^{5} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

20 I believe because 15 divided by 4 is 3.75 so I then divided 75 by 3.75 giving me 20:)

Answer:

Base = 10 ft. and the height = 6.

Step-by-step explanation:

Area of triangle = 1/2bh

base is 4 + h  ⇔  base = 4 + h

height = h

Using the formula for the area of triangle substitute into the formula the given facts.

A = 1/2bh

30 = 1/2(4 + h) (h)

30 = 1/2(4h + h²)     Multiply both sides by 2

60 = 4h + h²

-60 =           -60      Add -60 to both sides

0 = h²+ 4h -60        

(h + 10)(h - 6) = 0      Factor

h + 10 = 0    h - 6 =0

h = -10         h = 6

reject any negative number and use the positive answer for h.

So h = 6      and the base = 4 + 6 ; base = 10

Answer:

3/2

Step-by-step explanation:

Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio

s : 2s : sroot3

The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3

In this diagram the short leg is (root3)/2 .

(root3)/2 × root3 = 3/2

See image.

Answer:

u777766665655566667777777777777

76p is the equivalent expression of 53p + (16p + 7p)

An expression is combination of variables, numbers and operators.

The given expression is 53p + (16p + 7p)

Fifty three times of p plus sixteen p plus seven p.

In the given expression p is the variable and plus is the operator.

We need to find the equivalent expression.

Equivalent expressions are expressions that work the same even though they look different.

53p + (16p + 7p)

76p

Hence, 76p is the equivalent expression of 53p + (16p + 7p)

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(-3x³+2x²+4x+24) (x-2)

---------------------------------

8x

[tex]\huge \bf༆ Answer ༄[/tex]

Conversion from degree to radian ~

Conversion from radians to degree ~

The required measures of the angles in radians and degree are given as  π/2 radians and -36° respectively.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
An angle of 90° measures
in radians,
angle = π/180 × Ф
angle = π/180 × 90 = π/2 radians

Similarly,
An angle of -pi/5 radians
in degrees,
angle = 180 / π × -π/5
angle = -36°

Thus, the required measures of the angles in radians and degree are given as  π/2 radians and -36° respectively.

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Answer:

cosA=root8/3 is the answer

Answer:

m=1352

Step-by-step explanation:

(118.64-24)/0.07=m

Step-by-step explanation:

1 _21:00_ , _22:10_, 1:10

2. 1:20

3. 18:00

4. 21:35

1. 21:00, 22:10, 1 hr and 10 minutes

2. 20 minutes

3. 18:40

4. 21:35

The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.

Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.

During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.

Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.

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Answer:

It's B

Step-by-step explanation:

Just took it

Check the picture below.

so then γ ≈ 180 - 69 - 43, γ ≈ 68.

The percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.

The median is a measure of central tendency. The median of a given data set shows the middle number in a given set of scores when they arranged in ascending or descending order.

The box plots in the question shows the random sample of both boys and girls how much time they had spent on math homework in a week. We can see from the box plot that the percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.

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Answer:

Solve for n

n=log5  (− 2 /y  −20x−5),y<−40x−10

Step-by-step explanation:

Answer:

The first step.

Step-by-step explanation:

Answer:

look it up in internet and find th right answers

Answer:

g(x)=3|x| is the first box

f(x)=1/3|x| is the second box

Step-by-step explanation:

you can solve these type of questions by looking at the slope which is in front of the x.

since 1/3 is smaller than 3 it's going to have lower slope resulting in 3 to incline faster

Answer:

the first one's right i think

Answer:

$10.12

Step-by-step explanation:

Step one:

given data

we are told that the cost of binoculars is $155.75

and also the sales tax is 7%

Step two:

We want to first solve for the sales tax which is 7% of  $155.75

=7/100* 155.75

=0.070*155.75

=10.12

Cassie will pay a tax of $10.12

Also Cassie will pay a total amount of

= 155.75+10.12

=$165.87

Answer:

for 3, 4 or both?

4. is probably zero

Step-by-step explanation:

Wait is 4 a question?

[tex]cos^2 x + \cos^2 y = \cos(2x + 2y)\\\\\implies \dfrac{d}{dx} (\cos^2 x + \cos^2 y) = \dfrac{d}{dx} \cos(2x+2y)\\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-\sin(2x+2y) \left(2+2\dfrac{dy}{dx} \right) \\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-2\sin(2x+2y) -2\sin(2x+2y)\dfrac{dy}{dx} \right) \\\\\implies 2 \sin(2x+2y) \dfrac{dy}{dx} - 2 \cos y \sin y \dfrac{dy}{dx} = 2 \cos x \sin x-2\sin(2x+2y)[/tex]

[tex]\implies \sin(2x+2y) \dfrac{dy}{dx} - \cos y \sin y \dfrac{dy}{dx} = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}\\\\\implies y'(x) = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}[/tex]

The cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97

Given:

Length = 25 yd

width = 26 yd

Height = 5.1 ft

convert yard to feet

25 yd = 75 ft

26 ft = 78 ft

Volume of the pool = length × width× height

= 75 × 78 × 5.1

= 29,835 cubic ft

1 gallon = 0.134 cubic ft.

222,649.3 gallon = 29,835 ft

charges per 1000 gallon = $1.50

Total charges = 222,649.3 gallon / 1000 gallon × $1.50

= 222.6493 × 1.50

= 333.97395

Approximately,

$333.97

Therefore, the cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97

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(a) It looks like you're saying

[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]

Find the critical points of F(x). By the fundamental theorem of calculus,

F'(x) = x - 3x² + 7

The critical points are where the derivative vanishes. Using the quadratic formula,

x - 3x² + 7 = 0   ⇒   x = (1 ± √85)/6

Compute the second derivative of F :

F''(x) = 1 - 6x

Check the sign of the second derivative at each critical point.

• x = (1 + √85)/6 ≈ 1.703   ⇒   F''(x) < 0

• x = (1 - √85)/6 ≈ -1.370   ⇒   F''(x) > 0

This tells us F attains a minimum of

[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]

(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.

• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0

• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0

• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0

This tells us that

• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)

• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)

(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :

F''(x) = 1 - 6x = 0   ⇒   6x = 1   ⇒   x = 1/6

Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.

• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0

• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0

This tells us that

• F(x) is concave up over (-∞, 1/6)

• F(x) is concave down over (1/6, ∞)

Step-by-step explanation:

follow the steps in the picture. I've started it for you all you need to do is finish