X+y=11
Graphing which function

Answer:

10.6

Step-by-step explanation:

A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.

Let the length of the cable required be represented by x.

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]

   = 64 + 49

[tex]x^{2}[/tex] = 113

x = [tex]\sqrt{113}[/tex]

  = 10.63

x = 10.6

The length of the cable required is 10.6 in feet.

The length of the cable needed to support the tenth wall is approximately 10.6 ft.

The situation forms a right angle triangle.

Right angle triangle has one of it side as 90 degrees.

Therefore,

The tent wall is the opposite side of the triangle.

The table feet from the base of the tent is the adjacent side of the triangle.

Using Pythagoras's theorem the cable needed can be found.

Therefore,

c² = 64 + 49

c = √113

c = 10.6301458127

length of the cable ≈ 10.6 feet

learn more on right triangle here: https://brainly.com/question/22734015

Answer:

8 servings

Step-by-step explanation:

Take the total ounces and divide by the number of ounces per serving

42/5 =8.4

Round down since we don't want to short someone on their soup

8

Answer:

1/2 pounds or 0.5 pounds, 3/6 = 1/2 :)

hope i helped

Step-by-step explanation:

Answer:

0.5 pound/share

Step-by-step explanation:

 Divide 3 pounds by 6 shares, obtaining 0.5 pound/share

Answer:

1.5 cubic metres

Step-by-step explanation:

Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.

The total number of parts = 1 + 2 + 3 = 6 parts.

The amount of marvel present the concrete mix = amount of marvel / total mix

= 3 parts / 6 parts = 1/2

Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:

Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres

Answer: 10

Step-by-step explanation:

10

Answer:

Statement A is correct

Step-by-step explanation:

Statement A is correct:  Model A1 (0.25) is more prefered than Model C3 (0.15)

Answer:

WE reject the Null and conclude that one of the drug is more effective than the other.

Step-by-step explanation:

Given :

Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5

Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3

This is a matched pair sample :

The hypothesis :

H0 : μd = 0

H1 : μd ≠ 0

Hence, we intun the difference between the two groups of value :

Difference, d = -8.9,-2.2,-8.8,1,-5.9,-3.6,-10,1.9,-10.4,-2.8

The test statistic :

dbar ÷ (Sd/√n)

dbar = mean of difference = Σd / n = - 49.7 / 10 = - 4.97

Standard deviation of difference, Sd = 4.51

Test statistic :

-4.97 ÷ (4.51/√10)

Test statistic = - 3.485

The sample size, n = 10

df = n - 1 ; 10 - 1 = 9

Critical value (0.10, 9) = 1.833

If Test statistic > |Critical value |

Since 3.486 > 1.833 ; WE reject the Null and conclude that one of the drug is more effective than the other

Answer:

The standard deviation of the number of education majors in the sample is of 3.34.

Step-by-step explanation:

The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Standard deviation:

The standard deviation of the hypergeometric distribution is:

[tex]\sigma = \sqrt{\frac{nk}{N}(1 - \frac{k}{N})(\frac{N-n}{N-1})}[/tex]

In this question:

300 freshmen means that [tex]N = 300[/tex]

110 are education majors, which means that [tex]k = 110[/tex]

60 are chosen, which means that [tex]n = 60[/tex]

Find the standard deviation of the number of education majors in the sample.

[tex]\sigma = \sqrt{\frac{60*110}{300}(1 - \frac{110}{300})(\frac{240}{299})} = 3.34[/tex]

The standard deviation of the number of education majors in the sample is of 3.34.

Answer:

20 doses

Step-by-step explanation:

400 milli. = 0.4 grams

8/0.4 = 20 doses

Answer:

28.2 %

Step-by-step explanation:

Increase = 17.95 - 14 = $3.95

%age increase = 100 * 3.95 / 14

= 28.214

Answer:

g(x)=x-3

Problem:

If f(x+3)=x+6 find inverse of function f(x).

Step-by-step explanation:

Let u=x+3, then x=u-3.

Make this substitution into our given:

f(u)=(u-3)+6

Simplify:

f(u)=u+(-3+6)

f(u)=u+3

Now let's find the inverse of f(u)...

Or if you prefer rename the variable...

f(x)=x+3

Now, we are going to solve y=x+3 for x.

Subtracting 3 on both sides gives: y-3=x.

Interchange x and y: x-3=y.

So the inverse of f(x)=x+3 is g(x)=x-3.

Answer:

The answer is g(x)=x-3

Step-by-step explanation:

If f(x+3)=x+6 find inverse of function f(x).

Let u=x+3, then x=u-3.

Make this substitution into our given:

f(u)=(u-3)+6

Simplify:

f(u)=u+(-3+6)

f(u)=u+3

Now let's find the inverse of f(u)...

Or if you prefer rename the variable...

f(x)=x+3

Now, we are going to solve y=x+3 for x.

Subtracting 3 on both sides gives: y-3=x.

Interchange x and y: x-3=y.

So the inverse of f(x)=x+3 is g(x)=x-3.

Answer:

2x +4 = 9

x = 5/2

Step-by-step explanation:

Let x = number

2x +4 = 9

Subtract 4 from each side

2x+4-4 = 9-4

2x = 5

Divide by 2

2x/2 =5/2

x = 5/2

Answer:

b. 01285 esa es, espero este buena y que te ayude

Answer:

Step-by-step explanation:

From the given information:

We can see that:

[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]

From equation (1), if we multiply it by 2, we will get what we have in equation (2).

It implies that,

x + 2y + 3z = 0    ⇔   2x + 4y + 6z = 0

And, W satisfies the equation x + 2y + 3z = 0

i.e.

W = {(x,y,z) ∈ R³║x+2y+3z = 0}

Now, to determine the distance through the plane W and point is;

[tex]y = [1 \ 1 \ 1]^T[/tex]

Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0

Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:

[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]

[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]

[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]

[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]

[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]

Answer:

4

Step-by-step explanation:

AD=4+8=12=DE thus angle EAD= angle AED=90÷2=45

angle ACB=90-45=45 thus CB=AB=4

Answer:

incorrect answer above

Answer:

C

Step-by-step explanation:

On a number cube from 1 to 6, there are only two numbers available that are equal to or greater than 5: 5 and 6. Out of the six possible options, only two options could meet these conditions. Therefore, the probability is 2/6. However, this can be further simplified as both 2 and 6 can be divided by two, which would equal 1/3.

Answer:

The answer is C. -82 + 26i

(8+6i)(-5+7i) = -82+26i

Answer:

Number of limes are 20

Number of oranges are 22

Number of cherries are 26

Step-by-step explanation:

number of pieces of total candies = 68

Let the number of limes is y.

Number of orange = y + 2

Number of cherry = 4 + y + 2

So,

According to the question

y + y + 2 + 4 + 2 + y = 68

3 y + 8 = 68

3y = 60

y = 20

Number of limes are 20

Number of oranges are 22

Number of cherries are 26

1. Move terms to the left side

2.Subtract the numbers

3.Use the quadratic formula

4.Simplify

5.Separate the equations

6.Solve

Rearrange and isolate the variable to find each solution.

Solution,

Solution

x=5±√39

m = [tex]\frac{\sqrt{3}}{2}[/tex]

theta = 60 degrees or pi/3

The best way to figure these sorts of questions out is memorizing the unit circle. There are many tricks that can help! For example, from (0,1) to the left and right, the x-values of the points go from sqrt(3) to sqrt(2) to 1.

Hope this helps!

Answer:

f(x)=27.63(1.03)^x

Step-by-step explanation:

Answer:

X=10

Step-by-step explanation:

2x-,8<12

2x>12+ 8

2x>20

x>10

Answer:

= -10√3 - √3 . 5^3/2

Step-by-step explanation:

Apply the distributive law: a(b + c) = ab + ac

a = -5 √3, b = 2, c = √5

-5 √3 . 2 + -(5√3) √5

Apply minus-plus rules: + (-a) = -a

= -5 . 2√3 - 5 √3 √5

Simplify

= -10√3 - √3 . 5^3/2

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

[tex]\frac{7}{9}[/tex] ÷ [tex]\frac{1}{3}[/tex] =              Flip the second fraction over (reciprocal) and multiply

[tex]\frac{7}{9}[/tex] x [tex]\frac{3}{1}[/tex] =              Multiply straight across. Numerators then denominators.

[tex]\frac{7}{9}[/tex] x [tex]\frac{3}{1}[/tex] = [tex]\frac{21}{9}[/tex] = [tex]\frac{7}{3}[/tex]     Reduce.

Answer:

-1/4

Step-by-step explanation:

Take two points on the line

(-4,-1) and (0,-2)

Using the slope formula

m = (y2-y1)/(x2-x1)

   = ( -2 - -1)/( 0 - -4)

    = (-2+1)/ ( 0+4)

    -1/4

Step-by-step explanation:

a) [tex]x^2 - 5x + 4 = (x - 1)(x - 4)[/tex]

b) [tex]x^2 - 10x + 9 = (x - 1)(x - 9)[/tex]

c) [tex]x^2 - 16x + 64 = (x - 8)^2[/tex]

Answer:

UW  = 6.3

Step-by-step explanation:

Given that,

VU = 7

∠U = 25°

We need to find the value of UW. It can be solved using trigonometry. So,

[tex]\cos\theta=\dfrac{B}{H}[/tex]

Where

B is base and H is hypotenuse

So,

[tex]\cos(25)=\dfrac{UW}{7}\\\\UW=7\times\cos(25)\\\\UW=6.3[/tex]

So, the value of UW is 6.3.

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.​

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

[tex](9.85)^2=x^2+(x+5)^2[/tex]

[tex]97.0225=x^2+x^2+10x+25[/tex]

[tex]0=2x^2+10x+25-97.0225[/tex]

[tex]0=2x^2+10x-72.0225[/tex]

Here, [tex]a=2, b=10,c=-72.0225[/tex]. Using the quadratic formula, we get

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}[/tex]

[tex]x=\dfrac{-10\pm \sqrt{676.18}}{4}[/tex]

Approximating the value, we get

[tex]x=\dfrac{-10\pm 26}{4}[/tex]

[tex]x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}[/tex]

[tex]x=\dfrac{16}{4},\dfrac{-36}{4}[/tex]

[tex]x=4,-9[/tex]

Distance cannot be negative so [tex]x\neq -9.[/tex]

Now we have [tex]x=4[/tex]

[tex]x+5=4+5[/tex]

[tex]x+5=9[/tex]

Therefore, the base is 4 m and the height is 9 m.

The base, height to the top of the ladder and height of the ladder when connected together we will get a triangle and then apply Pythagoras theorem we get base 4.0 m and height 9 m.

According to this theorem, the hypotenuse l,  base b and opposite side a are connected by the equation written as follows:

hypotenuse² = base² + opposite side²

l² = a² + b².

Thus if we know either two sides or the triangle we can calculate the length of the unknown side of the triangle. It is given that the length of ladder is 9.85 m. It is placed against a wall and the base that is distance between foot and wall is 5 m less than the height to the top.

Assuming a triangle connecting these three points, the hypotenuse is the length of the ladder 9.85 m and let x be the base and opposite side that is the height to the top be x + 5. Now apply Pythagoras theorem.

9.85² = (x+5)² + x²

97.02 = 2 x² + 10x + 25

2 x² + 10x -72.02 = 0

Now solve for x using quadratic equation we get x = 4.00. The base of the triangle is 4 m and opposite side that is the height = x +5 = 4 +5 = 9m.

Therefore, base is 4 m and height to the top of the ladder is 9 m.

To find more about Pythagoras theory, refer the link below:

https://brainly.com/question/23295505

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9514 1404 393

Answer:

  [tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]

Step-by-step explanation:

It's pretty straightforward. You want ...

  f(x) - g(x)

Substituting the given function definitions gives ...

  [tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]

Answer:

Very hard question i don't help you