4. A regular pentagon has side lengths given below. Find the length of one side.
4q+1 = 11-q
r+s
s+t-1
3r
a) 9
b) 4
c) 3
d) 2

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For Exercises 17 And 18, Find The Acute Angle Between The Given Lines By Using Vectors Parallel To The Lines.

y = x , y = 2 x + 3

The acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

We are given the lines:

y = x

y = 2 x + 3

The formula for finding the angles between two vectors is given by:

cos θ = u · v / | u | | v|

We know that (0,0) and (1, 1) lies on the line y = x.

Now, vector u for the line y = x will be:

u = (1,1) - (0,0) = {1, 1}

(0,3 ) and (1, 5) lies on the line y = 2 x + 3

Similarly, vector v will be equal to:

v = (1, 5) - (0, 3) = {1, 2}

cos θ = {1, 1} · {1, 2} / √1 + 1 √1 + 4

cos θ = 1 + 2 / √10

cos θ = 3 / √10

θ = cos⁻¹ ( 3 / √10)

θ = 18.4349°

Therefore, the acute angle between the lines y = x and y = 2 x + 3 is 18.4349°.

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The addition is the operation that appears first, the division is the operation that is selected first in order to evaluate and multiplication is the operation that is not included in the given expression.

The given expression can be evaluated using the BODMAS rule which tells the order of priority to give to solve an equation with multiple operations

BO stands for Bracket off means to solve the bracket first

D stands for division

M stands for multiplication

Stands for addition

S stands for subtraction

Now we should look at the expression given which is 62 + 14 ÷ 2 - 8

Although the addition operation appears first in the given expression, we would select the division operation first that can be bracketed  because of BODMAS rule and then addition and then Subtraction at last which results

62 +( 14 ÷ 2) - 8

62 + 7 -8

69 -8

61

Hence, Using the BODMAS rule the expression is solved and the result is 61

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Answer:

7% of the number is 1.

Step-by-step explanation:

21%=3

Divide both sides by 3

7%=1

Answer:

1

Step-by-step explanation:

let x be the number.so.......

if 21%of a number means 21÷100*the number(x)=3

21÷100×X=3 so when we solve this first we have to criss-cross and then 21*X=3*100

then we both divide by 21 in order to get x .so x is going to be 100 divided by 7

then.......

we are asked to get how much percent of 100÷7 is 7% so...let the answer be y

7÷100*X=y

7÷100*100*7 =Y

when calculated the answer will possibly be 1 :)))

in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

Here the parent function is:

f(x) = x^2

And the transformed function is the one graphed in the lower right side of the given image.

Notice that the y-intercept of the transformed function is y = 600.

The x-intercepts are x = -10 and x = 30

Then the polynomial is something like:

y = a*(x + 10)*(x - 30)

Using the fact that the y-intercept is y = 600, then:

600 = a*(0 + 10)*(0 - 30) = a*-300

600/-300 = a = -2

The transformed function is:

g(x) = -2*(x + 10)*(x - 30)

Expanding that:

g(x) = -2( x^2 + 10x - 30x - 300)

Completing squares we get:

g(x) = -2*(  x^2 - 20x - 300)

      = -2*(x^2 - 2*10*x - 300)

Now we can add and subtract 100, so we get:

-2*(x^2 - 2*10*x - 300 + 100 - 100)

-2*(  (x - 10)^2 - 400)

Finally, expanding that:

g(x) = -2*(x - 10)^2 + 800

Writing it in function notation, we get that the transformed function is:

g(x) = -2*f(x - 10) + 800

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The vector u is  [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex].

The linear combination 2u + 3v + 5w  is 19/3 i + 17/3 j + 6k.

According to the given question.

v = (2, 3, 1)

w = (1, 1, 1)

And

3u + 2v + 4w = (1, 2, 3)

From,

v = (2, 3, 1)

⇒ v = 2i + 3j + 1k

w = (1, 1, 1)

⇒ w = i + j + j

a). Let vector u be xi + yj + zk

Here,

3u + 2v + 4w = (1, 2, 3)

⇒ 3u + 2v + 4w = i + 2j + 3k

⇒ 3(xi + yj + zk) + 2(2i + 3j + k) + 4(i + j +k) = i + 2j + 3k

⇒ 3xi + 3yj + 3zk + 4i + 6j + 2k + 4i + 4j + 4k = i + 2j + 3k

⇒3xi + 3yj + 3zk + 8i + 10j + 6k = i + 2j + 3k

⇒ 3xi + 3yj + 3zk  = i + 2j + 3k - 8i -10j -6k

⇒ 3xi + 3yj + 3zk = -7i -8j -3k

⇒ xi + yj + zk = (1/3)(-7i -8j-3k)

⇒ xi + yj + zk = [tex]\frac{-7}{3} i -\frac{8}{3}j -k[/tex]

b). The linear combination

2u + 3v + 5w

= 2(-7/3i -8/3j - k ) + 3(2i + 3j + k) + 5(i + j + k)

= -14/3 i -16/3j -2k + 6i + 6j + 3k + 5i + 5j + 5k

= -14/3 i -16/3j -2k  + 11i + 11j + 8k

= 19/3 i + 17/3 j + 6k

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Answer:

4. 8.4×10^5

Step-by-step explanation:

The exponent of ×10 is the amount of places that you move the decimal. When the exponent is negative, you move the decimal to the left and when it is positive, you move it to the right. Number 1 and 2 are wrong right away because they move the decimal to the left which is not what we want. Number 3 is wrong because there are not enough 0's when we move the decimal. So, option 4 is correct. I hope this helps!

Answer:

14

Step-by-step explanation:

7/4:4 = x:32

x = 32(7/4) / 4 = 14

The thickness of each cookie is 0.75 inch.

The cookies are in cylindrical container, hence, the shape of cookies will also be cylindrical. Now, the volume of cylinder is given by the formula : V = πr²h, where V refers to volume, r refers to radius and h represents height.

So, volume of 12 cookies will be equal to the cylindrical container.

Radius of cookies = Diameter÷2

Radius of cookies = 5÷2

Radius of cookies = 2.5 inches

Taking π as 3.14

Volume of a stack of cookies = 3.14×2.5²×h

Volume of a stack of cookies = 19.625h

Relating both the volumes to find the value of h

19.625h = 176.715

h = 176.715 ÷ 19.625

Performing division to find the height

h = 9 inches

So, height of 12 cookies is 9 inches

Height of 1 cookie = 9 ÷ 12

Height of 1 cookie = 0.75 inch

Thus, the thickness of each cookie is 0.75 inch.

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Answer:

about 33%

Step-by-step explanation:

Answer:e

Step-by-step explanation:

e

Answer:

4. 4(x+1)

5. 7(d+4)

6. y(y+3)

Answer:

I could be totally wrong but ill tr7

Step-by-step explanation:

4. 12 OR 4x+4

5.  56 (28+28)

6. y^2 + 3y

Answer:

∠ LOE = 20°

Step-by-step explanation:

since OJ is perpendicular to OE then ∠ JOE = 90°

from the diagram

∠ JOL + ∠ LOE = ∠ JOE ( substitute values )

6x + 10 + x + 10 = 90

7x + 20 = 90 ( subtract 20 from both sides )

7x = 70 ( divide both sides by 7 )

x = 10

Then

∠ JOE = x + 10 = 10 + 10 = 20°

Answer:    x = 1

Step-by-step explanation:

Since the slope is undefined, that means it will be a vertical line.  The equation of a vertical line is:  x = h, where h is the x-value/coordinate it runs through.  Based on your given point (1, 3), the x-coordinate is 1, so that makes the equation of your line x = 1.

The value of A + H is 25 for the given sequence.

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given that sum of any three consecutive terms is 30

Since c = 5

So a + b + c = 30

a + b = 25

⇒ (a+b)+(c+d+e)+(f+g+h)

⇒ 25 + 30 + 30 = 85

Now,

a+b+c+d+e+f+g+h = 85

a + h +(b+c+d)+(e+f+g) = 85

a + h + 30 + 30 = 85

a + h = 25

Hence "The value of A + H is 25 for the given sequence".

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Answer:

15 minutes=1km

1 minute=?

(15m:m)×1km

minutes cancel minutes

15×1km=15km

The number of players the team can bring to the tournament are 15

Firstly we need to form the equation. The components of equation based on given information are as follows -

Total amount raised by softball team = Cost of bus + Cost of meal × number of players

Let the number of players be represented with x.

1943.50 = 1148.50 + 53×x

Rewriting the equation

53x = 1943.50 - 1148.50

Performing subtraction to Right Hand Side of the equation

53x = 795

Shifting 75 to Right Hand Side of the equation

x = 795 ÷ 53

Performing division at Right Hand Side of the equation

x = 15

Hence, 15 players the team can bring to the tournament.

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Answer:

35 small pies

Step-by-step explanation:

  Let the number of large pies be 'l' and

        The number of small pies be 's'.

Total pies sold = 45

⇒  l + s  = 45  ------------(I)

         l = 45 - s  -------(II)

Cost of 45 pies = $120

         Cost of 1 large pie = $5

         Cost of 'l' large pies = 5*l = 5l

    Cost of 1 small pie = $2

   Cost of 's' small pie = 2*s = 2s

         5l + 2s  = 120 --------------(III)

Solving : substitution method

Substitute l = 45 -s in equation (III)

         5*(45 - s) + 2s = 120

       5*45 - 5*s + 2s = 120

        225 - 5s + 2s  = 120   {Combine like terms}

               225 - 3s   = 120

                      -3s     = 120 - 225    {Subtract 225 from both sides}

                           -3s = -105

                              s = -105 ÷ (-3)    {Divide both sides by (-3)}

                             s = 35

Substitute s = 35 in equation (II),

     l = 45 - s

       = 45 - 35

    l = 10

            [tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]

Answer:

yes this is correct

Step-by-step explanation:

this is correct because angle gqh is adjacent to mqk, meaning they are the same degree which would mean kqg and hqm are adjacent

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Consumer affairs investigator records the repair cost for 10 randomly selected VCRs. A sample mean of $72.82 and standard deviation of $24.17 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the VCRs. Assume the population is approximately normal. Construct the 90% confidence interval. Round your answer to two decimal places.

We get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

We are given that the number of VCRs are 10.

So, we get that:

Sample size = n = 10

Now, we get the degree of freedom as:

d o f = n - 1

d o f = 10 - 1

d o f = 9

For 90% confidence interval , critical value will be:

t (0.10, 9) = 1.833

Lower limit of 90% confidence interval will be:

Lower interval  = Mean - t (0.10,9) × s / √n

= 72.82-1.833 × 24.17 /√10

= 58.81

Upper limit of 90% confidence interval will be:

Upper interval = Mean + t (0.10,9) × s /√n

= 72.82 + 1.833 × 24.17/√10

= 86.83

Therefore, we get that the critical value of the 90 % confidence interval is 1.833 and the interval is (58.81, 86.83).

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Based on the given.

If [tex]m∠2 = 59°[/tex]

Then, [tex]m∠4 = 59 °[/tex]

(reason: vertically opposite angles are equal)

If [tex]m∠4 = 59 °[/tex]

Then, [tex]m∠1⟹ 180 - 59 = 121 °[/tex]

(reason: angles on a straight line = 180°)

If [tex]m∠1 = 121°[/tex]

Then, [tex]m∠3 = 121°[/tex]

(reason: vertically opposite angles are equal)

Therefore:

[tex]m∠1 = 121°[/tex]

[tex]m∠3 = 121°[/tex]

[tex]m∠4 = 59 °[/tex]

See attached image for the placement of the values.

Answer:

More, by 0.05 or [tex]\frac{1}{20}[/tex] inches more.

Explanation:

Find out if the amount of rain was more or less by subtracting the desired outcome from the real outcome. If the answer comes out as positive then the amount of rain was more and if the answer is negative, it was less.

Workout:

[tex]\sf real \ outcome - desired \ outcome[/tex]

[tex]3.8 - 3\dfrac{3}{4}[/tex]

[tex]3.8 - 3.75[/tex]

[tex]0.05[/tex]

Hence, The rain was more than ginny expected by 0.05 inches more.

[tex]4 \div \frac{2}{5} [/tex]

[tex]4 \times \frac{5}{2} [/tex]

[tex]2 \times 5[/tex]

[tex]10[/tex]

Answer:10

Step-by-step explanation:

first step 4× 5/2
second step 4x5
                       2

third step is to simplify 20/2 which is
10

​

Answer:5 teams

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

1. Change the equation to x + -4 1/3 = 9 2/3

2. Add 4 1/3 to each side of the equation to get rid of the -4 1/3

3. You will be left with x = 14

the angle measures less than 90°, thus, the correct classification is acute.

First, let's define the possible angles that we have here:

Notice that the angles HML and LMK should add up to 180°, then we can write:

∠HML + ∠LMK = 180°

132° + ∠LMK = 180°

∠LMK = 180° - 132° = 48°

Now we can see that:

∠JML = ∠JMK + ∠LMK

∠JML = 41° + 48° = 89°

So the angle measures less than 90°, thus, the correct classification is acute.

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Answer:
3(x - 8) < 15

Step-by-step explanation:

3(x - 8) < 15

3x - 24 < 15

3x < 39

x < 13

Answer: 6 cups of milk

Step-by-step explanation:

Set-up proportion

[tex]\frac{1}{12} =\frac{x}{72}[/tex]

1*72=72/12=6

6 cups of milk

Answer: a. 12x+19

b. 67

Step-by-step explanation:

a. P=a+b+c+d

P=x+7+2x+2+8x+x+10

P=x+2x+8x+x+7+2+10

P=3x+9x+19

P=12x+19

b. P=12(4)+19

P=48+19

P=67