Find the value of x in each case

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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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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: 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

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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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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:

18, 20 and 22.

Step-by-step explanation:

Let the lowest number be n, then:

n + n + 2 + n + 4 = 60

3n + 6 = 60

3n = 54

n = 18.

So the other 2 are 20 and 22.

From the arc length given radius yielded is 22.91 cm.

What is the arc length?

The primary angle:

40°

Arc size

20 cm

Recall the arc length formula.

[tex]l=(\frac{Theta}{360} )*(2\pi r)[/tex]

Inserting the values:

20 =[tex]\frac{40}{360} *(2\pi r)[/tex]

[tex]r=\frac{36(20)}{10\pi }[/tex]

=72/π

=22.918cm the radius is.

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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 current price of the item = 400 dollars

The price in 8 years from today = 543.23 dollars

Given the rate of inflation = 3.9%

The exponential function modelling the future price, p(t) in t years for a certain item is, [tex]p(t)=400(1.039^t)[/tex]

We have to find the current price of the item. This is given by substituting t = 0 in p(t).

That is, p(0) = 400 x 1 = 400 dollars

Therefore current price = 400 dollars

To find the price of the product in 8 years, substitute t = 8 in p(t).

That is, p(8) = [tex]400(1.039^8)[/tex] = 543.23 dollars

Therefore, the future price of the item in 8 years = 543.23 dollars

The question is incomplete. Find out the complete question below:

If the rate of inflation is 3.9% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)= 400(1.039^t).Find the current price of the item and the price 8 years from today.

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Answer:
3(x - 8) < 15

Step-by-step explanation:

3(x - 8) < 15

3x - 24 < 15

3x < 39

x < 13

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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Measures of central tendency assist in the discovery of a data set's middle, or average. The mean is the only set of measurements that will have to recalculate.

Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.

Given that Mrs. temple has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. Now, if she made a mistake, the highest grade should be 10 points higher. Therefore, there will be no change in the median because the median is measured by the center value or is affected by the center value.

Also, the mode will not change because it is the most common value in a given data set. Therefore, the one that is repeating a lot of time.

Further, the only value that will change is the mean, because it is the sum of the observations divided by the number of observations, now since the sum is changed, therefore, the mean will be changed.

Hence, the mean is the only set of measurements that will have to recalculate.

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Answer:5 teams

Step-by-step explanation:

Step-by-step explanation:

[tex] \sqrt{} 4(m - 1) ^{2} = \sqrt{} 4 [/tex]

Answer:

4(m-1)^2=4

(2(m-1))^2=2^2

2(m-1)=2

2m-2=2

2m=4

m=2

Answer:

12p − 33q + 16

Step-by-step explanation:

Let's simplify step-by-step.

12(p+5)−11(3q+4)

Distribute:

=(12)(p)+(12)(5)+(−11)(3q)+(−11)(4)

=12p+60+−33q+−44

Combine Like Terms:

=12p+60+−33q+−44

=(12p)+(−33q)+(60+−44)

=12p+−33q+16

=12p−33q+16

The cost of 45 blank CD's will be equal to $ 14.85.

It is given that 15 blank CD's costs $5.

We have to find out what will be the cost of 45 blank CD's.

What is the unitary method?

The unitary method is a method in which we find the value of a unit and then the value of the required number of units.

As per the question ;

Cost of 15 blank CD's = $5

So ;

The cost of 1 blank CD will be ;

= 5 ÷ 15

= $ 0.33

And

The cost of 45 blank CD's will be ;

= 45 × $0.33

= $ 14.85

Thus , the cost of 45 blank CD's will be equal to $ 14.85.

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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.

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:

y = 3 x - 9

Step-by-step explanation:

Find the equation of the line in slope-intercept form with the properties:

point: p_1 = (5, 6)

point: p_2 = (6, 9)

The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):

m = (9 - 6)/(6 - 5) = 3

Substitute the slope m = 3 and point (x_1, y_1) = (5, 6) into the point-slope equation y - y_1 = m (x - x_1):

y - 6 = 3 (x - 5)

Add 6 to both sides:

y = 6 + 3 (x - 5)

Distribute: 3 (x - 5) = 3 x - 15:

Answer: y = 3 x - 9

Answer:

about 33%

Step-by-step explanation:

Answer:e

Step-by-step explanation:

e

According to Dr. Aguilera's findings, excessive levels of anxiety are associated with poor academic performance. Sleep duration, on the other hand, is unrelated to excellent or poor academic performance.

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According to given conditions, m+n is equal to 409.

Consider the diagram below.

In the hexagon ABCDEF, let

AB = BC = CD = 3;

DE = EF = FA = 5;

Arc BAF is equal to one-third of the circle's circumference.

Hence, ∠BCF = ∠BEF = 60°;

Similarly, ∠CBE = ∠CFE = 60°;

Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.

∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.

Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.

∴ Δ ABQ is similar to Δ EDQ

[tex]\frac{AQ}{EQ} = \frac{BQ}{DQ} = \frac{AB}{ED} = \frac{3}{5}[/tex]

Also,

[tex]\frac{\frac{AD - PQ}{2} }{PQ + 5} = \frac{3}{5}[/tex]  

and [tex]\frac{3 - PQ}{\frac{AD + PQ}{2} } = \frac{3}{5}[/tex]

On solving these simultaneous equations, we get AD = 360/49

∴ m + n = 409.

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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

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°

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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[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

​

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:

is B espero que esto te ayude yo también estoy nececicando ayuda con mis trabajos

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.