What is the length of each leg of the triangle below?

Answer: A

Step-by-step explanation:

[tex]\sin \theta[/tex] is equal to the y-coordinate.

Answer: square root 3/2

Step-by-step explanation:

Answer:

5,-1  

Step-by-step explanation:

edited.... I gave 1/3   AC  earlier (misread the Q)

   This means AC is divided into fourths

x    from  6 to 2 is -4     1/4th of this added to 6 is

    6 - 1/4 * 4 =   5

y    from 1 to -7  is -8    1/4th of this added to 1 is

                   1 - 1/4 * 8 = -1  

The answers are :

a)

b)

Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.

Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.

As B lies to the left of the y-axis, its x-coordinate is negative.

As C lies to the right of the y-axis, its x-coordinate is positive.

Point D can be found using g(x). D is clearly the x-intercept so take y = 0.

Point E lies at the intersection of f(x) and g(x). So they have to be equated.

Answer:

see explanation

Step-by-step explanation:

(a)

A lies on the y- axis with x- coordinate of zero

substitute x = 0 into either of f(x) or g(x) for y- coordinate

g(0) = 2(0) + 1 = 0 + 1 = 1

then A (0, 1 )

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

B and C lie on the x- axis with y- coordinate of zero

let f(x) = 0 and solve for x , that is

1 - x² = 0 , then

x² = 1 ( take square root of both sides )

x = ± [tex]\sqrt{1}[/tex] = ± 1

then B (- 1, 0 ) and C (1, 0 )

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

D is the point on the x- axis where g(x) crosses

let g(x) = 0 and solve for x

2x + 1 = 0 ( subtract 1 from both sides )

2x = - 1 ( divide both sides by 2 )

x = - [tex]\frac{1}{2}[/tex]

then D (- [tex]\frac{1}{2}[/tex] , 0 )

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

(b)

E is the point of intersection of f(x) and g(x) so equate them, that is

2x + 1 = 1 - x² ( subtract 1 - x² from both sides )

x² + 2x = 0 ← factor out x from each term

x(x + 2) = 0

equate each factor to zero and solve for x

x = 0 ← x- coordinate of A

x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E

substitute x = - 2 into g(x) for corresponding y- coordinate

g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3

then E (- 2, - 3 )

The equation 7x + 28 = 7(x + 4) has infinite many solutions

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

7x + 28 = 7(x + 4)

Open the bracket

7x + 28 = 7x + 28

Subtract 7x from both sides of the equation

28 = 28

Subtract 28 from both sides of the equation

0 = 0

The above equation is true, because both sides of the equation are the same

This means that the equation has infinite many solutions

Hence, the equation 7x + 28 = 7(x + 4) has infinite many solutions

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Secured loans exist as loans for which the borrower posts some collateral. This exists in contrast to loans that exist created only on the ground of creditworthiness and trust in the borrower, for which no collateral exists pledged (unsecured loans).

The difference between a secured loan and an unsecured loan exists a secured loan needs collateral and an unsecured loan does not.

Secured loans exist backed by an asset, like a house in the case of a mortgage loan or a car with an auto loan. An unsecured loan on the other hand lives not connected to any of your assets and the lender can't automatically seize your property as payment for the loan.

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Answer:

(x+1)(x-2)(x-1)(x-1+2¡) multiply all together

Step-by-step explanation:

(x+1)(x-2)(x-1)(x-1+2¡)

multiply all together u have your answer

❄ Hi there,

keeping in mind that the sum of complementary angles is 90°,

set up an equation, letting [tex]\angle2[/tex]  be x  –

[tex]\triangleright \ \sf{\angle1+x=90}[/tex]                 {and we know that [tex]\boxed{\angle1=45}[/tex]}

[tex]\triangleright \ \sf{45+x=90}[/tex]

[tex]\triangleright \ \sf{x=90-45}[/tex]

[tex]\triangleright \ \sf{x=45}[/tex]

[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]

      __________

Keeping in mind that a right angle is 90°,

set up an equation, letting [tex]\angle1[/tex] be x:

[tex]\triangleright \ \sf{x+\angle2=90}[/tex]                       {and we know that [tex]\boxed{\angle2=63}[/tex]}

[tex]\triangleright \ \sf{x+63=90}[/tex]

[tex]\triangleright \ \sf{x=27}[/tex]

[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]

❄

She paid a simple interest of $3,125.00 on the borrowing of $25,000

What is simple interest?

The simple interest on a loan or an investment can be determined as the principal multiplied by interest multiplied by the number of periods.

This is quite different from compound interest where the interest earned previously would earn interest in the future alongside the principal

I=PRT

I=interest on loan=unknown

P=amount borrowed=$25,000

R=interest rate=1% per month

T=12.5 months( from December 2 2011 to December 1 2012 makes one year and from December 1-16 gives 15 days, which is 0.5 of one month)

I=$25,000*1%*12.5

I=$3,125.00

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Answer:

4 hours

Step-by-step explanation:

Hour1-

Bicycle = 24.50

ElectricScooter = 32

Hour2-

Bicycle = 34

ElectricScooter = 39

Hour3-

Bicycle = 43.5

ElectricScooter = 46

Hour4 -

Bicycle = 53

ElectricScooter = 53

Answer:

(9/3) * 4 * 2

Step-by-step explanation:

:DDDD

Answer:

2(9 / 3) * 4

Step-by-step explanation:

this is one of the many ways to solve this

9/3 is 3

2 times 3 is 6

6 times 4 is 24

therefore 2(9 / 3) * 4 is 24

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

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

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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The statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK. Option B and E

Ray NL creates two angles in the lower right quadrant.

The two angles created form a total of  90°, so the two angles formed are complementary. The relation is given as;

∠MNL + ∠KNL = ∠MNK = 90°

Hence ∠MNL and ∠KNL are complementary

∠GNM and ∠JNK are both right angles (and also vertical angles). They sum up to180°. They can be said to be supplementary.

∠GNM and ∠JNK are supplementary

Thus, the statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK

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Answer:

16 batches

Step-by-step explanation:

we can divide 12 by 3/4 or 0.75: 12/0.75 = 16

Answer:

80 in.²

Step-by-step explanation:

The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.

Square: area = s²

Square: side = 4 in.

Triangular side: area = bh/2

Triangular side: base = 4 in.; height = 8 in.

Area of the base: s² = (4 in.)² = 16 in.²

Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²

Surface area = 16 in.² + 64 in.² = 80 in.²

Step-by-step explanation:

x×1/2×1/4×3/4

x×3/32

3/32x

The order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1. This tells us tgat the highest probability is number 4 while the lowest is 1.

In mathematics, this is the concept that is used to talk about the likelihood of having an event occurring.

The probability of these items have been calculated below

1. Winning the Lottery

probability = 1/49P6

= 0.00000000009932

2. Rolling a 7:

we have to find the group of 7's

= (2,5) (1,6), (3,4), (4, 3), (6,1), (5,2)

= 6/36 = 0.1666

3. Drawing the Ace of Spade

1/52 = 0.019

4. 2 Heads in a Row:

1/2 x 1/2

= 0.25

5. Marbles:

3 + 4+ 5 = 12

3/12 * 3/12 * 3/12

= 0.01562

Hence the order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1

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Answer:

angle <B = 76

Step-by-step explanation:

The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.

We can write the following equation with this information to find the value of angle <B

<B + 71 = 147 subtract 71 from both sides

<B = 76

Answer:

C. x > 5 or x < - 3

Step-by-step explanation:

Step 1:

x - 1 > 4

x > 4 + 1

x > 5

Step 2:

x - 1 < -4

x < -4 + 1

x < -3

HP: {x > 5 or x < -3} (c)

a) 88 degrees

b) 44 degrees

we just need to reflect the graph of g(x) around the y-axis, and then shift the whole graph 5 units upwards.

Here we have two functions:

[tex]g(x) = ln(x)\\\\f(x) = ln(-x) + 5[/tex]

Ok, let's start with g(x), which graph we know. If we reflect it around the y-axis, then the new function will be:

f(x) = g(-x)

If now we shift it up 5 units, then we get:

f(x) = g(-x) + 5

Replacing g(x):

f(x) = ln(-x) + 5

Which is our function

So we just need to reflect the graph of g(x) around the y-axis, and then move the whole graph 5 units upwards.

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Answer:

6%

Step-by-step explanation:

Got it right on the test.

Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:

p = 98/150 = 0.6533.

Out of the next 75 couples, the amount is:

A = 0.6533 x 75 = 49

Hence, out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.

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Answer:

Below

Step-by-step explanation:

Using the given law of cosines    c = 26   a = 50   b = 29

      and cos c   is  cos x  

26^2 = 50^2 + 29^2 - 2(50)(29) cos x

-2665 = -2900 cos x

cos x = 2665/2900

x = arc cos ( 2665/2900) = 23.2°

Answer:

3/10

Step-by-step explanation:

There are totally 5 disks. On the first pick, there are 3 red discs. So

P(red disc on first pick ) = 3/5

Assuming that a red disc has been picked the first time, there will be 2 red discs and 2 blue discs so

(P red disc on second pick given red disc on first pick) = 2/4

P(red disc on both picks) = 3/5 x 2/4 = 3/10

a) The target cost for Model J20, assuming that the historical markup on product cost and selling price is maintained, is $200 per unit.

b) The required cost reduction per unit is $30 per unit ($230 - $200).

c) An evaluation of the three engineering improvements together to determine if the required cost reduction (drift) can be achieved as follows:

While the calculated cost reduction, including direct materials, is $25, the required reduction to achieve the target markup cost is $30.

Thus, the expected target cost reduction does not add up with the calculated cost reduction, envisaged by the engineers.

Model J20 Selling price per unit = $460

Direct materials $175

Direct labor 40

Factory overhead 15

Total $230

Direct labor rate = $30 per hour

Direct labor rate per minute = $0.50 ($30/60)

Direct labor hours per unit = 1¹/₃ hours ($40/$30) or 80 minutes

Normal direct labor time = 80 minutes

Plastic printer cover =        -15 minutes

Total new direct labor time = 65 minutes

Direct labor rate per unit = $32.50 ($0.5 x 65)

Additional inspection time = 6 minutes

Injection molding machine = 1 minute

Direct materials cost = $155 ($175 - $20)

Historical markup = 200% ($460/$230 x 100)

Target cost based on historical markup = $200 ($400 x 100/200)

Required cost reduction per unit is $30 per unit ($230 - $200)

1. Direct labor reduction of $7.50 per unit ($40 - $32.50)

2. Additional inspection $3 per unit (6 x $0.50)

3. Injection molding productivity improvement $0.50 per unit

4. Material cost reduction = $20

Total savings are $25 per unit ($7.50 - $3 + $0.50 + $20).

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Answer:

below

Step-by-step explanation:

1) slope = rise / run

2 coordinates are (-4, 0), (0, 2).

2 - 0 = 2

0 -- 4 = 4

2 / 4 = 1/2 so the slope is 0.5 or ½

2) it crosses the y axis at the average of the origin and 4.

4 + 0 = 4 / 2 = 2 so y intercept is 2.

3) in y= mx + b form

f(x) = ½x + 2, or, f(x) = 0.5x + 2

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₀: μ ≠ 7

Next, we would calculate the t-test as follows:

[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]

t = 0.08/0.0668

t = 1.198.

For the p-value, we have:

P-value = P(t < 1.198)

P-value = 0.1262.

Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.

In conclusion, yes the mean discharge differs from 7 fluid ounces.

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