What is the value of x in the triangle?

Answer:

2

Step-by-step explanation:

44 = 2² × 11

40 = 2³ × 5

50 = 2 × 5²

GCF = product of common factors with lower exponent

GCF = 2

The greatest common factor of 44, 40, and 50 will be;

⇒ 2

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called Greatest common factors.

Given that;

The numbers are,

⇒ 44, 40 and 50.

Now,

The factors are find as;

⇒ 44 = 2 × 2 × 11

⇒ 40 = 2 × 2 × 2 × 5

⇒ 50 = 2 × 5 × 5

Hence, The greatest common factor of 44, 40, and 50 will be;

⇒ 2

Thus, The greatest common factor of 44, 40, and 50 will be;

⇒ 2

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(a) The side length of the square is 8 m, so its area is 64 square m.

(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.

(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.

Answer:

4

Step-by-step explanation:

1/37 of 111+1/3 of 3= 4

1/37 of 111 +1/3 of 9=6

1/37 of 111 +1/3 of 1=3.3

Answer:

4    ^x27

3

Step-by-step explanation:

2x4^2x2(6x3^2)

9

Simplifies to:

4   ^x27

3

=

4    ^x27

3  

Using translation concepts, the equation of F(x) is given as follows:

-3(x + 1)² - 4.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The effect of the transformations on G(x) = x² is given as follows:

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Answer:

395.84

Step-by-step explanation:

V=πr2h=π·3^2·14

Answer:

1/18

Step-by-step explanation:

So to find the probability of two independent events, you simply multiply the two probabilities. So the probability of rolling any individual number is 1/6 because there's 6 possibilities, and there are no duplicate numbers. So the probability of rolling a 2 the first time is 1/6. The probability of rolling a number greater than 4 has a probability of 2/6, since the numbers 5 and 6 are both greater than 4. This can be further simplified to 1/3. Multiplying these two probabilities gives you 1/18

Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Total number of sections on the spinner = 5

Number of sections with green or yellow sections = 2

Number of trials = 150

Now, the number of times Tamika should expect the spinner to land on green or yellow is,

Expected Number of lands on green or yellow = 150 × (2/5) = 60

Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.

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The nurse prepares a 1,000 ml IV of 5% dextrose and water to be infused over 8 hours.

We have given that,

5% dextrose infused over 8 hours.

We have to determine the ml of iv fluid is infused after 6 hours.

A value mixture problem involves combining two ingredients that have different prices into a single blend.

The infusion set delivers 10 drops per milliliter.

The nurse should regulate the IV to administer approximately 21 drops per minute.

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Answer:

The inverse is 5x-6

Step-by-step explanation:

To find the inverse of a function

y = ( x+6) /5

Exchange x and y

x = ( y+6)/5

Solve for y

Multiply each side by 5

5x = (y+6)/5 *5

5x = y+6

Subtract 6  from each side

5x-6 = y+6-6

5x-6 =y

The inverse is 5x-6

Step-by-step explanation:

[tex]f(x) = \frac{x + 6}{5} [/tex]

[tex] \: [/tex]

[tex]y = \frac{x + 6}{5} [/tex]

[tex] \frac{y + 6}{5} = x[/tex]

[tex]y + 6 = 5\times x[/tex]

[tex]y + 6 = 5x[/tex]

[tex]y = 5x - 6[/tex]

[tex] {f}^{ - 1} (x) = 5x - 6[/tex]

The answer is D.

Perimeter of the shape = 27.15 units.

Area = 32.3 units²

The Perimeter of the shape = 1/2(perimeter of circle) + hypotenuse and height of the triangle

Perimeter = = 1/2(2π(5/2)) + [√(9² + 5²)] + 9 = 7.85 + 10.3 + 9 = 27.15 units.

Area = 1/2(area of circle) + area of triangle = 1/2(πr²) + 1/2(bh)

Area = 1/2(π2.5²) + 1/2(5)(9)

Area = 9.8 + 22.5

Area = 32.3 units²

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thanks

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The average fat content of the ten hot dog samples is: 21.91

To calculate the average fat of the hot dog samples we must add all the values and divide the result by the number of values as shown below:

Note: This question is incomplete because there is some information missing. Here is the complete information:

Question: What is the average fat of the hot dogs?

Hot Dogs' fat

Sample 1: 25.2

Sample 2: 21.3

Sample 3: 22.9

Sample 4: 17.0

Sample 5: 29.8

Sample 6: 21.0

Sample 7: 25.5

Sample 8: 16.0

Sample 9: 20.9

Sample 10: 19.5

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Using the z-distribution, it is found that since the p-value is greater than 0.05, the proportion does not differ from 23%.

At the null hypotheses, it is tested if the proportion is of 23%, that is:

[tex]H_0: p = 0.23[/tex]

At the alternative hypotheses, it is tested if the proportion differs from 23%, hence:

[tex]H_1: p \neq 0.23[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The parameters are given as follows:

[tex]p = 0.23, n = 200, \overline{p} = \frac{51}{200} = 0.255[/tex]

The value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.255 - 0.23}{\sqrt{\frac{0.23(0.77)}{200}}}[/tex]

z = 0.84.

Using a calculator and considering a two-tailed test, as we are testing if the proportion is different of a value, with z = 0.84, the p-value is of 0.4.

Since the p-value is greater than 0.05, the proportion does not differ from 23%.

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Answer:

.

Step-by-step explanation:

Answer:

$21.44 or answer D

Step-by-step explanation:

68.99-57=11.99

37.80 x 25/100=9.45

9.45+11.99=21.44

hope this helps you

The measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.

If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.

From the given triangle, it is observed that one of the angles is 90°, showing the given triangle is a right-angle triangle.

From the Δ ABC we found;

tan 45° = AB/BC

1=AB/BC

AB=BC

sin 45° = AB/AC

(1/√2)=AB/AC

AC = √2 AB

From the graph, it is observed that

AB=BC =3 units

AC=  √2 AB

AC = 3√2 units

Hence, the measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.

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Step-by-step explanation:

1) X-intercept: -2; -4;

Y-intercept: 0.533;

2) asymptotes: x= -3 and x= -5;

3) if x→ -5(-0), then y→+∞;

if x→ -5(+0), then y→-∞;

if x→ -3(-0), then y→-∞;

if x→ -3(+0), then y→+∞;

The question was incomplete. Below you can find the missing content.

ABC is a right-angled triangle.

b=16 cm

∠C=38°

Calculate the length of AB. Give your answer correct to 2 decimal places.

The picture is also attached below.

The length of the side AB is 9.85 cm.

From the triangle, it is given that

b= AC=16 cm

∠C=38°

Given that ΔABC is a right-angled triangle.

where ∠B=90°

So, here we can apply the  SOH CAH TOA identity

As we know the value of sinθ is the ratio of the opposite side and the hypotenuse of the angle θ.

So, sinθ = opposite side/ hypotenuse

In triangle ΔABC

⇒ sin 38°= AB/AC

⇒ sin 38°= AB/16

⇒ AB= 16 sin 38°

⇒ AB= 9.85 cm

Therefore the length of the side AB is 9.85 cm.

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Answer:

There's no underlined digit

Answer:

See below

Step-by-step explanation:

3 is in the 10 000 place    = 30 000

   ( just put zeroes in place of all of the following numbers)

Answer: (r+8)/4

Step-by-step explanation:

Not much really to explain...

Answer: The function is decreasing for all real values of x where x < 1.5.

Step-by-step explanation:

The axis of symmetry is [tex]x=\frac{4-1}{2}=1.5[/tex]

Since the coefficient of [tex]x^2[/tex] is positive, the graph opens upwards.

So, the function is decreasing for all real values of x where x < 1.5.

The slope intercept equation is 3y+ 2x = -4.5,

The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

let the two points from the graph is (4, -4) and (-2, 0)

then

m= 4/ -6= -2/3

and the intercept is 1.6 as the line intersects the y- axis.

So, the slope intercept is

y= -2/3x - 1.6

3y= -2x - 4.5

3y+ 2x = -4.5

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Using the median concept, it is found that the statement is true.

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

In this problem, we have that the 50th percentile is of 33.2 hours, hence the 54th percentile has to be above 33.2 hours = above 31 hours, hence the statement is true.

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The transformations rule for changing DEF into D"E"F is

(b) T-5,0-RO. 90° (x,y)

To transform a shape is to alter its dimensions and relative placement.

To convert from DEF to D"E"F, use this rule:

(b) T-5,00 RO, 90°(x, y)

From the complete question,

When DEF is spun 90 degrees counterclockwise, it becomes GH.

Then, 5 units were subtracted from the right and translated to the left.

Assume a rotation of 90 degrees counterclockwise, and write it as:

RO, 90°(x,y)

As a symbol, the leftward translation of 5 units looks like this:

T-5,0(x,y)

When both transformations are combined, we have:

T-5,0 R0.90° (x. y)

In conclusion, the transformations rule for changing DEF into D"E"F is

(b) T-5,0-RO. 90° (x,y)

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Answer:

x = 65 , y = 64

Step-by-step explanation:

y - 16 and 2y + 4 are same- side interior angles and sum to 180° , that is

y - 16 + 2y + 4 = 180

3y - 12 = 180 ( add 12 to both sides )

3y = 192 ( divide both sides by 3 )

y = 64

then

2y + 4 = 2(64) + 4 = 128 + 4 = 132

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

2y + 4 is an exterior angle of the triangle , then

x + 67 = 132 ( subtract 67 from both sides )

x = 65

Answer:

B

Step-by-step explanation:

3kx + 2kx = 10 ← collect like terms on left side

5kx = 10 ( isolate x by dividing both sides by 5k )

[tex]\frac{5kx}{5k}[/tex] = [tex]\frac{10}{5k}[/tex]

x = [tex]\frac{2}{k}[/tex]

[tex]\displaystyle\\\binom{10}{7}=\dfrac{10!}{7!3!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=4\cdot3\cdot10=120[/tex]

Answer:

  (c)  36°

Step-by-step explanation:

We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.

Angle 1 is one of 5 congruent central angles, so its measure is ...

  ∠1 = 360°/5 = 72°

Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:

  ∠2 = 72°/2 = 36°

The measure of angle 2 is 36°.

Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...

  ∠3 = 90° -∠2 = 90° -36° = 54°