Determine the measure of

CD
from the diagram below.

x = 65

Step-by-step explanation:

cos theta = 25/x

cos theta = x/169

25/x = x/169

x² = 169 x 25

x = 65

The missing length x = 65, using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

In the question, we are asked to find the value of x.

In the right triangle ABC, by Pythagoras' Theorem,

AC² + BC² = AB²,

or, x² + BC² = (144 + 25)²,

or, BC² = 169² - x² ... (i).

In the right triangle ACD, by Pythagoras Theorem,

AD² + DC² = AC²,

or, 25² + DC² = x²,

or, DC² = x² - 25² ... (ii).

In the right triangle BCD, by Pythagoras Theorem,

BD² + DC² = BC²,

or, 144² + x² - 25² = 169² - x² {Substituting BC² = 169² - x² from (i) and DC² = x² - 25² from (ii)},

or, x² + x² = 169² + 25² - 144² {Rearranging},

or, 2x² = 28561 + 625 - 20736,

or, 2x² = 8450,

or, x² = 4225,

or, x = √4225 = 65.

Thus, the missing length x = 65, using the Pythagoras Theorem.

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Answer:

(D) is equal to 8 so that means that u have to divide and multiply all in one

Answer:

Reflection

Step-by-step explanation:

a)rational number :

1)(3+4 )/2

=7/2 =3.5

2)(3.5+4)/2

=7.5/2 =3.25

b)irrational number :

1)10/3=3.33....

2)11/3=3.66....

......I hope it will help you. ..

Answer:

The real numbers, which can be represented by the ratio of two integer numbers, are called rational numbers, say P/Q where Q is not equal to zero.

The actual numbers that cannot be expressed as the two integer ratio are called irrational numbers.

Step-by-step explanation:

a)rational number :

1)

(3+4 )/2

=7/2 =3.5

2)

(3.5+4)/2

=7.5/2 =3.25

b)irrational number :

1)

10/3=3.33....

2)

11/3=3.66....

3)

√13

Answer:

D. None of the above

Step-by-step explanation:

The two right triangles have different sizes. Therefore, their areas cannot be the same as well.

Congruent triangles have the same three angles that are congruent to each other and three side lengths that are congruent or equal to each other. The two triangles only have equal angles bit different corresponding side lengths. Therefore, they cannot be congruent.

The correct answer is "None of the above".

Answer:

PROPORTIANAL SIDE LENGTHS

Step-by-step explanation:

I JUST TOOK THE TEST

Answer:

D. 7:10

Step-by-step explanation:

The Correct Answer

Answer:

hope it helps you............

Answer:

2(y - 2)(y + 1)

Step-by-step explanation:

Given

2y² - 2y - 4 ← factor out 2 from each term

= 2(y² - y - 2) ← factor the quadratic

Consider the factors of the constant term (- 2) which sum to give the coefficient of the y- term (- 1)

The factors are - 2 and + 1, since

- 2 × 1 = - 2 and - 2 + 1 = - 1 , then

y² - y - 2 = (y - 2)(y + 1)

Then

2y² - 2y - 4 = 2(y - 2)(y + 1) ← in factored form

Answer:

Step-by-step explanation:

2143.57

Answer:

y = 0.9

Step-by-step explanation:

1.05 + 0.7y = 3.5y - 1.47

-3.5y + 0.7y = -1.47 - 1.05

-2.8y = -2.52

y = 9/10 = 0.9

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]0.7\left(1.5+y\right)=3.5y-1.47[/tex]

[tex]1.05+0.7y=3.5y-1.47 \gets \textsl{Expand}[/tex]

[tex]1.05+0.7y-1.05=3.5y-1.47-1.05 \gets Subtract\; 1.05 \from\:both\:sides[/tex]

[tex]0.7y=3.5y-2.52[/tex]

[tex]0.7y-3.5y=3.5y-2.52-3.5y[/tex]

[tex]\mathrm{Subtract\:}3.5y\mathrm{\:from\:both\:sides} \nwarrow[/tex]

[tex]-2.8y=-2.52[/tex]

[tex]\frac{-2.8y}{-2.8}=\frac{-2.52}{-2.8} \hookleftarrow \mathrm{Divide\:both\:sides\:by\:}-2.8[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{y=0.9}}}}}[/tex]

[tex]\bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet \bullet[/tex]

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

Answer:

1/54

Step-by-step explanation:

1/9 x 1/6

Answer:

3 1/2 hours

Step-by-step explanation:

time = distance/speed

440/110 = 4 hours

440/880 = 1/2 hours

4 minus 1/2 is 3 1/2

Answer:

hi

Step-by-step explanation:

i just need some points sorry not sorry

Answer:

<3=75°

Step-by-step explanation:

Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)

So <3+2x+95=180

<3+2x=180-95

<3+2x=85( let's call this equation 1)

Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71

Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)

So <3+8x+71=180

<3+8x=180-71=109

Thus, <3+8x=109(let's call this equation 2)

Now solving equation 1 and 2 simultaneously:

Make <3 the subject of equation 1

<3=85-2x

Put <3=85-2x into equation 2

85-2x+8x=109

6x=24

x=24/6=4

Now, remember that angle 2x+95 becomes

2(4)+95

8+95=103°

Therefore<3=180-105=75°

Answer: Fran's speed while swimming​ upstream = 1.4 km/h

Step-by-step explanation:

Given: Fran's swimming speed = 2.1 ​km/h

Speed of river = 0.7 km/h

The direction against the stream is called upstream.

Speed in Upstream = Fran's swimming speed - Speed of river

= 2.1-0.7  km/h

= 1.4 km/h

hence, Fran's speed while swimming​ upstream = 1.4 km/h

9514 1404 393

Answer:

  acute

Step-by-step explanation:

The third angle is ...

  180° -49° -82° = 49°

So, the triangle has two angles the same, 49°. When two angle are the same, the triangle is an isosceles triangle.

The largest angle, 82°, is less than 90°, so is an acute angle. The classification acute, right, or obtuse is based on the measure of the largest angle.

The triangle is an acute isosceles triangle.

Answer:

16 Miles

Step-by-step explanation:

For every week you simply multiply the number of miles from the previous week by 2, therefore

Week 1: 1

Week 2: 2

Week 3: 4

Week 4: 8

Week 5: 16

Answer:

Tan A

Step-by-step explanation:

Tan B = opposite / Adjacent = AC / BC

Reciprocal of Tan B = 1 ÷ Tan B

1 ÷ Tan B = 1 ÷ AC/BC = 1 * BC / AC = BC / AC

Reciprocal of Tan B = BC / AC

the reciprocal of tan B is equivalent to :

Tan A = opposite / Adjacent = BC / AC

Hence, the reciprocal of Tan B is Tan A

Answer:

Note: Images are not in order. Check page number on pictures to make sure you have the right Answer.

Have a Good Day! God bless!

Step-by-step explanation:

Question 6 “A”

Question 7 “D”

Question 8 “B”

Question 9 “B”

Question 10 “A”

Note: Answers From 1 to 5 in order here:

Question 1 “ B”

Question 2 “A”

Question 3 “B”

Question 4 “D”

Question 5 “D”

Answer:

The answer is

[tex]2 {x}^{2} + 3x - 1 = 0[/tex]

Why? Below I explain

Step-by-step explanation:

That formula has three variables a, b and c.

So, a = 2, b = 3 and c = -1

Because the formula is written like

[tex] \frac{ - b + - \sqrt{ {b}^{2} - 4 \times a \times c} }{2 \times a} [/tex]

Answer:

[tex]\textbf{HELLO!!}[/tex]

[tex]21\left(2-y\right)+12y=44[/tex]

[tex]42-21y+12y=44[/tex]

[tex]~add ~similar\:elements[/tex]

[tex]42-9y=44[/tex]

[tex]Subtract~42~from~both~sides[/tex]

[tex]42-9y-42=44-42[/tex]

[tex]-9y=2[/tex]

[tex]Divide\:both\:sides\:by\:}-9[/tex]

[tex]\frac{-9y}{-9}=\frac{2}{-9}[/tex]

[tex]y=-\frac{2}{9}[/tex]

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

hope it helps...

have a great day!

Answer:

2y -6

Step-by-step explanation:

5y-3(y + 2)

Distribute

5y -3y - 6

Combine like terms

2y -6

Answer:

Step-by-step explanation:

A = [tex]pe^{rt}[/tex]

A = 100[tex]e^{.08 *15}[/tex]

A=. $332.01

The value of the investment after 15 years is $332.01.

Option A is the correct  answer.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

The continuous compounding formula is given by:

[tex]A = Pe^{rt}[/tex]

Where:

A = the ending amount

P = the principal (initial investment)

e = the mathematical constant (approximately equal to 2.71828)

r = the interest rate (as a decimal)

t = the time period (in years)

Using this formula, we can find the value of the investment after 15 years:

A = 100 \times e^{0.08 \times 15} ≈ $332.01

Therefore,

The value of the investment after 15 years is $332.01.

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Answer:

Step-by-step explanation:

[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]

The length of B'C' is 0 units.

It is the movement of the shape in left, right, up, and down direction.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The length of AD = 5 units.

Since the rectangle translates down by 4 units,

The length of A'D' =5 units.

The width of the original rectangle is AB, which is 3 units.

Since the rectangle translates to the right by 2 units,

The width of the new rectangle = 3 units.

Now,

The length of B'C' is the same as the length of AD', which is 5 units.

Subtracting 5 units from 5 units gives us a length of 0 units.

Thus,

The length of B'C' is 0 units.

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Answer:

It depends on what shape you have. Here are some formulas for different shapes.

Step-by-step explanation:

Rectangular prism: 2lw + 2lh + 2wh

Cylinder: 2 pi r² + 2 pi rh

Sphere: 4 pi r²

Cone: pi r² + pi rl

Square-based pyrimid: 1/2lp +B

I hope this helps!

Answer:

P(r ≥ 15) = 0.9943.

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

625 trials and a probability of a 4.4% success on a single trial.

This means that [tex]n = 625, p = 0.044[/tex]

Mean and standard deviation:

[tex]mu = E(X) = np = 625*0.044 = 27.5[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{625*0.044*0.956} = 5.13[/tex]

P(r ≥ 15)

Using continuity correction, this is [tex]P(r \geq 15 - 0.5) = P(r \geq 14.5)[/tex], which is 1 subtracted by the p-value of Z when X = 14.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14.5 - 27.5}{5.13}[/tex]

[tex]Z = -2.53[/tex]

[tex]Z = -2.53[/tex] has a p-value of 0.0057

1 - 0.0057 = 0.9943

So

P(r ≥ 15) = 0.9943.

Answer:

B. √2^5

Step-by-step explanation:

(2^½. 2^¾)²

= 2¹ . 2^(1½)

= 2^(2½)

= 2^(5/2)

=√2^5

Answer:

sqrt(1^2 + 2^2)

[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

a) The third interior angle of this triangle is 180 - 20 x.  

The three interior angles must sum up to 180 degrees.

Therefore,  60 + 7x + 5 + 180 - 20x = 180, or

                       65  + 180 - 13x = 180, or

                               65 -  13x     = 0

Finally, 13x = 65, and so x = 5

Answer:

Step-by-step explanation:

Answer:

rs.1680.67

Step-by-step explanation:

His salary = x

remaining % = 100 - 65 = 35%

= 100 - 15 = 85%

x × 35/100 × 85/100 = 500

x = 1680.67

Answer:

7+x

Step-by-step explanation:

X will be the unknown

Answer:

ok so

8.5*150000

1275000 cm into kilometers is

12.75 kilometers

Hope This Helps!!!