Find the value of x in the triangle
shown below.

X
85
67

Answer:

A

Step-by-step explanation:

[tex]f(x) = y[/tex] (output)

[tex]y = 16\\y = 2^x\\2^x = 16\\2^x = 2^4\\x = 4[/tex]

x = number of rounds

y = number of points

In the 4th round, 16 points will be rewarded.

The value of the function at x = 4 will be 16. Then the correct option is A.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The exponent is given as

y = a(b)ˣ

The exponent function is given below.

f(x) = 2ˣ

Then the value of the variable x when the value of the function is 16.

f(x) = 16

2ˣ = 16

2ˣ = 2⁴

x = 4

The value of the function at x = 4 will be 16. Then the correct option is A.

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Answer:

21-14a

Step-by-step explanation:

You have to distribute the (2/3) into the (15-21a) then add it to the 11.  So after distributing the (2/3) into the (15-21a) is (10-14a).  Then add that to the 11

Answer:

-14a + 21

Step-by-step explanation:

11 + 2/3(15 - 21a)

Expand brackets.

11 + 2/3(15) + 2/3(-21a)

11 + 30/3 + -42/3a

Evaluate.

11 + 10 + - 14a

21 + - 14a

Answer: All three of the altitudes lie entirely outside the triangle.

Step-by-step explanation:

The orthocenter is the center of the triangle formed by creating all the altitudes of each side.  

The altitude of a triangle is formed by creating a line from each vertex that is perpendicular to the opposite side.  

In acute traingle , the orthocenter lies inside it.

In right angled triangle, the orthocenter lies on the triangle.

In obtuse triangle , the orthocenter lies outside the triangle because all the three altitudes meet outside .

So, the best explains why the orthocenter of an obtuse triangle is outside the triangle : All three of the altitudes lie entirely outside the triangle.

Answer: It’s A on edge

Answer:

The answer is option C

The balance will be C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest,

then the interest amount earned is given by:

[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]

The formula will become

A (n) = 700 • (1 + 0.03)^(n – 1)

Where n = 5 years

A (5) = 700 • (1 + 0.03)^(5 – 1)

A (5) = 700 • (1 + 0.03)^(4)

Thus, the account balance at the beginning of 5 years or at the end of 4 years;

A (5)=700×(1+0.03)^(4)

A (5)=787.8

Hence, The answer is C. A(n) = 700 • (1 + 0.03)^(n - 1); $787.86.

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Answer:

x = 4

Step-by-step explanation:

The equation given is a radical equation, we will solve using the steps below:

√x+5 + √x = 15÷√x+5

√x+5 + √x  = [tex]\frac{15}{\sqrt{x+5} }[/tex]

Multiply both-side of the equation by [tex]\sqrt{x+5}[/tex]

[tex]\sqrt{x+5}[/tex](√x+5 + √x)  = [tex]\frac{15}{\sqrt{x+5} }[/tex]  × [tex]\sqrt{x+5}[/tex]    ----------------------------------(2)

Note

[tex]\sqrt{x+5}[/tex]  ×   [tex]\sqrt{x+5}[/tex]  = x +5

Also at the right-hand side of the equation  [tex]\sqrt{x+5}[/tex] cancel-out  [tex]\sqrt{x+5}[/tex] leaving us with just 15

so equation(2) becomes

x+5 +√x  [tex]\sqrt{x+5}[/tex] = 15

subtract 5 from both-side of the equation

x+5-5 +√x  [tex]\sqrt{x+5}[/tex] = 15-5

x +√x  [tex]\sqrt{x+5}[/tex] = 10

subtract x from both-side of the equation

x-x +√x  [tex]\sqrt{x+5}[/tex] = 10-x

√x  [tex]\sqrt{x+5}[/tex] = 10-x

square both-side of the equation

(√x  [tex]\sqrt{x+5}[/tex]) ² = ( 10-x)²

x (x+ 5) =  ( 10-x)(10-x)

open the bracket

x² + 5x = 100 - 20x + x²

subtract x² from both-side of the equation

x² -  x² + 5x = 100 - 20x + x² - x²

5x  = 100 - 20x

collect like term

5x + 20x = 100

25x = 100

divide both-side of the equation by 25

25x/25 = 100 /25

x = 4

Answer:

Multiply every coordinate from the old one by 0.75

Step-by-step explanation:

I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.

The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.

Answer:

x, y ----> 3/4x, 3/4y

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

2πr (230/360) = 2(3.142)(40) = 160.59 cm = circumference

160.59 = 2πr

base radius = 25.56 cm

Use pythagorean formula for semi-vertical height

40² = h² + 25.56²

h = 30.77 cm

volume = 1/3πr²h

V = 1/3(3.142)(25.56)²(30.77) = 21,053.98 cm³

Answer:

Angle:

When two lines/rays intersect at a point, they form an angle.

=> Angles may be in radians and degrees.

See the attached file in which two rays intersect to form an angle.

Answer:

[tex]\boxed{\mathrm{view \: explanation \: and \: attachment}}[/tex]

Step-by-step explanation:

Two lines (arms/rays) intersect at one point (vertex) creating an angle.

Answer:

r=2

Step-by-step explanation:

y = k x^r  is the formula for a direct variation

y = k x^ -r is the formula for a indirect variation

20= 5 (1/2)^ -r

Divide each side by 5

4 = (1/2) ^ -r

Rewriting

2^2 = 2^ -1 ^ -r

2^2 = 2 ^ r

The bases are the same so

2 =r

Answer:

r=-2

Step-by-step explanation:

because i had this questiion and i got it right

Answer: {Route2, Route3, Route4} (Total 3  outcomes)

Step-by-step explanation:

Given: There are 4 different routes from Ben's house back to their home in Garland.

Let Sample space for all outcomes: {Route1, Route2, Route3, Route4 }

Ben  chooses Route 1.

The possible outcomes of the routes taken by the family if Ben  chooses first:

{Route2, Route3, Route4}

Hence, the possible outcomes of the routes taken by the family if Ben  chooses first: {Route2, Route3, Route4} (Total 3 choices)

Greetings from Brasil...

Using Cossine we will get the length L of ladder

COS 35 = 5/L

Answer:

the expansion is 6a-4b+b

the simplification is 6a-3b

Answer:Hey there...

Step-by-step explanation: 2(3a - 2b) + b

 Apply Distributive property

                                      (2*3a - 2*2b) + b

                                      ( 6a - 4b) + b

                                       2b + b

                                    = 3b

Hope this helps :)

Answer:

A is the correct answer

Hope this helps :)

Answer:

Step-by-step explanation:

This is because you have to substitute numbers.

So,

f(x) = 4 * 2^x

f(1) = 4 * 2^1 = 8

f(2) = 4 * 2^2 = 16

f(3) = 4 * 2^3 = 32

This shows exponential growth. Hope this helped!

Hope this helps,

Kavitha

Step-by-step explanation:

-3x² + 2y² + 5xy -2y + 5x² - 3y²

= -3x² + 5x² +2y² -3y² + 5xy -2y

= 2x² - y² +5xy -2y

2 terms

Answer:

d = 9

Step-by-step explanation:

Use the slope formula to calculate m and equate to m = 3

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(d, 21)

m = [tex]\frac{21-6}{d-4}[/tex] = [tex]\frac{15}{d-4}[/tex] = 3 ( multiply both sides by d - 4 )

3(d - 4) = 15 ( divide both sides by 3 )

d - 4 = 5 ( add 4 to both sides )

d = 9

Answer:

h = 7 units

Step-by-step explanation:

Jessica made an error with the [tex]\frac{1}{2}[/tex] in that she multiplied A by it instead of dividing.

Given

A = [tex]\frac{1}{2}[/tex] bh

with A = 17.5 and b = 5, then

17.5 = [tex]\frac{1}{2}[/tex] × h × 5 ( multiply both sides by 2 to clear the fraction )

35 = 5h ( divide both sides by 5 )

h = 7

it is wrong .

Jessica's mistake:

A = 1/2bh

1/2A • b = h >she should multiply the area with 2 not 1/2 and divide the area by b rather than multiply by b

1/2 (17.5)(5) = h

43.75 = h

correct answer:

A = 1/2bh

2A/b=h

h=2(17.5)/5

h=7

Answer:

Step-by-step explanation:

To solve for BC we use sine

sin ∅ = opposite / hypotenuse

From the question

AC is the hypotenuse

BC is the opposite

So we have

sin 58 = BC / AC

sin 58 = BC / 14

BC = 14 sin 58

BC = 11.87

BC = 11.9 to one decimal place

Hope this helps you

Answer:

[tex]\boxed{BC = 11.9 \ cm}[/tex]

Step-by-step explanation:

Sin A = [tex]\frac{opposite}{hypotenuse}[/tex]

Where A = 58°, Opposite = BC and AC = 14 cm

Sin 58 = [tex]\frac{BC}{14}[/tex]

BC = 0.848 * 14

BC = 11.9 cm

Answer:

The diagram shows a playground which is a combination

of three different shapes. TSVU is a square, SRQV is a

trapezium and PQVU is a parallelogram. Calculate the

total area of the playground

Answer:

x=20

Step-by-step explanation:

3x + 2x + 80=180

5x+80=180

5x=100

x=20

Answer:

x = 20 degrees

Step-by-step explanation:

For this problem, it is important to know that the measure of a line is 180 degrees.  With this in mind, let's build an equation:

3x + 80 + 2x = 180

Now that we have this equation, let's solve for x.

3x + 80 + 2x = 180

5x + 80 = 180

5x = 100

x = 20

Hence, x is 20 degrees.

Cheers.

Answer:

The solution of the system of equations are;

(-2, -6) and (4, 6)

Step-by-step explanation:

-2·x + y = -2...............(1)

[tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]........(2)

Equation (1) gives;

y = 2·x - 2

From which we have;

[tex]2 \cdot x - 2 = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex]

[tex]0= -\dfrac{1}{2} \cdot x^2 + x + 4[/tex]

x² -2·x -8 = 0

(x - 4)·(x + 2) = 0

x = 4 or x = -2

The y-coordinate values are;

y = 2×(-2) - 2 = -6 and y = 2×(4) - 2 = 6

The solution points are;

(-2, -6) and (4, 6).

The points where the equation, -2·x + y = -2 and the equation [tex]y = -\dfrac{1}{2} \cdot x^2 + 3 \cdot x + 2[/tex] intersect are  (-2, -6) and (4, 6).

Answer:

StartFraction x over 7.5 EndFraction = StartFraction 12 over 1 EndFraction

Step-by-step explanation:

Here, in this question, given that Rosa earns $12 in an hour, she earns x dollars in 7.5 hours. So we are interested in finding the value of x.

Let’s write this in terms of proportion;

$12 = 1 hour

$x = 7.5 hours

$12 * 7.5 hours = $x * 1 hour

So this can be rewritten as;

$x/7.5 = $12/1 hour

Answer: Start Fraction x over 7.5 End Fraction Start Fraction 12 over 1

explanation:

Answer:

-5/24 miles

Step-by-step explanation:

The submarine descends at a rate of -5/6 miles every 4 minutes.

To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:

[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]

=> D = -5 / (6 * 4) = -5/24 miles

Therefore, the submarine's depth is -5/24 miles.

Answer:

-1 1/5

Step-by-step explanation:

I took the test and this was the correct answer :D

Answer:

45°

Step-by-step explanation:

Since the diagonal cuts the square into two triangles, the angles b, a, and , c all add up to 180°. Because the shape is a square we know that one of the angles is right/90° meaning the two remaining angles are 45°. Angles a, and c had the diagonal drawn through so those two angles are each 45° and b is 90°, and since they are asking for bac we know that they want the middle angle, i.e angle A.

Since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.

Thus, since ABCD is a square, and AC is the diagonal of the square, therefore, the measure of angle BAC would be: B. 45°.

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Answer:Sin

Step-by-step explanation:

right angled triangle special trig functions can be applied

Answer:

60

Step-by-step explanation:

The measurement of the angle Q will be equal to 60°.

An isosceles trapezoid is a convex quadrilateral with one pair of opposite sides bisected by a line of symmetry. It is a subset of the trapezoid. It can also be defined as a trapezoid with equal lengths for both legs and base angles.

Given that the angle S= 120. The measure of the angle Q will be calculated as:-

∠Q = ∠R = 120°

The pair of the two angles with the two parallel lines are supplementary.

∠R + ∠Q = 180

120 + ∠Q = 180

∠Q = 180 - 120 = 60

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Answer:

Total number of animals in the group = 170

Step-by-step explanation:

Let the number of sheep = a

Number of dragons in the group = 75

Number of dragons opposite dragons = 37

Number of sheep opposite to the dragon = 1

Number of sheep left = a - 1

Number of sheep opposite to sheep = [tex]\frac{(a-1)}{2}[/tex]

Since. number of sheep opposite to sheep is 10 more than of dragons opposite dragons,

[tex]\frac{(a-1)}{2}[/tex] = 37 + 10

[tex]\frac{(a-1)}{2}=47[/tex]

a - 1 = 94

a = 95

Then total number of animals in the group = Total number of sheep + Total number of dragons

= 95 + 75

= 170

Therefore, total number of animals in the group are 170.

Answer:

A. - 4

Step-by-step explanation:

f(4) = 4(4) - 20 = 16 - 20 = - 4

Answer:

Step-by-step explanation:

From the diagram, mAD lies on the line BDF. Sum of angle on a straight line is 180°. According to the line BDF; mAB + mAD = 180°

From the diagram, mAB = 43°. Substituting this value into the above equation;

mAB + mAD = 180°

43° + mAD = 180°

mAD = 180°-43°

mAD = 137°

Hence, the measure of angle mAD is 137°

Answer:

Es lo mismo, la unica diferencia es que se ve differente. La tabla de frecuencia tiene dos lados igual a la de la tabla de barras.