If the two remote interior angles of a triangle measure 60 degrees and 38 degrees , what is the measure of the exterior angle.

Answer:

2(2+1)-[2-(-3)]

(2×3)-5

6-5=1

Answer:

the answe will be -71 I think

sorry if I got it wrong

1) This is a case in which inscribed angles intercept an arc. So we can write out the following about the measure of ∠KJL

Note that in this case, the same case applies to both angles.

The value of x will be -7. The expression is solved using the identity.

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Given expression;

\(\rm log_2(\frac{1}{128}) = x\)

The expression is solved using the identity as;

\(\rm log_e1 = x\\\ e^x=1\)

Apply the identity;

\(\rm log_2(\frac{1}{128}) = x \\\\ 2^x = \frac{1}{128}\\\\ 2^x = \frac{1}{2^7} \\\\ 2^x = 2^{-7} \\\\ x = -7\)

Hence the value of x will bed -7.

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Alternatively, the gcf of 12 and 56 can be found using the prime factorization of 12 and 56:

The prime factorization of 12 is: 2 x 2 x 3.

The prime factorization of 56 is: 2 x 2 x 2 x 7.

The prime factors and multiplicities 12 and 56 have in common are: 2 x 2.

2 x 2 is the gcf of 12 and 56.

gcf(12,56) = 4.

Answer:

6.9−8=2

Step-by-step explanation:

(8−5)2.3−8=2

Subtract 5 from 8 to get 3.

3×2.3−8=2

Multiply 3 and 2.3 to get 6.9.

6.9−8=2

Subtract 8 from 6.9 to get −1.1.

−1.1=2

Compare −1.1 and 2.

False

Solution:

Given a circle of center O

Arc XY subtends an angle of 155°, since the angle is less than 180°, then arc XY is a minor arc.

Hence, the answer is option B

Answer:

y = \(\frac{4}{5}\) x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 4 ) and (x₂, y₂ ) = (5, 8) ← 2 points on the line

m  = \(\frac{8-4}{5-0}\) = \(\frac{4}{5}\)

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = \(\frac{4}{5}\) x + 4 ← equation of line

Answer:

There are 5 books in 1 box

Step-by-step explanation:

It is quite easy to solve. You have to use division to figure out how many books go in each box. Our division equation will be: 20 ÷ 4 = ?

We will divide 20 by 4 and our answer is 5.

We can double-check our answer by doing multiplication. 5 x 4 = 20, leading us back to the original 20 books that are in boxes.

So, there are 5 books in each box.

Hope this helps! <3

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

The population density of otter, raccoon, fox and bobcat is 0.3125, 1.66, 0.0803 and 0.0267 per acre

Total park area of the state park = 112 acres

Number of Otter = 35

Number of Raccoon = 186

Number of Fox = 9

Number of Bobcat = 3

The formula of population density is given by:

Population Density = Number of animals/Area of land

Population density of Otter in the park = 35/112 = 0.3125 Otter per acre

Population density of raccoon in the park = 186/112 = 1.66 Raccoon per acre

Population density of fox in the park = 9/112 = 0.0803 Fox per acre

Population density of bobcat in the park= 3/112 = 0.0267 bobcat per acre

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The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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Answer:

The solution set is: (-1,3)

We want to find the set of the x-values of the points that belong to the given graph and have an y-value larger than zero.

The set is: s = (-1, 3)

To find the set, we need to see the x-values of the points on the graph such that y > 0.

y > 0 means that we only look at the region of the graph that is above the x-axis.

We can see that this region goes from x =-1 to x = 3

Then for all the x-values between x = -1 and x = 3 the points p(x, y) on the graph have an y-value larger than zero.

Notice that because the value must be larger than zero, then the particular x-values:

x = -1 and x = 3 are not in the set.

So the set must be written as:

s = (-1, 3)

This is the set in the interval notation.

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Answer:

500

Step-by-step explanation:

150(100) = 15000 / 30 = 500

Answer:

\(\sf\frac{q-2ts}{2(s+t)} =r\)

Step-by-step explanation:

q = 2ts + 2sr + 2rt

First, subtract 2ts from both sides.

q - 2ts = 2sr + 2rt

Now, take the common factor out.

q - 2ts = 2r ( s + t )

Divide both sides by ( s + t ).

\(\sf\frac{q-2ts}{(s+t)} =2r\)

Now divide both sides by 2 and make "r" the subject.

\(\sf\frac{q-2ts}{2(s+t)} =r\)

Answer:

m=1

Step-by-step explanation:

\(m=\frac{8-6}{2-0} =\frac{2}{2} =1\)

I hope this help you

Answer:

x=ln(4)

Step-by-step explanation:

e^2x +3e^x- 28=0  

u^2 + 3u - 28 = 0   ==> substitute u for e^x

u^2 - 4u + 7u - 28 = 0

u(u-4) + 7(u-4) = 0

(u-4)(u+7)=0    ==> simplify

u-4=0                     u+7=0

u=4                             u=-7

e^x=4                     e^x=-7       ==> substitute e^x for u

ln(e^x)=ln(4)           ln(e^x)=-7    ==> take natural log on each side

x=ln(4)                   x=ln(-7), which is not possible since natural log>0

x=ln(4)

Answer:

\({e}^{x} = y \\ {y}^{2} + 3y - 28 = 0 \\ (y - 4)(y + 7) = 0 \\ y = 4 \\ y = - 7 \\ {e}^{x} = 4 \\ x = ln(4) \\ x = ln( - 7)\)

Step-by-step explanation:

first you need to tranfer 1 to RHS do the addition

n/3 = 8+1

=) n/3 = 9

then you need to transfer 3 to RHS and multiply

=> n = 9 x 3

there for n = 27

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer:

(2) 21 years old

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

\(3 - ( - 8) = 11\)

\(11 - ( - 2) = 13\)

Answer:

The answer would be 1

Step-by-step explanation:

If you would like to evaluate 2 * a - b for a = 2 and b = 3, you can do this using the following steps:

2 * a - b = 2 * 2 - 3 = 4 - 3 = 1

The correct result would be 1.

The interest rate that he should invest his initial amount compounded quarterly is 0.11001626264163722.

To calculate the interest rate that Tumelo should invest his initial amount at, compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the future value (goal amount) of R28000,

P is the initial amount of R14600,

r is the interest rate (to be determined),

n is the number of times the interest is compounded per year (quarterly compounding),

t is the number of years (6 years).

Plugging in the given values, the equation becomes:

28000 =\(14600(1 + r/4)^(^4^*^6^)\)

To solve for r, we need to isolate it on one side of the equation. We can do this by dividing both sides by 14600 and then taking the 6th root of both sides:

\((28000 / 14600)^(^1^/^(^4^*^6^)^) = 1 + r/4\)

Taking the 6th root of (28000 / 14600) and subtracting 1, we find:

r/4 = (28000 / 14600)^(1/(4*6)) - 1

Multiplying both sides by 4, we obtain:

r = 4 * [(28000 / 14600)^(1/(4*6)) - 1]

Therefore, r = 0.11001626264163722

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Answer:

To find the radius..just divide them by two

For the diameter multiply by two

Circumference formula is

\(2\pi \: r\)

Answer:

Step-by-step explanation:

in this triangle

X^2=a^2+b^2

X^2=15^2+8^2

x^2=225+64

x^2=289

x=17

Answer:

X is always equal to 1 no matter the equation. In this it looks like you are using Pyth. Theory. If its not sorry, but X = 1  

Step-by-step explanation:

\(A^{2} +B^{2}=C^{2} \\15^{2}+8^{2} \\225+64\\C^{2}=289\\\sqrt289\\C=17\)  

The length of the square is 1.75 inches, while the king's height is 2.25 inches.

Define length.

The length of an object or the extent of a one-dimensional object along its longest dimension is measured physically. It is a basic idea in physics and geometry and is frequently expressed in terms of meters (m), centimetres (cm), feet (ft), or inches (in).

According to the information provided, the square length to king's height ratio is 3.5 to 4.5 inches. Let's use this ratio to determine the square's length when the king is 2.25 inches tall.

We may make a proportion to get the square's length:

(square length) / (king's height) = 3.5/4.5

king's height = 2.25

Let's substitute the given values:

(square length) / 2.25 = 3.5/4.5

To solve for the length of the square, we can cross-multiply:

(square length) = (2.25) x (3.5/4.5)

(square length) = 1.75

Therefore, the length of the square is 1.75 inches, while the king's height is 2.25 inches.

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Answer:

B. -4, -3

Step-by-step explanation:

The equation x^(2) + 7x + 12 can be factored using the AC method resulting in

( x + 4 )( x + 3 ).  So x = -4, -3. You can use foil to check.

Hence, the bottom prism's width is 6 cm as volume of the cube and the bottom prism together make up the structure's overall volume.

Volume is the amount of space occupied by an object or three-dimensional area of space in physics and mathematics. Depending on the unit of measurement, it is frequently stated in cubic quantities such cubic metres (m3), cubic centimetres (cm3), or cubic feet (ft3). By multiplying an object's length, breadth, and height (or depth) together, the volume of a space can be determined. In other circumstances, it may be more difficult to determine the volume, particularly for things with irregular shapes, and may call for sophisticated mathematical methods or specialised tools.

given

Find the volume of the cube at the top of the structure to start. An equal number of sides make up a cube, hence its volume is:

V(cube) = s3 + 93 + 729 cm3

Let's now use the letter "w" to indicate the bottom prism's width. The bottom prism's volume is:

V(bottom prism) = length, breadth, and height = 8 w, 4 w, and 32 w, respectively.

The volume of the cube and the bottom prism together make up the structure's overall volume:

Total value: 729 + 32w = V(cube) + V(bottom prism)

Since we are aware that the volume is 921 cm3, we can create the following equation:

921 = 729 + 32w

729 from both sides are subtracted, giving us:

192 = 32w

When we multiply both sides by 32, we get:

w = 6

Hence, the bottom prism's width is 6 cm as volume of the cube and the bottom prism together make up the structure's overall volume.

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Answer:

Average speed was 60mph so 240 ÷ 4 = 60