There are 27 brown cows and black cows in a field. Then some of the cows go into the barn. Now there are 38 cows in the field. How many cows went into the barn?

Step-by-step explanation:

3(6+b)-(2b+1)

=18+3b-2b+1

=18+1+3b-2b

=19+b

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

−x+y+1

Step-by-step explanation:

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

plug 1 in for t

\(F(t)=4(\frac{1}{2^3^t})\\ F(1)=4(\frac{1}{2^3^*^1})\\ F(1)=4(\frac{1}{2^3})\\ F(1)=4(\frac{1}{8})\\ F(1)=\frac{4}{8} \\F(1)=\frac{1}{2}\)

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Multiply the number of possible outcomes of pulling a marble out times the number of possible outcomes o rolling the die to find the total amount of outcomes in the sample space.

There are 4 different possibilities of pulling a marble out of a box: white, green, blue and orange. Since the die has 12 outcomes, then the total amount of outcomes in the sample space is:

Answer:A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.Apr 8, 2018

Answer:

\(sqrt{-64} =8i\\\\sqrt{-15} =isqrt{15} \\sqrt{-100} =10i\\sqrt{-25} =2i\sqrt{6}\)

Step-by-step explanation:

I hope this helps

The perimeter of the trapezoid is given as follows:

44 cm.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6.

Hence the perimeter is given as follows:

P = 18 + 10 + 10 + 6 = 44 cm.

The trapezoid is given by the image presented at the end of the answer.

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Answer:

340.8 m

Step-by-step explanation:

Find the area of rectangles:

15 x 8 = 120

6x8=48

16x8=128

Find area of triangle:

1/2 5.6 x 16 = 44.8

Add together:

120 + 48 + 128 + 44.8 = 340.8 m

Hope this helps :)

The period of oscillation is 3 seconds

A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.

The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds

Oscillation can also be vibration or revolution or cycle.

Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.

This means that the period of the particle is 3 seconds.

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Answer:

As x→∞, y→-∞

Step-by-step explanation:

Notice how as the x values increase, the y values get closer to negative infinity. As the x values decrease into the negatives, the y values get closer to positive infinity.

Answer:

Slope = 1/5

Step-by-step explanation:

Given equation,

→ -x + 5y = 10

The slope-intercept form,

→ y = mx + b

→ slope = m

Now the slope-intercept form is,

→ -x + 5y = 10

→ 5y = x + 10

→ y = (x + 10)/5

→ [ y = (1/5)x + 2 ]

Then the required slope will be,

→ y = (1/5)x + 2

→ Slope = m = 1/5

Hence, the required slope is 1/5.

Answer:

\(\textsf{Slope}=\dfrac{1}{5}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Given equation:

\(-x+5y=10\)

To find the slope of the given equation, use algebraic operations to isolate y.

Add x to both sides of the equation:

\(\implies -x+5y+x=10+x\)

\(\implies 5y=x+10\)

Divide both sides of the equation by 5:

\(\implies \dfrac{5y}{5}=\dfrac{x+10}{5}\)

\(\implies y=\dfrac{1}{5}x+\dfrac{10}{5}\)

\(\implies y=\dfrac{1}{5}x+2\)

The coefficient of x is the slope of the equation.

Therefore, the slope of the given equation is ¹/₅.

Answer:

D. x = −1

Step-by-step explanation:

In the graph, the vertex of the parabola hits point (-1,-2). Therefore, the axis of symmetry is x = -1. It is not y = -2, since the parabola opens vertically, not horizontally.

Answer:

Oldest to newest:

10^-35, 10 ^-10, 0

Step-by-step explanation:

Scientific notation

To figure out the power of 10 think "how many places do I move the decimal point?"

When the number is 10 or greater the decimal point moves to the left, and the power of 10 is positive.

When the number is smaller than 1 the decimal point moves to the right, so the power of 10 is negative.

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

The answer is A, 20%.

Step-by-step explanation:

If you find 30 out of 150, it is 20%. A simple way to do it is add 30 up until you get 150. So in this case it is 5 times. Then you do 100% divided by 5 which is 20%. Hope this helps!

The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

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Answer:

21 x 33 = 693

16 x 7 divided by 2 = 216

17.6 x 17.6 divided by 2 = 154.9

19 x 7.8 = 148.2

7 + 2 x 5.5 divided by 2 = 24.8

10 x 12 = 120

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