The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 7 meters. The top horizontal side is labeled 6 meters. The base of the left triangle formed by the height is 2 meters. Numerical Answers Expected

Answer:

14.8 feet

Step-by-step explanation:

since this is creating a right triangle you can use the Pythagorean theorem which is a^2 + b^2 = c^2, and by plugging in the one leg length and the hypotenuse length you get 14.8324 which rounds up to 14.8

The  distance between the ground and the top of the ladder is 14.8 feet.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

Hypotenuse= 16 foot,

Base = 6 feet

Using Pythagoras theorem,

H² = B² + P²

16² = 6² + P²

256 = 36 +P²

P² = 256-36

P= 14.83 feet

Hence, the distance between the ground and the top of the ladder is 14.8 feet.

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Answer:

0

Step-by-step explanation:

[tex]10 + ( - 8) - 2 \\ = 1 0 - 8 - 2 \\ = 2 - 2 \\ = 0[/tex]

Answer: 0

Step-by-step explanation: -8+-2 is -10 and -10+10 is 0

The probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

Probability is synonymous with possibility. It is concerned with the occurrence of a random event.

Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.

Given data;

Total number of sample,n(S) = 100 person

No of female or left-handed is,n(E) =5

P(E) is the probability that a randomly selected person from the sample will be female or left-handed

The probability that a randomly selected person from the sample will be female or left-handed is found as;

P(E) = n(E)/n(S)

P(E) = 5 / 100

P(E) = 0.05

Hence the probability that a randomly selected person from the sample will be female or left-handed will be 0.05.

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The equation of the line is: y + 3 = -6(x + 2) [point-slope form] or y = -6x - 15 [slope-intercept form].

Given a point (-2, -3) and a slope (m) of -6, you can write the equation of the line in point-slope form by substituting (a, b) = (-2, -3) and m = -6 into y - b = m(x - a):

y - (-3) = -6(x - (-2))

y + 3 = -6(x + 2) [point-slope form]

Rewrite in slope-intercept form as:

y + 3 = -6(x + 2)

y + 3 = -6x - 12

y = -6x - 12 - 3

y = -6x - 15 [slope-intercept form]

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The way to solve the polynomial using the methods is given below.

Polynomial by factoring:

An example is (t² + 5t + 4) / +t + 4)

= (t + 1)(t + 4)/(t + 4)

= t + 1.

Dividing polynomial by long division:

Divide the first term of the dividend by the first term of the divisor.

Put this as the first term in the quotient.

Subtract to create a new polynomial.

Continue until you can't divide anymore.

Dividing polynomial by synthesic division:

Step 1: Set up the synthetic division.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row.

Step 4: Add the column created in step 3.

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Answer:

Probability of rolling a sum of 5 is 1/9.

There are 36 different combinations because 6(first roll)*6(second roll) = 36. The only possible combinations are {1,4},{2,3}{2,3}and{4,1}

4/36 = 1/9

Step-by-step explanation:

The value of X is given so put the value of X in 1/4 (2)^x

Answer:

3

Step-by-step explanation:

AD/AB = AE/AC

8/10 = 12/AC

AC = 12(10/8)=15

EC = 15 - 12 = 3

=========================================================

Explanation:

This is the given piecewise function

[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]

We can rewrite things like this

[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]

I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.

The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]

-----------

As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get

h(a) = 3a+2

h(7) = 3(7)+2

h(7) = 23

Answer: B

Step-by-step explanation:

Plug in x for 3. Then solve.

4*(1/3)^3

4*1/9

4/9

76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or

Answer:

A. 81

Step-by-step explanation:

F(x)=[tex]3^{x}[/tex]

if x=4, then F(4) = [tex]3^{4}[/tex] = 3×3×3×3=81

Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7

The number of cases of flu on day 15 will be 1001 flus

Exponential functions are expressed as y = ab^x

Given the expression below

[tex]f(x)=10001+999e^{-0.6030x}[/tex]

In order to determine the number of cases of flu on day 15, we will substitute x = 15 into the expression to have:

[tex]f(x)=10001+999e^{-0.6030(15)}\\f(x)=10001+999e^{-9.045}\\f(15) = 10001+0.11786\\f(15) \approx 10001[/tex]

Hence the number of cases of flu on day 15 will be 1001 flus

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Answer:

Step-by-step explanation:

Evaluate the function for the value x=15.

f(x)f(15)f(15)=10001+999e−0.6030x=10001+999e−0.603(15)≈894.565217

Rounded to the nearest whole number, there will be 895 cases on day 15.

By using trigonometric properties, we will see that:

tan(x) = 3/4.

Remember that the sine of the difference is:

sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).

Here we have:

sin(90° -x ) = 0.8

Expanding the sine:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)

We know that:

sin(90°) = 1 and cos(90°) = 0, then:

sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).

Then we have:

cos(x) = 0.8

And we want to find the tangent of x, which is:

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

We already know that cos(x) = 0.8

Now, remember that:

[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]

Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.

Replacing cos(x) we get:

[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]

Then the tangent of x is:

[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]

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Answer: -2

Step-by-step explanation:

We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.

Answer:

  A.  KM

Step-by-step explanation:

A circle is named by its center. Circle K has its center at point K.

A radius is a line segment that extends from the center of the circle to a point on the circle. Point K must be one end of any radius.

Segment KM is a radius.

Segments between points on the circle are chords. The other named segments in the answer choices are all chords of the circle.

Answer:

Volume of a cylinder = 1,100cm³

Step-by-step explanation:

Volume of a cylinder = πr²h

Given

π = 22/7

r = 5cm

h = 14cm

Substitute the given information in the problem.

Volume of a cylinder = 22/7 × (5cm)² × 14cm

Volume of a cylinder = 22/7 × 25cm² × 14cm

Volume of a cylinder = 1,100cm³

The answer is (A) f(x) = x+4.

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the profit (P) in thousands for security camera with price of x, hence for a profit of at least $471, 000:

-(x - 32)² + 1000 ≥ 471

-(x² - 64x + 1024) + 1000 ≥ 471

-x² + 64x - 1024 + 1000 - 471 ≥ 0

-x² + 64x - 495 ≥ 0

x = 55 or x = 9

The prices in dollars at which Nathan can make a profit of at least $471, 000 are $55 and $9

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The transformed function is y = 1/3(log(x/3 + 4)) + 1

The parent logarithmic function is

y = log(x)

When shifted left by 4 units, we have:

y = log(x + 4)

When shifted up by 3 units, we have:

y = log(x + 4) + 3

When compressed vertically by 1/3, we have:

y = 1/3(log(x + 4) + 3)

This gives

y = 1/3(log(x + 4)) + 1

When stretched horizontally by 3, we have:

y = 1/3(log(x/3 + 4)) + 1

Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1

We have:

f(x) = log[-(x – 5)] + 4

Set the radicand greater than 0

-(x - 5) > 0

Divide by -1

x - 5 < 0

Add 5 to both sides

x < 5 -- this represents the domain

A logarithmic function can output any real number.

So, the range is [tex]-\infty < f(x) < \infty[/tex]

In the domain, we have:

x < 5

This means that the interval of decrease is [tex]-\infty < x < 5[/tex]

Rewrite as an equation

x = 5 --- this represents the equation of asymptote

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Answer:$986,4000



Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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Step-by-step explanation:

Answer:

Adults: 79 tickets

Students: 237 tickets

Step-by-step explanation:

a + b = 316    Eq. 1

b = 3a            Eq. 2

a = adults

b = students

Replacing Eq. 2 in Eq. 1

a + 3a= 316

4a = 316

a = 316/4

a = 79

from the Eq. 2

b = 3a

b = 3*79

b = 237

Check:

from the Eq. 1

a + b = 316

79 + 237 = 316

Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).

The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

A diagonal is XZ.

X(2, 5) = (x1, y1)

Z(0, 0) = (x2, y2)

Plug in the values

[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]

= (1, 2.5).

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Answer:

b.) 0

Explanation:

⇒ f(g(-1))

go from right to left while solving such function questions.

⇒ f(-1 + 2)

⇒ f(1)

⇒ (1)² -2(1) + 1

⇒ 0

Step-by-step explanation:

[tex]f(x) = {x}^{2} - 2x + 1[/tex]

[tex]f(x) = {(x - 1)}^{2} [/tex]

[tex]g(x) = x + 2[/tex]

[tex] \: [/tex]

[tex] = f(g( - 1))[/tex]

[tex] = {(x - 1)}^{2} [/tex]

[tex] = {((x + 2) - 1)}^{2} [/tex]

[tex] = {(( - 1 + 2) - 1)}^{2} [/tex]

[tex] = {(1 - 1)}^{2} [/tex]

[tex] = {0}^{2} [/tex]

[tex] = 0[/tex]

The answer is B.

Answer: A

Step-by-step explanation:

The expressions are equivalent by the distributive property.

the original height of the plant was 2mm. The correct option is the second one.

We know that the function:

y = 2 + 4x

Represents the height of a plant in mm, as a function of x, the hours kepts in sunlight.

The y-intercept is the value that y takes when we evaluate in x = 0.

So, the y-intercept is the height of the plant when it is exposed to zero hours of light.

In this case:

y = 2 + 4*x

Evaluating in x = 0

y = 2 + 4*0 = 2

This means that the original height of the plant was 2mm. The correct option is the second one.

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The volume of the piece of the metal Gina is found to be 22.82 cubic cm.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Given the density of the metal = 9.2g/cm3

Given the mass of the piece of the metal = 210 g

Assuming the volume of a piece of metal to be V

The expression for the density is shown below:-

Density = Mass / Volume

9.2 = 210 / V

V = 210 / 9

V =  22.82 cubic cm.

Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.

The complete question is given below:-

Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?

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