Help plz! I don't know how to find the domain!


Find the domain.

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

Answer:

3-(-6)​ = 9

Step-by-step explanation:

3-(-6) simplifies to 3 + 6.

We would have to distribute the outside negative into the inside to get rid of the parenthesis. Then, we would add.

\(3-(-6)\\\\-1 * -6 = 6\\\\3-(-6)=\boxed{3+6}=9\)

Hope this helps.

Answer:

9%

Step-by-step explanation:

p*r*t = Interest

$6000*x*10 years = $5400

interest ÷ time ÷ principal = rate

5400 ÷ 10 ÷ 6000 = 0.09

0.09 = 9%

The amount of juice served this year is given as follows:

513 gallons.

The amount of juice served this year is obtained applying the proportions in the context of the problem.

The amount last year was given as follows:

540 gallons.

The percentage of this year's amount relative to last year's amount is given as follows:

95%, due to the decay of 5%, 100 - 5 = 95%.

Hence the amount of juice served this year is given as follows:

0.95 x 540 = 513 gallons.

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Step-by-step explanation:

can't answer this without a picture of the graphs and equations

Answer:

f(t) =, for>0

-148)=, for 1>0

0 1- 100)=,for>0

of +13)

-25,for1>0

0-5-10

-252, for r>0.

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Answer:

Step-by-step explanation:

FALSE

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees

Answer:

.20x = 72, so x = 360

.30(360) = 108

Answer:

m^2

Step-by-step explanation:

area of square=side^2=m^2

Step-by-step explanation:

Answer:

\(4\text{x}^6\)

Step-by-step explanation:

Area of the square pasture = L² where:

M is the

length of one side of the pasture

Given

\(\text{M} = 2\text{x}^3\)

\(\text{Area of the pasture} = (2\text{x}^3)^2\)

\(\text{Area of the pasture} =2\text{x}^3\times2\text{x}^3\)

\(\text{Area of the pasture} = 4\text{x}^{3+3}\)

\(\text{Area of the pasture} = 4\text{x}^6\)

Hence the area of the pasture is \(\bold{4x^6}\)

Answer:

\(\frac{2}{5}\)

Step-by-step explanation:

Use the following equation:

slope (m) = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Let:

\((x_1 , y_1) = (4 , 4)\\(x_2 , y_2) = (9 , 6)\)

Plug in the corresponding numbers to the corresponding variables:

m = \(\frac{6 - 4}{9 - 4} = \frac{2}{5}\)

\(\frac{2}{5}\) is your slope.

Answer:

\(m = \frac{2}{5} \)

Step-by-step explanation:

Slope is equal to the change in y over the change in x, or rise over run.

\(m = \frac{change \: in \: y}{cahnge \: in \: x} \)

The change in x is equal to the difference in x-coordinates  and the change in y is equal to the difference in y-coordinates.

\(m = \frac{y2 - y1}{x2 - x1} \)

Substitute in the values of x and y into the equation to find the slope.

\(m = \frac{4 - (6)}{4 - (9)} \)

Simplify.

\(m = \frac{2}{5} \)

Therefor, the answer is m = 2/5.

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

The original amount of the sale is $165

The given parameters are:

Bill after discount = $140

Discount = 15%

The original amount of the sale is calculated as:

Bill after discount = original amount * (1 - Discount)

So, we have:

140 = original amount * (1 - 15%)

This gives:

140 = original amount * 0.85

Divide by 0.85

Original amount = 165

Hence, the original amount of the sale is $165

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Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

In parallelogram QRST, if  n/Q=33°, m∠T = 33°.

In a parallelogram, opposite angles are congruent. When opposite angles are congruent, it means that the angles located on opposite corners of a shape are equal in measure. This is true for several types of shapes, including parallelograms, rectangles, and squares.

Since we know that ∠Q has a measure of 33°, the opposite angle (∠T) will also have the same measure. Therefore, m∠T = 33°.

Congruent opposite angles are important in geometry because they allow us to determine other angles or side lengths of a shape through the use of angles relationships and congruence.

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The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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Answer:

2/3

Step-by-step explanation:

Answer: 66.66%

Step-by-step explanation: You multiply 0.66666... by 100 and that gives you 66.66

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

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Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

\(h(t) = -16t^{2} + 32t + 128\)

How long will it take the projectile to hit the ground?

It happens when \(h(t) = 0\)

So

\(h(t) = -16t^{2} + 32t + 128\)

\(-16t^{2} + 32t + 128 = 0\)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}\)

\(\bigtriangleup = b^{2} - 4ac\)

In this question:

\(-16t^{2} + 32t + 128 = 0\)

So \(a = -16, b = 32, c = 128\)

\(\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216\)

\(t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2\)

\(t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4\)

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

Answer:

third

Step-by-step explanation:

both the points are negative therefore they would be in the third quadrant

Answer:

A and B

Step-by-step explanation:

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

The surface area of the triangular prism would be =324,000cm²

To calculate the surface area of the triangular prism the formula that should be given would be as follows:

Surface area of triangular prism;

Surface area of triangular prism;= bh+(b1+b2+b3)l

where:

base length = 20cm

height = 15cm

length = 18cm

SA = 20×15(20+15+25)×18

= 300×60×18

= 324,000cm²

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To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

By 'ASA' and 'HA' congruence theorems or postulates we get both triangle are congruent.

Since, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to Given that;

In both triangle HIJ and KLM,

IJ ≅ LM

∠J ≅ ∠M

Hence, To Prove:

ΔHIJ ≅ ΔKLM

             Statements                           Reasons

1). IJ ≅ LM                               1). Given

2). ∠J = m∠M                          2). Given

3). ΔHIJ ≅ ΔKLM                    3). By HA property Or AAS property of

                                                   congruence

Therefore, By ASA and HA congruence theorems or postulates we get both triangle are congruent.

triangle

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Answer:

a

Step-by-step explanation:

;)

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

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