A triangle has two sides of length 40 cm and an angle of 110°.
a) Determine the length of the third side. Then find the perimeter of the triangle.
47
b) Determine the area of the triangle

Answer:

-11x-3y^2

Step-by-step explanation:

(8x^2-9x^2-4x)+(x^2-3y^2-7x)

-x^2-4x+x^2-3y^2-7x

-4x-7x-3y^2

-11x-3y^2

Answer:

Step-by-step explanation:

[tex](8x^2-9x^2-4x)+(x^2-3y^2-7x)\\\\=8x^2-9x^2-4x+x^2-3y^2-7x\qquad\text{combine like terms}\\\\=(8x^2-9x^2+x^2)-3y^2+(-4x-7x)\\\\=-3y^2-11x[/tex]

Answer:

By SAS rule

Step-by-step explanation:

Required to Prove

ABC is congruent to DEC

Given

C is midpoint of AD and BE

As C is the midpoint of both line segments

AC=CD

BC=CE

and ∠ACB=∠DCE(Vertically opposite angles)

⇒By SAS(side-AC and DC, angle-∠ACB,∠DCE,side-BC and EC) congruency rule

triangle ABC is congruent to triangle DEC

Answer:

A standard deck contains 52 cards with 4 suits and hence 4 tens. The probability of being dealt 3 tens is thus 4/52 x 3/51 x 2/50. The denominator decreases as one card is removed from the deck each time. If the removed card is replaced, there would be no need for the decrease in the denominator.

Step-by-step explanation:

The value of b is: 4

Step-by-step explanation:

The given polygon is a convex polygon with three sides. A polygon with three sides is called triangle. The sum of interior angles of a triangle is 180°

So,

[tex]Sum\ of\ Angles = 180\\(b+41)+(101)+(b+30) = 180\\b+41+101+b+30 = 180\\2b+172 = 180\\2b = 180-172\\2b = 8[/tex]

Dividing both sides by 2

[tex]\frac{2b}{2} = \frac{8}{2}\\b = 4[/tex]

Hence,

The value of b is: 4

Keywords: Polygons, Triangles

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Answer:

a: x=-2, x=-1

c:x=-2.68, x=0.186

b:x=-3.6, x=1.6

d:x=-11, x=-3

Answer:

Each batch of scones needed 0.67 kg of flour

Step-by-step explanation:

16.45 - 6.4 = 10.05kg (remaining)

15 batches = 10.05kg

1 batch = 0.67kg

Answer: 55/7π

Step-by-step explanation:

circumference = 2πr

2πr = 55/7

r = 55/14π

d = 2r

d = 55/7π

Answer:

Step-by-step explanation:

1

2+2=4 because you add it ok well bye :)

Answer:

Step-by-step explanation:

1d

2a

3b

4c

The distributive property states that performing an operation on a sum or difference (either multiplication or division) is equivalent to performing that operation on each addend separately and then summing or subtracting the results. As an example, the statement 2*(3 + 4) can be rewritten as (2*3) + (2*4) to demonstrate the application of the distributive property.

The distributive property in mathematics states that the multiplication of a number by a sum is equivalent to the sum after each addend has been multiplied by that number individually. For example, if we had the expression 2*(3 + 4), using the distributive property, we could rewrite it as (2*3) + (2*4) which is 6 + 8, and both expressions equal to 14 (because 2*(3 + 4)=2*7=14).

So to match equivalent expressions using the distributive property, you would have to identify expressions that follow this rule. For example:

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Answer:

n=66

Step-by-step explanation:

5/6n=72-17

5/6n=55

n=55/(5/6)

n=(55/1)(6/5)

n=(11*6)/1

n=66/1

n=66

Answer:

66

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

The average number of locations chosen per potential customer in the coffee company's survey was 1.5.

To calculate the average number of locations chosen per potential customer, we need to know the total number of preferences selected by all 40 potential customers. The numbers given for each location are: 20 for grocery stores, 16 for drugstores, 14 for health food stores, and 10 for big box stores.

Adding these together gives a total of 60 preferences for the four locations (20+16+14+10). This total is then divided by the 40 potential customers to produce the average. Therefore, the average number of locations chosen per potential customer is 1.5 (60 ÷ 40 = 1.5).

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There are 60 miles in Jadon's trip.

Step-by-step explanation:

Distance covered by Jadon = 42 miles

This is 70% of his entire trip.

Let,

x be the total number of miles in Jadon's trip.

We know that,

70% of x = 42 miles

[tex]\frac{70}{100}*x=42\\0.7x=42[/tex]

Dividing both sides by 0.07;

[tex]\frac{0.7x}{0.7}=\frac{42}{0.7}\\x=60\ miles[/tex]

There are 60 miles in Jadon's trip.

Keywords: distance, percentage

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Answer:

2(4b-1)

Step-by-step explanation:

The domain of a function is the set of all possible input values for the function. Reflecting a graph over the x-axis does not change the domain of the function.

The domain of a function is the set of all possible input values for the function. When a graph is reflected over the x-axis, the y-values are negated. In this case, since the graph is a horizontal line, the y-values remain the same after reflection. Therefore, reflecting the graph over the x-axis does not change the domain of the function. The domain will still be the same set of real numbers that satisfy the given condition, which is 0 ≤ x ≤ 20.

When a function is reflected over the x-axis, the domain remains the same and the sign of each value in the range is negated.

When a function f(x) is reflected over the x-axis to form -f(x), it affects both the domain and the range. Let's break it down step by step:

Original Function: f(x)

Domain: The set of all possible input values for x in the function f(x).

Range: The set of all possible output values for f(x).

Reflected Function: -f(x)

Reflected Domain: The domain remains the same because reflecting over the x-axis does not change the x-coordinates. So, the reflected domain is the same as the original domain.

Reflected Range: The range is affected by the reflection. All the positive values in the original range become negative, and all the negative values become positive. If the original function had points (a, b), the reflected function will have points (a, -b). This essentially flips the original range values.

In summary:

Reflected Domain: Same as the original domain.

Reflected Range: The sign of each value in the original range is negated. For example, if the original function had a point (2, 3), the reflected function would have a point (2, -3).

The complete question is :

how does the reflection over the x-axis (-f(x)) affect the domain and range

Answer:

(B) π/12 + π/6 k

Step-by-step explanation:

Points of inflection are where f"(x) = 0 and changes signs.

f(x) = cos²(3x)

f(x) = (cos(3x))²

f'(x) = 2 (cos(3x))¹ × -sin(3x) × 3

f'(x) = -6 sin(3x) cos(3x)

Using double angle formula:

f'(x) = -3 sin(6x)

f"(x) = -3 cos(6x) × 6

f"(x) = -18 cos(6x)

0 = -18 cos(6x)

0 = cos(6x)

6x = π/2 + 2πk or 6x = 3π/2 + 2πk

We can simplify this to:

6x = π/2 + πk

x = π/12 + π/6 k

Answer:

24% could be going to school by walking

Step-by-step explanation:

By adding the given percentages of students traveling by car, bus, and bike, and subtracting from 100%, we find that 24% of students use other methods to travel to school.

To find the other method of traveling to school not mentioned among car, bus, and bicycle, we first need to add up the provided percentages for these modes of transportation: 20% (car) + 48% (bus) + 8% (bike) = 76%. Since all the percentages must add up to 100%, we subtract the sum of these percentages from 100% to determine the remaining percentage. Therefore, 100% - 76% = 24%. So, 24% of students travel to school by other methods that are not specified (walking, skateboarding, etc.).

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Final answer:

To find the most number of miles you can drive on one tank of gas, divide the total miles driven by the total gallons used to calculate the miles per gallon (MPG). Then, multiply the MPG by the number of gallons in the gas tank to find the maximum number of miles that can be driven on one tank.

Explanation:

To find the most number of miles you can drive on one tank of gas, you can use the given information. You know that you just drove your car 450 miles and used 50 gallons of gas. Therefore, to find the miles per gallon (MPG), divide the total miles driven by the total gallons used. In this case, 450 miles divided by 50 gallons gives you an MPG of 9. This means that for every gallon of gas, your car can travel 9 miles.

Now, you know that the gas tank on your car holds 15 1/2 (or 15.5) gallons of gas. To find the maximum number of miles you can drive on one tank of gas, multiply the MPG by the number of gallons in the tank. So, 9 MPG multiplied by 15.5 gallons equals 139.5 miles. Therefore, the most number of miles you can drive on one tank of gas is 139.5 miles.

The most number of miles you can drive on one tank of gas is 139.5 miles.

To determine the most number of miles you can drive on one tank of gas, follow these steps:

Calculate the car's average miles per gallon (mpg):

You drove 450 miles using 50 gallons of gas.

The average mpg is calculated by dividing the total miles driven by the total gallons of gas used: [tex]\frac{450 \text{ miles}}{50 \text{ gallons}} = 9 \text{ mpg}.[/tex]

Determine the capacity of one full tank of gas in your car:

The gas tank holds 15 1/2 gallons of gas. Convert 15 1/2 to a decimal: [tex]15 \frac{1}{2} = 15.5 \text{ gallons}.[/tex]

Calculate the most number of miles you can drive on one full tank of gas:

Multiply the car's average mpg by the gas tank's capacity: [tex]9 \text{ mpg} \times 15.5 \text{ gallons} = 139.5 \text{ miles}.[/tex]

Answer:

We conclude that the calibration point is set too high.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  1000 grams

Sample mean, [tex]\bar{x}[/tex] =  1001.1 grams

Sample size, n = 50

Alpha, α = 0.05

Population standard deviation, σ = 2.8 grams

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}[/tex]

We use One-tailed(right) z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778[/tex]

Now, [tex]z_{critical} \text{ at 0.01 level of significance } = 2.326[/tex]

Since,  

[tex]z_{stat} > z_{critical}[/tex]

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.

Final answer:

The null hypothesis is that the calibration point is set correctly and the alternate hypothesis is that the calibration point is set too high.

Explanation:

The appropriate null and alternate hypotheses for this hypothesis test are:

H0: The calibration point is set correctly (mean scale reading = 1000 grams)

H1: The calibration point is set too high (mean scale reading > 1000 grams)

This hypothesis test is a right-tailed test because the alternate hypothesis is testing for a value greater than the null hypothesis.

Answer:

[tex]x=36\°\\\angle P=71 \°,\angle N=73 \°,\angle M=36 \°[/tex]

Step-by-step explanation:

Given:

The triangle is shown below.

We know that the sum of all interior angles of a triangle is equal to 180°.

Therefore,

[tex]\angle M+\angle N+\angle P=180 \°\\\\x+2x+1+2x-1=180\°\\\\5x=180\°\\\\x=\frac{180}{5}\\\\x=36\°[/tex]

Now, plugging the value of 'x' in each angle measure and determining its values. We get:

[tex]\angle M=x=36\°\\\angle P=2x-1=2(36)-1=72-1=71\°\\\angle N=2x+1=2(36)+1=72+1=73\°[/tex]

Therefore, the value of 'x' is 36° and the measure of the three angles are 36°, 71° and 73°.

Answer: $14

Step-by-step explanation: To find out the price per dozen, we first need to understand that the word "dozen" means a grouping of 12. This means that 1/2 a dozen would be half of 12 which is 6.

If we double 6 to 12, we multiply by 2. We will also multiply by 2 for the price so we have 7 × 2 which simplifies to 14.

Therefore, Lola will charge $14 for her cupcakes.

I also provided an image to show the 1/2 dozen and dozen cupcakes.

Answer:

3

Step-by-step explanation:

She has enough money to buy 3 tubes which leaves with $3 for whatever else she desires

Selection of the digits, In accordance with the rules results to

671

What is place value

Place value is the value of a digit based on its position within a numeral, especially in the base-10 (decimal) number system.

Each digit in a number has a place value, and the position of the digit determines its contribution to the overall value of the number.

The digit in the hundreds place (6) comes first. Next is the tens digit (7) then lastly the ones digit (1)

This results to 671

Answer:

The total loss percentage is 6.25%.

Step-by-step explanation:

Let the cost price of the first cycle is $x.

So, for the first cycle, 25% profit is there for selling the cycle at $2500.

Then, [tex]x(1 + \frac{25}{100}) = 2500[/tex]

⇒ 1.25x = 2500

⇒ x = $2000

Again, let us assume that the cost price of the second cycle is $y.

So, by selling the cycle at $2500 there is a loss of 25%.

Therefore, [tex]y(1 - \frac{25}{100} ) = 0.75y = 2500[/tex]

⇒ y = $3333.33

Therefore, the total cost price of two cycles = $(2000 + 3333.33) = $5333.33 and total selling price is $(2500 + 2500) = $5000.

Therefore, the total loss percentage is [tex]\frac{5333.33 - 5000}{5333.33} \times 100 = 6.25[/tex] % (Answer)

Answer:

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\\text{Substitute}\ f(x)=-3x-5\ \text{and}\ g(x)=4x-2:\\\\(f+g)(x)=(-3x-5)+(4x-2)\qquad\text{combine like terms}\\\\(f+g)(x)=(-3x+4x)+(-5-2)\\\\(f+g)(x)=x-7[/tex]

Answer:

-1.28

Step-by-step explanation:

1=ln(x+4)

ln(x+4)=1

e^ln(x+4)=e^1

x+4=e

x=e-4=-1.28

The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

a) The rate of change is $475 per month

b) The initial value is $125

c) The independent variable is the number of months (x)

d) The dependent variable is the total cost after each month (y)

Step-by-step explanation:

The given is:

Assume that the total cost is y for x months

∵ The registration fee = $125 ⇒ paid once

∵  The parents pay $475 per month for  tuition

∵ The number of months is x

∴ The total cost y = 475 x + 125

The equation of the total cost is y = 475 x + 125, where y is the total cost for x months

∵ y = 475 x + 125 is in the form of the linear equation y = m x + b,

  m is the slope of the line and b is the y-intercept

∵ The slope of the line m is the rate of change y with respect to x

∴ m = 475

∴ The rate of change is $475 per month

a) The rate of change is $475 per month

∵ b is the initial value of y at x = 0

∴ b = 125

∴ The initial value is $125

b) The initial value is $125

∵ The independent variable is x

∴ The independent variable is the number of months (x)

c) The independent variable is the number of months (x)

∵ The dependent variable is y

∴ The dependent variable is the total cost after each month (y)

d) The dependent variable is the total cost after each month (y)

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Answer:

6[tex]\sqrt{5}[/tex]

Step-by-step explanation:

We can factorize 180 to get 2^2*3^2*5.

We know that 2^2 and 3^2 are squares so we can remove them from under the radical.

So, the simplified square root would be 6[tex]\sqrt{5}[/tex]

To remove perfect squares inside a square root, we simplify the number using prime factorisation. In this case, √180 simplifies to 6√5.

The given value is √180. To simplify it or remove perfect squares, we have to find the prime factors of the number under the square root. We can write 180 as 2 * 2 * 3 * 3 * 5. In square root simplifications, we usually group the factors into pairs, because a pair of same factors gives one factor outside the square root. Here, 2 * 2 becomes 2 and 3 * 3 becomes 3. There is an extra 5 inside the square root that cannot come out because it doesn't have a pair. Hence, √180 simplifies to 6√5.

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Answer:

The cost of one hamburger is $3.95.

Step-by-step explanation:

15.80/4=3.95

Answer:

$ 3.95

Step-by-step explanation:

it is 3.95 because you divide 15.80 by 4

Answer:

(24x)(19x2) 12/2 19

Step-by-step explanation:

(24x)(19x2) 12/2 19

Answer:

12.7 ft

Step-by-step explanation:

You're going to need to use acos

so

12 = acos (19) = 12.69

Then round up to 12.7

Answer:

b. y=10x

Step-by-step explanation:

                                                             1

                                                            1.5

                                                             2

                                                            2.5

y represents distance (miles): 5

                                                 10

                                                 15

                                                 20

                                                 25

let the 2 points be:  (1,10) and (2,20) [from the given information]

then the equation of it can be given as :

[tex]y-B=(\frac{D-B}{C-A} )*(x-A)[/tex]

[tex]y-10=(\frac{20-10}{2-1} )*(x-1)\\[/tex]

this is also equal to, [tex]y-10=10*(x-1)\\y-10=10x-10\\y     =10x-10+10\\y=10x[/tex]