Answer: X= 55
Step-by-step explanation:
The sum of exterior angles of any polygon will always equal to 360 degrees. which means, we can write:
360 = (x+10) + (2x+20) + 3x
x = 55
The exterior angles have values of 65, 130 and 165. The exterior that will have the largest value will correspond to the smallest interior angle and therefore have a value of 15 degree!. ;)
Final answer:
By calculating the value of x and using the relationship that each exterior angle and its corresponding interior angle are supplementary, we find that the measure of the smallest interior angle of the triangle is 115 degrees.
Explanation:
To find the measure of the smallest interior angle of the triangle, we first need to use the fact that the sum of the exterior angles of a triangle is always 360 degrees. So, we set up the equation (x+10) + (2x+20) + 3x = 360 and solve for x. This gives us:
x + 10
2x + 20
3x
Combining like terms, we get 6x + 30 = 360. Subtracting 30 from both sides, we get 6x = 330. Dividing both sides by 6, we find that x = 55 degrees. Therefore, the exterior angles are 65 degrees, 130 degrees, and 165 degrees. To find the smallest interior angle, we take the smallest exterior angle, 65 degrees and subtract it from 180 degrees (since the exterior angle and interior angle at the same vertex are supplementary). Thus, the smallest interior angle is 180 degrees - 65 degrees = 115 degrees.
Claire can run 100 meters in 17 seconds. what is her speed in meters per second?
How many 20 cm by 30 cm rectangular tiles would you need to tile the outdoor are shown below?
I calculated that the area of the shape is 10.95m squared, but the answer in the book (183 tiles) is different then the answer I got.
Where did I go wrong?
The issue was inconsistent units - converting everything to cm squared, the appropriate number of 20 by 30 cm tiles to cover an area of 10.95m squared is 183.
Explanation:The problem here involves area measurement and conversions. The area of the outdoor space is given in square meters (m²), while the area of the tiles is given in square centimeters (cm²). Therefore, the first step here is to convert all measurements to the same unit.
Since 1 meter is equal to 100 centimeters, we can convert the area of the outdoor space to square centimeters by squaring 100 (which equals to 10,000) and then multiplying it by the area in square meters. That gives us 109,500 cm².
Next, to find the area of a single tile we multiply its length by its width, which is 20 cm by 30 cm, giving us 600 cm². The number of tiles needed will be the total area divided by the area of one tile. So, 109,500 cm² divided by 600 cm² equals to about 182.5.
Since we cannot have a half tile, we round up that number to 183 tiles. Therefore, the correct answer is 183 tiles.
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The hu family goes out for lunch and the price of the meal is $45 the sales tax on the meal is 6% and the family also leaves a 20% tip on the pre-tax amount what is the total cost of the meal ?
if sin theta =1/4, theta in quadrant II, find the exact value of cos[theta +pi/6]
The exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II is (-√(45) - 1)/8, found by using the Pythagorean identity and the angle sum identity.
To find the exact value of cos(θ + π/6) when sin θ = 1/4 and θ is in quadrant II, we can use trigonometric identities and properties of angles. First, we use the Pythagorean identity to find cos θ. Since θ is in the second quadrant, cos θ is negative and solving for cos θ gives cos θ = -√(1 - sin² θ) = -√(1 - (1/4)²) = -√(15)/4.
Next, we apply the angle sum identity for cosine, which is cos(α + β) = cos α cos β - sin α sin β. Using this identity, we find:
cos(θ + π/6) = cos θ cos(π/6) - sin θ sin(π/6) = (-√(15)/4)(√(3)/2) - (1/4)(1/2) = -√(45)/8 - 1/8 = (-√(45) - 1) / 8.
what is this equation in slope intercept form? 4y+12x=0
The equation 4y + 12x = 0 in slope-intercept form is y = -3x. The slope (m) is -3, and since there is no constant term, the y-intercept (b) is 0.
Explanation:The equation provided, 4y + 12x = 0, can be converted into slope-intercept form, which is represented by y = mx + b. The slope, m, indicates the steepness of the line, while the y-intercept, b, denotes the y-value when x equals zero or where the line crosses the y-axis. Let's rearrange the equation step-by-step:
First, isolate the y variable by subtracting 12x from both sides: 4y = -12x.Next, divide each side by 4 to solve for y: y = -12x / 4.This simplifies to: y = -3x.Here, the slope (m) is -3, indicating a decrease in y by 3 units for every increase of 1 unit in x. The equation does not have a b term, thereby indicating that the y-intercept (b) is 0. Hence, the slope-intercept form of the equation is y = -3x + 0, which can be simplified to y = -3x.
A rectangle has a width of 7.9 ft and a perimeter of 27.2 ft.
Enter the length of the rectangle, in decimal form, in the box.
I just had the same question and the answer was 5.7. Hope this helps somebody
Fill in the blank: A concave polygon is ________ that _______ ...?
Are 37 and 65 71 82 are prime or composite number
3. All but one of the following statements contains a blunder. Which statement is correct? (a) There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight. (b) The correlation between number of seeds planted and amount of grass grown was found to be r = 0.23 acres. (c) The correlation between the gas mileage of a car and its weight is r = 0.71 MPG. (d) We found a high correlation (r = 1.09) between the height and age of children. (e) We found a correlation of r = -.63 between gender and political party preference.
The correct statement is (a), 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' Correlation values range from -1 to +1, and units or nominal variables can't be used.
Explanation:The correct statement among the given options is (a) 'There is a correlation of 0.54 between the social intelligence of a 6-year old and his weight.' In a correlation, the value ranges from -1 to +1 where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. The other statements, (b), (c), (d) and (e), are blunders because the correlation value (r) in (d) exceeds +1 which is impossible, the units in (b) and (c) are incorrectly applied as correlation doesn't have physical units, and in (e), gender is a nominal variable for which correlation cannot be calculated.
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A basketball player scored 19 times during one game. She scored a total of 25 points, two for each two-point shot and one for each free throw. How many two point shots did she make? How many free throws?
Answer:
Step-by-step explanation:
It said free points
Please help
F(x)=x^2 +1, g(x)=5x how to solve
You deposit 6000 in an account that pays 5.25 interest compounded semiannually. after 10 years, the interest rate is increased to 5.4% compounded quarterly. what will be the value of the account after 18 years. (round to the nearest dollar)
The account value after 18 years with an initial deposit of $6,000 and a change in interest rate and compounding periods is approximately $15,526 when rounded to the nearest dollar.
Explanation:To calculate the value of the account after 18 years with a change in the interest rate and compounding periods, we need to use the compound interest formula separately for the two different periods and rates.
First, we compound the original $6,000 at 5.25% semiannually for 10 years:
A = P(1 + r/n)(nt)
A = $6,000(1 + 0.0525/2)(2*10) = $6,000(1.02625)20 = $9,984.21 (rounded)
Now, we take the amount after 10 years and compound it at 5.4% quarterly for the remaining 8 years:
A = P(1 + r/n)(nt)
A = $9,984.21(1 + 0.054/4)(4*8) = $9,984.21(1.0135)32 = $15,526.14 (rounded)
So, after 18 years, the value of the account would be $15,526 (rounded to the nearest dollar).
What is 36/60 as a decimal?
Which of the following is a counterexample to that statement “All prime numbers are odd”
a:The statement has no counterexamples
b:What you are trying to prove
c:The theorems you will use
d: The definitions of important vocabulary
...?
How many atoms of oxygen are in one formula unit of Ca(No3)2?
1.) 7, 9, 11, 13, . . . is it 2.) 2,1, 1 , 1
2 4
A.) arithmetic A.) arithmetic
B.) geometric B.) geometric
C.) both C.) both
D.) neither D.) neither
If Martha earns $6.50 per hour for babysitting, how much will she earn in: 1.5 hours? 2.5 hours? 3.5 hours?
Martha earns $6.50 per hour, so for 1.5 hours, she will earn $9.75; for 2.5 hours, she will earn $16.25; and for 3.5 hours, she will earn $22.75. We simply multiply her hourly wage by the number of hours to find the total earnings for each duration.
If Martha earns $6.50 per hour for babysitting, we can find out how much she will earn for different numbers of hours by multiplying her hourly rate by the number of hours worked.
For 1.5 hours: $6.50 * 1.5 = $9.75For 2.5 hours: $6.50 * 2.5 = $16.25For 3.5 hours: $6.50 * 3.5 = $22.75As a result:
Martha will earn $9.75 for 1.5 hours of babysitting.Martha will earn $16.25 for 2.5 hours of babysitting.Martha will earn $22.75 for 3.5 hours of babysitting.
Explain why you can use subtraction to solve a division problem.
How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8 percent compounded annually? $117,817.20 or $454,144.00 or $112,817.20 or $549,144.
convert .98 to percent ...?
What is the value of the expression when a = 4, b = 3 ,and c = 10? 3a4b−c
Answer:
9yb
Step-by-step explanation:
Which completes the syllogism? If a polygon is a square, then it has four congruent sides. If a polygon has four congruent sides, then it is a rhombus. Therefore, …
A. if a polygon is a square, then it is a rhombus.
B.if a polygon is a rhombus, then it is a square.
C.if a polygon is a rhombus, then it is a parallelogram.
D.if a polygon has four congruent sides, then it is a square.
Answer:
Step-by-step explanation:
Solve for y. y 1.05 = 7.26 y = 8.31 y = -8.31 y = 6.21 y = -6.21
Move all terms not containing y to the right side of the equation. You should get y=6.21
FIND MISSING ANGLES
D1=
D2=
D3=
D4=
D5=
D6=
2 1/2 divided by 4. can you please answer i need help
Answer:
5/8
Step-by-step explanation:
Which statement describes the graph of f(x) = 4x2 + 20x + 25?
The graph does not intersect the x-axis.
The graph touches the x-axis at (–2.5, 0).
The graph intersects the x-axis at (–0.4, 0) and (0.4, 0).
The graph intersects the x-axis at (2, 0) and (5, 0).
The graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0)
Graph of a quadratic functionThe given function is f(x) = 4x² + 20x + 25
The table of values for the function from -1 to -4 is
x -1 -2 -3 -4
f(x) 9 1 1 9
The graph of the function is attached below
From the graph, we can observe that the graph touches the x-axis at the point (-2.5, 0)
Hence, the graph touches the x-axis at (–2.5, 0). The answer is the second option The graph touches the x-axis at (–2.5, 0).
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Which of the following algebraic equations could represent the sentence, "The product of a number and five is 11"?
a,x+ 5 = 11
b,x- 5 = 11
c,= 11
d,5x= 11
PLEASE ANYONE HELP MEEE!!!!
An equilateral triangle has an apothem of 5 cm. Find the perimeter of the triangle to the nearest centimeter.
A.
26 cm
B.
52 cm
C.
75 cm
D.
100 cm"
Explain why the graph shown may be misleading.
As they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.
What is graph?It is defined as the data representation in visual way, and it makes the appearance of the data simpler.
As we can see in the graph:
Total of 40 compact cars, 4 of 10 each.
Total of 30 mid-size, 3 of 10 each.
And Total of 20 trucks,
However, they all appear to have the same start and end points in the graph, with the mid-sizes being longer than the compacts and the trucks being considerably larger than the others above it, virtually implying that the amounts for all are identical for that period.
Thus, as they are lined out, the amounts must correlate horizontally, so the compacts should be longer than the rest, the mid-size behind it, and the trucks half-way between the compacts and the mid-size.
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A rectangle has an area of 3 square feet and a width of 1/2 foot. What is the length of the rectangle ?