Answer:
45.75 mph
Step-by-step explanation:
Let's call Sonya's speed before the rest stop "x" (in miles per hour). Then, we know that her speed after the rest stop was "x-5" miles per hour.
We can use the formula: distance = speed x time, to set up two equations based on the given information:
Equation 1: 170 = x * t1 (where t1 is the time Sonya drove before the rest stop)
Equation 2: 320 = (x-5) * (t1+3) (where t1+3 is the time Sonya drove after the rest stop)
We can solve for t1 in Equation 1 by dividing both sides by x:
t1 = 170/x
Now we can substitute this expression for t1 into Equation 2 and simplify:
320 = (x-5) * (170/x + 3)
320 = 170(x-5)/x + 3(x-5)
Multiplying both sides by x gives:
320x = 170(x-5) + 3x(x-5)
320x = 170x - 850 + 3x^2 - 15x
Simplifying and rearranging terms gives a quadratic equation:
3x^2 - 165x + 850 = 0
We can solve for x using the quadratic formula:
x = [165 ± sqrt(165^2 - 4(3)(850))] / (2*3)
x = [165 ± sqrt(27225 - 10200)] / 6
x = [165 ± sqrt(17025)] / 6
x = [165 ± 130.5] / 6
x = 45.75 or x = 9.25
We can ignore the solution x = 9.25 since it doesn't make sense in the context of the problem (Sonya's speed cannot be negative). Therefore, Sonya's speed before the rest stop was 45.75 miles per hour
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
Applying the tangent and the circle theorems, we have:
22. x ≈ 9.4; 23. Perimeter of triangle GHI = 168 units
24. m<NSR = 110°; 25. x = 10
How to Find the Missing Measures Using Circle and Tangent Theorems?22. Based on the tangent theorem, the triangle is a right triangle since the line is tangent to the radius of the circle. Therefore, based on the Pythagorean theorem, we have:
x = √[(7.4 + 4.6)² - 7.4²]
x ≈ 9.4
23. JH and HK are tangents, therefore they are equal. Thus:
7x + 4 = 13x - 20
7x - 13x = -4 - 20
-6x = -24
x = 4
Perimeter = GI + GJ + JH + HK + KI
GI = 52
HK = JH = 7x + 4 = 7(4) + 4 = 32
KI = 15
GJ = 52 - 15 = 37
Perimeter of triangle GHI = 52 + 37 + 32 + 32 + 15 = 168 units
24. Based on the angle of intersecting chords theorem, we have:
m<NSR = 1/2(170 + 50)
m<NSR = 110°
25. Based on the inscribed angle theorem, we have:
2(4x - 5) + 290 = 360
Solve for x:
8x - 10 + 290 = 360
8x = 360 - 280
8x = 80
x = 10
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If a is an inversely proportional to b and a =1.5 when b =30,what is a when b =5
The proportion is solved and value of a = 9 and constant is k =45
Given data ,
If a is inversely proportional to b, it means that their product remains constant
a * b = k
where "k" is the constant of proportionality.
Given that a = 1.5 when b = 30, we can substitute these values into the equation:
1.5 * 30 = k
k = 45
Now, we can use the value of k to determine the value of "a" when b = 5:
a * 5 = 45
Dividing both sides by 5:
a = 45 / 5
a = 9
Hence , proportionality constant is k = 45 and when b = 5, the value of "a" is 9
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Martha is saving money to buy a new computer that costs $1800. She received $200 for her birthday and has a job where she makes $150 each week.
a) Make a table and a graph for this situation.
b) Explain how you can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer.
c) Explain how you can tell from both the table and the graph whether this is an example of linear or non-linear growth.
a) A table and a graph for this situation is shown in the image below.
b) You can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer by comparing the week when her savings are both equal.
c) Since the x-value and y-value in both the table and the graph increase simultaneously, it is an example of linear growth.
How to complete the table and graph the function?In this scenario, the variable x would represent the number of weeks while the variable y would represent the total amount of savings. Since Martha received $200 for her birthday and makes $150 each week, a linear equation in slope-intercept form that models the situation is given by;
y = mx + c
y = 150x + 200
Next, we would use an online graphing calculator to make a table and a graph for this situation as shown in the image attached below.
Part b.
The table and the graph both have the total amount of savings (y) equal to $1,850 when x is equal to 11 weeks. This ultimately implies that, it would take Martha between 11 weeks to save enough money to buy this new computer.
Part c.
By critically observing the table and the graph, we can logically deduce that there is a linear relationship between the variables because both the x-value and y-value increase simultaneously.
Therefore, this is an example of a linear growth.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
i am a number between 17 and 25 i am a multiple of 3..... 6 is not a factor of mine
The answer choices are:
A. 4
B. 2 radical 5
C. 4 radical 2
D. 2 radical 10
The length of segment WK is given as follows:
B. [tex]2\sqrt{5}[/tex]
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The endpoints of the segment in this problem are given as follows:
K(-2,0) and W(-6,-2).
Hence the length of the segment is given as follows:
[tex]\sqrt{(2 - (-6))^2 + (0 - (-2))^2} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}[/tex]
Meaning that option B is the correct option in the context of this problem.
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The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Their responses, in number of tongue flicks per 20 minutes, are presented below.
523, 455, 693, 574, 370, 642, 336, 387, 727, 370,
302, 268, 693, 472, 710, 285, 744
Preliminary data analyses indicate that you can reasonably apply the z-interval procedure. Find a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards. Assume a population standard deviation of 190.0. Note: The sum of the data is 8551.
Confidence interval:
We can see here that the 90% confidence interval will be: 420.2 to 585.8.
What is confidence interval?An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.
We will find the sample mean first:
Sample mean = sum of data points / number of data points
Sample mean = 8551 / 17 = 503
Then the standard error will be:
Standard error = population standard deviation / square root of number of data points
Standard error = 190 / √(17) = 41.7
Confidence interval = Sample mean ± 1.645 × standard error.
where 1.645 is the z-score for a 90% confidence interval.
Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8
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Graph the numbers on the number line.
–4 and 3
The number line with the numbers -4 and 3 graphed is given by the image presented at the end of the answer.
How to graph the numbers on the number line?The origin point on the number line is given as follows:
0.
Hence positive numbers and negative numbers are plotted as follows:
Positive numbers are plotted to the right of zero on the number line.Positive numbers are plotted to the left of zero on the number line.The numbers for this problem are given as follows:
-4 and 3.
Hence they are plotted as follows:
-4 is plotted four units to the left of zero on the number line.3 is plotted three units to the right of zero on the number line.More can be learned about number line at https://brainly.com/question/24644930
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Triangle ABC is reflected across the line y=-x and rotated 90 degrees clockwise, draw the resulting image given the above transformation.
The resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).
To find the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise, we can follow these steps:
1. Draw Triangle ABC and the line y=-x on a coordinate plane.
2. Reflect Triangle ABC across the line y=-x to get its image, Triangle A'B'C'.
3. Draw the image Triangle A'B'C' on the coordinate plane.
4. Rotate Triangle A'B'C' 90 degrees clockwise around the origin to get its final image.
5. Draw the final image of Triangle ABC, which is Triangle A''B''C''.
To find the coordinates of the image points, we can use the transformation rules for reflections and rotations.
First, let's find the image points after reflecting Triangle ABC across the line y=-x:
- The point A(-2, 3) is reflected to the point A'(-3, 2) by swapping the x and y coordinates and changing their signs.
- The point B(4, 1) is reflected to the point B'(-1, -4) by swapping the x and y coordinates and changing their signs.
- The point C(1, 5) is reflected to the point C'(-5, -1) by swapping the x and y coordinates and changing their signs.
Now, let's find the image points after rotating Triangle A'B'C' 90 degrees clockwise around the origin:
- To rotate a point (x, y) 90 degrees clockwise around the origin, we can use the formulas (-y, x).
- Applying this formula to each image point, we get:
- A''(2, 3)
- B''(1, 4)
- C''(5, 1)
Therefore, the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).
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In 2005 an area vocational school had an enrollment of 325 men and 123 women. In 2006 there were 149 women. what was the percent increase of women students. The answer should be rounded to the nearest whole percent
The nearest Whole percent, the percent increase of women students is approximately 21%.
The percent increase of women students, we need to compare the number of women students in 2005 and 2006.
In 2005, the number of women students was 123.
In 2006, the number of women students was 149.
To find the increase, we subtract the initial value (2005) from the final value (2006):
Increase = Final Value - Initial Value
Increase = 149 - 123
Increase = 26
Next, we need to calculate the percent increase. The percent increase is given by the formula:
Percent Increase = (Increase / Initial Value) * 100
Plugging in the values:
Percent Increase = (26 / 123) * 100
Calculating the percent increase:
Percent Increase ≈ 21.14%
Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.
Therefore, the answer is 21%.
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Need help please guys
The subtraction of the two matrix is [31 6 12 -14 57 ]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
What is the matrix subtraction?The subtraction of the two matrix is calculated as follows;
The result to 4 multiplied by D is calculated as;
4[D] = [28 -24 12 -32 -36]
[8 -36 -24 24 36]
[32 8 20 -40 -12]
[40 -12 -16 12 - 28]
[4 -8 16 -20 -8 ]
The result to 3 multiplied by B is calculated as;
3[B] = [-3 -30 -24 -18 21]
[27 -9 -6 6 9]
[-15 -6 21 0 -21]
[30 -24 3 27 30]
[18 15 6 -24 -27]
The subtraction of the two matrix is calculated as follows;
4[D] - 3[B] = [31 6 12 -14 57]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
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A ___does not have an apex.
1. pyramid
2. prism
3. cone
Answer: 3. Prism
explanation: An apex is basically, the point where all lines meet at one point, and a prism is the one shape that doesn't have a apex. Hope this helps!
Pls help me find the area!!!
Answer:
Step-by-step explanation:
11+6+21+18=56 ft
squared
(Ratios MC) Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books. 05:11 5:6 06:11 6
_
5
The ratio which represents the ratio of paperback books to hardcover books is 6 : 5.
Given that,
Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed.
We have to find the ratio of the paperback books to hardcover books.
We have,
Number of paperback books = 6
Number of hardcover books = 5
We need to find the ratio of the paperback books to hardcover books.
Ratio = Number of paperback books / Number of hardcover books
= 6/5
Hence the ratio is 6/5.
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Find the smallest angle of ASTU. Assume that b is a
positive number.
The smallest angle that is in the triangle STU is 9 degrees.
How do we solve a triangle?A triangle can be solved by using information provided to determine the triangle's unknown side lengths and angles. Depending on the information at hand, a triangle can be solved in a variety of ways as we see here.
To find the side u
[tex]u^2 = (41b)^2 + (44b)^2 - 2(41b * 44b)Cos 128\\u^2 = 1681b^2 + 1936b^2 - 3608b^2Cos 128\\u^2 = 3617b^2 - 2221b^2\\u^2 = 1396b^2[/tex]
u = 37b
Then Using the sine rule;
a/Sin A = b/Sin B
37b/Sin 128 = 41b/SinB
B = sin-1 (41b * Sin 128/37b)
B = 61 degrees
Then;
C = 180 - (128 + 61)
C = 9 degrees
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450 cm into m and cm
Answer:
450 cm in meter is 4.5 meters
Step-by-step explanation:
450cm = 4.5m
Match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
The general equation is y=mx+b
where m is the slope and b is the y intercept.
So substitute the m and the b for the equation.
m=2, b = 5 : y = 2x+5
m=3 b = 5: y = 3x + 5
m = 5 b = 4: y = 5x + 4
solve (x+5)/(x+8)=1+(6)/(x+1)
Answer:
x = -5 2/3
Step-by-step explanation:
You want the solution to the rational equation ...
(x+5)/(x+8)=1+(6)/(x+1)
F(x) = 0Casting this into the form f(x) = 0, we have ...
[tex]\dfrac{x+5}{x+8}=1+\dfrac{6}{x+1}\\\\\\1-\dfrac{3}{x+8}=1+\dfrac{6}{x+1}\\\\\\\dfrac{6}{x+1}+\dfrac{3}{x+8}=0\\\\\\\dfrac{3(2(x+8)+(x+1))}{(x+1)(x+8)}=0\\\\\\3x+17=0\qquad\text{the numerator is zero when the fraction is zero}\\\\\\\boxed{x=-\dfrac{17}{3}}[/tex]
__
Additional comment
The attachment shows the left side and right side expressions are equal when x = -17/3 = -5 2/3.
<95141404393>
Supermarkets Agreement 2012 Adult Rate The normal weekly pay for an adult aged 21 and over is $565.90 Junior Rates The wage rates for a junior employee are based on a percentage of the adult rate.
How many people aged 16 and under 17 years can be employed for the same cost as one adult employee?
Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90.
The wage rates for a junior employee are based on a percentage of the adult rate, but the exact percentage is not provided. Therefore, it is impossible to determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee without knowing the specific percentage and calculating the wages accordingly Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90. To determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee, we need to know the percentage of the adult rate for junior employees. Once we have that information, we can calculate the number of junior employees that can be employed for the same cost as one adult employee.
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If the distance from 3rd base to home plate is 60 feet, and the average speed of a pitch is 40mph, how many seconds would you have to get to home from 3rd before the ball reaches the catcher?
You would need to reach home plate in 1.02 seconds before the ball reaches the catcher.
we need to convert the speed from mph to feet per second, since the distance is given in feet.
40 mph = 58.7 feet per second (rounded to one decimal place)
To calculate the time it takes to get from 3rd base to home plate, we can use the formula:
time = distance / speed
Plugging in the given values, we get:
time = 60 feet / 58.7 feet per second
time = 1.02 seconds
Therefore, you would need to reach home plate in 1.02 seconds before the ball reaches the catcher.
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the equation of a straight line L1 is given as 3x plus 2y is equal to 12. Another line L2 is perpendicular to L1 at (2,9).
(a) Find the equation of L2 in the fom y is equal to mx plus c where m and c are constants
(b) Another line L3 is parallel to L1 and passes through point (-4,-1). Find
(i) The equation of L2 in the form ax plus by is equal to c where m and c are intergers
(ii) The x and y intercepts of L3
(iii) The point of intersception between L2 and L3
The equation of L2 is y = 2x/3 + 23/3.
The equation of L3 is y = -3x/2 - 7.
The equation of L2 in standard form is 2x/3 - y = -23/3.
The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.
The point of intersection between L2 and L3 is (-6.769, 3.154).
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;
Equation of line 1 (L1): 3x + 2y = 12
y = -3x/2 + 12
Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;
y - y₁ = m(x - x₁)
y - 9 = 2/3(x - 2)
y = 2x/3 + 23/3
Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;
y - y₁ = m(x - x₁)
y + 1 = -3/2(x + 4)
y = -3x/2 - 6 - 1
y = -3x/2 - 7
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!! I’ll give brainlist !!
Can someone please help
Determine the measure of each arc.
The measures of the arcs are: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°
How to Determine the Measure of Arcs?To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.
16. m(MN) = m<QRN
Substitute:
m(MN) = 72°
17. m(NQR) = 180° [semicircle is equal to 180 degrees]
18. m(NQ) = 180 - 72
m(NQ) = 108°
19. m(MRP) = 180 + (180 - 95)
m(MRP) = 180 + 85
m(MRP) = 265°
20. m(QR) = 72° [central angle is equal to intercepted arc measure)
21. m(MR) = 180 - 72
m(MR) = 108°
22. m(QMR) = 360 - 72 = 288°
23. m(PQ) = 180 - 95 - 72 = 13°
24. m(PRN) = 360 - 95
m(PRN) = 265°
25. m(MQN) = 360 - 72
m(MQN) = 288°
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Scott equipment produces high-quality soccer balls if the fixed cost per ball is three dollars when the company produces $15,000 what is the fixed cost per ball went to produce 22,500 boss assume that both volumes are in the same relevant
The fixed cost per ball went to $4.5 when the company produce 22,500.
what is the fixed cost per ball went to produce?fixed cost per ball is three dollars when the company produces 15,000
fixed cost per ball went x to produce 22,500
So,
3 : 15000 = x : 22,500
3/15,000 = x/22,0/500
cross product
3 × 22,500 = 15,000 × x
67,500 = 15,000x
divide both sides by 15,000
x = 67,500 /15,000
x = 4.5
Therefore, the fixed cost per ball to produce 22,500 is $4.5
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1. What is the theoretical probability that the family has two dogs or two cats?
2. Describe how to use two different coins to simulate which two pets the family has.
3. Flip both coins 50 times and record your data in a table like the one below.
Result Frequency
Heads, Heads
Heads, Tails
Tails, Heads
Tails, Tails
Total 50
1. Based on your data, what is the experimental probability that the family has two dogs or two cats?
2. If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
3. How could you change the simulation to generate data for three pets?
The theoretical probability of having three dogs or three cats is p^3 + q^3.
The theoretical probability of the family having two dogs or two cats depends on the specific probability of each event. Let's assume that the probability of having a dog is 0.5 and the probability of having a cat is also 0.5 (which is a simplification). In this case, the probability of having two dogs is 0.5 x 0.5 = 0.25, and the probability of having two cats is also 0.5 x 0.5 = 0.25. Therefore, the theoretical probability of the family having two dogs or two cats is 0.25 + 0.25 = 0.5 or 50%.
To simulate which two pets the family has using two different coins, we can assign one pet to each coin face (e.g., heads for dog and tails for cat). Then, we can flip both coins and record the outcome to determine which pets the family has. For example, if the first coin shows heads and the second coin shows tails, the family has one dog and one cat.
After flipping both coins 50 times and recording the outcomes in a table, we can calculate the experimental probability of the family having two dogs or two cats. Let's assume that we observed 12 occurrences of two dogs, 10 occurrences of two cats, and 28 occurrences of other outcomes (e.g., one dog and one cat). The experimental probability of the family having two dogs or two cats is (12 + 10) / 50 = 0.44 or 44%.
If the family has three pets, the theoretical probability of having three dogs or three cats can be calculated using a similar approach. Let's assume that the probability of having a dog is p and the probability of having a cat is q (where p + q = 1). Then, the probability of having three dogs is p x p x p = p^3, and the probability of having three cats is q x q x q = q^3. Therefore, the theoretical probability of having three dogs or three cats is p^3 + q^3.
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The functions f(x) and h(x) share a common x-intercept.
f(x) = x2+4x
It is true that the functions f(x) and h(x) share a common x-intercept.
How to obtain the x-intercepts of a function?On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.
Function f(x) is defined as follows:
x² + 4x.
Hence the x-intercepts are obtained as follows:
x² + 4x = 0
x(x + 4) = 0
x = 0 and x + 4 = 0 -> x = -4.
On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.
Hence the x-intercept of function h(x) is given as follows:
x = -4.
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The aquarium, measuring 23 cm and 15 cm, is filled with water up to half its height. If we insert sand with a volume of 2350 cm3, by how much will the water level in the aquarium rise.
10.th grade
" tutors , went offline ....?
The water level in the aquarium will rise by 18 cm.
Volume calculationThe volume of water in the aquarium before adding the sand is given by:
Volume = (1/2) x 23 cm x 15 cm = 172.5 cm³
When the sand is added, its volume is 2350 cm³. Therefore, the new volume of water and sand in the aquarium is:
= 172.5 cm³ + 2350 cm³
= 2522.5 cm³
Let h be the height of the water level after adding the sand. The new volume of water in the aquarium is given by:
Volume = (1/2) x 23 cm x 15 cm x h
Setting this equal to the new total volume, we can solve for h:
(1/2) x 23 cm x 15 cm x h = 2522.5 cm³
h = 2522.5 cm³ / (1/2 x 23 cm x 15 cm) = 18 cm
Therefore, the water level in the aquarium will rise by 18 cm.
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Martin a une table ronde de 1 ,10m de diamètre il peut ajouter jusqu'à 5 rallonge de 40 cm chacune pour son repas d'anniversaire 10 personne seront présentes autour de cette table En comptant 60 cm par personne quel est le nombre minimal de rallonge qu'il doit installé
Camille took a friend for a birthday dinner. The total bill for dinner was $38.56 (including tax and a tip). If Camille paid a 22.1% tip, what was her bill before adding the tip?
(Round your answer to the nearest cent.)
Answer: $31.58
Step-by-step explanation:
Let us say that x is equal to the bill's amount before adding the tip. Please note that a percent divided by 100 becomes a decimal, so 22.1% / 100 = 0.221. We will write an equation to represent this situation.
x + 0.221x = $38.56
Next, we will solve by combining like terms.
1.221x = $38.56
Lastly, we will divide both sides of the equation by 1.221.
x = $31.58
Camille's bill was $31.58 before adding a 22.1% tip.
Find the probability that the product is a multiple of 3
The probability that the product is a multiple of 3 is given as follows:
p = 7/16.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are four numbers, hence the total number possible products are given as follows:
4² = 16.
The products that are multiples of 3 are given as follows:
1 x 3 = 3.2 x 3 = 6.3 x 1 = 3.3 x 2 = 6.3 x 3 = 9.3 x 4 = 12.4 x 3 = 12.7 products are multiples of 16, out of the 16 products, hence the probability is given as follows:
p = 7/16.
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Consider this unfinished equation.
4 + 9 = ____ + 3
What number should go in the blank space?
The number I should go in the blank space.
Answer: 4+9=10+3
Step-by-step explanation:
We can subtract the number, 4 to get 3. The extra one from the 4 would go to the nine.
Determine the equation of the circle with radius 9 and center ( − 1 , − 8 ).
The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8 )² = 81.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that the circle has a center of (-1, -8) and the radius is 9.
Hence; from the standard form of the equation of the circle:
Center ( h , k ) = ( -1, -8 )
h = -1
k = -8
And radius r = 9
Plug these values into the above formula and simplify.
( x - h )² + ( y - k )² = r²
( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²
Simplify
( x + 1 )² + ( y + 8 )² = 81
Therefore, the equation of the circle is ( x + 1 )² + ( y + 8 )² = 81.
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