Step-by-step explanation:
Step 1: Factor
[tex]b^2 + 5b + 6[/tex]
[tex]b^2 + 3b + 2b + 6[/tex]
[tex](b + 3)(b + 2)[/tex]
Answer: [tex](b + 3)(b + 2)[/tex]
(b + 2) (b + 3)
Step-by-step explanation:
b² + 5b + 6
Known :
a = 1
b = 5
c = 6
Asked :
Factorise b² + 5b + 6 = ...?
Answer :
p × q = c
p + q = b
So :
p × q = 6
2 × 3 = 6
p + q = 5
2 + 3 = 5
So, p = 2 & q = 3
So, factorise b² + 5b + 6 is (b + 2) (b + 3)
Hope it helpful and useful :)
The environment in which the organism lives can support at most 600 organisms. Assuming the trend continues, after how many years will the environment no longer be able to support the population?
Answer:
B.) 24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
This is for geometry and I am very confused.
Answer:
75
Step-by-step explanation:
Divide your value by 2 if your given value is the length of the center line that creates the middle two triangles within the hexagon. The quotient is the length of the hexagon side. If this value is 25, then the length of one side of the hexagon is 25 divided by 2, which is 12.5. Then you multiply that by 6 for each side and get 75. Hopes this helps. : )
A graph has time (hours) on the x-axis and total charge (dollars) on the y-axis. Points are at (0, 8), (2, 27), (4, 46), (6, 65). For the new year, the instructor is thinking of changing his rates. The equation of the possible new rates is represented in the graph. What is the y-intercept of the instructor's new rates? ( , )
Answer:
(0,8)
Step-by-step explanation:
Answer:
(0,8)
Step-by-step explanation:
find the volume of the trapezoidal prism will mark brainliest pls answer
a)29 in3
b)48 in3
c)228 in3
d)2016 in3
Answer:
C : 228 in³
Step-by-step explanation:
Find the area of the shape.
Answer:
The area is [tex]78.54units^2[/tex]
The area would be 78.5[tex]units^2[/tex] (pi=3.14)
Step-by-step explanation:
The formula for the area of a circle is : [tex]\pi *radius^2[/tex]
To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.16.
The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.
The final step would be to divide the area of 314.16 by 4, this gives you 78.54. This is because we are using the area to work out the area of just one quadrant.
1) Multiply pi by 10 squared.
[tex]\pi*10^2=314.16^2[/tex]
2) Divide 360 by 90.
[tex]360/90=4[/tex]
3) Divide 314.16 by 4.
[tex]314.16/4=78.54^2[/tex]
Pi=3.14:
To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.
The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.
The final step would be to divide the area of 314. by 4, this gives you 78.5. This is because we are using the area to work out the area of just one quadrant.
1) Multiply pi by 10 squared.
[tex]\pi*10^2=314^2[/tex]
2) Divide 360 by 90.
[tex]360/90=4[/tex]
3) Divide 314.16 by 4.
[tex]314/4=78.5^2[/tex]
Find the coordinates of point B along a directed line segment from A(3,4) and
C(3,9) so that the ratio of AB to BC is 4:1.
We have been given two points. [tex]A(3,4)[/tex] and [tex]C(3,9)[/tex]. We are asked to find the point B such that it divides line segment AC so that the ratio of AB to BC is 4:1.
We will use segment formula to solve our given problem.
When a point P divides segment any segment internally in the ratio [tex]m:n[/tex], then coordinates of point P are:
[tex][\right x=\frac{mx_2+nx_1}{m+n},y=\frac{my_2+ny_1}{m+n}\left][/tex]
[tex](x_1,y_1)=(3,4)[/tex] and [tex](x_2,y_2)=(3,9)[/tex].
[tex]m=4,n=1[/tex]
Upon substituting our given information in above formula, we will get:
[tex][\right x=\frac{4(3)+1(3)}{4+1},y=\frac{4(9)+1(4)}{4+1}\left][/tex]
[tex][\right x=\frac{12+3}{5},y=\frac{36+4}{5}\left][/tex]
[tex][\right x=\frac{15}{5},y=\frac{40}{5}\left][/tex]
[tex][\right x=3,y=8\left][/tex]
Therefore, the coordinates of point B would be [tex](3,8)[/tex].
How many solutions does the following equation have?
3x^2+10x+2=0
Answer:
one solution
Step-by-step explanation:
Please help!!! I will give 20 points and brainliest answer to the correct answer!!
Answer:
y-intercept = (0, 2.5)
x-intercept = (2.143, 0)
Step-by-step explanation:
y - intercept:
This is when x = 0 so
-7(0) - 6y = -15
-6y = -15
y = -15/-6
y = 2.5.
x_intercept:
-7x - 6(0) = -15
-7x = -15
x = -15 /-7
= 2.143.
a. Jamie has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 14 ft above the ground.
Draw a picture of the ladder leaning against the wall and label the lengths listed in the problem:
b. Use Trigonometry to find the angle formed between the ground and the ladder using your diagram and values from part 1a. Round to the nearest whole number. Show your work:
c. For safety reasons, Jamie wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe the way she has it positioned?
Answer:
B. ∠C = 69°
C. Jamie has positioned the ladder safely.
Step-by-step explanation:
A. In the figure attached length of ladder AC = 15 ft
and the top of the ladder is at the point A 14 ft above the ground.
B. SinC = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{14}{15}[/tex]
[tex]C=sin^{-1}(\frac{14}{15} )[/tex]
C = 68.96°
C ≈ 69°
C). For safety reasons, angle between the ladder and the ground should be less than 75°.
Existing angle between the ladder and ground is 69° which is less than the angle required for safety.
Therefore, Jamie has positioned the ladder safely.
help with question 17 pls
Step-by-step explanation:
Step 1: Find the line
Option A
(y - y_1) = m(x - x_1)
(y - 5) = 2(x - (-4))
y - 5 = 2(x + 4)
Option C
y - 5 = 2x + 8
y = 2x + 13
Option D
2x - y = -13
-y = -13 - 2x
y = 2x + 13
I think Option A, C, D
If m∠X = 55° and m∠Y = 75°, then m∠W = A) 20°. B) 35°. C) 105°. D) 130°.
Answer:
c
Step-by-step explanation:
I subtracted 180 with 75 and I got 105.
The measure of angle ∠W is 50°. None of the answer choices match this result exactly.
To find the measure of angle ∠W, we can use the fact that the sum of the angles in a triangle is always 180 degrees. If we already know the measures of ∠X and ∠Y, we can find ∠W as follows:
m∠X + m∠Y + m∠W = 180°
Given:
m∠X = 55°
m∠Y = 75°
Now, plug in these values:
55° + 75° + m∠W = 180°
Combine the known angle measures:
130° + m∠W = 180°
To find the measure of ∠W, subtract 130° from both sides of the equation:
m∠W = 180° - 130°
m∠W = 50°
Therefore, the correct answer is not among the options provided.
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The histogram shows the birth weights of 1000 mice.
Frequency density
18
20
6 8 10 12 14 16
Birth weights (grams)
Work out the number of mice with birth weights below 10 g.
Answer:
120
Step-by-step explanation:
Each square=x
6g-10g=4g 10g-12g=2g 12-14g=2g
15g-14g=1g 16g-15g=1g 20g-16g=4g
(4x3)+(2x8)+(2x11)+(1x23)+(1x19)+(4x20
12+16+22+23+19+8=1000
x=1000
1000÷100=10
1 box = 10
4×30=120
(I got this answer through help of others, it is not truly mine)
To find the number of mice with birth weights below 10 grams on a histogram, multiply the frequency by the given class width for that weight range and sum frequencies if multiple bars are relevant.
Explanation:The student is asking how to work out the number of mice with birth weights below 10 grams, based on a given histogram. Since the histogram is not displayed here, I will explain the general process for determining the number of mice under a certain weight category using a histogram. First, find the bar that represents the birth weights below 10 grams. The height of this bar corresponds to the frequency density for this class interval. If the class width (the range of values within the category) is 1 gram, then the frequency (number of mice) in this bar can be found by multiplying the frequency density by 1 gram. If the histogram does not provide frequency directly and instead gives frequency density, you must also know the class width to calculate the number of mice. Multiply the frequency density by the class width to find the frequency. If multiple bars (class intervals) cover birth weights below 10 grams, sum the frequencies of all relevant bars to calculate the total number of mice with weights below 10 grams.
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David rode his bicycle for 6 hours and he jogged for 8 hours during the past 2 weeks. If he continues bicycling and jogging at the same rate, how many hours will he ride his bicycle and jog in 24 weeks?
Answer:
He will ride his bicycle for 72 hours and jog for 96 hours.
Step-by-step explanation:
David rode his bicycle for 6 hours and he jogged for 8 hours during the past 2 weeks.
We can say that per week, he rode his bicycle for 3hours and jogged for 4 hours.
Assuming that he continues at the same rate, in 24 weeks, he will ride his bike for:
24 * 3 = 72 hours
And he will jog for:
24 * 4 = 96 hours.
He will ride his bicycle for 72 hours and jog for 96 hours.
Answer:
72 all you need to do is 24 x 3 and you get 72. :)
At a music store, a survey was conducted to find which genre of music the customers preferred. In the survey, every male customer was asked which genre of music was his favorite. Were the results of the survey valid?
A.
Yes, because the music store surveyed every tenth male customer.
B.
No, because the music store did not survey a sample that is representative of the population.
C.
No, because the music store did not have any female customers.
D.
Yes, because every male customer was surveyed.
Answer:
The answer is B
Step-by-step explanation:
I have study Island too and the answer C is wrong
Final answer:
The survey conducted only among male customers at a music store is not valid because it's not representative of the entire customer base, thereby introducing a selection bias.
Explanation:
The question asks whether the results of a music preference survey conducted only among male customers at a music store are valid. Answer choice B, No, because the music store did not survey a sample that is representative of the population, is correct.
A valid survey must aim to avoid selection bias by ensuring that its sample represents the entire population it intends to make statements about.
Surveying only male customers introduces a bias, as it excludes female customers, making the sample not representative of all music store customers. This compromises the survey's ability to accurately reflect the preferences of the entire customer base.
Solve this system of equations
{2x + y = 11
{5x - y = 10
Answer:
solution: (3, 5)
Step-by-step explanation:
Solve this system of equations
{2x + y = 11
{5x - y = 10
add the equations to use elimination method.
2x + 5x + y - y = 11 + 10;
7x = 21
x = 21/7 = 3
x = 3
y = 11 - 2x = 11 - 2*3 = 11 - 6 = 5
what is the midpoint of the x intercepts of f(x)= (x-4) (x+4)
Answer:
(0,16) or just 0 horizontally
Step-by-step explanation:
The x intercepts would be found by first setting these equations to equal zero!
[tex]x-4=0\\x+4=0[/tex]
Now we can add/subtract to solve for the zeros of the function!
[tex]x+4=0\\-4\\x=-4\\\\x-4=0\\+4\\x=4[/tex]
The mid-point between 4 and negative 4 is 0, so the vertex is at (4,-16)!
Use the distributive property to remove the parentheses. Simplify your answer as much as possible.
Answer:
9 - 24y
Step-by-step explanation:
12 ( 3/4 - 2y)
Distribute
12 * 3/4 - 12 * 2y
36/4 -24y
Simplfiy
9 - 24y
Here is the histogram of a data distribution.
5
4
3
2
1
1
2
9 '10
Which best describes the shape of this distribution?
Answer:
unimodal skewed
Step-by-step explanation:
The given histogram is unimodal skewed.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
This histogram is unimodal skewed.
There are two parts to this answer. The first part has to do with the number of modes.
This would be the item that is occurring the most frequently.
In this case the mode is only 4.
It is occurring more than any other.
The second part of this has to do with the distribution of the data as it is displayed on the histogram.
There are 4 pieces of data that are only occurimg one time on the right of the histogram.
We call this skewing the data.
When both sides looks almost the same we say it is symmetric.
Hence, the given histogram is unimodal skewed.
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Interpolate: Use the equation to determine what the student enrollment in 2003 likely was.
1244 students
Extrapolate: Use the equation to predict student enrollment in 2013.
2064 students
its answered ur welcome
Answer:
1244 students
2064 students
hope it helped
Step-by-step explanation:
Thanks
you were right
which picture shows the correct graph of |x|=3?
Answer:
[see picture]
Step-by-step explanation:
There were no given choices, but I did graph the equation using Desmos.
Choose the answer that is closest to this:
A company lost $400 dollars in March, $500 in April, and $300 in May. Write an integer for the average loss per month
Answer: 400
Step-by-step explanation:30+400+500=1200/3=400
Answer:
$400
Step-by-step explanation:
to find an average we add...
400+500+300=1200
then we divide..
$1200/3 months=
$400 per month
Hope this helps!
In deciding where to have lunch, a group of friends
looks at the websites for 2 pizzerias, 3 drive-throughs,
and 2 diners.
How many choices are the friends considering?
Answer:
5 pizza rolls
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
A 100-foot rope from the top of a tree house to the ground forms a 45 degree angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot
Answer:
The top of the tree house is 70.71ft high
Step-by-step explanation:
Kindly find attached rough sketch of the problem for your reference.
From the sketch we see that the rope at 45° and the tree house form a right angle triangle
Applying
SOH CAH TOA formula
using SOH
sin θ= h/100
h= sinθ*100
h= sin(45)*100
h= 0.7071*100
h= 70.71ft
find the exact length of the third side
Answer:
47
Step-by-step explanation:
The third side is called the hypotenuse, lets call that the x side.
So we are finding x.
The two other sides add up to the hypotenuse, x.
35 + 12 = 47
Please help!! what is the length of the line
Answer:
[tex]\sqrt136[/tex] (option D)
Step-by-step explanation:What is the exact value of sin 15°?
Answer:
Step-by-step explanation:
The result can be shown in multiple forms.
Exact Form:
√
6
−
√
2
4
Decimal Form:
0.25881904
…
The table below shows all of the possible outcomes of rolling a six-sided number cube and flipping a coin.
A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H 1, T 1. Column 3 is labeled 2 with entries H 2, x. Column 4 is labeled 3 with entries H 3, T 3. Column 5 is labeled 4 with entries H 4, T 4. Column 5 is labeled 4 with entries H 4, T 4. Column 6 is labeled 5 with entries H 5, T 5. Column 7 is labeled 6 with entries H 6, T 6.
Which outcome is represented by x?
rolling a two and the coin landing on tails
rolling a three and the coin landing on tails
rolling a two and the coin landing on heads
rolling a three and the coin landing on heads
Answer:
A: rolling a two and the coin landing on tails
Step-by-step explanation:
bc I got it right on edg 2020
Experimental probability: 3/10
The correct answer is rolling a two and the coin landing on the tails
ProbabilityA 3-column table with 10 rows.
Column 1 is labeled Trial with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Column 2 is labeled Outcome with entries H T, T T, H T, H H, H T, H T, T T, H T, T T, H H.
Column 3 is labeled Result with entries Fail, pass, fail, fail, fail, fail, pass, fail, pass, fail.
A pop quiz has 2 True/False questions. Paris used a 10-trial coin flip to simulate the results of guessing on the quiz. If T represents answering a question correctly, what is the experimental probability of correctly answering both questions by guessing?
Frequency of observed desired outcome: 3
Number of trials: 10
Experimental probability: 3/10
Therefore, the correct answer is
rolling a two and the coin landing on tails
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james has 4 and 3/4 feet of rope he plans to cut off 1 and 1/2. how much rope will be left
Answer:
3 and 1/4
Step-by-step explanation:
Consider the equation
2 5
x 2X-1
Solve for x.
Luther is building a model rocket for a science fair project. He attaches a nose cone to a cylindrical body to
form the rocket's fuselage. The rocket has a diameter of 4 inches and a total height (including the nosecone)
of 19 inches. The nosccone is 7 inches tall. What is the surface area of the rocket?
The total approximate surface area of Luther's rocket is 219.8 square inches.
Luther is building a model rocket and needs to calculate its surface area. His rocket consists of a cylindrical body with a nose cone. The diameter of the cylinder is 4 inches, the height of the cylindrical part is 12 inches (since the total height is 19 inches and the nose cone is 7 inches), and the height of the nose cone is 7 inches.
First, we calculate the surface area of the cylindrical body. The formula for the lateral surface area of a cylinder is 2πr*h, where r is the radius and h is the height. Half the diameter gives us the radius, which is 2 inches. Thus, the lateral surface area is 2π*2*12 = 48π square inches.
Next, we find the surface area of the two bases of the cylinder. The formula for the area of a circle is π[tex]r^2[/tex]. So, the area of one base is π*[tex]2^2[/tex] = 4π square inches. There are two bases, so we double this to get 8π square inches.
For the nose cone, we'll assume it is a cone whose slant height is the same as its height (because we do not have enough information to calculate the slant height if it were to differ). The surface area of a cone is πr*l, where l is the slant/linear height. Therefore, for the nose cone, we have π*2*7 = 14π square inches.
Now, we add the surface areas of the cylindrical part and the nose cone to get the total surface area of the rocket: 48π + 8π + 14π = 70π square inches.
Finally, multiplying 70π by approximately 3.14, we get the total approximate surface area of Luther's rocket: 70 * 3.14 = 219.8 square inches.
The correct answer is:
The surface area of the rocket is approximately [tex]\(48\pi + 2\pi(2 + \sqrt{53})\)[/tex] square inches, without numerical calculation.
To find the surface area of the rocket, we need to calculate the surface area of both the cylindrical body and the nose cone separately, then add them together.
1. Surface Area of the Cylindrical Body:
The cylindrical body's surface area can be calculated using the formula for the lateral surface area of a cylinder: [tex]\( A_{\text{cylinder}} = 2\pi rh \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
Given:
- Diameter = 4 inches (radius = 2 inches)
- Total height (including nose cone) = 19 inches
- Height of the nose cone = 7 inches
Radius r = 2 inches
Height of cylindrical body = Total height - Height of nose cone = 19 inches - 7 inches = 12 inches
[tex]\( A_{\text{cylinder}} = 2\pi \times 2 \times 12 = 48\pi \)[/tex] square inches
2. Surface Area of the Nose Cone:
The surface area of a cone can be calculated using the formula: [tex]\( A_{\text{nosecone}} = \pi r_{\text{nosecone}}(r_{\text{nosecone}} + \sqrt{h_{\text{nosecone}}^2 + r_{\text{nosecone}}^2}) \), where \( r_{\text{nosecone}} \) is the radius and \( h_{\text{nosecone}} \)[/tex] is the height.
Given:
- Height of nose cone = 7 inches
Since the diameter of the rocket is 4 inches, the radius of the nose cone is also [tex]\( \frac{4}{2} = 2 \)[/tex] inches.
[tex]\( A_{\text{nosecone}} = \pi \times 2 \times (2 + \sqrt{7^2 + 2^2}) = 2\pi(2 + \sqrt{53}) \)[/tex] square inches
3. Total Surface Area:
The total surface area of the rocket is the sum of the surface areas of the cylindrical body and the nose cone.
Total Surface Area = Surface Area of Cylindrical Body + Surface Area of Nose Cone
[tex]\( = 48\pi + 2\pi(2 + \sqrt{53}) \)[/tex] square inches
Now, you can compute the numerical value.