Answer:
Step-by-step explanation:either C or
B
cosA + cosB + cosC = 1 + 4sinA/2 sinB/2 sinC/2
[tex] \cos(A) + \cos( B ) + \cos(C) \\ = 2 \cos( \frac{A + B}{2} ) \cos( \frac{ A- B}{2} ) + 1 - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2\cos( \frac{\pi - C}{2} ) \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} \cos( \frac{A - B}{2} ) - 2 { \sin }^{2} \frac{C}{2} \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \sin \frac{C}{2}] \\ = 1 + 2 \sin \frac{C}{2} [ \cos( \frac{A - B}{2} ) - \cos( \frac{A + B}{2} )] \\ = 1 + 2 \sin\frac{C}{2} \times 2 \sin( \frac{ \frac{A + B}{2} +\frac{A - B}{2} }{2} ) \sin( \frac{ \frac{A + B}{2} - \frac{A - B}{2} }{2} ) \\ = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}[/tex]
What are the intercepts of y = 4x − 2?
Answer: y = −2
Step-by-step explanation:
0 = −4x − 2x = −1/2To find the y-intercept, substitute in 0 for x and solve for y. Y = − 4 * 0 −2Which then gives you y = - 2* Hopefully this helps:) Mark me the brainliest:)
Answer:
D
Step-by-step explanation:
(0.5, 0) and (0, -2)
Write the point-slope equation of the line that passes through (3, -1) and a slope of 2.
Answer:
y=2x+(-7)
Step-by-step explanation:
y=2x+c
solve for c
-1=2(3)+c
-1=6+c
-6-1=c
c=-7
y=2x+(-7)
Answer:
[tex]\large\boxed{y+1=2(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the slope m = 2 and the point (3, -1). Substitute:
[tex]y-(-1)=2(x-3)\\\\y+1=2(x-3)[/tex]
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 5 small boxes has a total weight of 57 kilograms. A delivery of 8 large boxes and 3 small boxes has a total weight of 126 kilograms. How much does each type of box weigh?
Final answer:
The large box weighs 13.5 kilograms and the small box weighs 6 kilograms.
Explanation:
To solve this problem, we can assign variables to represent the weight of each type of box. Let's say the weight of a large box is L and the weight of a small box is S.
From the given information, we can set up a system of equations:
2L + 5S = 57 (Equation 1)
8L + 3S = 126 (Equation 2)
We can solve this system of equations using the method of substitution or elimination. Let's use elimination:
Multiply Equation 1 by 8 and Equation 2 by 2 to eliminate the S variable:
16L + 40S = 456 (Equation 3)
16L + 6S = 252 (Equation 4)
Subtract Equation 4 from Equation 3:
34S = 204
Solve for S: S = 6
Substitute the value of S into Equation 1:
2L + 5(6) = 57
2L + 30 = 57
2L = 27
Solve for L: L = 13.5
Therefore, the large box weighs 13.5 kilograms and the small box weighs 6 kilograms.
The planets close to the sun are
A)
small and rocky.
B)
large and rocky.
C)
small and gaseous.
D)
large and gaseous.
Answer:
small and gaseous.
It would be A small and rocky and the planets names are Mercury, Venus, Earth, and Mars
PLEASE HELP ME!!!!!!!!!!!
Answer: to find f(-4)
Mia did a study for a health class about the effects of the length of a person's foot and their shoe size. Based on a graph of her data, she found that there was a relationship between the length of a person's foot and their shoe size. Which of the following is a valid conclusion? A. The length of a person's foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person's foot and their shoe size. B. There is no correlation between a person's shoe size and the length of their foot. C. A person's shoe size is a cause of the length of their foot. D. No conclusion can be drawn about the correlation or causation between a person's shoe size and the length of their foot.
Answer: The answer is A.
Step-by-step explanation: The only valid conclusion that is listed in the options is choice A. The correct one is that the length of a person’s foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person’s foot and their shoe size.
Factor 5n2 - 12n - 9 A) (n + 3)(5n - 3) B) (2n - 5)(n - 8) C) (3n - 1)(n + 2) D) (5n + 3)(n - 3)
Answer:
A. 2n-5
Step-by-step explanation:
Which value is the solution to the equation? -3(t-7) = 24
Answer:
-3(t - 7) = 24
t - 7 = -8
t = -1
Final answer:
The correct solution to the equation -3(t-7) = 24 is t = -1, which contradicts the reference indicating solutions for a different quadratic equation.
Explanation:
The equation presented, -3(t-7) = 24, does not yield the solutions t = 3.96 and t = -1.03 as the provided reference indicates. Instead, those solutions seem to be related to a different quadratic equation. To solve the given linear equation for t, you need to perform the following steps:
Distribute the -3 across the parenthesis: -3t + 21 = 24.Subtract 21 from both sides of the equation: -3t = 3.Divide both sides of the equation by -3: t = -1.Therefore, the solution to the equation -3(t-7) = 24 is t = -1.
PLZ HURRY! Identify the unit rate in the graph.
20; 3g*h. Hd. So, adding in the. Variables. Then 20
Answer:B) 10$
Usatestprep
250 people were asked to name their favorite fruit.
Berries/ 44%
Peaches 32%
Cherries 24%
A: Of those surveyed, how many people prefer peaches?
B: Which type of fruit did more than 100 people prefer
Answer:
Step-by-step explanation:
A. 250 x .32 = 80
B. 250 x .44 = 110 So, the answer is berries.
Final answer:
Out of 250 surveyed individuals, 80 people prefer peaches. Berries are the preferred choice of more than 100 people.
Explanation:
A total of 250 people were surveyed about their favorite fruit. To find out how many people prefer peaches, we calculate 32% of 250 people. This calculation is done by multiplying the total number of people by the percentage of those who prefer peaches:
250 people x 32% = 250 x 0.32 = 80 people
Therefore, 80 people prefer peaches.
To determine which type of fruit more than 100 people prefer, we apply the same calculation method. Here are the calculations:
Berries: 250 x 44% = 110 people
Peaches: 250 x 32% = 80 people
Cherries: 250 x 24% = 60 people
More than 100 people prefer berries.
give the equation of the line that passes through (1,5) and (-2,3)
Answer:
The equation in point slope form is y= 2/3x+13/3
Step-by-step explanation:
In order to find the equation you need to find the slope, to find the slope you need to graph the two points and use the rise over run method, after using this you can conclude that the slope (m) is 2/3.
To find the y intercept you should plug in one of the points into the point slope formula which is y=mx+b.
Using the first point I get the equation 5=2/3(1)+b, next you isolate the b to get the equation, -b=2/3-5
Then write all the numerators above the common denominator getting 2-15/3
With this you get -b=-13/3 and then you can divide both sides by -1 to get a positive b.
Plug all of these into y=mx+b getting y=2/3x+13/3
Please help, step by step, I need to show the work, I just don’t know how to do it
Answer:
B
Step-by-step explanation:
The volume (V) of a rectangular prism is
V = lbh
where l is the length, b the width and h the height
We are looking for 3 values that multiply together to give 10
Considering each of the options
A
100 × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 25 ≠ 10
B
10 × [tex]\frac{1}{2}[/tex] × 2 = 10
C
5 × 2[tex]\frac{1}{2}[/tex] × 2[tex]\frac{1}{2}[/tex] = 31.25 ≠ 10
D
10 × 10 × [tex]\frac{1}{2}[/tex] = 50 ≠ 10
B is the only possible dimensions for the prism
What is the value of sine of begin argument 45 degrees end argument?
Question 1 options:
fraction numerator square root of 2 over denominator 2 end fraction
fraction numerator square root of 3 over denominator 2 end fraction
square root of 2
square root of 3
Answer:
Option A
fraction numerator square root of 2 over denominator 2 end fraction
Step-by-step explanation:
The answer can be obtained using a calculator.
It corresponds to a notable identity
sin (45) = [tex]\sqrt{2}[/tex] / 2
sin (45) = 0.7071
[tex]\sqrt{2}[/tex] / 2 = 0.7071
Please see attached picture
Graph the following system of equations. Click on the graph until the correct graph appears.
y < -x
y ≤ x - 2
please quick 20POINTS
Answer:
See explanation
Step-by-step explanation:
1. Draw the dotted line y=-x. This line must be dotted, because the inequality y<-x is with sign < (without notion "or equal to"). Then shade the region that contains all values of y that are less than -x (bottom part that is shaded in red on the attached diagram).
2. Draw the solid line y=x-2. This line must be solid, because the inequality y≤x-2 is with sign ≤ (with notion "or equal to"). Then shade the region that contains all values of y that are less or equal to x-2 (bottom part that is shaded in blue on the attached diagram).
3. Their common part (region that is shaded in both red and blue colors) represents both inequalities.
It's this one, just did the test.
Identify which shapes are similar to shape A and which are not.
PLEASE HELP ME!!!
Similar is when a figure has the same shape, but different size.
Answer: 3, 1, 2
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Choose all of the statements listed here that are true about the change over time as indicated by the fossil record.
Birds and flowering plants inhabited this area at about the same time period.
Animals with shells and fish appeared on Earth before land plants.
Flowering plants were critical to the appearance of insects.
Vascular plants appeared during the same period as mammals.
Humans were the last to appear at this site.
Answer:
1,2, and 5
Step-by-step explanation:
This can be determined by looking at the graph
Answer:
The correct answer would be "Animals with shells and fish appeared on earth before land plants." and "Humans were the last to appear at this site."
Step-by-step explanation:
On the graph, it shows that the land plants were a little further ahead in time from the shelled animals and the fish, And the humans were shown last, even after the plants.
what is the answer to number 15 p.s. show how u got this ANSWER PLEASE
Answer:
The volume of the rectangular prism is [tex]V=442.341\ cm^{3}[/tex]
The surface area of the rectangular prism is [tex]SA=384.62\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=LWH[/tex]
substitute the values
[tex]V=(12.7)(8.1)(4.3)=442.341\ cm^{3}[/tex]
The surface area of the rectangular prism is equal to the area of its six faces
so
[tex]SA=2(8.1)(4.3)+2(12.7)(8.1)+2(12.7)(4.3)=384.62\ cm^{2}[/tex]
37) What is the value of x? 1/6 (3 - 2x)< 1/3 x
A) x > 3 4
B) x < 3 4
C) x > - 4 3
D) x < - 3 4
Answer:
A: x > 3/4
Step-by-step explanation:
First you simplify the equation.
Simplify 1/3x
Then Simplify the left side.
1/2-x/3<x/3
Move x/3 to the left side of the equation by subtracting it from both sides.
1/2-x/3-x/3<0
Now simplify the left side.
1/2-2x/3<0
Find the LCD of the terms of the equation. In this case it's 6.
Multiply each term by 6 and simply.
3-2x<2x
Move all terms that contain a x to the left side of the inequality.
3-4x<0
Subtract 3 from both sides.
-4x<-3
Now divide each term by -4 and simplify.
This gives us our answer of x > 3/4.
Hope this helps. :)
What is the product of 4xy and y2 + 2x?
The product of 4xy and (y^2 + 2x) is calculated by distributing 4xy to the terms in the parenthesis, resulting in the answer 4xy^3 + 8x^2y.
Explanation:The question is asking to calculate the product of 4xy and (y^2 + 2x). To solve it, you can distribute 4xy to the terms inside the parenthesis. This gives you:
Multiply 4xy by y^2 to get 4xy^3.Multiply 4xy by 2x to get 8x^2y.Therefore, the product of 4xy and (y^2 + 2x) is 4xy^3 + 8x^2y.
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answer this FAST!
4x^2–20x+25 for x= −2
Answer:
81
Step-by-step explanation:
To evaluate substitute x = - 2 into the expression
4( - 2)² - 20(- 2) + 25
= (4 × 4) + 40 + 25 = 16 + 40 + 25 = 81
What I the slope of the equation of the line below.
Answer:
the slope m = 3Step-by-step explanation:
Look at the picture.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, 4) and (-2, -2). Substitute:
[tex]m=\dfrac{-2-4}{-2-0}=\dfrac{-6}{-2}=3[/tex]
Answer:
-3
Step-by-step explanation:
Don’t know what to do
Answer:
104.65 km/hour
Step-by-step explanation:
We need to convert miles to kilometers. The miles cancel so
65 miles 1.61 kilometers 104.65km
--------------- * ------------------- = -----------------
hour 1 mile hour
The speed limit is 104.65 km/hour
Hector made a batch of pancakes for his guests
I think it is the first.I would choose that.
Answer:
9/6 and 3/2
Step-by-step explanation:
Let's remember the definition of "constant of proportionality":
The constant of proportionality is the constant value of the ratio k of two proportional quantities x and y; usually written y = kx.
In our case, x is the cups of milk and y is the cups of pancake mix. We need to find out k.
9 = k*6
9/6 = k
If we simplified the fraction, we have 3/2 (is equivalent to 9/6).
The correct answers are 3/2 and 9/6.
PLEASE HELP I WILL GIVE BRAINLIST!
To find the unit rate divide the total miles by the total hours:
225 / 4 = 56.25 miles per hour
15 POINTS HELP
A woodland jumping mouse hops along the ground along a parabolic path that can be modeled by the following equation: y = −0.2x2+1.3x (where x is the horizontal position in feet and y is the height in feet). What is the maximum height the mouse can jump?
Answer:
2.1125 feet
Step-by-step explanation:
the vertex will be the maximum value of this parabola.
the general form for a quadratic equation is: ax² + bx + c, for this equation,
a = -0.2, b = 1.3, and c = 0
find the vertex by first using the formula x = -b/(2a)
x = -1.3/(2*-0.2)
x = -1.3/-0.4
x = 3.25
Now plug in that x value to find the actual maximum height
y = -0.2(3.25)² + 1.3(3.25)
y = -0.2(10.5625) + 4.225
y = -2.1125 + 4.225
y = 2.1125 feet
The maximum height the mouse can jump is approximately 2.1125 feet.
To find the maximum height the mouse can jump, you need to determine the vertex of the parabolic path because the vertex represents the highest point on the path. The equation of the path is given as:
y = -0.2x^2 + 1.3x
To find the vertex, you can use the formula:
x_vertex = -b / (2a)
Where "a" is the coefficient of the x^2 term, and "b" is the coefficient of the x term in the equation.
In your equation, a = -0.2 and b = 1.3. Plug these values into the formula:
x_vertex = -1.3 / (2 * (-0.2))
x_vertex = -1.3 / (-0.4)
x_vertex = 3.25
Now that you have the x-coordinate of the vertex, you can find the corresponding y-coordinate by plugging it back into the equation:
y = -0.2x^2 + 1.3x
y_vertex = -0.2(3.25)^2 + 1.3(3.25)
Calculate:
y_vertex = -0.2(10.5625) + 4.225
y_vertex = -2.1125 + 4.225
y_vertex = 2.1125
for such more question on height
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A trapezoid has a height of 10 feet, and base measurements of 20 feet and 8 feet.
What is the area?
Suppose that in 20% of all traffic accidents involving an injury, driver distraction in some form (for example, changing a radio station or texting) is a factor. Find the probability that in a random sample of 275 such accidents between 15% and 25% involve driver distraction in some form. Assume the sample is large enough that the normal distribution applies
To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, calculate the z-scores for both percentages and use the standard normal distribution.
Explanation:To find the probability that between 15% and 25% of a random sample of 275 traffic accidents involving an injury involve driver distraction, we need to calculate the z-scores for both percentages and use the standard normal distribution.
First, calculate the z-score for 15%:Write two mixed numbers where the LCD is 12, but the product of the denominators in not 12?
Step-by-step explanation:
The prime factorization of 12 is
12 = 2²×3
To find denominators suitable for your purpose, you need to group the factors
{1, 2, 2, 3}
into two groups with different products that share at least one of the numbers that is not 1.
For example, your grouping could be (2, [2), 3], where a 2 is shared. That is, your denominators could be 2*2=4 and 2*3=6.
Another possible grouping is (1, [2), 2, 3], giving rise to denominators of 2 and 12.
Yet another is (1, [3), 2, 2], for denominators of 3 and 12.
Using the first grouping, a pair of mixed numbers matching your requirement might be
1 3/4, 5 1/6
Rounded to the nearest whole number, how many 2ft by 2 ft squares will fit into circle that has a diameter of 20 feet
Answer:
79
Step-by-step explanation:
A square that has side length [tex]l=2 ft[/tex] has area [tex]2^2=4ft^2[/tex].
A circle that has a diameter 20 feet has area [tex]A=\frac{\pi d^2}{4}[/tex]
We substitute the diameter into the formula to obtain;
[tex]A=\frac{\pi \times 20^2}{4}=100\pi ft^2[/tex]
The number of squares that has area 4 feet square that can fit into a circle with area [tex]100\pi ft^2[/tex] is
[tex]=\frac{100\pi}{4}=25\pi=78.5398[/tex]
When we round to the nearest whole number; we have 79 squares.
Approximately 79 squares of size 2 ft by 2 ft can fit into a circle with a diameter of 20 feet.
To accurately determine how many 2ft by 2ft squares can fit into a circle with a diameter of 20 feet, let's perform a step-by-step calculation:
1. Calculate the area of the circle:
[tex]\[ \text{Area of the circle} = \pi r^2 \][/tex]
Given the diameter is 20 feet, the radius r is 10 feet:
[tex]\[ \text{Area of the circle} = \pi \times 10^2 = 100\pi \approx 314.16 \text{ square feet} \][/tex]
2. Calculate the area of one 2ft by 2ft square:
[tex]\[ \text{Area of one square} = 2 \times 2 = 4 \text{ square feet} \][/tex]
3. Calculate the theoretical maximum number of squares that can fit into the circle by dividing the area of the circle by the area of one square:
[tex]\[ \text{Theoretical number of squares} = \frac{\text{Area of the circle}}{\text{Area of one square}} = \frac{314.16}{4} \approx 78.54 \][/tex]
4. Round to the nearest whole number:
[tex]\[ \text{Rounded number of squares} = 79 \][/tex]