Answer:
Vertex → (x, y) = (− 3, − 4)
x intercepts → (x, y) = (−5, 0) and (−1, 0)
y intercept → (x, y) = (0, 5)
Step-by-step explanation:
Set y = 0 = ( x + 3)^2 − 4
Add 4 to both sides
4 = (x + 3)^2
Square root both sides
± 2 = x + 3
Subtract 3 from both sides
x = − 3 ± 2
x intercepts → (x, y) = (− 5, 0)
and
(− 1, 0)
You may if you so choose determine the vertex from this point
x vertex is midway between the x intercepts then by substitution determine y. The method I used later takes less work.
Given
y (x + 3)^2 − 4
x vertex = (-1) ×(+ 3) = − 3
y vertex = − 4
Vertex → (x, y) = (− 3, − 4)
y intercept = + 3^2 − 4 = 5
ALGEBRA 2 - Exponential and Logarithmic Functions
John invests $25,000 in an account that pays 4.75% annual interest compounded continuously. How many years, to the nearest tenth, will it take for John’s investment to triple?
Answer:
The equation you would use to solve this problem is:
A = P * e^(rt)
Where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of years.
We can rearrange the equation to solve for t:
t = (ln(A/P)) / r
Plugging in the values we know:
t = (ln(3*25000/25000)) / (0.0475)
t = (ln(3)) / (0.0475)
t = 4.93 years
So it will take about 4.9 years for John's investment to triple, to the nearest tenth.
Step-by-step explanation:
Find the solutions to x² = 24.
OA. x= 16-√4
B. x = +2√6
O C.
x = +6√ √2
OD. x +4√6
Answer:
x = 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{24}[/tex] = [tex]\sqrt{(2)(2)(2)(3)}[/tex] We can pull out a pair of 2's
2[tex]\sqrt{(2)(3)\\}[/tex] = 2[tex]\sqrt{6}[/tex]
Please help easy
A) 30/40
B)22/40
C)18/40
D)10/40
Answer:
D
Step-by-step explanation:
GIVING BRAINLIEST! HELP
Answer:
Below
Step-by-step explanation:
125 kg * 2.204 pound/kg = 275.5 pounds
Answer:
D. 275.5 pounds
Step-by-step explanation:
1 kg = 2.204 lbs
=> 125 kg = (125 kg)(2.204 lbs/1 kg) = 275.5 lbs
What the function?
y = 2.5x + 8
Answer:
Step-by-step explanation:
This is a linear function with y-intercept (0, 8) and slope 2.5.
what is the value of x?
Answer:119
Step-by-step explanation:
because it's on oppisite sides on the outside
Answer:
C) 119°------------------------------
The two given two angles are alternate exterior angles and therefore congruent according to alternate exterior angles theorem:
x = 119°Definition:
Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.A straw is placed inside a rectangular box that is 9 inches by 5 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form?
Answer:
sq rt 122
Step-by-step explanation:
if the box is 9 inches length (base) then this applies
First find the base diagonal then find the furthest top to base diagonal after.
Pythagoras theorem
Base diagonal
9^2 + 5^2 = c^2
(sqrt) of 81+25 = c^2
(sqrt) of 106 = c^2 = 10.29563 inches
= 10.3 inches.
larger diagonal
We note the height is 4inches and we add this again squaring all digits on calculator
10.29563^2 + 4^2 = c^2
(sqrt) 121.999997 = c^2
= 11.045361017187261 = 11.08 = 11.1 inches
Radical form = sq rt 122
The diagonal of the straw in radical form is √122 inches.
What is rectangular prism?A rectangular prism is a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.
The rectangular box is in the shape of rectangular prism.
For the given situation,
Length of the rectangular box, l = 9 inches
Breadth of the rectangular box, b = 5 inches
Width of the rectangular box, w = 4 inches
The formula to find the diagonal of the rectangular prism is
[tex]d=\sqrt{l^{2}+b^{2}+w^{2} }[/tex]
⇒ [tex]d=\sqrt{9^{2}+5^{2}+4^{2} }[/tex]
⇒ [tex]d=\sqrt{81+25+16}[/tex]
⇒ [tex]d=\sqrt{122}[/tex]
Hence we can conclude that the diagonal of the straw in radical form is √122 inches.
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write as the opposite of a square root: -2 times square root of 3
the answer would be -144
you would have to multiply 3 by square 2, then multiply them which would be 3*4=12 and then you would square that which is 144 and because it is negative it would be -144
Please help don’t give link if your right you get brainliest
Answer:
rotation, dilation
Step-by-step explanation:
On the question it shows how it is supposed to be ordered, triangle LMN is similar to triangle PQR which means LM and PQ are similar sides and MN and QR are similar, etc.
it is rotation because the P is facing the left side while L is facing upward.
it is dilation because triangle PQR shrunk into a smaller triangle.
A scuba diver is at a depth of -14 ft. Her
elevation changes -2 ft per second. How many
seconds will it take her to reach a depth of
79ft? Write and solve an equation.
On solving the provided question, we can say that - by the help of unitary method seconds will it take her to reach a depth of 79ft is = 39.5
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
scuba diver is at a depth of = -14 ft
elevation changes = -2 ft per second.
seconds will it take her to reach a depth of 79ft is = 39.5
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Are 3 4 5 triangles always right?
No, three 4 5 triangles are not always right triangles.
A right triangle is a triangle in which one of the angles is a right angle (90°). Therefore, in order to be a right triangle, the following criteria must be met: a^2 + b^2 = c^2, where c is the longest side and a, b are the other two sides. In a 3 4 5 triangle, the longest side is 5, so a^2 + b^2 = c^2 becomes 3^2 + 4^2 = 5^2. Using simple algebra, this equation becomes 9 + 16 = 25, which is true. Therefore, a 3 4 5 triangle is a right triangle. However, if one of the sides is different, for example a 3 4 6 triangle, the equation becomes 9 + 16 = 36, which is not true. Therefore, a 3 4 6 triangle is not a right triangle. To summarize,3 4 5 triangles are right triangles, but three 4 6 triangles are not.
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Solve = 3/5k + 7/10 = 11/15k – 2/5
i get 11/2 is this wright answer??
The rate of growth dP / dt of a population of bacteria is proportional to the square root of t, where P is the population size and t is the time in days (0 ? t ? 10) as shown below.
dP/dt=k \sqrt{t}
The initial size of the population is 300. After 1 day the population has grown to 600. Estimate the population after 8 days. (Round your answer to the nearest whole number.)
The population of bacteria after 8 days is 7088
Here, we have been given an equation for the rate of growth of a population of bacteria
dP/dt = k√t
where P is the population size
and t is the time in days (0 ≤ t ≤ 10)
We rewrite above equation as,
dP = k√t dt
Integrating both sides, we get,
P = (2/3) × kt^(3/2) + C
We find the value of C.
For t = 0, P = 300 as the initial size of the population is 300.
Substitute t = 0 in above equation.
300 = 0 + C
C = 300
So, the above equation becomes,
P = 300 + (2/3) × kt^(3/2) .......(1)
Now we find the value of k.
After 1 day the population has grown to 600.
substitute t = 1, P = 600 in equation (1)
600 = 300 + (2/3) × k
(2/3)k = 300
k = 900/2
k = 450
So, the equation of population of bacteria after time t is:
P = 300 + [(2/3) × 450 × t^(3/2)]
P = 300 + 300 × t^(3/2)
P = 300 (1 + t^(3/2))
To find the population after 8 days, substitute t = 8
P = 300 (1 + 8^(3/2))
P = 7088.22
P ≈ 7088
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n/5+4 = -4. I need help very bad please
In order to get the value of n, which is what we are trying to find, it is important to know how to isolate the variable.
When something is added to n, you subtract to isolate n. Going with this logic, you would multiply by a number if you wanted to isolate n with a fraction.
[tex]\frac{n}{5}+4=-4[/tex]
The first step would be to get rid of the 4 on the left side so we can work on the variable. We can do this by subtracting both sides by 4, so the left side cancels out to 0.
[tex]\frac{n}{5}+4-4=-4-4[/tex]
[tex]\frac{n}{5} =-8[/tex]
Next, we can multiply both sides by 5, so we can isolate the variable, because it is being divided by 5.
[tex]\frac{n}{5} *5=-8*5[/tex]
n=-40
A circle has a diameter of 26 units. What is the area of the circle to the nearest hundredth of a Square unit?
Answer:
Your answer is 539.93
Step-by-step explanation:
A = pi*r²
A = pi* 13²
A = pi*169
A = 539.93
11a + 12b = does it equal 23ab or not
Answer:
no it doesn’t.
Step-by-step explanation:
Please if anyone can provide the answer I will manifest tranquility for eternity upon you, I have the brain capacity of an infant
Answer:
the ?=4
Step-by-step explanation:
i got it on desmos basically the vertex is 4 high so you would need to add 4 to get it up there
The times taken by 25 people to complete a puzzle are shown. Draw a frequency polygon for data.
To create a frequency polygon calculate the midpoint, locate the midpoints and connect them with lines.
What is a frequency polygon?A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.
So, we must determine the midpoint or average of the range for each category.
0 < t < 10 = 5
10 < t < 20 = 15
20 < t < 30 = 25
30 < t < 40 = 35
2. Add a point where the data of the axis Y and X form an intersection.
3. Connect the points.
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Given: (↔AB) ║ (↔CD)
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of (↔AB) is (?) . If the coordinates of point D are (5 , 5), the equation of line (↔CD) is y =(?) x +(?).
can someone please help me figure out what the (?) is.
Answer:
1. 56/5
2. -7/5
3. 12
Step-by-step explanation:
If x = 7 − p and y = 3p + 4, which of the following
expresses y in terms of x ?
f. 17-x
g. 25-x
h. 17-3x
j. 25-3x
k. 25-3x
Answer:
y = 25 - 3x
Step-by-step explanation:
x = 7 - p ⇒ p = 7 - x
y = 3(7-x) + 4
y = 21 - 3x + 4
y = 25 - 3x
In a closed system, an object with a mass of 1.5 kg collides with a second object. The two objects then move together at a velocity of 50 m/s. The total momentum of the system is 250 kg⋅m/s. What is the mass of the second object?
The mass of the second object will be 3.5 kg.
What is momentum?In Newtonian mechanics, momentum is calculated as the sum of an object's mass and velocity. It has both a magnitude and a direction, making it a vector quantity.
According to the collision theory, for a chemical reaction to take place, the reacting particles must come into contact with one another. The frequency of collisions affects the reaction's rate. According to the idea, responding particles frequently encounter without reacting.
The final momentum will be calculated by the expression given below,
(m₁ + m₂ ) V=250
( 1.5 + m₂ 0 x 50 = 250
1.5 + m₂ = 5
m₂ = 5 - 1.5
m₂ = 3.5 kg
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What are the coordinates of point Q?
Answer:
(4, 2.5)
Step-by-step explanation:
yeaahhhh help please i beg for your help -^-
Answer:
48
Step-by-step explanation:
Since it is a triangle, it should add up to be a total of 180 degrees.
I took 64 + 68 = 132
Since there's a missing angle, you can take 180 - 132 = 48
All the angles should add up to 180 so 64 + 68 + 48 = 180
Your welcome !!
Write the equation of the line, that passes through the points (- 6, 1) and (10, 0)
Equation:
Now, write an equation of a line that is parallel to the above line and passes through point (-7, 2) in all three forms below.
Point-Slope Form
Slope-Intercept Form
Standard Form
The equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the line passes through the points (- 6, 1) and (10, 0).
The slope of the line will be -
{m} = (0 - 1)/(10 + 6) = -1/16
{m} = -1/16
We can write the equation as -
y = - (1/16)x + c
For the point (10, 0), we can write -
0 = - (1/16) x 10 + c
0 = - (10/16) + c
c = 10/16
c = 5/8
So, we can write the equation as -
y = - (1/16)x + (5/8)
The equation of a line that is parallel to the above line and passes through point (-7, 2) is as follows -
y = - (1/16)x + c
2 = - (1/16) x - 7 + c
c = 2 - 7/16
c = 25/16
y = - (1/16)x + (25/16)
Therefore, the equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
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is the following table Proportional or Non proportional?
HELP PLS:(
Answer: proportional
Step-by-step explanation: I took the test and looked it up on 3 different websites like duh
help meh...............
Answer:
Angles 6, 4, and 2 are congruent to angle 8.
Step-by-step explanation:
By the Opposite Angles Theorem, angle 6 is congruent to angle 8.
By the Corresponding Angles Theorem, angle 4 is congruent to angle 8.
By the Corresponding Angles Theorem, angle 2 is congruent to angle 6, and angle 6 is congruent to angle 8, so angle 2 is congruent to angle 8 by the Transitive Property.
Khalil's birthday party costs $11, plus an additional $9 for each guest he invites. Is the total cost directly proportional to the number of guests?
Answer:
20, yes
Step-by-step explanation:
11+9=20
If he is charged $9 for each guest then it will make a huge impact to the number of guests.
Which value is an exact solution of the equation
Answer:
it's B
Step-by-step explanation:
becaus the exact form of m is the square root of 14
pls mark as brainliest lol
Answer:
[tex]\sqrt{14}[/tex]
Step-by-step explanation:
m is squared, so it would have to be the square root.
We take a sample of 80 observations from a large population with a mean of 1460 and a standard deviation of 270. The probability that the sample mean is between 1300 and 1400 is:
The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.
Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:
Standard deviation of the sample mean
= population standard deviation ÷ [tex]\sqrt {sample size[/tex]
[tex]= 270 \div \sqrt{80} = 27[/tex]
So the standard deviation of the sample mean is 27.
We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.
[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59
[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22
We need to find the area under the standard normal distribution curve between Z1 and Z2.
Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.
Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
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Answer:
first Q . mirror
Second Q. sight and touch
Answer: Smoothest surface: mirror
senses being used: sight and touch
hope this helps!
Step-by-step explanation: