The shortest distance between planet Q and planet R in standard form is given by
[tex]{1.64 \times 10}^{7} [/tex]
What is the shortest distance between Q and R?QP =
[tex]3.6 \times {10}^{6} [/tex]
RP =
[tex]1.6 \times {10}^{7} [/tex]
Applying the Pythagorean Theorem
QR² = QP² + RP²
QP² =
[tex] {(3.6 \times {10}^{6} )}^{2} + {(1.6 \times {10}^{7} )}^{2} [/tex]
QP² =
[tex](12.96 \times {10}^{12} ) + (2.56 \times {10}^{14} )[/tex]
Rewriting the expression
QP² =
[tex](12.96 \times {10}^{12} ) + (256 \times {10}^{12} )[/tex]
QP² =
[tex] {268.96 × 10}^{12} [/tex]
Find the square root
QP =
[tex] \sqrt{{268.96 × 10}^{12} } [/tex]
QP =
[tex]{16.4 × 10}^{6} [/tex]
Also written as
QP =
[tex]{1.64 \times 10}^{7} [/tex]
In conclusion, the shortest distance between planet Q and planet R is
[tex]{1.64 \times 10}^{7} [/tex]
Complete question:
The distances between some planets are given below.
Planet Q is 3.6 x 10 to the power of 6 km from planet P.
Planet R is 1.6 x 10 to the power of 7 km from planet P.
Work out the shortest distance between
planet Q and planet R. Give your answer in standard form.
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Write the given expression as an algebraic expression in x. tan(2 sin^-1(x))
The trigonometric ratio tan(2 sin⁻¹(x)) is expressed as 2sec(x)
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In the question given, we have;
tan(2 sin⁻¹(x))
tan = sin / cos
sin/cos(2 * 1/sin x)
The expression becomes 2/cosx or 2cos⁻¹(x)
But cos⁻¹ = sec
tan(2 sin⁻¹(x)) = 2sec(x)
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13 tenths + 8tenths + 32 hundredths
In the decimal for, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42
Decimal
Decimal means a number that has a decimal point followed by digits that show the fractional part.
Given,
Here we have the expression 13 tenths + 8 tenths + 32 hundredths
Now, we need to find the value of this expression.
We know that, Tenths means we have one digit after the decimal point and the hundredths have two digits after the decimal point.
So, in the given expression 13 tenths is written as 1.3
And the 8 tenths is written as 0.8
And finally, the 32 hundredths is written as 0.32
Now, we have to add these numbers, then we get,
=> 1.3 + 0.8 + 0.32
=> 2.42
Therefore, the value of 13 tenths + 8 tenths + 32 hundredths is 2.42
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(a) The school sells pens for $1.50 and notebooks for $2.50. The equation 1.50x+2.50y=601.50x+2.50y=60 describes the number of pens, x, and notebooks, y, that you can but for $60. Part A: Find the x- and y-intercepts. Tell what they represent. x-int: What does the x-intercept represent in the context of the problem? (b) BoldItalicUnderlineAlign Align Left Align Center Align Right Align Justify Increase IndentIncrease IndentSpecial Characters $$ 0 Words (c) y-int: What does the y-intercept represent in the context of the problem?
The x-intercept of the equation, 1.50 x + 2.50y = 60, is x = 40
The y-intercept of the equation, 1.50 x + 2.50y = 60, is y = 24
Determining the x-intercept and y-intercept of an equationFrom the question, we are to determine the x-intercept and y-intercept of the given equation.
The given equation is
1.50 x + 2.50y = 60
The x-intercept is the point where y = 0
and
The y-intercept is the point where x = 0
Determining the x-intercept
1.50x + 2.50y = 60
Put y = 0
1.50x + 2.50(0) = 60
1.50x + 0 = 60
1.50x = 60
x = 60/1.50
x = 40
The x-intercept is x = 40
Determining the y-intercept
1.50x + 2.50y = 60
Put x = 0
1.50(0) + 2.50y = 60
0 + 2.50y = 60
2.50y = 60
y = 60/2.50
y = 24
Hence, the y-intercept is y = 24
The x-intercept represent the number of pens that could be bought for $60 when one is not buying any notebooks.
The y-intercept represent the number of notebooks that could be bought for $60 when one is not buying any pens
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If 7 is lessened by 2 of a number, the result is the same as 3 subtracting of the number from 10. Write an equation to represent this situation. Use 'x' as the variable.
An equation to represent this situation x is 37/12. The components of a whole or group of items are represented by fractions.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is less than its denominator.Any number of equal parts is represented by a fraction, which also represents a portion of a whole.Here 7 is lessoned by 2 of a number.
Consider x be the number.
we get 2x - 7
the result is same as 3 subtracting of the number from 10.
therefore, we get 10 ( 3 - x )
from this two equations we get,
⇒ 2x - 7 = 10 ( 3 - x )
⇒ 2x - 7 = 30 - 10x
Simplifying we get,
⇒ -37 = - 12x
⇒ x = 37/12
Therefore, An equation to represent this situation x is 37/12.
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Given 1000 with 100<0, and 100<0 for all x in the interval with 1-1 and 1-03, the left, right, traperoidal, and midpoint rule approximations were used to estimate
08421 and 0.8895, and the same number of subintervals were used in each case. Match the rule to its estimate
Match
left endpoint
right endpoint
midpoint
trapezoidal
actual area
Definition
A) 0.7915
08410
0.8895
DJ08421
0.5405
The estimates were 0.7915, 0.8405, 08410
Answer:
Step-by-step explanation;
Use synthetic division to find the quotient if polynomial P(x) = x³ - 7 x + 6 is divided by x - 2
A) x²+2 x+3
B) x²-2 x-3
C) x²-2 x+3
D) x²+2 x-3
The polynomial function p(x) = x³ - 7x + 6 divided by x - 2 = x² + 2x - 3
Synthetic Division of PolynomialsSynthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.
We can represent the division of two polynomials in the form:
p(x)/q(x) = Q(x) + R/(q(x))
where,
p(x) is the dividendq(x) is the linear divisorQ(x) is quotientR is remainderThe polynomial function p(x) = x³ - 7x + 6 is divided by x - 2
x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)
x² + 3x - x - 3 = x² + 2x - 3
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A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. The plant's height, H (in meters), after x months is given by the following.
The plant's height after x months is 11.25 + 15x.
How to calculate the plants height?From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.
In this case, let the plant's height be H (in meters)
Let the number of months be x.
The plant height will be:
= 11.25 + (15 × x)
= 11.25 + 15x
This is the height.
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Complete question
A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?
Find all values of m for which the equation has two real solutions.
3x² + 7x - (m + 1) = 0
Answer:
m > - 5 1/12----------------------
Given is the quadratic equation.
A quadratic equation has two real solutions if the discriminant is positive.
Set inequality and solve for m:D = b² - 4ac, where a = 3, b = 7, c = - (m + 1)D = 7² + 4*3*(m + 1) 7² + 4*3*(m + 1) > 049 + 12m + 12 > 012m + 61 > 012m > - 61m > - 61/12 m > - 5 1/12Which of the following is equal to 6.6÷2
Answer:B
Step-by-step explanation:
A is equal to 6.3'.
none of the others are equal to 3.3 exactly.
Use the graph below to answer the following question: graph of parabola going through 0, 4, 2, negative 4, and 4, 4 What is the average rate of change from x = 0 to x = 4? Group of answer choices 0 1 4 8
The rate of change of the parabola on the interval [0, 4] is 0.
How to get the average rate of change?For any function f(x), we define the rate of change on an interval [a, b] as:
R = (f(b) - f(a))/(b - a)
Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:
(0, 4), (2, -4), (4, 4)
Then:
f(0) = 4
f(4) = 4
Replacing that in the rate of change formula we get:
R = ( f(4) - f(0))/(4 - 0)
R = (4 - 4)/4 = 0
The rate of change on that interval is 0.
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Each element in the domain of a function corresponds to______
element in the range.
Each element in the domain of a function corresponds to exactly one
element in the range.
What is an element ?
A pure substance made entirely of one species of atoms, or a chemical element, is a species of atoms with a specific number of protons in their nuclei. Chemical elements, in contrast to chemical compounds, cannot be converted through any chemical reaction into simpler substances.
The items in a set are its elements. A property that all the objects share may serve to define a set. Consider the set E, which consists of all positive even integers. E is equivalent to 2, 4, 6, 8, or 10 dots. E={2,4,6,8,10…}.
A function is a relation in which each element of the domain corresponds to exactly one element of the range.
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An isosceles triangle with congruent sides of length
49.3 inches has a perimeter of 121.7 inches Find the
length of the base.
The length of the base is 22.1
An isosceles triangle with congruent sides of length 49.3 inches has a perimeter of 121.7 inches
An triangle is said to be isosceles if two sides of the trainagle have same length.
The two sides of this triangle is congurent that is they have same length = 49.3
perimeter of a triangle is the summation of all three sides.
Perimeter = length + base + length
121.7 = 49.3 + base + 49.3
base = 121.7 - 99.6
base = 22.1
Therefore, the length of the base is 22.1
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10. Sean promotes certain brands on his social media page for compensation. His monthly profit can be modeled using
the quadratic function p(x) = -0.00425x² +7z-1000, where p(x) is the amount of profit earned over
number of days. The graph of the function is shown. Use the graph to find the zeros of the function and interpret
them in context.
Answer:
The zeros are (158.017, 0) and (1489.042, 0)
The profit earned in 158.017 days and 1489.042 days is equal to 0. This means that Sean only earns money (makes a profit) when the amount of days he promotes a brand is greater than 158.017 but less than 1489.042 days.
Option 2: Summarizing Data with a Measure of Center
A high school basketball player is creating a scout summary of their sophomore season. Here are the points scored during their 12 game season listed out. 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27. What measure of center would give the player the best picture of their points scored per game average? Explain how data can be skewed or how measures of center (mean, median, or mode) can be used in favor or against different scenarios in this essay. This is a essay please help!
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
What is mean, median and mode?
The sum of the numbers is added, and the result is divided by the total number of numbers in the list to determine the arithmetic mean. An average usually refers to anything like this. In a list with values ranging from smallest to largest, the median is the middle value. On the list, the mode appears the most frequently.
As given, a high school basketball player is creating a scout summary of their sophomore season.
The points are, 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27.
Arrange these numbers in ascending order,
0, 20, 22, 24, 27, 28, 29, 29, 30, 32, 33, 34.
So,
Mean = (0 + 20 + 22 + 24 + 27 + 28 + 29 + 29 + 30 + 32 + 33 + 34) / 12
Mean = 308 / 12
Mean = 28
Median = 29
Mode = 29 (2 times repeating)
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
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Logan's family drinks a total of 12 gallons of milk every 6 weeks.
a. How many gallons of milk does the family drink per week?
Answer: 2 gallons
Step-by-step explanation:
If they drink 12 gallons of milk every 6 weeks, to find how many gallons they drink per week, you need to divide the number of gallons by the time.
So,
12/6 = 2 gallons
Thus, they drink 2 gallons per week.
AR 14 What value of x makes this equation true?
12x-15=6-3x. F 7./3. G. 3/7. H5/7. J. 7/5
Answer: 7/5
Step-by-step explanation:
[tex]12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}[/tex]
You deposit $2100 in an account earning 3.6% interest compounded monthly. How much will you have in the account in 7 years?
The compound interest after 7 years is $2701.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
A = P (1 + r/12)[tex].^{n/12}[/tex]
A = 2100(1+3.6/12)[tex].^{7/12}[/tex]
A=2701
Hence the compound interest after 7 years will be $2701.
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a teacher gives out 12 boxes of crayons for students to use for an art project. each student is given 1/4 of a box of crayons. how many students are given crayons
Answer:
The answer is 48
Step-by-step explanation:
First you have to get the number or crayons ehich is 12 then you can multiply it by the denominator in 1/4 so 12x4=48
Solve the equation without using a calculator
[tex]\bf\log_x\big(2+\sqrt{3} \big)=log_{\big(x+6\big)}\big(1+2\sqrt{3} \big).[/tex]
Answer:
[tex]x=7+4\sqrt{3}[/tex]=====================
Given[tex]log_x(2+\sqrt{3})=log_{x+6}(1+2\sqrt{3})[/tex]Solve it in below steps[tex]2log_x(2+\sqrt{3})=2log_{x+6}(1+2\sqrt{3)}[/tex][tex]log_x(2+\sqrt{3})^2=log_{x+6}(1+2\sqrt{3})^2[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(13+4\sqrt{3})[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(7+4\sqrt{3}+6)[/tex]Let 7 + 4√3 = t, then[tex]log_xt = log_{x+6}(t+6)[/tex][tex]logt/logx=log(t+6)/log(x+6)[/tex][tex]logx/log(x+6)=logt/log(t+6)[/tex][tex]log_{x+6}x=log_{t+6}t[/tex][tex]x = t[/tex]The value of x is[tex]x=7+4\sqrt{3}[/tex]What is consumidores terciarios?
Hello..!
¿What is consumidores terciarios?
They are the ones that feed on carnivores and their parasites.
An example:
When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.
Organisms that eat secondary consumers are called tertiary consumers and are carnivores that eat carnivores, such as eagles or large fish.
Producers, or autotrophs, make their own organic molecules. Consumers, or heterotrophs, obtain organic molecules by eating other organisms.
A food chain is a linear sequence of organisms through which nutrients and energy pass from one organism to another through consumption.
What is the prime factorization of 144?
OA) 4 x 36
OB) 22x6
OC) 24x3²
OD) 12x12
The Prime factorization of 144 is ([tex]2^4[/tex]) x (3²).´
What is a factor?
A factor is a number/expression that divides another number/expression, leaves zero remainder . In other words, if multiplying two numbers/expressions gives us a product, then the numbers/expressions we are multiplying are factors of the product because they are divisible by the product.
Factors of 144:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Prime factorization:
144 = 2 x 2 x 2 x 2 x 3 x 3, which can also be written as
144 = ([tex]2^4[/tex]) x (3²).´
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-1.5x+3(-0.3x-1) simplify the linear expression
Answer: -2.4x-3
Step-by-step explanation:
Find the distance between the points (2,3) and (5,-2)
The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
The given points are (2,3) and (5, -2)
The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex] [tex](x_{2} ,y_{2} )[/tex] is
D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]
For evaluating the distance between the points (2,3) and (5, -2)
The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]
Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.
In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.
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{Question 19} Please help! Need by tonight! Thanks
Answer: 3, -1/3x - 1
Step-by-step explanation:
Answer:
y= -1/3x-1
Step-by-step explanation:
Find the slope of the line by plugging two points into the slope formula
[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]
[tex]\frac{-1-0}{0-(-3)}[/tex]
m= -1/3
Find the y-intercept by seeing where the graph intersects the y-axis
b = -1
y=mx+b
y= -1/3x-1
Find the final balance earned in an account with $845 invested at 4% annual simple
interest for 18 months.
The final balance is $895.7.
What is simple interest?
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Interest = principal ×rate× time
Given, principal = $845
rate = 4%
time = 18 months = 3/2 years.
After substituting the values, we get
Interest = 845(4)(3/2)/100
= 50.7
Final balance = initial balance + interest
Therefore,
Final balance = 845 + 50.7
= $895.7
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State what additional information is required in order to know that the triangles are congruentfor the reason given.
44 POINTS !
The additional information is required in order to know that the triangle are congruent is, GW ≅ WX.
What is congruent triangles?
If each of the three corresponding sides and each of the three corresponding angles in two triangles equals one another, then the two triangles are said to be congruent.
We have to show that the the triangles ΔVWX and ΔEWG are congruent by using the AAS (angle, angle, side) criteria.
From the given reasons,
∠V ≅ ∠E
∠VWX ≅ ∠EWG
From this the AA criteria is satisfied.
We want sides of the triangle are congruent.
From the figure, GW ≅ WX
Therefore, by AAS the two triangles ΔVWX and ΔEWG are congruent.
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Name three points collinear points on plane P.
Answer:
ABC
Step-by-step explanation:
Think of a plane as a piece of paper that went on forever in all directions. Which points would be on the paper? Three examples would be points A, B and C.
Find the y intercept
Because there is a slope of 0, the graph is a horizontal line.
Plug into the slope-intercept form: y=mx+b
Where
m = slope & b = y-intercept
m=0
y=-1
So,
y=(0)x+(-1)
therefore your final answer is:
y=-1
3. A grocer has 60kg of potatoes. In one day, he sells 50% of the
potatoes. What mass of potatoes does he sell?
Answer: 30kg
Step-by-step explanation:
100% = 60kg
50% = 100% /2
60kg(100%)/2 = 30kg(50%)
Answer:
Step-by-step explanation:
Proportion:
60 kg - 100%
X kg - 50%
X = 60·50% / 100% = 30 kg
SAFSADFASDSADSA HELPPPPPPP
Answer:
y = - [tex]\frac{10}{3}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{10}[/tex] x - 8 ← is in slope- intercept form
with slope m = [tex]\frac{3}{10}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{10} }[/tex] = - [tex]\frac{10}{3}[/tex] , then
y = - [tex]\frac{10}{3}[/tex] x + c ← is the partial equation of line h
to find c substitute (3, - 9 ) into the partial equation
- 9 = - 10 + c ⇒ c = - 9 + 10 = 1
y = - [tex]\frac{10}{3}[/tex] x + 1 ← equation of line h
