The midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).
What is the midpoint of the line segment described by the points; (-3, 8) and (-8, 2) as required in the task content?It follows from the task content that the midpoint of the line segment joining the two points (-3, 8) and (-8, 2) is to be determined.
Since the midpoint of a line is given by coordinates;
x = (x1 + x2)/2 and y = (y1 + y2)/2.
It follows that we have;
x = (-3+(-8))/2
x = -11/2
while; y = (8+2)/2
y = 10/2
y = 5.
Ultimately, the midpoint of the line segment described by the two endpoints; (-3, 8) and (-8, 2) according to the task content is; (-11/2, 5).
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You are building an entertainment center with shelves that are x in. deep by x in. long. The height of the unit will be twice the depth. If the volume of the unit will be 8,192 in³, what is the height, in inches, of the entertainment center?
Height of entertainment center will be 32 inches .
Given : Depth of entertainment center = x
Length of entertainment center = x
Height of entertainment center = 2 * depth = 2 * x = 2 x
To find : height of entertainment center .
Volume of entertainment center = depth * height * length
Substituting values in formula above :
8192 = x * x * 2 x
Solving for x ,
[tex]x^{3}[/tex] = 4096
x = 16
Hence , height of entertainment center = 2 x = 2 * 16 = 32 inches .
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Find the inverse of each function. Is the inverse a function? f(x)=1/4x
The Inverse of given function F(x) = 1 / 4x is F⁻¹(x) = 1 / 4 x
F(x) = 1 / 4x is a function of x.
Changing F(x) to the variable y
This means that F(x) = 1/4x becomes y = 1/4x.
Changing the variables x and y in the previously obtained equation
This means that we can deduce x = 1 / 4y from the equation y = 1 / 4x.
Solving the newly discovered equation for y
This means that we must simplify the equation by rearranging the terms in order to obtain the equation in terms of the variable x.
x = 1 / 4y
=> 4 y = 1 / x
=> y = 1 / 4 x
As a result, we obtain the required equation.
Switching the variable y with F⁻¹(x)
This assumes, y = 1 / 4 x becomes F⁻¹(x) = 1 / 4 x
Hence, the value of the given function F⁻¹(x) = 1 / 4 x
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Write each equation in logarithmic form.
10³=1000
We get the equation in logarithmic form as log₁₀ 1000 = 3.
A “logarithmic equation” is an equation which involves the “logarithm” of any expression which is containing a variable.
Now, we have been given an equation:
10 ³ = 1000
We need to write it in the logarithm form.
We know that, it will be written as:
log₁₀ 1000 = 3
Since the power goes after the equal sign, so 3 is placed after the equal sign.
The actual value is taken after log, so 1000 is placed there and the base number is taken as the base for the log, so 10 is taken as the base for the log.
Therefore, we get the equation in logarithmic form as log₁₀ 1000 = 3.
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-3(5+k)≥-23-k solve for k
what is the least common denominator 5/8 and 11/12
Answer:
LCD= 24
Step-by-step explanation:
[tex]\frac{5}{8}=\frac{15}{24}\\ \\\frac{11}{12}=\frac{22}{24}[/tex]
Simplify. (49)2=
someone, please help
Answer:
98
Step-by-step explanation:
(49)2
= 49 • 2
= 98
Therefore, (49)2 = 98
..............
Which of the following statements is true about the Pythagorean theorem?
Choose the correct statement below.
Answer:
B.
Step-by-step explanation:
The Pythagorean theorem only works with right triangles. a and b are the lengths of the legs. c is the length of the hypotenuse. The hypotenuse is the longest side of a right triangle.
Answer: B.
Alicia paid dollar 1.32 for a bag of pinto beans. the bean cost dollar .55 per lb. how much did the bag of pinto beans weigh?
Answer:
The answer is 2.4lbs
Step-by-step explanation:
1.32 divided by .55 is 2.4, meaning the bag weighed 2.4lbs :)
What is the product of 467×39
Answer:
18213
Step-by-step explanation:
Given equation,
→ 467 × 39
Let's solve the problem,
→ 467 × 39
→ 18213
Thus, the answer is 18213.
The table gives the average number of days of rain in each month of the year. Find the median of the
given data.
The median of a data set is 9.5
How to find mean and median of a data?Mean is the ratio of sum of the observations to the total number of observations.
Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.
The median of a data set is the middle number when all of the data points are ordered from smallest to largest. For the data set, the first thing you want to do is put them in order from smallest to largest gives you:
6 6 7 7 7 9 10 10 10 10 11 12
Then we will find the middle of the data set. Since there is an even number of twelve data points; it will be between the sixth and seventh point:
6 6 7 7 7 9 ^ 10 10 10 10 11 12
Now the average of those two in the middle to get the median:
9.5
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It took Earl ½ hour to do his science homework and ⅓ hour to do his math homework. How long did Earl work on homework?
Tyler’s cousin is 32. He is 8 years older than twice Tyler’s age. How old is Tyler?
Answer:
Step-by-step explanation:
half hisage. Then subtract
Answer: 12 years old
Step-by-step explanation:
You should use variables:
Set x as tyler's age.
32 = 2x + 8
32 - 8 = 2x
24 = 2x
12 = x
Therefore, Tyler is 12 years old.
What is the solution of 27³x=81 ?
Solution of exponential equation 27³x=81 is , [tex]x = \frac{1}{243}[/tex]
What is exponential equation ?In, mathematics a exponential equation or exponential function is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as .
[tex]a^n = x[/tex]
where, a = the base of function
x = main expression
n = exponential
Mathematically, if [tex]log_ax = n[/tex] is an logarithmic function then, this can be converted to exponential function as [tex]a^n = x[/tex] .
There are many formulas that are given to us for solving several simple and complex problems based on exponential functions and exponential equations.
According to given statement,
27³ x = 81
divide both side by 27³ , the equation becomes :
[tex]= > x = \frac{81}{27^3} \\\\= > x = \frac{3^4}{(3^3)^3}\\\\= > x = \frac{3^4}{3^9}\\\\= > x = \frac{1}{3^5} = \frac{1}{243}[/tex]
Thus solution for this equation is [tex]x = \frac{1}{243}[/tex]
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The weight of meteorite A is 7 times the weight of meteorite B. If the sum of their weights is 144 tons, find the weight of each.
Taking into account the definition of a system of linear equations, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, they must give the solution proposed in both equations.
Weight of each meteoriteIn this case, a system of linear equations must be proposed taking into account that:
"A" is the weight of meteorite A."B" is the weight of meteorite B.You know:
The weight of meteorite A is 7 times the weight of meteorite B. The sum of their weights is 144 tons.The system of equations to be solved is
[tex]\left \{ {{A=7B} \atop {A+B=144}} \right.[/tex]
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the first equation in the second one you get:
7B + B= 144
Solving:
8B= 144
B= 144÷8
B= 18 tons
Remembering that A= 7B, the value of A is calculated as:
A= 7×18
A= 126 tons
Finally, the weight of meteorite A and meteorite B is 126 tons and 18 tons respectively.
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with the expression 4(b-1) +10 find a term with 46
Answer:
b = 10
Step-by-step explanation:
You take the decimal, divide it by the addend and then you take the fraction and subtract that by the sum and then multiply your answer by 5.
A map is drawn to a scale of 1:75000.
(a) This scale can be expressed as | cm represents n km. Find 77.
(b) The distance between two towns on the map is 25 cm.
Find the actual distance, in kilometres, between the two towns.
(c) A lake has an actual area of 3.5 km.
Find the area, in square centimetres, of the lake on the map.
Give your answer correct to 3 significant figures.
We have been given that -
scale = 1:75000.
we have to find out
(a) scale expressed as 1 cm represents n km.
Map scale refers to the ratio between distance on a map and the corresponding distance on the ground. For example, on a 1:100000 scale map, 1cm on the map equals 1km on the ground
so 1,00,000 cm = 1 km.
(b) given -
distance between two towns on the map is 25 cm.
Find the actual distance, in kilometres, between the two towns.
Scale is given as 1:75000
for 25 cm distance = 25×75000 cm
= 18,75,000 cm
therefore 1875000 cm = 18.75 km.
the real distance between two points is 18.75 km.
(c) . The area of the lake in the real world is 3.5 square kilometers.
1 square kilometer is equal to 1 kilometers squared.
since 1 kilometer is equal to 100,000 centimeters, then 1 square kilometer is equal to 100,000^2 centimeters which is equal to 1 * 10^10 square centimeters.
3.5 square kilometers on the map is therefore equal to 3.5 * 10^10 square centimeters.
1 centimeter on the map is equal to 75000 centimeters in the real world.
1 square centimeter on the map is equal to 75000^2 centimeters in the real world which is equal to5625 * 10^6 square centimeters in the real world.
take 3.5 * 10^10 square centimeters in the real world and divide it by 5625 * 10^6 square centimeters and you get .0006 * 10^4 square centimeters which is equal to 6 square centimeters on the map.
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Crannapple juice costs $4.40 for a 20 ounce bottle. Pineapple juice costs $7.10 for a 30 ounce bottle. Which is the better deal?
Please help I have a day to complete or I’m failing haelppppp‼️
Brian learned to build a cajón from his grandfather. A cajón
is a box-shaped drum that you play by slapping the front.
Brian builds the cajón shown. How much wood will Brian need
to build the four vertical sides but not the top or bottom?
solve this: 7×8²+12÷2=
Answer:
454
Step-by-step explanation:
Answer: The Answer is 454.
Calculate the circumference of a circle if the radius is 28 inches
Answer: 176cm
Step-by-step explanation: To find the circumference of the circle, we will use the circumference formula: 2πr = 2 × 22/7 × 28
Pls help I’ll brainlest asap
Which expression represents the greatest value?
A.
B. -2 +0.5
U
-2 + (-1)
D.
-2+1
-2 + (-0.5)
Answer: I hope this helps.
Step-by-step explanation:
Answer:
The correct answer is -2+1.
So yeah
Write each expression in simplest form. (16 x¹/₄ y³/₃)⁻⁴
The Simplest form of the expression = [tex]2^{-16} x^{-1} y^{-4}[/tex]
We need to express as:
[tex]a^{m}[/tex]/[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
As the expression is given :
[tex](16 x^{1/4}y^{3/3} ) ^{-4}[/tex]
= 1/ [tex](16 x^{1/4} y^{3/3}) ^{4}[/tex]
= 1/[tex](2^{4} x^{1/4} y^{3/3}) ^{4}[/tex]
= 1/[tex](2^{16} x^{1} y^{4} )[/tex]
= [tex]2^{-16} x^{-1}y^{-4}[/tex] (Simplest form of the equation)
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help!!
three less than three-fourths of a number is negative 9.
how do you say that in digits and find the anwser.
Answer:
Step-by-step explanation:
Let n represent the unknown number-
[tex]\frac{3}{4}n-3=-9\\ \\ \frac{3}{4} n-3+3=-9+3\\ \\ \frac{3}{4} n=-6\\\\ \frac{4}{3}(\frac{3}{4}n)=\frac{4}{3}(-6)\\ \\ n=-8[/tex]
Unknown number = -8
Saying it in digits = [tex]\frac{3}{4}n-3=9[/tex]
PLEASE HELP ME WITH THIS QUESTION PLEASE!!!!!!!!
Use the graph to find the zero of the function f(x)=1/2x−3.
Answer:
x = 6
Step-by-step explanation:
The 'ZERO" of the function is the 'x' value(s) where it crosses the x-axis (and
'y' = ZERO)
Answer:
x = 6
Step-by-step explanation:
the zero of the function is the value of x on the x- axis where the graph crosses.
the graph crosses the x- axis at 6
then the zero is x = 6
Write an equation of a line that is perpendicular to y = 6x + 3 that passes through (−6, 4). y = 6x − 30 y = 6x + 40 y equals negative one-sixth times x plus 3 y equals negative one-sixth times x plus 5
Answer:
y equals negative one-sixth times x plus 5
This is correct, it's not plus 3, it's plus 5!
Expand each logarithm. State the properties of logarithms used. log 4 s⁴ t
The expanded form of the given logarithms ( log 4 s⁴ t) is = 2log(2) + 4log(s) + log(t).
Property of logarithms:The features of the log are used to increase a single logarithm into numerous logarithms (or) compression multiple logarithms together into a single logarithm. A logarithm is simply another way of writing exponents. Thus, logarithm properties are obtained from exponent properties.
According to the given data:log (4 s⁴ t)
can be written as log (4 s⁴ t):
Property used in the solving (log b*c = log b + log c) and (log ₐᵇ = b log a)
log (4 s⁴) + log( t)
log (4 ) + log(s⁴) + log( t)
Expand log (s⁴) by moving 4 outside the log.
log (4 ) + log(s) + log( t)
The expression also can be written as :
2log(2) + 4log(s) + log(t)
The expanded form of the given logarithms ( log 4 s⁴ t) is = 2log(2) + 4log(s) + log(t).
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write an equation of the line passing through points (-2,-6) and (4,6)
Answer:
your equation is Y = 6
Step-by-step explanation:
Use Midpoint Formula to find the slope M first
Name the coordinates of both points x1 = -2, y1 = -6, x2 = 4, y2 = 6
Plug them in the formula
M = y2 - y1/ x2 - x1
M =( 6 - 6)/( 4 - (-2))
M = 0/6
M = 0
Then use point slope formula
Plugin the slope M = 0 in the formula and pick one of the points above. Name the coordinates of the point X1 = 4 and y1 = 6
y - y1 = m(x - x1)
y - 6 = 0(x - 4)
y - 6 = 0
y = 6
your equation is Y = 0x + 6 but keep in this form y = b
This is a horizontal Line
At a grocery store, Daniel wants to buy 3 1/5 lb of ham.
What decimal should the digital scale show?
Write 3 as a fraction and then divide.
Decimal should the digital scale show is 0.2
The grocery store asked me to buy 3 [tex]\frac{1}{5}[/tex] pounds of ham. You will be asked to find the number of decimal places displayed by the digital scale.
3 [tex]\frac{1}{5\\}[/tex] lbs = 3 lbs + [tex]\frac{1}{5}[/tex] lbs
[tex]\frac{1}{5}[/tex] = 0.2
3 [tex]\frac{1}{5}[/tex] = 3.2
Therefore, the digital scale is displayed in decimal.
Real numbers, natural numbers, whole numbers, rational numbers, and other sorts of numbers can all be categorized in mathematics. There are decimal numerals among them. Integer and non-integer numbers are represented using this format as a standard.
One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.
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