After solving the equation, x = 3/2 is the value of x in [tex]3^{2x}[/tex] = 27
⇒ [tex]3^{2x}[/tex] = 27
⇒ [tex]3^{2x}[/tex] = [tex](3)^3[/tex]
⇒ 2x = 3
⇒ x = 3/2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Put together the whole solution.
694÷41 is equal to 10+3+2+1 with a remainder.
694 divided by 41 is
remainder
.
694 divided by 41 goes into 16 times with remainder 38.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Now, We can use long division in finding the remainder.
Place the divisor which is 41, outside the long division sign, and 694 under the long division sign as;
41 ) 694 ( 16
- 41
---------
284
- 246
----------
38
Hence, 694 divided by 41 goes into 16 times with remainder 38.
Since, 10 + 3 + 2 + 1 = 16
Therefore, 694 divided by 41 is 16 with remainder 38.
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a. Name a pair of vertical angles.
b. Name an angle supplementary to RPS
c. Name a pair of complementary angles.
d. Name an angle adjacent to TPU.
1) The vertical angle will be
∠RPQ= ∠TPU
Vertical angles are angles opposite each other where two lines cross.
Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other. Real-life settings where vertical angles are used include; railroad crossing sign, letter “X'', open scissors pliers etc.
2) angle ∠QPR and angle ∠TPS are supplementary to ∠RPS
Supplementary angles are two angles whose measures add up to 180° . The two angles of a linear pair
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly,
3) complementary angle will be
∠QPR and ∠RPS
When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles.
4) The adjacent angle will be ∠TPS
The two angles are said to be adjacent angles when they share the common vertex and side. The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle. Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.
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The density of Oats is 410kg/m³ The density of wheat is 770 kg/m³ 1025kg of oats and 616 kg of wheat are mixed together. What is the total volume of the mixture?
The most appropriate choice of density will be given by
Total volume is 3.3 [tex]m^{3}[/tex]
What is density?
Ans : Density is mass per unit volume of a substance.
The density of Oats is [tex]410[/tex] [tex]kg/m^{3}[/tex]
volume of 1025 kg of oats = [tex]\frac{1025}{410}[/tex] [tex]m^{3}[/tex]
= 2.5 [tex]m^{3}[/tex]
Density of wheat is 770 [tex]kg/m^{3}[/tex]
volume of 616 kg of wheat = [tex]\frac{616}{770}[/tex] [tex]m^{3}[/tex]
= 0.8 [tex]m^{3}[/tex]
Total volume = (2.5 + 0.8) [tex]m^{3}[/tex]
= 3.3 [tex]m^{3}[/tex]
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a. Before a basketball game, a referee noticed that the ball seemed under-inflated. She dropped it from 6 feet and measured the first bounce, as 36 inches and the second bounce as 18 inches. Write an exponential function to model the height of the ball.
The exponential function to model the height of the ball is
h = 72*[tex](1/2)^{n}[/tex]
According to the question we have been given that
at first bounce the height of the ball is = 36 inches
and at the second bounce the ball is at the height = 18 inches
The exponential model is given as
h = a.[tex]b^{n}[/tex] (1)
where h = height of the ball
n = number of bounces
Putting the different values of h and n in equation (1) and getting the value of a and b, we get
when h = 36 and n=1
36 = a.[tex]b^{1}[/tex]
36 = a.b (2)
when h = 18 and n =2
18 = a.[tex]b^{2}[/tex]
18 = a.b.b
18 = 36.b
b = 1/2
substituting the value of b in equation (2) we get
a = 72
Hence putting the value of a and b in equation (1), the exponential function to model the height of the ball is
h = 72*[tex](1/2)^{n}[/tex]
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What is the value of x in the figure shown below?
Help quick pls
Question two:
ABC is rotated ____ degrees ____ around point ____ to create abc
Triangle ABC is rotated 85° around the point D to create A'B'C'.
What is rotation?Rotation is a transformation in which a figure is turned around a point . This point is fixed and is called the center of rotation.
From the given diagram we can see that the triangle is rotated about the fixed point D with an angle of 85° such that A' is new location of A and B' and C' are new locations of B and C respectively.
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if A= [2 6] prove that (A')' = A
3 7
4 9
Answer:if A= [2 6] prove that (A')' = A
3 7
4 9
Step-by-step explanation:
Read each question. Then write the letter of the correct answer on your paper.Use the sum of cubes formula to factor x³+64 .
(A) (x+4)(x²-4 x+4) (B) (x+4)(x²+4x+4) (C) (x+4)(x²-4 x+16) (D) (x+4)(x²+4 x+16)
The solution of factorization of x ³ + 64 is ( x + 4 )( x ² - 4 x + 16 ) [ Option C ].
The question asks to factorize the given polynomial, that is, x ³ + 64.
The question clearly states that we need to use the sum of cubes formula to factor the given polynomial x ³ + 64.
Sum of cube formula is given as
a ³ + b ³ = ( a + b ) ( a ² - a b + b ² ).
Substitute the values of variable a and b from the given polynomial x ³ + 64
x³ + 64 can be written as x ³ + 4 ³
=> a = x and b = 4
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 4 ² )
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 16 )
This matches with the option c among the multiple choices for this question.
Therefore, we get the solution of factorization of x ³ + 64 as ( x + 4 )( x ² - 4 x + 16 ).
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The temperature dropped 6 degrees celsius every hour for 6 hours. what was the total number of degrees the temperature changed in the 6 hours?
Answer:
36°C
Step-by-step explanation:
[tex]|-6(6)|=36[/tex]
Given lines p and q are parallel, find the value of x that makes each diagram true.
In the given diagram the value of x is is 140° and 25° respectively
In the diagram a, when you have 2 parallel lines cut by a transversal, the corresponding angles are equal and the value of x is equal to the corresponding angle as they are vertical angles, vertical opposite angles are equal.
In the diagram b, angle x is equal to the angle that is supplementary to 155° (Sum of supplementary angles is equal to 180°)
180-155=25°
In the given diagram the value of x is 140° in the diagram a and 25° for the diagram b respectively
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Your question is incomplete as the diagram is missing but the above answer might help you out.
A/an is calculated by dividing the difference between a data value and the mean by the standard deviation.
Answer:
z score
Step-by-step explanation:
expanded form of which decimal. Santo chose C as the correct answer.How did he get that answer?
Applying proportions, the decimal value is given by:
B. 32.064.
Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for digit values in a number.
For this problem, we just have to apply the digit values of the number to find the decimal value, adding the factors, hence:
3 x 10 = 30. (3 tens)2 x 1 = 2 (2 ones).6 x 1/100 = 0.06 (6 hundredths).4 x 1/1000 = 0.004 (4 thousandths).Hence:
30 + 2 + 0.06 + 0.004 = 32.064.
The decimal value is given by:
B. 32.064.
Santo got the wrong answer because he counted 6 and 4 as the tenths and hundredths digits, instead of hundredths and thousandths.
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I NEED HELP SOMEONE HELP ME!!
The grid above shows the graph of the parent
function f(x) = Ixl and a translated functions
graph.
Write the equation for the translated graph.
i need to write an equation pls help
Answer:
g(x) = | x + 2 | + 1
Step-by-step explanation:
the parent function f(x) = | x | has its vertex at the origin
the translated function has the form
g(x) = | x - h | + k
where (h, k ) are the coordinate of the vertex
the vertex of g(x) is at (- 2, 1 ) , then
g(x) = | x - (- 2) | + 1 , that is
g(x) = | x + 2 | + 1
What is any term raised to the zero power equal to?
Answer: Therefore, it is proven that any number or expression raised to the power of zero is always equal to 1. In other words, if the exponent is zero then the result is 1.
Step-by-step explanation: have a good day!
Suppose a student picks 3 points at random from A, B, C, and D shown below. Find the probability that these randomly chosen points are collinear.
B
The probability that 3 randomly selected points from A, B, C, and D are collinear is
(Type an integer or a simplified fraction.)
The probability that 3 randomly selected points from A, B, C, and D are collinear is; 3/4
How to Identify Collinear Points?
Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear.
Now, from the given image, there are 4 points but only three of them namely A, B and C are collinear. Thus, the 4 possible points picked could be; ABC, ABD, ACD, BCD
Thus, there are only three that can be collinear and so the probability is; 3/4
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please help me thank u
Super pets charges $20 for the application fee to dog sit. after that, it charges $10 per hour.
fancy pets charges $60 for the application fee to dog sit. after that, it charges $2 per hour.
a) write a linear equation to model each company. make sure to label each one.
Answer:
Super = 20 + 10x
Fance = 60 + 2x
Step-by-step explanation:
→ Start with the set fee for both
Super = 20 +
Fancy = 60 +
→ Assign a new variable to denote hours
x
→ Complete
Super = 20 + 10x
Fance = 60 + 2x
Which distribution is positively skewed? O A B. О с. D. HTT 6 10 02 4 6 8 10 12 14 16 18 20 22 24 26 28 30
So, this distribution is positively skewed.
What is positively skewed distribution?A positively skewed distribution, also known as a right-skewed distribution, is a type of distribution in statistics in which most values are centered around the left tail and the right tail is longer. The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left.
Given Data
6 10 02 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Mean = [tex]\frac{6 + 10+2+4+6+8+10+12+14+16+18+20+22+24+26+28+30}{17}[/tex]
Mean = [tex]\frac{256}{17}[/tex]
Mean = 15.05
The distribution is said to be negatively skewed if the mean is lower than the mode. Positive skewness occurs when the mean exceeds the median in the distribution. The distribution is said to be negatively skewed if the mean is lower than the median.
So, this distribution is positively skewed.
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what is the midpoint of a line segment with the endpoints (8,-3) and (-5,-9)
Answer: (3/2,-6)
Step-by-step explanation:
Answer:
Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.
Midpoint = [(8+(-5))÷2, (-3+(-9))÷2]
= (3/2, -12÷2)
= (3/2, -6)
A recipe says it produces the best summer drink the recipe calls for 1/2 cups of lemonade for every 1 1/2 cups of iced teas if 16 cups of the summer drink are made how many of those are cups of lemonade use the table to help you find your answer
The solving of fraction shows that there are 4 cups of lemonade use the table.
What is fraction?A fraction seems to be a part of a whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by that of the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in both the numerator and the denominator.
Why is it critical to understand fractions?Fractions help children know the nature of numbers but instead their interactions (e.g., the meaning of division) (e.g., the meaning of division). If a child does not grasp how fractions work, he will struggle to understand algebra later in life.
According to the given data:Based on the given conditions, formulate:
= [tex]16 \times \frac{1}{2} \div\left(\frac{1}{2}+1 \frac{1}{2}\right)[/tex]
Convert the expression into a fraction:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{1}{1}+\frac{1}{2}\right)\right)}[/tex]
Expand the fraction to get the least common denominator:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{1 \times 2}+\frac{1}{2}\right)\right)}[/tex]
Calculate the product or quotient:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{2}+\frac{1}{2}\right)\right)}[/tex]
Write the numerators over common denominator:
= [tex]\frac{16}{2 \times \frac{1+2+1}{2}}[/tex]
Write the numerators over common denominator:
= [tex]\frac{16}{2 \times \frac{3+1}{2}}[/tex]
Calculate the sum or difference:
= [tex]\frac{16}{2 \times \frac{4}{2}}[/tex]
Calculate the sum or difference:
= 16 /2
Cross out the common factor:
= 4
This shows that there are 4 cups of lemonade use the table.
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Simplify the following expression: -9x+8+2x-6*
Answer:
7x+2
Step-by-step explanation:
-9x+8+2x-6
8-6
-9x+2+2x
combine like terms
-9x+2+2x
-9+2
7x+2
Need help with this question image attached
help me with this !! please
we get the graph of the quadratic function by plotting the points on the graph paper.
We are given the quadratic function as:
f (x) = x²
We need to graph the function and find the values of the function for some given points of x.
For x = - 2, we get that:
f (x) = x²
f (- 2) = (- 2)²
f (- 2) = 4
For x = - 1, we get that:
f (x) = x²
f (- 1) = (- 1)²
f (- 1) = 1
For x = 0, we get that:
f (x) = x²
f (0) = (0)²
f (0) = 0
For x = 1, we get that:
f (x) = x²
f (1) = (1)²
f (1) = 1
For x = 2, we get that:
f (x) = x²
f (2) = (2)²
f (2) = 4
Plotting these points on the graph, we obtain the graph of the quadratic function.
Therefore, we get the graph of the quadratic function by plotting the points on the graph paper.
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Point I is on line segment HJ. Given IJ = 3 and HI = 14, determine the length
НЈ.
The length of hJ is 17.
Given, the line HJ has a length
HJ = ?
HI = 14
IJ = 3
Since line HJ = HI + IJ
= 14+3
=17
Therefore the length of HJ will be 17.
A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
The line is here! It extends endlessly in both directions and has no beginning or conclusion.
the measurement or extent of something from end to end; the greater of two or the greatest of three dimensions of a body is called length.
In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.
Types of Line Segment
Parallel Line. Two lines in the same plane either meeting each other or not.
Intersecting Lines.
Concurrent Lines.
Collinear Points.
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Let f(x)=4 x, g(x)=1/2x+7 , and h(x)=-2 x+4 . Perform each function operation. (f⁰g)(x)
The value of the composite function (h⁰ g)(x) calculated by function operation is 2x+28 .
A function is described as the relationship between a set's domain and range and its elements. f, g, or h are frequently used to denote functions.
Each element of an algebraic function, denoted by the formula y=g(x), is connected to a single value of x.
(h ∘ g)(x) can also be expressed as h[g(x)] , which signifies that the value of x=g(x) will be replaced in the function h, is referred to as a composite function.
A composite function is produced by combining two existing functions to produce a third, distinct function.
In h of g of x, the output of one function becomes the input of another.
Given functions are:
f(x)=4 x and g(x)=1/2x+7
Therefore (f ∘ g)(x)=f[g(x)]
=f(1/2x+7)
=4×(1/2x+7)
=2x+28
Therefore the value of the function operation (f⁰ g)(x) is 2x+28
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Type the correct answer in the box. Use numerals instead of words. Use / for the fraction bar.
A cooler contains 14 bottles of water and 10 bottles of lemonade.
Colleen randomly selects 2 bottles from the cooler without replacement.
The probability, as a fraction in simplest terms, that Colleen selected a bottle of water and then a bottle of lemonade is
The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is 35/138
What is probability and multiplication rule of probability?Probability is the measure of that how likely is an event can occur.
Probability of an event = Favorable outcomes of the event / total outcomes
Multiplication rule of probability states that probability of two events happening at the same time = (probability of one event )*(probability of another event )
Given that A cooler contains 14 bottles of water and 10 bottles of lemonade. Colleen randomly selects 2 bottles from the cooler
Total bottle = 14 +10 = 24
Let E be the event that Colleen selects a bottle of water first
Probability of E = 14/24
Let F be an event that Colleen selects bottle of lemonade when at the same time a bottle of lemonade is already taken out
Probability of F = 10/23
Therefore , The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is
= Probability of E * Probability of F = (14/24)*(10/23) =35/138.
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Please help correct answers only
Answer: 110%
Step-by-step explanation:
B is the midpoint of AB. If the coordinates of B are (11,20) and A are (3,8) what are the coordinates of C?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +3}{2}~~~ ,~~~ \cfrac{ y +8}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(11~~,~~20)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +3}{2}=11\implies x+3=22\implies \boxed{x=19} \\\\\\ \cfrac{ y +8}{2}=20\implies y+8=40\implies \boxed{y=32}[/tex]
What is the sum of the 3rd square number and the 3rd cube number?
Answer:
36
Step-by-step explanation:
[tex]3^{2}[/tex] = 9 (3x3)
[tex]3^{3}[/tex] = 27 (3x3x3)
9 + 27 = 36
11 People fit comfortably in a 6 feet by 6 feet area. Use this value to estimate the size of a crowd that is 18 feet by 30 feet