The expression 8(x+4) is a product between 8 and (x+4), which is a number (8) and a sum.
Then, it correspond to Option B: The product of a number and a sum.
Use the imaginary number I to rewrite the expression below as a complex number simplify all radicals
Here, we want to use the imaginary number to rewrite the given expression as a complex number
Mathematically, the complex number can be written as;
[tex]i\text{ = }\sqrt[]{-1}[/tex]Thus, we have;
[tex]\begin{gathered} -\sqrt[]{-4\text{ }}\text{ = -1 }\times\text{ }\sqrt[]{-4} \\ \\ =\text{ -1 }\times\text{ }\sqrt[]{-1\text{ }}\text{ }\times\text{ }\sqrt[]{4} \\ \\ =\text{ -1 }\times\text{ i }\times\text{ }\sqrt[]{4} \\ =\text{ -1 }\times\text{ i }\times\text{ }\pm2 \\ \\ =\text{ -2i or 2i} \end{gathered}[/tex]Simplify
4b² x 2b³/8b
Answer:
b^4
Step-by-step explanation:
4b^2 (2b^3)/8b = b^4
It's easy and complicated
find the zeros of the function.f(x) = 3x^2 + 6
f(x) = 3x^2 + 6
0 = 3x^2 + 6 (Replacing f(x) by 0)
-6 = 3x^2 (Subtracting 6 from both sides of the equation)
-6/3 = x^2 (Dividing by 3 on both sides of the equation)
-2 = x^2 (Dividing)
[tex]\begin{gathered} \sqrt[]{-2}\text{ = x (Taking the square root on both sides of the equation)} \\ \sqrt[]{-1}\text{ }\cdot\sqrt[]{2}\text{= x (Separating terms)} \\ \sqrt[]{2}i=x\text{ (Changing }\sqrt[]{-1}\text{ for i)} \end{gathered}[/tex]There are no real solutions. The complex solutions are:
[tex]\pm\sqrt[]{2}i[/tex]-2/2 in simplest form is -1, right?
Answer:
Yes
Step-by-step explanation:
Yes, dividing a negative number by a positive number will equate to another negative number.
Applying this logic, -2 divide by 2 is simply -1
Evaluatesin^-1 (sin3pi/4)Show your reasoning.
Given the expression:
[tex]\sin ^{-1}(\sin \frac{3\pi}{4})[/tex]The exact value of:
[tex]\sin (\frac{3\pi}{4})=\frac{1}{\sqrt[]{2}}[/tex]Then:
[tex]\sin ^{-1}(\sin \frac{3\pi}{4})=\sin ^{-1}(\frac{1}{\sqrt[]{2}})[/tex]Evaluating, we have:
[tex]\frac{\pi}{4}[/tex]Evaluate x−1/3 when x=−2/3.
Given that x=-2/3
[tex]x-\frac{1}{3}=\frac{-2}{3}-\frac{1}{3}[/tex]Then,
[tex]\begin{gathered} x-\frac{1}{3}=\frac{-2-1}{3} \\ x-\frac{1}{3}=\frac{-3}{3} \\ x-\frac{1}{3}=\frac{-1\times3}{3\times1} \\ x-\frac{1}{3}=\frac{-1}{1} \\ x-\frac{1}{3}=-1 \end{gathered}[/tex]Therefore the value for x-1/3 is -1.
Give the name (monomial, binomial,trinomial, etc.) and the degree of thepolynomial.12x4+ 3x - 1Name? [?]Degree? [ ]Enter
The solution:
Given:
Required:
Give the name of the given expression, and state the degree.
The given expression is a Polynomial (since it has 3 terms)
The degree is 4 because it has 4 as its highest power of the unknown)
Therefore, the correct answers are:
Name = polynomial
Degree = 4
Arie's pet shop is selling geckos at 12 and a half percent off! if geckos were originally $20 each, what is the sale price?
DIscount = 121/2 % 0ff
[tex]\begin{gathered} \text{Sales price = 12}\frac{1}{2}\text{ }\times\text{ 20} \\ \text{ =}\frac{\frac{25}{2}}{100}\text{ }\times20\text{ } \\ \text{ } \\ \text{ =}\frac{25}{200}\text{ }\times20\text{ = }\frac{500}{200}\text{ = \$2.5} \end{gathered}[/tex]Graph A Graph B 5 2 X X 3 2 3 4 5 Which table and graph represent the equation y = 2x? O A. Table B and graph A O B. Table A and graph B O C. Table B and graph B O D. Table A and graph A
Given:
The equation is y = 2x.
The objective is to find which of the table values match the with a given graphs.
The general equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope and b represents the y intercept.
Consider the graph A and find the slope of the equation.
Take two coordinates from the graph as,
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,2) \end{gathered}[/tex]The formula to find the slope of the equation is,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{1-0} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]Fro mthe graph A, the value of y intercept is 0.
Substitute the obtained values in the equation of straight line.
[tex]\begin{gathered} y=2x+0 \\ y=2x \end{gathered}[/tex]Thus, the given equation, coordinates of the table A matches with the graph A.
Hence, option (D) is the correct ant
Simple probabilityLeslie is a biologist. She is going to randomly select one animal from her lab to study. There are 5 salamanders, 3 crayfish, and 12 minnows in her lab.If necessary, round your answer to 2 decimal places.
Given:
number of salamanders = 5
number of crayfish = 3
number of minnows = 12
To find:
the probability of salamanders
To determine the P(salamanders), we will divide the number of salamanders by total animals
Total animals = 5 + 3 + 12
Total animals = 20
[tex]\begin{gathered} P(salamanders)\text{ = }\frac{5}{20} \\ \\ P(salamanders)\text{ = }\frac{1}{4} \end{gathered}[/tex]In decimal place:
[tex]P(salamanders)\text{ = 0.25 \lparen2 dp\rparen}[/tex]Find the range of allowable values based on the given information. Round to the nearest tenth. 24; can vary by 3.5%
Round to nearest tenth is 0.9 in percentage .
What does the % mean?
A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Per 100 is what the word percent means. The letter "%" stands for it.By dividing the value by the sum of the values, and then multiplying the outcome by 100, one can get the percentage. The formula for calculating percentage is (value/total value)100%.Percent is derived from the Latin word per centum, which means "by the hundred."24×3.5% = 0.84
so round to nearest tenth is 0.9.
Learn more about percentage
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6.Which of the following represents a graph with a rate of change of ?
Solution:
The rate of change of a graph is the same as the slope of the graph.
The graph that has a rate of change of 1/2 is the graph with a slope of 1/2.
To calculate the slope of a graph,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Considering two clear points from graph C, picking the points (2,-1) and (4,0)
[tex]\begin{gathered} \text{where} \\ x_1=2 \\ y_1=-1 \\ x_2=4 \\ y_2=0 \\ \\ \text{Substituting these values in the formula to get slope,} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-(-1)}{4-2} \\ m=\frac{0+1}{4-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Therefore, the graph that represents a rate of change of 1/2 is the graph of option C.
what is the coordinates of midpoint of EF write your answer as an integer or a decimal or mixed number in simplest form
To calculate the midpoint between 2 points we must add both points and divide them by 2
[tex]\frac{P_1+P_2}{2}=P_M[/tex][tex]\begin{gathered} P_1=0 \\ P_2=-4 \end{gathered}[/tex][tex]\begin{gathered} P_M=\frac{-4+0}{2} \\ P_M=-2 \end{gathered}[/tex]I still don't understand square root Calculate √2654
Given:
[tex]\sqrt[]{2654}[/tex]The square root of a number is the inverse operation of the square operation of a number.
The square root of a number is the number that when multiplied by itself gives the original number as the result.
To find the square root of 2654, we have:
[tex]\begin{gathered} \sqrt[]{2654} \\ \\ =51.5 \end{gathered}[/tex]The number given, 2654 is not a perfect square.
A square root of a perfect square is a non decimal number.
Apply the formula:
[tex]\begin{gathered} \sqrt[]{x}=\sqrt[]{y}+\frac{x-y}{2\ast\sqrt[]{y}} \\ \\ \text{Where y is the closest p}\operatorname{erf}ect\text{ square} \end{gathered}[/tex]y is the closest perfect square.
[tex]\begin{gathered} \sqrt[]{2654}=\sqrt[]{2601}+\frac{2654-2601}{2\ast\sqrt[]{2601}} \\ \\ \sqrt[]{2654}=51+\frac{2654-2601}{2\ast51} \\ \\ \sqrt[]{2654}=51+\frac{53}{102} \\ \\ \sqrt[]{2654}=51+0.51=51.51 \end{gathered}[/tex]If the number is a perfect square, the square root of the number would be a non decimal number.
ANSWER:
51.5
how much interest earned on 124 ar 4% for one year
The principal amount is 124
The interest rate is 4% [in decimal, 4% is 4/100 = 0.04]
To get the interest amount, we mutiply the principal with the interest rate (in decimal).
The answer is:
[tex]124\cdot0.04=4.96[/tex]Instructions: Match the linear equation with its graph. Label the slope and -intercept.
Given the following question:
[tex]y=-3x+1[/tex]Graph 3 is the same as y = -3x + 1
For part B:
[tex]\begin{gathered} y=-3x+1 \\ y=mx+b \\ m=slope \\ b=y-intercept \\ m=-3 \\ b=1 \end{gathered}[/tex]can someone please help me solve the "evaluate Ramon's equation" with the given from the above .so, based on that information. the equation that would correctly show the relationship between the number of seconds and the number of minutes would be 60 × s = m?
In the first table, we can see that 1 minute is equal to 60 seconds, thats why 2 minutes has 120 seconds and 3 minutes has 180 seconds.
Therefore, the second table must be
If we suppose that Ramon is correct, then the number of seconds would be less than the number of minutes. However, we saw that its no correct, then Ramon equation will not let him the correct number of minutes.
The correct equation must be
[tex]60xm(number\text{ of minutes = s (number of seconds)}[/tex]If ƒ = {(5, 1), (6, 2), (7, 3), (8, 1), (9, 7)}, then the range of ƒ is:
ANSWER
[tex]R:\lbrace1,2,3,7\rbrace[/tex]EXPLANATION
We want to identify the range of the given function.
The range of a function is the set of all y values of the function. In other words, it is the set of all output values of the function.
The given points are in the form:
[tex]f=(x,y)[/tex]Therefore, the range of the function is:
[tex]R:\lbrace1,2,3,7\rbrace[/tex]That is the answer.
Translate figure A 8 units to the left to form figure A'. Then reflect figure A' across the x-axis to form figure A". Draw figures A' and A”. Is figure A congruent to figure A"? How do you know?
Initial points
(-7, 2) (-7, 4) (-4, 2) (-4, 4) (-2, 7)
translate 8 units to the left
(-6, -7) (-4, -7) (-6, -4) (-4, -4) (-1, -2)
reflexion
Reflexion
27.(08.04 MC)The volume of a fish tank is 50 cubic feet. If the density is 0.5fish/feet cubed, how many fish are in the tank?
ANSWER:
25 fish
STEP-BY-STEP EXPLANATION:
We have been given that the volume of a fish tank is 50 ft^3 and the density is 0.5 fish/ft^3. To find the number of fish in the tank, we need to multiply the volume of the tank by the density. Just like this:
[tex]\begin{gathered} n=50ft^3\cdot0.5\frac{fish}{ft^3} \\ n=25\text{ fish} \end{gathered}[/tex]Therefore, there are 25 fish in the tank.
In ASTU, the measure of ZU=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measureof ZT to the nearest tenth of a degree.
In ASTU, the measure of ZU=90°, US = 5.9 feet, and TU = 2.6 feet. Find the measure
of ZT to the nearest tenth of a degree.
step 1
In the right triangle STU
we have
tan(T)=SU/TU -------> by opposite side divided by the adjacent side
substitute given values
tan(T)=5.9/2.6
using a calculator
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.
First we have to find the values in which each factor equals zero.
In the first factor is going to be 5
In the second factor is going to be 7
Then we divide the number line by three parts
First part: Numbers less than 5
Second part: Numbers between 5 and 7
Third part: Numbers greater than 7
We choose any number belonging to each interval
First part: zero (0) because is less than 5
Second part: 6 because is a number between 5 and 7
Third part: 8 because it is a number greater than 7
Then we replace the numbers in the factors and operate
First part: (0-5)*(0-7) = (-5)*(-7)= 35 ( positive)
second part: (6-5)*(6-7) = (1)*(-1)= -1 ( negative)
third part: (8-5)*(8-7) = (3)*(1)= 3 ( positive)
Since we are searching for numbers that replaced in the equation give us negative results the intervals for the inequality must be
[5,7] which is represented in option C
The radius of a circle is 4 feet. What is the area of a sector bounded by a 180° arc?Give the exact answer in simplest form. ____ square feet.
The area of asemicircle is:
[tex]A=\frac{\pi\cdot r^2}{2}[/tex][tex]A=\frac{\pi\cdot4^2}{2}=\frac{\pi\cdot16}{2}=\pi\cdot\frac{8}{1}=8\cdot\pi\text{ ft}^2[/tex]Therefore, the area of the semicircle in 8*pi ft^2
translate each Graph as specified below(a)the graph of y=(x)+4 is shown. Translate it to get the graph of y=f(x)+4(b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x-2).
Solution:
Given the graphs (a) and (b)
a) The function of graph (a) is
[tex]f(x)=-4\sqrt{x+3}+1[/tex]The graph of the function is shown below
Translating it to get the graph of
[tex]y=f(x)+4[/tex]The translated function becomes
[tex]\begin{gathered} y=f(x)+4 \\ y=(-4\sqrt{x+3}+1)+4 \\ y=-4\sqrt{x+3}+1+4 \\ y=-4\sqrt{x+3}+5 \end{gathered}[/tex]The translated graph is
b) The function of graph (a) is
[tex]g(x)=-|x|[/tex]The graph of the function is shown below
Translating it to get the graph of
[tex]y=g(x-2)[/tex]The translated function becomes
[tex]\begin{gathered} y=g(x-2) \\ y=-|x-2| \end{gathered}[/tex]The translated graph is
what is the following is a solution for x / 4 >10
Given the inequality;
[tex]\frac{x}{4}>10[/tex]Multiplying both sides by 4, we have;
[tex]\begin{gathered} \frac{x}{4}\times4=10\times4 \\ x>40 \end{gathered}[/tex]so, the range of solutions of x are numbers that are greater than 40 (40 is not included).
From the options the only possible solution is;
[tex]x=47[/tex]Because 47 is greater t
Translate: "ten more than the product of 8 and a number is less than 26"in numbers
ten more than the product of 8 and a number is less than 26 :
Let the number is x :
product of 8 and a number = 8x
ten more than the product of 8 and a number = 10 more than 8x
ten more than the product of 8 and a number = 10 + 8x
ten more than the product of 8 and a number is less than 26
ten more than the product of 8 and a number < 26
10 + 8x < 26
Answer : 8x + 10 < 26
Consider parallelogram ABCD below.Use the information given in the figure to find x, m ZADB, and m ZA.350Х2x160M ZADB = 0m 2A =1130D© 2021 McGraw-Hill Education.Search for anythingoBI
The diagram is a parallelogram.
from the properties of a parallelogram, opposide are equal. Hence
|AD|=|BC|,
Where |AD|=2x and |BC|=6
[tex]\begin{gathered} 2x=6 \\ \text{dividing both side by 2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]which of the following expression has the same value select all that apply
A tortilla measures 8 inches in diameter, shown below. What is the tortilla'sarea?8 inches0 0 40x square inches20 0 641 square inches0 0 41 square inchesc) O 321 square inches0 0 161 square inches
A tortilla has a circular shape. The area of the circle can be given by the following expression:
[tex]A=r^2\cdot\pi[/tex]We were given the diameter of the tortilla, the radius is half the diameter, therefore:
[tex]undefined[/tex]If x and 2x-15 represent the measure of the acute angles of a right triangle, find the value of x.
In a right triangle, the measure of acute angles is represented by x and 2x -15 then the value of x is equal to 35.
As given in the question,
In a right triangle,
One of the angle is of measure 90°.
Other two angles are acute angles.
Measure of two acute angles are given as x and 2x -15.
Sum of the three angles in a triangle is 180°.
x + 2x -15 + 90° = 180°
⇒3x +75° = 180°
⇒ 3x = 105°
⇒ x = 35°
Therefore, in a right triangle, the measure of acute angles is represented by x and 2x -15 then the value of x is equal to 35.
Learn more about right triangle here
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