ANSWER
5x
EXPLANATION
We want to find the Greatest Common Factor, GCF, of the expression given:
[tex]45x^2\text{ + 10x}[/tex]To do this, we have to factor out the terms that are common between the two terms in the expression.
We have:
[tex]5x(9x\text{ + 2)}[/tex]As we can see, 5x is the greatest factor that is common to the two terms.
Therefore, the Greatest Common Factor is 5x.
What are the roots of the polynomial equation?x2−14x−32=0Enter your answers in the boxes.x1= x2=
Answer:
[tex]\begin{gathered} x_1\text{ = -2} \\ x_2=\text{ 16} \end{gathered}[/tex]Explanation:
Here, we want to get the roots of the given polynomial
We can have the expression re-written as follows:
[tex]\begin{gathered} x^2-16x+2x-32\text{ = 0} \\ x(x-16)+2(x-16)\text{ = 0} \\ (x+2)(x-16)\text{ = 0} \\ x\text{ + 2 = 0, x = -2} \\ x-16\text{ = 0, x = 16} \end{gathered}[/tex]4. Which expression is equivalent to 9-^2•9^-35. The expression 2^3•4^26. Are (10^-3)^2 and (10^-2)3(NUMBER 4 & 5 & 6)
Answer
Question 4
Option A is correct.
9⁻⁵
Question 5
Option C is correct.
2⁷
Question 6
Option B is correct.
Yes, both expressions are equal to 10⁻⁶
Question 7
3⁰ + 3⁻² = 1 (1/9) = (10/9)
Explanation
To answer these questions, we will use the laws of indices.
- When a variable carries a power and is raised to an extra power, the answer is the variable carrying the product of these two powers.
- When a variable is raised to the power of a negative number, this is the same as 1 over that variable raised to the positive value of that power
- When the same variable, carrying different powers are multiplied with each other, then, the result is that same variable raised to the power of the sum of the two powers from before multiplication.
- When any number or variable is raised to the power of 0, the answer is 1.
Question 4
[tex]9^{-2}.9^{-3}=9^{-2}\times9^{-3}=9^{-2+(-3)}=9^{-2-3}=9^{-5}[/tex]Question 5
[tex]\begin{gathered} 2^3.4^2 \\ \text{But} \\ 4^2=(2^2)^2=2^{2\times2}=2^4 \\ 2^3.4^2=2^3\times2^4=2^{3+4}=2^7 \end{gathered}[/tex]Question 6
To know the answer to this, we will solve the two expressions
[tex]\begin{gathered} (10^{-3})^2=10^{-3\times2}=10^{-6} \\ (10^{-2})^3=10^{-2\times3}=10^{-6} \end{gathered}[/tex]We can see that both expressions are equal to 10⁻⁶
Question 7
3⁰ + 3⁻²
3⁰ = 1
3⁻² = (1/3²) = (1/9)
3⁰ + 3⁻² = 1 + (1/9) = 1 (1/9) = (10/9)
Hope this Helps!!!
Find the GCF of 6 and 20
The factor of 6 = 3,2,6,1
and factor of 20 = 2,5,10,4, 1
GCF : The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
2 is the largest common factor of 6 and 20
Answer : 2
I’m not understanding the problem it says the numerator of the exponent is ?
Given:
Expression is
[tex]\sqrt[7]{y^4}[/tex]Required:
The numerator of the exponent.
Explanation:
We will use exponent formulas
[tex]\sqrt[b]{x^a}=x^{\frac{a}{b}}[/tex]Now,
[tex]\sqrt[7]{y^4}=y^{\frac{4}{7}}[/tex]Answer:
Hence, numerator of the exponent is 4.
I'll send the question
Answer
Option A is correct.
1 is the only option provided that satisfies the given inequality.
Explanation
We are asked to pick the right option that satisfies the given inequality.
To do this, we will just solve the given inequality equation
8x + 2 < 18
Subtract 2 from both sides
8x + 2 < 18
8x + 2 - 2 < 18 - 2
8x < 16
Divide both sides by 8
(8x/8) < (16/8)
x < 2
So, the solution of this will be the numbers less than 2.
Of the options, we can see that only 1 is less than 2 and that is the answer for this question.
Hope this Helps!!!
Determine whether the lines are parallel, perpendicular, intersect, or coincide.y=2x+5y=2x-1
Answer:
Parallel.
Explanation:
Given the lines:
[tex]\begin{gathered} y=2x+5 \\ y=2x-1 \end{gathered}[/tex]Comparing with the slope-intercept form of a line: y=mx+b
[tex]\begin{gathered} \text{Slope of y=2x+5 is 2} \\ \text{Slope of y=2x-1 is 2} \end{gathered}[/tex]Since the slopes of the two lines are the same, they are parallel.
order the steps involved in using common denominators to order a list of fractions. Use the least common multiple to write equivalent fractions with common denominators.order the fractions by ordering the numerators.use the list of multiples to find the least common multiple list the multiples of all the denominators in the listrewrite the list using the original fractions
Order the steps involved in using common denominators to order a list of fractions.
Step 1. Find the least common denominators. Given a set of fractions with unlike denominators, find the least common denominators shared by the fractions.
[tex]\begin{gathered} E\mathrm{}g\text{ }\frac{1}{3}\text{ + }\frac{1}{4} \\ \text{The least common denominator will be 3 x 4} \\ =\text{ 12} \\ \text{Hence, the least common denominator is 12} \end{gathered}[/tex]Step 2. Determine the equivalent fractions sharing the lowest common Denominators.
Assuming the pattern continues, what is the recursive formula for f (n) for the sequence 5 comma 3 comma nine fifths comma twenty seven twenty fifths and continues question mark
Given:-
[tex]5,3,\frac{9}{5},\frac{27}{25},\ldots[/tex]To find:-
Which function suits the sequence.
Considor the function,
[tex]f(n)=f(n-1)(\frac{3}{5}),f(1)=5[/tex]When n = 2. we get,
[tex]\begin{gathered} f(2)=f(2-1)\times\frac{3}{5} \\ f(2)=f(1)\times\frac{3}{5} \\ f(2)=5\times\frac{3}{5} \\ f(2)=3 \end{gathered}[/tex]So the second term is 3.
When n = 3. we get,
[tex]\begin{gathered} f(3)=f(3-1)\times\frac{3}{5} \\ f(3)=f(2)\times\frac{3}{5} \\ f(3)=3\times\frac{3}{5} \\ f(3)=\frac{9}{5} \end{gathered}[/tex]So the third term is 9/5.
When n = 4. we get,
[tex]\begin{gathered} f(4)=f(4-1)\times\frac{3}{5} \\ f(4)=f(3)\times\frac{3}{5} \\ f(4)=\frac{9}{5}\times\frac{3}{5} \\ f(4)=\frac{27}{25} \end{gathered}[/tex]So the fourth term is 27/25.
So this is the function which suits for the given sequence.
Preservatives such as salt help keep food fresh. Imaan made 18 loaves of bread using the same recipe and baking method. In nine of them, she used no salt. In the other nine, she used salt. After the loaves were baked, she placed each of the loaves in a plastic bag and left them close together on the counter in her kitchen. Each day she looked at them to see if any mold had started to grow.What is the independent variableandDependant variableWhat are the Constants
independent variable: the salt
dependent variable: the mold
constants: the same methos to baked bread
Two sides of triangle measures 15 inches and 18 inches which of these is not apossible length for third side of the triangle
To determine the possible lenghts of the thir
An accident investigator measured the skid marks of one of the vehicles involved in an accident. Thelength of the skid marks was 250 feet. Use the formula s=1(24d) (?"s equals square root of 24*d") tofind the speed of the vehicle before the brakes were applied. Round your answer to the nearesttenth. The units are mi/hr
Given the equation:
[tex]s=\sqrt[]{24d}[/tex]Where d is the distance and (s) is the speed
We will find the value of (s) when d = 250 feet
So, substitute with d = 250, and solve for (s)
[tex]s=\sqrt[]{24\cdot250}=\sqrt[]{6000}\approx77.459667[/tex]Rounding to the nearest tenth
so, the answer will be:
Speed = s = 77.5 mi/hr
Suppose that an individual has a body fat percentage of 19.7% and weighs 167 pounds. How many pounds of her weight is made up of fat? Round your answerto the nearest tenth
Answer:
32.9 pounds of her weight is made up of fat.
Step-by-step explanation:
This question can be solved using a rule of three.
Her weight is of 167 pounds, which is 100% = 1. How much is 19.7% = 0.197?
167 pounds - 1
x pounds - 0.197
Applying cross multiplication
x = 167*0.197 = 32.9
32.9 pounds of her weight is made up of fat.
Find the Measure of an interior angle of regular hexagon (6 sides polygon).X=Hunt sum=(n-2)180
it is known that formula for the sum of the interior angles of a polygon is
sum = (n - 2) 180 (given )
here n is the number of side of a polygon
here we have 6 sides in a regular hexagon
so put n = 6
sum = (6 - 2) x 180
sum = 4 x 180 = 720 degrees.
the sum of all 6 interior angles is 720 degrees,
as all the interior angles are equal in a regular hexagon
so the measure of interior angle (x) is
x = 720/6
x = 120 degrees
so each interior angle is 120 degrees.
The human body needs about 50 grams of protein daily. A hamburger contains about 20 grams of protein. What percent of the daily needs is the protein in the hamburger?
To answer this question, we can proceed as follows:
1. We have that the total of protein the human body needs daily is 50 grams.
2. A hamburger contains about 20 grams of protein.
Then, to find the asked percent, we can proceed as follows:
[tex]\begin{gathered} \frac{20}{50}\cdot100\%=\frac{2}{5}\cdot100\%=\frac{2\cdot100\%}{5}=2\cdot\frac{100\%}{5}=2\cdot20\%=40\% \\ \end{gathered}[/tex]Therefore, the hamburger has 40% of the protein we need daily.
Logan deposite $5,250.00 in a cd that pays 3.75% simple interest he keeps the money in the account for 5 years but doesn't make amy deposits or withdrawal. How much interst will be earn after 5 years?
To find the interest after 5 years
We will use the formula
[tex]S.I=\frac{PRT}{100}[/tex]WHERE
P is the principal
R is the rate
T is the time
S. I is the simple interest
From the question
P= $5,250.00
R= 3.75
T= 5
Substitute the values into the formula:
S.I =
[tex]SI\text{ =}\frac{5250\times3.75\times5}{100}[/tex][tex]=\frac{98437.5}{100}[/tex]=$984.375
Hence;
The interest earned after 5 years is $984.375
Evaluate -9x-13 when x=6Just checking my answer, no need for deep explanation
Given
[tex]-9x-13[/tex]Set x=6 and simplify, as shown below
[tex]\begin{gathered} x=6 \\ \Rightarrow-9x-13=-9*6-13=-54-13=-67 \end{gathered}[/tex]Therefore, the answer is -67the definition of an addictive identity is A. add zero to the number you want to keep the same. B. 38 + 0 = 38. or C.add one to the number you want to keep the same
In mathematics, the additive identity of a set that is equipped with the operation of addition is an element that, when added to any element x in the set, yields x.
The "Additive Identity" is 0 because adding 0 to a number does not change it
Option A is correct
Use slope-intercept form to write the equation of a linethat has a slope of -3 and passes through the point(1, -5).Use the drop-down menus to select the proper valuefor each variable that is substituted into the slope-intercept equation.X222IntroDone
,We have the next information
slope=-3
point=(1,-5)=
First, we will use the point-slope form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a point where the line passes through
(x1,y1)=(1, -5)
m=-3
we substitute the values
[tex]y+5=-3(x-1)[/tex]then in order to obtain the slope-intercept form we isolate the y
[tex]y=-3x+3-5[/tex]the slope-intercept form is
[tex]y=-3x-2[/tex]the equation of the line in slope-intercept form is y=-3x-2
Use the chart for the question.4. CJ reads 12 pages in one book and 8 pages in another.How long does it take him to read all of the pages? Explain.
First find the total number of pages read
12 +8 = 20 pages
We can use ratios to determine how long it will take
6 pages 20 pages
------------ = -----------
21 minutes x minutes
Using cross products
6 * x = 21 * 20
6x = 420
Divide each side by 6
6x/6 = 420/6
x =70
It will take 70 minutes.
What is the domain of the function?Type the domain using interval notation example : (#,#]
The domain of the function is described as a set of values of x where the function exists. Based on the plot given, the permissible values of x start at -1 and the function will continue to exist for any values of x greater than or equal to -1 until infinity. Hence, the domain of this function using interval notation is [-1, ∞). Note that -1 is an acceptable value of x based on the plot since the point where the plot starts (at x = -1) is shaded black, hence, we use a bracket sign at the left-hand side of the notation.
a jar contains 450 solid-colored marbles, each of which is either white, red ,blue , yellow or green. The results of a random selection of 30 of the 450 marbles are shown in the table above. Based on this one sample , which of the following is the best estimate of the number of red marbles in the jar.
Our problem involves probability. One thing that we must take note of probabilities is that the higher the number of a certain thing is, the higher probability of it happening. For example, in a lottery the higher the number of of tickets that you will buy the higher the chances of you winning the lottery.
Now let us talk about the basic formula of the probability of an event happening. The probabilty of an event happening is just the ratio of the number of a certain outcome to the total number of outcomes. Presenting it as an equation we get:
[tex]P(A)=\frac{\text{Number of a certain Outcome}}{\text{Total number of Outcome}}[/tex]what is the minimum amount of money that Reggie needs to make on friday to average $160 per day?
Let y represent the minimum amount of money Reggie needs to make to average $160 per day
The average is given as
[tex]\frac{145\text{ + 210+50+205+y}}{5}\text{ = 160}[/tex][tex]\begin{gathered} \frac{610+y}{5}\text{ = 160} \\ \\ 610+y=\text{ 5(160)} \\ 610+y=800 \\ y=\text{ 800-610} \\ y=190 \end{gathered}[/tex]The correct answer is $190
the question is long so ill send a pic of it.
we have that
the linear equation is
y=22.8x+105
Answer please to this question
Answer:
A
Step-by-step explanation:
this is the best way since domain is x
Which choice best represents the solution to the equation below?6(x - 5) = 72A: x = 17B: x = 12C: x = 72D: x = 7
The solution to the equation is:
[tex]\begin{gathered} 6\mleft(x-5\mright)=72 \\ (x-5)=\frac{72}{6} \\ x-5=12 \\ x=12+5 \\ x=17 \end{gathered}[/tex]The solution is x=17.
8) Order the numbers from greatest to least"10 points-17. TheTT- 2✓n-√7.-2, zTI V822-V7,-2Option 1Option 2TI V8-17,-2.22π V82.2.-2, – 7OOption 3Option 4
You have the values.
First I'll express the values as decimal numbers
[tex]-\sqrt{7}\cong-2.64[/tex][tex]\frac{\sqrt{8}}{2}\cong1.41[/tex][tex]\frac{\pi}{2}\cong\frac{3.14}{2}\cong1.57[/tex][tex]-2[/tex]The negative square root of 7 is less than -2.
And the square root of 8 divided two is less than pi divided by two.
The correct order is:
[tex]-\sqrt{7},-2,\frac{\sqrt{8}}{2},\frac{\pi}{2}[/tex]Option 1
Can someone help me please im stuck on this problem.... 1/3÷13/9=
The given problem can be solved as,
[tex]\frac{1}{3}\times\frac{9}{13}=\frac{3}{13}[/tex]Thus, the required solution is 3/13.
If a triangle ABC is at: A = ( 3, 6 ) B = ( 1, 7 ) C = ( - 2, - 4 ) and if it is translated right 6 and down 3, find the new point B'.
Solution: B': (7,4)
As we have a triangle, we move each point according to the statement of exercise. We have B = (1,7). As we have to move right 6, that would be increasing X value. So, we have:
X initial: 1. We move right 6, X final= 1+6; X final=7
We down 3, so that would be decreasing Y value.
Y initial= 7. We move down 3, Y final=7-3; Y final=4
According to that, the new point B' would be= (7,4)
ASSIGNMENTSCOURSESAssignment 5. Conditional ProbabilityAct 1 of 3SECTION 2014Two number cubes are rolled for two separate events:Event A is the event that the sum of numbers on both cubes is less than 10.Event B is the event that the sum of numbers on both cubes is a multiple of 3Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blepoza10NEXT QUESTIONASK FOR HELPTURNI
The total number for the sample space for two cubes rolled is 36
1,1; 1,2....; 1,6
2,1; 2,2..; 2,6
. .
. .
6,1; 6,2...; 6,6
Event A (less than 10; 1 - 9)
(1,1); (1,2); (1,3); (1,4); (1,5); (1,6)
(2,1); (2,2); (2,3); (2,4); (2,5); (2,6)
(3,1); (3,2); (3,3); (3,4); (3,5); (3,6)
(4,1); (4,2); (4,3); (4,4); (4,5)
(5,1); (5,2); (5,3); (5,4)
(6,1); (6,2); (6,3)
The sample space has 30 elements
[tex]Pr\text{ (<10) = }\frac{30}{36}\text{ = }\frac{5}{6}[/tex]P (A) = 0.83
Event B (sum of numbers on both cubes is a multiple of 3)
Event A already happened, we have Event B as:
(1,2); (1,5)
(2,1); (2,4)
(3,3); (3,6)
(4,2); (4,5)
(5,1); (5,4)
(6,3)
The sample space has 11 elements
[tex]Pr\text{ (multiple of 3) = }\frac{11}{30}\text{ = 0.367}[/tex]P (B|A) = 0.37
In many epidemics, the cumulative number of cases grows exponentially, at least over a limited time. A recent example is the spread of the Influenza A (HIN1) virus, commonly called thwhich affected Mexico and the United States especially. On April 24, 2009, there were seven cumulative cases of swine flu in the United States reported to the World Health Organization.next two weeks, the cumulative number of cases in theUnited States increased by about 40% each day. If this growth rate had continued, what would have been the cumulative numberthe United States reported 20 days after April 24? (Round your answer to the nearest whole number.)cases
If the growth is exponential, it follows the formula:
P=Po*