Answer:
10.736
Step-by-step explanation:
11 1/9 - 3/8 =10/53/72
= 10.736
Please show me how to factorize this
[tex]5x {}^{3} - 9x {}^{2} - 17x - 3[/tex]
Answer:
(x - 3) (5x + 1)(x + 1).
Step-by-step explanation:
5x^3 - 9x^2 - 17x - 3
As the first coefficient is 5 and the last -3, so product is -15, we could try if (x-3) is a factor:
By the Factor Theorem, if x-3 is a factor then f(3) = 0.
f(3) = 5(3)^3 - 9(3)^2 - 17(3) - 3
= 135 - 81 - 51 - 3 = 0
So, x - 3 is a factor.
Now divide:
x - 3)5x^3 - 9x^2 - 17x - 3(5x^2 + 6x + 1 <------- Quotient
5x^3 - 15x^2
6x^2 - 17x
6x^2 - 18x
x - 3
x - 3
.......
Factoring 5x^2 + 6x + 1:
= (5x + 1)(x + 1)
So, the answer is:
(x - 3) (5x + 1)(x + 1).
Screenshot down below
The number of miles that is covered is 1458 miles.
What is the gas mileage?The term gas mileage refers to the distance that have been covered by the car using a given volume of gas. It is common that the unit that is used to measure the volume of the gas is the US gallon.
We have been told that;
420 miles could be covered by the use of 20 gallons
1 mile can be covered by the use of 1 mile * 20 gallons/ 420 miles
= 0.048 gallons
If 1 mile requires 0.048 gallons
x miles requires 70 gallons
x = 1 mile * 70 gallons/0.048 gallons
x = 1458 miles
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3. Find the equation of a line passing through (5,-6) parallel to : x + 3y = 8
The general slope intercept form is : y = m * x + b
Where m is the slope and b is y - intercept
Given the equation of the line : x + 3y = 8
Write the equation in slope intercept form to find the slope of the line
so, solve for y :
[tex]\begin{gathered} x+3y=8 \\ 3y=-x+8 \\ \\ y=-\frac{1}{3}x+\frac{8}{3} \end{gathered}[/tex]So, the slope of the given line = -1/3
The parallel lines have the same slope
so, the slope of the required line = -1/3
And the equation will be :
[tex]y=-\frac{1}{3}x+b[/tex]Find the value of b using the given point ( 5 , -6 )
When x = 5 , y = -6
[tex]\begin{gathered} -6=-\frac{1}{3}\cdot5+b \\ -6=-\frac{5}{3}+b \\ -6+\frac{5}{3}=b \\ \\ b=-\frac{13}{3} \end{gathered}[/tex]So, the equation of the line will be :
[tex]y=-\frac{1}{3}x-\frac{13}{3}[/tex]it can be written as : 3y = -x - 13
[tex]x+3y=-13[/tex]Each square on a grid represents 1 unit on each side. Match the numbers with the slopes of the lines.
The slope of the given lines are:
Graph 1 = 1/3
Graph 2 = -1/3
Graph 3 = 3
Graph 4 = -3
How to Find the Slope of a Line?To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:
Slope of a line (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Find the slope of Graph 1:
Using two points on the line, (0, 0) and (3, 1):
Slope of graph 1 (m) = (1 - 0)/(3 - 0)
Slope of graph 1 (m) = 1/3
Find the slope of Graph 2:
Using two points on the line, (0, 0) and (-3, 1):
Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3
Slope of graph 2 (m) = -1/3
Find the slope of Graph 3:
Using two points on the line, (0, 0) and (1, 3):
Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1
Slope of graph 3 (m) = 3
Find the slope of Graph 4:
Using two points on the line, (0, 0) and (-1, 3):
Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1
Slope of graph 4 (m) = -3
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What is the lowest common multiple of 19 & 9
Solution:
LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.
The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.
There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.
To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.
In this case, we get:
Then, the LCM would be:
[tex]3\text{ x 3 x 19 = }171[/tex]so that, the correct answer is:
[tex]171[/tex]Please help!! Ignore the X on A!
Answer:
AC= 3.2
Step-by-step explanation:
two trianglesare similar
so AC : BC = DF : EF
AC : 4 = 3:2.4
4×3.2 = AC×4
12.8=4×AC >>>> (÷4) both sides
3.2= AC
after two weeks, Akira and Taro biked a total 276 miles. after 3 weeks they had biked a total of 413 miles. how many miles did they ride in third week?
From the given question
There are given that the :
After two weeks, the total miles is 276 and after 3 weeks, the total miles are 413
Now,
The total miles did they ride in the third week is:
[tex]413-276=137[/tex]Hence, the total miles in the third week is 137.
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package
costs $265 and covers the entrance fee for guests, a private party room, and an activity
guide. Estelle upgraded her package to include a favor for each of her 8 guests, bringing the
total to $305.
Which equation can you use to find f, the cost of each favor?
265(f+ 8) = 305
265f + 8 = 305
How much did each favor cost?
Submit
8f +265 305
8(f+265): = 305
By using proportions, it is discovered that each favor costs $5.
Using the rule of three and proportions, this problem can be resolved.
The party's price is increased by $40 with the addition of 8 favors.
A proportion is an equation that sets two ratios at the same value.
How much does one favor cost?Using the rule of three and proportions, this problem can be resolved.
The party's price is increased by $40 with the addition of 8 favors.
The threes rule states:
$40 for 8 favors
$1 for 1 favor
Cross-multiplication application
8x=40
x= 40/8
x = 5
There is a $5 fee for each favor.
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).
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-20 greater than or equal to 5v
Write the inequality for the statement and solve for v
[tex]\begin{gathered} -20\ge5v \\ -\frac{20}{5}\ge v \\ -4\ge v \end{gathered}[/tex]It means that v is less than or equal to -4. The solution set for this inequality is:
[tex](-\infty,-4\rbrack[/tex]What is the equation in slope-intercept form of the line that passes through the point(4,-11) and is perpendicular to the line represented by y=4x-1?
Answer:
y = (-1/4)x - 10
Step-by-step explanation:
y = 4x - 1
y = -1/4x - 1
(4, -11),
(x₁, y₁)
y - y₁ = m(x - x₁)
y - (-11) = (-1/4)(x - 4)
y + 11 = (-1/4)x + 1
-11 -11
-------------------------------
y = (-1/4)x - 10
I hope this helps!
7. |4n+ 2|= 34 solve for “N”
By solving |4n+2|=34 solve for N we get 8 .
What is N factor?
The factorial of a non-negative integer n, denoted by n!, is the product of all positive of integers less than or equal to n. The factorial of n also equals to the product of n with the next smaller factorial: For example, These are value of 0! is 1, according to the convention for an empty of product.
Sol-|4n+2|=34
Split into two equations
4n+2 = 34 or 4n+2=-34
4n+2 =34
Rearrange variable to the left side of the equation
4n =34-2
Calculate the sum or difference
4n=32
Devide both side of the equation by the coefficient of variable
n=32/4
Cross out the common factor
n=8
When n=8
LHS = |4×8+2|=34
RHS =34
LHS =RHS
Thus 8 is valid.
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Write the equation for the vertical line and horizontal line that passes through each point. V(5, -2) AndT(10, -3)
Given
V(5, -2)
T(10, -3)
Procedure
For V:
The equation of the horizontal straight line corresponds to y = -2.
The equation of the vertical straight line corresponds to x = 5
For T:
The equation of the horizontal straight line corresponds to y = -3.
The equation of the vertical straight line corresponds to x = 10
which one of these options is the best definition of extrapolation? group of answer choices fitting a line to data that is non-linear using a given y-value and a linear regression equation to predict an x-value. using a linear regression equation and any x-value to predict any y-value. using an x-value far from observed x values to predict a y value
Answer: Extrapolation ,from the above can be defined as using a linear regression equation and any x- value to predict any y-value.
Step-by-step explanation:
Extrapolation regression makes use of estimated regression equation to predict a new value y for specific X values not in the range of the sampled data used to estimate our regression equation
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5. Eggs are packaged in cartons of 12.
Which of these numbers of eggs can be packaged
in full cartons? How do you know?
a) 96 b) 56 c) 60 d) 74
Answer: C) 60
Step-by-step explanation: If you keep adding 12 the only number that I get on the list is 60.
A model of a ship is made to a scale of 3:400
The surface area of the model is 7200 cm²
Calculate, in m², the surface area of the ship.
Answer:
Given:
Model : Ship = 3 : 400
The surface area of the model = 7200 cm²
To Find:
The surface area of the actual ship in m²
Let's start with the map scale given:
Model : Ship = 3 : 400
We start by adding in a unit. Usually, we choose the units associated with the model:
Model : Ship = 3 cm : 400 cm
Now, according to tot the question, we know that the actual ship is in m:
Model : Ship = 3 cm : 400 ÷ 100 m
Model : Ship = 3 cm : 4 m
The question asked for surface area, so the units have to be in squares:
Model : Ship = (3 cm)² : (4 m)
Model : Ship = 9 cm² : 16 m²
Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:
Model : Ship = 9 cm² : 16 m²
Model : Ship = 9÷9 cm² : 16÷9 m²
Model : Ship = 1 cm² : 16/9 m²
Finally, we can find the required units by multiplying both sides with the required units:
Model : Ship = 1 cm² : 16/9 m²
Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²
Model : Ship = 7200 cm² : 12800 m²
Answer: The surface area of the ship is 12800 m²
(by the way, this was copied from the same website)
hope this helps :)
Use the appropriate compound interest formula to compute the balance in the account after the stated period of time
$19,000 is invested for 2 years with an APR of 4% and daily compounding.
Compound interest exists as the interest you gain on interest. The balance in the account after 2 years is $42266.
What is meant by compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
'Compound interest' simply indicates earning interest on your savings, and also, eventually, on the interest that those savings earn.
The appropriate formula is
A = P(1 +r/n[tex])^{(nt)[/tex]
where P = 19,000, r = 0.4, n = 365, t = 2.
substitute the values in the above equation, we get
A = 19,000(1 +0.4/365[tex])^{(365 \times2)[/tex]
simplifying the above equation, we get
A = 42266.7592
The balance in the account after 2 years is $42266.
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You downloaded a video game to your computer. You have a 60-minute free block of time for the game. It
takes 5 minutes to set up the game and 7 minutes to play each level of the game. Write an inequality to
determine the number of levels you can play in 60 minutes. How many levels can you play for free? Write an Inequality
An inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Here, it is given that :
Time for setting up the game = 5 minutes
Time to play each level = 7 minutes
Let l represent the number of levels played.
So, Time to play l levels = 7l
So, b = 5+7l
Now we are required to Write an inequality to determine the number of levels you can play in 60 minutes.
So, the inequality becomes :
5 + 7l ≤60
Hence an inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60
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Express the function graphed on the axes below as a piecewise function.104-10-8-6-4-2246810-6
Step 1
Find the equation of both lines using
[tex]\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{y-y_1}{x-x_1}[/tex]Where,
[tex]\begin{gathered} y_1=-9 \\ y_2=\text{ -2} \\ x_1=\text{ -6} \\ x_2=1 \end{gathered}[/tex]Hence,
[tex]\frac{-2-(-9)}{1-(-6)}=\frac{y-(-9)}{x-(-6)}[/tex][tex]\begin{gathered} \frac{7}{7}=\frac{y+9}{x+6} \\ y+9\text{ = x+6} \\ y\text{ = x+6-9} \\ y\text{ = x-}3 \end{gathered}[/tex]For the second line we will have
[tex]\begin{gathered} \frac{-4-(-8)}{1-5}=\text{ }\frac{y-(-8)_{}}{x-5} \\ \frac{4}{-4}=\frac{y+8}{x-5} \\ -1(x-5)\text{ = y+8} \\ -x+5\text{ = y+8} \\ y\text{ =- x+5-8} \\ y\text{ = -x-3} \end{gathered}[/tex]Step 2
Hence expressed the graphed solution as a piecewise function
[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ \square \\ -x-3,-18. A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of
materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality
12n> 170 +3.50n represents the situation in which the artist makes a profit.
a. Will the artist make a profit if he sells 15 necklaces? Show how you know.
b. Solve the inequality and explain what the solution means in regards to the jewelry artist.
By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. In mathematics, larger than symbol (>), less than symbol (<), less than or equal to a symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), and not equal to a symbol (≠).So, is the artist in profit if he sells 15 necklaces:
The cost to rent a booth is $170.The cost of making a necklace is $3.50.The selling price is $12.Inequality is 12n ≥ 170 +3.50n: (let n = 15)
12n ≤ 170 +3.50n12(15) ≤ 170 +3.50(15)180 ≤ 170 + 52.5180 < 222.5Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.
If f(x) =5x2 - 3x + 1, calculate the following
Answer:
a) 199
f(-6)= 5(-6)^2 - 3 (-6) + 1 =199
b) 37
f(3)= 5(3)^2 - 3 (3) + 1 =37
Match the polynomial expression on the left with the simplified version on the right.
Given the following question:
First expression:
[tex]\begin{gathered} \frac{12x^3-14x^2+16x-8}{3x-2} \\ \text{ Factor the expression:} \\ 12x^3-14x^2+16x-8=2(6x^3-7x^2+8x-4) \\ \frac{2\left(6x^3-7x^2+8x-4\right)}{3x-2} \\ \text{ Factor:} \\ 2\left(6x^3-7x^2+8x-4\right)=(3x-2)(2x^2-x+2) \\ =(3x-2)(2x^2-x+2)=2\left(3x-2\right)\left(2x^2-x+2\right) \\ \frac{2\left(3x-2\right)\left(2x^2-x+2\right)}{3x-2} \\ \text{ Cancel the common factor:} \\ -(3x-2) \\ 4x^2-2x+4 \end{gathered}[/tex]Second expression:
[tex][/tex]I need answer and work shown step by step and if graph needs to be shown please show it as well
SOLUTION.
AC and BD will intersect at the mid-point between points A and C.
So let's find the mid-point between points A and C
Point A(-2, 4) and point C(-6, 0)
This becomes
[tex]\begin{gathered} \text{Mid}-poi\text{nt = (}\frac{x1+x2}{2}),(\frac{y1+y2}{2}) \\ \\ =\frac{-2-6}{2},\text{ }\frac{4+0}{2} \\ \\ =\frac{-8}{2},\text{ }\frac{4}{2} \\ \\ \text{Mid-point= (-4, 2) } \end{gathered}[/tex]Therefore, the correct answer is option C.
evaluate 7*2*7*5 using properties of numbers. Name the property used in each step.
The simplified expression of 7 * 2 * 7 * 5 is 490
How to evaluate the expression?The expression is given as
7*2*7*5
Rewrite the expression properly
This is done as follows
7 * 2 * 7 * 5
The factors of the expression have different basis
i.e. Basis = 7 , 2 and 5
This means that we cannot apply the law of indices
Solving further, we have the following equation:
7 * 2 * 7 * 5 = 7 * 2 * 7 * 5
Rearrange the factors
So, we have
7 * 2 * 7 * 5 = 7 * 7 * 2 * 5
Evaluate the products of 7 and 7 in the above equation
So, we have
7 * 2 * 7 * 5 = 49 * 10
Finally, we have
7 * 2 * 7 * 5 = 490
Hence, the simplified expression of the expression given as 7 * 2 * 7 * 5 is 490
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The simplified expression of the given 7 x 2 x 7 x 5 will be; 490
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is given as;
7 x 2 x 7 x 5
Rewrite the expression properly as follows;
7 x 2 x 7 x 5
The factors of the expression have different basis that is;
Basis = 7 , 2 and 5
Thus we can't apply the law of indices
Solving further, we have the equation;
7 x 5 x 7 x 2 = 7 x 2 x 7 x 5
Rearrange the factors;
7 x 2 x 7 x 5 = 7 x 7 x 2 x 5
7 x 2 x 7 x 5 = 49 x 10
Finally, we have the following
7 x 2 x 7 x 5 = 490
Hence, the simplified expression of the given 7 x 2 x 7 x 5 will be; 490
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Help quickly please…..!!!!!!!!
The equation without fraction is 51 - 8x = 0
What are Linear equations?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.So, the equation is:
5 - 2/3 x = 3/4Rewrite in a more simplified form:
first, take the LCM, we get -
(15 - 2x) / 3 = 3/4Now, take LHS denominator 3 to RHS:
15 - 2x = (3 * 3) / 415 - 2x = 9 / 4Now, take 4 from RHS to LHS:
4(15 - 2x) = 960 - 8x = 9At last, decrease 9 by 60:
60 - 9 - 8x = 051 - 8x = 0Therefore, the equation without fraction is 51 - 8x = 0
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Jayden was out at a restaurant for dinner when the bill came. His dinner came to $29. After adding in a tip, before tax, he paid $34.22. Find the percent tip
The percent tip when Jayden's dinner bill is $29 is 18%.
According to the question,
We have the following information:
Bill of Jayden's dinner = $29
After adding the tip, Jayden paid $34.22.
Now, we will find the percent tip.
First, we will find the amount added to the bill.
$(34.22-29)
$5.22
Now, let's take the percent tip to be x%.
x% of 29 = 5.22
29x/100 = 5.22
29x = 522
x = 522/29 (29 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 18%
Hence, the percent tip on Jayden's dinner is 18%.
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What's the midpoint of line segment (5,10) , and (-3,6)?
Answer:
(1; 8)
Step-by-step explanation:
x = (5 + (-3))/2 = 1
y = (10 + 6) = 8
the variance inflation factor (vif) is another measure that can detect a high correlation between three or more predictor variables even if no pair of predictor variables has a particularly high correlation. what is the smallest possible value of vif? (absence of multicollinearity).
Variance inflation factor can have a value as low as one (absence of multicollinearity). A VIF number greater than 5 or 10 generally denotes collinearity that is problematic.
The variance of bj is not inflated at all if the VIF is 1, which indicates that there is no association between the jth predictor and the other predictor variables.
VIF equal to 1 signifies that there is no correlation between the variables. A VIF of 1 to 5 indicates a moderate correlation between the variables. Variables are highly linked when the VIF is greater than correlated2.
VIF = 1.0 if all independent variables are orthogonal to one another. VIF = infinity if there is perfect correlation.
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AB = 2x-2, BC = 3 and AC = 3x-5 find x
we can made a visula representation of the problem so:
So we can made an equation like:
[tex]\begin{gathered} AB+BC=AC \\ 2x-2+3=3x-5 \end{gathered}[/tex]and we can solve for x so:
[tex]\begin{gathered} 2x+1=3x-5 \\ 5+1=3x-2x \\ 6=x \end{gathered}[/tex]Answer: X=6
Step-by-step explanation: you can set AB plus BC to AC because they both are equal to the full line so..
2X-2+3=3X-5
First off add like terms so..
-2+3= 1 and then add 5 to the negative 5 and 1 which now leaves you with
2X+6=3X
Now you see more like terms ( 2X,3X)
Now subtract 2X from 3x which will leave you with
6=1X
Now to separate X and get you answer you see it’s 1X and 1X = X prior to defined answer, therefore you will be with X=6. Have a great day
What is the equation of a line that is parallel to −2x+3y=−6 and passes through the point (−2, 0)?
Enter your answer in the box.
Answer:
[tex]y=\frac{2}{3}x +\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]-2x+3y=-6\\3y=2x-6\\y=\frac{2}{3}x-2\\ \\\\Then\\y-0=\frac{2}{3}(x-(-2)\\ y-0=\frac{2}{3}x+\frac{4}{3} \\Therefore, the answer is y=\frac{2}{3}x+\frac{4}{3}[/tex]
For A Brainlist !! Please Help Iwill Mark Brainlist I appreciate it so much I think its D but im not sure
The operations which must be part of the inverse function g(x) are:
Add 3Divide by 2.What is an inverse function?An inverse function can be defined as a type of function that is obtained by reversing or undoing a mathematical operation in a given function (f(x)).
In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.
Generally speaking, the inverse of multiplication is division while addition is the inverse of subtraction. In this context, we can reasonably and logically deduce that a "division by 2," followed by an "addition of 3" to the function f(x) are the operations that must be part of the inverse function g(x).
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