Answer:
[tex]f(x)=x^{2} +13x+30[/tex]
Step-by-step explanation:
1. Whenever you write a quadratic function with zeros, you want to put it into a formula like this:
[tex]f(x)= (x-p) (x-q)[/tex]
p and q are the zeros
2. Your zeros are (-3) and (-10). When plugging in the zeros, you always flip the sign on the number. Because you would plug it in as: [tex]f(x) = (x-(-3)) (x-(-10))[/tex]
Two negative signs equal positive signs, so the equation will look like this:
[tex]f(x)=(x+3)(x+10)[/tex]
3. Solve the equation:
a. Use the foil method: [tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
[tex]f(x)=x^{2} +10x+3x+30[/tex]
b. Collect like terms
[tex]f(x)=x^{2} +(10x+3x)+30[/tex]
c. Simplify
[tex]f(x)=x^{2} +13x+30[/tex]
Hope that helps!
it on go math book grade 8 and the question is a bicyclist started riding at 8:00 am the diagram below shows the distance the bicyclist had traveled at different times what was the bicyclist's average rate of speed in miles per hour? 8:00 am 4.5 miles 8:18 am 7.5 miles 8:48
The average rate of speed in miles per hour is 15miles/hour.
What is the rate of speed ?
Acceleration, or the rate at which your speed is changing, is referred to as "rate of speed." Distances per time are used to measure "speed" (eg miles per hour). "Rate of speed" is expressed using units of distance per unit of time. Speed is determined by dividing the distance by the time.Calculating the units for speed requires knowledge of the units for both time and distance. Since the distance is measured in metres (m) and the time is measured in seconds, the units in this example will be metres per second (m/s) (s). Average speed combines the ideas of speed, which is a change in location, and average, which refers to a mean calculated from numerous data points, into a single phrase.Given that, a 4.5miles distance covered in 18 min and 7.5miles in 30 min
Converting miles/min to miles/hour and calculating the average,
Then
[(4.5 miles/18min )+(7.5miles/30min)]/2
[15miles/hour + 15miles/hour]/2 = 15miles/hour
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An algebraic expression is described as 7 less than the product of 22
and the sum of t and 18. What is the value of this expression when
t = 13?
Step-by-step explanation:
22×(t + 18) - 7
t = 13
so,
22×(13 + 18) - 7 = 22×31 - 7 = 682 - 7 = 675
What is the slope of the line that passes through the points (10,3) and (7,0)? Write your answer in simplest form.
Given two points on a line, we can find its slope using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(7,0) \\ \Rightarrow slope=\frac{10-7}{3-0}=\frac{3}{3}=1 \end{gathered}[/tex]Thus, the slope is equal to 1.
Find the difference: (2x − 8) - (x + 5)
Darren and his two siblings' ages are three consecutive odd numbers. if the sum of their ages is 51, what are the three ages?
Darren age is 15
and 1st sibling is x+2= 17 yrs
2rd sibling is x+4 = 19 yrs
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here, it is given that :
Darren and his two siblings' ages are three consecutive odd numbers and the sum of their ages is 51.
Let Darren age be x
and since they are odd consecutive numbers, his two siblings age will be
1st sibling age will be = x+2
2rd sibling age will be = x+4
If the sum of their ages is 51
that is,
x+x+2+x+4= 51
solving for x:
3x+6 = 51
3x+6-6=51-6
3x = 45
3x/3 = 45/3
x = 15 yrs
Therefore, x is 15, therefore Darren age is 15
and 1st sibling is x+2= 17 yrs
2rd sibling is x+4 = 19 yrs
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Write the coordinates of the vertices after a rotation 270° clockwise around the origin.
The coordinates of the vertices when rotated 270° counterclockwise around the origin are:
K' = ( 4, 1 )
L' = ( 7, 1 )
M' = ( 7, 0 )
N' = ( 4, 0 )
When a point P( a, b ) is rotated 270° counterclockwise around the origin, we flip a and b and reverse the sign of a.
Therefore,
The rule to rotate a point P ( a, b ) after a rotation 270° counterclockwise around the origin is:
P ( a, b ) → P' ( b, - a )
Now, consider the points on the graph:
L = ( - 1, 7 )
K = ( - 1, 4 )
N = ( 0, 4 )
M = ( 0, 7 )
When the coordinates are rotated 270° counterclockwise.
L ( - 1, 7 ) → L' ( 7, 1 )
K ( - 1, 4 ) → K' ( 4, 1 )
N ( 0, 4 ) → N' ( 4, 0 )
M ( 0, 7 ) → M' ( 7, 0 )
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NEED DONE ASAP
The diameter of a speck of dust is about 0.00002 inches. Which of these is an appropriate estimate for the diameter of the speck of dust?
A
2×10−5in.
B
2×10−4in.
C
2×104in.
D
2×105in.
The diameter of the speck of dust is written as;
⇒ 2 × 10⁻⁵ inches.
Option A is true.
What is Number system?
A way for system of writing to express the number is called number system.
Given that;
The diameter of the speck of dust = 0.00002 inches.
Now,
Find the estimate number of the diameter of speck of dust as;
Since, The diameter of the speck of dust = 0.00002 inches.
The number = 0.00002 inches
It can be written as;
0.00002 inches = 2 × 10⁻⁵ inches.
Therefore,
The diameter of the speck of dust is written as;
⇒ 2 × 10⁻⁵ inches.
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For f(x) = -x-4 find the value of x for which f (x) = 1
Answer:
x = -5
Step-by-step explanation:
f(x) = -x-4
Let f(x) = 1
Find x
1 = -x-4
Add 4 to each side
1+4 = -x-4+4
5 = -x
Multiply each side by -1
-5 =x
x = -5
Answer:
x = -5
Step-by-step explanation:
Given that,
f ( x ) = - x - 4
If, f ( x ) = 1,
Let us find the value of x.
For that, replace f ( x ) with 1.
f ( x ) = - x - 4
1 = - x - 4
First, add x to both sides.
x + 1 = -4
Now, subtract 1 from both sides.
x = -4 - 1
x = -5
Write an equation in slope-intercept form for each line described.
18.) passes through (5,-3), perpendicular to y=-2x+4
19.) passes through (-2,4), parallel to y=9
20.) passes through (3,5), perpendicular to y=1/3x+12
The equation of the line in slope-intercept form passes through (5,-3), parallel to y = - 2x + 4 is y = - 2x + 8 and equation of the line passes through (3,5), perpendicular to y = 1/3x + 12 is y = - 3x + 18.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know that parallel lines have same slopes and perpendicular lines have slopes that are negative reciprocals of each other.
Given a line passes through (5,-3), perpendicular to y = - 2x + 4.
The slope of this line is - 2 and hence line parallel to it will also have a
slope of - 2.
∴ The equation of the line in slope-intercept form is,
- 3 = 5(-2) + b.
- 3 = - 10 + b.
b = 8.
The required line is y = - 2x + 8.
Given a line passes through (3,5), perpendicular to y = 1/3x + 12.
The given line has a slope of 1/3 so the line perpendicular to it will have a slope of - 3 ( as the negative reciprocal of 1/3 is - 3/1 = - 3 ).
∴ The equation of the line in slope-intercept form is,
3 = 5(-3) + b.
3 = - 15 + b.
b = 18.
So, y = - 3x + 18.
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jackie used to be on the phone 3 1/2 times as much as her brother. Her parents threatened to take away the phone, so she cut down to 2/5 of the time she used to be on the phone. How many times as much as her brother is jackie now on the phone?
The number of times as much as her brother is Jackie now on the phone is 1 2/5 times.
How to calculate the fraction?From the information, Jackie used to be on the phone 3 1/2 times as much as her brother and her parents threatened to take away the phone, so she cut down to 2/5 of the time she used to be on the phone.
Therefore, the times that she's using as much as her brother will be:
= Original times × Fraction cut
= 3 1/2 × 2/5
= 7/2 × 2/5
= 7/5
= 1 2/5 times.
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A karaoke machine regularly costs $153 and is on sale for 25% off. What is the discount?
A karaoke machine regularly costs $153 but due to a discount on sale of 25%, it will cost $114.75 due to a reduction of $38.25.
What is a discount?Discounts are sums of money or percentages taken off of a product's usual selling price. A good or service's price is decreased by the discount.
Discount describes the circumstance when the price of a bond will be less than its face value.
According to the question, the given values are :
Original Price of the Karaoke machine = $153
Discount = 25%
So, the reduction will be :
= 153 ×(25/100)
Reduction = $38.25
Hence, the discount he gets on the karaoke machine is $38.25 or we can say that the karaoke machine will cost $114 after a reduction of 25%.
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Answer:
its 38.25
Step-by-step explanation:
I did the 3.07 test on flvs and got it right
bye, UwU :3
1/2+3/6=
what will the answer be
The value of the fraction expression 1/2 + 3/6 is 1.
The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers.
The smallest number (non-zero) that is a multiple of all the numbers is known as the least common multiple of two or more numbers.
Consider the expression,
1/2 + 3/6 = x
Consider the fraction 3/6,
The factors of 3 are 1 and 3.
The factors of 6 are 1, 2, 3, and 6.
Therefore, the GCF or greatest common factor is 3.
Therefore,
3/6 = ( 3 ÷ 3 ) / ( 6 ÷ 3 ) = 1/2
So, the value of the expression will be:
x = 1/2 + 3/6
x = 1/2 + 1/2
As the denominators of the fractions are equal.
x = ( 1 + 1 )/ 2
x = 2/2
x = 1
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1 An amount of Php 2,000,000 is invested for 5 years at a 5% interest rate. 2. An amount of Php 500,000 is invested in a financial institution. At what interest rate will it earn Php 4,000 in 18 months?
Answer:
it may be in round about 3600000000..
The interest rate earned in 18 months will be $300
What is interest rate?The amount that a lender charges a borrower for the use of assets on top of the principal is known as the interest rate.The money generated from a deposit account at a bank or credit union is likewise subject to an interest rate.Simple interest is used in most mortgages. Compound interest, which is applied to both the principle and the accrued interest from earlier periods, is used in some loans, nevertheless.The interest rate will be lower for a borrower who the lender deems to be low risk. The interest rate on a loan will be greater if it is thought to be high risk.The interest rate on savings accounts and certificates of deposit that is earned at a bank or credit union is known as the annual percentage yield (APY). Compound interest is used in savings accounts and CDs.First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
putting time into years for simplicity,
18 months ÷ 12 months/year = 1.5 years,
then, solving our equation
I = 4000 × 0.05 × 1.5 = 300
I = $300.00
The simple interest accumulated
on a principal of $4,000.00
at a rate of 5% per year
for 1.5 years (18 months) is $300.00.
Therefore, the interest rate earned in 18 months will be $300
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How do you decide which operations to use when writing an equation?
Answer:The order of operations tells us the order to solve steps in expressions with more than one operation.
Step-by-step explanation: First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right.
can someone help me...........
Answer:
?=5
Step-by-step explanation:
8
[tex] {8}^{4 - 2 +3} = {8}^{?} \\ {8}^{5} = {8}^{?} \\ 5 = {?}[/tex]
Solve the system of equations by elimination.-2x + 2y + z = 143x - 2y + z = -5-x + y - 2z = -8c
x= -3, y = 1, z = 6
Explanation:
-2x + 2y + z = 14 ....equation 1
3x - 2y + z = -5 ....equation 2
-x + y - 2z = -8 ....equation 3
Note: Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
Subtract equation 2 from 1:
-2x - 3x +2y -(-2y) + z - z = 14 -(-5)
-5x + 2y + 2y + 0 = 14 + 5
-5x + 4y = 19 ....equation 4
Due to the first equation we derived where we only have x and y. We need to solve the second equation in such a way we get only x and y.
This means we find a way to eliminate z in the second subtraction.
To do this, we multiply 1 by 2. Then we add both equations to eliminate z
-4x + 4y + 2z = 28 ....equation 1
-x + y - 2z = -8 ....equation 3
Add equation 3 and 1:
-4x + (-x) + 4y + y + 2z + (-2z) = -8 + 28
-4x - x + 5y + z + 2z - 2z = 20
-5x + 5y = 20 ....equation 5
-5x + 4y = 19 ....equation 4
-5x + 5y = 20 ....equation 5
subtract equation 4 from 5 (we will be eliminating x):
-5x -(-5x) + 5y - 4y = 20 - 19
-5x + 5x + y = 1
y = 1
we substitue the value of y in any of the equation between 4 and 5:
using equation 4:
-5x + 4(1) = 19
-5x + 4 = 19
-5x = 19-4
-5x = 15
x = 15/-5
x = -3
we substute for both y and x in any of the initial equation to get z:
using equation 2:
3(-3) -2(1) +z = -5
-9 - 2 + z = -5
-11 + z = -5
z = -5 + 11
z = 6
There are 400 counters in a box.
The counters are red or yellow or green.
3
of the counters are red.
82 of the counters are yellow.
What percentage of the counters are green?
the green would be 15% of the counters
The number of counters that are green is 162 and the percentage of counters that are green is 42 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total number of counters = 400
The number of counters that are red = 3/8 of total number of counters
= ( 3/8 ) x 400
= 3 x 50
= 150 counters
The number of counters that are yellow = 82 counters
So , the number of counters that are green =
Total number of counters - number of counters that are red - number of counters that are yellow
The number of counters that are green = 400 - 150 - 82
= 168 counters
Now , the percentage of counters that are green =
( number of counters that are green / total number of counters ) x 100
The percentage of counters that are green = ( 168 / 400 ) x 100
= 168 / 4
= 42 %
Hence , the number of counters that are green is 168 and the percentage of counters that are green is 42 %
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−3x+y=4
Solve for y:
y=
x
Create a table:
x y
-1
0
1
2
3
Slope:
y-intercept:
Skip to navigation
The equation is solved for y as: y = 3x + 4.
Slope = 3
Y-intercept = 4.
How to Find the Slope and Y-intercept of a Line?Slope = change in y/change in x.Y-intercept is the value of y whenever the value of x equals zero.Given the equation, -3x + y = 4, rewrite to solve for y:
y = 3x + 4
To create a table, substitute the values of x into y = 3x + 4.
For x = -1:
y = 3(-1) + 4
y = 1
For x = 0:
y = 3(0) + 4
y = 4
For x = 1:
y = 3(1) + 4
y = 7
For x = 2:
y = 3(2) + 4
y = 10
For x = 3:
y = 3(3) + 4
y = 13
The table is:
x | y
-1 1
0 4
1 7
2 10
3 13
The slope of y = 3x + 4 is m = 3.
The y-intercept (b) = 4.
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help! (functions) I don’t understand how to do this
A function from set A to set B is a relation that pairs each element of set A to exactly one element of B.
Here, we are given two functions as shown in the figure. We can answer the questions as follows-
1. a. the given function represents the countries to which the chocolate companies belong to.
b. the function represents the square of the a number
2. Both the relations are functions because for every value in the first circle there is one and only one unique value in the second circle. This, is the basic property of a function.
3. a. Domain: (Neuhaus, Cote d'Or, Leonidas, Toblerone, Lindt, Hershey's, Baci)
Range: (Belgium, Switzerland, USA, Italy)
b. Domain: (1, -1, 2, -2, 5, -5)
Range: (1, 4, 5)
4. a. (Neuhaus, Belgium) is one ordered pair of the given function
b. (1, 1) is one ordered pair of the given function
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if you cant read it it says : Use the distributive property for the expression 4(m + 7) - 6(4-) and simplify
Explanation
The distributive property tells us how to solve expressions in the form of a(b + c)
[tex]a(b+c)=ab+ac[/tex]Then,
Step 1
apply distributive property operate
[tex]\begin{gathered} 4(m+7)-6(4-m) \\ 4\cdot(m)+4\cdot7-6(4)+6(m) \\ 4m+28-24+6m \end{gathered}[/tex]
Step 2
add similar terms
[tex]\begin{gathered} 4m+28-24+6m \\ 10m+4 \end{gathered}[/tex]so, the answer is
[tex]D)10m+4[/tex]I hope this helps you
Which of the number below are whole numbers?
Answer:
D and F
Step-by-step explanation:
8060 and 609 are whole numbers.
whole numbers: Whole numbers include 0 and natural numbers (1,2,3,4......). They don't include fractions, decimal and negative integers.
ill give brainlest if u can answer this corectly
Answer:
The rate in m³/m² is 40m³/m².
1 m³ is literally a cube with sides that are 1 m in length. 1 m = 100 cm, so each side of this cube is 100cm in length. Finding the volume means multiplying length by width by height:
100(100)(100)=1,000,000 cm³ in 1m³.
We know that we have 25,000cm³ of mulch; we divide to find how many cubic meters this is:
1,000,000/25,000 = 40 m³.
This makes the rate 40m³/m².
Step-by-step explanation:
Constant of Proportionality PROPORTIONALITY OF EACH GRAPH. NOT ALL CHOICES WU BE USED. 1/2 3 4 1 I 2 2. 1/4
Choose any point on each line different from (0,0) to find the constant of proportionality.
Notice that, for example, in the first graph, the point (4,4) lies in the line.
Divide the y-coordinate over the x-coordinate to find the constant of proportionality. This method is only valid when the point (0,0) is in the line.
For the first graph, the constant of proportionality is:
[tex]\frac{4}{4}[/tex]Which is equal to 1.
For the second graph, notice that the point (8,4) is in the line. Again, divide the y-coordinate over the x-coordinate to find the constant of proportionality:
[tex]\frac{4}{8}[/tex]Which is equal to 1/2.
For the third graph:
Notice that the point (4,8) is in the line of the third graph.
By dividing 8/4, we notice that the constant of proportionality is equal to 2.
liam descended from the summit of K2 to an elevation of 23,201.06 feet. what was the change in elevation.
Liam descended 5,050.25 feet. Elevation is defined as the distance above sea level. Elevations are typically expressed in meters or feet.
What is meant by elevation?The angle of elevation is formed by the intersection of the horizontal line and the line of sight. If the line of sight is directed upward from the horizontal line, the resulting angle is an angle of elevation. "rise over run" is an easy-to-remember equation for calculating change in elevation as a decimal, which means the rise (the change in vertical distance) divided by the run (the change in horizontal distance).
The angle of elevation is the angle formed by the horizontal line of sight and the upward line of sight. For example, if you're standing on the ground and looking up at the peak of a mountain, you can calculate the angle of elevation.
Therefore,
Liam descended from the summit of K2 (elevation= 28,251.31 feet) to an elevation of 23,201.06 feet.
You have to find the difference between 28,251.31 feet and 23,201.06 feet. To find the difference you have to subtract:
28251.31 - 23,201.06 = 5,050.25 feet
Hence, Liam descended 5,050.25 feet.
The complete question is:
Liam descended from the summit of K2 (elevation= 28,251.31 feet) to an elevation of 23,201.06 feet. How many feet did Liam descend? What was his change in elevation?
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Find the value of x.
Answer:
10
Step-by-step explanation:
They (50 & 5x) are parallel angles, therefore 5x equals 50.
This means that to find x, you will need to find a common factor between 5 and 50, which is 5. 50/5=10
x=10
All of the following names of the polygon above are correct EXCEPT for:
Answer: Uhhhh there are no names for me to choose from- but it's basically any shape with straight lines and is closed. hope this helps
Step-by-step explanation:
a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits in . no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in . a set of plates in which each possible sequence appears exactly once contains license plates. find .
The value of N/10 is 372.
The characters can be chosen from the word "AIME" or the number "2007".
There are 7 different characters that can be picked, with 0 being the only number that can be repeated twice.
There are two possible cases.
The first case is given below :
If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 7!/(7-5)!.
If 0 appears 0 or 1 time in the sequence, the number of possible sequences is 2520.
The second case is given below :
If 0 appears twice in the sequence, the number of places to fill 0 is 5C2.
If 0 appears twice in the sequence, the number of places to fill 0 is 10.
The number of ways to place the remaining three characters is 6!/(6-3)!.
The number of ways to place the remaining three characters is 120.
The total number of ways in the second case is 10*120 = 1200.
The total number of ways is 2520 + 1200.
The total number of ways is 3720.
N = 3720
We have to find the value of (N/10).
N/10 = 3720/10
N/10 = 372
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The voltage V of an audio speaker can be represented by V= 4 sqrt P , where P is the power of the speaker. An engineer wants to design a speaker with 625 watts of power. What will the voltage be?
The voltage of the audio speaker given the equation, V = 4√P, is 100.
What is the voltage?The given equation to determine the voltage is : V = 4√P
Where: P = 625 watts
The first step is to determine the square root of 625. The square root of a number is the number that is exactly half the value of the number. When the half is multiplied by itself, it yields the original number. For example, the square root of 25 is 5. 5 multiplied by 5 is 25.
√625 = 25 watts
The next step is to multiply 25 watts by 4. Multiplication is the process that is used to determine the product of two or more numbers.
25 x 4 = 100
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While shopping for supplies for the party, she is trying to decide which soda is the better deal. She can buy a 138 ounce bottle of soda for $3.20 or she can buy twelve 12ounce cans of cola for $3.60. Find the unit rate for the bottle.
Find the unit rate for the cans.
Answer:
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
Step-by-step explanation:
Cans oz/can Total oz Price ($) Cost ($/oz)
1 138 138 3.20 $0.023
12 12 144 3.60 $0.025
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
The unit rate for the bottle is $0.023/oz
The unit rate for the cans is $0.025/oz
a fair die has four faces numbered one to four. what is the probability of rolling a two exactly three times in ten rolls of the die?
For a fair die has four faces numbered one to four, the probability of rolling a two exactly three times in ten rolls of the die is 25.02% determined using binomial distribution.
Binomial distribution is used to determine the probability of observing a specified number of successful outcomes in a specified number of trials and is given by:
P(x:n,p) = nCx px (1-p)n-x
Where n is the number of experiments, x is a random variable, and p is the probability of success in a single experiment.
The probability of rolling a two in one trail = ¼ = 0.25
In the give case,
n = 10
x =3
p = 0.25
Therefore,
P(3) = 10C3 0.25^3 (1-0.25)^(10 – 3)
Solving 10C3 = 10!/3!(10-3)! = 120
P(3) = 120. 0.25^3 (1-0.25)^(10 – 3) = 0.2502
Hence, the probability of rolling exactly 2 three times in a ten trails is 25.02%
Learn more about Binomial distribution:
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