You have the following expression:
x² + 6x
In order to complete the square, take into account that 6 is two times the product of the first coeffcient by the second one in the binomial (a+ b)², then, you have:
6 = 2ab
a=1 because is the coeffcient of the term with x², then for b you obtain:
b = 6/2(1) = 3
the third term of the trynomial is the squared of b.
A 5-gallon radiator is full and contains a 40% solution of antifreeze. how much needs to be drained out and replaced with pure antifreeze to obtain a 70% solution?
Solution:
Let x be the number of antifreeze solution. Thus;
[tex](0.4)x+1(5-x)=0.7x[/tex]We would solve for x;
[tex]\begin{gathered} 0.4x+5-x=0.7x \\ \\ 5=x-0.4x+0.7x \\ \\ 5=1.3x \\ \\ x=\frac{5}{1.3} \\ \\ x=3.85 \end{gathered}[/tex]Hence, the amount needs to be drained out is;
[tex]\begin{gathered} 5-x=5-3.85 \\ \\ =1.15 \end{gathered}[/tex]Answer: 1.15 gallon
Write a numerical expression then match words with the expression
Numerical expression: 30 - 10 - 7
In words: Elizabeth had $30, if she spent $10 to buy some pizza and $7 on a soda, how much money does she have left?
Rafael wants to construct a square inscribed in a circle. He divides the circle into six equal arcs and then draws line segments between four ofthe points. What was the first error Rafael made?:toThe first error Rafael made wasV. A square is constructed by first
The first error Rafael made was that he made six arcs instead of taking the perpendicular bisector of the diameter and then making 4 arcs.
A square is constructed first by taking the perpendicular bisector of the diameter and making the four arcs and then joining them to make the square.
A shipping center keeps track of the number of customers in each store at Lunch times the data shows the number of customers in the 15 different stores in the shopping center last su day.
A histogram is a representation that organizes a group of data points into specified ranges.
For the given data:
4, 18 , 20, 17, 16, 23, 19, 14, 8, 8, 6, 12, 20, 14, 18
A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph what is the speed of the flying carpet
The most appropriate choice for speed will be given by-
Speed of the flying carpet is 15.2 mph
What is speed?
The distance travelled by the body per unit time is called speed of the body.
If d is the distance travelled by the body and t is the time taken, then
speed = [tex]\frac{d}{t}[/tex]
Speed is a scalar quantity as the direction is not taken into account.
Here,
Let the speed of the flying carpet be [tex]x[/tex] miles
A flying carpet flies 2.4 miles with the wind
Time taken flying with the wind = [tex]\frac{2.4}{x +4}[/tex]
The flying carpet flies 1.4 miles against the wind
Time taken flying against the wind = [tex]\frac{1.4}{x - 4}[/tex]
By the problem,
[tex]\frac{2.4}{x +4} = \frac{1.4}{x-4}[/tex]
[tex]2.4(x - 4) = 1.4(x + 4)\\2.4 x - 9.6 = 1.4 x + 5.6\\2.4 x - 1.4 x = 9.6 + 5.6\\[/tex]
[tex]x = 15.2[/tex] mph
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Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
x − 3y = −3
4x + 3y = 18
Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.)
(x, y) =
The system of linear equations has one and only one solution.
x = 3 and y = 2.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
x - 3y = -3 _____(1)
4x + 3y = 18 ______(2)
We will solve the equation to check its solutions.
x - 3y = -3 can be written as:
x = -3 + 3y ____(3)
Putting in (2) we get,
4(-3 + 3y) + 3y = 18
-12 + 12y + 3y = 18
15y = 18 +12
15y = 30
y = 2
Putting in (3)
x = -3 + 3 x 2 = -3 + 6 = 3
x = 3
We see that,
x = 3 and y = 2
Putting in the equation it is satisfied.
x - 3y = -3
3 - 3 x 2 = -3
3 - 6 = -3
-3 = -3
4x + 3y = 18
4x3 + 3x2 = 18
12 + 6 = 18
18 = 18
Thus,
The system of linear equations has one and only one solution.
x = 3 and y = 2.
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hey there Ms or Mr could you help me out with this please?
If a quadrilateral is a parallelogram, then its opposite sides are congruent therefore:
[tex]\begin{gathered} GH\cong JI \\ and \\ GJ\cong HI \end{gathered}[/tex]Using the distance formula:
[tex]\begin{gathered} GH=\sqrt[]{(5-1)^2+(3-1)^2} \\ GH=\sqrt[]{16+4} \\ GH=\sqrt[]{20} \\ JI=\sqrt[]{(0-4)^2+(3-5)^2} \\ JI=\sqrt[]{16+4} \\ JI=\sqrt[]{20} \\ GH\cong JI \end{gathered}[/tex][tex]\begin{gathered} GJ=\sqrt[]{(0-1)^2+(3-1)^2} \\ GJ=\sqrt[]{1+4} \\ GJ=\sqrt[]{5} \\ HI=\sqrt[]{(4-5)^2+(5-3)^2} \\ HI=\sqrt[]{1+4} \\ HI=\sqrt[]{5} \\ GJ\cong HI \end{gathered}[/tex]Step 2:
The diagonals are given by:
[tex]\begin{gathered} JH=\sqrt[]{(0-5)^2+(3-3)}^2 \\ JH=\sqrt[]{25} \\ JH=5 \\ GI=\sqrt[]{(4-1)^2+(5-1)^2} \\ GI=\sqrt[]{9+16} \\ GI=\sqrt[]{25} \\ GI=5 \\ JH=GI \\ 5=5 \\ so\colon \\ JH\cong GI \end{gathered}[/tex]help meeeeeee pleaseee !!!!
The function that represents the cost function is c(x) = 75 + 0.25x
What is the Cost FunctionTo find the cost function c(x), we have to write a linear equation or linear function to represent this.
Initial charge = 75charge per copy = 0.25x = number of copiesThe cost function can be expressed as a function of the number of copies made which can be represented as
[tex]c(x) = 75 + 0.25x[/tex]
The cost of printing x number of pages is c(x) = 75 + 0.25x
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3/4 times x equals 3.45 solve for x
4.6
1) Since 3/4x = 3.45, then we can solve it for x
3/4x = 3.45 Multiply both sides by 4 to eliminate the fraction
3x =13.80 Divide both sides by 3
x= 4.6
2) So x is equal to 4.6, and that is the answer
The average age of 6men is 35years and the average age of 4 of them is 32years. Find the age of the remaining 2 men if one is 3years older than the other
The age for two men is 39.5 and 42.5.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
Given:
Average of 6 men = 35
Average of 4 men = 32
So, Total age of 6 men
=6x35
=210 years
and, Total age of 4 men
=32 x 4
=128 years
Then, the remaining age for 2 people
= 210 - 128
=82 years
Let the age for two be x and y
then , x+ y=82
and x-y=3
On solving
2x =85
x=42.5 years
and y=39.5 years
Hence, the age for two men is 39.5 and 42.5.
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Function ggg can be thought of as a translated (shifted) version of f(x)=x^2f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f has a vertex at the point 0, 0. A parabola labeled g has a vertex at the point negative 4, negative 5.
Write the equation for g(x)g(x
The equation for g(x) is g(x) = x²-3
When x=0, f(x)= 0 and so has a vertex at (0,0)
Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.
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In 2017 the population of Rexburg, Idaho was 28,337 people. The population was expected to grow at a rate of about 1.21% per year. Based on these numbers, what would we predict the population of Rexburg will be in the year 2020?
Answer:
29,378 people
Step-by-step explanation:
[tex]28337 \times {1.0121}^{3} = 29378[/tex]
What’s the correct answer answer asap for brainlist
Answer: C
Step-by-step explanation: A is definitely not correct. not b. not d
The money was distributing un equally. Because of the great depression, the lower classes made less money
Hey can someone please help me? I’m confused. I’ll give brainliest
Answer:
1.50t + 3 < 9
Step-by-step explanation:
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
total cost of taking and Gatorade is less than $9
Answer:
1.50t + 3 < 9
Step-by-step explanation
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
the total cost of taking and Gatorade is less than $9
2.2.PS-141You are running a fuel economy study. One of the cars you find is blue. It can travel 39miles on21241 gallons of gasoline. Another car is red. It can travel 22 miles ongallon of gasoline. What is455the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallonof gasoline?CHEThe unit rate for the blue car is mile(s) per gallon.(Simplify your answer. Type an integer, proper fraction, or mixed number.)Enter your answer in the answer box and then click Check Answer.Clear AllICheck Answer2partsremainingReview progressQuestionof 8BackNext →
The blue car has traveled the greater distance on one gallon of gasoline
Explanation:The formula for calculating the unit rate is expressed as shown:
[tex]\text{Rate = }\frac{Distance}{\text{number of gallons}}[/tex]For the blue car
Distance = 39.5miles
Gallons of gasoline = 1.25 gallons
Get the unit rate:
[tex]\begin{gathered} \text{Unit rate = }\frac{39.5}{1.25} \\ \text{Unit rate = 3}1.6\text{ }miles\text{ per gallon} \end{gathered}[/tex]The unit rate of the blue car as a mixed fraction is 31 3/5 miles per gallon
For the red car
Distance traveled = 22.4 miles
Gallons of gasoline = 0.8 gallons of gasoline
Get the unit rate of the red car;
[tex]\begin{gathered} Unit\text{ rate = }\frac{22.4}{0.8} \\ \text{Unit rate = }28\text{miles per gallon} \end{gathered}[/tex]From the unit rates, we can see that the blue car has traveled the greater distance on one gallon of gasoline since its unit rate is greater than that of the red car.
I'll give brainliest!
Answer:
9 is the answer
Answer: 9 cubes
Step-by-step explanation:
9 * 9 is 81 which makes the floor of it
since its a cube, we multiply 81 by 9, giving 729
Look at this graph: 101 9 8 7 6 5 4 3 2. 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
The slope can be calculated as the quotient between the difference in the y-coordinates of two points, and the difference in the x-coordinates of the same two points.
We pick any 2 known points, like (0,2) and (5,4).
We calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{5-0}=\frac{2}{5}=0.4[/tex]Answer:
The slope is m=2/5=0.4
[First Person To Answer Will Get 5 Stars And Brainlyest] Help Please.
Distance is the total movement of an object without any regard to direction. Total distance jogged by Linsey is 420 yards.
What is distance?
Distance is the total movement of an object without any regard to direction
Given data
vertex 1 is at ( -4, - 1)
vertex 2 is at ( - 4, 5)
vertex 3 is at (2,5)
vertex 4 is at ( 2, -1 )
Lindseys jogs along the edge of the park in order from vertex 1 to the vertex 2 , vertex 2 to vertex 3 and vertex 3 to vertex 4 and then back to vertex 1. One unit in the coordinate grid is 20 yards.
Let us calculate distance vertex 1 and vertex 2of (-4,-1) and (-4,5)
x₁=-4,x₂=-4, y₂=5, y₁=-1
Distance=√(x₂-x₁)²+(y₂-y₁)²
Substitute the values x₁=-4,x₂=-4, y₂=5, y₁=-1 in distance formula
=√(-4+4)²+(5-(-1))²
=√6²
=6
Since 1 one unit on the coordinate gride equal 20 yd.
so 6×20=120 yards.
Now for four vertices we get 4×120=480 yards.
So total distance jogged by Linsey is 420 yards.
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Find the value of x. Write an equation andsolve, showing ALL the work.
Given:
The objective is to find hte value of x.
The value of x can be calculated by basic proportionality theorem.
[tex]\frac{12}{14}=\frac{9}{x}[/tex]Thus, the required equation is obtained.
The value of x is,
[tex]\begin{gathered} x=9\cdot\frac{14}{12} \\ x=\frac{9\cdot14}{12} \\ x=\frac{126}{12} \\ x=10.5 \end{gathered}[/tex]Hence, the value of x is 10.5
can you please cancer C what is the explicit function and the relationships for the term please I dont understand
EXPLANATION
Given the sequence:
C. 3, 12, 27, 48, 75
First, we need to calculate the difference between terms:
12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27
Arithmetic relationship: 9, 15 , 21, 27
To obtain the sequence we use the following formula:
[tex]a_n=a_1+(n-1)d[/tex]Now, we need to calculate the appropriate difference between terms:
15-9 = 6 21-25 = 6 27 - 21 = 6
So the constant difference is 6 and the nth term will be:
nth = 6n + 3
*a1=3
So, the relationship will be:
n Value Relationship
1 12 3 + (6*1 +3)
2 27 12 + (6*2 + 3)
3 48 27 + (6*3 + 3)
4 75 48 + (6*4 + 3)
5 108 75 + (6*5 + 3)
n n-1 + (6n+3) n-1 + (6n+3)
Explicit function: y = (n-1) + (6n+3)
You visit your favorite restaurant and order an appetizer for $5.99, a drink for $4.50, your meal for $10.99, and dessert for $3.75. The sales tax is 9%. and you
would like to leave an 18% tip. Find the total cost of your meal.
Using percentages, we can conclude that the total cost of the meal is approximately $33.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Frequently, it is indicated by the percent sign, "%".By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total cost of the meal:
$5.99 + $4.50 + $10.99 + $3.75 = $25.23Sales tax on the bill: 9%
25.23/100 × 9 = $2.2977Total bill printed on bill: $25.23 + $2.2977 = $27.527718% tip of the bill:
27.5277/100 × 18 = 4.954986Rounding off: $5Total cost of meal: $27.5277 + $5 = $32.5277
Rounding off: $33Therefore, using percentages, we can conclude that the total cost of the meal is approximately $33.
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Which expression is equivalent to 7a-8-12a +4?A.-gaB.31aC. -5a - 4D.19a + 12
Step 1
Rearrange the expression to bring like terms together.
[tex]\begin{gathered} 7a-8-12a+4 \\ 7a-12a\text{ -8+4} \end{gathered}[/tex]Step 2
Simplify to get the final answer
[tex]-5a-4[/tex]Hence the right answer is option C
48% of people in a certain country like to cook and 54% of people in the country like to shop, while 26% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or both? The probability that a randomly selected person in the country enjoys cooking or shopping or both is ________
The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
48% of people in a certain country like to cook.
And, 54% of people in the country like to shop, while 26% enjoy both activities.
Now,
Probability to like the cook P (C) = 48%
Probability to like the shop P (S) = 54%
Probability to like the both activity P (C∩S) = 26%
So, Probability to like the both activity P (C ∪ S) is calculated as;
P (C ∪ S) = P (C) + P (S) - P (C ∩ S)
P (C ∪ S) = 48% + 54% - 26%
P (C ∪ S) = 102% - 26%
P (C ∪ S) = 76%
P (C ∪ S) = 0.76
Thus, The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
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The circle graph shows how the annual budget for a company is divided by department. Use this graph to answer the questions below.(a) Which department gets approximately one-fourth of theannual budget?Select OneSupportEngineeringMediaEditorialResearch(b) Approximately what percentage of the budget goes toEngineering and Support combined?20% O 40%60%80%SalesХ5?
Observe the given graph carefully.
In a circle graph, the circle is divided into different sectors, each characterized by its central angle.
The complete circle measures 360 degrees. So the complete distribution (100% data) corresponds to 360 degrees.
In the given problem, we are concerned with the budget,
[tex]360^{\circ}=100\text{ percent budget}[/tex](a)
Consider the following,
[tex]\begin{gathered} \text{ Total budget}=360^{\circ} \\ \frac{1}{4}\times\text{ Total budget}=\frac{1}{4}\times360^{\circ}=90^{\circ} \end{gathered}[/tex]So, one-fourth of the budget will correspond to the department which covers the 90-degree sector of the circle graph.
As observed from the graph, the most suitable department under this criteria is the Engineering Department.
Thus, Engineering Department gets approximately one-fourth of the annual budget.
(b)
Consider that the departments Engineering and support combiningly cover a little more than one-third of the area of complete circle.
Consider the following,
[tex]\begin{gathered} 360^{\circ}=100\text{ percent} \\ 120^{\circ}=\frac{120}{360}\times100=33.33\text{ percent} \end{gathered}[/tex]Note that the area covered by the department is a little more than one-third, so the corresponding percentage value must also be a little more than 33.33%.
From the available options, 40% is the value available next to 33.33%, so this should be the most suitable choice.
Thus, it can be concluded that approximately 40% of the annual budget goes to the departments Engineering and Support combined.
Therefore, option (b) is the correct choice.
Pls helppppppppppp
It’s not c
Answer: it would be D because m∠NSO+m∠OSL+m∠LSM+m∠MSN=360°
and m∠LSM+m∠SML+m∠MLS≠360° doesnt equal 360 degrees so that one is wrong ∠LSM≅∠NSM is a false statement same with m∠LSO+m∠MSO=180° its false so it would be (D)
hope i helped
Step-by-step explanation:
Once again, you're trying to get out of the classroom. The distance to the door from your desk is d meters. Your first step is 1/6 that distance. Each successive step is 1/6 the previous distance. How far have you traveled? Express each result using exponetial notation for 8 steps, 12 steps, 20 steps, and n steps.
Given:
The distance to the door from your desk is d meters.
Your first step is 1/6 that distance =
[tex]\frac{1}{6}d[/tex]Each successive step is 1/6 the previous distance.
so, the second step =
[tex]\frac{1}{6}\cdot\frac{1}{6}d=(\frac{1}{6})^2d[/tex]The third step =
[tex]\frac{1}{6}\cdot(\frac{1}{6})^2d=(\frac{1}{6})^3d[/tex]And so on,
So, for the step number n, the formula will be :
[tex]=(\frac{1}{6})^n\cdot d[/tex]So, for 8 steps
You will have traveled =
[tex]=(\frac{1}{6})^8\cdot d[/tex]For 12 steps =
[tex]=(\frac{1}{6})^{12}\cdot d[/tex]For 20 steps =
[tex]=(\frac{1}{6})^{20}\cdot d[/tex]For n steps =
[tex]=(\frac{1}{6})^n\cdot d[/tex]
Find the slope of a ramp with a height-to-distance ratio of 1 to 12 feet.
The slope of a ramp with a height-to-distance ratio of 1 to 12 feet is 4.76 degrees.
What is the slope of a line?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The tangent relation or the height-to-distance ratio helps to determine the slope of the line.
It is given that the height-to-distance ratio of a slope is given as 1 to 12 feet.
So,
[tex]\tan \alpha = 1/12\\\alpha= \tan^{-1}1/12\\\alpha= 4.76^\circ[/tex]
So, the slope of the ramp is about 4.76 degrees.
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Given that (9,-8) is on the graph of f(x), findthe corresponding point for the functionf(x - 2).Enter the correct answer.0000 CDONEClear allDOO
(7,-8)
1) Considering that f(x-2) is a transformation of f(x). Precisely, a horizontal translation to the right.
2) So, we can write out the following:
[tex]\begin{gathered} f(x)=x \\ f(9)=-8 \\ \\ f(x-2)=x \\ f(9-2)=-8 \\ f(7)=-8 \end{gathered}[/tex]Note that a horizontal translation just "pushes to the right". So there was no vertical shift.
3) Hence, the answer is (7,-8)
use the provided equation below to complete the table and graph
Answer:
Explanation:
To complete the table, we need to replace each value of x and calculate the value of y.
So, if x = - 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}x-2 \\ y=\frac{3}{8}(-16)-2 \\ y=-6-2 \\ y=-8 \end{gathered}[/tex]If x = -8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(-8)-2 \\ y=-3-2 \\ y=-5 \end{gathered}[/tex]If x = 0, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(0)-2 \\ y=0-2 \\ y=-2 \end{gathered}[/tex]If x = 8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(8)-2 \\ y=3-2 \\ y=1 \end{gathered}[/tex]If x = 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(16)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]So, the complete table is:
x y
-16 -8
-8 -5
0 -2
8 1
16 4
Finally, we can graph the table, so:
Find the distance between the two points in simplest radical form.
(6,9) (9,6)
Answer:
3√2
Step-by-step explanation:
[tex] \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } [/tex]
[tex] \sqrt{ {( - 3)}^{2} + {3}^{2} } [/tex]
[tex] \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} [/tex]