Answer:
x=1/6
Step-by-step explanation:
3x+4=9x+3
isolate x
1=6x
1/6=x
[tex]======================================[/tex]
First, let's move all the x's to the left:
3x+4=9x+3
3x-9x+4=3
Now, move 4 to the right:
3x-9x=3-4
Combine Like Terms:
-6x=-1
Divide both sides by -6:
x=[tex]\displaystyle\frac{1}{6}[/tex]
[tex]=========================================[/tex]
Notes:Hope everything is clear.Let me know if you have any questions!Always remember: [tex]\boxed{Knowledge~is~power!}[/tex]Good luck & enjoy your day!Answered by:[tex]\mathcal{Diamond}[/tex] ([tex]\boxed{An~Emotional~Helper}[/tex])
One side of this regular hexagon has been extended to form an exterior angle.
Use given information to find m Angle p.
Check the picture below.
how many milillerters of cholcolat milk are in the container shown
Naoki asked 200 students about their favorite movie genres. Of the 105 students who preferred comedy, 68 of them were girls. 94 of the students surveyed were boys. Construct a two-way table summarizing the data.
Here is the completed two-way frequency table:
Comedy Action Total
Boys 37 57 94
Girls 68 38 106
Total 105 95 200
How to complete the two-way table?Number of boys that prefer comedy = number of students that prefer comedy - Number of girls that prefer comedy
105 - 68 = 37
Number of boys that prefer action = total numer of boys - Number of boys that prefer comedy
94 - 37 = 57
Total number of students the prefer action = Total number of students - total number of students that prefer comedy
200 - 105 = 95
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|x-b|=c, only one solution is -3
Answer:
x-b=-3
Step-by-step explanation:
1. Simplify
|x-b|=c
x-b=c
If c=-3 then,
Answer= x-b=-3
You put $125.32 at the end of each month in an investment plan that pays 2.5% interest, compounded monthly. how much will you have after 23 years? round to the nearest cent. a. $46,683.28 b. $4,564,471.88 c. $2,949.39 d. $3,832.84
After 23 years $125.32 will be matured to $46,683.28.
What is the formula for recurring investment?The formula for Recurring maturity is given by:
[tex]A=Pn +\frac{ P*n*(n+1)}{24} *\frac{r}{100}[/tex]
Where A=matured amount
P =Principal value
n=Number of months
r=Interest rate(annual)
We have P= $125.32
n=23*12 = 276 months
r=2.5*12 =30%
Put these values in the above formula
we get A= $46,683.28
Therefore, After 23 years $125.32 will be matured to $46,683.28.
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What is the partial fraction decomposition of StartFraction 6 x + 17 Over (x + 1) squared EndFraction?
Answer:
6/(x + 1) + 11/(x + 1)^2.
Step-by-step explanation:
6x + 17 / (x +1)^2 = A / (x + 1) + B /(x + 1)^2
Multiply through by (x + 1)^2:
6x + 17 = A(x + 1) + B
Let x = -1, then:
-6 + 17 = 0 + b
So B = 11.
Let x = 1:
6 + 17 = A(1+1) + 11
23 = 2A + 11
A = (23-11)/ 2
A = 6.
1. (03.04)
What are the zeros of f(x) = (x - 5)(x – 4)(x - 2)? (2 points)
Answer:
for x=5, x=4 , x=2
Step-by-step explanation:
zero points, the x values that make this formula to be zero.
5-5=0
4-4=0
2-2=0
these values satisfied
Please I need help with these, use the picture to answer the questions below
Each dashed line segment is a(n)?
There are _____ congruent triangles in a regular hexagon.
Find the perimeter.
Find the radius of this hexagon.
Answer:
There are 6 congruent triangles in a regular hexagon.
The triangles are equilateral (all sides are equal in length).
Using side length of equilateral triangle formula:
[tex]\sf x=\sqrt{\dfrac{4}{3}h^2}[/tex]
where x is the side length and h is the height
[tex]\sf \implies x=\sqrt{\dfrac{4}{3}\cdot 6^2}[/tex]
[tex]\sf \implies x=\sqrt{48}[/tex]
[tex]\sf \implies x=4\sqrt{3} \ units[/tex]
Therefore, perimeter = 6 × 4√3 = 24√3 units
Radius = side length of triangle = 4√3 units
Side Be a
[tex]\\ \rm\rightarrowtail h=\dfrac{\sqrt{3}}{2}a[/tex]
[tex]\\ \rm\rightarrowtail 6=\dfrac{\sqrt{3}}{2}a[/tex]
[tex]\\ \rm\rightarrowtail 12=\sqrt{3}a[/tex]
[tex]\\ \rm\rightarrowtail a=12/\sqrt{3}[/tex]
[tex]\\ \rm\rightarrowtail a=4\sqrt{3}[/tex]
Perimeter:-
4(4√3)=16√3units
What are the solutions for the following system of equations?
y = 8x + 7
y = -x2 - 5x+7
(0,7) and (13, 97)
0 (0,7) and (-13, -97)
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
[tex](0,7),(-13,-97)[/tex]
Equation Form:
[tex]x=0,y=7\\x=-13,y=-97[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(8*x+7)=0
Equation of a Straight Line
Solve y-8x-7 = 0
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.'
n this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-8x-7 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000
y-intercept = 7/1 = 7.00000
Calculate the X-Intercept :
When y = 0 the value of x is 7/-8 Our line therefore "cuts" the x axis at x=-0.87500
x-intercept = 7/-8 = -0.87500
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 23.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 23.000 - 7.000 = 16.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 16.000/2.000 = 8.000
Geometric figure: Straight Line
Slope = 16.000/2.000 = 8.000
x-intercept = 7/-8 = -0.87500
y-intercept = 7/1 = 7.00000
Pull out like factors :
-x2 - 5x - 7 = -1 • (x2 + 5x + 7)
Trying to factor by splitting the middle term
2.2 Factoring x2 + 5x + 7
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +7
Step-1 : Multiply the coefficient of the first term by the constant 1 • 7 = 7
Step-2 : Find two factors of 7 whose sum equals the coefficient of the middle term, which is 5 .
-7 + -1 = -8
-1 + -7 = -8
1 + 7 = 8
7 + 1 = 8
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Find the Vertex of y = -x2-5x-7
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens down and accordingly has a highest point (AKA absolute maximum) . We know this even before plotting "y" because the coefficient of the first term, -1 , is negative (smaller than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is -2.5000
Plugging into the parabola formula -2.5000 for x we can calculate the y -coordinate :
y = -1.0 * -2.50 * -2.50 - 5.0 * -2.50 - 7.0
or y = -0.750
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = -x2-5x-7
Axis of Symmetry (dashed) {x}={-2.50}
Vertex at {x,y} = {-2.50,-0.75}
Function has no real roots
Solve Quadratic Equation by Completing The Square
3.2 Solving -x2-5x-7 = 0 by Completing The Square .
Multiply both sides of the equation by (-1) to obtain positive coefficient for the first term:
x2+5x+7 = 0 Subtract 7 from both side of the equation :
x2+5x = -7
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
-7 + 25/4 or, (-7/1)+(25/4)
The common denominator of the two fractions is 4 Adding (-28/4)+(25/4) gives -3/4
So adding to both sides we finally get :
x2+5x+(25/4) = -3/4
Adding 25/4 has completed the left hand side into a perfect square :
x2+5x+(25/4) =
(x+(5/2)) • (x+(5/2)) =
(x+(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2+5x+(25/4) = -3/4 and
x2+5x+(25/4) = (x+(5/2))2
then, according to the law of transitivity,
(x+(5/2))2 = -3/4
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x+(5/2))2 is
(x+(5/2))2/2 =
(x+(5/2))1 =
x+(5/2)
What is the smallest number greater than 1 that is both triangular and square
Answer:
36
Step-by-step explanation:
triangular numbers are
1, 3, 6, 10, 15, 21, 28, 36, .....
square numbers are
1, 4, 9, 16, 25, 36, ..........
the smallest number that is triangular and square is 36
What is the most specific name for the figure?
A(-4a, -2a)
B(-9a, -2a)
C(-5a, a)
D(0, a)
A. Trapezoid
B. Rectangle
C. Square
D. Rhombus
Answer: D
Step-by-step explanation:
The quadrilateral will be a rhombus. Then the correct option is D.
What is the quadrilateral?The definition of a quadrilateral is a planar form with four sides, four vertices, and four angles. Concave and convex are the two primary kinds.
Type of quadrilateral are:
Trapezoid.Rectangle.Parallelogram.Rhombus.Square.Kite.The length of the side CD is given as,
CD² = (0 + 5a)² + (a - a)²
CD = 5a units
The length of the side BC is given as,
BC² = (- 5a + 9a)² + (a + 2a)²
BC² = (4a)² + (3a)²
BC² = 25a²
BC = 5a units
The length of the adjacent sides is equal. Then the quadrilateral will be a rhombus.
Thus, the correct option is D.
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Algebra
U perpendicure
All changes saved
4. Identify the equations as parallel lines, perpendicular lines, or neither.
Equation 1: -2x+5y=3
Equation 2: 2y=5x+1
perpendicular
Neither
parallel
Answer: Neither
Step-by-step explanation:
Which ratio is not equivalent to 3/5 ?
A. 15/20
B.6/8
C.30/50
D.12/20
Answer:
A & B
Step-by-step explanation:
15/20 is not equal
6/8 is not equal
30/50 is equal
12/20 is equal
Hey there!
3/5
= 3 ÷ 5
= 0.60
= 60%
• So, we’re looking for something that’s equivalent to 0.60 or 60%
Option A.
15/20
= 15 ÷ 20
= 15 ÷ 5 / 20 ÷ 5
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option A. could possibly be your equivalent to your fraction
Option B.
6/8
= 6 ÷ 8
= 6 ÷ 2 / 8 ÷ 2
= 3 / 4
= 3 ÷ 4
= 0.75
= 75%
So, Option B. isn’t equivalent because it’s too big and not what we’re looking for!
Option C.
30/50
= 30 ÷ 50
= 30 ÷ 5 / 50 ÷ 5
= 6 / 10
= 6 ÷ 2 / 10 ÷ 2
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option C. could possibly be your equivalent to your fraction.
Option D.
12/20
= 12 ÷ 20
= 12 ÷ 2 / 20 ÷ 2
= 6 / 10
= 6 ÷ 2 / 10 ÷ 2
= 3 / 5
= 3 ÷ 5
= 0.60
= 60%
So, Option D. could possibly be your equivalent to your fraction.
To sum it all up, your answer is:
Option B. 6/8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
How many different triangles can you make if you are given the measurments or two sides an angle that is not between those two sides
Answer:
2.
Step-by-step explanation:
This is called the ambibuous case where 2 sides are given and angle opposite one of these sides.
2 traingles are possible.
pls help and explain im actually confused thxx
Answer:
(2x,2y)
Step-by-step explanation:
Hope this helps!!!
Find the Area. First person that answers this and gets it correct gets brainliest.
Answer:
Step-by-step explanation:
Break up the shape into a trapezoid and rectangle:
Trapezoid area = (Top + Bottom) * Height / 2
= (9 + 20) * (21-16) / 2
= 29 * 5 / 2
= 72.5
Rectangle area = Length * Width
= 20 * 16
= 320
Combining, the total area = 72.5 + 320
= 392.5 in^2
Answer:
A = 392.5 in²
Step-by-step explanation:
The composite figure is made up of a rectangle and a trapezoid.
Calculate the area of the rectangle:
[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=20 \times 16\\&=320\; \sf in^2\end{aligned}[/tex]
Calculate the area of the trapezoid:
[tex]\begin{aligned}\textsf{Area of a trapezoid}&=\dfrac{\text{base}\;a+\text{base}\;b}{2} \times \text{height}\\&=\dfrac{9+20}{2} \times (21-16)\\&=\dfrac{29}{2} \times 5\\&=72.5\; \sf in^2\\\end{aligned}[/tex]
Therefore, the area of the composite figure it the sum of the area of the rectangle and the area of the trapezoid:
[tex]\begin{aligned}\textsf{Total area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of trapezoid}\\&=320+72.5\\&=392.5 \; \sf in^2\end{aligned}[/tex]
Therefore, the area of the composite figure is 392.5 in².
A bike shop has 35 bicycles and tricycles with a total of 81 wheels. How many bicycles and how many tricycles are in the shop?
Answer:
There are 24 bicycles and 11 tricycles in the shop
Step-by-step explanation:
We can make a system of equations to find the answer:
x for bicycles and y for tricycles:
x + y = 35
2x + 3y = 81
2x because bicycles have 2 wheels, 3y because tricycles have 3 wheels, and have set the total to 81 because 81 wheels in total.
Solving, we will find that there are 24 bicycles and 11 tricycles in the shop.
A group of friends wants to go to the amusement park. they have $285.75 to spend on parking and admission. parking is $13.75, and tickets cost $34 per person, including tax. how many people can go to the amusement park?
Answer:
assuming they only have to pay for parking once, 8 friends can go, if each person has to pay for parking and ticket only 5 people can go, Im assuming it'll be 8 for the answer tho I hope I'm right
There are 8 people can go to the amusement park.
What is Unitary Method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Total amount = $285.75
Parking = $13.75
Price of ticket per person = $34.
So, money left after paying for parking
=285.75 - 13.75
= 272
Now, number of people in amusement park
= 272/34
=8
Hence, 8 people can go to the amusement park.
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14. How much interest will you earn if depositing $25,000 to grow continuously at 9%
interest rate for 12 years?
Answer:
Step-by-step explanation:
i think this is the answer
Find the value of x
Tell wether the side lengths form a Pythagorean triple
Answer:
8.49 and No
Step-by-step explanation:
C² - b² = a² (pythagorus rule rearranged for a²)
9² - 3² = a²
81 - 9 = a²
a² = 72
a = 8.49 and no they aren't a triple.
HELPPPPPPPPPPPPPPPPPPP
Answer:
i dont know use the internet
Step-by-step explanation:
this is the right way
WILL GIVE LOTS OF POINTS
Jenny has 9 cars available to rent. Let C be the number of cars she would have left after renting R of them. Write an equation relating C to R. Then graph your equation
9-R= C
hope this helps :)
Rewrite 4.86 x 10^12 in decimal notation.
help pleaseee
Answer:
second one down
4 860 000 000 000
Step-by-step explanation:
count out 12 zeros after the 4 and you will find the one in decimal notation
The decimal notation for the given scientific notation is 4860000000000. (option b)
What is decimal notation?The decimal notation is an alternate method to represent the fractional value. It means that it is the fractional representation using base 10. The fractions can be converted into decimals and vice versa.
Given is a scientific notation, 4.86 × 10¹², we need to convert it into a decimal notation,
4.86 × 10¹²
= 4.86 × 10,000,000,000,000
= 4.86 × 100 × 100000000000
= 486 × 100000000000
= 48600000000000
Hence, the decimal notation for the given scientific notation is 4860000000000. (option b)
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Noah finds some nickels and pennies in his change purse. How many coins does he
have if he has 100 nickels and 120 pennies? How many coins does he have if he has n
nickels and p pennies?
He has 100 + 120 = 220 coins in his purse.
He has n + p coins if he has n nickels and p pennies.
The dot plot below shows the results of a recent patient survey at Brookwood Medical Center. Use
the data to answer the following questions. If necessary, round your answer to the nearest tenth.
Find the mean and median scores.
Answer:
the median is 3.5
Step-by-step explanation:
there are 27 dots 27/2=13.5 therefore the answer is the 13th dot and a half 3.5 :) (i dont know for sure but i think the mean is 3)
The mean is 3 and the median is 3 for this list of numbers.
From the dot pot,
Arrange the number in order:
1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
Now,
Mean = Average of all the values.
Median = Midvalue of the number.
Now,
There are 30 numbers in the list, so the mean is:
Mean = 90/30 = 3
To find the median, we need to find the middle number.
Since there are an even number of numbers in the list, we take the average of the two middle numbers:
The middle two numbers are both 3, so the median is:
Median = (3 + 3)/2 = 3
Therefore,
The mean is 3 and the median is 3 for this list of numbers.
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What is the value of z in the triangle ? Enter your answer in the box . Round your final answer to the nearest hundredth.
Answer:
32.97 inches
Step-by-step explanation:
Given
27 in. is the length one of the legsSolving
cosine function gives the ratio of the adjacent side of the angle and the hypotenuseTake cos35°cos35° = 0.819cos35° = 27/z⇒ 27/z = 0.819⇒ z = 27/0.819⇒ z = 32.97 inchesA pick-up weighing 1.4 t is loaded with 40 bags of cement each weighing 50 kg. What in the total weight of the pick-up and its load.
Answer:
3.4 tonnes
Step-by-step explanation:
Kg --> tonnes = / 1000
50 x 40 / 1000 = 2. 2 + 1.4 = 3.4.
A circle has a circumference of 6. It has an arc of length 1.
What is the central angle of the arc, in degrees?
The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:
6= πd and then divide both sides of the equation by π you get that d = 1.90
To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:
1 = 0.9549θ
Answer:
60
Step-by-step explanation:
1/6 x 360
Central angle is equal to measure of intercepted arc.
60 degrees
Zoe considers the lunch choices as she looks at the menu. What is the probability that she will choose cheese pizza, apple, milk?
Meal: Cheese Pizza, Cheeseburger, Hotdog, Salad
Side: Banana, Apple, Yogurt
Beverage: Milk, Water, Juice
Multiple choices:
1/10
1/21
1/12
1/36
Answer:
1/10
Step-by-step explanation:
There are ten options and Salad is one of them; therefore, the answer would be 1/10.
solve this system of equations using substitution, show your work (ANSWER QUICK PLEASE)
Answer: x=18/5 y=127/5
Step-by-step explanation:
For both equations
1. subtract from both sides
2. divide to find what the variable equals