Answer:
x=[tex]\frac{3}{2}[/tex] and x=[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\sqrt{36x^2-60x+25}=4[/tex]
=> [tex]\sqrt{36x^2-60x+25}^{2} =4^{2}[/tex]
=> [tex]{36x^2-60x+25}=16[/tex]
=> [tex]36x^2-60x+25-16=16-16[/tex]
=> [tex]36x^2-60x+9=0[/tex]
=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}}{2\cdot \:36}\\\\\sqrt{\left(-60\right)^2-4\cdot \:36\cdot \:9}=48[/tex]
=> [tex]x_{1,\:2}=\frac{-\left(-60\right)\pm \:48}{2\cdot \:36}[/tex]
=>[tex]x_{1} = \frac{-\left(-60\right)+48}{2\cdot \:36}\\\\x_{1}=\frac{60+48}{2\cdot \:36}\\\\x_{1}=\frac{108}{72} \\\\\\x_{1}=\frac{3}{2}\\[/tex]
=> [tex]x_{2}=\frac{-\left(-60\right)-48}{2\cdot \:36}\\\\x_{2} =\frac{60-48}{2\cdot \:36}\\\\x_{2}=\frac{12}{2\cdot \:36}\\\\\x_{2}=\frac{12}{72}\\\\x_{2}=\frac{1}{6}[/tex]
What is 55 increased by 10%?
Answer:
10% of 55
=> 10/100 × 55
=> 1/10×55
=> 5.5
55 increased by 10% => 55 + 5.5
=> 60.5
hope that helps ✌
Answer:
Step-by-step explanation:
10% of 55
10/100*55
1/10*55
5.5 <--- That is 10% of 55
55+5.5 = 60.5
If A = 2m + 1 and B 2m2 - 1 + 8m, find an expression that
equals 3 A + B in standard form.
Please help
Answer:
2m² + 14m + 2
Step-by-step explanation:
3A + B
= 3(2m + 1) + 2m² - 1 + 8m ← distribute parenthesis by 3
= 6m + 3 + 2m² - 1 + 8m ← collect like terms
= 2m² + 14m + 2 ← in standard form
Match the system of equations on the left with the number of solutions on the right
Answer:
top to bottom, the answers are b, c, a
Step-by-step explanation:
One way to find the solution to a system of equations is to substitute values in. For the first one,
y=2x+3
y=2x+5,
we can substitute 2x+3 =y into the second equation to get
y=2x+5
2x+3 = 2x+5
subtract 2x from both sides
3 = 5
As 3 is not equal to 5, this is never equal and therefore has no solution
For the second one,
y= 2x+7
y = (-2/3)x + 10
We can plug y=2x+7 into the second equation to get
2x + 7 = y = (-2/3)x + 10
2x + 7 = (-2/3)x + 10
add (2/3)x to both sides to make all x values on one side
2x + (2/3)x + 7 = 10
subtract 7 from both sides to make only x values on one side and only constants on the other
2x + (2/3)x = 3
(6/3)x + (2/3)x = 3
(8/3)x = 3
multiply both sides by 3 to remove a denominator
8x = 9
divide both sides by 8 to isolate x
x=9/8
There is only one value for when the equations are equal, so this has one solution
For the third one
y = x-5
2y = 2x - 10
Plug x-5 = y into the second equation
2 * y= 2*(x-5)
2 * (x-5) = 2x - 10
2x-10 = 2x-10
add 10 to both sides
2x=2x
As 2x is always equal to 2x, no matter what x is, there are infinitely many solutions for this system
Can someone help me pls
Answer:
No solution
Step-by-step explanation:
A solution for a system of equations entails that all variables are the same. In this case, it means that both x and y must be the same.
Looking at the graph, there is no spot where y=3x+3 and 3x-y=2 intersect
To confirm, we can look at the equations. If we make them both equal to y, we can set them equal to each other.
For y=3x+3, this is already set to y. For 3x-y=2, we can add y to both sides and subtract 2 from both sides to get
3x-2=y
3x+3=y
Since the x and y values must be the same, we can say that
3x-2=3x+3
subtract 3x from both sides
-2 = 3
Since -2 is not equal to 3, we can confirm that there are no solutions to this system of equations
Melissa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 59 and costs an additional 0.15 per mile driven. The second plan has an initial fee of 50 and costs an additional 0.20 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?
Answer:
Step-by-step explanation:
Let
x = cost per mile
y = Total cost
Plan 1:
y = 59 + 0.15x
Plan 2:
y = 50 + 0.20x
Equate the total cost of the two plans
59 + 0.15x = 50 + 0.20x
59 - 50 = 0.20x - 0.15x
9 = 0.05x
x = 9/0.05
= 180
x = 180 miles
y = 50 + 0.20x
= 50 + 0.20(180)
= 50 + 36
= 86
y = 86
xpower4 minus 16 bracket b minus c whole power 4
Answer
6372 - power 4
Step-by-step explanation:
a two digit number divided by another two digit number,we get 3.675 what are the numbers?
Answer:
Step-by-step explanation:
I can't get the exact answer you've given, but I can tell you some things about it. The largest number in the denominator is 30 or 31. That's because 31 * 3 is 93 exactly. However the fraction is a problem and will likely push you over 100.
3.675 * 31 = 113 something. So 31 is too big.
The closes I came was 98 / 26 which is 3.769
Determine the x-intercept and the y-intercept for the graph of this equation:
2x - 3y + 36 = 0
QUESTION:- DETERMINE THE X-INTERCEPT AND THE Y-INTERCEPT FOR THE GRAPH OF THE EQUATION.
EQUATION:- 2x - 3y + 36 = 0
STANDARD EQUATION:- y=mx+c
where
m-> slope.c-> Y-INTERCEPTx&y are the coordinates.SO GIVEN EQUATION:- 2x - 3y + 36 = 0
WE CAN SOLVE THIS TO CHANGE IN FORMAT OF STANDARD EQUATION
[tex]2x - 3y + 36 = 0 \\ 2x + 36 =3y \\ y = \frac{2}{3} x + \frac{36}{3} \\ y = \frac{2}{3} x + \frac{ \cancel{36}^{ \: \: 12} }{ \cancel3} \\ y = \frac{2}{3} x + 12 \\ [/tex]
SO :-
[tex]m = \frac{2}{3} \\ y - intercept = 12 \: ans[/tex]
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \frac{2}{3} = \frac{0 - 12}{x - 0} \\ 2x = ( - 12) \times 3 \\ x = \frac{ - \cancel{12}^{ \: \: 6} \times 3 }{ \cancel{2}} \\ x = - 18 \: \: ans[/tex]
Simplify the following expressions:
a) (√3 +√7)^2
b) (√5 -√3)^2
c) (2√5 + 3√2)^2
1.) 10+2√21
2.) 8-2√15
3.) 38+2√10
solution to all the answers:
NUMBER 1:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√3 +√7)^2, then it should look like this: 3 + 2√21 + 7.
=> add the numbers: 10 + 2√21.
NUMBER 2:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (√5 -√3)^2, then it should look like this: 5 - 2√15 + 3.
=> add the numbers: 8 - 2√15.
NUMBER 3:
=> use (a + b)^2 + 2ab + b^2 to expand the expression (2√5 + 3√2)^2, then it should look like this: 20 + 12√10 + 18.
=> add the numbers: 38 + 12√10.
I HOPE THIS HELPED!!
2x(9x-4)-3x(6x-7)=26
Answer: x=2
Step-by-step explanation:
[tex]2x(9x-4)-3x(6x-7)=26\\18x-8x-18x+21x=26\\10x-18x+21x=26\\-8x+21x=26\\13x=26\\x=2[/tex]
Laurie Corporation uses the FIFO method in its process costing system. Department A is the first stage of Laurie Corporation's production process. The following information is available for conversion costs for the month of May for Department A:
Units Work in process, beginning (25% complete with respect to conversion costs) 8.000 Started in May 40,000 Completed in May and transferred to Department B 38,000 Work in process, ending (60% complete with respect to conversion costs) 10.000
How many are the equivalent units of production for conversion costs for the month? O
A. 42,000 units
B. 36,000 units
C. 44,000 units
D. 38,000 units
Answer:
A.
Step-by-step explanation:
42,000 units
The volume of a one is 80 cubic cm what is the volume of the cylinder with the same base and height of the cone
Answer:
240 cubic cm
Step-by-step explanation:
Volume of a cone = 1/3(nr^2h)
volume of a cylinder = nr^2h
n = 22/7
r = radius
The volume of a cone is 1/3 that of a cylinder
to determine the volume of the cylinder with the same parameters as a cylinder, multiply the volume of the cone by 3
80 x 3 = 240 cubic cm
Five years from now peters age will be 2+3 times his current age Identify the equation represent the situation
Answer:
1.5 yrs
Step-by-step explanation:
let the present age=x
x+5=2+3x
3x-x=5-2
2x=3
x=3/2=1.5 years
Answer:
3x + 2 = x + 5.
Step-by-step explanation:
Peter is currently x years old. In 5 years, his age will be x + 5. According to the prompt, Peter's age will be 2 + 3 times his current age, x, which can be represented as 2 + 3x. 2 + 3x is the same age as x + 5, so we can represent it as...
2 + 3x = x + 5
3x - x = 5 - 2
2x = 3
x = 1.5
This means that Peter is 1.5 years old.
Hope this helps!
I need help please I don't understand
Answer:
57.2
Step-by-step explanation:
This is a right triangle so we can use trig ratios.
We are asked to find a side when we know a angle adjacent to that side. And we are given a side opposite of that angle. We can use Tangent to find the side length.
[tex] \tan(40) = \frac{48}{x} [/tex]
Take the reciprocal of both sides.
[tex] \frac{1}{ \tan( 40) ) } = \frac{x}{ 48} [/tex]
Multiply both sides by 48.
[tex] x = \frac{1}{ \tan(40) } \times 48[/tex]
[tex]x = 57.2[/tex]
Please help me to solve these questions as soon as possible. Thank you
1) 6 is a common factor of 36 and y. Find the possible value of y.
A. 25 B. 48 C.57 D. 81
2)Which of the following shows 180 as the product of prime factors？
A. 180=2×90
B.180=2×2×45
C.180=2×2×3×15
D.180=2×2×3×3×15
Answer:
1) B, 48
2) C. 180=2x2x3x15
Step-by-step explanation:
A moving company uses plastic wrap to bundle groups of boxes together. If a portion of plastic wrap that measures 900 inches in length is used to bundle each group of boxes, how many groups of boxes can be bundled using 1500 feet of the same type of plastic wrap?
Answer: 20 boxes
Step-by-step explanation:
First and foremost, we need to know that 1 foot = 12 inches. Therefore, 1500 feet will be converted to inches and this will be:
1500 feet = 1500 × 12 = 18000 inches
Since each group of box requires 900 inches, then the number of group of boxes that can be used in this case will be:
= 18000/900.
= 20 groups of boxes
35x - 11 = 107... fill in the digit on the right side of the equation so that each equation has an integer solution.
Answer:
...=
Step-by-step explanation:
First step to these problems will be to move the -11 to the side with the 107_
That will give us 35x=107_ +11.
Next, we know 35=5 times 7, and be now can say that 107_+11 will be a multipe of 5 and 7 at the same time. If it's a multiple of 5, then it has to end in a five or zero, so the blank can be four or nine. If it has to be a multiple of seven, too, than the only 1070 because that is divisible by 7, whereas 1075 is not.
I hoped you liked this answer. If you have any more questions, you can always ask me!
It should be noted that in the equation 35x - 11 = 107, x will be 3.371.
What's the value of x?To solve the equation 35x - 11 = 107, we can follow these steps:
Add 11 to both sides of the equation to isolate the term with the variable:
35x - 11 + 11 = 107 + 11
This simplifies to:
35x = 118
Divide both sides of the equation by 35 to solve for x:
(35x) / 35 = 118 / 35
This simplifies to:
x = 118 / 35
The result, in decimal form, is approximately:
x ≈ 3.37
Learn more about equation
https://brainly.com/question/2972832
#SPJ2
3. Grace has twice as much money as tad
Together they have $36. How much Money
des Tad have?
Answer:
Tad has 12 dollars and Grace has 24
Step-by-step explanation:
Grace has twice as much, 24 is double 12. So Tad has 12 dollars.
PLEASE HELP AND EXPLAIN!!
Answer:
D
Step-by-step explanation:
This isnt a cartisean coordinate plane so A is wrong. One of our points is at
[tex] - 3 + i[/tex]
Because it coincide with real number 3, and negative imaginary number i.
Conjugates are terms with opposite inverse of terms.
So our conjugates is
[tex] - 3 - i[/tex]
The definition of a circle
Answer:
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)
Explanation:
Oxford dictionary definition
Step-by-step explanation:
a circle is a shape consisting of all points in a plane that are at a given distance from a given point the center
please help me with this question
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The usual glide slope for landing is about 3°. The descent rate here of 0.25 km/min corresponds to 15 km/h. For the slope to be 3°, the forward speed of the airplane would need to be 286 km/h, about 154 knots.
This is not unreasonable for an approach speed for a (very) heavy airplane. Usually, the rate would be a little lower, but we wanted something that would fit on the grid provided.
Find the average rate of change of a function that contains the points (-2,3) and (2,5). -2, -1/2, 1/2, 2
Answer:
The answer is "[tex]\frac{1}{2}[/tex]".
Step-by-step explanation:
Given points:
[tex](-2,3)\\\\(2,5)\\\\[/tex]
average rate=?
[tex]x_1=-2\\\\y_1=3\\\\x_2=2\\\\y_2=5[/tex]
[tex]average\ rate=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{5-3}{2-(-2)}\\\\=\frac{5-3}{2+2}\\\\=\frac{2}{4}\\\\=\frac{1}{2}[/tex]
HELP ASAP LIKE PLEASE
Answer: (3b+2)(b+2)
Step-by-step explanation:
which of the following equations is an example of direct variation?
Answer:
C
Step-by-step explanation:
[tex] \frac{x}{3} [/tex]
Trong các phương trình sau, phương trình bậc nhất một ẩn là:
A. x+x2=0 B.+1=0
C.
x-2=0 D.(x+3)(2x-1)=0
Step-by-step explanation:
hey can I have this question in English write can totally ask your question I don't think that I am doing this for purposes please ask this question and English so I can ask this question please ask this question in English if you I am from India so I don't know this all languages Thank you
What is the area that f this composite figure?
Answer:
Answer of this qn is 96cm^2
Attached Math question document. Find the value to complete this calculation.
To find the missing value divide both sides by -7:
28/-7 = 4
The missing value is 4
Answer= -4
Step-by-step explanation:
negative × negative = positve. therefore if 7×4=28 , then -7×-4=28
Please help me solve this last problem guys
Answer:
[tex]\frac{x+4}{4x-4}[/tex]
Step-by-step explanation:
In this figure, a line through points X and Y will _____
Answer:
D.
Step-by-step explanation:
The line will be a straight line and will go through AB in the center. Therefore, it will be the perpendicular bisector.
The van traveled 120 miles in 7 hours. How long would it take to travel 1400 miles at the same speed? (A) 5/3 hrs (B) 81 2/3 hrs (C) 49/6 hrs (D)24000 hr
Answer:
[tex]81\frac{2}{3}[/tex] hours
Step-by-step explanation:
Hi there!
1) Create a proportion
The van traveled 120 miles in 7 hoursThe van travels 1400 miles in x hours[tex]\frac{7h}{120mi}=\frac{x}{1400 mi}[/tex]
[tex]\frac{7}{120}=\frac{x}{1400}[/tex]
2) Solve for x
[tex]\frac{7}{120}=\frac{x}{1400}[/tex]
Multiply both sides by 1400
[tex]\frac{7}{120}*1400=\frac{x}{1400}*1400[/tex]
[tex]\frac{245}{3} =x[/tex]
[tex]\frac{245}{3} =x[/tex]
[tex]81\frac{2}{3} =x[/tex]
Therefore, it would take the van [tex]81\frac{2}{3}[/tex] hours to travel 1400 miles at the same speed.
I hope this helps!
