Translating the situation to a mathematical sentence, and solving, we find that the solutions are: [tex]x = 5 \pm 3\sqrt{2}[/tex]
The translation of the problem given is:
[tex](x - 5)^2 + 1 = 19[/tex]
Then, solving:
[tex](x - 5)^2 = 18[/tex]
[tex]x^2 - 10x + 25 = 18[/tex]
[tex]x^2 - 10x + 7 = 0[/tex]
Which is a quadratic equation with [tex]a = 1, b = -10, c = 7[/tex]. Then:
[tex]\Delta = (-10)^{2} - 4(1)(7) = 72[/tex]
[tex]x_{1} = \frac{-(10) + \sqrt{72}}{2}[/tex]
[tex]x_{2} = \frac{-(-10) - \sqrt{72}}{2}[/tex]
[tex]\sqrt{72} = \sqrt{9 \times 8} = \sqrt{3^2 \times 2^3} = 6\sqrt{2}[/tex], then:
[tex]x_1 = 5 + 3\sqrt{2}[/tex]
[tex]x_2 = 5 - 3\sqrt{2}[/tex]
The solutions are [tex]x = 5 \pm 3\sqrt{2}[/tex]
A similar problem is given at https://brainly.com/question/13094243
how do you use subsitution for5x+2y=4
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
5*x+2*y-(4)=0
Equation of a Straight Line
1.1 Solve 5x+2y-4 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"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.
In 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 5x+2y-4 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2.00000
y-intercept = 4/2 = 2
Calculate the X-Intercept :
When y = 0 the value of x is 4/5 Our line therefore "cuts" the x axis at x= 0.80000
x-intercept = 4/5 = 0.80000
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 2.000 and for x=2.000, the value of y is -3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -3.000 - 2.000 = -5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -5.000/2.000 = -2.500
Geometric figure: Straight Line
Slope = -5.000/2.000 = -2.500
x-intercept = 4/5 = 0.80000
y-intercept = 4/2 = 2
Please help me this is due please help
Step-by-step explanation:
so levt's label the video games as "P"
if 6P=207.54$
1P= X
1P × 207.54$ = 6P × X
1P × 207.54$ = 6P × X => P eliminates P on the right side
6P 6P. => 6P eliminates 6P on the left side
207.54$ = X
6
X = 34.59$
Step-by-step explanation:
Let the cost of 1 video game = x
6 video games = $207.54
1 video game = x........cross multiply
6x = 207. 54............ divide both sides by 6
x = 34.59
therefore, 1 video game costs $34.59
there years ago Ava lent her sister $400 to buy some clothes. today Ava's sister pay her loan in full with $454. what simple annual interest rate did she pay?
Answer:
4.5% per year
Complete the equation. ( − 4 ) 2 =
Answer:
-16
Step-by-step explanation:
multiply 4x4 and then determine if its negative or positive
If the volume of the cube was 27 (each side length is 3 units), what would the new volume be if each side length of the cube was reduced to 2 units?
clapped
Step-by-step explanation:
Can someone help me with this
-6 + x = -7
+6 +6 add 6 to both sides, 6's cancel out on the left.
________
x = -1, is the answer.
Hope this helps! Let me know if you have any other questions related to this problem. :)
Answer:
x= -1
Step-by-step explanation:
-6+x = -7
x = -7+6
x= -1
A watch worth Rs. 5400 is offered for sale at Rs. 4590 , then the percent of discount offered during the sale is
Answer:
15%
Step-by-step explanation:
4590 = 5400 - D% × 5400
4590 = 5400 - D/100 * 5400
4590 = 5400 - 54D
54D = 5400 - 4590
D = 810 / 54
D = 15%
Dont forget to give me the brainliest.
3 sss, aas, sas, or not enough information
Answer:
AAS
Step-by-step explanation:
I'm pretty sure its this, but im sorry if im wrong!
expand and simpifly 2(x+7) + 3(x+1)
Answer: 5x+17
Step-by-step explanation:
2(x+7) + 3(x+1)
2x+14 + 3x+3
5x+17
Answer:
5x+17
Step-by-step explanation:
expanded:
2x+14 + 3x+3
simplified:
-collect like terms-
2x+3x=5x
14+3=17
So, if the average family earned $4,000 per month, how much would they send back
out to pay debreach month
What kinds of things could you do with that money?
Simplify the radical please I need sleep it's 1 am I wake up at 4
Answer:
[tex]4cba*\sqrt{5bc}[/tex]
Step-by-step explanation:
[tex]\sqrt{4^{2} *5a^{2}b^{2}bc^{2} c }[/tex]
[tex]4cba*\sqrt{5bc}[/tex]
what is the converse of "If you know Spanish, you can join the Foreign Language Club."
Answer:
If you can join the foreign language club then you know spanish.
Giving me brainlest or sth will be appreciated
plz help thxxxxxxxxxxxxxxxxxx
Answer:
slope is positive 2/1
Step-by-step explanation:
Answer:
a) the slope is 2 because the line goes from (4,1) to (5,3)
I d k any of the bonus questions tho sorryyyy
Step-by-step explanation:
1.4×10−5 and 2.8×10−4
Answer:
Step-by-step explanation:
Step one- is solving the left side of the equation using PEMDAS, 1.4x10 = 14
Step two- 14-5 = 9
Step 3 - 2.8 times 10 = 28
Step 4 - 28- 4 = 24
The answer is 9 and 24
In a triangle abc angle a =x and angle b=2x what is the size of angle c
Answer:
∠c = 180 - 3x
Step-by-step explanation:
Triangle interior angles = 180.
Remember this fact:
The sum of the angles of any polygon = (number of sides in the figure - 2)(180)
∠a = x
∠b = 2x
∠c = 180 - 3x
0.4(-1.08) = ?
what is the product?
Answer: -0.432
Step-by-step explanation:
0.4*1.08 would be 0.432 add the negative sign to get -0.432
The product of 0.4 and -1.08 is -4.240.
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
To multiply 0.4 and 1.08, we need to follow few steps
first multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.
0.40
1.08
___________
240
000+
040++
____________
4.240
As there is a negative sign infront if 1.08, we will put minus sign to the product value
So 0.4(-1.08) is -4.240
Hence the product of 0.4 and -1.08 is -4.240.
To learn more on Multiplication click:
https://brainly.com/question/5992872
#SPJ2
What is an equation in point slope form for the line perpendicular to..
Answer:
b
Step-by-step explanation:
And since we're perpendicular to y is equal to 3x plus 9, we know the slope of the two lines that are perpendicular
K times 3 is minus 1, so k is minus 1/3,
Only b and c match. Plug in the point negative 6,5.
The answer is b.
. Ramu took a loan of 50000 rupees from a bank which charges 10% interest, compounded an- nually. He repaid 10000 rupees after one year and 15000 rupees after two years. How much should he pay at the end of three years to settle the loan?
Answer:
= 30,550 rupee owed
Step-by-step explanation:
yr1 = 50000 x 0.10^1 = 5000
5000 - 10000 = 5000 credit from debt.
yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt
yr 3 = 50000 x 1.10^3 = 50 debit from debt
5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =
19500 paid of initial and nothing owed on interest.
50000-19500= 30,500 rupees owed + 50 rupee interest.
= 30,550 rupee owed
The amount he should pay at the end of the three years to settle the loan is; 41,550 Rupees
Compound InterestWe are given;
Investment = 50000 rupees
Annual Interest Rate = 10% = 0.1
Since the interest is compounded annually, then number of times of compounding = 3
Thus;
Amount to pay after 3 years is;
A = 50000(1 + 0.1)³
A = 50000 × 1.1³
A = 66500 Rupees
Now, we are told that he has already paid 10000 rupees after one year and 15000 rupees after two years. Thus, amount he now owes to settle the loan = 66500 - (10000 + 15000) = 41,550 Rupees
Read more on Compound Interest at; https://brainly.com/question/2455673
Help WITH THE MATH PLEASE QUICK
Answer:
Step-by-step explanation:
2x - 3 = 135 {Corresponding angles are congruent}
2x = 135 + 3
2x = 138
Divide both sides by 2
x = 138/2
x = 69
[tex]\small\boxed{\begin{array}{cc} \hline\sf \normalsize {Math \: \: \: Question}\\ \hline\end{array}}[/tex]
=================================
2× - 3 = 135
2× = 135 + 3
2× = 138
× = 138/2
× = 69
=================================
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Run it up hb gotchu w them points
Answer:
C
Step-by-step explanation:
Answer:
This one is C
Step-by-step explanation:
Express each number in scientific notation.
a) 1 300 000 c) 882 500 000
b) 12 500 d) 51 670 000
Answer:
1.3 x 10^6
8.825 x 10^8
1.25 x 10^4
5.167 x 10^7
Step-by-step explanation:
Find the sum.
(1−5q)+2(2.5q+8)
Answer:
14.5q+2
Step-by-step explanation:
Evaluate the expression (ill give brainiest)
Answer:
2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Substitute the given values into the expression
2 ( [tex]\frac{1}{16}[/tex] + ([tex]\frac{1}{4}[/tex] )² ) + 5([tex]\frac{1}{2}[/tex] )
= 2 ( [tex]\frac{1}{16}[/tex] + [tex]\frac{1}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]
= 2 ([tex]\frac{2}{16}[/tex] ) + [tex]\frac{5}{2}[/tex]
= 2 ([tex]\frac{1}{8}[/tex] ) + [tex]\frac{5}{2}[/tex]
= [tex]\frac{1}{4}[/tex] + [tex]\frac{10}{4}[/tex]
= [tex]\frac{11}{4}[/tex]
= 2 [tex]\frac{3}{4}[/tex]
Find the quotient of 902÷27
(It has a remainder)
Answer:
The quotient of 902 divided by 27 equals 33 and the remainder is 11.
Movie tickets now average $9.75 per ticket, but are increasing 7% each year.
What is the growth factor?
Answer:
The Tickets grow approximately ¢68 or $0.68 each year
Step-by-step explanation:
7% of 9.75 = 0.68
A percentage is out of a fraction of 100; 7/100
Hope This Helps!
The line through (-2, 3) with slope 2/3 in point slope form
Answer:
y - 3 = 2/3(x + 2)
Step-by-step explanation:
slope = 2/3
point-slope form --> y - y1 = m(x - x1)
y - 3 = 2/3(x - -2)
y - 3 = 2/3(x + 2)
point slope form of the line is y - 3 = 2/3(x + 2)
Answer:
y - 3 = 2/3(x + 2)
is 3 a rational answer
Answer:
YES!!
Step-by-step explanation:
All rational numbers can be expressed as a fraction whose denominator is non-zero. Here, the given number, 3 can be expressed in fraction form as 3⁄1. Hence, it is a rational number.
Please help. I'll mark the answer as brainliest.
thanks for the points
Step-by-step explanation:
hehe
Please help I have 15 minutes left for my assessment. Thank you!
Answer:
57kg
Step-by-step explanation:
We need to find the length of each piece of metal:
We already know that 2 of them are 6m and 8m and this would be the same for the pieces of metal opposite.
So we have four lengths - 6m, 6m, 8m, and 8m
To find the last length, we need to use pythagoras theory
a² + b² = c² where c is the slanted side, or the diagonal
6² + 8² = c²
36 + 64 = 100
c² = 100
c = √100 = 10
So the five lengths are 6m, 6m, 8m, 8m, and 10m and the total is 38m
If:
1m = 1.5kg
38m = ?kg
We have to multiply both sides by 38
1m × 38 = 38m
1.5kg × 38 = 57kg
So, the total weight of metal in the frame is 57kg
8/7 divided by 5/2?
Answer:
16/35
Step-by-step explanation:
(8/7)/(5/2)
8/7 * 2/5
16/35