Let
[tex]x = 6 + \dfrac1{2 + \dfrac1{6 + \dfrac1{2 + \cdots}}}[/tex]
Then
[tex]x = 6 + \dfrac1{2 + \dfrac1x}[/tex]
and solving for x gives
[tex]x = 6 + \dfrac x{2x + 1}[/tex]
[tex]x = \dfrac{13x + 6}{2x + 1}[/tex]
[tex]x(2x+1) = 13x + 6[/tex]
[tex]2x^2 + x = 13x + 6[/tex]
[tex]2x^2 - 12x - 6 = 0[/tex]
[tex]x^2 - 6x - 3 = 0[/tex]
By the quadratic formula,
[tex]x = 3 \pm 2\sqrt{3}[/tex]
but x must be a positive number, so only the positive square root solution is valid.
[tex]x = 3 + 2\sqrt{3}[/tex]
We identify a = c = 3 and b = 2, so a + b + c = 8.
A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?
Enter the correct answer in the box.
Answer:
The scale is 1:18 for the entire room, 1 inch in the diagram for 18 inches IRL
Step-by-step explanation:
12 inches = 1 foot
Convert the feet to inches, then divide both sides of the ratio by the # of inches in the diagram
So for length:
10:(15*12)
10:180
1:18
And for width:
8:12(12)
8:144
1:18
Answer:
18 inches
Step-by-step explanation:
The question asks for scale of inches in the drawing and the actual room, so first convert 15 ft and 12 ft into inches.
1 foot= 12in x 1ft= 12 inches
15 feet= 12in x 15ft = 180 inches
12 feet= 12in x 12ft = 144 inches
The room is 180 inches long and 144 inches wide.
To find the scale, set up a proportion to the drawing to the room.
[tex]\frac{10}{8} =\frac{180}{144}[/tex]
You can see that the scale is 18 inches because to get from 180 to 10, you multiply by 18, and the same thing as 8, you would multiply 8 by 18 to get to 144.
For a given two-digit number, the second digit is 2 more than 5 times the
first digit. Also, 5 times the first digit is 3 more than the second digit. Find
the two-digit number.
Answer:
no solution
Step-by-step explanation:
U=5t+2
5t=u+3
5t=5t+5
t=t+1
0=1
No solution
Ivy bought a bike for $67.82. The sales tax was $4.79. How much money did Ivy spend on the bike before taxes?
Answer: $63.03
Step-by-step explanation:
$67.82 - $4.79 = 63.03
Solve each proportion 3 = 72 – 7
1. 3/7 = 72/x
By cross multiplication we get :
➟ 3x = 72 × 7
➟ x = 72 × 7/3
➟ x = 24 × 7
➟ x = 168
2. m/8 = 8/20
By cross multiplication we get :
➟ 20m = 8 × 8
➟ 20m = 64
➟ m = 64/20
➟ m = 16/5
the domain and range in this graph will be:
a. Domain : all real nums, Range : all real nums
b. Domain : - 4 Range: 2
c. domain: 2 range : 5
Answer:
a.
Step-by-step explanation:
this is a line going from -infinity to +infinity in x and in y direction.
for b or c to be right the function would have to be a single point, as nothing else is valid as value.
indicate which property is illustrated below. 10 x + 11 x=(-10 + 11) x
Answer:
distributive property
Step-by-step explanation:
I ASSUME that you meant to lead the equation with a negative sign.
- 10x + 11x = (-10 + 11)x
A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under
the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer in the box to complete the inequality.
р
Answer:
The answer is <-2
Step-by-step explanation:
Answer: I'm late but here you go
Step-by-step explanation:
the sum of twenty four and forty is nineteen more than a number. what is the number?
im struggling lol
Topic 3: Performance Assessment Form A
Due 11/18/21
Recall the function V that you wrote in Question 1 to represent the volume of the soil in the frame. Choose an online tool or paper to graph the function V
to identify the x-intercepts. List them in order from least to greatest.
0
1
2
3
4
5
3
The x-intercepts are -
, and
Part
Which, if any, of the x-intercepts has meaning in the context of the problem? Explain.
B 1
Ω 6
Roviow progress
Question 3
oro
Back
Next →
Answer:
Suppose, for example, we graph the function
f
(
x
)
=
(
x
+
3
)
(
x
−
2
)
2
(
x
+
1
)
3
.
Step-by-step explanation:
find the slope from the pair of the points
(-3,-4) (1,5)
Answer:
2.25
Step-by-step explanation:
m = 9 / 4 = 2.25
points belong to an increasing, linear function.
Equation: y = 2.25x + 2.75.
BRAINLIEST?
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test.
B. Yes, because it passes the vertical line test
C. Yes becquse it has two straight lines
D. No because it is not a straight line
Answer: A. No because it fails the vertical line test
The graph does not represent function because it fails the vertical line test.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The "function" would pass the vertical line test if the two lines meet at an angle larger than 90 degrees and the base line is horizontal.
Here, the vertical line test indicates that it is invalid.
The "vertical line test" primary consideration whenever it appears in an option. In this instance, failing the vertical line test is defined as all x values having two y values.
Thus, graph does not represent function.
Learn more about Function here:
https://brainly.com/question/12954651
#SPJ2
Hey everyone! Need this question ASAP. Can anybody help me? (Look at photo)
Two relationships are described below: Relationship A: It took 2 people 12 hours to build a deck. It would have taken 3 people 4 hours to build the same deck. Relationship B: Jack earned $24 after 3 hours of work. Then, he earned $40 after 5 hours of work. Which statement is true about these relationships?
Answer:
im pretty sure its b but if its not then i apologise
Christina has these two tiles. Draw a new shape she can create with both tiles. Then name the shape and how many sides the new shape has.
Square and triangle
Answer:
quadangle
Step-by-step explanation:
a square made of triangles and If a triangle is called a triangle, why is a square not called a quadangle?
Squares and triangles can be combined to form a pentagon
The new shape is a pentagon.The shape has 5 sides.The two shapes are given as:
SquareTriangleWhere the base of the square equals the side length of the triangle
When these shapes are combined i.e. when the base of the triangle is merged with the side length of the square, then it forms a pentagon.
See attachment for the image of the new shape.
From the attached image, we can see that the shape has 5 sides
Read more about pentagons at:
https://brainly.com/question/9317617
The number of blocks has 9 in the ones place. The number in the hundreds place is one more than the number in tens place. Those two numbers equal 11. how many blocks are there?
Answer:
659
Step-by-step explanation:
11-1=10;10/2=5;5+1=6;6+5=11
the hundreds place has 6
the tens place has 5
the ones place has 9
659
A runner is 7/8 mile from the finish line. If she can travel 3/8 mile per minute, how long will it take her to finish the race?
Answer:
2 1/3 minutesStep-by-step explanation:
Distance:
d = 7/8 mileSpeed:
s = 3/8 mpmTime:
t = d/st = 7/8 : 3/8 = 7/8 * 8/3 = 7/3 = 2 1/3 minAnswer:
Step-by-step explanation:
Evaluation the following:
A.
[tex] \sqrt{ \frac{32 {y}^{2} }{72 {x}^{2} } } [/tex]
B.
[tex] \sqrt[3]{ \frac{125 {m}^{3} }{36 {m}^{2} } } [/tex]
C. if
[tex] x1 = 2 \: and \: x2 = 1 \\ and \: y1 = 3 \: and \: y2 = - 1[/tex]
then find the value of :
[tex] \sqrt{ \frac{x2}{y2} - \frac{y2}{x2} } [/tex]
Answer:
A. √32y²/72x²= 32y/72x
Step-by-step explanation:
√32y²/72x²= 32²/72²
= 32/72.
B. √125m³/36m²
=4192.6/108
=38.8203.
C. √x²/y²-y²/x²
therefore, x²=1, y²=-1
that is, √1/-1 - -1/1= -1(-)-1=0.
Find the equation of the tangent line at the given point on the following curve.
x² + y² = 25, (-4,-3)
The equation of the tangent line to the point (-4,-3) is y=
There are 13 pieces of chicken at the dinner table. After dinner, only 3 pieces are left. How many pieces were eaten at dinner?
16
8
7
10
Answer:
10
Step-by-step explanation:
13 pieses - 3 pieces = 10 pieces that are eaten
Answer:
10
Step-by-step explanation:
6. Simplify: -7(3x) + 2(3x – 2). What is the value of the expression if x = 4
Answer:
its x
Step-by-step explanation:sus?
If 6 units equal 12 inches, what is the value of 1 unit?
is this linear or not?
Answer:
Linear
Step-by-step explanation:
Answer:
NoStep-by-step explanation:
You have the system with two quadratic equations.
Both equations are of degree two.
This is therefore not linear.
Find the geometric mean between 18 and 7. Write your answer in radical form.
• 3 square root of 14
• 126
• 9 square root of 7
• 128
Answer: Choice A
Work Shown:
[tex]m = \text{geometric mean of x and y}\\\\m = \sqrt{x*y}\\\\m = \sqrt{18*7}\\\\m = \sqrt{9*2*7}\\\\m = \sqrt{9}*\sqrt{2*7}\\\\m = 3\sqrt{14}\\\\[/tex]
answer????plssssssss i will give money
Answer:
62.3538290725
Step-by-step explanation:
Sorry That All I Could Get For You
Answer:
gimme money
Step-by-step explanation:
Expand and simplify the following
√3 (√3 - 1)
√5 (√10 + √2)
Answer:
3 - [tex]\sqrt{3}[/tex]
10+[tex]\sqrt{10}[/tex]
Step-by-step explanation:
[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] - 1) → 3 - [tex]\sqrt{3}[/tex]
[tex]\sqrt{5}[/tex] ([tex]\sqrt{10}[/tex] + [tex]\sqrt{2}[/tex] ) → [tex]\sqrt{50}[/tex] + [tex]\sqrt{10}[/tex] → 2[tex]\sqrt{25}[/tex] + [tex]\sqrt{2}[/tex][tex]\sqrt{5}[/tex] → 2(5)+ [tex]\sqrt{10}[/tex] → 10+[tex]\sqrt{10}[/tex]
Please help!!!
A. (-4,2)
B. (-4,-2)
C. (2,-4)
D. (2,4)
Answer:
A
Step-by-step explanation:
Have a nice day
Plz help me well mark brainliest!!
Answer:
x=-52
1/3x-2/3=-18
multiply both sides by 3
x-2=-54
x=-54+2
x=-52
determine the slope and y intercept and write the equation in slope intercept form
Answer: slope is 2 and the y-intercept is 1 intercept form is y=2x+1
Step-by-step explanation:
If a certian perosn has a mass of 250kg on earth, would that person's mass be on the moon, if the moon's gravity is 1.62m/s2? *
10 points
245kg x 1.62m/s2
245 x 1.62m/s2
It remains the same
The person would be weightless
Answer:
Weight On the Moon: 41.34 kilograms
Step-by-step explanation:
please help me i’ll give brainlist
Answer:
See explanation below
Step-by-step explanation:
1. 0.65 = 65/100
not 65/1000
65/1000 is 0.065. We want 0.65.
2. 0.65 = 65/100 = 13/20
If a ½ gallon of paint covers ⅙ of a wall, continuing at this rate how much paint is needed for the entire wall?
Answer:
3 gallons
Step-by-step explanation:
