Answer:
I’m not entirely sure what the question is asking but...
The spinner has a 1/4 chance of landing on green
with this, being a 12 section game wheel, it means that 3 of the sections are green.
Find the product of all real values of $r$ for which $\frac{1}{2x}=\frac{r-x}{7}$ has exactly one real solution.
Answer:
-14
Step-by-step explanation:
Observe first that $x=0$ is not a solution to the equation since it makes the denominator of $\frac{1}{2x}$ equal to 0. For $x\neq 0$, we may multiply both sides by both denominators and move all the resulting terms to the left-hand side to get $2x^2-2rx+7=0$. Observe that there are two ways the original equation could have exactly one solution. Either $2x^2-2rx+7=0$ has two solutions and one of them is 0, or else $2x^2-2rx+7=0$ has exactly one nonzero solution. By trying $x=0$, we rule out the first possibility.
Considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the solutions of $ax^2+bx+c=0$, we find that there is exactly one solution if and only if the discriminant $b^2-4ac$ is zero. Setting $(-2r)^2-4(2)(7)$ equal to 0 gives $4r^2-4(14) = 0$. Add 4(14) and divide by 4 to find $r^2=14$. The two solutions of this equation are $\sqrt{14}$ and $-\sqrt{14}$, and their product is $\boxed{-14}$.
The value of r from the given equation is r=(2x²+7)/2x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is [tex]\frac{1}{2x}=\frac{r-x}{7}[/tex].
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
By cross multiplication, we get
7=2x(r-x)
7=2rx-2x²
2rx=7+2x²
r=(2x²+7)/2x
Therefore, the value of r from the given equation is r=(2x²+7)/2x.
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The expansion of (1 + 4x)5 is
Answer:
5+20x
Step-by-step explanation:
multiply 5 to 1 and 4x respectively
The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70
Answer:
d = 245Step-by-step explanation:
d is directly proportional to the square of a speed v
d = av²
5 = a•10²
5 = 100a
a = 0.05
d = 0.05v²
d = 0.05•70²
d = 0.05•4900
d = 245
the cost of cementing a wall 8 feet wide and 24 feet long at 14.40 a square yard is
will mark brainlist
Answer:
$307.20
Step-by-step explanation:
8×24=192
Convert 192 square feet to square yards, which is 21.3333
Then multiple: 21.333×14.40=307.1999
Then round to the nearest hundredths
The final answer is $307.20
HELP ME PLEASE The student's in Roberto's school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. What are the length and width of the scale drawing in feet
Answer:
Length = 3.2feets ; width = 6feets
Step-by-step explanation:
Given the following :
Actual dimension of Mural:
8feets by 15feets
Scale drawing ratio of Mural :
2feets : 5feets
This means :
2 Feets on paper equals 5 Feets of actual drawing:
Therefore, with actual dimension of Length = 8feets ;
Length of scale drawing = (2/5) * 8 = 3.2feets
Actual dimension of width 15feets ;
Width of scale drawing = (2/5) * 15 = 6 Feets
Pls answer this urgently
Answer:
The pic there has a step by step explanation
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[tex]\frac{(3^-2)^2 * (5^2)^-3 * ( t ^-3)^2 }{( 3^-2) ^5 ( 5^3) ^-2 ( t ^-4)^3}[/tex]
[tex]= \frac{\frac{1}{1265625^t12} }{1}[/tex]
[tex]= \frac{\frac{1}{992640625^t6} }{1}[/tex]
[tex]= \frac{992640625^t6}{1265625}[/tex]
[tex]= \frac{922640625tttttt}{1265625}[/tex]
[tex]= 729t^6[/tex]
Answer : [tex]729t^6[/tex]
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If this helped you, could you maybe give brainliest..?
❀*May*❀
Find the solutions to $x^2 + 64 = 0.$[tex]Find the solutions to $x^2 + 64 = 0.$[/tex]
Answer:
x=8i,\:x=-8i
Step-by-step explanation:
x^2+64-64=0-64
x^2=-64
x=\sqrt{-64},\:x=-\sqrt{-64}
x=8i,\:x=-8i
Evaluate 2^2⋅4^3=
Your answer
Answer:
256
Step-by-step explanation:
First, handle the exponent:
2²=4 (2*2=4) and 4³=64 (4*4=16*4=64)
Now multiply those two outcomes:
4*64=256
This equation is also known as 4⁴
It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in minutes. If the book has 300 pages, it will take him minutes to read it.
Answer:
a)45min
b)900min
Step-by-step explanation:
We were told that it takes Matt 3 minutes to read one page in a book.
It implies that 3minutes = 1page of the book
Then he continues to read at the same pace, he can read 15 similar pages in minutes.
a)Then, he can read 15 similar pages in
15x3 minutes.which is 45minutes.
b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins
Answer: has anyone seen my dad?
A file that is 276 megabytes is being dowloaded . If the downloaded is 16.7% complete how many megabytes have been dowloaded? Round ur answer to the nearest tenth ( can ya please hurry and answer thank you)
Answer: 46.1 megabytes
Step-by-step explanation:
I don’t understand how to solve this. Please help!
Answer:
GH = 16; CH = 12
Step-by-step explanation:
First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.
The right angle is marked.
(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:
GH = GB +BH = 8 + 8
GH = 16
__
(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.
Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.
CH = 12
You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.
__
In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Answer:
[tex] 9.3 + b = 14.5 [/tex]
Step-by-step explanation:
Longest side of ∆ = 2a = 6.2 cm
If the shortest side is, a, and we are told that the longest side is twice the shortest side, therefore, length of shortest side is
The sum of the 3 sides = perimeter = 14.5 cm
Thus,
[tex] a + 2a + b = 14.5 cm [/tex]
Plug in the values of a and b
[tex] 3.1 + 6.2 + b = 14.5 [/tex]
The equation that can be used to find the side lengths is [tex] 9.3 + b = 14.5 [/tex]
Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?
A. 0.3883
B. 0.5937
C. 0.5
D. 0.4063
Answer:
D. P(5+ 6's) = 0.4063
Step-by-step explanation:
Binomial distribution.
For the distribution to be applicable, the experiment must
1. Have a know and constant number of trials
2. Probability of success of each trial remains constant (and known if available)
3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.
4. Independence between trials.
Let
n = number of trials = 25
p = probability of success of each trial = 1 / 6
x = number of successes (0 ≤ x ≤ n) = 5
C(n,x) = number of combinations of picking x identical objects out of n
Applying binomial distribution
P(x,n) = probability of x successes in an experiment of n trials.
= C(n,x) * p^x * (1-p)^(n-x)
For n = 25 trials with probability of success (roll a 6) = 1/6
and x = 5,6,7,8,...25
It is easier to calculate the complement by
P(5+ 6's) = 1 - P(<5 6's)
= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )
1- (
P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961
P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051
P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532
P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883
P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171
)
= 1 - 0.59373
= 0.40626
= 0.4063 (to 4th decimal place)
Which of the following are true statements about the expression 5 + (-5)
1. the expression equals 0.
2. The expression equals 10.
3. The expression describes the number that is 5 to the left of 5 on the number line.
4. The expression describes the number that is 5 to the right of 5 on the number line.
Answer:
[tex]\huge\boxed{\sf The \ expression\ equals \ zero}[/tex]
Step-by-step explanation:
=> 5 + (-5) [ + (-) = - ]
=> 5 - 5
=> Zero
Answer:
The answer is option A-The expression equals 0.
Step-by-step explanation:
The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?
Answer:
(a) (x -3)^2 = -6(y +5.5)
Step-by-step explanation:
The equation of a parabola can be written as ...
(x -h)^2 = 4p(y -k)
where (h, k) is the vertex, and p is the distance from the focus to the vertex.
The vertex is half-way between the focus and directrix, so is ...
(h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)
The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...
-7 -(-5.5) = -1.5
Then the equation for the parabola is ...
(x -3)^2 = 4(-1.5)(y -(-5.5))
(x -3)^2 = -6(y +5.5) . . . . matches the first choice
it’s a 425 mile drive from San Jose to Los Angeles.
it’s about 320 mile Drive from San Jose to Santa Barbara.
write an equation showing that the distance traveled on the first day plus the distance traveled on the second is equal to 425 miles
Answer:
The answer is below
Step-by-step explanation:
The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.
The distance traveled the second day = Distance from Santa Barbara to Los Angeles.
But From San Jose to Los Angeles = 425 mile. Therefore:
Distance From San Jose to Los Angeles = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles
425 = 320 + Distance from Santa Barbara to Los Angeles.
Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile
The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles
The distance traveled the first day + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles
The distance traveled the first day + The distance traveled the second day = 425 miles
What is the slope of the line? x + 3 y = 10 x+3y=10x, plus, 3, y, equals, 10 Choose 1 answer: Choose 1 answer: (Choice A) A 1 3 3 1 start fraction, 1, divided by, 3, end fraction (Choice B) B 1 10 10 1 start fraction, 1, divided by, 10, end fraction (Choice C) C − 1 10 − 10 1 minus, start fraction, 1, divided by, 10, end fraction (Choice D) D − 1 3 − 3 1
Answer:
-1/3Step-by-step explanation:
The standard from of equation of a line written in slope-intercept format is expressed as y = mx+c where c is the slope of the line and c is the y-intercept.
Given the equation of the line x+3y = 10, to get the slope of the line, we need write he equation in standard from first by making y the subject of the formula as shown;
[tex]x+3y = 10\\\\subtract\ x \ from \ both \ sides\\\\x+3y-x = 10 -x\\\\3y = -x+10\\\\Divide \ through\ by \ 3\\\\\frac{3y}{3} = -\frac{x}{3} +\frac{10}{3} \\\\[/tex]
[tex]y = -\frac{1}{3}(x) +\frac{10}{3} \\[/tex]
Comparing the resulting equation with y = mx+c, the slope 'm' of the equation is -1/3
The slope of the line is -1/3.
the correct option is D.
To find the slope of the line given by the equation x + 3y = 10, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.
Let's rearrange the equation to solve for y:
x + 3y = 10
3y = -x + 10
y = (-1/3)x + 10/3
Comparing this equation to the slope-intercept form, we can see that the coefficient of x (-1/3) represents the slope.
Therefore, the slope of the line is -1/3.
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Which of the following can be used to express the total area of a figure?
A. (5)(4x)(3x)
B. 12x^2 + 15x
C. (3x + 4x) (5)
D. 3x (4x + 5)
Answer:
The answer is option BStep-by-step explanation:
The figure above is a rectangle
Area of a rectangle = length × width
From the question
The total length of the rectangle = 3x
The total width of the rectangle = 4x + 5
So the area of the figure is
A = 3x( 4x + 5)
Expand
We have the final answer as
A = 12x² + 15xHope this helps you
PLEASE ANSWER QUICKLY ASAP
Answer:
67°
Step-by-step explanation:
● cos<PQR = adjacent/hypotenus
● cos<PQR = 5/13
● cos< PQR = 0.384
Using a calculator:
● cos^-1(0.384) = 67°
● <PQR = 67°
What is the real part of 4 - 5i
Answer:
5i is an imaginary number
In these questions it contains two parts
real and imaginary parts . thus answer to these questions is 5i
Explanation
Complex Number is the number which contains both real and imaginary numbers i is the specified elements. 5i is an imaginary parts number and 4 is real part number.
Thus we conclude that above statement for the question is correct.
To know more about the complex number
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Between what two consecutive integers on the number line is the graph of the sum sqrt(30) + sqrt(50)?
Answer:
sqrt(30)+sqrt(50) = 12.5482933869171364 which is between m and n 12 and 13
help me please ;))) (yes im very rich that's why I'm giving out lots of points -_- (and brainly ;))
Answer:
(I) 17.25 miles
(ii) 1hr56mins20seconds
(III) 4hrs47mins38seconds
Step-by-step explanation:
(I) read from the lowest distance given
(ii) read from the longest time given
(III) added all times together to get total cycling time
Step-by-step explanation:
here,
shortest distance is 17.25 miles
the longest time is 1:56:20 hrs:mins:secs
total time is 4:47:38
an inch worm is how long in general
Answer:
A inch
Step-by-step explanation:
A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years
Answer:
$6488.19
Step-by-step explanation:
To solve this problem we use the compounded interest formula:
[tex]amount = principal(1 + (r \n))^({n}{t})[/tex]
a = $2600(1+(0.0675/1))¹*¹⁴
a = $6488.19
0.0000458 as scientific notation
Answer:
4.58 * 10 ^ -5
Step-by-step explanation:
0.0000458
Move the decimal 5 places to the right to get a number between 1 and less than 10
00004.58
That will give us an exponent of -5 ( the negative is because we moved it to the right)
4.58 * 10 ^ -5
━━━━━━━☆☆━━━━━━━
▹ Answer
4.58 * 10⁻⁵
▹ Step-by-Step Explanation
The decimal point is moved 5 times to the left, meaning the scientific notation will be negative. Therefore, the answer is 4.58 * 10⁻⁵.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
solve for x 13x + 7 = 5x - 20
Answer:
13x + 7 = 5x - 20
Step-by-step explanation:
SOLVE for X
13x + 7 = 5x - 20
-------------------------
-5x -7
------------------------
8x=-27
x= -3.375 or -27/8
Answer:
x = -27/8
Step-by-step explanation:
combine the x terms. To do this, subtract 5x from both sides. We get:
8x + 7 = -20.
Next, subtract 7 from both sides, obtaining:
8x = -27, or x = -27/8
Please answer this question now
Answer:
54 degrees
Step-by-step explanation:
Measure of arc DCB is 125*2 = 250.
So, measure of arc BAD is 360-250 = 110.
So, measure of arc AD is 110 - 56 = 54 degrees
A train moves at a speed of 90 km/hr. How far will it travel in 36 minutes?
Answer:
(90/60)*36 = 54 km
Step-by-step explanation:
Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?
Answer:
25/4 laps or (6.25 laps)
Step-by-step explanation:
1 lap = 1 1/5 miles
kellyn plans to jog 7 1/2 miles
1 lap
number of laps = 7 1/2 miles x -------------- = 25/4 laps or (6.25 laps)
1 1/5 miles
Solve the equation for x
Answer:
the answer is 5
Step-by-step explanation:
2x/5 - 9 = -7
2x/5 = -7 + 9
2x/5 = 2
2x = 2 * 5
2x = 10
x = 10/2
x = 5
Answer:
x = 5
Step-by-step explanation:
2
--- x - 9 = -7 add 9 both sides
5
2
--- x - 9 + 9 = -7 + 9
5
2
--- x = 2 multiply both sides by 5
5
2
5 * --- x = 2 * 5
5
2x = 10
x = 10 / 2
x = 5
