Answer:
-4.3
Step-by-step explanation:
Solve each equation by completing the square.
X^2 +2x-5=0
N^2-20n+2=4
Step-by-step explanation:
x² + 2x - 5 = 0
that is the same as
x² + 2x + 1 = 6
(x + 1)² = 6
x + 1 = ±sqrt(6)
x = -1 ± sqrt(6)
x1 = -1 + sqrt(6)
x2 = -1 - sqrt(6)
n² - 20n + 2 = 4
this is the same as
(n - 10)² = 102
n - 10 = ±sqrt(102)
n = 10 ± sqrt(102)
n1 = 10 + sqrt(102)
n2 = 10 - sqrt(102)
The denominator of a fraction is 8 more than its numerator. If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2. Find the fraction
pleases help as soon as possible..thank you so much
Answer:
The fraction is 13/21.
Step-by-step explanation:
The denominator of a fraction is 8 more than its numerator.
Let x be the numerator: x
So the denominator is: x + 8
[tex]\frac{x}{x + 8}[/tex]
If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 1/2.
It will become:
[tex]\frac{x - 1}{x + 8 + 3} = \frac{1}{2}[/tex]
[tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex]
Now, by using cross multiplication, multiply (x - 1) by 2 and (x+11) by 1.
It will become:
2x - 2 = x + 11
Now transpose and combine the same values. Make sure to change the integer sign. If the integer is positive, change it to negative when you transpose it.
2x - x = 11 + 2
x = 13
So the value of x is 13. Now to check if it is correct. Go back to the equation([tex]\frac{x - 1}{x + 11} = \frac{1}{2}[/tex])
Put the value of x in it.
[tex]\frac{13-1}{13+11} = \frac{1}{2}[/tex]
[tex]\frac{12}{24} = \frac{1}{2}[/tex]
12/24 is equivalent to 1/2 so that is correct.
Now, to find the main fraction. Go back to the original equation which is;
([tex]\frac{x}{x + 8}[/tex])
Put the value of x.
[tex]\frac{13}{8 + 13}[/tex]
= 13/21
Not a verified expert but I put much effort to answer your question. Hope it helps:)
28. Overhead Projectors Your teacher draws a circle on an overhead projector.
The projector then displays an enlargement of the circle on the wall. The circle
drawn has a radius of 3 inches. The circle on the wall has a diameter of 4 feet.
What is the scale factor of the enlargement?
a
A scale factor is a factor that can be used to either increase or decrease the size of a given figure. Therefore, the scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
Scale drawing is a type of drawing that requires the use of a factor to either enlarge or reduce the size of a given figure. The factor required is called a scale factor. It can be expressed as:
scale factor = [tex]\frac{length of side of image}{length of side of object}[/tex]
In the given question, the radius of the circle drawn is 3 inches, while that on the wall has a diameter of 4 feet.
Thus;
diameter of circle = 2 * 3
= 6 inches
But;
1 feet = 12 inches
So that;
x = 6 inches
⇒ x = [tex]\frac{6}{12}[/tex]
= [tex]\frac{1}{2}[/tex]
x = 0.5 feet
Thus, the diameter of the circle is 0.5 feet.
So that;
scale factor = [tex]\frac{0.5 feet}{4 feet}[/tex]
= 0.125
scale factor = [tex]\frac{1}{8}[/tex]
The scale factor of the enlargement is [tex]\frac{1}{8}[/tex].
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The first term of a geometric sequence is -2 and the common ratio is 3, What is the sixth term of the sequence?
Also, Write the Recursive Rule fo the seqeunce from above ^
Answer:
a₆ = - 486
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = - 2 and r = 3 , then
a₆ = - 2 [tex](3)^{5}[/tex] = - 2 × 243 = - 486
The recursive rule allows a term in the sequence to be found by multiplying the previous term by the common ratio, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] with a₁ = - 2
7. Write an inequality that matches the graph shown.
Step-by-step explanation:
first, we define the line.
the slope is -3 (as for every increase of x by 1 unit, y changes by -3 units, which makes the slope -3/1 = -3).
the y-intercept is 2.
so, the line is
y = -3x + 2
now the graph shows that we need to define all y values that are below (and that means smaller than) the result values of the line function.
the line is not included.
therefore the inequality is
y < -3x + 2 or 3x + y < 2
47-?=50-35 please help
Answer:
x = 32
Step 1: Solve the right-hand side of the equation.
47 - x = 50 - 35
=> 47 - x = 15
Step 2: Subtract '47' from both ends.
=> 47 - x = 15
=> -x = 15 - 47
Step 3: Solve for x.
=> -x = -32
=> x = 32.
Hoped this helped.
What is the answer? I have looked and there is no question that is close to mine.
Answer:
Since there is a right angle, this is a right-angled triangle and we can solve for x using Pythagoras Theorem that goes [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse (longest side of the triangle).
In this case, x would be the c.
Substitute in values of a and b:
[tex]10^2+10^2=c^2[/tex]
[tex]c^2=200[/tex]
[tex]c=\sqrt{200}[/tex]
[tex]c=10\sqrt{2}[/tex] (Option A)
what is |-9| i need help
Answer:
9
Step-by-step explanation:
absolute value makes everything positive. for example |-3| = 3 and if its already positive it stays positive, for example |5| = 5
In carbon dioxide molecules, for every 2 oxygen
atoms there is 1 carbon atom. How many oxygen atoms
combine with 50 carbon atoms to form carbon dioxide
molecules?
Answer:
100 oxygen molecules simple math
Which ordered pair is NOT in the solution set of −2x + 3y ≥ 12?
A. (-3,5)
B. (-5,0)
C. (0,6)
D. (-5,3)
Answer:
B
Step-by-step explanation:
The ratio of the number of baskets made by Salem to the number of baskets made by Khaled is 3 to 4. Salem made 12 baskets. How many baskets did Khaled make?
Answer:
Khaled made 16 baskets.
Step-by-step explanation:
3 12
-- = ---
4 x
12 / 3 = 4
4 x 4 = 16
x = 16
3n + 75 = 50 + 2n what does the n equalin the equation
Answer:
n= -25
Step-by-step explanation:
Answer:
-25
Step-by-step explanation:
Move 2n to the other side to subtract it 3n-2n=n and move 75 to the other side to balance the equation 50-75=-25 so n=-25
A map was made with a scale in which 3 inches represents 450 miles. The actual distance between two cities is 1,350 miles. What is the distance between the same two cities on the map?6 inches
Answer:
Step-by-step explanation:
(450 miles/3 inches) = 150 miles/inch
(1,250 miles)/(150 miles/inch) = 8.3333 inches
When the actual distance between two cities is 1350 miles the distance between the same cities on the map is 9 inches.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
On scale 3 inches represents the actual distance = 450 miles.
To find the distance on scale when actual distance = 1350
Since, 3 inches = 450 miles
1 inch = 450 / 3 = 150 miles
150 miles = 1 inches
1 mile = / 1/ 150 inches
1350 miles = 1350 / 150 inches = 9 inches
The required distance on scale is 9 inches.
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6.0 x 10^6 in scientific notation
Answer:
6,000,000
Step-by-step explanation:
the amount of 0's you add is one less than the exponent listed (for example, the exponent here is 6, so add 5 0's)
Enter the percent as a fraction. Then enter the fraction in simplest form.
Answer:
1/25
Step-by-step explanation:
Divide both the numerator and denominator by 4 to simplify it. That would get you 1/25
Which is not a way to write the answer to this problem?
Answer:
D. 887 ÷ 43 ≈ 21
Step-by-step explanation:
a
Kenny took a total of 10 quizzes over the course of 2 weeks.
How many weeks of school will Kenny have to attend this quarter
before he will have taken a total of 45 quizzes?
weeks
Helppp <3
Answer:
he would do 9 weeks of school
Step-by-step explanation:
count by fives
The quotient of a number x and 4 is at most 5.
Answer:
x ÷ 4 ≤ 5
Step-by-step explanation:
Need help with this pls asap
Answer:
x=3-2i
Step-by-step explanation:
According to my calculations, this should be good
AYOOOO HELP!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
Value of x= `
4x+5y-6z =2
x= (2-5y+6z) divided by 4
For example : if x is 2.5
2.5 = 2 - 5x2 + 6x3
does anyone know the answer to this? thank you!
Answer:
[tex] \alpha = \frac{arc \: length}{radius} \\ arc \: length = \alpha \times radius \\ = 50 \times \frac{\pi}{180} \times 7 \\ arc \: length = 350 \times \frac{\pi}{180} \\ = 1.94 \times \pi \\ = 6.1metre \\ thank \: you[/tex]
Helppppppppppp asapppppppppppp
Answer:
Step-by-step explanation:
First, you have to use the law of cosines which is c² = a² + b² - 2abcosФ where Ф is the angle measure between sides a and b. So, just plug-in a = 10, b = 12, and Ф = 72 into the equation and you will get (I won't show all the calculations):
c = 13.0321
Then plug that into the area formula to get:
(0.5)(10)(12)(0.225496911)
Which is about:
13.53
I need help with this what is 4x58
Answer:
232
Step-by-step explanation:
4*58=232
PLEASEEEEEEE HELP ME GUYS!!
Select the function that is odd.
A. f (x) = sin (x)
B. f (x) = cos (x) + sin (x)
C. f (x) = cos^3 (x)
D. f (x) = sin^2 (x)
Carswell has a spinner with three equal sections labeled Stop, Go, and Wait.
He spins the spinner three times. How many outcomes are in the sample space of the experiment?
The outcomes are
(Stop,Go,wait)(Stop,Stop,Stop)(Stop,Go,Stop)(Stop, wait,Stop)(Stop,Stop,Wait)(Wait,Stop,Stop)(Go,Stop,Stop)(Go,Go,Go)(Wait,Wait,Wait)Total Outcomes=3×3=9
x/7 + y/5 =12
2x/5 - y/7 =9
Answer:
x = 35 ,y = 35
Step-by-step explanation:
x = 35
y = 35
GIVING BRAINLIEST
Wynter likes to take the long way to school each morning. He walks 4 blocks south and then 4 blocks west to arrive at the school. Today he is running late and decides go directly to school to save time. (Assume there is nothing obstructing his path.) If one block is 320 feet, how many feet will he travel if he goes directly to school? Round to the nearest tenth of a foot.
Distance travel by Drew = 1,315.21 feet (Approx)
What is distance?Distance is a measure of how far apart two objects or locations are using numbers. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Sometimes, the symbol |AB| is used to represent the distance between two points.
Given:
Total block in north = 3
Total block in west = 3
1 block = 310 feet
Find:
Distance travel by Drew
Computation:
Total distance in north = 3 × 310 = 930 feet
Total distance in west = 3 × 310 = 930 feet
Distance travel by Drew = Total distance in
north? + Total distance in west?
Distance travel by Drew = v9302 + 9302
Distance travel by Drew:
= V864,900 + 864,900
Distance travel by Drew = V1,729,800
Distance travel by Drew = 1,315.21 feet (Approx)
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Use the properties of multiplication to solve.
(4 x 13) x 25
Mrs. Ashton buys journals for the students in her language arts class. She pays $64.48 for all of the journals. If there are 26 students in her class, how much does each journal cost?
Answer:
Each journal costs $2.48
Step-by-step explanation:
Let X be the cost of a single journal.
You can write this equation to represent the problem:
26x = 64.48
(26 times the cost of the journal is $64.48)
Then just solve for x by dividing both sides by 26:
[tex]26x=64.48\\\frac{26x}{26} =\frac{64.48}{26}\\x=2.48[/tex]
Each journal costs $2.48