The solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
How to Find the Solutions to a Quadratic Equation?Given the quadratic equation, -9x² + 49 = 0, we can factorize to find the roots (the values of x) as shown below:
-9x² + 49 = 0
-(9x² - 49) = 0
Divide both sides by -1
-(9x² - 49)/-1 = 0/-1
9x² - 49 = 0
9x² - 49 + 49 = 0 + 49
9x² = 49
Divide both sides by 9
9x²/9 = 49/9
x² = 49/9
Take the square root of both sides
√x² = √(49/9)
x = ±7/3
Therefore, the solutions to the quadratic equation, -9x² + 49 = 0, are: C. x = 7∕3, –7∕3.
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In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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Create and solve a proportion: to find the cost of 4 hamburgers if 5 hamburgers cost $21.98.
Answer:
4/x = 5/21.98 ; x=17.584
Step-by-step explanation:
subes la x al otro lado , multiplicas el 21.98 con el 4 y luego lo divides entre 5, así resulta q x es igual a 17.584
Answer:
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Select all figures that have at least one line of symmetry.
Answer:the heart and planet are the only ones
Step-by-step explanation:
the clover looks like maybe but the stem is curved. the planet the line goes verticle through the rings
The sum of three consecutive numbers is 33 more than the smallest of the numbers. Find
the numbers.
Answer:
15, 16 and 17
Step-by-step explanation:
Consecutive numbers mean numbers that are separated by 1 from each other. For example 5, 6 and 7 are three consecutive numbers and 5 is the smallest
Let the smallest number be x
Then the next consecutive number is x + 1
The next one after that is x + 2
Sum = x + x + 1 + x + 2 = x + x + x + 1 + 2 = 3x + 3
We are told that this sum is 33 more than the smallest number x
So 3x+3 = x + 33 Subtract x from both sides
3x - x + 3 = x + 33 -x
==> 2x + 3 = 33
Subtract 3 from both sides
==> 2x + 3 - 3 = 33 -3
==> 2x = 30
Divide both sides by 2
==> 2x/2 = 30/2
==> x = 15
So the smallest number is 15 and the three numbers are 15, 16 and 17
Verify by adding 15+16 +17 = 48
15 + 33 = 48 so consistent
A: The three consecutive numbers are 15, 16, 17.
Explanation:
Let x, y, z be the numbers.
x + y + z = x + 33
y = x + 1
z = x + 2
We will solve this system of equations using the substitution method.
x + x + 1 + x + 2 = x + 33
x + x + x - x = 33 - 1 - 2
2x = 30
x = 15
y = 15 + 1 = 16
z = 15 + 2 = 17
Solving for x + y + z = x + 33:
15 + 16 + 17 = 15 + 33
48 = 48
A: 15, 16, 17.
How many milliliters of a 28% sugar Solution do we need to mix with 75 milliliters of a 10% sugar solution so that the resulting mixture is a 13% sugar solution?
We need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.
Let the amount of 28 % sugar solution be x ml.
We are given that:
10 % sugar solution = 75 ml
Total solution = 75 ml + x ml
We need the solution to be 13 % sugar solution.
So, we get that:
28 % x + 10 % ( 75 ) = 13 % ( 75 + x )
28 x + 750 = 13 ( 75 + x )
28 x + 750 = 975 + 13 x
28 x - 13 x = 975 - 750
15 x = 225
x = 225 / 15
x = 15
Therefore, we need to mix 15 ml of 28 % of solution to get the resulting mixture as a 13 % sugar mixture.
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Write a rule to describe each transformation.
Transfomation using X and Y co-odrinate points
K(-3,2) , L(-4,3), M(-3,3), N(-1,2) → K'(0,2) , L'(-1,3) , M'(0,3), N'(2,2)
What is a transformation ?
Transformations of co-ordinates can be calculated by taking reference from the original figure to the transformed figure by adding or subtrating the point values depending upon where they have transformed in X and Y co-ordinate.
In the given figure there are 4 points K,L,M,N and they have been transformed to K', L',M',N' each point having X and Y co-ordinate values.
K has moved 3 units right so 0
L has moved 3 units right so -1
M has moved 3 units right so 0
N has moved 3 units right so 2
K(-3,2) , L(-4,3), M(-3,3), N(-1,2) → K'(0,2) , L'(-1,3) , M'(0,3), N'(2,2)
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PLEASE LIST THEM I NEED HELP!
Answer:
{(1,0),(3,0),(0,-3),(-3,0),(-4,-4)}
Step-by-step explanation:
This is all I could get from the cropped out picture.
Please show me how to solve this: Katie and Tara are making crafts for their school's craft fair. For every 7 Tara makes, Katie makes 9. If they made a total of 240 crafts, how many did each girl
make?
Answer:
Tara makes 7x =7*15 = 105 crafts and Katie made 9x = 9*15 = 135 crafts.
Step-by-step explanation:
Crafts tara and katie make resoectively are in the ratiob 7:9. Let's say 7x and 9x.
Now,
7x + 9x = 240
so, x = 240/16
so, x = 15
A study was performed with a random sample of 5 people from a certain city. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
High sample size is typically crucial in order to be able to draw generalizations from a sample, aside from avoiding bias. Since the sample size is modest, it will thus be possible to draw general conclusions about the study utilizing a larger sample, in my opinion.
The size of the sample has a significant impact on whether an experiment is legitimate. The central limit theorem states that as sample size rises, the sample mean approaches the population means value.
Because of this, generalizing from just five samples regarding a population of city dwellers won't produce a result that can be generalized.
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Juan and Mahdi are to run a race, but Juan can run 18 meters per second, whereas Mahdi can run 6 meters per second. If Mahdi has a 228 -meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? Round your answer to the nearest whole number.
Answer:
19 seconds
Step-by-step explanation:
You want to know the time it takes for Juan, running 18 m/s, to overtake Mahdi, running 6 m/s, if Mahdi has a 228 meter head start.
Closing timeThe time to close the gap between the runners will be ...
time = distance/speed
time = (228 m)/(difference in speeds) = (228 m)/(18 m/s -6 m/s)
time = (228 m)/(12 m/s) = (228/12) s = 19 s
It will take Juan 19 seconds to catch Mahdi.
__
Additional comment
The fastest human runner will not exceed 12.3 meters per second, especially over a 300+ meter distance.
Solve x/4>_-1 and -4x-4<_-3 and write the solution in interval notation. If there is no solution, type the no solution symbol.
The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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Directions: Write the following in set-builder notation. Input your answer inside the box provided for each given. Do not put a space in between symbols in your answer. Follow the format of the given example below.
1. A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
2. E is the set of letters in the word “notation”.
Answer:
1. A = {x:x is the set of natural number <= 10}
2. E = {x:x is the set of natural number <= 8}
√58 what would be the answer to this?
The square root of 58 is around 7.6
The entire number is, 7.61577310586...
Line segment AB has a midpoint M. The coordinates of point A are (-5,8) and the coordinates of point M are (-1,-3) what are coordinates of point B
Answer: (-4,7)
Step-by-step explanation:
4x-6*x=238
solve for x
Answer:
x=-119
Step-by-step explanation:
[tex]4x-6x=238[/tex]
[tex]-2x=238[/tex]
[tex]\frac{-2x}{-2}=\frac{238}{-2}[/tex]
[tex]x=-119[/tex]
Evaluate the expression:
2
3
+
6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathsf{\dfrac{2}{3} + 6}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{6\times3}{3\times1}}[/tex]
[tex]\mathsf{= \dfrac{2}{3} + \dfrac{18}{3}}[/tex]
[tex]\mathsf{= \dfrac{2 + 18}{3 - 0}}[/tex]
[tex]\mathsf{= \dfrac{20}{3}}[/tex]
[tex]\mathsf{= 6 \dfrac{2}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{20}{3}\ or\ 6 \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Solve for X
A- 68
B- 2
C- 17
D- 34
Answer:
The value of x = 17
Step-by-step explanation:
=> 4x + 2 = 70°
=> 4x = 70 - 2
=> 4x = 68
=> x = 68/4
=> x = 17
−12 + −9 = ? I need an answer!
Answer: -21
Step-by-step explanation:
What is 6.4% written as a decimal number? 64.0 6.4 0.64 0.064
Answer:
0.064
Step-by-step explanation:
To convert just muiltiply the percent by 100.
just need the second one done please
Answer: 15
Step-by-step explanation:
order all the numbers from least to greatest and then find the one in the middle
Using the slope formula, find the slope of the line through the given points.
(9,4) and (6,7)
Answer:
The slope of the line is -1.
We can find this by using the slope formula, where [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. Substitute in our points; [tex]\frac{7-4}{6-9} =\frac{3}{-3}[/tex]. Remember that a negative in either the numerator or the denominator of a fraction makes the entire fraction negative, so [tex]\frac{3}{-3}=-\frac{3}{3}[/tex] Remember that an identical numerator and denominator is equal to 1. Same rule applies here, except it's negative, so the slope of the line is -1. You can see this in action if you were to use a graphing tool. I recommend checking out desmos graphing calculator.
what is the value of 10 to the power of -16 written as a fraction
Answer: 1e-16
Step-by-step explanation:
Steps
(x)n = (10)-16
=
1
10 x 10 x .... x 10
=
1
10000000000000000
= 1e-16
Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.
complementary angles m < DFG = 48, m < JKL = 42 is value of x .
What is the opposing angle to the above example?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So m < DFG < + m < JKL = 90
Now replace the expressions and solve for x
x + 5 +x - 1 =90
2x + 4 = 90
2x = 90 - 4
2x = 86
x = 43
Now replace x with 43 and find out each angle
m < DFG = x + 5
m < DFG = 43 + 5 = 48
m < DFG = 48
m < JKL = x - 1 = 43 - 1 = 42
m < DFG = 48
m < JKL = 42
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The graph of the curve C with equation y = f(x) is transformed to give
the graph of the curve S with equation y = f(-x) - 5
The point on C with coordinates (8, 3) is mapped to the point Q on S.
Find the coordinates of Q
Answer:
(-8,-2)
Step-by-step explanation:
f(-x) - 5 is horizontally reflected and moved down 5 units from f(x)
So first reflecting we get
(-8,3)
Then moving down 5 units we get
(-8.-2)
if this was helpful pls give me brainliest <3
PLEASE HELP!!! ASAP!! FIND THE DOMAIN AND RANGE OF THEESE GRAPHS
Answer:
Domain: [-2, infinity)
Range: [-4, infinity)
Step-by-step explanation:
There's only one graph I see.
Domain is how far the graph extends on the x axis.
Range is how far the graph extends on the y axis.
Which measurement is closest to the circumference of the circle in square centimeters
Answer:
the measurement of the circumference of a circle is 21
How many times larger is 6.945 × 1010 than 1.5 × 108?
463
216
21.6
4.63
Answer:
The only answer is 46.3. I'm not sure whether or not you mixed up one of the decimals, but this is the only answer out of the others.
I hope this helps.
The number 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸. As a result, option A is right and the other choices are false.
What is a Fraction?A fraction is a number that, when stated mathematically, designates a component of a whole. A fraction is a portion or division of any whole, which could be any number, a specific sum, or an actual object.
The horizontal bar known as the fractional bar divides the numerator and denominator of every fraction into these two halves.
There are several types of fractions, some of them are :
Proper fractionImproper fractionUnit fractionMixed fractionEquivalent fractionAccording to the question,
(6.945 × 10¹⁰) / (1.5 × 10⁸)
= 463
Hence, it is concluded that 6.945 × 10¹⁰ is 463 times more than 1.5 × 10⁸.
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If anyone can help me to solve this!!
Math
The product of 84.12 and which number will have three decimal places?
The product of 84.12 and 19.3 will have three decimal places.
Here, we are given a number 84.12. As we can see this number has 2 decimal places. We need to find a number such that when it is multiplied by 84.12, the result has 3 decimal places.
Let us look at each option one by one,
1. 4.22
4.22 has 2 decimal places and hence if we we multiply it by 84.12, it will give us 4 decimal places. Thus, it is not the correct option.
2. 10.51
Again, 10.51 has 2 decimal places and hence if we we multiply it by 84.12, it will give us 4 decimal places. Thus, it is not the correct option.
3. 14.163
14.163 has 3 decimal places and hence if we we multiply it by 84.12, it will give us 5 decimal places. Thus, it is not the correct option.
3. 19.3
19.3 has 1 decimal place and hence if we we multiply it by 84.12, it will give us 2 decimal places. Thus, 19.3 is the correct option.
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Your question was incomplete. Check for full content below-
The product of 84.12 and which number will have three decimal places? 4.22
10.51
14.163
19.3
((12-4)(3-2))^2 + square root of 64
Answer: 72
Step-by-step explanation: First step that I did was to subtract 12 and 4 to get 8. I then subtracted 3 and 2 to get 1. Then since 8 and 1 are in the parenthesis, I multiplied 8 and 1 to get 8. 8 to the 2nd power then comes out to 64. 64 adding the square root of 64 which is 8 then comes out to 64 plus 8 because the square root of 64 is 8. 64 plus 8 equals 72.