Answers
Step-by-step explanation:
well, the starting equation and the target format have been given.
let's do the multiplications and compare the target with the starting information.
from there we see what is different or missing.
x² + 14x + 13 = 0
and
(x - p)² = q
x² - 2px + p² = q
x² - 2px + (p² - q) = 0
now let's compare the different parts :
x² = x²
-2px = 14x
-2p = 14
p = -7
p² - q = 13
-7² - q = 13
49 - q = 13
36 - q = 0
q = 36
so, the square (x - p)² = (x + 7)² is completed when
x² + 14x + 49 = 0
but we have only "+ 13". so we need to add 36 to get 49. but we need to do it on both sides, to keep the equation true :
x² + 14x + 13 + 36 = 36
x² + 14x + 49 = 36
(x + 7)² = 36
just as we calculated already above.
and now this can be solved by pulling the square root on both sides (a quadratic equation has always 2 solutions)
x + 7 = ±6
x1 = 6 - 7 = -1
x2 = -6 - 7 = -13
Related Questions
Round to the nearest cent 6 divided by 2.29
Answers
Answer: $0.38
Step-by-step explanation:
2.29/8=
0.38167=
0.38167=$0.38
write the slope-intercept form of the equation of the line through the given point with the given slope.
through: (-2,-5) and slope= -3
Answers
y = -3x - 11
calculator
A group of friends watched a comedy movie marathon starring a group of comedians. The graph below shows the number of movies watched and the number of hours of sleep the friends had slept between Saturday and Sunday. Each dot represents one of the friends.
First Options:
Increased
Decreased
remained the same
Second Options:
A positive
A negative
No
Third Options:
Numbers of hours of sleep
Genre of the movies
Actors in the movies
Answers
There is no relationship between the number of movies and the number of sleep hours.
What is a relationship?It is always a thing of importance to show data by the use of a scatter plot. The scatter plot must always have two axes. The vertical (y axis ) and the horizontal (x axis). It is always common to plot the independent variable on the x axis and the dependent variable on the y axis.
The scatter plot thus represented shows how one variable is related to another. In this case, we are trying to obtain how the number of sleep hours tend to be related with the number of movies and this has been shown on the scatter plot that is shown in the question above.
It is clear from the statements in the question that the line of best fit would show that as the number of movies remained constant, the number of sleep hours decreased. This now implies that there is no relationship between the number of movies and the number of sleep hours.
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How can I solve 2z+–
4z–2z–2
Answers
Answer:
Step-by-step explanation:
=-4z-2
1/2-3/4 con su procedimiento por favor
Answers
Answer:
-0.25
Step-by-step explanation:
1). When beginning, you need to find the least common multiple (lcm), which would be 2.
2). Divide 3 by 2 leaving you with 1.5.
3). Then divide 1.5 by 2 leaving you with -1/4.
4). Convert -1/4 into a decimal.
5). Final answer -0.25.
Answer: -0.25
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2}-\frac{3}{4}=\\\\ \frac{1*2}{2*2} -\frac{3}{4} =\\\\\frac{2}{4} -\frac{3}{4}=\\\\ \frac{2-3}{4} =\\\\\frac{-1}{4} =\\\\-\frac{1}{4} =\\\\-0.25[/tex]
A rocket flies 10 km vertically, then 20 km at an angle of 15° to the vertical and finally 60 km at an angle of 26° to the vertical. Calculate the vertical height of the rocket at the end of the third stage.
Answers
The vertical height of the rocket at the end of the third stage is 83.2 km.
We are provided that the rocket travels first 10 km vertically up (OA), then the rocket travels for 20 km (AC) at an angle of 15° from point A.
Let rocket travels 'a' distance vertically up(AB) during this,
then, rocket travels for travels for 60 km (CD) at an angle of 26° from point C.
Let rocket travels ' b' distance vertically up (BX) during this.
So,
Total Vertical Height Covered = 10 + a + b
So, According to diagram
In ΔABC
[tex]cos \ 15[/tex]° [tex]= \frac{a}{20}[/tex]
[tex]\\a = 20 * cos 15[/tex]° = 19.32km
In ΔCDE
[tex]cos \ 26[/tex]° [tex]= \frac{b}{60}[/tex]
[tex]\\b = 60 * cos 26[/tex]° = 53.9km
Since,
Total Distance = 10 + a +b
Total Distance = 10 + 19.32 + 53.9
Total Distance = 83.2 km
Therefore, Vertical height of the rocket at the end of third stage = 83.2 km
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HELP ME SOLVE PLEASEEEE
Answers
Answer: It is m<U = 60 and m<V = 120 (x = 20)
Step-by-step explanation:
1. We know that these 2 angles are supplementary, which means both adds up to 180 degrees.
2. So first, we do this:
3x + 2(m<U) = 180
2a. We do this to find m<U
3. We can also notice that 3x is m<U, so substituting m<U with 3x makes sense. 3x + 2(3x) = 180
4. We then simplify:
3x + 6x = 180
9x = 180
5. We will then divide:
x = 20
6. With the new found info, we substitute x with 20:
m<U = 3(20)
m<V = 2(3(20))
7. Doing the math, it becomes:
m<U = 60
m<V = 120
(i) You can add both up if you want to make sure, but it is correct
3[9 - (6-3)] – 10
How do I do this problem?
Answers
Answer: 8
Step-by-step explanation: Use pemdas
3[9 - (6-3)] – 10 : Complete parentheses (6-3)
3[9 - 3] - 10 : Complete equation in parentheses
3[6] - 10 : Multiply 3 and 6
18 - 10 = 8
Answer:
8
Step-by-step explanation:
3[9 - (6-3)] – 10
3 [9 - (3)] - 10
3 (6) - 10
18 - 10
8
This problem is about "order of operations." These are the rules we all agree upon that dictate which order we do mathematical operations. We use the acronym PEMDAS to help remember them:
P - parentheses first, then:
E - exponents (powers, square roots, etc)
MD - multiplication and division (from left-to-right)
AS - addition and subtraction (from left-to-right)
A common tangent is the point at which a line in the same plane as a circle intersects the circle.
Answers
Answer:
the angle made by that line is tangent
h04Y 8 6 2 V -10 -8 -6 U 52 + 6 e 12 -4 -6 -8 -10-
Answers
Answer:
I don't think this is possible to solve,
Step-by-step explanation:
We put 6 lemons in a bag to fill it.
to fill it.
Which of the following numbers of lemons can fill
entire bags?
How do you know?
96, 46, 42, 60, 63, 72, 85
Answers
Use grids to find all the factor pairs for each number
Answers
All the factor pairs are given using the grids:
17 × 1 = 176 × 4 = 426 × 22 = 13237 × 1 = 3729 × 1 = 298 × 6 = 48What are factor pairs?A factor pair is defined in mathematics as a set of two factors that, when multiplied together, yield a specific product.In other words, we multiply a pair of numbers to get a product. In the multiplication statement, for example, 6 7 = 42, 6 and 7 are one of the factor pairs that give us the product 42.So,
17 × 1 = 176 × 4 = 426 × 22 = 13237 × 1 = 3729 × 1 = 298 × 6 = 48(Refer to the grids given below)
Therefore, all the factor pairs are given using the grids:
17 × 1 = 176 × 4 = 426 × 22 = 13237 × 1 = 3729 × 1 = 298 × 6 = 48Know more about factor pairs here:
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Perform the indicated operation.
-10 + 15
a) -25
b) 25
c) -5
d) 5
Answers
Answer: d)
-10 + 15 = 5
Answer:
D. 5
Step-by-step explanation:
-10 + 15 Can be rewritten as 15-10
15-10=5
The answer is 5.
Hope this helps!
Please mark as brainliest if correct!
17
20%
√.5
| -0.5|
Which list shows the values in order from least to greatest?
Answers
Answer:
√.5, 20%, |-0.5|, 17
Step-by-step explanation:
√.5 = -0.5,
20% = 0.2,
|-0.5| = 0.5,
17 = 17
Sole this algebraic expression shown in the picture below:
Answers
The value of x from the expression given is - 5
What are algebraic expressions?Algebraic expressions are expressions composed of variables, terms, factors, coefficients and constants.
They are also made up of mathematical operations such as addition, subtraction, division, multiplication, etc.
Given the expression, let's find the value of x
3(x + 1) = 2(x - 1)
Expand the bracket
3x + 3 = 2x - 2
collect like terms
3x - 2x = -2 - 3
Subtract like terms
x = - 5
Thus, the value of x from the expression given is - 5
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help pls! i dont understand!!
Answers
Answer:
d -2+5
Step-by-step explanation:
Answer:
I think it would be -2 +5
Step-by-step explanation:
Since one of the lines is going from 0 to -2, one number would be negative 2. Then, since the other line is going from -2 to 3 that would be a total of 5 points. I believe the answer would be -2 + 5.
Sorry if it's wrong
Have a good day
CAN SOMEONE PLEASE HELP ME 25 points ITs MATH
Answers
Answer:
64h^24
Step-by-step explanation:
(4h^4)^4 / 4h^-8
4^4 * h^16 / 4h^-8
64h^24
Step-by-step explanation:
as I said already in my answer to the duplicate post :
(4h⁴)⁴ = 4^1×4 × h^4×4 = 4⁴h¹⁶
for exponent of exponent we multiply.
n^-a = 1/(n^a)
1/(4h^-8) = 1/4 × h⁸
and together we get
4⁴h¹⁶ × 1/4 × h⁸ = 4³h²⁴
A bag contains 3 red marbles, 5 blue marbles and 4 green marbles. If
two marbles are drawn out of the bag, what is the exact probability
that both marbles drawn will be red?
+-
Answer:
Submit Answer
Answers
the probability of drawing 2 red marbles from the bag will be 0.0455.
Number of Red marbles = 3
Number of blue marbles = 5
Number of green marbles = 4
Total marbles = 3 + 5 + 4 = 12
Probability of drawing 2 red marbles from the bag will be:
P = 3 / 12 × 2 / 11
P = 6 / 132
P = 3 / 66
P = 1 / 22
P = 0.0455
Therefore, the probability of drawing 2 red marbles from the bag will be 0.0455.
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PLEASE HELP ME WITH MY GEOMETREY WILL GIVE BRAINLIEST.
Answers
m = 0.15 (8.6 - s)
The amount in moles, m, of a reactant s seconds after the start of a chemical reaction is given by
the equation above. Which of the following is the best interpretation of the number 8.6 ?
Answers
The best interpretation of the number 8.6 according to the task content is; The completion time of the reaction.
What is the best interpretation of the number 8.6?It follows from the task content that the number 8.6 as given in the task content can be agreed to be the completion time of the reaction.
This follows from the fact that, at time, s = 8.6, amount in moles, m of the reactants remaining becomes, 0 in which case, the reaction is complete.
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The points B(7,-9), C(7,-2), and D(0, 0) form a triangle. Plot the points then
click the "Graph Triangle" button. Then find the perimeter of the triangle. Round
your answer to the nearest tenth if necessary.
Click on the graph to plot a point. Click a point to delete it.
-109-8
5 6 7
с
9
10
Answers
The perimeter of the triangle formed by the points B(7,-9), C(7,-2) and D(0,0) is 25.68 square units.
Perimeter is defined as the distance or the enclosed path that surrounds the 2-D shapes or polygon. The perimeter of a triangle is the sum of all the three sides of a triangle.
The perimeter of a triangle formed by the points B(7,-9), C(7,-2) and D(0,0) can be determined by finding the distance between two points.
The distance between two points A(x1,y1) and B(x2,y2).
√[(x2-x1)²+(y2-y1)²]
Therefore, BC = √(7-7)²+(-2+9)²
BC = √49
BC = 7 square units.
and CD = √(0-7)²+(0+2)²
CD = √53
CD = 7.28 square units.
and DB = √(7-0)²+(-9-0)²
DB = √130
DB = 11.40 square units.
Therefore, perimeter of triangle formed from given points is BC+CD+DB = 7+7.28+11.40 = 25.68 square units.
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Taylor is buying presents for members of his family. He wants to spend $10 less on his brother then he spends on his sister and six dollars more then twice the amount he spends on his sister on his mother. If taylor has $100 to spend how much does he intend to spend on his brother
Answers
Answer:
the answer is:
$90 ))
Step-by-step explanation:
100 - 10= 90
5. Which equation in point-slope form contains the points (6, 2) and (2, 4)?
O,
O
O
O
y-2=-2(x-6)
y-4=--(x-6)
y-4--2(x-2)
y-2---(x-6)
Answers
Step- by - step
( 6,2) and (2,4)
m= y2-y1/x2-x1
m=4-(2)/2-(6)
m=2/-4
m= - 1/2
y-y1=m(x-x1)
y-2= - 1/2 (x-6)
y-2= - x/2 + 3
y= - x/5 + 5
Reorder terms
y= - 1/2 ( x+5 )
Remove parentheses
y= - 1/2x+5
Point- slope form
y-2= - 1/2 (x-6)
write 1001 in binary form
Answers
Answer:
1111101001
Step-by-step explanation:
Binary 1001 = 9. « Previous (1000) Next (1010) ».
T(0,-2), U(2,-1), V(3,-4) reflected over the x-axis
Answers
We get the reflection of points T, U and V as T' = (0, 2), U' = (0, 1) and V' = (0, 4) over the x- axis.
We are given some coordinates:
T(0, - 2), U(2, - 1), V(3, - 4)
We have to first plot them on a graph.
Now, we have to reflect them over x - axis.
To reflect over x- axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
For point T:
Additive inverse of - 2 = 2
T' = (0, 2)
For point U:
Additive inverse of - 1 = 1
U' = (0, 1)
For point V:
Additive inverse of - 4 = 4
V' = (0, 4)
Therefore, we get the reflection of points T, U and V as T' = (0, 2), U' = (0, 1) and V' = (0, 4) over the x- axis.
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A family pass to the amusement park costs $54. Using the Distributive Property, write an cost in dollars of 8 family passes.
Answers
Carmen is making a strawberry drink. The recipe calls for 5 parts strawberry juice to 3 parts water. Carmen would like to make 64 fluid ounces of the strawberry drink. How many fluid ounces of strawberry juice and water does Carmen need?
----Carmen will need
__ fluid ounces of strawberry juice and
__ fluid ounces of water to make 64 fluid ounces of strawberry drink.
Answers
Answer:960
Step-by-step explanation:
which number produces an irrational number when multiplied by 1/3?
A. 0.166
B. 2
C. 2/3
D. square root of -17
I think its B
Answers
Answer:
Step-by-step explanation:
Your answer is D because the number is irrational to start, and therefore will be irrational if divided by a rational number.
What is the GCF of 72, 90, and 162?
Answers
Answer:
18
Step-by-step explanation:
Prime factorization of the numbers:
72 = 2 × 2 × 2 × 3 × 3
90 = 2 × 3 × 3 × 5
162 = 2 × 3 × 3 × 3 × 3
GCF(72, 90, 162)
= 2 × 3 × 3
= 18
Answer: 18
Step-by-step explanation:
Factors for 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors for 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Factors for 162: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162
Khloe bought snacks for her team's practice. She bought a bag of chips for $2.69 and a 15-pack of juice bottles. The total cost before tax was $39.14. How much was each bottle of juice
Answers
Each bottle of juice is 2.43