The given equation x² + 6x - 5 can be written in the form of (x + a)² + b as
(x + 3)² - 14.
What is completing the square in quadratic equations?In math, we can state that the process of "completing the square" is taking a quadratic equation of the form ax² + bx + c = 0 and changing it to write it in the form a(x + p)² + q = 0. Find the roots of a quadratic equation often using this method.
Given quadratic equation is x² + 6x - 5.
To convert it in the form (x + a)² + b, where a and b are numbers.
x² + 6x - 5
x² + 2 × 3x + 3² - 3² - 5 (convert the equation into a perfect square)
(x + 3)² - 9 - 5
(x + 3)² - 14
Hence, the required equation is (x + 3)² - 14.
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The sum of a number and its half is thirty. Find the number
Answer:
20
Step-by-step explanation:
The sum of a number and its half is thirty. Find the number:
the formula would be:
1.5x = 30
divide both sides by 1.5:
1.5x/1.5 = 30/1.5
x = 20
check:
20 = 20
1/2 of 20 = 10
20 + 10 = 30
Answer:
x+0.5x=30
1.5x=30
x=20
The equation 3(2x + 2) = 3x − 15 models the change in water level in a lake in one month. Solve for x, which is change in height in inches.
x = −7
x equals negative seventeen thirds
x = 3
x = 7
Answer:
x = -7
Step-by-step explanation:
Answer:
x=-7
Step-by-step explanation:
Determine whether the relation is a function (explanation please)
A function is defined as a relation where each input value is paired with exactly one output value. The input -1 has 2 outputs, thus the relation is not a function.
If a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5?of the sales price . How much did he pay ?
If a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75
The original price of the item = $825
The off offered by the store = 1/4
The off offered by the coupon = 1/5
Total off = 1/4 + 1/5
= 9/20
Then the selling price = The original price of the item - The original price of the item× (9/20)
= 825 - 825×9/20
= 825-371.25
= $453.75
Hence, if a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75
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33 POINTS & BRAINIEST !! PLEASE BE QUICK!!
The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
The inequality is:
Let the number is x:
-0.96 ≥ 0.3x
0.3x ≤ -0.96
x ≤ -0.96 /0.3
x ≤ -3.2
x ∈ (-∞, -3.2]
As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.
The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x
Thus, the number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.
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Solve the following system of equations
2x -9y = -1
-4x -3y = -19
(See picture attached)
Solution :-
2x - 9y = -1
2x = 9y - 1
x = 9y - 1 / 2 _________ (1)
Now, substitute it here!
-4x - 3y = - 19
-4 (9y - 1 /2) - 3y = -19
(-36y + 4 - 6y / 2) = -19
(-42y + 4 / 2) = -19
-42y + 4 = -38
-42y = -38 - 4
-42y = -42
y = 1
Value of x :
Substituting the value of y that is 1 in this equation. x = 9y - 1 / 2
x = 9(1) - 1 / 2
x = 9 - 1 / 2
x = 8 / 2
x = 4
PLease help me I am about too have a big exam
Answer:
70 square units
Step-by-step explanation:
Since it is half a big rectangle, (10*14)/2=70
please help ill give brainly
Answer:
1. B
2. D
Step-by-step explanation:
2. 26(2)-2
26(2)=52
52-2=50
3. Which number is an irrational number?
A. 5.12
B.
c. -- 1/2
D. -√25
19
V
The number which is an irrational number as required to.ve identified among the answer choices given is; Choice B; √19.
What is an irrational number?
An irrational number, as the name implies is any real number that cannot be expressed as the quotient of two integers (fraction). It follows that such a number cannot be expressed , a/b, where a and b are both integers.
On this note, the number which cannot be expressed in such form is; Choice B; √19.
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The perimeter of a rectangle is 96cm. If the longer side of the rectangle is two times the length of the Shorter side. Find the area of the rectangle
The area of the rectangle will be 512[tex]cm^{2}[/tex] .
let the longer side of the rectangle be "l" and the shorter side of the rectangle be "b".
Hence, the perimeter of rectangle = 2(l+b)
we are given the perimeter =96cm
thus, 2(l+b)=96
l+b = 96/2
l+b =48
also, we are given the condition that the longer side of the rectangle is two times the length of the Shorter side.
Thus, l=2b, substituting this in l+b=48 we get
2b+b=48
3b=48
b=48/3
b=16cm, now substituting this in l=2b,
l=2(16)
l=32cm
area of the rectangle = length x breadth
=l x b
=32 x 16
= 512[tex]cm^{2}[/tex]
What is the difference between perimeter and area?
Area and perimeter are two crucial characteristics of two-dimensional shapes in mathematics. The area of a shape describes the space it occupies, whereas the perimeter describes how far the shape's boundary extends.
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Midpoint formula (3,-8)(5,-2.5)
Answer:
Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.
Midpoint = [(3+5)÷2, (-8+(-2.5))÷2]
= (8÷2, -10.5÷2)
= (4, -5.25)
four minus 7 times a number is equal to 12 minus 3 times the number
Answer:
number is - 2
Step-by-step explanation:
let the number be n then 7 times the number is 7n and 3 times the number is 3n, so
4 - 7n = 12 - 3n ( add 3n to both sides )
4 - 4n = 12 ( subtract 4 from both sides )
- 4n = 8 ( divide both sides by - 4 )
n = - 2
A package falls from an airplane and hits there ground 12 seconds later. How high was the airplane flying?
The plane was flying at a height of 706.32 m .
The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:
Initial formula: v = u + at
The second formula is s = ut + 0.5at2.
The third formula is v2 = u2 + 2as.
Let t stand for the package's flight time, s for the plane's altitude, and u for the packet's initial vertical velocity since it is simply dropped.
Given: t = 12 seconds for the delivery to arrive to the ground
With t = 12 and u = 0 in the second equation of motion, we so obtain
s = 0*t + 0.5*9.81*12² = 706.32 m
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what are the zeros in the problem y = 2(x+3)(x+3)-1
The zeros in the equation y = 2(x+3)(x+3)-1
[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]
This is further explained below.
What are the zeros in the problem?2(x+3)(x+3)-1
Set 2(x+3)(x+3)-1 equal to 0 .
2(x+3)(x+3)-1=0
Solve for x.
Simplify [tex]2(x+3)(x+3)-1[/tex]
[tex]$2 x^2+12 x+17=0$[/tex]
Use the quadratic formula to find the solutions.
[tex]\frac{-b \pm \sqrt{b^2-4(a c)}}{2 a}[/tex]
Substitute the values a=2, b=12, and c=17 into the quadratic formula and solve for x.
[tex]\frac{-12 \pm \sqrt{12^2-4 \cdot(2 \cdot 17)}}{2 \cdot 2}[/tex]
Simplify.
[tex]x=\frac{-6 \pm \sqrt{2}}{2}[/tex]
In conclusion, The final answer is the combination of both solutions.
[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]
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If anybody knows how to do this pls anwser thansdk
Answer:
Either A or B.
Step-by-step explanation:
Each number in the sequence is being added by 6.
So you can use the equation: x+6
The ninth term in the sequence would be 36 because 30+6=36
10(-8-2c) simplify expressions
YOU GET 50 POINTS ANMD BRAINLEST IF YOU ANSWER THIS CORRECTLY
Can someone please help me with this problem?
Find the number that makes the ratio equivalent to 4:5. 28:_
Answer:
7
Step-by-step explanation:4*7=28
Therefore 5*7=35
28:35= 4:5
Your original grades on your exams were: 75, 85, 90, 90,
100, 75, 80, 100, 90.
You retake the exams and now your scores are:
85, 85, 100, 90, 100, 85, 80, 100, 90.
By how many percentage points did you improve
your average score?
Hint: Find the mean of both sets of data. Then
find the difference between the two. Round to
the nearest %.
His grades improved by 2.2 %
What is mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given: Original grades = 75, 85, 90, 90,
100, 75, 80, 100, 90.
And grades after the retake = 85, 85, 100, 90, 100, 85, 80, 100, 90.
So the sum of the original scores = 785.
Thus the percentage can be calculated by 785/ total marks
= 785/ 900 × 100 = 87.2 %
And the sum of the grades after retake= 805
Thus the percentage will become = 805/900 × 100 = 89.4 %
The mean of the first set is 87 and the mean of the second set is 89.
Thus the difference between the two is 2.
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Factor completely.
25 - 9x²
IF YOU CHECK YOU WILL FIND THAT THIS IS A DIFFERENCE OF TWO SQUARES
[tex] = (5 - 3x)(5 + 3x)[/tex]
ATTACHED IS THE SOLUTION
a) Work out
Give
(5 x 10^3) * (9 x 10^7)
your answer in standard form.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(5\times10^3) \times (9\times10^7)}[/tex]
[tex]\mathsf{= (5\times 10\times 10\times 10)\times (9\times 10\times10\times10\times 10\times10\times10\times 10)}[/tex]
[tex]\mathsf{= (5\times 100\times 10) \times (9\times 100\times 100\times 100 \times 10)}[/tex][tex]\mathsf{= (5\times 1,000) \times {(9\times 10,000\times 1,000)}}[/tex]
[tex]\mathsf{= (5,000)\times(90,000\times1,000)}[/tex]
[tex]\mathsf{= (5,000)\times (90,000,000)}}[/tex]
[tex]\mathsf{= 5,000\times 90,000,000}}[/tex]
[tex]\mathsf{= 450,000,000,000}[/tex]
[tex]\mathsf{= 4.5\times10^{11}}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{4.5\times 10^{11}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which critical value is appropriate for a 99% confidence level where n17, is unknown, and the population appears to be normally distributed? question content area bottom part 1 a. 2.567 b. 2.921 c. 2.898 d. 2.583
The critical value that is appropriate for a 99% confidence level where n17, is unknown, and the population appears to be normally distributed is 2.921 (Option B).
What is the Critical Value in statistics?A Critical value is the value of the test statistic that establishes the upper and lower boundaries of a confidence interval or the statistical significance threshold in a statistical test.
How did we arrive at the above conclusion?
We are given:
n=17, where n is the size of the set
df = n-1; (df means degree of freedom)
= 17-1
df = 16, at 99% confidence level.
Here we apply the t-test because the data is normally distributed.
∝ = 1-99% [Shere ∝ is the significance level)
= 0.01
∝/2 = 0.01/2
= 0.005
hence,
[tex]t_{\alpha /2} ,df[/tex] = [tex]t_{0.005}[/tex], 16 = 2.921. this is derived using the T-Table.
The above leads us to conclude therefore that Option B is correct.
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Every 10th week tamika visits the zoo. every 12th week she visits the local pet rescue. if she visited both this week, how many weeks will it be until she visits both in the same week again?
Answer:
60 weeks.
Step-by-step explanation:
10 and 12 both are divisible by 60, thus itll be 60 weeks before she visits them both in the same week again
jimmys saving account makes 0.7% interest every month if he puts 200 in the account 2 months ago how much is in therenow round to the nearest cent
If jimmys saving account makes 0.7% interest every month if he puts 200 in the account 2 months ago, then 202.81 is in therenow round to the nearest cent
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given
jimmys saving account makes 0.7% interest every month.
The initial deposit is 200 in the account
After two months of time, we need to the find the total amount in account.
0.7% is converted to decimal
0.7/100=0.007
So after two months
A is amount after two months
r is rate of interest
t is time period
[tex]A=P(1+r)^{t}[/tex]
=200(1+0.007)²
=200(1.007)²
=202.8
Hence 202.8 is there now in Jimmys savings accout
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Find the dividend. ___ ÷ 22 = 1.9
4,180
418
41.8
4.18
Answer:
x = 41.8Step-by-step explanation:
Find the dividend. ___ ÷ 22 = 1.9
4,180
418
41.8
4.18
x : 22 = 1.9
x = 22 * 1.9
x = 41.8
Answer:
x = 41.8
Step-by-step explanation:
Solve this equation -4(X-26)=-200
Answer:
x = 76
Step-by-step explanation:
First, distribute -4:
-4x + 104 = -200
Isolate x:
-4x = -200 - 104 = -304
x = -304/-4 = 76
w = 2x squared + 1
workout the value of w when x = -3
Answer:
-35
Step-by-step explanation:
w = 2x^2 + 1
= (2 x -3)^2 +1
= -6^2 + 1
=-36 + 1
= -35
The function $d(t)=300,000t$ represents the distance (in kilometers) that light travels in $t$ seconds.
a. How far does light travel in 15 seconds?
kilometers
b. How long does it take light to travel from the Sun to Earth?
Between
seconds and
seconds.
The distance of the light travels in 15 seconds is 4500000 kilometers.
How to illustrate the information?It should be noted that a function is simply used to illustrate the relationship between the variables that are given.
In this case, the function is given as d(t) = 300000t. Therefore, it should be noted that the distance of the light travels in 15 seconds will be:
d(t) = 300000t
where t = 15
d(t) = 300,000 × 15
distance = 4,500,000 kilometers
The distance is 4500000 kilometers.
Note that the second question wasn't written properly and hence can't be solved.
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4x+3y
Please help me or im going to have a F all year
The values of x and y in the system of equations are x = 1 and y = 2
What are linear equations?Linear equations are equations that have constant average rates of change.
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
4x + 3y = 10
y - x = 1
Make y the subject in the second equation, by adding x to both sides of the equation
y - x + x = x + 1
This gives
y = x + 1
Substitute y = x + 1 in 4x + 3y = 10
4x + 3(x + 1) = 10
4x + 3x + 3 = 10
Evaluate the like terms
7x = 7
This gives
x = 1
Substitute x = 1 in y = x + 1
y = 1 + 1
Evaluate
y = 2
Hence, the solution for the system of linear equations 4x + 3y = 10 and y - x = 1 are x = 1 and y = 2
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Possible question
Solve for x and y in the following system of equations
y - x = 1
4x + 3y = 10