The number that we need to add to "complete the square" when solving x² – 14x – 40 = 0 using the method of completing the square is 49.
To solve a quadratic equation using the method of completing the square, we need to add the square of half of the coefficient of the x term to both sides of the equation.
This will convert the left side of the equation into a perfect square trinomial.
Then, we can take the square root of both sides and isolate the variable x.
To solve the quadratic equation x² – 14x – 40 = 0 using the method of completing the square, we need to add the square of half of the coefficient of x to both sides.
The coefficient of x is -14, so half of it is -7.
The square of -7 is 49.
Therefore, we need to add 49 to both sides of the equation to "complete the square".
Now, we have: x² – 14x + 49 = 40 + 49
Simplifying this gives: (x - 7)² = 89
Taking the square root of both sides gives: [tex]x - 7 = \pm\sqrt{89}[/tex]
Adding 7 to both sides gives:[tex]x = 7 \pm\sqrt{89}[/tex]
Therefore, the number that we need to add to "complete the square" when solving x² – 14x – 40 = 0 using the method of completing the square is 49.
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On a number line 1.77 would be located where?
Step-by-step explanation:
1.77 would be closer to 2
Suppose your friend's parents invest $ 10,000 in an account paying 5% compounded annually. What will the balance be after 8 years?
Answer:
A = $14,745.544
Step-by-step explanation:
The equation for compound interest is
A = P (1+i)t
A = final value
P = amount invested (principal) (10000)
i = interest rate, expressed as a decimal (.05)
t = number of years invested (8)
This formula assumes annual compounding.
Plugging in what we know.
A = 10000(1.05)^8
A = 10000 (1.47745544)
A = $14,745.544
Help me plsssssssssssss
Answer:
3/1/4
That's the expression represents Lena's speed in miles per hour
A submarine starts 15 meters above sea level and travels 95 meters below sea level. How far did the submarine travel? *
The height attained by the submarine in the sea will be 80 meters.
What is the height?
Height is a vertical distance travelled by any object. Here the submarine is going down in the sea from 15 meters to 95 meters below the sea.
So the height attained by the submarine will be:-
H= 95-15
H= 80 meters.
Therefore the height attained by the submarine in the sea will be 80 meters.
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You wish to test the following claim (
H
a
) at a significance level of
α
=
0.002
.
H
o
:
μ
=
63.5
H
a
:
μ
<
63.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size
n
=
62
with mean
M
=
56.3
and a standard deviation of
S
D
=
13.2
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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given that (3x+2) is a factor of 3x^3+bx^2-3x-2. find the value of b?
Answer:
[tex]b = 2[/tex].
Step-by-step explanation:
By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].
Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:
[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].
Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:
[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].
Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:
[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].
[tex]b = 2[/tex].
look at the attachment and solve
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
What is a perpendicular bisector?A perpendicular bisector of a line segment is a line segment that is perpendicular to and passes through the middle of the line segment (left figure). A line segment's perpendicular bisector can be drawn using a compass by drawing circles centred at and with radius and connecting their two intersections.
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
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NEED HELP ASAP - Which
represents the inverse of the function f(x) = 4x?
h(x) = x + 4
• h(x) =x-4
h(x) = =3/4x
O h(x) = 1/4
Answer:
O h(x)=1/4
Step-by-step explanation:
What is the circumference of the circle? (use 3.14 for pi)
(WORTH 30 POINTS)
Answer:
119.32
Step-by-step explanation:
[tex]A = 2 * 3.14 * 19 = 119.32[/tex]
Help. Please and thanks
Step-by-step explanation:
24.
AC = 12 = cos(angle) × AB = cos(angle) × 13
imagine a circle with center in A and radius 13.
that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.
cos(angle) = 12/13 = 0.923076923...
angle = 22.61986495...°
so, B is the right answer.
25.
we have a right-angled triangle.
from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.
at this ground point there is the right angle.
at the ladder ground point we have 70°.
so, the angle at ladder/wall point is
180 - 90 - 70 = 20°.
remember, the sum of all angles in a triangle is always 180°.
the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).
the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.
we can use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite of the associated angles.
so, we have
20/sin(90) = 20/1 = 20 = height/sin(70)
height = 20×sin(70) = 18.79385242... ft
so, D is the right answer.
can anyone help me identify the center and radius on these 3 pls , brainly
Answer:
Note that #1 starts at #3 and #3 on this list ends at #5 on your page.
Center, 0 | Radius, 15Center, 0 | Radius, [tex]\sqrt{178}[/tex]Center, 0 | Radius, 7What is the full number (all 0's and what not) of 4.385e+30
Answer:
4 385 000 000 000 000 000 000 000 000 000.
Step-by-step explanation:
Wellllll.....e +30 means 10^30
Please help me on this question I’m very confused I will give you brainless??
To solve this problem, we need to use the theorem which states that the sum of angles in a triangle is equal to 180 degrees. The value of m<FED is equal to 120 degrees. From the diagram given, m<CBD is complimentary with m<BED
Sum of Angles in a TriangleThe value of m<FED can be calculated by summing the entire entity and equating to 180 degrees.
Data;
m<FED = (16x - 8)m<EFD = 35m<EDF = 2x + 9[tex]35+(16x-8)+(2x+9) = 180[/tex]
Reason: The sum of angles in a triangle is equal to 180 degrees.
But we would need to solve for the value of x.
[tex]35+(16x-8)+(2x+9) = 180\\35 + 16x - 8 + 2x + 9 = 180\\36+ 18x = 180\\180 - 36 = 18x\\18x = 144\\x = \frac{144}{18} \\x = 8[/tex]
Let's substitute the value of x into m<FED
[tex]m < FED = 16x - 8\\x = 8\\m < FED = 16(8) - 8 \\m < FED = 128 - 8\\m < FED = 120^0[/tex]
The value of m<FED is equal to 120 degrees.
From the diagram given, m<CBD is complimentary with m<BED
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Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.
The diagram is not drawn to scale.
∠AOC=
Answer:
AOC = 124°
Step-by-step explanation:
Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;
This can be written like so:
(3x + 94) + (x + 30) + (2x - 4) = 180
This equation can be solved to find x:
6x + 120 = 180
6x = 180 - 120
6x = 60
x = 10
AOC = 3(10) + 94
= 30 + 94
= 124
Answer:
angle AOC = 124
Step-by-step explanation:
3x + 94 + x + 30 + 2x - 4 = 180 ( ^'s on a STR line)
6x = 180 - 120
6x = 60
x = 10
sub x into 3x + 94
3(10) + 94 = 124
share the ration .....
Answer:
Tom: £166
Ben: £581
Step-by-step explanation:
In the ratio 2 : 7 there are 9 portions total (2 + 7 = 9).
£747 / 9 = £83
For Tom:
£83 * 2 = £166
For Ben:
£83 * 7 = £581
Checking our work:
Since the decimals are the same, this means the ratios are equal.
2/7 = 0.2857
166/581 = 0.2857
The length and width of a rectangle are consecutive even integers. The perimeter is 92 meters. Find the length and width!
Answer:
w represents the width
w + 2 represents the length
2(w + w +2) = 76 formula for perimeter
w + w + 2 = 38 divide both sides by 2
2w + 2 = 38 combine like terms
2w = 36 subtract 2 from both sides
w = 18 divide both sides by 2
The Ferris wheel at the museum park has a height requirement of 48 inches your little sister is 45 inches tall how much taller does she need to go before she can ride the Ferris wheel
Answer:
3 inches
Step-by-step explanation:
48 - 45 = 3
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207
The mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
What is the mean?The mean is the average of a set of data or numbers.
It is a typical value that averagely represents the dataset.
The mean can be computed by dividing the total by the number of data values.
Data and Calculations:Atlanta $163
Minneapolis $125
Boston 177
New Orleans 167
Chicago 166
New York 245
Cleveland 126
Orlando 146
Dallas 123
Phoenix 139
Denver 120
Pittsburgh 134
Detroit 144
San Francisco 167
Houston 173
Seattle 162
Los Angeles 160
St. Louis 145
Miami 192
Washington, D.C. 207
Total = $3,181
Mean = $159.05 ($3,181/20)
Question Completion:What is the mean hotel room rate?
Thus, the mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
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Is 2/3 < 3/4 , or is 3/4 < 2/3 ? Explain how you know.
Answer:2/3 < 3/4
Step-by-step explanation: 3/4 is greater than 2/3.
30 POINTS. HELP!
Which of the three types of discontinuities (removable, jump, and infinite), would be represented by a limit that can only be found by simplifying a rational expression or multiplying by a conjugate? Why?
Answer:
jump equation
bu multiplying by a conjugate
how do I solve this?
✓ Be sure your photo is not blurry
7x-3(5x+2)-6(7+2x)
Answer:
-20x-48
Step-by-step explanation:
7x-(15x +6)-6(7+2x)
7x-(15x+6)-(42+12x)
7x-15x-6-42-12x
(7x -15x-12x)+(-6-42)
=-20x-48
Answer:
-20x - 48
Step-by-step explanation:
7x - 3(5x +2) - 6*(7 + 2x) = 7x + (-3)*5x + (-3)*2 + (-6)*7 + (-6)*2x
= 7x - 15x - 6 - 42 - 12x
= 7x - 15x - 12x - 6 -42 {Combine like terms}
= -20x - 48
If f(x) = 3x+2, find f(f¹(14))
Answer:
f(f¹(14)) = 134
Step-by-step explanation:
Given :
f(x) = 3x + 2Find the value of f(14) :
f(14) = 3(14) + 2f(14) = 42 + 2f(14) = 44Therefore, f(f¹(14)) = f(44).
Solving :
f(44) = 3(44) + 2f(44) = 132 + 2f(f¹(14)) = 134Which conditional probabilities are correct? check all that apply. p(d | f) = startfraction 6 over 34 endfraction p(e | d) = startfraction 7 over 25 endfraction p(d | e) = startfraction 7 over 25 endfraction p(f | e) = startfraction 8 over 18 endfraction p(e | f) = startfraction 13 over 21 endfraction
The conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
How to determine the true conditional probabilities ?The conditional probability P(A|B) is calculated using:
P(A | B) = P(A and B)/P(B)
Using the above formula and the data in the complete question (see attachment), we have the following computations:
P(D | F) = 6/34
P(E | D) = 7/25
P(D | E) = 7/18
P(F | E) = 8/18
P(E | F) = 8/34
By comparing the above computations with the options, the conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
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Answer:
A, B, D
Step-by-step explanation:
yw :)
3) A customer in a bookstore is interested in eleven books on sale.
How many ways can she select three books to buy?
Find p write your answer in simplest radical form
Answer:
[tex]p =[/tex] [tex]7\sqrt{2}[/tex]
Step-by-step explanation:
The side length ratio for a 45-45-90 angle triangle is [tex]1:1:\sqrt{2}[/tex]
The length of the bottom adjacent side of the 90-degree angle is 7, so p would be [tex]7\sqrt{2}[/tex]
Find any 2 irrational no. Between 0.1 and 0.12
0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.
Step-by-step explanation:
Any two irrational Numbers between 0.1 and 0.12 will be those numbers which will be=> greater than 0.1 and smaller than 0.12
And those numbers are = 0.10100100010000 and 0.110100100010000.You can also choose any other numbers too.
___________________Irrational Number :
Irrational numbers are non terminatingNon recurring / repeatingWrite the equation of the line in fully simplified slope-intercept form.
Answer:
The answer to writing this graph in fully simplified slope-intercwpt form is y = 1/5x - 7.
Maya has savings of $40,000. She invests in a bond mutual fund that pays 5% interest each year. Ignoring compounding, what are Maya's total savings after 20 years?
Answer:50,000 x 0.04 x 20=40,000
The total saving after 20 years 50,000+40,000=90,000$
3.2 × 10^7
write in expanded form
Answer:
32000000
Step-by-step explanation:
3.2 x 10 = 32
you will have 10^6 left
32 x 10^6 = 32000000
just add 6 zeroes
Answer:
32, 000, 000.
Step-by-step explanation:
3.2 x 10^7 <======= move the decimal 7 places to the right
32,000,000.