Answer:
Please use " ^ " for exponentiation: x^2 + 2x + 8 ≤ 0.
Let's solve this by completing the square:
x^2 + 2x + 8 ≤ 0 => x^2 + 2x + 1^2 - 1^2 + 8 ≤ 0. Continuing this rewrite:
(x + 1)^2 + 7 ≤ 0
Taking the sqrt of both sides: (x + 1)^2 = i*sqrt(7)
Then the solutions are x = -1 + i√7 and x = -1 - i√7
There's something really wrong here. I've graphed your function, x^2 + 2x + 8, and can see from the graph that there are no real roots, but only complex roots. Please double-check to ensure that you've copied down this problem correctly.
Answer:
B. The Empty Set
Step-by-step explanation:
Hope this helps!!! Have a great day!!!! : )
Help please!!! Thanksss
Answer:
6:00 p.m.
hope this helps :)
(05.05)
Based on the graph, what is the initial value of the linear relationship?
-4
-3
5/3
5
Answer:
5
Step-by-step explanation:
The initial value is when x=0
When x=0, y =5
The initial value is 5
Does the relation define a function? If it does, state the domain of the function.
Does the relation define a function? If it does, state the domain of the function
Answer: Choice A
Yes; Domain = {m, n, p, q}
We have the inputs (think of them as the x values) as m, n, p and q. They make up the domain. The domain is the set of all allowed inputs. We do not have any repeated inputs, which is why we have a function. Any given input leads to exactly one output.
Please answer this question now
Answer:
825 or 500
Step-by-step explanation:
Depends, if it is talking about just an up-down, it is 500, but if it is just distance in general, it would be 825 because 325+500=825
Hope this will help
According to a commercial, 4 out of 5 dentist recommend a certain brand of toothpaste. Suppose There are 120 dentist in your area. What is the expected number of dentist who recommend the brand? What is the standard deviation?
4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.
WILL GIVE BRAINLIEST PLZ HELP
Answer:
y = -5x - 9.
Step-by-step explanation:
(-2, 1)
(0, -9)
(1 - -9) / (-2 - 0) = (1 + 9) / (-2) = 10 / (-2) = 5 / (-1) = -5
Since -5 is the slope, and the y-intercept is at (0, -9), we have an equation of y = -5x - 9.
Hope this helps!
Answer:
y=-5x-9
Step-by-step explanation:
Change in x = +2
Change in y=-10
-10/2=-5
m=-5
plug in an point
example:
1=-5(2)+B
B=-9
To check your answer:
y=-5x-9
plug in an point for x given on the chart:
-5(0)-9=-9
14
Select the correct answer
Which equation describes the line graphed above?
OA y = -41 - 5
OB. y = -x - 4
oc y = -51 - 4
Answer:
Option B
Step-by-step explanation:
Hope it is right
The value of equation describes the line graphed is,
⇒ y = -1/5x - 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, -4) and (5, -5).
Now,
Since, The equation of line passes through the points (0, -4) and (5, -5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 5 - (-4)) / (5 - 0)
m = - 1 / 5
Thus, The equation of line with slope - 1/5 is,
⇒ y - (-4) = -1/5 (x - 0)
⇒ y + 4 = -1/5x
⇒ y = -1/5x - 4
Therefore, The equation of line passes through the points (0, -4) and
(5, -5). will be;
⇒ y = -1/5x - 4
Learn more about the equation of line visit:
https://brainly.com/question/18831322
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Determine which one of the following statements is true.
A. Linear growth will always exceed exponential growth.
B. Linear growth will always exceed quadratic growth.
C. Quadratic growth will always exceed exponential growth.
D. Exponential growth will always exceed linear growth.
Answer:
D. Exponential growth will always exceed linear growth.
Step-by-step explanation:
An "exponential growth function" would always exceed the "linear growth function" in the end because the "x-values" tends to get larger in continuation, so the change rate associated with the "exponential function" also increases in continuation whereas the "linear functions' change rate is considered as constant.
In the question above, option D is correct.
The logistic growth function f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t EndFraction describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 20 months? Round to nearest whole number.
Answer:
8685 butterflies
Step-by-step explanation:
Given the logistics growth function expressed as f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t which describes the population of a species of butterflies t months after they are introduced to a non threatening habitat, to know the number of butterflies expected butterflies are expected in the habitat after 20 months, we will substitute t = 20 into the function.
f(20) = 440/1+13.7exp-(0.28×20)
f(20) = 440/1+13.7exp-(5.60)
f(20) = 440/1+(13.7× 0.003698)
f(20) = 440/1+0.05066
f(20) = 440/1.05066
f(20) = 8684.9
This means there will be approximately 8685 butterflies in the habitat after 20months.
3/x-2, i'm confused as to what the horizontal asymptote is. The resources I found online conclude that it has a horizontal asymptote of y=0. I know that in order for a horizontal asymptote to be y=0, the denominator has to have a greater degree than the numerator. Im confused because doesn't the numerator have the same degree as the denominator (degree of 1)?
Answer:
The Horizontal Asymptote is at x=3
Step-by-step explanation:
Here is a way to remember this
One way to remember this is the following pnemonic device: BOBO BOTN EATS DC
EABOBO -Exponents are bigger on bottom, y=0
EABOTN -Exponents are bigger on top, none
EATS DC - Exponents are the same, divide coefficients
3/x-2 the exponents are the same, divide leading coefficients
3/1 = 3 the horizontal asymtote is at x=3
Marked price of a pen is Rs 20. It is sold at a discount of 15%. Find the selling price?
Answer:
Rs 17Step-by-step explanation:
Solution,
Marked price ( MP ) = Rs 20
Discount % = 15%
Selling price ( SP ) = ?
let's find the discount amount:
Discount amount = Discount % of MP
plug the values
= 15% of 20
Calculate
= Rs 3
Discount amount = Rs 3
Now, let's find the SP
Selling price ( SP ) = MP - discount amount
plug the values
= Rs 20 - Rs 3
Calculate the difference
= Rs 17
Hope this helps..
Best regards!!
Find the value of x in the triangle shown below.
Answer:
x=48
Step-by-step explanation:
The other angle is 66° because it's an isosceles triangle
so
180=66+66+x
180=132+x
x=48
Answer:
48 degrees
Step-by-step explanation:
Since the triangle is iscoceles because it has two sides with a length of 7, two angles will be 66 degrees and the missing angle will be the sum of total angles in a triangle minus the other two 66 degree angles. 180 - 66 - 66 = 48
Help pleaseeee with atleast one❤️
Answer:
3) 23 cm
4)10.1
5)50
A rectangle measures 6 cm by 4 cm. Another rectangle with adjacent sides 8 cm and x cm is geometrically similar to it. Find the two possible value of x.
Answer:
5 1/3 or 5.33333333333333333333333333333333333333333333333333333
Step-by-step explanation:
to find the scale factor, you must divide the two equal sides.
[tex]\frac{6}{8}[/tex]
which equals
[tex]\frac{3}{4}[/tex] or 0.75
Now, the way to get the value of x is to divide 4 by 3/4 0r 0.75
[tex]\frac{4}{0.75}[/tex]
Which equals
5.333 repeating or 5 1/3
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
How many times greater is 1,000,000,000 than 1,000,000?that is how many groups of 1 million are there in 1 billion? Please help.
Answer:
1,000
Step-by-step explanation:
1,000,000 x 1,000 = 1,000,000,000
1,000,000,000 has 4 more zeros than 1,000,000 and 1,000 has 4 zeros so there 1000 is the answer.
IF U DO THIS FOR ME I WILL GIVE U TONS OF POINTS PLSSSS HELP AND DO THE WHOLE THING :)
Instructions
Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table.
Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following.
Show all work for calculations. List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.). Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box? What is the surface area of the box if it is scaled up by a factor of 10?
What is the volume of the box?
What is the volume of the box if it is scaled down by a factor of 1 over 10?
Answer:
Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet. ... If you are using a ruler with a centimeter (cm) scale, then your units are going to be in cm, and if you ... We have to do the same thing to volume like we did with the surface area.
:)
Answer:
Rectangular prism
I chose a box of cereal.
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base.
The shape of the cross-section would be a rectangle in dimensions.
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base + perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box =[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box = L*W*H 20*8*32-5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10?
we know that
the volume of the smaller box =[scale factor]³volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box =[1/10]³*5,120 5.12 cm³
the answer part 6) is
5.12 cm³
The length is 6 in., the width is 2 in., and the height is 16 in.
Angle ABC is a straight angle. MAngleDBC = 130° and Ray B E bisects AngleABD. The center of line A C is point B. Two lines extend from point B. One line extends to the left and contains point E. Another line extends up and to the left and contains point D. What is mEBA? °
Answer:
25°
Step-by-step explanation:
Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:
∠DBC + ∠ABD = 180°
130 + ∠ABD = 180°
∠ABD = 180° - 130°
∠ABD = 50°
∠ABD is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).
The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW
Since E is the interior of ∠ABD, then:
∠ABD = ∠EBA + ∠DBE
But ∠EBA = ∠DBE
∠ABD = 2∠EBA
50 = 2∠EBA
∠EBA = 25°
Answer:
The answer is 25 degrees
PLZZ HELPP WILL GIVE BRAINLIEST Graph the line y=25x+3. Use the line tool and select two points on the line. THIS IS A K12 TEST PLZZ
Step-by-step explanation:
you can use any value either in place of x or y to find the corresponding coordinate but if you want to find the x and y intercept you can desigate x as zero and find the y intercept and vice versa.
so to find x and y intercept
y=25x+3. to find x intercept designate y as zero
0=25x+3
-3=25x
x= -3/25. p( -3/25,0)
y=25x+3 to find y intercept designate x as zero
y=25(0)+3
y=3. p(0,3)
the above y and x intercept indicates the points that the line of equation pass through when drawn graphically.
Six different books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right. How many possible arrangement are there?
Answer:
720 ways
Step-by-step explanation:
At first their are six books, that means that there are six different positions to put them. The first book to be placed would have 6 position, when the first book is placed, to place the second book there would be 5 position since one position has been used by the first book. After placing the second book, to place the third book there would 4 available position, and it follows this manner i.e for the fourth book 3 available position, for the fifth book 2 available position and for the sixth book, one available position.
Therefore the number of ways to arrange the books on the shelf from left to right = 6 × 5 × 4 × 3 × 2 × 1 = 6! = 720 ways
PLEASE HELPP!!!
Find C to two decimal places and find the measure of angle B.
Answer:
<B = 32°
c = 9.43
Step-by-step explanation:
To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.
58° + 90° = 148°
180° - 148° = 32°
The measure of <B is 32°.
To find the length of side c, use the Pythagorean Theorem.
a² + b² = c²
5² + 8² = c²
25 + 64 = c²
89 = c²
c = √89
c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)
The length of side c = 9.43.
Hope that helps.
Given that Arccos (√3/2)=β, what are all the angle measurements for right triangle ABC?
Answer:
30°, 60° and 90°
Step-by-step explanation:
Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.
Note that a right angled triangle is made up of two acute angles and a right angled (90°)
Let's get one of the acute angles first
If Arccos (√3/2)=β
β = cos^-1 √3/2
β = 30°
This shows that one of the acute angles is 30°
To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.
90+30+x = 180
120+x = 180
x = 180-120
x = 60°
All the angle measurement for the right angled triangle are 30°, 60° and 90°
In solving the formula
A = (1/2)bh, in solving for h, you could first multiply both side by 1/2.
True or False
Answer:
False
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex] bh ( multiply both sides by 2 to clear the fraction )
2A = bh ( divide both sides by b )
[tex]\frac{2A}{b}[/tex] = h
Find the distance from point M to point N on the graph shown. Round your answer to
the nearest hundredth.
possible solutions:
1. 4.24 units 2. 8.49 units
3. 8.60 units 4. 12.00 units
Answer:
3. 8.60 units
Step-by-step explanation:
Distance from point M(-2, 4) to point N(5, -1) can be calculated using the distance formula, [tex]d = \sqrt{(x_{2} - x_1)^2 + (y_2 - y_1)^2}[/tex]
M(-2, 4) => (x1, y1)
N(5, -1) => (x2, y2)
Plug in the values into the formula
[tex] d = \sqrt{(5 - (-2))^2 + (-1 - 4)^2} [/tex]
[tex] d = \sqrt{(7)^2 + (-5)^2} [/tex]
[tex] d = \sqrt{49 + 25} [/tex]
[tex] d = \sqrt{74} [/tex]
[tex] d = 8.60 units [/tex]
Answer:
Step-by-step explanation:
PLEASE HELP. YOU NEED TO FIND SLOPE. THANK YOU!
Answer:
5
Step-by-step explanation:
Due to the direction the line is facing it can be concluded that its slope is positive.
You need two definite points on the line to find the slope.
(x¹,y¹) ( x²,y²)
Points (5,20) (0, -5)
Slope = (y² - y¹) ÷ (x² - x¹)
= (-5 - 20) ÷ (0 -5)
= (-25) ÷ (-5)
= 5
Have a great day!
Solve the inequality.
9p+23<41
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
p < 2
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
9p < 18
p < 2
Which of the following equations have no solutions?
Choose all answers that apply:
-602 + 32 = –60r – 32
-60.X + 32 = 32.r – 60
-60r = 32 — 322 – 60
-602 + 32 = -60r - 60
Answer:
-60.X + 32 = 32.r – 60
Because we only have one equation for 2 unknowns.
Step-by-step explanation:
All the equations have solution for r but the one that has 2 unknowns (r and X).
That is because we only have one equation and 2 unknowns.
Then, we only can express one unknown in function of the other and have an indeterminate solution.
A tissue sample is three cells thick. Each cell has a thickness of 0.000004m. What is the thickness of the tissue sample in mm. Give your answer in standard form. PLZ SHOW WORKING
Answer:
4000 nm
Step-by-step explanation:
Conversion from meters to nanometers: 1 meter is 1(10⁹) nm
Step 1: Convert 0.000004 to scientific notation
0.000004 = 4(10⁻⁶)
Step 2: Convert by multiplication
4(10⁻⁶) x 1(10⁹) = 4000 nm
*HELP* Select the correct answer. What is the value of this expression when t = -12? -3|t − 8| + 1.5 A. 61.5 B. 13.5 C. -10.5 D. -58.5
Answer: D
Step-by-step explanation:
If we substitute -12 into this equation we get:
[tex]-3[-12-8]+1.5[/tex]
[tex]-3[-20]+1.5[/tex]
Because -20 is in absolute value, we simply just use 20.
Thus,
[tex]-3(20)+1.5\\= -60+1.5\\= -58.5[/tex]
Answer:
D
Step-by-step explanation:
Which of the following relation is correct
Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
In order to solve this problem lets first find the inverse of this function. This is done below:
[tex]y = x^2 + 8\\[/tex]
We first swap x and y.
[tex]x = y^2 + 8[/tex]
We now isolate y.
[tex]y^2 = x - 8\\y = \sqrt{x - 8}\\f^{-1}(x) = \sqrt{x - 8}[/tex]
Functions are relations between two groups of numbers, in such a way that one number on the input group must generate a singular answer from the output group. This holds true for both f(x) and its inverse, therefore both are functions.
factorize (X + 2 y)square - (2 x minus y) square
Answer:
- (x - 3y)(3x + y)
Step-by-step explanation:
Given
(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL
= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute
= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms
= - 3x² + 8xy + 3y² ← factor out - 1 from each term
= - 1(3x² - 8xy - 3y²) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.
product = 3 × - 3 = - 9 and sum = - 8
The factors are - 9 and + 1
Use these factors to split the xy- term
3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )
= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term
= (x - 3y)(3x + y)
Thus
(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)