What number should be added to both sides to complete the square? x^2 + 8x = 4
16
8
4
32
Answer:
16
Step-by-step explanation:
x² + 8x = 4 ⇔ x² + 8x + 16 = 4 + 16 ⇔ x² + 2×4x + 4² = 20 ⇔ (x + 4)² = (2√5)²
Remark : (2√5)² = 20
Solve for X. 11
180
9
80
Answer:
11x+1+80=180
11x+81=180
11x=99
x=9
11(9)+1= 99+1=100°
Will someone please help me
Answer:
[tex]4.53 \times 10^{- 1}[/tex]
Step-by-step explanation:
We have to divide [tex]1.6 \times 10^{- 10}[/tex] by [tex]3.53 \times 10^{- 10}[/tex] and we have to write the answer in scientific notation.
Now, [tex](1.6 \times 10^{- 10}) \div (3.53 \times 10^{- 10})[/tex]
= [tex](\frac{1.6}{10^{- 10}})\div (\frac{3.53}{10^{- 10}})[/tex] {Since using the property of exponent [tex]x^{- a} = \frac{1}{x^{a} }[/tex] }
= [tex](\frac{1.6}{10^{- 10}}) \times (\frac{10^{- 10}}{3.53} )[/tex]
{Since we know the mathematical operation [tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}[/tex] }
= [tex]\frac{1.6}{3.53}[/tex]
= 0.45325
= [tex]4.53 \times 10^{- 1}[/tex] (Answer) {Rounded the coefficient to two decimal places}
is 1.15 a rational number
Answer:
No
Step-by-step explanation:
The given number is 1.15. Here, the digits after the decimal are terminating, so the given number is rational, NOT irrational. Thus, 1.15 is NOT an irrational number.
use the graph of f at the right to complete each of the parts (a) through (h)
Answers:
a. The domain of f is ]-∞ , ∞[
b. The range of f is [-4 , ∞[
c. f(1) = 5
d. The vales of x for which f(x) is -3 are 7 and 9
e. The points at which the graph crosses the x-axis are (6,0) and (10,0)
f. The point where the graph of f crosses the y-axis is (0,5)
g. The values of x for which f(x) < 0 are ]6 , 10[
h. f(-7) is positive
Explanation:
Part a:
The domain of the function refers to all the possible x-values that can be used as an input for this function.
Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.
In interval notation, this is written as:
Domain = ]-∞ , ∞[
Part b:
The range of the function refers to all the possible y-values that can be used as an output for the function.
From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.
This means that the range of the function starts from -4 (included) and extends to positive infinity.
In interval notation, this is written as:
R = [-4 , ∞[
Part c:
f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.
From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.
Doing this, we will find that the value of y at x=1 is 5
Therefore:
f(1) = 5
Part d:
f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3
To get the value of x, we go y=-3 and move horizontally till we intersect the graph.
Doing this, we will find that the value of y is -3 at x = 7 and x = 9
Part e:
The points where the graph crosses the x-axis are the points that have y-value equal to 0
Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)
Part f:
The point where the graph crosses the y-axis is the point that has x-value equal to 0
Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)
Part g:
f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)
Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)
In interval notation, this is written as ]6 , 10[
Part h:
f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7
From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞
This means that, at x=-7, the value of y is 5 which is a positive value
Hope this helps :)
Joey has 3 liters of lemonade to share with 6 friends. He
decides put 0.5 liter of lemonade in each of his friends
6 cups, then drink any leftover lemonade himself. How
much lemonade will Joey get to drink?
A. O liters
B. 0.2 liter
C. 0.5 liter
D. 0.8 liter
E. 1 liter
Answer:
A. O liters
Step-by-step explanation
.5 x 3L = 0 liters left
Answer:A
Step-by-step explanation:
3*2=6 6-6=0
Write an inequality that represents the verbal expression.
All real numbers less than 74.
{x < 74; x ∈ R}
Solution:
Given verbal expression is all real numbers less than 74.
R represents the set of all real numbers.
To write the verbal expression into inequality.
Let us assume that the set of all real numbers which is less than 74 are x.
So, all real numbers less than 74 means x < 74 and
x belongs to real numbers.
Therefore, the inequality is {x < 74; x ∈ R}.
32=27+5x solve for x
Answer:
x = 1
Explanation:
32=27+5x
Simplify both sides of the equation.32=5x+27
Flip the equation.
5x+27=32
Subtract 27 from both sides.5x+27−27=32−27
5x=5
Divide both sides by 5.5x/5 = 5/5
x = 1
Answer:
x=1
Step-by-step explanation:
1) subtract
32-27=27-27 +5x
2) 5 = 5x
3) divide by 5
4) x = 1
Coefficient of 5x/6?
Answer:
5
Step-by-step explanation:
The coefficient is the number that is followed by an exponent. In this expression 5 is followed by x, making it a coefficient.
Final answer:
The coefficient of 5x/6 is the numerical factor 5/6, which is the fraction representing the relationship of numbers in front of the variable 'x'.
Explanation:
The coefficient of the term 5x/6 is the numerical factor that is multiplied by the variable 'x'. In this fraction, the numerator is 5 and the denominator is 6. Therefore, the coefficient of the term is 5/6. It is important to separate the coefficient (the number in front of the variable) from the variable itself when doing mathematical operations like addition, subtraction, or algebraic simplification.
If y varies directly as x and y=8 when x=2, find x=6.
Step-by-step explanation:
X=ky
2=8k
K=4
X=4y
6=4y
Y=1. 5
Answer:
Step-by-step explanation:
y varies directly as x
y ∞ x
y = kx
and y=8 when x=2
8 = 2(k)
8 = 2k
k = 8/2
k = 4
y = 4x
find y when x=6
y = 4(6)
y = 24
The frequency table shows the number of points scored during 30 Bulldogs
basketball games. On a piece of paper, draw a histogram to represent the
data. Then determine which answer choice matches the histogram you drew
the answer is the that 80-89 is the longer
Step-by-step explanation:
The answer choice that matches the histogram drawn is option C.
What is an histogram?A histogram is used to represent data graphically. The histogram has a y-axis which shows the frequency and an x - axis which shows the class interval. The correct option should match the information provided in the frequency table.
In this case, we have 5 intervals, that means the histogram must have 5 bars, where their height represents the frequency.
Having said that, the first bar must have a height of 4 units, the second one of 9 units, the third one of 5 units, the fourth one of 8 units and the fifth a height of 4 units.
Therefore, the right answer is C., because that's the histogram with the described heights.
To learn more about histograms, please check: brainly.com/question/14473126
#SPJ7
Given lines AC and DE are parallel, which pair of angles are
NOT congruent to each other?
A) HBC and ABE
B) CBE and HBA
C) DEG and BEF
G) GEF and FEB
Answer:
G
Step-by-step explanation:
Which numbers are perfect squares? Check all that apply
37:57
1
2
16
18
32
44
94
100
ANSWER: 1, 16, 100 are perfect squares.
STEP-BY-STEP EXPLANATION:
A perfect square is a number that can be expressed as the product of two equal integers.
1 x 1 = 1
4 x 4 = 16
10 x 10 = 100
Answer:
1, 16, 100 (a, c, h)
please mark brainliest
What is the inverse of f(c)= 9/5 c +32
Answer:
C(F) = 5/9 F-160/9
Step-by-step explanation:
Answer:
C(F) =
5/9
F −
-16/9
⇒ 160/9
Step-by-step explanation:
Your Welcome :D
The audience thinks 30% of Brandon's jokes are funny. What fraction of Brandons jokes does the audience think are funny?
Answer: 3/10
Step-by-step explanation:
3/10 • 100 = 30%
PLZ HELP ASAP!
a gallon of latex paint can cover 500 square feet. maria has a rectangular room whose dimensions are 14 feet by 25 feet, with 7-foot ceilings. how many gallon containers of paint does she need to buy to paint two coats on each wall?
Maria needs to purchase three gallons of paint to cover her room walls with two coats, as calculations show she needs slightly more than two gallons.
Explanation:To calculate how many gallons of paint Maria needs, first determine the total area of the walls. Each rectangular wall is 14 feet by 7 feet, with an area of 98 square feet, and each of the longer walls is 25 feet by 7 feet, with an area of 175 square feet. Thus, there are two of each, resulting in a total area of 2(98) + 2(175) = 546 square feet. Since Maria wants to apply two coats of paint, the total area to be painted doubles to 1,092 square feet. Given that one gallon covers 500 square feet, Maria needs 1,092 / 500 = 2.184 gallons. Therefore, Maria should purchase three gallons of paint to have enough for two coats, since paint is only sold by the gallon.
Which expression are equivalent to: -2y -8+4y
Answer: 2y−8
Step-by-step explanation:
1) Simplify step-by-step.
−2y−8+4y
=−2y+−8+4y
2) Combine Like Terms:
=−2y+−8+4y
=(−2y+4y)+(−8)
=2y+−8
Answer:
both A and B
Step-by-step explanation:
The basic price for an annual dental checkup and cleaning is $50. If the dentist finds any cavities in there will be an additional charge of $100 for each cavity tour dentist will have to find. Write an expression to describe the cost of the visit if the dentist finds n cavities
Answer:
100n+50
Step-by-step explanation:
the dentist charges $100 dollars per cavity found. Per indicates multiplication. Since there is an additional fee, we add $50 to the $100n, which will make the expression
$100n+50
What is the surface area of the right triangular prism shown below. For grading purposes your answer should include only numbers.
Answer: [tex]SA=189\ mm^2[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the Surface area of a Right triangular prism:
[tex]SA=ph+2B[/tex]
Where "p" is the perimeter of the base, "h" is the height of the prism and "B" is the area of the base.
You can identify that the height is:
[tex]h=9\ mm[/tex]
The area of a triangle can be found with this formula:
[tex]A=\frac{bH}{2}[/tex]
Where "b" is the height of the triangle and "H" is its height.
Knowing this formula, you can find the area of the base of the prism. This is:
[tex]B=\frac{6\ mm*4.5\ mm}{2}\\\\B=13.5\ mm^2[/tex]
Since the perimeter of a figure is the sum of the lenghts of its sides, "p" is:
[tex]p=4.5\ mm+6\ mm+7.5\ mm=18\ mm[/tex]
Therefore, substituting values into the formula, you get:
[tex]SA=(18 mm)(9} mm)+2(13.5} mm^2)\\\\SA=189\ mm^2[/tex]
is 213 2.3 greater less or equal to
Answer:
2 1/3 > 2.3
Step-by-step explanation:
There are a couple of ways you can compare these numbers. One is to convert 2 1/3 to a decimal fraction. It is the repeating decimal ...
2 1/3 = 2.3333333...
Compared to 2.30, we see that 2 1/3 has a 3 in the hundredths place, where 2.3 has 0. Thus 2 1/3 is greater than 2.3.
__
You can convert them both to improper fractions and then to fractions with a common denominator.
2 1/3 = 7/3 = 70/30
2.3 = 23/10 = 69/30
70/30 > 69/30 . . . . so 2 1/3 > 2.3
Are two obtuse triangles always, sometimes, or never similar
Answer:
My Answer Is ALWAYS.
Why I Think So:
It's Because As You Said...They Have Obtuse Angle, Which Can Never Change.
Obtuse triangles are sometimes similar if they have congruent angles; however, simply being obtuse does not guarantee similarity. The angles must match exactly among the triangles for them to be considered similar.
Explanation:Two obtuse triangles are sometimes similar but not always.
For two triangles to be similar, they must have exactly the same angle measurements, although the side lengths can differ by a consistent ratio.
In the case of obtuse triangles, they will be similar if they have one obtuse angle that is the same measure in both triangles and their other corresponding angles are also equal.
However, just having obtuse angles is not sufficient for similarity; the angles must be congruent, and in the case of an obtuse triangle, the other two angles must be specifically tailored so that all three angles are congruent to another triangle's angles.
The concept of triangle similarity falls under the Uniqueness of Solutions which denotes that a triangle is determined by three known elements, but these do not always provide a unique solution.
While often seen in the context of right triangles, such as when applying the Pythagorean Theorem, for obtuse triangles, similarity is determined by angle congruence rather than side lengths.
This implies that if two obtuse triangles have all three angles congruent, they are similar by definition. If not, they are not similar
Phyllis is going to take a 5-hour-17-minute flight from Orlando, Florida, to Las
Vegas, Nevada, that leaves at 11:05 a.m. Orlando time. If Orlando is in the
eastern time zone and Las Vegas is in the Pacific time zone, what will be the
local time in Las Vegas when the flight arrives?
Use the following to help you answer the question.
12:00 p.m. eastern time = 11:00 a.m. central time = 10:00 a.m. mountain
time = 9:00 a.m. Pacific time.
Answer:
Step-by-step explanation:
ok...so she leaves Orlando at 11:05 am.....the flight takes 5 hr and 17 minutes..
11:05 am + 5 hrs = 4:05 pm.....4:05 + 17 minutes = 4:22 pm.
so she arrives at 4:22 pm eastern time....(orlando time)...but Las Vegas is pacific time
so if 12 pm eastern = 9 am pacific.....a difference of 3 hrs
so the local time in Las Vegas when her plane lands is :
4:22 pm - 3 hrs = 1:22 pm <===
Answer:1:22 p.m.
Step-by-step explanation:
The point slope form of the equation of the line that passes through -5,-1 and 10,-7 is y+7= -2/5(x-10). What is the standard form of this equation
2x + 5y = -15 is the standard form of equation
Solution:
Given that,
The point slope form of the equation of the line that passes through (-5, -1) and (10, -7) is given by:
[tex]y + 7 = \frac{-2}{5}(x-10)[/tex]
We have to write the standard form of the equation
The standard form of an equation is Ax + By = C
In this kind of equation, x and y are variables and A, B, and C are integers
Let us convert the given equation into standard form
[tex]y + 7 = \frac{-2}{5}(x-10)\\\\\text{Simplify the right hand side of equation }\\\\y + 7 = \frac{-2x}{5}+\frac{20}{5}\\\\y + 7 = \frac{-2x +20}{5}\\\\5(y+7) = -2x + 20\\\\\text{Simplify the left hand side of equation }\\\\5y + 35 = -2x + 20\\\\\text{Move the variables to left side of equation and constants to right side }\\\\2x + 5y = 20 - 35\\\\2x + 5y = -15[/tex]
Thus the standard form of equation is found
What is the correct solution
-3(6-r)=6
-18-3r=6
-3r=24
r=-8
Answer:-3(6-r)=6
-18+3r=6
3r=6+18
3r=24
r=24/3
r=8
Step-by-step explanation:
If johny has 10 apples and Suzie has 2 apples. How many more apples does johny have?
9x divided by -2x sqared
Answer:
-9/2x
Step-by-step explanation:
The temperature in miami Florida is 22 degrees warmer than three times the temperature in bangor,Maine. The temperature In miami is 82 degrees.
Answer:
Temperature in Maine = 20
Step-by-step explanation:
22-82 =
60
60/3 =
20
2z + 3/8 =3 7/8
How do I work out this problem.
Answer:
z = 1.75
Step-by-step explanation:
2z + 3/8 = 3 7/8
2z = 3 7/8 - 3/8
2z = 3 4/8 or 2z = 3 1/2
z = 3 1/2 / 2 or 3.5 / 2
z = 1.75
a sum expression that equals -3/4
Answer:
2 1/4 - 3 = -3/4 can be a simple equation.
The area of an equilateral triangle is given by A =3^1/2/4s^2. Find the length of the side s of an equilateral triangle with an area of 12^1/2 square inches.
Answer:
The length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches
Step-by-step explanation:
Given that the area of an equilateral triangle is given by
[tex]A=3^\frac{1}{2}s^2[/tex]
It can be written as
[tex]a=\frac{\sqrt{3}}{4} s^2[/tex] Square inches (1)
To find the length of the side s os an equilateral triangle
Given that area of an equilateral triangle is [tex]12^\frac{1}{2}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches
It can be written as
[tex]A=12^\frac{1}{2}[/tex]
[tex]A=\sqrt{12}[/tex] square inches (2)
Now comparing equations (1) and (2) we get
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{12}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{4\times 3}[/tex]
Dividing by [tex]\frac{\sqrt{3}}{4}[/tex] on both sides we get
[tex]\frac{\frac{\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}}=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{4}}[/tex]
[tex]\frac{\sqrt{3}}{4}s^2\times\frac{4}{\sqrt{3}}=2\sqrt{3}\times\frac{4}{\sqrt{3}}[/tex]
[tex]s^2=8[/tex]
[tex]s=\sqrt{8}[/tex]
Therefore [tex]s=2\sqrt{2}[/tex] inches
Therefore the length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches