Step-by-step explanation:
To complete the square, take half of the second coefficient, square it, then add the result to both sides.
(-8/2)² = (-4)² = 16
x² − 8x + 16 = 9 + 16
Solving:
(x − 4)² = 25
x − 4 = ±5
x = 4 ± 5
x = -1 or 9
Answer:
part 1: x^2 + -8 x=9
part 2: Add 16 to each side
part 3: (x-4)^2 =25
part 4: -1 and 9
An Impressionist painting increases in value
at an average rate of 9% a year. If the origi-
nal cost of the painting to the Museum of
Art was $1500, what was the value of the
painting (to the nearest dollar) at the end of
a 20-year holding period?
Answer:
A = $8406.6
Step-by-step explanation:
Given:
Average rate [tex]r=9\%[/tex]
Initial cost of painting [tex]a = \$1500[/tex]
Time [tex]t = 20\ years[/tex]
We need to find the final amount of painting at the end of a 20-year.
Solution:
Using Exponential Growth rate formula as:
[tex]A = a(1+r)^t[/tex] ----------(1)
Where:
A = Final amount
a = Initial amount.
r = Rate as a decimal.
t = Time.
Now, we substitute all given values in equation 1.
[tex]A = 1500(1+0.09)^{20}[/tex]
[tex]A = 1500(1.09)^{20}[/tex]
Substitute [tex]1.09^{20} = 5.60[/tex] in above equation.
[tex]A = 1500\times 5.60[/tex]
A = $8406.62
Therefore, value of the painting at the end of a 20-year A = $8406.6
Javier used the expression below to represent his score in a game of mini-golf.
3x + x + 5 – 2x
If he simplifies the expression, which statements are true about the parts of the simplified expression? Select three options.
The constant is 2.
The coefficient is 2.
The constant is 5.
The coefficient is 5.
There are two terms.
Answer:
The three true options are B, C and E.
Step-by-step explanation:
Let's simplify the expression that represent the score of Javier in a game of mini-golf:
3x + x + 5 – 2x
2x + 5
Which statements are true about the parts of the simplified expression? Select three options.
A. The constant is 2.
It's false. The constant is 5.
B. The coefficient is 2.
It's true. The coefficient of x is 2.
C. The constant is 5.
It's true.
D. The coefficient is 5.
It's false. 5 is the constant and the coefficient of x is 2.
E. There are two terms.
It's true. The two terms are 2x and 5.
The three true options are B, C and E.
tHE ANSWER IS 3 ANSWERS. bce
Angle A and Angle B are supplementary angles. If
mZA = (2x + 26)° and m
And angle B = (x + 25)°, then find the measure
of angle B.
Find the lateral surface area of the figure. A 798 B 210 C 816.8 D 69.7
the lateral surface area of the figure is 660 sq ft
(but the answer is not matching with the options)
Step-by-step explanation: this figure is called cylinder. the lateral surface area means the area of curved surface.
here the diameter is 10 ft
so radius = diameter/2 = 10/2 ft = 5ft
again, height = 21ft
now the lateral surface area = perimeter of the circular surface X height
= 2X pie X r X h ( here r is the radius and h is height and we will take pie as 22/7)
= 2 X (22/7) X 10 X 21 sq ft
= 2 X 22 X 5 X 3 sq ft
=660 sq ft
( suggest you to recheck the options)
Given :-
Diameter :- 10ft. , radius :- 5ft. Height:- 21 ft.To find :-
Lateral surface area of CylinderSolution:-
Formula for finding lateral surface area of Cylinder = 2πrhputting the known values ,
LSA of Cylinder = 2×3.14×5×21 ft²
LSA = 659.4 ft²
If E be an event, then P(E) + P(not E) = _____________.
Answer:
1
Step-by-step explanation:
If P(E) = p
Then P(not E) = 1-p
Answer:
A
Step-by-step explanation:
What was the net yardage the team had after those 4 plays ?
A loss of 8 yards is represented as -8
Multiply this by 4 to get -8*4 = -32
Can someone explain this to me?
Answer:
y=42 degrees.
Step-by-step explanation:
The sum of angles in a triangle = 180 degrees.
One angle in that small triangle is y, one is 48, and one is unknown.
The sum of angles on one line is 180 degrees.
One of the angles on the line that unknown angle lies on is 90 degrees, so the unknown angle is 90 degrees, too.
90 + 48 = 138
180 - 138 = 42.
22) 4x + 6y=-6
4x – 4y=-16
Answer:
4x + 6y = -6
-4x + 4y = 16
10y = 10
y = 1
4x - 4 = -16
4x = -12
x = -3
(-3,1)
If the store bought a leash for $6.20, how much will the retail price be for that leash?
Answer:
2.50 punds
Step-by-step explanation:
plus with the money
One quart of water-resistant paint covers 75 square feet. A swimming pool is in the shape of a rectangular prism with a length of 20 feet, a width of 10 feet, and a height of 5 feet. How many quarts should you buy to paint the swimming pool with two coats of paint?
18.66 quarts of paint is needed to paint the swimming pool with two coats of paint
Solution:
Given that,
A swimming pool is in the shape of a rectangular prism
Length = 20 feet
Width = 10 feet
Height = 5 feet
Find the surface area of prism
[tex]A=2(wl+hl+hw)[/tex]
Where, "l" is the length and "w" is the width and "h" is the height
[tex]A = 2(10 \times 20 + 5 \times 20 + 5 \times 10)\\\\A = 2(200+100+50)\\\\A = 2 \times 350\\\\A = 700[/tex]
Thus surface area area of prism is 700 square feet
Given that,
One quart of water-resistant paint covers 75 square feet
Therefore,
1 quart paint = 75 square feet
x quart = 700 square feet
This forms a proportion
[tex]1 \times 700 = 75 \times x\\\\x = \frac{700}{75}\\\\x = 9.33[/tex]
Thus 9.33 quarts of paint is needed to cover 700 square feet
How many quarts should you buy to paint the swimming pool with two coats of paint
For two coats of paint we need = 9.33 + 9.33 = 18.66 quarts of paint
Answer:this answer is incorrect.
You can’t paint the top of the pool.
You need to subtract 2 of the top layer’s surface area. The answer is you would need to buy 14 quarts.
Step-by-step explanation:
What is the measure of angle x?
Enter your answer in the box.
Answer:
Step-by-step explanation:
Just like regular numbers, angles can be added to obtain a sum, perhaps for the purpose of determining the measure of an unknown angle. Sometimes we can determine a missing angle because we know that the sum must be a certain value. Remember -- the sum of the degree measures of angles in any triangle equals 180 degrees. Below is a picture of triangle ABC, where angle A = 60 degrees, angle B = 50 degrees and angle C = 70 degrees.
The angles of this triangle are 50, 60, and 70 degrees.
If we add all three angles in any triangle we get 180 degrees. So, the measure of angle A + angle B + angle C = 180 degrees. This is true for any triangle in the world of geometry. We can use this idea to find the measure of angle(s) where the degree measure is missing or not given.
Answer:
48 degrees
Step-by-step explanation:
The sum of 42 and x should get 90 degrees, so if you subtract 42 from 90 you get 48.
Hope this helped :)
Solve the inequality 4/3 < -8/3y
Answer:
y<-1/2
Step-by-step explanation:
divide each side by -8/3, and flip the sign because you are dividing by a negative.
Amy received a $60 gift card to the frozen yogurt shop for her birthday. The shop sells yogurt sundaes for $4 and yogurt cones for $3. If x represents the number of yogurt sundaes and y represents the number of yogurt cones, complete the following:
a) Write the inequality that represents this scenario
b) List one solution based on your inequality & solve for the amount spent based on the coordinate solution you chose.
Answer:
a) 4x + 3y ≤ 60
b) 6 for x and 11 for y
Step-by-step explanation:
b) 4x + 3y ≤ 60
4(6) + 3(11) ≤ 60
24 + 33 ≤ 60
57 ≤ 60
how many triangles can be drawn with side lengths of 3 inches, 5 inches, and 6 inches???
Answer:
4 congruent triangles
Step-by-step explanation:
since there is no one of the sum of two sides is less then the third side, so it's possible to form a triangle
Use straightedge and compass, it can draw 4 triangles at a common base
The number of triangles that can be drawn with side lengths of 3 inches, 5 inches, and 6 inches is 1 triangle due to the triangle inequality theorem.
To determine the number of triangles, we can use the triangle inequality theorem. For a triangle to exist, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is less than 6, so only 1 triangle can be formed.
What is 763 divided by8
Answer: 763 divided by 8 equals 95.375 .
Step-by-step explanation: Just put it on a piece of paper and divide.
what is an equation of a line that passes through the point (3,-1) and has a slope of 2
Answer:
y=2x-7
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=2(x-3)
y+1=2x-6
y=2x-6-1
y=2x-7
If y = f(x) = A(0.5)* + B is increasing on the interval (-0, o), which statement must be true?
A) A > 0
B) A < 0
C) B < 0
D) B > 0
Answer:
B) A < 0
Step-by-step explanation:
I had the same question, and got it right.
Answer:
B
Step-by-step explanation:
it puts it between -0 and 0
Jin bought a book that costs 5.60 if the tax rate is 7% how much tax did he pay
Answer:
$5.99
Step-by-step explanation:
5.6*1.07
1.07 is the tax plus the original price
is 5.992
which rounds up to $5.99
Gilda wrote cletus a check for 184.27, and cletus deposited the check into his checking account where was cletus ' signature
Answer:only on the back of the check
Step-by-step explanation:
Cleo bought 10 feet of ribbon for costumes. He used 2 feet of ribbon last week. He cut of the remaining ribbon into one- sixth foot pieces. How many pieces of ribbon does Cleo have?
Answer:
48 pieces
Step-by-step explanation:
Given:
Cleo bought 10 feet of ribbon.
He used 2 feet of ribbon last week.
He cut of the remaining ribbon into one- sixth foot pieces.
Question asked:
How many pieces of ribbon does Cleo have ?
Solution:
Total length of ribbon = 10 feet
He has used length of ribbon = 2 feet
Remaining length of ribbon = 10 - 2 = 8 feet
He cut remaining ribbon into = [tex]\frac{1}{6}foot[/tex]
Number of pieces of ribbon = [tex]8\div\frac{1}{6}[/tex]
= [tex]8\times6 = 48 pieces[/tex]
Therefore, Cleo have 48 pieces of ribbon.
Siven that f(x)=x2 - 7 and g(x)= 4 - x, find (f - g)(1), if it exists.
Answer:
- 9
Step-by-step explanation:
Note that (f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x² - 7 - (4 - x)
= x² - 7 - 4 + x
= x² + x - 11
Thus
(f - g)(1) ← substitute x = 1 into (f - g)(x)
= 1² + 1 - 11
= 1 + 1 - 11
= - 9
What is the best estimate of 11 1/5÷2 3/4
Answer:4
Step-by-step explanation:
Evaluate the expression: a(b – c) if a = -8, b = 12, and c = 4
-128
-100
-64
0
Answer:
-8(12-4)
-8(8)
=`-64
answer is c
Briefly describe whether or not a disconnected graph is always a bad thing.
Whether a disconnected graph is problematic depends on its application. In network theory, it might represent critical separations, but in connected systems like transportation, it signifies issues. The context, such as economic, ecological, or psychological networks, determines its value.
Explanation:A disconnected graph is not inherently a bad thing; its value depends on the context in which it is used. For example, in network theory, a disconnected graph might accurately represent separate clusters within a network, indicating areas that do not communicate or interact with each other. This could be critical for understanding the structure of social networks, the Internet, or ecological systems. On the other hand, in applications where connectivity is essential, such as in the design of transportation or communication networks, a disconnected graph could signify a problem that needs addressing. Thus, it's crucial to consider the specific needs of the application or system being analyzed.
Economists use graphs to depict connections and costs, highlighting the importance of understanding the underlying story a graph tells. The fact that all graphs have a genealogy and a narrative is essential in interpreting them correctly. For instance, a graph showing disconnected components in an economic network could indicate areas of inefficient resource allocation or potential opportunities for improvement.
Ultimately, whether a disconnected graph is seen as a disadvantage depends on the goals of the analysis. In ecological studies, reconnecting fragmented landscapes is often beneficial, although careful planning is needed to avoid drawbacks. Similarly, in the context of relational connectivity theory (RCT), connectivity and the loss thereof have profound implications on wellbeing, demonstrating that the concept of dis/connection transcends mathematical graphs and touches on broader socio-psychological themes.
What is the solution to the equation 4 x minus 6 = 10 x minus 3?
Answer:
x=-1/2
Step-by-step explanation:
Answer:
The answer is -1/2
Step-by-step explanation:
It is -1/2 because of math
What is the solution to the equation 5 (x minus 6) = 2 (x + 3)?
Answer:
1. Distribute
5x-30=2x+6
2. Combine like terms
5x=2x+36
3. Simplify to get x by itself(36 divide 3)
3x=36
x=12
Step-by-step explanation:
The value of the given equation 5 (x minus 6) = 2 (x + 3) will be x = 19.5.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
As per the given,
5 (x minus 6) = 2 (x + 3)
5(x - 6) = 3(x + 3)
5x - 30 = 3x + 9
5x - 3x = 9 + 30
2x = 39
x = 19.5
Hence "The value of the given equation 5 (x minus 6) = 2 (x + 3) will be x = 19.5".
For more about the equation,
brainly.com/question/10413253
#SPJ6
What is the answer to r/10+4=5
Answer:
r=10
Step-by-step explanation:
Take 4 away from 5 to isolate your variable. Now you have r/10= 1. figure out the unknown value by placing ten on top which is the same as 1.
Solve for u. -24 = u ÷ 6
u = ____
The value of u is -144
Solution:
Given that,
[tex]-24 = u \div 6[/tex]
We have to solve for "u"
From given,
[tex]-24 = u \div 6[/tex]
Convert the division problem into multiplication, by changing the division sign to multiplication sign. Then invert the number to right of division sign
Thus we get,
[tex]-24 = u \times \frac{1}{6}\\\\\frac{u}{6} = -24[/tex]
Isolate for u
[tex]u = -24 \times 6\\\\On\ multiplying\ both\ we\ get\\\\u = -144[/tex]
Thus the value of u is -144
Which expressions have a value of 16/81? Check all that apply.
Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2
Answer:
First and last option is correct.
[tex](\frac{2}{3})^{4}=\frac{16}{81}[/tex]
[tex](\frac{4}{9})^{2}=\frac{16}{81}[/tex]
Step-by-step explanation:
Given:
There are four options.
(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2
We need to check all given options for value of 16/81.
Solution:
Using rule.
[tex](\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}[/tex]
Solve for option [tex](\frac{2}{3})^4[/tex].
[tex](\frac{2}{3})^{4}=\frac{2^4}{3^4}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{16}{81}[/tex]
Solve for option [tex](\frac{16}{3})^4[/tex].
[tex](\frac{16}{3})^{4}=\frac{16^4}{3^4}=\frac{16\times 16\times 16\times 16}{3\times 3\times 3\times 3}=\frac{65536}{81}[/tex]
Solve for option [tex](\frac{4}{81})^2[/tex].
[tex](\frac{4}{81})^{2}=\frac{4^2}{81^2}=\frac{4\times 4}{81\times 81}=\frac{16}{6561}[/tex]
Solve for option [tex](\frac{4}{9})^2[/tex].
[tex](\frac{4}{9})^{2}=\frac{4^2}{9^2}=\frac{4\times 4}{9\times 9}=\frac{16}{81}[/tex]
Therefore, expression [tex](\frac{2}{3})^4[/tex] and [tex](\frac{4}{9})^2[/tex] have a value of [tex]\frac{16}{81}[/tex].
Answer: Which expressions have a value of StartFraction 16 Over 81 EndFraction? Check all that apply.
Best Option A, D
(A) <===== correct answer
(D) <===== correct answer
Step-by-step explanation:
How do I solve these using the elimination method:
x+y+z=20
13x+0y+6z=132
150x+90y+139z=2601
Answer:
(x=6,y=5,z=9)
Step-by-step explanation:
The given system is
x+y+z=20 ------>(1)
13x+0y+6z=132 ------->(2)
150x+90y+139z=2601------>(3)
Make y the subject in the first equation to get: [tex]y=20-x-z-------(4)[/tex]
Put equation (4) in equation (3) to get:
150x+90(20-x-z)+139z=2601
150x+180-90x-90z+139z=2601
60x+49z=801---->(5)
We solve equation (2) and (5) simultaneously
13x+6z=132 ------->(2)
60x+49z=801---->(5)
Make x the subject in equation (2) to get:
[tex]x=\frac{132-6z}{13}[/tex]
Put it in (5)
[tex]60(\frac{132-6z}{13})z+49z=2601[/tex]
[tex]\frac{277z+7920}{13}=801[/tex]
[tex]277z+7920=10413[/tex]
[tex]277z=2493[/tex]
[tex]z=9[/tex]
[tex]x=\frac{132-6*9}{13}=6[/tex]
From 6+y+9=20
y=20-15=5