Answer:
x = -4
Step-by-step explanation:
1. (2x2 + 8x) - (x2 - 16) = 0
2. Factoring x2+8x+16
The first term is, x2 its coefficient is 1 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16
Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 8 .
-16 + -1 = -17
-8 + -2 = -10
-4 + -4 = -8
-2 + -8 = -10
-1 + -16 = -17
1 + 16 = 17
2 + 8 = 10
4 + 4 = 8 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 4
x2 + 4x + 4x + 16
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+4)
Add up the last 2 terms, pulling out common factors :
4 • (x+4)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+4)
Which is the desired factorization
Multiply (x+4) by (x+4)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4) and the exponents are :
1 , as (x+4) is the same number as (x+4)1
and 1 , as (x+4) is the same number as (x+4)1
The product is therefore, (x+4)(1+1) = (x+4)2
(x + 4)2 = 0
3.
Solve : (x+4)2 = 0
(x+4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Answer:
x = -4
Step-by-step explanation:
=> 2x²+8x = x²-16
=> 2x²- x² + 8x + 16 = 0
=> x² + 8x + 16 = 0
Using mid-term break formula
=> x² + 4x + 4x + 16 = 0
=> x(x+4)+4(x+4) = 0
=> (x+4)(x+4) = 0
=> (x+4)² = 0
Taking square root on both sides
=> x+4 = 0
=> x = -4
Find the y-intercept of the following equation. Simplify your answer. 25 POINTS WILL MARK BRAIN
y = –10x + 7
y-intercept =
Answer:
7
Step-by-step explanation:
y=mx+b
b= y-intercept
So 7 is your answer
FInd the circumference of this circle:
Diameter - 32
π = 22/7
Answer:
The circumference of circle is 101 units.
Step-by-step explanation:
Given that the diameter of circle is 32 units so you have to find radius by dividing it by 2 :
[tex]radius = diameter \div 2[/tex]
[tex]radius = 32 \div 2[/tex]
[tex]radius = 16 \: units[/tex]
Next, we have to apply circumference formula, C = 2×π×r where r represents radius which is 16 units :
[tex]c = 2 \times \pi \times r[/tex]
Let π = 22/7,
Let r = 16,
[tex]c = 2 \times \frac{22}{7} \times 16[/tex]
[tex]c = 32 \times \frac{22}{7} [/tex]
[tex]c = \frac{704}{7} [/tex]
[tex]c = 101 \: units \: (3s.f)[/tex]
__________________________________
Hey!!
Solution,
Diameter=32
Radius=32/2=16
Circumference of circle=?
Now,
Circumference of circle=2 pi r
=2*22/7*16
=100.57
hope it helps...
Good luck on your assignment
_________________________________
11. In a group of six young pupils the mean weekly amount of pocket money is £5. When a new pupil joins, the mean weekly pocket money increases to £6. What does the new pupil receive each week ?
Answer:
£12
Step-by-step explanation:
Mathematically, we know that the mean is calculated by dividing the sum of the numbers by the count of the numbers.
Now, when they were 6 and the mean is £5, this means that the total is simply
6 * 5 = £30
Now, when a new student join, there is an increase in the value of the mean.
A new student joining means they are now 7 with the total now 7 * £6 = £42
Now the difference between the total of 6 and 7 will be £42 - £30 = £12
This value represents what the new pupil receive each week
Helpppppp meeeee please URGENT
True or False
Answer:
false
Step-by-step explanation:
you cant have same size without congruent
Bess drew a rectangular prism that is 12 units long, 8 units wide, and 13 units tall. What is the volume of the rectangular prism? A. 109 cubic units B. 156 cubic units C. 970 cubic units D. 1,248 cubic units
Answer:
D. 1,248 cubic units
Step-by-step explanation:
the volume of the rectangular prism = length*width*height = 12*8*13 = 1248 cubic units
Answer: D. 1,248 cubic units
Step-by-step explanation:
The formula for a rectangular prism volume is: V = Length x Width x Height.
In this question it already gives us all of the sides that we need! So all we need to do is just multiply all the sides together to get the volume.
12 x 8 x 13 = 1,248. Therefore D is correct!
Hope this helped you!
At the pebble pick at a school carnival the probability of drawing a pebble that wins a pencil is 50% a pebble that went to CD is 25 and a pebble that one is the book is 25% how good is Zack design a spinner that can win those Simulator 2 probability of winning each prize
Find the measurement which is most accurate to 45.76 kg.
A. 45.77 kg
B. 45.78 kg
C. 45.79 kg
D. 45.81 kg
Answer:
A. 45.77 kg
Step-by-step explanation:
The measurement with the smallest difference from 45.76 is 45.77 kg.
Help me please on this question
Answer:
Step-by-step explanation:
Given : QP║RT and QR║US
To prove: ∠1 ≅ ∠5
Statements Reasons
1). QP║RT 1). Given
2). QR║US 2). Given
3). ∠1 ≅ ∠2 3). Alternate angles
∠2 ≅ ∠5
4). ∠1 ≅ ∠5 4). Transitive property
Reasons for third step,
PQ║RT and QR is a transverse therefore, ∠1 and ∠2 will be alternate angles.
Similarly, QR║US and RT is a transverse therefore, ∠2 and ∠5 will be the alternate angles.
¿que es la trigonometria?
Answer:
I don't speak Spanish but I know what your asking. Trigonometry is a thing in physics.
Step-by-step explanation:
. It was a very freaky weather day. The temperature started out at 7⁰C in the morning and went to -15⁰C at noon. It stayed at that temperature for eight hours and then rose 8⁰C. How far below the freezing point (0⁰C) was the temperature at 8 p.m.?
Answer:
8 hours after noon (12 pm) is at 8 pm
At 8pm, temperature was -15°C
So, temperature was -15° below freezing point (0°)
Answer:
- 15
Step-by-step explanation:
8 hours after noon is at 8 p.m.
At 8 p.m., temperature was -15 C
Thus, temperature was -15 below freezing point at 8 p.m.
Hope that helps!
Which property justifies this statement: 6d(3d+2) = 18d^2 + 12d
Answer:
Distributive property
Step-by-step explanation:
write 55g as a percentage of 2.2kg
Answer:
2.5%
Step-by-step explanation:
55 grams * 0.001 kg/1 gram=
0.055kg/2.2 kg = 0.025 kg
0.025*100% = 2.5%
Line JK passes through points J(-4,-5) and K(-6, 3). If the equation of the line is written in slope-intercept form, y = mx + b,
what is the value of b?
-21
-4
11
27
Mark this and retum
Save and Exit
Nex
Answer:
A
Step-by-step explanation:
If the equation of the line is written in slope-intercept form, y = mx + b then the value of b will be -21; the correct answer is option A.
What is the slope of a straight line?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. That is why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
Formula for slope, thus, is;
Slope = (y₂ - y₁) / (x₂ - x₁)
Parameters;
J(-4, -5) and K(-6, 3)
= (3 - (-5)) / (-6 - (-4))
= (3 + 5) / (-6 + 4)
= 8 / -2
= -4
Substitute one of the coordinates into the formula to solve for b
y = mx + b
y = -4x + b
3 = -4(-6) + b
3 = 24 + b
3 - 24 = b
b = - 21
Read more about Slope of a line here
brainly.com/question/20848
#SPJ6
Andrea's living room floor is a rectangle 12 feet by 15 feet. She wants to buy a rug that is geometrically similar to her living room floor. Which size of rug should she buy? *
Answer:
180 square feet
Step-by-step explanation:
A rug that is geometrically similar to her room floor is one that has the same size as her room floor.
The floor has dimensions 12 feet by 15 feet.
The area of the floor and hence, the rug is:
A = 12 * 15 = 180 square feet
She should buy a rug that is 180 square feet
How many 3’s are in 1/8?
Answer:
There are none
Step-by-step explanation:
Because 1/8 = 0.125
Just divide 1 over 8
The number of 3's in the given fraction number 1/8 is, Zero
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
A fraction number, 1/8
The number of 3's = ?
⇒ 1/8 = 0.125
There is no number 3 present in the result of this division
Hence, the number of 3's is Zero
To know more about Fraction check:
https://brainly.com/question/8482939
#SPJ2
can sumone help with this pls
Answer:
D
Step-by-step explanation:
The range means the possible values of the y coordinate which is y ≥ 1 in this function
HELP PLEASE ! Factor the polynomial completely.
18x^2y-2y
Answer:
2y( 3x-1)(3x+1)
Step-by-step explanation:
18x^2y-2y
Factor out the greatest common factor 2y
2y( 9x^2 -1)
The term in the parentheses is the difference of squares
a^2 - b^2 = (a-b)(a+b)
2y( 3x-1)(3x+1)
Hey school system is reducing the amount of dumpster loads of trash removed each week in week five there are 45 dumpster load the waste removal in Wheaton there were 30 dumpster load removed assume that the reduction in the amount of waste each week is Linnea write an equation in function form to show the amount of trash removed each wwHey school system is reducing the amount of dumpster loads of trash removed each week in week five there a 45 dumpster load the waste removal in Wheaton there were 30 dumpster loads removed assume that the reduction in the amount of waste each week is linear write an equation in function form to show the amount of trash removed each week
Answer:
y = -3x + 60
Step-by-step explanation:
For the answer to the question above,
let x = number of weeks let y = amount of waste.
The linear equation may be expressed as,y = mx + b
m and b are the slope and y - intercept, respectively. Substituting the corresponding values,
(Week 5) 45 = 5m + b
(Week 10) 30 = 10m + b
Solving for m and b gives the values as m = -3 and b = 60. Thus, the equation is
y = -3x + 60
Answer: C
Step-by-step explanation: the other dude is right, he just didnt change y to f(x) (f of x).
If m<2 BOE = 130° and m< COB = 80º,
find the measure of the indicated arc
in circle 0.
mCBE =
Answer:
The answer is 210°.
Step-by-step explanation:
Given that ∠BOE = 130° and ∠COB is 80°. So in order to find ∠CBE, you have to add up together :
∠CBE = ∠BOE + ∠COB
∠CBE = 130° + 80°
∠CBE = 210°
(Correct me if I am wrong)
please see the attached picture...
Hope it helps...
Good luck on your assignment...
2l of punch for 15 people how many litre of punch for 90 people
Answer:
12
Step-by-step explanation:
A convex polyhedron is made of 12 congruent faces like the one shown below. What is the name of the solid? A) dodecahedron ANSWER: A B) icosahedron C) pentagonal pyramid D) pentagonal prism
Answer: dodecahedron
Step-by-step explanation:
Answer:
Option A
Explanation:
Decahedron
the blueprints at addison circle is a sculpture that took 18,000 worker-hours to construct using over 410,000 pounds of steel. The piece of art is placed within a traffic circle with a diameter of 133 feet. find the area of the circle. Round to the nearest tenth of a square foot.
Answer:
Area = 13,898.5 ft^2
Step-by-step explanation:
Here, we are tasked with calculating the area of the circle given the value of the diameter.
Mathematically, the area of a circle is;
A = pi * d^2/4
Where d here is 133 feet
A = 22/7 * 133 * 133 * 1/4 = 13,898.5 ft^2
A special die has a number on each face. The sums of the opposite faces are all equal. Five of the numbers are 5,6,9,11, and 14. What number is on the sixth face?
Answer:
The missing number is 15.Step-by-step explanation:
The sum of the opposite faces is 20, because 14 + 6 = 20 and 11 + 9 = 20, so we just need to find the answer to the equation
5 + x = 20
Solving for x, we have
x = 20-5
x = 15.
Therefore, the missing number is 15.
А
is a number written with a variable to indicate the product of the number and the variable in a term.
Answer:
Coefficient
Step-by-step explanation:
The blank word is coefficient.
Coefficient is a number written with a variable to indicate the product of the number and the variable in a term.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Let the expression,
y = mx.
Here, x and y are the variables.
And m is the constant.
So, m is multiplied to the variable x.
That means, coefficient is a number written with a variable to indicate the product of the number and the variable in a term.
Therefore, coefficient is a number written with a variable to indicate the product of the number and the variable in a term.
To learn more about the expression;
brainly.com/question/24242989
#SPJ6
if the sum of two ratinol numbers is 30 and there ratio is 2:3 then find the numbers please help me with this
Answer:
12 and 18
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5
30 ÷ 5 = 6 ← value of 1 part of the ratio
2 parts = 2 × 6 = 12
3 parts = 3 × 6 = 18
The numbers are 12 and 18
Hi there I need help with this please
Answer:
4(x-6)=45
Step-by-step explanation:
x is the number
so a number decreased by six
x-6
all multiplied by 4
4(x-6)
is 45
4(x-6)=45
FAST ANSWER PLEASE THANKS
Answer:
(f • g)(x) = x² - 6x + 7
Step-by-step explanation:
Suppose
f(x) = x² - 2
g(x) = x - 3
Determine
(f • g)(x) = ...
We can compose the functions by doing the following
(f • g)(x) = f(g(x))
(f • g)(x) = f(x - 3)
(f • g)(x) = (x - 3)² - 2
(f • g)(x) = x² - 6x + 9 - 2
(f • g)(x) = x² - 6x + 7
I hope this helps!
Solve for x. -7x= -8x+7
Answer:
x = 7
Step-by-step explanation:
-7x= -8x+7
Add 8x to each side
-7x+8x= -8x+8x+7
x = 7
Answer:
The value of [tex]x[/tex]:
[tex]x = 7[/tex]
Step-by-step explanation:
Solve for [tex]x[/tex]:
[tex]-7x = -8 x + 7[/tex]
Add both sides by [tex]8x[/tex]:
[tex]-7x + 8x = -8x + 8x + 7[/tex]
[tex]x = 7[/tex]
So, the final answer is [tex]x = 7[/tex] .
Calculate the surface area of each polyhedron. Pls!! Show work
Answer:
Step-by-step explanation:
Triangle: bh/2 = 8*9/2 = 36 cm²
bottom square: 8*8 = 64 cm²
total surface area: 36*4 + 64 = 208 cm²
If 28 g of cashew nuts contains 14 g of fats.
How many grams of fat are there in 42g of cashew nuts?
Answer:
21 g
Step-by-step explanation:
Use ration method
28:14 = 42:x
To find x,
(14 x 42) divided by 28, which equals 21g