Answer:
B. x= -1
Step-by-step explanation:
axis of symmetry is: [tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-4}{2(2)} \\x=\frac{-4}{4}\\x=-1[/tex]
The axis of symmetry for the given parabola equation y = 2x²+ 4x - 1 is x = -1.
The axis of symmetry of a parabola in the form y = ax² + bx + c can be found using the formula x = -b/(2a). For the given equation y = 2x² + 4x - 1, we can identify a as 2 and b as 4. Substituting these values into the formula for the axis of symmetry gives us x = -4/(2²) = -1.
The length of the sides of a triangle are 2x +y/2, 5x/3+y + ½ and 2/3x +2y +5/2. If the triangle is equilateral, find its perimeter.
Answer:
Step-by-step explanation:
If the triangle is equilateral :
2x +y/2 = 5x/3+y + ½ = 2/3x +2y +5/2
so the perimeter is : P = 3(2x +y/2) or 3(5x/3+y + ½) or 3(2/3x +2y +5/2)
the simplest is : P = 3(2x +y/2)
P = 6x + (3y)/2
Write the number which is exactly a third of the way from 2.6 to 3.5. Please explain how you get the answer.Thanks
3.5-2.6=0.9
0.9÷3=0.3
2.6+0.3=2.9
answer is 2.9
since there are 6.6 laps in a mile, how many laps will you have to make to run 5 miles?
Answer:
33 laps
Step-by-step explanation:
we know that
There are 6.6 laps in a mile
so
using proportion
Find how many laps will you have to make to run 5 miles
so
Let
x ----> the number of laps
[tex]\frac{6.6}{1}\frac{laps}{mile}=\frac{x}{5}\frac{laps}{mile} \\ \\x=6.6*5\\ \\ x=33\ laps[/tex]
Identify the real zeros for f(x) = 3x2 + 2x + 4.
A) 1 and −1
B) 0 and −1
C) no solution
D) infinite solutions
Answer:
c: no solution
Step-by-step explanation:
Final answer:
The function f(x) = 3x^2 + 2x + 4 has no real zeros because the discriminant (b^2 - 4ac) is negative, indicating that the roots of the quadratic equation are complex.
Explanation:
The question asks us to identify the real zeros of the function f(x) = 3x2 + 2x + 4. To find the real zeros, we look for values of x that make f(x) equal to zero. We can approach this by attempting to solve the quadratic equation 3x2 + 2x + 4 = 0 using the quadratic formula, which is x = [-b ± √(b2 - 4ac)]/(2a), where a = 3, b = 2, and c = 4.
Inserting these values into the formula, we get:
x = [-2 ± √((2)2 - 4*3*4)]/(2*3)
x = [-2 ± √(4 - 48)]/(6)
x = [-2 ± √(-44)]/(6)
Since the part under the square root (√(-44)) is negative, this indicates that the solutions for x are complex, not real. Therefore, the equation 3x2 + 2x + 4 has no real solutions.
After a deposit of $250, a withdrawal of $312, and a
deposit of $15, the balance in a savings account is
$67.50. What was the balance (b) before the deposits
and withdrawal?
Answer:
55
Step-by-step explanation:
A roll of fabric was 120 inches long. A customer bought 3 feet of the fabric.
How many feet of fabric were remaining?
The 7 feet of fabric were remaining.
To solve this problem step by step:
1. Convert the length of the roll of fabric from inches to feet.
- 120 inches ÷ 12 inches/foot = 10 feet
2. Subtract the length purchased by the customer from the total length of the roll.
- 10 feet - 3 feet = 7 feet
So, the customer bought 3 feet of fabric, leaving 7 feet remaining.
1. To convert inches to feet, we know that there are 12 inches in a foot. So, we divide the length of the fabric in inches by 12 to get the length in feet.
- 120 inches ÷ 12 inches/foot = 10 feet
2. Next, we subtract the length purchased by the customer (3 feet) from the total length of the roll (10 feet) to find out how much fabric remains.
- 10 feet - 3 feet = 7 feet
Therefore, the customer bought 3 feet of fabric, leaving 7 feet remaining.
Complete question:
A roll of fabric was 120 inches long. A customer bought 3 feet of the fabric.
How many feet of fabric were remaining?
What is the area of the right triangle 8 and 2
Answer:
Step-by-step explanation:
fv xcfvsvsvfber
Answer:
D
Step-by-step explanation:
The area (A) of a triangle is calculated using the formula
A= [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 8 and h = 2, so
A= 0.5 × 8 × 2 = 8 units² → D
Solve the simultaneous equations using both elimination and substitution method.
Answer:
x=1 and y = 9
Step-by-step explanation:
Solving using elimination method:
In elimination method we solve equations such that one variable cancels out and we find the value of other variable.
x + 7y = 64
x + 3y = 28
Subtracting both equations:
x + 7y = 64
x + 3y = 28
- - -
___________
0 +4y = 36
y= 36/4
y=9
Putting value of y in one of the equation,
x+7y = 64
x + 7(9) = 64
x + 63 = 64
x = 64-63
x = 1
So, x=1 and y=9
Solving using substitution method:
In substitution method, we substitute value of one variable into other value
x + 7y = 64 (1)
x + 3y = 28 (2)
From 1
x = 64 -7y
Putting value of x in eq(2)
(64 -7y) + 3y = 28
64 -7y +3y =28
64 - 4y = 28
-4y = 28 -64
-4y = -36
y = -36/-4
y = 9
Putting value of y in eq (1)
x + 7y = 64
x + 7(9) = 64
x + 63 = 64
x = 64 - 63
x = 1
So, x=1 and y = 9.
Evaluate 9x + 3xy − 2 for x = 3 and y = −3.
Answer:
- 2
Step-by-step explanation:
Given
9x + 3xy - 2
Substitute x = 3 and y = - 3 into the expression
= 9(3) + 3(3)(- 3) - 2
= 27 - 27 - 2 = - 2
Answer:
C
Step-by-step explanation:
Just did it on edg
round 939,515 to the nearest ten
Answer:
939,520
Step-by-step explanation:
You round up because you have a 5 in the tens place and as the saying goes: "Five or more up the score, four or less let it rest"
The number 939,515 rounded to the nearest tens is 939520.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, A number 939515 and we have to round it to the nearest ten.
To round this number to the nearest ten we'll look at the digit at the unit's place.
The digit at the unit place is 5 so we'll add 1 to the tens digit and make the unit digit zero.
Therefore the number 939515 rounded to the nearest tens place is
939520.
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I have to find the volume and the surface area of a cereal box.
12 inches tall
8 inches wide
please show all your work
Answer:
Volume: 8x1x12=96 inches^3
Surface area: 8x1x2=16
1x12x2=24
8x12x2=192
the total surface is: 16+24+192=232 inches^2
12 in tall * 8 in wide = 96 in area. You need a third value to find a volume.
A cone has a lateral area 100 pi and total surface area 136 pi. Find its radius.
Answer:
Radius of the cone is 6 unit.
Step-by-step explanation:
Given:
Lateral Surface Area of Cone, LSA = 100π unit²
Total Surface Area of cone, TSA = 136π unit²
Let, r be the radius of cone.
According to the question,
Total Surface area = lateral surface area + Area of circle
136π = 100π + πr²
πr² = 36π
r² = 36
r = 6
Therefore, Radius of the cone is 6 unit.
The radius of the cone is 6 units.
To solve for the radius of the cone, we need to use two formulas: the lateral area (LA) and the total surface area (TSA) of a cone. The given values are:
Lateral area (LA) = 100πTotal surface area (TSA) = 136πWe use the following formulas:
Lateral area (LA) = πrl, where r is the radius and l is the slant height.Total surface area (TSA) = πr² + πrl.From the given values:
100π = πrl (Lateral area)From the first equation, we can express l in terms of r:
l = 100 / r
Substitute l in the second equation:
136 = r² + r(100 / r)
=> 136 = r² + 100
Rearrange the equation to solve for r:
r² = 136 - 100
=> r² = 36
=> r = √36
=> r = 6.
what does 1v+6v=7 equal
Answer: v = 1
1v + 6v = 7 Combine like terms
7v = 7 Divide both sides by 7
v = 1 Answer!
Answer:
v=1
Step-by-step explanation:
You can add the similar variables (1v and 6v) to get 7v. now your equation should be 7v=7. divide each side by 7 so that the variable stands alone. 7/7 = 1, so v=1.
X - 10 = 10 solve for x
Answer:
x=20
Step-by-step explanation:
20-10=10
Answer:
x = 20
Step-by-step explanation:
x - 10 = 10
+10
cancel out the 10 and do the same thing to both sides
x = 20
very simple
If I were to use the distributive property to simplify 3(10+15x) would you multiply 3 times 10 and add 15x to it?
Answer:
No!
The answer is 30 + 45x See below. Very important question.
Step-by-step explanation:
No!
If you do that, you are violating the properties of the distributive property.
You must multiply both sides of the plus sign by 3
3(10 + 15x) = 3*10 + 3*15x
3(10 + 15x) = 30 + 45x
Compare 7 x 10^3 and 2 x 10^3.
Answer
5000
Step-by-step explanation:
You convert the numbers into standard #'s which gets you 7000 and 2000. Subtract 7000 - 2000 and you get 5000.
7x10^3 is 3-1/2 times the size of 2x10^3.
the length of a rectangle is 6cm longer than its width.
if the perimeter of the rectangle is 32cm, find its area.
Answer:
A = 55 cm²
Step-by-step explanation:
Here, L = W + 6 cm, and P = 2W + 2L = 2W + 2(W + 6 cm) = 32 cm
Then 2W + 2(W + 6 cm) = 32 cm becomes:
2W + 2W + 12 cm = 32 cm, or
4W = 20 cm.
Therefore, W = 20 cm / 4 = 5 cm
The area of this rectangle is A = L · W = (5 cm + 6 cm) · (5 cm), or
A = (11 cm)(5 cm), or A = 55 cm²
Final answer:
The area of the rectangle is calculated by solving for the width using the given perimeter, then finding the length, and finally multiplying the two. The width is 5 cm, the length is 11 cm, and the area is 55 cm².
Explanation:
Let's denote the width of the rectangle as w centimeters. According to the problem, the length of the rectangle is 6 cm longer than its width, so we can express the length as w + 6 cm.
The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 32 cm, we can write the equation 2(w + 6) + 2w = 32.
Solving this equation:
2w + 12 + 2w = 32
4w = 32 - 12
4w = 20
w = 5 cm
Now that we have the width, we can find the length:
l = w + 6
l = 5 + 6
l = 11 cm
The area of the rectangle is found by multiplying the length by the width, A =[tex]l \(\times\) w[/tex], which gives us:
A = [tex]11 \(\times\) 5[/tex]
A = 55 cm²
What is the volume of the come with radius 5 m and height 6 m ? Express the answer in terms of pi.
A. 35pi m^3
B. 47pi m^3
C. 50pi m^3
D. 63pi m^3
Answer:
C
Step-by-step explanation:
The volume (V) of a cone is calculated using the formula
V = [tex]\frac{1}{3}[/tex] πr² h
where r is the radius and h the perpendicular height
here r = 5 and h = 6, hence
V = [tex]\frac{1}{3}[/tex] × π × 5² × 6
= 2π × 25 = 50π m³ → C
The volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]
How to get the volume of the cone
The formula for the volume v of a cone is given by:
[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]
The variables in the formula are:
r is the radius of the base of the cone.
his the height of the cone.
Given a cone with radius r = 5 meters and height h = 6 meters, substitute these values into the formula:
[tex]\[ V = \frac{1}{3} \times \pi \times (5^2) \times 6 \]\[ V = \frac{1}{3} \times \pi \times 25 \times 6 \]\[ V = \frac{1}{3} \times \pi \times 150 \]\[ V = 50 \pi \][/tex]
Therefore, the volume of the cone is [tex]\( 50\pi \, \text{m}^3 \).[/tex]
What is the volume of this right cone?
[tex]\bf \textit{volume of a right-circular cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=15 \end{cases}\implies V=\cfrac{\pi (12)^2(15)}{3}\implies V=720\pi[/tex]
43 plus what equals 112
The number that when added to 43, would give the result of 112 can be found to be 69.
How to find the number ?To find the number that, when added to 43, equals 112, you can use algebraic reasoning.
Let's represent the unknown number with the variable "x". The equation can be set up as:
43 + x = 112
To solve for "x," we need to isolate it on one side of the equation.
First, subtract 43 from both sides of the equation:
43 + x - 43 = 112 - 43
The 43 on the left side cancels out:
x = 112 - 43
Simplifying the right side of the equation:
x = 69
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To solve the equation 43 + x = 112, subtract 43 from both sides to isolate 'x'. The value of 'x' is 69.
Explanation:To find the number that, when added to 43, equals 112, we can use algebra. Let's use the variable 'x' to represent the unknown number. So, the equation is 43 + x = 112.
To isolate 'x', we need to move 43 to the other side of the equation.
By subtracting 43 from both sides, we get x = 112 - 43. Evaluating the subtraction, we find that x = 69.
The average revenue of a TV manufacturing unit is given by r(x)=75x^2-5x^3/2 where x is the number of TVs sold by the firm. Find the total revenue generated by the firm.
Answer:
The total revenue generated by the firm is:
[tex]P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]
Step-by-step explanation:
The average cost per TV is:
[tex]r(x) =\frac{P(x)}{x}[/tex]
Where x is the number of televisions sold and P is the firm's income for all the televisions sold
In this problem we know the equation r(x).
Then P(x) will be:
[tex]P(x) = x*r(x)[/tex]
Therefore if [tex]r(x)=75x^2-5x^{3/2}[/tex] then
[tex]P(x) = x*(75x^2-5x^{3/2})[/tex]
[tex]P(x) = 75x^{2+1}-5x^{\frac{3}{2}+1}\\\\P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]
Answer:
Px =75x^3-5x^5/2
Step-by-step explanation:
Here is a quadratic equation. is it in Standard form? 2x^2-7x-3=0
Answer:
Yes
Step-by-step explanation:
The standard form for a quadratic equation in the US has the terms in decreasing order by power on the left of the equal sign, and the right side zero. Preferably, the leading coefficient is positive. This might also be called "general form." Elsewhere, the "standard form" may be different.
Using a "15% off" coupon, Dianne saved $12.75 on a new chair for her home office. What was the chair's regular price? How much did she pay?
Answer:
The original price was $85
She spent $72.25
Step-by-step explanation:
When x equals the price of the chair:
12.75/15 = x/100
15 x = 1275
x = $85
To find the price she paid:
85 - 12.75 = $72.25
is an isosceles trapezoid below x=
Answer:13
Step-by-step explanation:
5x+15=7x-11
7x. 7x
2x+15=11
+15 +15
2x =26
———
2
x = 13
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The value of x is 13.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
In an isosceles trapezoid, the angles formed at the ends of any one of the parallel lines are congruent. Therefore, we can write,
5x+15 =7x-11
15+11=7x-5x
26=2x
x = 13
Hence, the value of x is 13.
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About what distance in feet would a person be 8 seconds after experiment begins
is this the full question?
What is 12/20 written as a decimal
should be 20%
Hope this helps
Answer:it's 12.20
Step-by-step explanation:
What is the maximum number of relative extremes contained in the graph of this function f(x)=3x^4-x^2+4x-2
Answer:
Maximum number of relative extremes contained in the graph of this function = 3.
Step-by-step explanation:
We have been given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].
Degree of the given function = 4.
Because degree is the highest power of variable.
Then relative number of extrema = degree - 1 = 4 - 1 = 3
Hence final answer is 3.
Use substitution to solve the linear system of equations.
y = 4x
3x + 5y = -46
(-8, -2)
(8, -2)
(-2, 8)
(-2, -8)
Answer:
(-2,-8)
Step-by-step explanation:
y=4x
3x+5y=-46
3x+5(4x)=-46
3x+20x=-46
23x=-46
x=-2
y=4(-2)
y=-8
I need help for number 7 please please
Answer:
They averaged 79 km per hour
Step-by-step explanation:
To find the average distance, take the kilometers and divide by the hours
1106 km/ 14 hours
79 km / hours
They averaged 79 km per hour
79
79x14 is 1106. hope this helps
A 25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?
17 and 8
Step-by-step explanation:
8 is the shortest board so multiply 8 by 2 add the 1 foot more gives you 17