length=8 units
Step-by-step explanation:
LET,A=16 unitsL=a unitsB=a-6 unitsL*B=AReplacing value of L with 'a'. and B with 'a-6',a(a-6)=16a*a-a*6=16a^2-6a=16a^2-6a-16=0a^2-8a+2a-16=0a(a-8)+2(a-8)=0(a-8)(a+2)=0Either,. a-8=0first value a=8Or,. a+2=0second value a=-2(Rejected due to negative)therefore, a=L=8Length=8 unitsIs the following shape a rectangle? How do you know?
Which of the following is the solution set for -3t + 11 > 20?
t < 3
t > 3
t < -3
t > -3
Answer:
t < -3
Step-by-step explanation:
-3t + 11 > 20
subtract 11 from both sides
-3t > 9
Divide both sides by -3
when multipying or dividing by a negative the inequality must be reversed
t < -3
Trong k gian vecto R^3 , cho hệ B={u(2,1,-1),v=(3,2,5) , w=(1,-1,m)} a)xác định giá trị m để B là một cơ sở k gian R^3
Answer:
Dhhdhdhgdgdgd djjdhdhdhfh dbdjhdhfv djjdhfhhb is a hdhdh yhvggfff tghrh9
Instructions: Using the image, find the slope of the line. Reduce all fractions and enter using a forward slash (i.e.
"/"). If the slope is undefined, enter "undefined
Answer:
Δy = 5 Δx = 1
slope = [tex]\frac{5}{1}[/tex] = 5
Step-by-step explanation:
Please halp due today its fill in the blanks dont do it randomly please
fill in the blanks with the words at the bottom
In 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. In 1999, tuition had risen to $221 per credit hour. Determine a linear function C(x) to represent the cost of tuition as a function of x, the number of years since 1990 C(x)= *answer here*
Answer:
The cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95
Step-by-step explanation:
A linear function is a polynomial function of the first degree that has the following form:
y= m*x + b
where
m is the slope of the function n is the ordinate (at the origin) of the functionSo, in this case: C(x)= m*( x-1990) + b where x is the number of years since 1990.
Given the coordinates of two points, it is possible to determine the slope m of the line from them using the following formula:
[tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
In this case, you know that in 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. And in 1999, tuition had risen to $221 per credit hour. So:
x1= 1990y1= 95x2= 1999y2= 221So the value of m is:
[tex]m=\frac{221 - 95}{1999 - 1990}[/tex]
[tex]m=\frac{126}{9}[/tex]
m= 14
So C(x)= 14*( x-1990) + b. In 1999, tuition had risen to $221 per credit hour. Replacing:
221= 14*(1999 - 1990) + b
221= 14*9 +b
221= 126 + b
221 - 126= b
95= b
Finally, the cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95
25% of 1 min (in sec)
21
1
Simplify:
(Enter answer as a reduced fraction.)
3
12
Submit Question
Step-by-step explanation:
21/1
When a denominator is equal to 1, the fraction might be simplified, using this formula:
a/1=a
21/1=21
3/12
Reduce fraction
3/12=3÷3/12÷3
=1/4 or 0.25
Martin had 60kgs of sugar. He put the sugar weighing 3/4 kg. How many packets did he fill ??
Answer:
45kg
Step-by-step explanation:
60.3/4=45
Convert 4years to months.
Answer:
56 months 12+12x2=56 hope this helps
Step-by-step explanation:
If x = 2.7, 5x = ____. (Input decimals only, such as 12.7.)
Answer:
5x=13.5
Step-by-step explanation:
Well, we know that 1x=2.7. So, if we want 5x we need to multiply 2.7*5 becuase 1x=2.7, so 5x=2.7*5.
Multiply. 2.7*5=13.5
So, 5x=13.5.
Hope this helps!
Answer:
13.5
Step-by-step explanation:
5x = ?
Replace 'x' with 2.7.
5(2.7) = ?
5(2.7) = 13.5
Hope this helps.
Is the relation a functi
on? ____ 1. {(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)} a. yes b. no
Answer:
No
Step-by-step explanation:
This relation is a function because the x values have a repeating number (15).
Which choice is equivalent to the fraction below when x is an appropriate value? 4/4-sqrt(6x)
Answer: Choice C) [tex]\frac{8+2\sqrt{6x}}{8-3x}[/tex]
======================================
Work Shown:
[tex]y = \frac{4}{4-\sqrt{6x}}\\\\y = \frac{4(4+\sqrt{6x})}{(4-\sqrt{6x})(4+\sqrt{6x})}\\\\y = \frac{4(4+\sqrt{6x})}{4^2 - (\sqrt{6x})^2}\\\\y = \frac{4(4+\sqrt{6x})}{16-6x}\\\\y = \frac{2*2(4+\sqrt{6x})}{2(8-3x)}\\\\y = \frac{2(4+\sqrt{6x})}{8-3x}\\\\y = \frac{8+2\sqrt{6x}}{8-3x}\\\\[/tex]
This shows why choice C is the answer.
----------------
Notes:
If you have a+sqrt(b) in the denominator, multiply top and bottom by a-sqrt(b) which is the conjugate, and that will rationalize the denominator.In the second step, I multiplied top and bottom by 4+sqrt(6x) to rationalize the denominatorIn step 3, I used the difference of squares rule. In the step afterward, the square root is eliminated.A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.
Answer:
Our two numbers are:
[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]
Or, approximately 7.66 and 3.66.
Step-by-step explanation:
Let the two numbers be a and b.
One positive real number is four less than another. So, we can write that:
[tex]b=a-4[/tex]
The sum of the squares of the two numbers is 72. Therefore:
[tex]a^2+b^2=72[/tex]
Substitute:
[tex]a^2+(a-4)^2=72[/tex]
Solve for a. Expand:
[tex]a^2+(a^2-8a+16)=72[/tex]
Simplify:
[tex]2a^2-8a+16=72[/tex]
Divide both sides by two:
[tex]a^2-4a+8=36[/tex]
Subtract 36 from both sides:
[tex]a^2-4a-28=0[/tex]
The equation isn't factorable. So, we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = -4, and c = -28. Substitute:
[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]
So, our two solutions are:
[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]
Since the two numbers are positive, we can ignore the second solution.
So, our first number is:
[tex]a=2+4\sqrt{2}[/tex]
And since the second number is four less, our second number is:
[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]
Answer:
[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]
Step-by-step explanation:
Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:
[tex]x^2+(x-4)^2=72[/tex]
Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:
[tex]x^2+x^2-2(4)(x)+16=72[/tex]
Combine like terms:
[tex]2x^2-8x+16=72[/tex]
Subtract 72 from both sides:
[tex]2x^2-8x-56=0[/tex]
Use the quadratic formula to find solutions for [tex]x[/tex]:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]
In [tex]2x^2-8x-56[/tex], assign:
[tex]a\implies 2[/tex] [tex]b \implies -8[/tex] [tex]c\implies -56[/tex]Solving, we get:
[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]
Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].
Verify:
[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]
the answer to this question
Answer:
1 square unit
Step-by-step explanation:
Area of the shaded region
= Area of the triangle with base 3 units and height 1 unit - Area of triangle with base 1 unit and height 1 unit.
= 1/2 *3*1 - 1/2 *1*1
= 1.5 - 0.5
= 1 square unit
Solve it !!
[tex]78 + 2 \div 2[/tex]
Answer:
79
Step-by-step explanation:
78 +2 ÷ 2
PEMDAS says divide first
78 + (1)
Then add
79
What is the value of x when h(x) = -3?
Answer and Step-by-step explanation:
The answer is -7 (A.)
This is determined by looking at the graph. If you to to the x-point of -3 units, you will see there is a point at a y-value of -7 (units down).
#teamtrees #PAW (Plant And Water)
Please helpppp
Graph the system of inequalities {y>2x+1/ y>|x|. Which two quadrants does the solution lie in?
Answer:
Option (1)
Step-by-step explanation:
We have to graph the system of inequalities given.
y > 2x + 1 -----(1)
y > |x| --------(2)
For inequality (1),
Solution area will be the area above the dotted line y = 2x + 1
Similarly, solution area of the second inequality will be the area above the dotted lines of y = |x|
Solution area of the system of inequalities will be the common area of both the graphs of the given system.
That will lie in quadrants 1 and 2.
Option (1) will be the answer.
a square garden has an area of 6400 square find its perimeter
CAN SOMEONE HELP ME PLZ
Answer:
what is it's perimeter?
help please asap!!!Working too please not just the answers
Answer:
62
Step-by-step explanation:
12+12+3+3+7+10+15
you just add all the sides
Please help I really need ur help please
Answer:
y = 3x - 30
Step-by-step explanation:
First, put both equations into slope-intercept form.
x + 3y - 4 = 0
3y = -x + 4
y = (-1/3)x + (4/3)
2x + 5y - 20 = 0
5y = -2x + 20
y = (-2/5)x + 4
For a line to be perpendicular to y = (-1/3)x + (4/3), its slope should be the opposite and reciprocal of this line's slope.
The slope of y = (-1/3)x + (4/3) is (-1/3). The slope of a perpendicular line is 3.
To find the x-intercept of y = (-2/5)x + 4, plug in 0 for y and find x.
0 = (-2/5)x + 4
x = 10
The equation of the line right now is y = 3x + b
Plug in (10, 0) to find the y-intercept.
0 = 3(10) + b
b = -30
The equation of the line is y = 3x - 30
a shop sells three types of boots (football, rugby and hiking) sales are usually in the ratio 6:2:3
last month 24 pairs of football boots were sold
how many boots altogether were sold last month
Answer:
44
Step-by-step explanation:
divide 24 by 6 then multiply it by all the number then add it all
please make me brainliest
What is the solution to the system of equations?
Support your answer and justify your reasoning.
Answer in complete sentences.
Answer:
The solution to the system is (-2,6)
Step-by-step explanation:
I said the solution to the system is (-2,6) because that is where both lines cross, meaning that's the solution.
Hope this is hepful.
What is EG?
EG = ____
Answer:
EG = 26
Step-by-step explanation:
We use the angle-bisector theorem here
The theorem is that given an angle that is bisected in a triangle, it splits the opposite side into two parts, with the ratio of the sides facing the angle and the adjoining leg equal for the two bisections
So, we have this as;
EF/ED = GD/FG
x/24 = x+10/54
54(x) = 24)x + 10)
54x = 24x + 240
54x-24x = 240
30x = 240
x = 240/30
x = 8
But;
EG = EF + FG
EG = x + x + 10 = 2x + 10
EG = 2(8) + 10
EG = 16 + 10 = 26
The temperature rose by 15°C from morning till noon. If the temperature
was less than 50°C at noon, write and solve an inequality to show the
possible temperature in the morning (use t to represent the temperature
in the morning)
Please help meeee
Step-by-step explanation:
answer is in photo above
Evaluate f(3)
A. 18
B. 12
C. 4
D. 21
Answer:
the answer is c you will thank us later
what is the equation of the following graph in vertex form?
Answer:
y = (x + 1)²
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 1, 0) , then
y = a(x + 1)² + 0
To find a substitute (0, 1), the y- intercept into the equation
1 = a(0 + 1)² = a
y = (x + 1)²
I need help ASAP. I will give brainliest.
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = x-7
m = 1
b = -7
y = 4
m=0
b = 4
y = -2x+3
m = -2
b = 3
2 more than the sum of y and x as an algebraic expression
Answer:
(x+y)+2
hope this helps
Need help -2<2×-3<1
Answer:
[tex]-2 < 2x - 3 < 1 \ = \ \frac{1}{2} < x < 2[/tex]
Step-by-step explanation:
[tex]-2 < 2x - 3 < 1\\\\-2 + 3 < 2x - 3 + 3 < 1 + 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ adding \ by\ 3 \ ]\\\\1 < 2x + 0 < 4\\\\1 < 2x < 4\\\\\frac{1}{2} < \frac{2x}{2} < \frac{4}{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ divide \ by \ 2 \ ]\\\\\frac{1}{2} < x < 2[/tex]
Answer:
1/2 < x < 2
Step-by-step explanation:
-2<2x-3<1
Add 3 to all sides
-2+3<2x-3+3<1+3
1<2x<4
Divide all sides by 2
1/2 < 2x/2 <4/2
1/2 < x < 2