Here all the given equations are in the form of
[tex]ax^2+bx+c=0[/tex]
The value of [tex]x[/tex] can be determined by the perfect square method as follows:
[tex]ax^2+bx+c=0[/tex]
[tex]\Rightarrow x^2+\frac{b}{a}+\frac{c}{a}=0[/tex]
[tex]\Rightarrow x^2+2\times\frac{b}{2a}+\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2+\frac{c}{a}=0[/tex]
[tex]\Rightarrow \left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2-\frac{c}{a}[/tex]
[tex]\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\;\cdots(i)[/tex]
Now, for [tex]x^2+3x-4=0[/tex]
[tex]a=1, b=3, c=-4[/tex]
So, from equation (i)
[tex]x=\frac{-3\pm\sqrt{3^2-4\times1\times(-4)}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{3\pm\sqrt{9+16}}{2}[/tex]
[tex]\Rightarrow x=\frac{3\pm5}{2}[/tex]
[tex]\Rightarrow x=\frac{3+5}{2},\frac{3-5}{2}[/tex]
[tex]\Rightarrow x= 4, -1[/tex]
Similarly, for [tex]9x^2+12x+4=0[/tex]
[tex]a=9, b=12, c=4[/tex]
So, from equation (i)
[tex]x=\frac{-12\pm\sqrt{12^2-4\times9\times4}}{2\times9}[/tex]
[tex]\Rightarrow x=\frac{-12\pm0}{18}[/tex]
[tex]\Rightarrow x=\frac{-2}{3}[/tex]
For [tex]x^2-2x-3=0[/tex]
[tex]a=1, b=-2, c=-3[/tex]
[tex]x=\frac{-(-2)\pm\sqrt{(-2)^2-4\times1\times(-3)}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{2\pm\sqrt{16}}{2}[/tex]
[tex]\Rightarrow x=\frac{2\pm4}{2}[/tex]
[tex]\Rightarrow x=\frac{6}{2},\frac{-2}{2}[/tex]
[tex]\Rightarrow x=3.00, -1.00[/tex]
For [tex]x^2-6x+9=0[/tex]
[tex]a=1, b=-6, c=9[/tex]
[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4\times1\times9}}{2\times1}[/tex]
[tex]\Rightarrow x=\frac{6\pm0}{2}[/tex]
[tex]\Rightarrow x=3.00[/tex]
For [tex]2x^2-4x-3=0[/tex]
[tex]a=2, b=-4, c=-3[/tex]
[tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4\times2\times(-3)}}{2\times2}[/tex]
[tex]\Rightarrow x=\frac{4\pm\sqrt{40}}{4}[/tex]
[tex]\Rightarrow x=\frac{4\pm2\sqrt{10}}{4}[/tex]
[tex]\Rightarrow x=\frac{4+2\sqrt{10}}{4},\frac{4-2\sqrt{10}}{4}[/tex]
[tex]\Rightarrow x=2.58, -0.58[/tex]
An office building is 111ft high. About how tall is this in meters?
Answer:
33.8328
Step-by-step explanation:
Divide the length value by 3.281
The sum of three numbers is 154
The second number is 8 times the first.
The third number is 16 less than the second.
What is the third number?
Answer:
64
Step-by-step explanation:
x+8x+(8x-16)=154
17x=170
x=10
10+80+64=154
A scientist studied the migration patterns of two types of whales. The humpback whale traveled 2,000 miles in 25 days. The gray whale traveled 2,250 miles in 30 days. Assuming the humpback whale travels the same distance each day, what is the unit rate for the humpback whale in miles per day?
Answer:
it is 80 miles
Step-by-step explanation:
2000 divided by 25 is 80 therefore you multiply 80 x 30
Hii.Picture attached, thanks
Answer:
the answer is b 36*
Step-by-step explanation:
Can someone help me with these questions.
Answer:
C ( x = 2 (multiplicity of 2), x = -2, x = -4)
A ( x = 5 (crosses), x = -3 (touches))
Step-by-step explanation:
Here are a couple of rules that helped me come to these answers.
1. When finding a zero, you flip the value inside of the parenthesis. For example (x + 2) would have the zero of x = -2.
2.The multiplicity of something is how many times the same zero is there. It is the exponent outside of the equation. For the first question, the (x - 2) has an exponent of 2, thus it has the multiplicity of 2.
3. The multiplicity determines whether the line just touches (or "bounces" off) the x axis or crosses the x axis. If the multiplicity is odd, it crosses the axis. If the multiplicity is even, it just touches the axis. A good way to remember this is with linear and quadratic equations. A linear is commonly know as only having an exponent of 1 (an odd) number and would cross the x axis. A quadratic equation has an exponent of two (an even number) so the line "bounces" on a graph.
find the value of x. round the length to the nearest tenth. PLZ HELP ME.
Answer:
x ≈ 7.9 ft
Step-by-step explanation:
cos∅ = adjacent over hypotenuse
Since we are dealing with a right triangle, we can use trigonometry to help us solve for missing values:
cos44° = x/11
11cos44° = x
x = 7.91274
x ≈ 7.9 ft
(please help me) 3/4 - ? =1/12
Answer: 2/3
Step-by-step explanation:
What are the coordinates of the point LaTeX: \frac{1}{4}
1
4
of the way from A(−6, −3) to B(10, 9)?
girlll i need that answer to
what is the product for 1.7+-3.2
Answer:
-1.5
Step-by-step explanation:
do you not have a calculator???
Answer:-1.5
Step-by-step explanation:
1.7 + -3.2 = -(3.2-1.7)= -1.5
in the sahara desert one day it was 136 Fahrenheit, in the Goni desert a temperature of -50 degrees Fahrenheit was recorded, What is the difference between these two temperature
Answer:
186 degrees Fahrenheit
Step-by-step explanation:
If you get rid of the - in -50 than it is 50 and 50+136=186
Answer:
186 Fahrenheit
Step-by-step explanation:
Difference= steam point-ice point
=136-(-50)
=136+50
=186F
URGENT AND EASY TO DO -7(7x+8)≤287 PLEASE
Answer:
x≥−7
Step-by-step explanation:
Answer:
x [tex]\geq[/tex] -7
Step-by-step explanation:
-49x - 56 [tex]\leq[/tex] 287
-49x [tex]\leq[/tex] 343
x [tex]\geq[/tex] -7
note: if you're going to divide by a negative number you need to flip the sign.
increasing or decreasing?
slope?
y and x intercept?
other points the line goes through?
equation if the line?
Answer:
slope = 1/2
The x-intercept is (8, 0). The y-intercept is (-4, 0).
(2, -3), (4, -2), (6, -1)
y = (1/2)x - 4
Step-by-step explanation:
1)
slope = rise/run
Start at (0, -4) and go to (2, -3).
Start at (0, -4) and go 1 unit up. That is a rise of 1.
Now go 2 units right to arrive at (2, 3). That is a run of 2.
slope = rise/run = 1/2
2)
The line crosses the x-axis at (8, 0).
The x-intercept is (8, 0).
The line crosses the y-axis at (-4, 0).
The y-intercept is (-4, 0).
3)
Here are some points: (2, -3), (4, -2), (6, -1)
4)
y = mx + b
y = (1/2)x - 4
Answer:
Below in bold.
Step-by-step explanation:
The line is rising to the right so it has an increasing slope.
The slope of the line is 4/8 = 1/2.
Reading from the graph the x intercept is (8, 0).
The y-intercept is (0, -4).
The line passes through the points (2, -3) and (6, -1).
The equation of the line is:
y = (1/2)x - 4.
Order the numbers from least to greatest, 19/2, 9.4, 80
Answer:
9.4, 19/2, 80
Step-by-step explanation:
Here's the question.
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION RQ PLS!!!!!!!!
Answer:
10.19 ftStep-by-step explanation:
Circumference formula
C = 2πrSolving for radius
64 = 2*3.14rr = 64/2*3.14r = 10.19 ftParallelograms PQRS and QRTU are standing on
the same base QR and between the same parallel
lines PT and QR. Prove that the area of
parallelograms PQRS and QRTU are equal.
Parallelograms PQRS and QRTU have the same base QR and height. it proves that areas are equal as base × height remains constant.
To prove that the area of parallelograms PQRS and QRTU are equal,
Use the concept that parallelograms with the same base and between the same parallel lines have equal areas.
Parallelograms PQRS and QRTU
Same base QR
Between the same parallel lines PT and QR
Proof,
Draw a diagram with parallelograms PQRS and QRTU sharing the common base QR and being situated between parallel lines PT and QR.
Since PQRS and QRTU share the same base QR and are between the same parallel lines PT and QR, their heights (perpendicular distances from base QR) are equal.
Let's call this height 'h'.
The area of a parallelogram is given by the formula:
Area = base × height.
For PQRS, its area would be: Area of PQRS = QR × h.
For QRTU, its area would be: Area of QRTU = QR × h.
Since both parallelograms have the same base 'QR' and the same height 'h', their areas are equal.
Therefore, it is proved that the area of parallelograms PQRS and QRTU are equal.
learn more about parallelograms here
brainly.com/question/31220364
#SPJ2
y=2x+5
y=2x-1
parallel
perpendicular
or neither
Which of the following equations represent linear function?
Answer:
click them all and whatever shows up right then keep that.. bc thats big ideas.. i know how that works
Step-by-step explanation:
I need help with these two anyone can help?
Answer:
The first one is option one and the second one is option two
Step-by-step explanation:
Chef rita is cooking for a sunday brunch. She knows that 22 pancakes can feed 8 people. she is wondering how many people (p) she can feed with 55 pancakes. She assumes each person eats the same quantity of pancakes. How many people can Rita feed with 55 pancakes?
Simplify 4x + 5x - 2.
Answer:
1x-2
Step-by-step explanation:
you subtract 4x from 5x and you get 1x-2
Answer:
9x - 2
Step-by-step explanation:
combine like terms
In a group of 150 people, 39 of them wear glasses. What is the probability of randomly selecting a person who does not wear glasses?
A. 111/150
B. 39/111
C. 111/189
D. 189/150
E. 39/150
Answer:
A. 111/150
Step-by-step explanation:
Because we know that 39 people out of the 150 in the group wear glasses, we need to subtract that from the total. This gives us 111 people that don't wear glasses.
Therefore, the probability of choosing someone not wearing glasses is 111/150.
what is 9x2y-3 if x = 5 and y = 3.
Answer:
267
Step-by-step explanation:
23,465 rounded to the nearest ten thousand
Answer:
23,718
The 2 is in the ten thousands place. There is a 3 in the thousands place. Since 3 is less than 5, 2 stays the same and everything after it turns into 0s.
20,000
Answer: 20,000
Which of the following is a rational number?
v1, v2, v3, v5
Answer:
5
Step-by-step explanation:
-6(5.7)=
please help
Answer:
-34.2
Step-by-step explanation:
when u multiply those 2 numbers, it makes -34.2
Answer: G = 35.2
Step-by-step explanation: G - 6 x 5.7 = 1
G - 34.2 = 1
G = 1 + 34.2
G = 35.2
G = 176/5 , G = 35 1/5
Please Hurry!!!
If angle 1 is 110°, what would the other angle measures have to be in order for m || n and
q || p?
Angle 2 =
°
Angle 3 =
°
Angle 4 =
Answer: Angle 2 is 110
Angle 3 is 70
Angle 4 is 70
Step-by-step explanation:
:)
Step-by-step explanation:
angle 2= 110
angle 3=70
angle 4=70
awnser all of them pls
First is false, second true, third is true , last is false. Wording is messed up on some gives the hint! Page 1<<<
13 is D no here << second page
El equivalente a (x +8)(x-8) es:
Answer:
x^2 - 64
Step-by-step explanation:
(x + 8)(x - 8) = x^2 - 8x + 8x - 64 = x^2 - 64
What is 0.4(20 - 10m) = 2.5 - 2m - 12.5
Solve for M
Thanks!
Answer:
the answer is m = 9 your welcome