Answer:
Step-by-step explanation:
x^2 + 2x - 3 =0
x^2 + 3x - x -3 = 0
(x) x (x+3) - (x + 3) = 0
(x+3) x (x-1) = 0
x+3=0
x-1=0
x=-3
x=3
x1 =-3, x2 = 1
Answer:
[tex]x=1,\\x=-3[/tex]
Step-by-step explanation:
The quadratic formula is given by [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], where [tex]x[/tex] represents both real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex].
Thus, with the given quadratic [tex]x^2+2x-3[/tex], we can assign values:
[tex]a=1[/tex][tex]b=2[/tex] [tex]c=-3[/tex]Substituting in these values to the quadratic formula, we have:
[tex]x=\frac{-2\pm\sqrt{2^2-4(1)(-3)}}{2(1)}, \\\\x=\frac{-2\pm\sqrt{16}}{2},\\\\x=\frac{-2\pm 4}{2},\\\\\begin{cases}x=\frac{-2+4}{2},x=\frac{2}{2}=\boxed{1}\\x=\frac{-2-4}{2},x=\frac{-6}{2}=\boxed{-3}\end{cases}[/tex]
Verify by factoring:
[tex]x^2+2x-3=0,\\(x+3)(x-1)=0,\\\begin{cases}x+3=0,x=\boxed{-3}\:\checkmark\\x-1=0,x=\boxed{1}\:\checkmark\end{cases}[/tex]
The braking distance (dm) of a car is directly
proportional to the square of its speed (v m/s)
When the speed of the car is increased by
50%, what is the percentage change in its
braking distance?
Answer:
Step-by-step explanation:
We can assign variables as:
d = original breaking distance
b = original speed of the vehicle
d′ = increased breaking distance
b′ = increased speed of the vehicle
We can look at it this way, originally it was like this:
d=kb2
Now, if we increase the speed to b’ which 200% more than b, we will have
d′=k(b′)2
d′=k(b+2b)2
d′=k(3b)2
d′=9kb2
Obtaining the difference between d and d’, we have
d′−d=9kb2−kb2
d′−d=8kb2
in terms of d
d′−d=8(kb2)
d′−d=8d
Adding d on both sides of the equation,
d′=d+8d
Which means the original breaking distance is increased by 800%. This is similar to the phrase “the speed of the vehicle is increased by 200%” which translates to “b + 2b”.
Hope this answer helps you :)
Have a great day
Mark brainliest
There is a 100% increase in the braking distance after 50% increase in speed.
What is speed?A body is said to be of speed v m/s if it travels v meter per second.
How to solve it?The braking distance of a car is directly proportional to the velocity of its speed(v m/s)
When the speed of the car is increased by 50% then the speed of the car v m/s becomes (3v/2) m/s.
The braking distance of a car is directly proportional to the square of its speed hence, the braking distance becomes
v²c where c is some constant.
So, the braking distance after 50% of the car speed is increased becomes (3v/2)²c₁, where c₁ is some constant.
Hence, the percentage change in the car's braking distance is
[tex]\frac{\frac{9}{4}-\frac{3}{2}}{\frac{3}{2}}[/tex]
[tex]=\frac{\frac{9-6}{4}}{\frac{3}{2}}\\=1[/tex]
That means there is a 100% increase in the braking distance after 50% increase in speed.
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1/9 (2m - 16) = 1/3 (2m + 4)
Answer:
[tex]m=7\frac{5}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{9}(2m - 16)=\frac{1}{3}(2m + 4)[/tex]
[tex]\frac{2}{9}m - 1\frac{7}{9} =\frac{2}{3}m+ 1\frac{1}{3}[/tex]
[tex]\frac{2}{9}m - 1\frac{7}{9} -1\frac{1}{3} =\frac{2}{3}m+ 1\frac{1}{3}-1\frac{1}{3}[/tex]
[tex]\frac{2}{9}m - 3\frac{1}{9} =\frac{2}{3}m[/tex]
[tex]\frac{2}{3}m-\frac{2}{9}m= \frac{2}{9}m -\frac{2}{9}m - 3\frac{1}{9}[/tex]
[tex]\frac{4}{9}m= - 3\frac{1}{9}[/tex]
[tex]\frac{4}{9}m/\frac{4}{9} = - 3\frac{1}{9}/\frac{4}{9}[/tex]
[tex]m=7\frac{5}{16}[/tex]
what are the coordinates of the image of point K(1,3) after a reflection over the line y = -1
(sorry image is crooked)
Answer:
(1. -3. is the answer. the first option
Answer: (-3,3)
Step-by-step explanation:
Please answer these 2 questions for me!!
Answers:
C) 5/14A) 2/16===========================================
Explanations:
We have 5+9 = 14 people who don't have a dog. Of this total, 5 have a cat. So that's where 5/14 comes from. We ignore the top row because we know 100% that this person doesn't have a dog (based on what the "given" says).Focus on the top row. This is because we're given or told that the person completed the hw. We have 2 people who failed the test out of 14+2 = 16 people who did the hw. The fraction 2/16 reduces to 1/8, but it appears your teacher doesn't want you to reduce.I need a fast answer to (4x) + (3x -8) = 90 for vertical angles.
Answer:
x = 14
4x = 56
3x - 8 = 34
Step-by-step explanation:
(4x) + (3x -8) = 90
7x + (-8) = 90
7x - 8 = 90
7x (- 8 + 8) = 90 + 8
7x = 98
7x/7 = 98/7
x = 14
4 x 14 = 56
3 x 14 = 42 - 8 = 34
56 + 34 = 90
The pie chart shows student participation in the fundraisers at Mountain View Middle School. What does the chart tell you about the fundraisers? Check all that apply.
20% of students participated in dances.
50% of students participated in the school carnival.
25% of students participated in the car wash. Carnival
30% of students participated in the bake sale.
10% of students participated in the talent show.
Answer:
A, B, and D
Step-by-step explanation:
just look at the chart 5Head
Answer:
A,B,E
Step-by-step explanation:
Determine the perimeter of a regular octagon that has a distance from its center to any of its vertices of 10
inches. Round your answer to the nearest tenth of an inch.
Answer:
61.2 in
Step-by-step explanation:
Draw a segment from O perpendicular to AB forming a right triangle.
Call the point of intersection J.
m∠HAB = (8 - 2)180/8 = 135
m∠BAO = 135/2 = 67.5
AJ/10 = cos 67.5
AJ = 10 cos 67.5
AB = 2(10 cos 67.5)
Perimeter = 8(AB) = 8(2)(10 cos 67.5) = 61.2 in.
The perimeter of a regular octagon that has a distance from its center to any of its vertices of 10 inches would be 61.2 inches.
What is a polygon?A polygon is a closed figure made up of three or more line segments connected end to end.
First, we draw a segment from O perpendicular to AB forming a right triangle.
Let say the point of intersection J.
∠HAB = (8 - 2)180/8
= 135
∠BAO = 135/2
= 67.5
AJ/10 = cos 67.5
AJ = 10 cos 67.5
AB = 2(10 cos 67.5)
Perimeter = 8(AB)
= 8(2)(10 cos 67.5)
= 61.2 in.
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For the inverse variation equation p=8/V
what is the value of Vwhen p=1/2?
Answer:
v = 16
Step-by-step explanation:
p = 8/v and p = 1/2. Equating these two, we get 8/v = 1/2.
Inverting both sides, we get v/8 = 2.
Find the vaue of v by multiplying both sides by 8: v = 16
why in math, whenever you do an explanation, for example, 2x - 20, the subtraction sign make the 20 a negative number?
Answer:
The negative sign is put before numbers to make them negative, or make their signs the opposite of what the are.
You have a 20.
+ 20
You don't need to put the + there if there is nothing before it, but that is a positive 20.
If you put a negative in front of it;
- (+ 20) = - 20
If you have a negative in front of parenthesis;
50 - (2x - 20)
50 - 2x + 20
70 - 2x
subtract w from 8 in algebric expression will be
Answer:
Step-by-step explanation:
according to the question ur algebraic expression is
8-w
The algebric function will be 8-w
Insert parentheses into the expresstion 15+3-6×4 to make it equal 48
Answer:
(15+(3-6))x4
Step-by-step explanation:
1. 3-6 = -3
2. 15+-3 = 12
3. 12x4 = 48
ANSWER QUICK
Suppose you deposited $200 in a savings account 4 years ago. The simple interest rate is 2.5%.
The interest that you earned in those 4 years is $20.00. Which of the following is/are true?
Answer:
Which of the following what?
Step-by-step explanation:
Not enough information.
Answer:
I didn't understand but
Step-by-step explanation:
200÷4 =50 and 50÷20 it gives you 2.5
Given the triangle below, what is m
A. 46.2
B. 41.40
C. 48.4
D. 38.6°
Answer:
B 41.4
Step-by-step explanation:
complete Pythagoras for general triangles :
c² = a² + b² - 2ab×cos(C)
with "c" being the side opposite of the angle C.
=>
8² = 10² + 12² - 2×10×12×cos(C)
64 = 244 - 240×cos(C)
240×cos(C) = 244 - 64 = 180
cos(C) = 180/240 = 18/24 = 3/4 = 0.75
C = 41.40962211... ≈ 41.4
Name the relationship: complementary, supplementary, vertical, or adjacent.
Answer:
vertical opposite angle
vertical opposite angle
vertical opposite angle
Answer: vertical
Step-by-step explanation: :)
What is the solution of x2 − 10x + 25 = 81?
x = −14 or x = −4
x = 14 or x = −4
x = 14 or x = 4
x = −14 or x = 4
Answer:
x = −14 or x = −4
Step-by-step explanation:
Answer:
wait
Step-by-step explanation:
= 1 4
= − 4
Inequality Graphs (A)
Write the inequality for each graph.
Answer:second number lone wants to eat first so 2<1
Step-by-step explanation:
-1<1
Identify the value of x. a- 12 b- 24 c- 36 d- 6.
Answer:
6
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(5+4) * 4 = x^2
9*4 = x^2
36 = x^2
Taking the square root of each side
6 =x
Answer:
d-6
Step-by-step explanation:
Tom makes a 8% commission on the sale of all the cars that he sells. He sells $140,000 worth of cars this month. What is the commission for the month?
Answer:
$11,200
Step-by-step explanation:
Just multiply the percent times the total
8% * 140000 = .08 * 140000 = 11200
Find the measure of the interior angles.
Answer:
x=22
Step-by-step explanation:
4x+2+x+3x+2=180
collect like terms
4x+x+3x=180-(2+2)
8x=180-4
8x=176
make x the subject of the formula
x=176/8
x=22
Answer:
4x + 2 + x + 3x + 2 = 180 (all angles of a triangle will equal 180 degrees)
Combine like terms:
8x + 4 = 180
-4 -4
8x = 176
Divide by 8 on both sides:
X = 22
So now we find the angles.
4 x 22 + 2 = 90 degrees for 4x + 2
3 x 22 + 2 = 68 degrees for 3x + 2
22 degrees is for X
Write an equation of the line in point slope form given the information below slope= 7 point (1,4)
Answer:
y-4=7(x-1)
Step-by-step explanation:
y-y1=m(x-x1)
y-4=7(x-1)
The equation of the line with a slope of 7, passing through the point (1,4), in point-slope form is y = 7x - 3.
To write the equation of a line in point-slope form, we use the formula:
y - y₁ = m(x - x₁)
where m represents the slope of the line and (x₁, y₁) represents the coordinates of a point on the line.
In this case, the given slope is 7 and the point (1,4) lies on the line. Plugging in the values into the formula, we have:
y - 4 = 7(x - 1)
Simplifying the equation, we can distribute the 7:
y - 4 = 7x - 7
To isolate y, we can add 4 to both sides of the equation:
y = 7x - 7 + 4
y = 7x - 3
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What are you Thoughts on türkey ?
Answer:
Turkey, country that occupies a unique geographic position, lying partly in Asia and partly in Europe. Throughout its history it has acted as both a barrier and a bridge between the two continents
Step-by-step explanation:
Answer:
Hi !!!U remember me?I love Turkey!!!In another right angle triangle the hypotenuse is 53, and the one of the side lengths is 28. Please find the missing side length.
Answer:45
Step-by-step explanation:
This is the pythagorean theroem. So you would have sides a, b, and c, of the triangle.
[tex]a^{2}+b^{2}=c^{2} so\\c^{2}-b^{2}=a^{2} \\53^{2}-28^{2}=a^{2} \\a^{2}=2025\\a= \sqrt{2025} =45[/tex]
Answer:
The answer is 45
Step-by-step explanation:
Solve 3b = 6v – 3b, for v.
6b-6
b
b-6
0
Answer:
b = v
Step-by-step explanation:
3b = 6v – 3b
Add 3b to each side
3b+3b = 6v – 3b+3b
6b = 6v
Divide by 6
6b/6 = 6v/6
b = v
In the diagram, MN is tangent to K at M, NP is tangent to K at P, MN = 128 and NP = 2x + 70. Find x
SHOW YOUR WORK
Answer:
A
Step-by-step explanation:
Tangents that are both tangent to a same point equal each other. sk
[tex]2x + 70 = 128[/tex]
[tex]2x = 58[/tex]
[tex]x = 29[/tex]
7/18 times 3 in simplest form
Answer:
21/18 which simplifies to 7/6
Step-by-step explanation:
Which of the following sets represents the domain of the function shown? (5 points)
{(2, 7}, (15, 13), (21, –4), (24, 18)}
a
{–4, 2, 7, 13, 15, 18, 21, 24}
b
{(7, 2), (13, 15), (–4, 21), (18, 24)}
c
{2, 15, 21, 24}
d
{–4, 7, 13, 18}
Answer:
c {2, 15, 21, 24}
Step-by-step explanation:
The domain is the input values
Domain {2,15,21,24}
Can someone please help with this asap its worth a lot of points. (: .
Someone please help me thank you
Answer:
[tex]x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]
Step-by-step explanation:
Ensure that the equation is in the form of ax² +bx +c= 0.
5x² -x +1= 3
5x² -x +1 -3= 0 (-3 on both sides)
5x² -x -2=0
Here, a= 5, b= -1, c= -2.
Use the quadratic formula below to solve for x.
[tex]\boxed{x = \frac{ - b± \sqrt{b^{2} - 4ac } }{2a} }[/tex]
[tex]x = \frac{ - ( - 1)± \sqrt{( -1 )^{2} - 4(5)( - 2)} }{2(5)} [/tex]
[tex]x = \frac{1± \sqrt{1 + 40} }{10} [/tex]
[tex]x = \frac{1± \sqrt{41} }{10} [/tex]
[tex]∴x = \frac{1 + \sqrt{41} }{10} \: \: or \: \: x = \frac{1 - \sqrt{41} }{10} [/tex]
Step-by-step explanation:
First, lets understand the question. When it says to find all the "real" solutions, that means you should not give any solutions containing an imaginary number. An imaginary number is basically where we accept that there exists an i (imaginary number) that is equal to [tex]\sqrt{-1\\}[/tex] (square root of negative 1). So we are not considering this concept in this question.
Let's start solving then. Can you think of an equation that may help you solve this problem? The biggest clue is that x is squared. If you said the quadratic formula, then you are perfectly correct!
Remember in order to use the quadratic formula, you must get your equation into the form:
[tex]ax^{2} +bx +c=0[/tex]
Let's do it! Right now we have:
[tex]5x^{2} - x +1=3[/tex]
Get rid of the 3 by subtracting it from both sides:
[tex]5x^{2} -x+1 -3 = 3 - 3\\5x^{2} -x-2=0[/tex]
Okay! it looks like our quadratic form now! By comparing it we can figure out what a, b, and c are in this case:
[tex]a = 5,{ }\\ b = -1, { }\\c = -2[/tex]
Let's get out our quadratic formula now:
[tex]\frac{ -b\frac{+}{} \sqrt{b^{2} -4ac} }{2a}[/tex]
All that's left to do is insert values and solve! (Be really careful when dealing with the negatives):
[tex]\frac{ -1\frac{+}{} \sqrt{(-1)^{2} -4(5)(-2)} }{2(5)}[/tex]
[tex]=\frac{ -1\frac{+}{} \sqrt{41} }{10}[/tex]
Removing the plus/minus we get two answers:
[tex]=\frac{ -1+ \sqrt{41} }{10}\\\\or\\\\=\frac{ -1-\sqrt{41} }{10}[/tex]
These are the most simplified forms! It turns out we didn't even have to worry about imaginary solutions because we didn't end up with a negative sign under the square root. Hope this helps, and good luck!
need help on this please giving brainlest! :)
Answer:
a) (-4, 5)
b) (4, -5)
Step-by-step explanation:
Just reverse the signs or use desmos as a better example.
Answer:(4,-5) and (-4,5)
Step-by-step explanation: anything reflected from the x or y axis is the postive version which is -4 has an absolute value of 4
34x divided by 6
What is x?
Answer:
x = 17/3
Step-by-step explanation: