Given:
The quadratic function is:
[tex]f(x)=x^2+3x-4[/tex]
To find:
The zeros of the given quadratic function.
Solution:
We have,
[tex]f(x)=x^2+3x-4[/tex]
Splitting the middle term, we get
[tex]f(x)=x^2+4x-x-4[/tex]
[tex]f(x)=x(x+4)-1(x+4)[/tex]
[tex]f(x)=(x+4)(x-1)[/tex]
For zeros, [tex]f(x)=0[/tex].
[tex](x+4)(x-1)=0[/tex]
[tex]x=-4,1[/tex]
Therefore, the correct option is (b).
HELP ASAP WILL MARK BRAINLIEST!!!!!
A Ferris wheel car moves from point C to point D on the circle shown below:
D
38°
А ferris wheel car moves from point C to D on the circle shown below:
d = 20 ft
What is the arc length the car traveled, to the nearest hundredth?
2.18 feet
4.31 feet
5.84 feet
6.63 feet
Answer:
AL= 6.63
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2[tex]\pi 10[/tex]
C = 20[tex]\pi[/tex]
[tex]AL = \frac{38}{360} 20\pi[/tex]
AL= 6.63
The length of the arc travelled by the car is 6.63 feet.
What is the arc length of a circle?The distance along the part of circumference of any circle or any curve (arc) is called arc length of a circle.
Formula for calculating the arc lengthArc length = θ×[tex]\frac{\pi }{180}[/tex]× r
where,
θ is central angle of arc
r is the radius of circle
What is diameter of the circle?The diameter of a circle is any straight line segment that passes through the center of the circle and whose end points lie on the circumference of the circle.
Formula for the calculating arc lengthdiameter = 2× radius
According to the given question
we have
θ = 38 degrees
diameter = 20ft
⇒ radius = [tex]\frac{20}{2}[/tex]
⇒ radius = 10
Therefore,
the arc length the car traveled = 38×[tex]\frac{\pi }{180}[/tex]× 10
= 38×[tex]\frac{3.14}{180}[/tex]×10
=[tex]\frac{1193.2}{180}[/tex]
=6.63 feet
Hence, the arc length the car travelled is 6.63feet.
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The HCF and LCM of two numbers x and 126 are 24 and 840 respectively. Find the value of x.
Answer:
x=160
Step-by-step explanation:
x×126=24×840
[tex]x=\frac{24 \times840}{126} =160[/tex]
How many solutions does the nonlinear system of equations graphed below
have?
• A. One
• B. Two
• C. Four
O D. Zero
SUBMIT
Select the two values of x that are roots of this equation.
x² + 3x-6=0
A. X=
-3+ /33
2
B. x=-3-83
c. x. -3-15
D. x. -3*4/15
please help
Answer:
[tex]x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 + - \sqrt{9 + 24} }{2} \\ x1 = \frac{ - 3 - \sqrt{33} }{2} \\ x2 = \frac{ - 3 + \sqrt{33} }{2} [/tex]
does anyone know how to solve this ?
Answer:
D) 144π sq. units
Step-by-step explanation:
The formula for finding the surface area of a sphere is 4π
Substitute 6 in for r. 4π = 144π
Answer:
144π sq. units
Step-by-step explanation:
The formula to determine the surface area of a sphere is: 4πr^2
But there’s no digit of pi given. Therefore we will use the formula but ignoring pi:
4πr^2
= 4r^2
= 4(6^2)
= 4(36)
= 144
Surface area is measured in square units.
Therefore the answer is 144π. The answer will be the true answer surface area once we know what π to use. For now, π will be just a variable next to 144 and will be later multiplied to it.
I hope you understand this! Hope I helped!
Una bañera en forma de trapecio tiene un area de 60 metro ademas se sabe que su base mayor es 3/2 mas grande que su base menor calcule la altura cuando la base menor es 18 metros
Respuesta:
3,2 metros
Explicación paso a paso:
Área del trapecio:
A = 1/2 (a + b) h
h = altura; ayb son las bases
Área, A = 60
Sea una base más pequeña = a = 18;
b = 18 + 3/2 = 19,5
La altura se puede calcular así;
60 = 1/2 (18 + 19,5) h
60 * 2 = 37,5 horas
120 = 37,5 h
h = 120 / 37,5
h = 3,2 metros
Simplify the expression. (6)8 + (6)3
Answer:
66
Step-by-step explanation:
Use the PEMDAS order. Multiplication comes before addition so it simplifies to 6(8)+(6)3
=48+18
=66
ratio of 55 paise is to 1 rupees
Answer:
You have to equal the unit first,
as 1 Rupee = 100 paise,
so,
55paise: 100paise,
= 11:20
I hope it hepled : )
Can someone help me with this math homework please!
Answer:
See step by Step
Step-by-step explanation:
Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.
Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.
Spencer's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 + 4x= - 4x + 2 + 4x[/tex]
[tex]10x - 2 = 2[/tex]
[tex]10x = 2 + 2[/tex]
[tex]10x = 4[/tex]
[tex]x = \frac{4}{10} [/tex]
[tex]x = 0.4[/tex]
Jeremiah's method:
[tex]6x - 2 = - 4x + 2[/tex]
[tex]6x - 2 - 6x = - 4x + 2 - 6x[/tex]
[tex] - 2 = - 10x + 2[/tex]
[tex] - 2 - 2 = - 10x[/tex]
[tex] - 4 = - 10x[/tex]
[tex] \frac{ - 4}{ - 10} = x[/tex]
[tex]0.4 = x[/tex]
As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.
If y = 2x3 - 4x and dx, dt equals 4 , find dy, dt when x = 1. Give only the numerical answer. For example, if dy, dt = 3, type only 3
Work Shown:
y = 2x^3 - 4x
dy/dt = 2*3*x^2*dx/dt - 4*dx/dt
dy/dt = 2*3*1^2*4 - 4*4
dy/dt = 8
notice how I used the chain rule for step 2.
Someone to give me the answer on the number line please
Answer:
Step-by-step explanation:
Equation for the total volume of the bucket has been given as,
V = 4 + 2t
Here V = Total volume
t = elapsed time
Table for the input-output values,
t 0 1 2 3 4
V 4 6 8 10 12
Therefore, line passing through the given points in the table will be the graph for the equation.
If f(x) = 5x + 40, what is f(x) when x = –5?
answer
1. -9
2. -8
3. 7
4. 15
Answer:
option 4
Step-by-step explanation:
f(x) = 5x + 40
f(x = - 5) = 5 ( - 5) + 40
= - 25 + 40
= 15
f(x) = 5x + 40
f(-5) = 5(-5) + 40
= 15
Ans: 15
FG has a midpoint at M(5, 7). Point G is at (9,5). Find the coordinates of point F. Write the coordinates as decimals or integers.
The circumference of a steering wheel of a car is 20 inches. What is the radius of
the steering wheel?
40 in.
20 in
100 in.
10 in.
The radius of the steering wheel is 10 inches.
What is a circle?A circle is the defined as a closed, two-dimensional curved shape in the geometry. Every point on the circle is equal distance from a certain point known as the centre of circle. A circle is a two-dimensional form that is measured in terms of radius.
What is the circumference of a circle?Circumference of a circle is defined as perimeter of circle is defined as the enclosing boundary of a curved geometrical figure called a circle. It is the product of π and its diameter.
Circumference (C) = π × d , where d is the diameter of a circle.
Given data as :
Circumference of a steering wheel of a car = 20π inches
Circumference(C) = 20π inches
Substitute the value of c in formula of Circumference :
20π = π × d [ diameter(d) = 2 radius(r) ]
20π = π × 2 r
Divided by 2π both the sides
10 = r
r = 10
r = 10 inches
Hence, the radius of the steering wheel is 10 inches.
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Question seems to be incomplete the correct question would be
The circumference of a steering wheel of a car is 20π inches. What is the radius of
the steering wheel?
If f(x)=5X-2 and g(x) = x+1, find (f -g)(x)
Answer:
Step by step explanation
a
find the shortest distance between the lines 3x+4y+10=0 and 3x+4y+20=0
Answer:
the lines are parallel they are 10 units apart
Step-by-step explanation:
The shortest distance between these two parallel lines is 2.5
Given equations:
3x + 4y + 10 = 0 ----- (1)
3x + 4y + 20 = 0 ---- (20)
To find:
the shortest distance between the two lines
The slope and y-intercept of the first equation is calculated as;
3x + 4y + 10 = 0
4y = -3x - 10
[tex]y = \frac{-3x}{4} - \frac{10}{4} \\\\y = \frac{-3x}{4} - \frac{5}{2}[/tex]
The slope = -³/₄ and the y-intercept = - ⁵/₂ = - 2.5
The slope and y-intercept of the second equation is calculated as;
3x + 4y + 20 = 0
4y = -3x - 20
[tex]y = \frac{-3x}{4} - \frac{20}{4} \\\\y = \frac{-3x}{4} - 5[/tex]
The slope = -³/₄ and the y-intercept = - 5
The two equations have the same slope = -³/₄
This shows that they are parallel with different y-intercepts
The shortest distance between the two lines is at their y-intercepts
The shortest distance between these two lines is calculated as;
[tex]distance = \sqrt{(-5 - (-2.5) )^2} \\\\distance = \sqrt{(-5+ 2.5)^2} \\\\distance = \sqrt{(-2.5)^2 } \\\\distance = \sqrt{6.25} \\\\distance = 2.5[/tex]
Thus, the shortest distance between these two parallel lines is 2.5
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Which of the following are possible
side lengths for a triangle?
A. 4, 9,4
B. 3, 8, 12
C. 8,8,9
As we know,
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
A. 4, 9, 4
[tex]4 + 9 > 4[/tex]
[tex]9 + 4 > 4[/tex]
[tex]4 + 4 < 9[/tex]
B. 3, 8, 12
[tex]3 + 8 < 12[/tex]
[tex]8 + 12 > 3[/tex]
[tex]12 + 3 > 8[/tex]
C. 8, 8, 9
[tex]8 + 8 > 9[/tex]
[tex]8 + 9 > 8[/tex]
[tex]9 + 8 > 8[/tex]
By observing the above,
the possible side lengths of a triangle are C. 8, 8, 9.
What is the mode of the set of numbers {55, 57, 59, 61, 62, 63, 64, 64, 65, 68, 69)
Answer:
64
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. So, just look for the number that appears the most.
I hope this helps!
What is the measure of side B’C’?
Find the measure of each numbered angle for each figure
Answer:
Angle 1 is 58. Angle 2 is 32.
Step-by-step explanation:
The measure of Angle ACB is 90 because C is on the circle and A and B connect to form a diameter of the circle. So, Angle 1 and Angle 2 add up to 90 (total degrees in triangle - 90). Now you can add the expressions the question gave for Angle 1 and Angle 2, and you get 7x + 6. So you have the equation 7x + 6 = 90. Solve the equation and you get x = 12. Now you can plug in that value for x into the expressions for Angles 1 and 2 to find their measures.
Vince weights 160, and his friend Nadir weights 140 pounds. Nadir calculated that his weight on another planet would be about 56 lb. Approximately what would weigh on the other planet?
Answer:
64 lb
Step-by-step explanation:
you can solve this problem by using a proportion, then cross multiply and divide. (better explained in yt videos).
Find the measure of the missing angle using the exterior angle sum theorm
Answer:
r = 30°
Step-by-step explanation:
According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.
Someone please help me ASAP please
Answer:
hey mate
plz mark it as brainliest
Choose ALL terms like 5x?
92
No answer text provided.
-8.7
522
3
43
5
-5.0
Answer:
strange question...
I assume it is asking which ones can be expressed as "5x"
those are all the ones that are a multiple of 5
5, -5x , & 5x^2 satisfy that
Step-by-step explanation:
The terms that are like 5x are: -8x and 4x as they both have the variable x raised to the power of 1 (x).
Given are some algebraic terms 9x², -8x, 5x², 3, 4x, 5 and -5, out of these we need to choose the terms which are like 5x.
To determine the terms with properties similar to 5x, we need to look for terms that have the same variable (x) raised to the same power (1).
The terms that have similar properties to 5x are those with the variable x raised to the power of 1 (x) or simply x.
From the given terms:
9x² - This term has x raised to the power of 2, not 1.
-8x - This term has x raised to the power of 1 (x), similar to 5x.
5x² - This term has x raised to the power of 2, not 1.
3 - This is a constant term and does not have x.
4x - This term has x raised to the power of 1 (x), similar to 5x.
5 - This is a constant term and does not have x.
-5 - This is a constant term and does not have x.
Hence the terms that are like 5x are: -8x and 4x.
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3(y+6)=30 solve equation
Answer:
3(y+6)=30
3y + 18 = 30
18 - 30 = 3y
12 = 3y
12/3 = y
4 = y
or
y = 4
y = 2x + 3
y=2x-1
The system has how many solutions?
one solution
two solutions
no solution
an infinite number of solutions
pls help me don't know what to do
Answer:
x=15
Step-by-step explanation:
The 60 degree angle and the (x+45) degree angle are both the same degree because they are vertical angles.
So to solve, just subtract 45 from 60
60-45=15
That's your answer!
Hope this helps!
CAN SOMEONE PLEASE HELP ME!!
Answer:
29.8
Step-by-step explanation:
a^2+b^2=c^2
a^2+7^2=11^2
a = h = 8.5
A= 1/2*b*h
A= 1/2*8.5*7
A=29.8
Which is the graph of the equation y-1=- f (x-3)?
What number should be subtracted from -3/4 to get 5/6?
Answer:
Let that rational number to be subtracted be x.Given,-5/6 - x = 4/9= - x = 4/9+5/6= - x = 23/18x = - 23/18.
Step-by-step explanation:
