Answer:
see explanation
Step-by-step explanation:
Given
6x² + x - 1 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 6 × - 1 = - 6 and sum = + 1
The factors are + 3 and - 2
Use these factors to split the x- term
6x² + 3x - 2x - 1 = 0 ( factor the first/second and third/fourth terms )
3x(2x + 1) - 1(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(3x - 1) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
3x - 1 = 0 ⇒ 3x = 1 ⇒ x = [tex]\frac{1}{3}[/tex]
Please Help Asap, Thank You!
Given :△ABC (to the right), AB = 15, BD = 9,
AD ⊥BC m∠C = 30°. Find the perimeter of triangle.
Answer:
48 + 12√3 units
Step-by-step explanation:
ALL LENGTHS MUST BE POSITIVE (I did this to avoid writing ± and showing that only + works)
1. Find AD (you'll find why later): 15² = 9² + AD² --> AD² = 144 --> AD = 12
2. 30-60-90: 12-DC-AC --> AC = 24, DC = 12√3 (side opposite of 90 is double side opposite of 30, side opposite of 60 is √3 times the opposite of 30)
P = AB + BD + DC + AC = 15 + 9 + 12√3 + 24 = 48 + 12√3 units
The perimeter of triangle △ABC is found by summing all sides of the triangle, resulting in 51.
Explanation:In this question, we are dealing with the triangle △ABC. We know that AB = 15, BD = 9, AD is perpendicular to BC, and m∠C = 30°. Remember, the sum of all sides in a triangle constitutes the perimeter.
Given that AB=15 and BD=9, and as BD is the opposite side of m∠C = 30°, we know that the hypotenuse is twice the length of the opposite side in a 30-60-90 triangle. Thus, AD = 2BD = 18. Since AD is also perpendicular to BC, AD divides the triangle into two right triangles.
We know that the side adjacent to ∠C is half the length of the hypotenuse in a 30°-60°-90° triangle. Hence, CD = AD/2 = 18/2 = 9. Now, BC = BD + CD = 9 + 9 = 18. Summing up all sides of the triangle, the perimeter of △ABC = AB + BC + AC = 15 + 18 + 18 = 51.
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Pls does anyone know the answer??
Answer:
The on the bottom is right.
Step-by-step explanation:
Answer:
A is the correct answer
Step-by-step explanation:
Which expression represents the area of the rectangle
(2x+7)(4x+5)?
So we'll do FOIL (first, outer, inner, last)
The equation is (4x+5)(2x+7)
First, 4x·2x=8x²
Outer, 4x·7=28x
Inner, 5·2x=10x
Last, 5·7=35
Add like terms and you get:
8x²+38x+35
The area of the rectangle represented by the expression (2x+7)(4x+5) is calculated by distributing and combining like terms, yielding the answer 8x^2 + 38x + 35.
Explanation:The expression (2x+7)(4x+5) represents the area of rectangle in Algebra. The area of a rectangle is calculated as length times width, and in this case, the length is 2x+7 and the width is 4x+5.
To calculate the area, we will need to multiply these two expressions, also known as using the distribution property of multiplication over addition.
Apply the distributive property:
2x * 4x = 8x^22x * 5 = 10x7 * 4x = 28x7 * 5 = 35Combine like terms:
8x^2 + 10x + 28x + 35 = 8x^2 + 38x + 35.So, the area of the rectangle is represented by the expression 8x^2 + 38x + 35.
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Plz help me with this
Only the last two options are true.
The first one is false, because 4.5 is the value of the maximum of f(x), not the point where it is reached.
The second one is false, because g(x) has a maximum of 9, so it is a downward-facing parabola (just like f(x)), so it doesn't have a minimum.
The third one is true, because the maximum value of f(x) is 4.5, and the maximum value of g(x) is 9, which is twice the maximum of f(x)
The last one is false (see point 2).
Answer:
The third and last one.
Step-by-step explanation:
First, by looking at the graph you can tell that the parabola peaks where x = 0.5, not 4.5, so this one is incorrect.
The second one is incorrect, because the value of the g(x) at 0 is 9, but he function is less at other values such as when x is -3 and the g(x) is 0.
The maximum value of the g(x) is 9. We can tell this because points with an equal difference of x values away from x = 0 (where g(x) = 9), also have the same y values. Because 9 is twice of 4.5, and 4.5 is the maximum value of the f(x), the third one is correct.
Lastly, The last one is true, because quadratic functions only have a minimum or a maximum value and we already know that both of these functions have a maximum value.
Simplify the expression. X^2-x/2x-2x^2
Answer:
[tex]\large\boxed{\dfrac{x^2-x}{2x-2x^2}=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2-x}{2x-2x^2}=\dfrac{x^2-x}{-2(x^2-x)}\\\\\text{cancel}\ (x^2-x)\\\\=-\dfrac{1}{2}[/tex]
Look at the picture above. Tell me the steps that I need to use to get the answer.
Answer:
¹¹⁹/₁₂₀ gallon
Step-by-step explanation:
1. Total amount of paint owned: 1 ¹/₅ + 1 ¹/₆ + ⁷/₈ = ³⁸⁹/₁₂₀ gallons
2. Total amount of paint used: 3 * ³/₄ = ⁹/₄ gallons
3. Amount left: ³⁸⁹/₁₂₀ - ⁹/₄ = ¹¹⁹/₁₂₀ gallon
how do you rewrite 1/27 as an expression with a negative exponent
Answer:
3^-3
Step-by-step explanation:
27 = 3^3
so
1/ 27= 1 / 3^3 = 3^-3
To write the fraction \( \frac{1}{27} \) as an expression with a negative exponent, you can use the property of exponents that states \( a^{-n} = \frac{1}{a^n} \), where \( a \) is any non-zero real number and \( n \) is a positive integer.
Applying this property to \( \frac{1}{27} \), we can see that the fraction is the reciprocal of \( 27 \) raised to the first power. Thus, we rewrite the expression \( \frac{1}{27} \) by flipping the position of \( 27 \) to the numerator and making the exponent negative:
\( \frac{1}{27} = 27^{-1} \)
So, \( 27^{-1} \) is the same as \( \frac{1}{27} \). When you calculate \( 27^{-1} \), you get the value of approximately \( 0.037037037037037035 \), which represents the decimal equivalent of the fraction \( \frac{1}{27} \).
ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image?
Answer: The answer would be C. Please give me a thanks :) bye!
Step-by-step explanation:
Help on number nine please?
im pretty sure true because they do not intersect and are not parallel :)
Answer:
true
Step-by-step explanation:
72 subtract 3 equals 36
That is not true. 72-3=69
find the height of the cylinder V=271.4in3
h=271.4/6π≈14.4 inches.
If the volume and the rafius of the cylinder is 271.4 cubic inches and 6 inches. Then the height of the cylinder will be 2.4 inches.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
If the volume of the cylinder is 271.4 cubic inches and the radius of the cylinder is 6 inches.
Then the height of the cylindr will be
We know the volume of the cylinder is given as
V = πr²h
Then we have
271.4 = π x 6² x h
271.4 = 36π x h
271.4 = 113.1 x h
h = 2.4
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pls pls pls help
I need help
Use the formula A = bh to determine which parallelograms have the same area.
What is that area?
Answer: Parallelograms
have an area of
square units.
Answer:
Parallelograms I, II, and IV
Step-by-step:
Area of parallelograms:
I. A=3*5=15 units squared
II. A=5*3=15 units squared
III. A=4*4=16 units squared
IV. A=5*3=15 units squared
So, parallelograms I, II, and IV have the same area of 15 units squared.
Answer:
Parallelograms I, II, and IV have an area of 15 square units
Step-by-step:
Area of parallelograms:
I. A=3*5=15 units squared
II. A=5*3=15 units squared
III. A=4*4=16 units squared
IV. A=5*3=15 units squared
So, parallelograms I, II, and IV have the same area of 15 units squared.
Darian is multiplying 34
3
4
by 12
1
2
.
Answer:
408
Step-by-step explanation:
because is you use long multiplication you will get 12*34=408.
Comstock nut company has 500 pounds of peanuts to package if each package contains one and one four pounds how many packages are needed?
Answer:
2000
Step-by-step explanation:
500/0.25. :) hope this helped
Comstock Nut Company can make 400 packages of peanuts by dividing the total weight of peanuts (500 pounds) by the weight of each package (1.25 pounds). Ounces or grams would be suitable to measure a handful of peanuts.
Explanation:To calculate how many packages Comstock Nut Company can make, we simply divide the total weight of the peanuts by the weight of each package. They have 500 pounds of peanuts and each package weighs 1 and 1/4 pounds (which is the same as 1.25 pounds).
Number of packages = Total weight of peanuts ÷ Weight per package
Number of packages = 500 pounds ÷ 1.25 pounds/package
When you divide 500 by 1.25, you get 400. Therefore, Comstock Nut Company can make 400 packages of peanuts.
When it comes to choosing the best unit of measurement, for a handful of peanuts, we would typically use ounces or grams since they are small quantities that don't weigh much, similar to how Jeffrey should use ounces to label packages of steak when most are less than a pound.
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Marilyn has a bag of coins. The bag contains 25 wheat pennines, 15 Canadian pennies, 5 steel pennies, and 5 Lincoln pennies. She picks a coin randomly from the bag. What is the probability that she picked a steel penny or a lincoln penny? A.) 10% B.) 20% C.) 50% D.) 30%
Answer:
B
Step-by-step explanation:
In probability, "AND" means to multiply and "OR" means to add.
Here they want probability of steel penny ( P(s) ) "OR" probability of lincoln penny ( P(l) ).
Let's find the individual probabilities and "ADD" them.
P(s) = 5/50 (since there are 5 steel pennies and there are 50 coins in total)
P(l) = 5/50 (since there are 5 lincoln pennies and there are 50 coins in total)
So probability of 5 steel penny and 5 lincoln penny = 5/50 + 5/50 = 10/50 = 1/5
1/5 is equal to 20%, correct answer is B
What is the zero of the following function?
Answer:
D
Step-by-step explanation:
The zero of the function is the point on the x- axis where the graph crosses
That is x = - 5
Answer: OPTION D
Step-by-step explanation:
The zero of the function is the intersection of the function with the x-axis.
A function intersects the x-axis when the value of y is zero ([tex]y=0[/tex])
Then, you can observe in the graph attached that the function intersects the x-axis at the point (-5,0), where the x-coordinate is -5 and the y-coordinate is 0:
[tex]x=-5\\y=0[/tex]
Therefore, you can identify that the zero of the function shown in the figure is:
[tex]x=-5[/tex]
This matches with the option D.
Please I need help with this one
Answer:
Cone
Step-by-step explanation:
the base is formed when the triangle is turned in a circle. the base is a triangle.
The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?
A. 20 cubic cm
B. 20/3 cubic cm
C. 20/27 cubic cm
D. 3 cubic cm
Answer:
the answer is C. 20/27 cubic cm.
Step-by-step explanation:
V = LWH
length 5(1/3 cm)
width 2(1/3 cm)
height 2(1/3 cm)
V = (5/3 cm) (2/3 cm) (2/3 cm)
V = 20/27 cubic cm.
Answer:
c
Step-by-step explanation:
Rhea had a score of a 70 on her first quiz and a score of a 77 on her second quiz. What is the percent increase from her first quiz score to her second quiz score?
The answer is:
The percent increase from her first quiz score to her second quiz score is 10%.
Why?To know what is the percent increase from her first quiz to her second quiz, first we need to calculate the increase points, then, represent it in porcentage value.
Then, calculating her increas in points, we have:
[tex]Increase=SecondQuizScore-FirstQuizScore\\Increase=77points-70points=7points\\Increas=7points[/tex]
Now, calculating the percent increase, we have:
[tex]Increase(Percentage)=\frac{Increase(points)}{FirstScore}*100\\\\Increase(Percentage)=\frac{7}{70}*100\\\\Increase(Percentage)=0.10*100=10[/tex]
Hence, the percent increase from her first quiz score to her second quiz score is 10%.
Have a nice day!
Answer:
10%
Step-by-step explanation:
increase percentage is = difference /initial value x 100
=77-70/70 x 100
=10
Find the values for c and d that would make the following equation true. (cy^2)(4y^d)=-20y^3
Answer:
c = -5 and d = 1
Step-by-step explanation:
First, multiply out (cy^2)(4y^d). We get: 4cy^(2+d).
We equate this result to the right side of the equation: - 20y^3.
Then, equating the exponents and solving for d, we get: 2 + d = 3, or d = 1.
Equating the coefficients, we get 4c = -20, or c = -5.
Tickets numbered 1 to 20 are mixed up and drawn at random. What is the probability that the ticket drawn has a number which is a multiple of three or five.
8/15
2/5
9/20
1/2
Answer:
B. 2/5
Step-by-step explanation:
First we write down the numbers.
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.
Multiplies of three or five above are: 6,9,10,12,15,16,19,20 (there are 8)
So 8/20.
8/20 simplified is 2/5
So, it's B.
To make six cakes Fred uses four and a half cups of sugar. How much sugar does he need for one cake?
Answer:
1.333 cups
Step-by-step explanation:
if you divide 6 by 4.5 you get 1.333
15 Points Please Answer Thx
Answer:
18
Step-by-step explanation:
There are 6 possible outcomes for the number and each one of those can land with all three different colors.
This means that the total amount of outcomes is 6*3 or 18.
Will give Brainlest! Help plz
41000 is 100%
29000 is ? %
?=29000x100/41000~70.73%
72/10 is equal to which number
It is equal to 7.2
Hope this helps.
Answer:
7.2
Step-by-step explanation:
Imagine math 2021
which of the statememts below are true for linear functions? Select all that apply.
That's is correct answer
Which graph matches the equation y = -(x-2)2
The equation y = -(x-2)² represents a parabola opening downwards with a vertex at (2, 0). To find the matching graph, plot several points by calculating y for chosen x values and then connect the points to reveal the parabola's shape.
Explanation:The student is asking for the graph that matches the equation y = -(x-2)². This equation represents a parabola that opens downwards due to the negative sign in front of the parenthesis. To plot this, we'll need to create a table of values by choosing different x values, inserting them into the equation, and calculating the corresponding y values. After plotting these points, we'll see the shape of the parabola. Its vertex, the highest point on the graph due to the downward opening, will be at (2, 0) since the equation is in the form y = -a(x - h)², where (h, k) is the vertex of the parabola.
Steps for Plotting:Choose x values around the vertex (2, 0).Calculate y for each x.Plot the points on the coordinate plane.Connect the points to form a parabola.A triangle has 2 congruent sides and 1 right angle.What is the triangle? List all that apply.
Answer:
When a triangle has two congruent sides it is called an isosceles triangle
Step-by-step explanation:
can i have some help please?
Answer:
C is the correct answer
nicole worked for 6 hours and 15 minutes. how should she write that on her time card
A. 7.0
B. 6.25
C. 6.15
D. 6.75
Answer:
B since 6 is a whole number for hours it would be 6 and 15 is 1/4 of 60 it would be 0.25 meaning, 6.25
Step-by-step explanation:
The time card will have 6.25 hours.
What are the steps in converting measurement of time?To convert units of measurement for time, here are the steps.
Step #1: Identify the units used.
Step #2: Determine the relationship between the units.
Step #3: Determine the conversion factor (in fraction form).
Step #4: Multiply the original measurement by the conversion factor.
Given:
6 hours and 15 minutes
= 6 + 15/60
=6 + 1/4
=6+0.25
=6.25 hours
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