Answer:
Option D. [tex]-(4x-3)(5x-2)[/tex]
Step-by-step explanation:
we have
[tex]f(x)=-20x^{2}+23x-6[/tex]
Equate the function to zero
[tex]-20x^{2}+23x-6=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]-20x^{2}+23x=6[/tex]
Factor the leading coefficient
[tex]-20(x^{2}-(23/20)x)=6[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]-20(x^{2}-(23/20)x+(529/1,600))=6-(529/80)[/tex]
[tex]-20(x^{2}-(23/20)x+(529/1,600))=-(49/80)[/tex]
[tex](x^{2}-(23/20)x+(529/1,600))=(49/1,600)[/tex]
Rewrite as perfect squares
[tex](x-(23/40))^{2}=(49/1,600)[/tex]
[tex](x-(23/40))=(+/-)(7/40)[/tex]
[tex]x=(23/40)(+/-)(7/40)[/tex]
[tex]x=(23/40)(+)(7/40)=30/40=3/4[/tex]
[tex]x=(23/40)(-)(7/40)=16/40=2/5[/tex]
therefore
[tex]-20x^{2}+23x-6=-20(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(5)(4)(x-(3/4))(x-(2/5))[/tex]
[tex]-20x^{2}+23x-6=-(4x-3)(5x-2)[/tex]
can someone help with factoring the trinomial below
If the solution to 4 - 2x > x + 16 is x < a, what is the value of a?
A) 6
B) 4
C) 2
D) -4
E) -6
Help with math!!!!!!
The sum of three consecutive odd integers is 18 less than 5 times the middle number. Find the 3 integers. Use an algebraic solution
X +(x+2) + (x+4) = 5(x+2)-18
3x+6 = 5x+10-18
3x+6 = 5x-8
3x=5x-14
-2x=-14
x=7
(x+2) =9
(x+4) =11
7 + 9+ 11 =27
5(9)-18 =45-18 =27
3 numbers are 7, 9 & 11
If GH is the angle bisector of FGI, which statement about the angle is true
The angle bisector of a given angle divides it into two equal parts. If GH is the angle bisector of FGI, angle FGH and angle HGI will be equal.
Explanation:If GH is the angle bisector of FGI, it means that it splits the angle FGI into two equal parts. Hence the angles FGH and HGI are equal.
For example, if angle FGI is 60 degrees, then the angle FGH and HGI (formed as a result of the bisector) would each be 30 degrees because the bisector divides the 60 degrees into two equal parts. This is the fundamental concept of an angle bisector in geometry.
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Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
The function f(x) = 5x is an exponential function true or false
Solve for 4/x+2 = 2/x x and determine if the solution is extraneous or not.
x = −2, extraneous
x = −2, non-extraneous
x = 2, extraneous
x = 2, non-extraneous
The given equation is:
4/(x + 2) = 2/x
First we get the value of x by doing cross multiplication so that all variables are in the numerator side:
4 x = 2 (x + 2)
4 x = 2 x + 4
2 x = 4
x = 2
An extraneous solution is one in which if we plug in the value of x back into the equation, the resulting values would be wrong.
Plug x = 2 back into the original equation:
4 / (2 + 2) = 2 / 2
4 / 4 = 2 / 2
1 = 1 (TRUE!)
Since the value of x = 2 satisfies the equation, then the solution is non-extraneous.
Answer:
x = 2, non-extraneous
Write “$4,915 for 72 shares of stock” as a unit rate. Round to the nearest hundredth if necessary.
divide
4915/72 = 68.2638
so $68.26 per stock is the unit rate
Ryan spent $3.25 on lunch every day, Monday through Friday. If he had $20 at the start of the week, how much money will he have left after Friday?
The amount of money left after Friday is $3.75.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Amount of money spent for the lunch every day is $3.25.
Total amount of money Ryan have is $20.
Now, number of total days from Monday to Friday is 5.
So,
The amount spent for lunch for 5 days by Ryan
= 5 × $ 3.25 = $16.25 (by unitary method)
Therefore,
The amount of money left after Friday
[tex]\$20 - \$16.25\\= \$3.75[/tex]
Hence, the amount of money left after Friday is $3.75.
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Find the value of angle M
opposite angels = 180
so 6m+13 +4m+7 =180
combine like terms
10m+20=180
10m =160
m=160/10 = 16
Angle M = 6m = 6(16) = 96 degrees
The area of a book cover is 63.8 in². The width of the book is the difference of the length and 3 inches. Let x represent the book's length. Which quadratic equation represents the area of the book cover?
x(x - 3) = 63.8
x(3 - x) = 63.8
2x - 3 = 63.8
x + x - 3 = 63.8
The correct quadratic equation representing the area of the book cover is [tex]\( x(x - 3) = 63.8 \)[/tex].
To understand why this is the correct equation, let's break down the information given in the question:
1. The area of the book cover is given as 63.8 square inches.
2. The width of the book is the difference between the length and 3 inches. If we let [tex]\( x \)[/tex] represent the length of the book, then the width can be represented as [tex]\( x - 3 \)[/tex].
3. The area of a rectangle (which is the shape of the book cover) is calculated by multiplying its length by its width.
Using the information above, we can set up the equation for the area of the book cover as follows:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
[tex]\[ 63.8 = x \times (x - 3) \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 63.8 = x^2 - 3x \][/tex]
This is a quadratic equation in standard form. The other options given do not correctly represent the relationship between the length, width, and area of the book cover:
[tex]- \( x(3 - x) = 63.8 \)[/tex] incorrectly represents the width as [tex]\( 3 - x \)[/tex] instead of [tex]\( x - 3 \)[/tex].
[tex]- \( 2x - 3 = 63.8 \)[/tex] is a linear equation, not a quadratic one, and does not represent the area calculation.
[tex]- \( x + x - 3 = 63.8 \)[/tex] simplifies to [tex]\( 2x - 3 = 63.8 \)[/tex], which is also a linear equation and does not represent the area calculation.
Use the following graph of the function f(x) = 2x^3 + x^2 - 3x + 1
What is the average rate of change from x = -1 to x = 1
A) -1
B) 1
C) 2
D) 4
a line perpendicular to a plane, would intersect the plane at one what
A line perpendicular to a plane, would intersect the plane at one point.
Perpendicular linesWhen a line is perpendicular directly away from the plane, the line will tend to intersect the plane at one points or single points.
The reason why the line intersect the plane is because the line cannot point to other places except directly away from the plane.
Therefore a line perpendicular to a plane, would intersect the plane at one point.
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Solve the inequality. Graph the solution set. 26 + 6b 2(3b + 4)
we have
[tex]26 + 6b\geq2(3b + 4)[/tex]
Applying the distributive property on the right side
[tex]26 + 6b\geq6b+8[/tex]
subtract [tex]6b[/tex] from both sides
[tex]26\geq 8[/tex] -------> is true
for all real numbers the inequality is true
therefore
the graph is a shaded area everywhere.
the answer is
the solution is all real numbers
The solution is all real numbers.
It is required to find the solution.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Applying the distributive property on the right side
26+6b≥6b+8
Then subtract 6b from both sides we get,
26≥8
For all real numbers the inequality is true.
Therefore, the solution is all real numbers.
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70 decreased by twice a number
Use The variable n to represent the unknown number
The required expression of the given statement is 70-2n.
Given that,
To determine the expression for the given statement 70 decreased by twice a number.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the number be n,
According to the question,
Number = n
70 decreased by twice the number,
So
= 70 - 2n
Thus, the required expression of the given statement is 70-2n.
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Factor the expression.
In a test of a gender-selection technique, results consisted of 248 baby girls and 13 baby boys. based on this result, what is the probability of a girl born to a couple using this technique? does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
What is the equation of the graph below?
A graph shows a parabola that opens up and does not cross the x axis. The axis of symmetry is x equal negative 2. The parabola crosses through the points negative 1, 4 and negative 3, 4.
y = − (x − 2)2 + 3
y = (x + 2)2 + 3
y = − (x + 3)2 + 2
y = (x − 3)2 + 2
What is the value of b in the equation below?
when dividing subtract the powers
so you would do 6-2 = 4
so b = 4
Answer:
The value of b is 4.
Step-by-step explanation:
The given equation is
[tex]\frac{5^6}{5^2}=a^b[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, the given equation can be written as
[tex]5^{6-2}=a^b[/tex]
[tex]5^{4}=a^b[/tex]
On comparing both the sides, we get
[tex]a=5,b=4[/tex]
Therefore the value of b is 4.
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If measure B= 60 degrees and a = 10 meters, find b.
Answer: A. 17.32m
Step-by-step explanation:
Just took edge test
Answer:A
Step-by-step explanation:
An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the radius, in inches, of the circle? Express your answer as a mixed number.
To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula: inradius = (area of the triangle) / (semiperimeter of the triangle). First, we need to find the area and semiperimeter of the triangle. Then, we can calculate the inradius and find the radius of the circle.
Explanation:To find the radius of the circle inscribed in the isosceles triangle, we can use the formula for the inradius of a triangle. The inradius is given by the formula:
inradius = (area of the triangle) / (semiperimeter of the triangle)
First, we need to find the area of the triangle. Since it is an isosceles triangle with equal sides of 5 inches, we can split it into two congruent right triangles. The height of each right triangle can be found using the Pythagorean theorem:
height = sqrt(5^2 - (6/2)^2) = sqrt(25 - 9) = sqrt(16) = 4 inches
Now, we can find the area of the triangle:
area = (1/2) * base * height = (1/2) * 6 * 4 = 12 square inches
Next, we need to find the semiperimeter of the triangle:
semiperimeter = (5 + 5 + 6) / 2 = 16 inches
Finally, we can calculate the inradius:
inradius = 12 / 16 = 3/4 inches
Therefore, the radius of the circle is 3/4 inches.
What is the value of 64? 60 = 1 61 = 6 62 = 36 63 = 216
Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3+3b^2-b + 12)
Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Given that WXYZ is a rhombus, find the value of x. A. 15 B. 20 C. 30 D. 45
In this problem, we are given the equations of the two sides of a rhombus.
Equation 1 is 4 x – 10
Equation 2 is 2 x + 20
Since the given shape is a rhombus, therefore the two sides have equal sides. Hence, we can simply equate equation 1 and equation 2:
4 x – 10 = 2 x + 20
2 x = 30
x = 15
Therefore the answer is:
A. 15
4 x – 10 = 2 x + 20
2 x = 30
x = 15
A farmer had 17 sheep. all but 9 died. how many live sheep were left
30 POINTS!!!!!!!
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 99m long and 72m wide.
Find the area of the training field. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
1273 hola aaaaa oigan busco novia
A man can run a mile in 4 minutes. calculate his average speed in kilometers per hour. show your work. (1 mile = 1.61 km)
1 mile =1.61km
60 minutes per hour
60/4 = 15 ( he can run 15 miles in one hour)
15 x 1.61 = 24.15 km per hour
round your answer if needed
The man's average speed in kilometers per hour is calculated by first converting the distance the man runs to kilometers, based on the 1 mile equals 1.61 kilometers conversion factor, and then converting time to hours, based on the 60 minutes in 1 hour conversion factor. The calculated speed is approximately 24.04 kilometers per hour.
Explanation:The man runs a mile in 4 minutes. Given that 1 mile equals 1.61 kilometers, we can first change the distance the man runs into kilometers: 1 mile * 1.61 km/mile = 1.61 km. Thus, the man's speed is 1.61 km per 4 minutes.
To convert this speed into kilometers per hour, we need to convert the time from minutes to hours. We know that 1 hour is equivalent to 60 minutes, so 4 minutes is equivalent to 4/60 = 0.067 hours. Therefore, the man's average speed in kilometers per hour is 1.61 km divided by 0.067 hours, which equals about 24.04 km/hr.
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A store sells two sizes of fresh wreaths. an? 18-inch wreath costs ?$1515?, and a? 22-inch wreath costs ?$3535. in one? day, the number of? 22-inch wreaths sold was fourfour more than twicetwice the number of? 18-inch wreaths, for a total of ?$820820. how many of each were? sold
The number of 18 inches of wreaths sold was 9 while 22 inches were 51.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say a number of 18 inches of wreaths is x while 12 inches is y.
Given that,
In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths.
So,
y = 5x + 6
And
Total amount
15x + 35y = 1920
⇒ 3x + 7y = 384
By substitution,
3x + 7(5x + 6) = 384
38x = 342
x = 9
So y = 5(9) + 6 = 51
Hence "The number of 18 inches of wreaths sold was 9 while 22 inches were 51".
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The given question is incorrect, the correct question is ;
A store sells two sizes of fresh wreaths. An 18-inch wreath costs $15, and a 22-inch wreath costs $35. In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths, for a total of $1920. How many of each were sold? .... The number of 18-inch wreaths sold was and the number of 22-inch wreaths sold was