The given Quadratic equation is
[tex]4x^2- 8x - 13 = 0\\\\4(x^2- 2 x - \frac{13}{4}) = 0\\\\ (x-1)^2-1^2- \frac{13}{4}=0\\\\ (x-1)^2=\frac{\sqrt{17}}{4}\\\\ x-1=\pm\frac{\sqrt{17}}{4}\\\\ x=1 +\frac{\sqrt{17}}{4} \text{or} x=1-\frac{\sqrt{17}}{4}[/tex]
These are the steps to determine the roots as well as solve the quadratic equation.
You can find the mistake by looking at the procedure of solving the quadratic equation by completing the square solved above.
Answer:
step 3
Step-by-step explanation:
what must be done to the expression x + 108 to make it equal x?
To make the expression x + 108 equal to x, subtract 108 from both sides of the equation.
Explanation:To make the expression x + 108 equal to x, we need to subtract 108 from both sides of the equation. This will give us:
x + 108 - 108 = x - 108
Simplifying the equation, we get:
x = x - 108
However, if we are not solving an equation and simply need to simplify the expression x + 108 to make it equal to x, then the answer is that nothing can be done. The expression cannot be simplified to make it equal to x without additional information or context.
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Which expression is equivalent to (2g^5)^3/(4h^2)^3
Answer:
Step-by-step explanation:
It’s A
Round 846 to the nearest hundred___________ and 3756 to the nearest thousand ________
Use the table below to answer this question:
x y
0 2
1 -1
2 -6
Find the average rate of change for the given function from x = 0 to x = 2.
If a=6 and b=5 what is the value of (A2-b2)2
How many days are between march the 15th and august the 15th?
Answer:21 weeks and 6 days
Step-by-step explanation:
lol im late its 2021
Graph the hyperbola with equation quantity x plus four squared divided by sixteen minus the quantity of y plus three squared divided by twenty five = 1.
Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo. Yesterday she had seven clients and earned $500. Let x represent only the clients that got a cut and y represent the clients that got a cut and color combo.
Which of the following equations could be used to represent this situation.
1. y=7-x
2. x + y= 500
3. 120x + 35y= 500
4. (35+120) (x + y)= 500
5. 35x + 120y= 500
Check all that apply
Answer:
Option 5th is correct
[tex]35x+120y = 500[/tex]
Step-by-step explanation:
Here, x represents only the clients that got a cut and y represent the clients that got a cut and color combo.
As per the statement:
Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo.
" Charges $35 for a cut" translated to 35x
"$120 for a cut and color combo" translated to 120y
It is also given that yesterday she had seven clients and earned $500.
⇒[tex]35x+120y = 500[/tex]
therefore, an equations could be used to represent this situation is, [tex]35x+120y = 500[/tex]
The midpoint of A (-4, 2) and B(8, 5) is
Answer: The midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
Step-by-step explanation: We are given to find the midpoint of the points A(-4, 2) and B(8, 5).
We know that
the co-ordinates of the midpoint of the points (a, b) and (c, d) are given by
[tex]M=\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).[/tex]
Therefore, the co-ordinates of the midpoint of the points (-4, 2) and B(8, 5) will be
[tex]M=\left(\dfrac{-4+8}{2},\dfrac{2+5}{2}\right)=\left(\dfrac{4}{2},\dfrac{7}{2}\right)=(2,3.5).[/tex]
Thus, the midpoint of the points A(-4, 2) and B(8, 5) is M(2, 3.5).
5,200 g divided by 583.1 mL
there is 1 gram per 1 milliliter so just divide them
5200/583.1 = 8.91785
you don't say if it needs to be rounded to a certain amount
so since the mL has one decimal place
round to 8.9mL
Name a pair of complementary angles.
A. angle A E C and angle B E D
B. angle B E C and angle C E D
C. angle A E C and angle C E D
D. angle D E A and angle A E D
Find the GCF of the first two terms and the GCF of the last two terms of the polynomial. 5h^3+20h^2+4h+16
the distance across the center of a circle is called the?
What does "a"equal to?
Melissa has three different positive integers. she adds their reciprocals together and gets a sum of 1. what is the product of her integers?
First let us assign the three positive integers to be x, y, and z.
From the given problem statement, we know that:
(1/x) + (1/y) + (1/z) = 1
Without loss of generality we can assume x < y
< z.
We know that:
1 = (1/3) + (1/3) + (1/3)
Where x = y = z = 3 would be a solution
However this could not be true because x, y, and z must all be different integers. And x, y, and z cannot all be 3 or bigger than 3 because the sum would then be less than 1. So let us say that x is a denominator that is less than 3. So x = 2, and we have:
(1/2) + (1/y) + (1/z) = 1
Therefore
(1/y) + (1/z) = 1/2
We also know that:
(1/4) + (1/4) = (1/2)
and y = z = 4 would be a solution, however this is also not true because y and z must also be different. And y and z cannot be larger than 4, so y=3, therefore
(1/2) + (1/3) + (1/z) = 1
Now we are left by 1 variable so we calculate for z. Multiply both sides by 6z:
3z + 2z + 6 = 6z
z = 6
Therefore:
(1/2) + (1/3) + (1/6) = 1
so {x,y,z}={2,3,6}
Final answer:
The product of Melissa's integers is 120.
Explanation:
The product of Melissa's integers is 120.
Let the integers be a, b, and c.
According to the given information, 1/a + 1/b + 1/c = 1.
By finding common denominators and simplifying, you can determine that a * b * c = 120.
There are five boys and five girls in a class. The teacher randomly selects three different students to answer questions. The first student is a girl, the second student is a boy, and the third student is a girl. Find the probability of this occuring.
Final answer:
The probability of selecting a girl, then a boy, and then another girl from a class with 5 girls and 5 boys is 10.42%.
Explanation:
The probability of a specific sequence of students being selected in a random draw can be calculated by multiplying the probabilities of each event occurring in succession. Since there are five boys and five girls in the class, the probability of drawing a girl first is 5/10, or 1/2. After drawing one girl, there are now four girls and five boys left, so the probability of drawing a boy second is 5/9. Finally, with one girl and one boy already picked, there are three girls and four boys left, making the probability of drawing a girl third 3/8.
To find the overall probability, we multiply these individual probabilities:
Probability = (First girl drawn) × (Second boy drawn) × (Third girl drawn)
Probability = (1/2) × (5/9) × (3/8)
Probability = (1 × 5 × 3) / (2 × 9 × 8)
Probability = 15 / 144
Probability = 0.1042 or about 10.42%
Final answer:
The probability of the teacher randomly selecting a girl, a boy, and another girl from a class of 5 boys and 5 girls is 5/6.
Explanation:
To find the probability of the teacher randomly selecting three different students, we need to consider the number of possible outcomes and the number of favorable outcomes. In this case, there are 10 students to choose from and the teacher needs to select one girl, one boy, and another girl. To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes.
The number of favorable outcomes is 5 for the first girl, 5 for the boy, and 4 for the second girl (since the first girl has already been selected). So the total number of favorable outcomes is 5 x 5 x 4 = 100.
The number of possible outcomes is the total number of ways to choose 3 students from the 10 available. This can be calculated using the combination formula: C(10, 3) = 10! / (3!(10-3)!) = 120.
Therefore, the probability of selecting a girl, a boy, and another girl is 100/120 = 5/6.
which of the following are not techniques used in geometric constructions with paper folding. Check all that apply
A. Creating arcs and circles work the compass
B. Drawing line segments
C. Measuring lengths of line segments by folding the paper and matching the endpoints
D. Folding the paper and aligning marks seen through the paper
There are two correct answers which are not techniques used in geometric constructions with paper folding and these are:
A. Creating arcs and circles work the compass
C. Measuring lengths of line segments by folding the paper and matching the endpoints
In geometric folding, a straight line becomes a crease or a fold. This is achieved by a person by folding a piece of paper and flattening the crease rather than drawing lines to make a guide. Therefore this means that shapes like arcs, curves, circles by using the compass, and measurement of line segments are not used. However, constructions using compass have a long history in Euclidean geometry.
The following are not techniques used in geometric constructions with paper folding:
A. Creating arcs and circles with the compass.
C. Measuring lengths.
What is a geometric construction?A geometric construction can be defined as a process that is used to draw angles, lines, and other geometric figures (shapes), especially through the use of only a compass and straightedge such as a ruler without measurements.
In Geometry, the techniques that should be used in geometric constructions with paper folding include the following:
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What is the 12th term of the arithmetic sequence where a1 = 5 and a6 = 20?
Which of the following is FALSE? The diagonals of a parallelogram bisect each other. The diagonals of a rhombus bisect each other. The diagonals of a square bisect each other. The diagonals of a kite bisect each other
Answer:
The diagonals of a kite bisect each other
Step-by-step explanation:
Let analyse all possible answer:
a. The diagonals of a parallelogram bisect each other
True, it is one of the properties of a parallelogram
b. The diagonals of a rhombus bisect each other
True, In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
c. The diagonals of a square bisect each other.
True, it is one of the properties of a square
d. The diagonals of a kite bisect each other
Wrong, because we do not know what shape of the kite is, it can have a really strange shape that we can not identify where the diagonals are as you can see in the attached photo.
Give an example of a function that is integrable on the interval [-1,1], but not continuous on [-1,1]. explain.
Which point is a solution of x + 2y ≤ 4?
A. (2,4)
B. (1,1)
C. (3,5)
D. (-1,5)
NEED HELP!!!!!!!!!!!!!!!
Which factorizations can be used to identify the real zeros of the function f(x)=-20x^2+23x-6 ?
A. (-10x+2)(2x+3)
B. -(10x+2)(2x-3)
C. -(4x-3)(5x+2)
D. -(4x-3)(5x-2)
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]
Find the volume of a cone with radius 30 in and slant height 50 in.
The volume of cone is 37,680 cubic inch.
What is volume?Space is used by every three-dimensional object. This space is estimated concerning its volume. The volume of an object in three-dimensional space is the amount of space it occupies within its boundaries. The capacity of the object is another name for it.
An object's volume can help us figure out how much water is needed to fill it, like how much water is needed to fill a bottle, aquarium, or water tank.
Given radius of cone = r = 30 inch
slant height = l = 50 inch
volume of cone = V = 1/3πr²h
relation between height, radius, and slant height is given by
l² = h² + r²
where l = slant height, h = height and r = radius
h = [tex]\sqrt{l^{2} - r^{2} }[/tex]
h = [tex]\sqrt{50^{2} - 30^{2} }[/tex]
h = √1600 = 40 inch
V = 1/3πr²h = 1/3π × (30)² × 40
V = (3.14 × 900 × 40)/3
V = 37,680 cubic inch
Hence the volume is 37,680 cubic inch.
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Triangle LMN has vertexes at L(-1, -6), M(1, -6), and N(1, 1). Find the measure of angle L to the nearest degree.
Which is a description of the graph that would represent the inequality below?
12 – 2x < 16
The graph of the inequality 12 - 2x < 16 is represented by an open circle at -2 on a number line, with shading to the right, indicating all values greater than -2.
To describe the graph representing the inequality 12 - 2x < 16, we first need to solve for x. Subtracting 12 from both sides of the inequality, we get -2x < 4. Dividing both sides by -2 (and remembering to flip the inequality symbol when dividing by a negative), we have x > -2.
Graphically, this is represented on a number line with an open circle at -2 and a shaded area to the right of -2, indicating that x can be any number greater than -2.
What is the length of the diagonal of a cube with a side length of 5 cm? Round to the nearest tenth. 7.1 cm 8.7 cm 21.3 cm 26.7 cm
The required length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
What is diagonal?A diagonal is a straight line that connects two non-adjacent corners of a polygon, such as a square, rectangle, or any other shape with four or more sides. For a given quesiton, the diagonal of a cube with side length s is given by the formula d = s√3.
Here,
As mentioned in the question, we have given a cube with a length of its side is 5 cm.
We know that the diagonal of a cube with side length s is given by the formula d = s√3.
Substituting s=5 into this formula, we get:
d = s√3.
d = 5√3
Rounding to the nearest tenth, we get d = 8.7 cm.
Therefore, the length of the diagonal of a cube with a side length of 5 cm is approximately 8.7 cm.
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Flying against the wind, an airplane travels 2280 km in 4 hours. Flying with the wind, the same plane travels 6650 km in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?
A student is running a 3-kilometer race. He runs 1 kilometer every 2 minutes. Select the function that describes his distance from the finish line.
Final answer:
A function that describes a student's distance from the finish line in a 3-km race, running 1 km every 2 minutes, is a linear function represented by the formula f(t) = 3 - 0.5t, where t is time in minutes. This function shows a direct and proportional decrease in distance as time progresses.
Explanation:
The question asks for a function that describes the student's distance from the finish line in a 3-kilometer race, given that they run at a constant pace of 1 kilometer every 2 minutes. To find this function, we can use the concept of a linear relationship between time and distance.
Since the student is 3 kilometers away from the finish line at the start and runs 1 kilometer every 2 minutes, we can set up the function f(t) = 3 - 0.5t, where t represents time in minutes. This function decreases linearly because for every increase of 2 minutes in time, the distance from the finish line decreases by 1 kilometer. After 6 minutes, the function will read f(6) = 0, indicating that the student has reached the finish line.
An example will make this clear: After 4 minutes, the student has run 2 kilometers (since 4 minutes is twice 2 minutes, and the student runs 1 kilometer every 2 minutes), so his distance from the finish line is 3 km - 2 km = 1 km. We use f(t) = 3 - 0.5t and substitute t = 4 to get f(4) = 3 - 0.5(4) = 1 kilometer from the finish line.
If a baseball team's ratio of wins to losses is 5 to 4, what is the ratio of wins to total games played?
In 1995, 57.5% of students at Gardiner University graduated in 4 or fewer years of study. In 2009 that number had fallen to 52.8%. What was the rate of change of percent of students graduating within 4 years from 1995 to 2009?