The missing constant in the perfect square is 25
Perfect squares of a quadratic equationA quadratic equation is of the form:
[tex]ax^2+bx+c[/tex]
The giving perfect square is:
[tex]x^2+10x[/tex]
Comparing the two equations above:
a = 1, b = 10
The coefficients a, b, and c are related by the equation:
[tex]b^2=4ac[/tex]
Substitute a = 1, b = 10, and solve for c
[tex]10^2=4(1)c\\\\4c=100\\\\c=\frac{100}{4} \\\\c = 25[/tex]
Therefore, the missing constant in the perfect square is 25
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Where does the normal line to the parabola y = x − x2 at the point (1, 0) intersect the parabola a second time?
The normal line to the parabola [tex]y=x-x^2[/tex] at the point [tex](1,0)[/tex] intersect it second time at the point [tex](-1,-2)[/tex].
The given equation is:
[tex]y = x-x^2[/tex]at point,
[tex](1,0)[/tex]then,
→ [tex]y' = 1-2x[/tex]
So, at (1,0),
→ [tex]y' = 1-2\times 1[/tex]
[tex]= -1[/tex]
Since,
This is the slope of the tangent, we take its negative reciprocal to get the slope of normal:
= [tex]-\frac{1}{(-1)}[/tex]
= [tex]1[/tex]
The normal line has slope 1 and goes through (1,0):
→ [tex]y-0=1(x-1)[/tex]
→ [tex]y = x-1[/tex]
We want to know where this intersects [tex]y = x-x^2[/tex], we get
→ [tex]x-1=x-x^2[/tex]
→ [tex]x^2=1[/tex]
→ [tex]x = \pm 1[/tex]
hence,
The point corresponding to (1,0) is the one we started with, so we want x=-1:
→ [tex]x = -1[/tex]
→ [tex]y = x-x^2[/tex]
By substituting the value of "x", we get
→ [tex]= -1-1[/tex]
→ [tex]= -1[/tex]
Thus the answer above is right.
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Help identify!!!! ADB
The value of angle ADB in the triangle ADB is determined as m∠ ADB = 95⁰. (Option A).
How to calculate angle ADB?
The value of angle ADB is calculated by applying intersecting chord theorem and principle of sum of angles in a triangle.
The intersecting chord theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.
So the value of angle A is calculated as follows;
m ∠ BAC = ¹/₂ x arc BC
m ∠ BAC = ¹/₂ x 110
m ∠ BAC = 55
The value of angle ADB is calculated as follows;
m ∠ ABD + m ∠ ADB + m ∠ BAD = 180 (sum of angles in a triangle)
30 + m ∠ ADB + 55 = 180
m ∠ ADB + 85 = 180
m ∠ ADB = 180 - 85
m ∠ ADB = 95⁰
Find all complex solutions of x^2+5x-5=0.
(If there is more than one solution, separate them with commas.)
The complex solutions of x^2+5x-5=0 are (-5 + √45)/(2) and (-5 - √45)/(2).
Explanation:To find the complex solutions of x2+5x-5=0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Substituting the values a=1, b=5, and c=-5 into the formula, we get:
x = (-5 ± √(5^2 - 4(1)(-5)))/(2(1))
Simplifying further,
x = (-5 ± √(25 + 20))/(2)
x = (-5 ± √(45))/(2)
Since the square root of 45 cannot be simplified, we can write the solutions as:
x = (-5 ± √45)/(2)
Therefore, the complex solutions to the equation x2+5x-5=0 are:
x = (-5 + √45)/(2), (-5 - √45)/(2)
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Given the Arithmetic sequence A1,A2,A3,A4 A1,A2,A3,A4 45, 58, 71, 84 What is the value of A43 A43 ?
Kit folds a bandana diagonally before tying it around her head. The side length of the bandana is 16 in. About how long is the diagonal?
The length of the diagonal of Kit's bandana tied around her head is approximately 22.63 inches long.
Kit folds a bandana diagonally.
To find the length of the diagonal (hypotenuse of a right triangle), we can use the Pythagorean theorem.
The bandana side length (a) is 16 in.
Let x be the length of the diagonal.
Using a^2 + a^2 = x^2, we get 16^2 + 16^2 = x^2. Solving this gives x ≈ 22.63 in.
Formula for volume and surface area of a cylinder and explain why
A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
What is the mean salary of a salesperson at the company
Square sandbox with sides 3 feet long. She wants to put sand 0.85 feet deep in the box. What is the exact measure, in cubic feet of sand, tat Maija needs?
To find the volume of sand needed for Maija's sandbox, multiply the length, width, and depth. As the sandbox is a square, both the length and width are 3 feet. The depth is 0.85 feet. Thus, Maija needs 7.65 cubic feet of sand.
Explanation:This question is about calculating volume, specifically the volume of sand that Maija needs for her sandbox. The volume of a box is calculated by the formula: volume = length x width x height. Since the sandbox is square, the length and width are both 3 feet. The height, or in this case, the depth of the sand, is 0.85 feet.
Therefore, the volume of sand needed is calculated as follows: Volume = 3 ft x 3 ft x 0.85 ft = 7.65 cubic feet. So, Maija needs exactly 7.65 cubic feet of sand for her sandbox.
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Find the slope of the line that contains the points named c (3,8),d (-2,5)
[tex]\bf c(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad d(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-8}{-2-3}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}[/tex]
Answer:
3/5
Step-by-step explanation:
To find the slope, we use the formula
m = (y2-y1)/(x2-x1)
= (5-8)/(-2-3)
= -3/-5
=3/5
The slope is 3/5
Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime?
Answer:
4
Step-by-step explanation:
Probability help please? In a certain instant lottery game, the chances of a win are stated as "1 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. (round to three decimal places) I am confused and need a step by step instructions. Please help
Final answer:
To convert the chances of a '1 in 19' win into a probability value, you divide 1 by 19 to get 0.05263 and then round to 0.053. Therefore, the lottery win probability is 0.053.
Explanation:
To express the likelihood of a win in a lottery game as a probability value between 0 and 1, when the chances of a win are stated as "1 in 19", you follow these steps:
Understand that "1 in 19" means there is one chance to win for every 19 trials, so the total number of possible outcomes is 19 (18 losses + 1 win).
Express the chance to win as a fraction with the number of wins (1) over the total number of potential outcomes (19).
Convert the fraction into a decimal by dividing the numerator (1) by the denominator (19), which gives you approximately 0.05263.
Round the result to three decimal places, as requested, which gives you a probability value of 0.053.
Therefore, the probability of winning the lottery game is 0.053.
Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67
The correct answer is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
The sum using summation notation, assuming the suggested pattern continues, can be written as:
[tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
[tex]-8 - 3 + 2 + 7 + \ldots + 67 = \sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
Explanation:
- The pattern appears to be an arithmetic progression with a common difference of 5.
- The first term is -8, and the common difference is 5.
- The nth term of an arithmetic progression can be expressed as [tex]a_n = a_1 + (n-1)d[/tex], where [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference.
- Substituting [tex]a_1 = -8[/tex] and [tex]d = 5[/tex], we get [tex]a_n = -8 + 5(n-1)[/tex].
- The sum of the first 20 terms of this arithmetic progression can be represented using the summation notation, with the index [tex]n[/tex] ranging from 1 to 20.
Therefore, the sum using summation notation is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex].
Complete question:
Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
summation of the quantity negative eight plus five n from n equals zero to fifteen
summation of negative forty times n from n equals zero to infinity
summation of negative forty times n from n equals zero to fifteen
summation of the quantity negative eight plus five n from n equals zero to infinity
A bird's nest is on top of a power pole that is 30 feet tall. The bird is above the nest and the angle formed from the nest to the bird is 25°. The horizontal distance from the bird to the pole is 100 feet. Approximately how far is the bird above the ground?
I need help with number 17
Evaluate the expression below when y = -3.
2y + 7
-4y − 10
i need help#awnser
replace y with -3
2y + 7 becomes 2(-3) + 7 = -6 +7 =1
-4(-3)-10 = 12-10 = 2
find the area of the kite
The diagonals are 3 cms long each. The area of the kite in the given figure is 9 [tex]cm^2[/tex].
Mathematically, a quadrilateral with two pairs of adjacent sides that are congruent (have equal length) is termed a "kite". Note that not all quadrilaterals with congruent adjacent sides are kites. Kites have numerous applications in geometry, including the study of polygons, symmetry, and angles. They can be used to solve geometric problems and to analyze relationships between sides, angles, and diagonals within the quadrilateral.
Given that the length of the diagonals = 3 cm.
It is known that
Area of a quadrilateral with equal diagonals = product of the diagonals.
Area = 3 [tex]\times[/tex] 3.
Area = 9 [tex]cm^2[/tex].
The area of the kite is 9 [tex]cm^2[/tex].
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Can you guys help me with 3-8 please thank you <3
77+14 is the same as blank +11
WILL GIVE BRAINLIEST!! PPLEASE HELP!!
The graph of which function does not contain the point (0, 1)?
A.
y=(3/4)^x
B.
y=-2^x
C.
y=3^x
D.
y=(1/2)^x
The number of chips of different colors in vicky's bag is shown below: 5 blue chips 11 pink chips 9 white chips vicky takes out a chip from the bag randomly without looking. she replaces the chip and then takes out another chip from the bag. what is the probability that vicky takes out a blue chip in both draws? 5 over 25 multiplied by 5 over 25 equals 25 over 625 5 over 25 plus 5 over 25 equals 10 over 25 5 over 25 multiplied by 4 over 24 equals 20 over 600 5 over 25 plus 4 over 24 equals 220 over 600
The probability that Vicky takes out a blue chip in both draws is 5/25 x 5/25 = 25/625.
What is the probability that vicky takes out a blue chip in both draws?
Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
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Need some help on geometry practice problems!
The table below shows the number of students in a school who like tacos and/or pizza:
Like Tacos Do Not Like Tacos Total
Like Pizza 57 13 70
Do Not Like Pizza 12 15 27
Total 69 28 97
What is the relative frequency, by row, of students who like both tacos and pizza?
0.18
0.46
0.81
0.83
Answer:
Relative frequency, by row, of students who like both tacos and pizza is:
0.81
Step-by-step explanation:
Like Tacos Do Not Like Tacos Total
Like Pizza 57 13 70
Do Not Like Pizza 12 15 27
Total 69 28 97
The relative frequency by row is calculated as the ratio of the frequency of the required field to the total frequency of that row
Hence, relative frequency, by row, of students who like both tacos and pizza is:
57/70
=0.81
Mia's perents said that she can use a space in the yard that measures. 13 feet long by 9 feet wide for her wildflower garden. What is the area of the garden
The area of 13 feet long by 9 feet wide wildflower garden is 117 square feet.
Use the concept of a rectangle defined as:
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
To find the area of her garden,
Multiply the length and width of the space.
In this case,
the length is 13 feet and the width is 9 feet.
So, the area of Mia's garden would be,
13 feet x 9 feet = 117 square feet.
Hence,
The area of the garden is 117 square feet.
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how do you know when to rewrite square trinomials and difference of squares as separate factors
Recognizing the specific forms of square trinomials and the difference of squares allows you to rewrite them as separate factors, simplifying algebraic expressions and facilitating further mathematical operations.
Knowing when to rewrite square trinomials and the difference of squares as separate factors depends on the algebraic expression you are dealing with. Let's consider each case separately.
1. Square Trinomials:
- Square trinomials have the form [tex]\(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\)[/tex], where(a) and (b) are algebraic expressions.
- These trinomials can be factored into the square of a binomial: [tex]\((a + b)^2\) or \((a - b)^2\).[/tex]
- You should rewrite a square trinomial as separate factors when you encounter an expression that matches the form of a perfect square trinomial. Recognizing this pattern allows you to simplify the expression.
2. Difference of Squares:
- The difference of squares has the form [tex]\(a^2 - b^2\),[/tex] where (a) and (b) are algebraic expressions.
- This expression can be factored into the product of conjugates: [tex]\((a + b)(a - b)\).[/tex]
- You should rewrite a difference of squares as separate factors when you have an expression in the form [tex]\(a^2 - b^2\)[/tex]. Recognizing this pattern helps you simplify and factor the expression efficiently.
represent each of the fractions below both with a diagram and with words. A.2/3. B.1 1/8. C.6/9.
How do I find the linear equation for y=4x-5
(02.01 LC)
Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime?
A. 1 unit
B.2 units
C. 3 units
D. 5 units
Answer:
The correct option is C.
Step-by-step explanation:
It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.
Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.
Corresponding sides of congruent figures are congruent.
[tex]AB\cong A'B'[/tex]
[tex]AB=A'B'[/tex] (Definition of concurrent segment)
[tex]3=A'B'[/tex] (AB=3 units)
The length of A'B' is 3 units. Therefore the correct option is C.
Identify the function that best models the data.
Solve x2 + 2 = 6 by graphing the related function.
Answer:
[tex]x=-2,x=2[/tex]
Step-by-step explanation:
we have
[tex]x^{2}+2=6[/tex]
we know that
The solution of the function is equivalent to solve the following system of equations
[tex]y=x^{2}+2[/tex] ------> equation A
[tex]y=6[/tex] ------> equation B
The x-coordinate of the intersection point both graphs is the solution of the given function
Using a graphing tool
see the attached figure
The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]
therefore
The solution of the given function are
[tex]x=-2,x=2[/tex]