For this case we have the following quadratic equation:
[tex]2x ^ 2-4x + 9 = 0[/tex]
The solutions are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 2\\b = -4\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (9)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-72}} {4}\\x = \frac {4 \pm \sqrt {-56}} {4}\\x = \frac {4 \pm \sqrt {-1 * 56}} {4}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 14}} {4}\\x = \frac {4 \pm2i \sqrt {14}} {4}\\x = \frac {2 \pm i\sqrt {14}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {2 + i \sqrt {14}} {2}\\x_ {2} = \frac {2-i \sqrt {14}} {2}[/tex]
Answer:
OPTION E: [tex]\frac{2+\sqrt{14}i}{2}[/tex]
Step-by-step explanation:
Given the Quadratic equation [tex]2x^2-4x+9=0[/tex], you can find the roots by applying the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case you can identify that:
[tex]a=2\\b=-4\\c=9[/tex]
Then you can substitute values into the Quadratic formula:
[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(2)(9)} }{2(2)}[/tex]
[tex]x=\frac{4\±\sqrt{(56} }{4}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex], then:
[tex]x=\frac{4\±2\sqrt{14}i}{4}[/tex]
Simplifying, you get:
[tex]x=\frac{2(2\±i\sqrt{14}i)}{4}\\\\x=\frac{2\±\sqrt{14}i}{2}\\\\\\x_1=\frac{2+\sqrt{14}i}{2}\\\\x_2=\frac{2-\sqrt{14}i}{2}[/tex]
The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio? a. –16 b.–11 c. –4 d.–1
let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK
[tex]\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)[/tex]
Answer:
-11
Step-by-step explanation:
J =(–25, 10)
K=(5, –20)
Point L divides JK into a 7:3 ratio
To find the coordinates of L we will use section formula.
Formula : [tex]x=\frac{mx_2+nx_1}{m+n}[/tex] and [tex]y=\frac{my_2+ny_1}{m+n}[/tex]
m: n = 7: 3
[tex](x_1,y_1)=(-25,10)\\(x_2,y_2)=(5,-20)[/tex]
Substitute the values
[tex]x=\frac{7(5)+3(-25)}{7+3}[/tex] and [tex]y=\frac{7(-20)+3(10)}{7+3}[/tex]
[tex]x=-4[/tex] and [tex]y=-11[/tex]
Hence the y coordinate of L is -11
-1/4x+5=3/4. I can't get access to the answer to this question! And, my request on "contact us" will not go through!!
For this case we must solve the following linear equation:
[tex]- \frac {1} {4} x + 5 = \frac {3} {4}[/tex]
Subtracting 5 from both sides of the equation we have:
[tex]- \frac {1} {4} x = \frac {3} {4} -5\\- \frac {1} {4} x = \frac {3-20} {4}\\- \frac {1} {4} x = - \frac {17} {4}[/tex]
Multiplying by 4 on both sides of the equation:
[tex]-x = -17[/tex]
Multiplying by -1 on both sides of the equation we have:
[tex]x = 17[/tex]
Answer:
[tex]x = 17[/tex]
Answer: [tex]x=17[/tex]
Step-by-step explanation:
You need to solve for the variable "x":
The first step is to subtract 5 from both side of the equation, then:
[tex]-\frac{1}{4}x+5-5=\frac{3}{4}-5\\\\-\frac{1}{4}x=-\frac{17}{4}[/tex]
The final step is to multiply both sides of the equation by -4.
Therefore, the value of the variable "x" is the following:
[tex](-4)(-\frac{1}{4}x)=(-\frac{17}{4})(-4)\\\\x=17[/tex]
You need to buy 5 notebooks for your classes at school.Each notebook costs $2.79. What is the total cost before tax?
Answer:
$13.95
Step-by-step explanation:
You need to multiply the 5 notebooks with the costs of each notebook, which gives you the total costs before tax.
Can anyone help me with this GEOMETRY
Answer:
B.) 83.7758
Step-by-step explanation:
Answer:
83.75 cubic inches
Step-by-step explanation:
We are given the diameter of a cone 8 inches, and height 5 inches and we are to find the volume of this cone.
(diameter is 8 inches so radius will be 4 inch)
We know that the volume of a cone is given by:
Volume of cone = [tex] \pi r ^ 2 \frac { h } { 3 } [/tex]
Substituting the given values in the above formula:
Volume of cone = [tex] \pi \times 4 ^ 2 \times \frac { 5 } { 3 } [/tex] = 83.75 cubic inches
(diameter is 8 inches so radius will be 4 inches)
Determine the output, f(x), if the input to the function box below is 8.
f(x)=3x-1
Answer:
The output is 23
Step-by-step explanation:
we know that
f(x) ----> is the output
x ----> is the input
we have that
f(x)=3x-1
For x=8 (input)
Find the value of f(x) (output)
f(8)=3(8)-1=23
The output is 23
Find the value of x.
a 25
b40
c45
d60
Which formula can be used to find the nth term of a geometric sequence where the first term is 8 and the common ratio is –3?
Answer:
f(n)=8(-3)^(n-1)
The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,
⇒ - 8/3 × (- 3)ⁿ
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
We have to given that;
The first term is, 8
And, the common ratio is –3
Now,
The nth term of a geometric sequence is:
⇒ T (n) = arⁿ⁻¹
Put a = 8 and r = - 3
⇒ T (n) = 8 (- 3)ⁿ⁻¹
⇒ T (n) = - 8/3 × (- 3)ⁿ
Thus, The formula which can be used to show the nth term of a geometric sequence where the first term is 8 and the common ratio is - 3 is,
⇒ - 8/3 × (- 3)ⁿ
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HELP PLEASE ANSWER!!!! (25 POINTS!!!)
What does it mean for an equation to have no solution or infinitely many solutions?
Answer:
An equation to have no solution means that the system of equations do not intersect at all and therefore will not have any solutions. If an equation has indefinite many solutions then the system of equations will have the same line since they are intersecting each other
Step-by-step explanation:
what is -3 and 2/7 minus 4 and 1/3 and can it be simplified
Answer:
Yes it can be simplified.
Answer: -7 and 13/21
Step-by-step explanation:
(-3 2/7) - (4 1/3)
Least common multiple for the denominator= 21
1. -23/7 - 13/3
2. -69/21 - 91/21 = -160/21
3. -7 13/21
please give step by step help to solve this equation
2(x-3)²-32=0
Answer:
x = 7
x = - 1
Step-by-step explanation:
2(x-3)²-32=0 Add 32 to both sides
2(x-3)² - 32+32 = 32 Combine
2(x - 3)² = 32 Divide by 2
2(x - 3)² /2 = 32/2 Do the division
(x - 3)² = 16 Take the square root of both sides
sqrt(x - 3)² = sqrt(16) Do the square root.
x - 3 = +/- 4
=====================
x - 3 = 4 Add 3 to both sides
x - 3+3 = 4+3
x = 7
=====================
x - 3 = - 4 Add 3 to both sides
x -3 +3 = - 4 + 3
x = - 1
Based on the survey, what is the probability that a person chosen at random is a diabetic patient or an eye patient
First, you must find the total number of people. Add together 32, 54, 78, 112, and 96 to get 372. Next, add the number of diabetic patients with the number of patients with eye problems (54 + 112 = 166).
Your fraction is now 116/372. Simplify this to get your answer, 29/93 or 0.31.
what values of c and d make the equation true?
Answer:
Third option.
Step-by-step explanation:
You need to cube both sides of the equation. Remember the Power of a power property:
[tex](a^m)^n=a^{mn[/tex]
[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d[/tex]
According to the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)[/tex]
Then. simplifying you get:
[tex]162x^cy^5=162x^6y^{(3+d)}[/tex]
Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:
[tex]c=6[/tex]
You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:
[tex]3+d=5\\d=5-3\\d=2[/tex]
Find the equation of the quadratic function with roots -8 and -6, "a" less than zero, and a vertex at (-7, 2).
ANSWER
[tex]y = - 2{x}^{2} -28x - 96[/tex]
EXPLANATION
We have that
[tex]x = - 8 \: \: and \: \: x = - 6[/tex]
are the roots of the quadratic function.
This implies that
[tex]x + 8 \: \: and \: \: x + 6[/tex]
are factors of the quadratic function.
The quadratic function will have an equation of the form:
[tex]y = a(x + 8)(x + 6)[/tex]
It was also given that, the vertex of the function is at
[tex](-7, 2)[/tex]
This point must satisfy the equation.
This implies that:
[tex]2= a( - 7 + 8)( - 7+ 6)[/tex]
This implies that,
[tex]2=-a[/tex]
[tex]a = - 2[/tex]
We substitute the value of 'a' to get the equation in factored form as:
[tex]y = - 2(x + 8)(x + 6)[/tex]
We expand the parenthesis to write the equation in standard form.
[tex]y = - 2( {x}^{2} + 6x + 8x + 48)[/tex]
[tex]y = - 2( {x}^{2} + 14x + 48)[/tex]
[tex]y = - 2{x}^{2} -28x - 96[/tex]
Or in vertex form, the equation is
[tex]y = - 2 {(x + 7)}^{2} + 2[/tex]
What are the vertex and x intercepts of the graph below?
Answer:
D. Vertex (1, -25); intercepts x = -4, 6
Step-by-step explanation:
Vertex
x = -b/2a
x = - (-2)/2(1)
x = 2/2
x = 1
y = 1^2 - 2(1) - 24
y = 1 - 2 - 24
y = -25
Vertex (1, -25)
x-intercepts when y = 0
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 = 0; x = 6
x + 4 = 0;x = -4
Answer
D. Vertex (1, -25); intercepts x = -4, 6
How many solution 6x-4 = x+6 has
Answer:
1 solution
Step-by-step explanation:
This is a linear equation and has one solution
6x - 4 = x + 6 ( subtract x from both sides )
5x - 4 = 6 ( add 4 to both sides )
5x = 10 ( divide both sides by 5 )
x = 10 ← only 1 solution
Taxi company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another if x represents the number of miles driven by taxi which linear equation can be used to solve this problem and how many miles did Isaac travel rounded to the nearest tenth
Answer:
The answer is B
Step-by-step explanation:
$2.50+$1.95=$27.46
-2.50
24.69
24.63/1.95
equal $12.80 or 12.8
Answer:
B) 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
Step-by-step explanation:
How does the context of a data set affect how the data is interpreted?
Answer:
Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average.
Step-by-step explanation:
The standard deviation can never be a negative number, due to the way it’s calculated and the fact that it measures a distance (distances are never negative numbers).The smallest possible value for the standard deviation is 0, and that happens only in contrived situations where every single number in the data set is exactly the same.
The standard deviation is affected by outliers (extremely low or extremely high numbers in the data set). That’s because the standard deviation is based on the distance from the mean. And remember, the mean is also affected by outliers.
The standard deviation has the same units as the original data.
Final answer:
The context of a dataset influences its interpretation by providing background information that affects understanding. Different contexts can lead to varying interpretations of the same dataset. Understanding context is essential for accurate data interpretation and decision-making.
Explanation:
The context of a data set affects how the data is interpreted by providing background information and circumstances that influence the understanding of the data. For example, in statistics, when analyzing a dataset related to economic growth, the context of the data such as the time period or the country it represents can significantly impact the conclusions drawn.Context can lead to different interpretations of the same data set. For instance, a graph showcasing unemployment rates over time can be interpreted positively or negatively based on the context. If the data is during a recession, the interpretation would differ from a period of economic growth.Understanding the context of a data set is crucial for accurate interpretation and decision-making. It helps in avoiding misinterpretations and ensures that conclusions drawn are valid and relevant to the situation at hand.What is the equation of a line that passes through points (0, 4) and (-4,-8)?
[tex]\text{Hey there!}[/tex]
[tex]\text{The slope formula is:}\dfrac{\bf{y_2\ - y_1}}{\bf{x_2\ - x_1}}[/tex]
[tex]\bf{y_2 = -8}[/tex]
[tex]\bf{y_1=4}[/tex]
[tex]\bf{x_2=-4}[/tex]
[tex]\bf{x_1=0}[/tex]
[tex]\text{Your equation should look like this:}\dfrac{-8 \ - 4}{-4 \ - 0}[/tex]
[tex]\text{Solve the numerator first (the top) then the denominator (the bottom) }[/tex]
[tex]\text{-8 - 4 = -12}[/tex]
[tex]\dfrac{-12}{-4 - 0}[/tex]
[tex]-4 - 0=-4[/tex]
[tex]\dfrac{-12}{-4} =\ ?[/tex]
[tex]\dfrac{-12\div-4}{-4\div-4}=\dfrac{3\div1}{1\div1}=3[/tex]
[tex]\boxed{\boxed{\bf{Answer: 3}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
3
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{Y_2-Y_1}{X_2-X_1}=\frac{Rise}{Run}[/tex]
[tex]\frac{(-8)-4}{(-4)-0}=\frac{-12}{-4}=\frac{-12\div-4}{-4\div-4}=\frac{3}{1}=3[/tex]
Therefore, the slope is 3 is the correct answer.
Each person in a group of 12 has one pet. Three people have a cat, 2 people have a dog, and the rest have a bird. What is the probability of a person having a cat or a dog?
Answer:
63 % for cats and 37 % for dogs
Step-by-step explanation:
which unit of measure would be appropriate for the area of a picture that is 20 centimeters tall and 15 centimeters wide
Answer:300 cm2(in the case of rectangle)
Step-by-step explanation:
The question is ambiguous.Something is missing.what is the shape of the object is not told here.
But if you consider it a "rectangle",the angles will be right angles.
area of a rectangle=length×breadth
=20cm×15cm
=300 centimetre2
Answer: square centimeters
Step-by-step explanation:
Hi, the answer to the question is square centimeters.
The lengths of the picture are in centimeters. So, when you calculate the area of the picture that is a triangle you obtain square centimeters.
Mathematically speaking:
20cm x 15 cm = 300 square centimeters
By multiplying the same unit you obtain the square unit.
Feel free to ask for more if it´s necessary or if you did not understand something.
What is the area of the polygon given below?
Answer:
D.
Step-by-step explanation:
To find this area, we can break it up into two rectangles, one with dimensions of 4x19 and another of 24x11. All we have to do is find the areas of both rectangles and add them together!
Since 4*19=76 and 11*24=264, we get D. 340 square units as our answer.
For this case we have that the area of the figure is given by the sum of the areas of two rectangles. The area of a rectangle is given by:
[tex]A = a * b[/tex]
Where:
a, b: They are the sides of the rectangle
[tex]A_ {1} = 24 * 11\\A_ {1} = 264[/tex]
On the other hand:
[tex]A_{2} = 4 * (4 + 11 + 4) = 4 * 19 = 76[/tex]
Thus, the total area is:
[tex]A_ {t} = 264 + 76\\A_ {t} = 340[/tex]
The total area is 340 square units
Answer:
Option D
an angle is formed by
It is formed by two rays lie in a plane.
factorise 4y^2 – 4y + 1
Answer:
[tex](2y-1)^{2}[/tex]
Step-by-step explanation:
[tex]4y^{2} -4y+1[/tex]
Sum = -4
Product = 1
Factors = -1 , -1
[tex](2y-1)^{2}[/tex]
The simplified formula for calculating monthly lease payment is:
A. MSRP + lease factor
B. depreciation fee + finance fee
C. MSRP - down payment
D. acquisition fee + down payment
The simplified formula for calculating the monthly lease payment for a car is the sum of the depreciation fee and the finance fee. These are calculated based on the car's initial cost, residual value, and the lease factor.
Explanation:In the context of car leasing, the simplified formula used to calculate the monthly lease payment is: depreciation fee + finance fee. The depreciation fee is calculated by subtracting the car's expected residual value at the end of the lease from its initial cost (MSRP) and then dividing this by the number of months in the lease. The finance fee is calculated as the sum of the MSRP and the residual value, multiplied by the lease factor or money factor which is essentially the interest rate.
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What is the simplified form of 400x100 ?
O
200x10
O
200x50
0
20x10
• 20x50
Answer: 200 x 10
Step-by-step explanation:
√400 x √100 = 40,000
√40,000 = 200
The solution is : The required simplified form is 20 × 10.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
We are given to find the simplified form of the following radical expression :
E = √400x100
We will be using the following property of radicals :
√x = x^1/2
and, √a* b = √a * √b
Therefore, we have
√400 x √100
= √40,000
now, we get,
√40,000
= √400 x √100
=√20² x √10²
=20x10
=200
Thus, the required simplified form is 20 × 10.
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draw a pentagon. Explain how you knew the number of sides and angles to draw.
Answer:
A pentagon is a 5 sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably a math equipment.
Step-by-step explanation:
A pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.
What is the pentagon?A pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape.
In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°.
A pentagon shape is a plane figure, or a flat (two-dimensional) 5-sided geometric shape.
The measure of each angle of a regular pentagon is given by the below formula. The measure of the central angle a regular pentagon makes a circle, i.e. total measure is 360°.
Hence, a pentagon is a 5-sided shape. Angles are very easy to draw. You could figure out the angles by drawing them or using a calculator or probably math equipment.
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M<9= 6x and m<11=120. Find the value of x so that line c is parallel to line d.
Answer:
The value of x is 20°
Step-by-step explanation:
we know that
m∠ 9 and m∠ 11 are corresponding angles
If line c is parallel to line d
then
m∠ 9 = m∠ 11
Substitute
6x=120°
x=20°
Answer:
20
Step-by-step explanation:
:))
The graph represents the distribution of the number of questions answered correctly on a 50-question math test.
what is the standard deviation of the data ?
4
8
12
14
Answer:
The answer I believe is 4.
Step-by-step explanation:
Answer: the answer is 4
Step-by-step explanation:
;)
Which quadratic function has Vertex (-1,4) and passes through (4,19)
HELP
Answer:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
Step-by-step explanation:
The equation of a quadratic function in vertex form is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
It was given in the question that the vertex of the parabola is (-1,4).
When we substitute the vertex into the formula we get:
[tex]f(x)=a(x+1)^2+4[/tex]
The parabola also passes through (4,19) hence it must satisfy its equation.
[tex]19=a(4+1)^2+4[/tex]
[tex]19-4=a(5)^2[/tex]
[tex]15=25a[/tex]
We divide both sides by 25 to get:
[tex]a=\frac{15}{25}= \frac{3}{5}[/tex]
Hence the quadratic function is:
[tex]f(x)=\frac{3}{5}(x+1)^2+4[/tex]
Find the x-intercepts for the parabola defined by this equation: y=-3x^2-6x+9
The x-intercepts of the parabola are [tex]\( x = -3 \) and \( x = 1 \)[/tex].
To find the x-intercepts of the parabola defined by the equation [tex]\( y = -3x^2 - 6x + 9 \)[/tex], we need to set y=0 and solve for x.
So, we have:
[tex]\[ -3x^2 - 6x + 9 = 0 \][/tex]
Now, let's solve this quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]where \( a = -3 \), \( b = -6 \), and \( c = 9 \).\[ x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(-3)(9)}}{2(-3)} \]\[ x = \frac{6 \pm \sqrt{36 + 108}}{-6} \]\[ x = \frac{6 \pm \sqrt{144}}{-6} \][/tex]
[tex]\[ x = \frac{6 \pm 12}{-6} \][/tex]
Now, we have two possible values for x:
1. When [tex]\( x = \frac{6 + 12}{-6} = \frac{18}{-6} = -3 \)[/tex]
2. When [tex]\( x = \frac{6 - 12}{-6} = \frac{-6}{-6} = 1 \)[/tex]