which numerical expression would provide the solutions to the equation 7x^2 + 4x - 8 = 14
Answers
7x^2 + 4x - 8 = 14-----------------> 7x²+4x-22=0
Step 1
Solving a second degree equation
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
a=7
b=4
c=-22
then
x1=[-4+√(4²-4*7*(-22))]/(2*7)-----------> [-4+√(632)]/(14)
x1=-(-4+25.14)/14=1.51
x2=[-4-√(4²-4*7*(-22))]/(2*7)-----------> [-4-√(632)]/(14)
x2=-(-4-25.14)/14=-2.08
the solutions of the system is
x1=1.51
x2=-2.08
to check the result
using a graph tool
see the attached figure
the answer is
the numerical expressions is
x1=[-b+√(b²-4ac)]/2a
x2=[-b-√(b²-4ac)]/2a
The quadratic equation 7x^2 + 4x - 8 = 14 does not have any real solutions.
Explanation:The given equation is a quadratic equation of the form at² + bt + c = 0, where a = 7, b = 4, and c = -22. To find the solutions, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values, we get:
x = (-4 ± √(4² - 4(7)(-22))) / (2(7))
Simplifying further, we get:
x = (-4 ± √(16 - 616)) / 14
x = (-4 ± √(-600)) / 14
The expression inside the square root is negative, which means there are no real solutions to the equation.
Related Questions
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
Enter your answer in the box.
ft²
Answers
Answer
Maximum area A_max = 11250 ft^2
Step-by-Step Explanation
Declaring Variables:-
The length of the rectangle = y
The width of the rectangle = x
Solution:-
- The perimeter of a rectangle can be expressed using the above two variables as follows:
Perimeter (P) = 2*Length + 2*Width
= 2* ( x + y )
- Since the barn is used as one of the sides (let's say y) we can subtract y
we don't need fencing for this side. The length of the fence required L is:
Length (L) = P - y
= 2*x + y
- We are given 300 feet of fencing. So we equate the length equal to 300 and develop a linear relationship between width and length of the barn.
300 = 2x + y
y = 300 - 2x
- The area (A) of the rectangle is given by the following expression:
A = Length*width
A = x*y
- Substitute the relationship developed between x and y in the Area (A) expression above. Then we have:
A = x*(300 - 2x)
A = 300x - 2x^2
- We will take first derivative of the expression of area (A) developed with respect to x and find the critical point of the area function by setting the first derivative A'(x) = 0.
A(x) = 300x - 2x^2
A'(x) = 300 - 4x
0 = 300-4x
x = 300 / 4 = 75 ft
- The critical point of the given function lies for the width (x) of 75 ft. We will plug in the critical value x = 75 ft back into the original function of Area and find the maximum area.
A(x) = 300x - 2x^2
A(75) = 300 (75) - 2(75)^2
A_max = A(75) = 11250 ft^2
- The maximum area that can be enclosed by the fencing is 11250 ft²
Answer:11250
Step-by-step explanation:
Which expression has an equivalent value to x^2 + 9x + 8 for all values of x?
(x + 1)(x + 8)
(x + 2)(x + 6)
(x + 4)(x + 4)
(x + 5)(x +4)
Answers
Which type of transformation maps trapezoid PQRS onto trapezoid P'Q'R'S'?
reflection
rotation
translation
dilation
Answers
Answer is DILATION
Answer: Dilation.
Step-by-step explanation:
From the given picture , it can be seen that the size of trapezoid P'Q'R'S' is decreased from trapezoid PQRS .
Reflection , rotation and translation are rigid motions that produces congruent images and do not change the size of the shapes.
But dilation is not a rigid motion because it changes the size of the shape by using a scale factor.
Hence, the transformation maps trapezoid PQRS onto trapezoid P'Q'R'S' is "Dilation".
Match the reasons with the statements in the proof.
Given: c | | d, m 4 = m 5
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
Substitution
2. m∠4 = m∠7
Vertical angles are equal.
3. m∠5 = m∠8
If lines ||, alternate interior angles are equal.
4. m∠7 = m∠8
Given
Answers
Prove: m 7 = m 8
1. c||d, m∠4=m∠5
GIVEN
2. m∠4 = m∠7
If lines ||, alternate interior angles are equal.
3. m∠5 = m∠8
Vertical angles are equal.
4. m∠7 = m∠8
Substitution
Answer:
Step-by-step explanation:
Given: c is parallel to d and ∠4=∠5.
To prove: ∠7=∠8
Proof:
Statement Reason
1. c║d, ∠4=∠5 Given
2.∠4=∠7 If lines ||, alternate interior angles are equal.
3.∠5=∠8 Vertical angles are equal
Since, ∠4=∠5, therefore ∠7=∠8
4.∠7=∠8 Substitution
HELP FAST!!!
What is the value of x? Enter your answer in the box. x = Triangle with angles labeled x minus 4 degrees, 3 x degrees, and 100 degrees.
Answers
[tex](x-4) +3x + 100 =180 combine like terms 4x + 96 = 180 subtract 96 from both sides 4x = 84 divide both sides by 4 x = 21 [/tex]
To find the value of x in the triangle, set up an equation using the triangle angle sum theorem and solve for x. The value of x is 21 degrees.
The problem involves finding the value of x in a triangle with given angle measures. According to the triangle angle sum theorem, the sum of the angles in any triangle is always 180 degrees. In this case, we are given two expressions for the angles in terms of x: x - 4 degrees and 3x degrees, plus a given angle of 100 degrees.
To solve for x, set up an equation using the given angles:
x - 4 + 3x + 100 = 180
Combine like terms to solve for x:
4x - 4 + 100 = 180
4x + 96 = 180
4x = 180 - 96
4x = 84
x = 84 / 4
x = 21
HELP HELP HELP PLEASE!!!!!
What is the area of this polygon?
Answers
Answer: 35.5 [tex]unit^2[/tex]
Step-by-step explanation:
For finding the area of this polygon we can divide it into triangles and rectangle,
By the below diagram,
The area of this polygon = Area of rectangle having dimension 4× 3 + Area of triangle having base 4 unit and height 3 unit +Area of triangle having base 7 unit and height 3 unit + Area of triangle having base 7 unit and height 2 unit,
=[tex]12 + \frac{1}{2}\times 4\times 3 + \frac{1}{2}\times 7\times 3 + \frac{1}{2}\times 7\times 2[/tex]
= [tex]12 + 6 + 10.5 + 7[/tex]
= [tex]35.5\text{ square unit}[/tex]
An object with reflectional symmetry can be created by reflecting it about an axis called the _____.
A. Point of symmetry
B. Line of symmetry
C. Symmetrical half
D. Equator of symmetry
Answers
Reflection symmetry is a symmetry with respect to the reflection and is also know as mirror symmetry, line symmetry or mirror-image symmetry.
When a figure undergoes a reflection and does not change , then the figure is said to has the reflectional symmetry.
An object with reflectional symmetry can be created by reflecting it about an axis called the Line of Symmetry.
Hope this helps ..!!
Thank you :)
Samuel has a collection of toy cars. his favorites are the 272727 red ones which make up 60\%60%60, percent of his collection.how many toy cars does samuel have?
Answers
1 % = 27 ÷ 60 = 0.45
100% = 0. 45 x 100 = 45
Samuel has 45 cars.
Answer:
Khan Academy said 45 hope it helps! :)
For each babysitting job, ashley charges $2.50 for bus fare plus $8 per hour for each hour she works. she charged $30.50 for her last babysitting job.
a. write a linear equation to represent the problem. be sure to define the variable you choose. __________
Answers
Variable: h = hours worked
linear equation: 30.50 = 2.50 +8h
pleaseeeeeee answer!!!!!!!!!!!!
There are eight planets in our solar system. Venus is the hottest planet, with an average temperature of 460°C. The average temperatures of some other planets are given in the table.
Venus 460°C
Earth 14°C
Mars -60°C
Neptune -214°C
The net change in temperature from Neptune to Mars is _______°C.
The net change in temperature from Earth to Neptune is ________°C.
The net change in temperature from Venus to Earth is _________°C.
Answers
The net change of temperatures between the planets is required.
Neptune to Mars is [tex]154^{\circ}\text{C}[/tex]
Earth to Neptune is [tex]228^{\circ}\text{C}[/tex]
Venus to Earth is [tex]446^{\circ}\text{C}[/tex]
The net change value is the distance of the net change from zero.
So, the absolute value of the change will be the net change.
Difference in temperature of Neptune and Mars
[tex]|-214-(-60)|=154^{\circ}\text{C}[/tex]
Difference in temperature of Neptune and Earth
[tex]|-214-14|=228^{\circ}\text{C}[/tex]
Difference in temperature of Venus and Earth
[tex]|460-14|=446^{\circ}\text{C}[/tex]
Learn more:
https://brainly.com/question/11953855?referrer=searchResults
Answer:
154 for neptune to mars is correct. The 228 and 446 is wrong.
Step-by-step explanation:.
Donnie is solving the equation 2x2=27+3x with the quadratic formula. Which values could he use for a, b, and c? a = 2, b = −3 , c = −27 a = 2, b = −27, c = −3 a = 2, b = 3, c = 27 a = 2, b = 27, c = 3
Answers
a= 2
b= -3
c= -27
The given equation is :
[tex] 2x^{2} =27+3x [/tex]
Now let us write it in standard form:
[tex] 2x^{2} -3x-27=0 [/tex]
Comparing it with general standard form:
[tex] ax^{2} +bx+c=0 [/tex]
So we have a=2, b=-3 and c=-27
First option is correct answer .
which of these is the best definition of an ellipse
Answers
therefore
the answer is the option D)
the set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant
You sell lemonade for $2 per cup and orange juice for $3 per cup. you sell a total of 100 cups for $240. write and solve a system of linear equations to find the number of cups and the number of lemonade and the number of cups of orange juice you sold. answer
Answers
2L + 3OJ = 240
-2L + -2OJ = -200
2L + 3OJ = 240
1OJ = 40
L + OJ = 100
L + 40 = 100
L = 60
Therefore : 60 cups of lemonade and 40 cups of orange juice.
To solve a linear equation in two variables, at least two equations are required. There are 60 lemonade and 40 orange juice cups.
What is Linear equation in two variable ?A linear equation in two variable can be written as ax + by = 0 where a and b are not equal to zero. It is used to represent a straight line.
Given that, rate of lemonade per cup = $2.
And, rate of orange juice per cup = $3.
Total number of cups sold = 100.
Total earning = $240.
Suppose the number of lemonade cup be x,
And, the number of orange juice cup be y.
Then, as per the question two equations can be formed given as,
x + y = 100 -------------------------(1)
2x + 3y = 240 -------------------------(2)
To find x and y, multiply equation (1) by 2 and substract it from equation (2),
2x + 3y - 2(x + y) = 240 - 2×100
=> y = 40
Substitute y =40 in equation (1) to get x as,
x + 40 = 100
=> x = 60.
Hence the number of lemonade cups are 60 and orange juice cups are 40.
To know more about Linear equation in two variable refer to,
https://brainly.com/question/24085666
#SPJ2
What is the vertex form of y=-2x^2-8x+10? Give the coordinates of the vertex, state if there is a minimum or maximum, and find the equation of the line of symmetry.
This is for Algebra 2 regular.
Answers
notice the leading term's coefficient, is -2, is negative, that means the parabola is opening downwards, is facing down, so it goes up up up, reaches the U-turn and then down down down, is a "hump" or a maximum point.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ \begin{array}{lcccl} y = & -2x^2& -8x& +10\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array} \qquad \left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{-8}{2(-2)}~~,~~10-\cfrac{(-8)^2}{4(-2)} \right)\implies \left( \cfrac{8}{-4}~~,~~10-\cfrac{64}{-8} \right) \\\\\\ \left( -2~~,~~10+8 \right)\implies (-2~~,~~18)[/tex]
and the line of symmetry, well is a vertical parabola, mirroring itself at the line x = -2, which is the x-coordinate of the vertex.
Find the reduced odds for and the reduced odds against the event of rolling a fair die and getting a 2, 4, or 5 odds for: to odds against: to
Answers
There are 3 ways of getting a 2, 4, or 5. There are also 3 ways of NOT getting a 2, 4, 5 (namely rolling a 1, 3, or 6). That means the odds FOR would be 3:3 = 1:1.
There are 3 ways of NOT getting a 2, 4, or 5 (again rolling a 1, 3, or 6). There are also 3 ways of getting a 2, 4, 5. That means the odds AGAINST would be 3:3 = 1:1.
Reduced odds for rolling a 2, 4, or 5: 1:1
Reduced odds against rolling a 2, 4, or 5: 1:1
To determine the reduced odds for and against rolling a 2, 4, or 5 on a fair six-sided die, we need to calculate the probabilities of these events.
Step 1: Calculate the probability of rolling a 2, 4, or 5.
There are three favorable outcomes (rolling a 2, 4, or 5) out of a total of six possible outcomes.
[tex]\[ P(\text{rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]
Step 2: Calculate the probability of not rolling a 2, 4, or 5.
There are three unfavorable outcomes (rolling a 1, 3, or 6) out of a total of six possible outcomes.
[tex]\[ P(\text{not rolling a 2, 4, or 5}) = \frac{3}{6} = \frac{1}{2} \][/tex]
Step 3: Calculate the odds for rolling a 2, 4, or 5.
Odds for an event are given by the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
[tex]\[ \text{Odds for rolling a 2, 4, or 5} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]
Step 4: Calculate the odds against rolling a 2, 4, or 5.
Odds against an event are given by the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
[tex]\[ \text{Odds against rolling a 2, 4, or 5} = \frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}} = \frac{3}{3} = 1:1 \][/tex]
Therefore, The reduced odds for and the reduced odds against the event of rolling a fair die and getting a 2, 4, or 5
Reduced odds for rolling a 2, 4, or 5: 1:1
Reduced odds against rolling a 2, 4, or 5: 1:1
Anybody got the answer to this?
Answers
s = R * teta
Where,
Radio
Teta: arc angle measured in radians.
We have then that the length of the arc in this case is:
s = (7.9) * (180-66.4)) * (pi / 180)
s = 15.7 cm
Answer:
The length of the AD arc is:
s = 15.7 cm
What type of number results when a negative number is multiplied by a positive number and vice versa?
A. A negative number
B. Zero
C. A positive number
Answers
A positive number results
when a negative number is multiplied by a positive number and vice versa.
This means your answer is option C.
Hope this helps you.
Have a great day! (:
What is the solution set of x/4≤9/x?
Answers
Answer:
x≤-6 or 0<x≤6.Option D.
Step-by-step explanation:
Given:
[tex]\frac{x}{4} \leq \frac{9}{x}.[/tex]
Subtract [tex]\frac{9}{x}[/tex] from both sides,
[tex]\frac{x}{4}-\frac{9}{x} \leq[/tex] 0
Simplifying by taking common denominator:
[tex]\frac{x^2-36}{4x}\leq[/tex]0
Factoring numerator:
[tex]\frac{(x+6)(x-6)}{4x}\leq[/tex]0
Computing the signs and selecting that one satisfies ≤ 0:
x≤ -6,0<x≤6.
Option D is the right answer.
5. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter. (1 point)
A. 41.4 cm, 8.3 cm
B. 30 cm, 5.8 cm
C. 41.4 cm, 4.3 cm
D. 8.3 cm, 5.8 cm
Answers
https://answers.yahoo.com/question/index?qid=20120518194118AAhi738
Answer:
Option D -8.3 cm, 5.8 cm
Step-by-step explanation:
Given : An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long.
To find : The longest and shortest possible lengths of the third side of the triangle?
Solution :
First we create the image of the question,
Refer the attached figure below.
Let a triangle ABC , where angle A has a bisector AD such that D is on the side BC.
The theorem is stated for angle bisector is
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides".
So, according to question,
Let BD=6 cm, DC=5 cm, AB=6.9 cm
and we have to find AC.
Applying the theorem,
[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]
[tex]\frac{6}{5}=\frac{6.9}{AC}[/tex]
[tex]AC=\frac{6.9\times 5}{6}[/tex]
[tex]AC=\frac{34.5}{6}[/tex]
[tex]AC=5.75[/tex]
[tex]AC=5.8 cm[/tex]
If we let AC=6.9 cm, find AB
Then,
[tex]\frac{BD}{DC}=\frac{AB}{AC}[/tex]
[tex]\frac{6}{5}=\frac{AB}{6.9}[/tex]
[tex]AB=\frac{6.9\times 6}{5}[/tex]
[tex]AB=\frac{41.4}{6}[/tex]
[tex]AB=8.28[/tex]
[tex]AB=8.3 cm[/tex]
Therefore, The shortest possible length is 5.8 cm and longest possible is 8.3 cm.
Hence, Option D is correct.
The graph of y = 12x2 will be more narrow than the graph of the parent function, y = x².
Question 2 options:
True
False
The quadratic function shown can be written in the form y = ax². Determine the equation of the quadratic function.
Question 4 options:
y = x²
y = -x²
y = 2x²
y = -2x²
Answers
Based on the graph attached, we know a will not be a negative number, since the graph is open upward instead of downward. A negative coefficient "flips" the graph. Since it goes through the point (1, 2) it will not be the parent function y = x²; if you substitute 1 in for x you would get a value of 1, not 2. Therefore the choice must be y = 2x².
Write a real world problem that you would represent with the equation 4x+5=37.
Answers
x=8
37-5=32
32/4=8.
A lamp manufacturer has daily production costs of C = 0.25n2 – 10n + 800, where C is the total cost in dollars for n lamps produced.
What is a reasonable domain for this function, given the problem's context?
A) all integers
B) all real numbers
C) all positive integers
D) all positive real numbers
Answers
The reasonable domain for the given cost function, considering the context of lamp production, is all positive integers (C) because lamps can only be produced in whole, positive quantities.
The lamp manufacturer's daily production costs are given by the function C = 0.25n2 - 10n + 800, where C represents the total cost in dollars and n is the number of lamps produced. Considering the context of the problem, where production numbers must be whole and non-negative, the reasonable domain for this function is all positive integers, which represents the count of lamps that can be produced. This is because the manufacturer cannot produce a fraction of a lamp, nor can they produce a negative number of lamps. Hence, the correct choice for the domain is (C) all positive integers.
In July 2010 there were approximately 500 million Facebook users. In July 2011 there were approximately 750 million Facebook users. How many more users were there in 2011. Write your answer in scientific notation
Answers
TWO QUESTION MUST ANSWER BOTH TO RECEIVE POINTS (PLEASE TAKE IT SERIOUSLY)
1) Line IJ has an equation of a line y = −3x − 8. Which of the following could be an equation for a line that is parallel to line IJ?
A) y = 3x + 7
B) y = 1 over 3x + 7
C) y = −3x + 7
D) y = −1 over 3x + 7
2) Find the perimeter of the shape below:
A) 12.4 units
B) 13.4 units
C)15.1 units
D) 16.8 units
Answers
an elephant in an african wildlife perserve is 59.3 years old the table shows some students estimates for the elephants age who correctly rounded the age of the elephants to the nearest year
Answers
Hope i helped:)
Have a nice day!
~Luis~
Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m∠A=
°
Answers
x + 2 + 3x + 6 = 180
4x + 8 = 180
4x = 172
x = 43
Now solve for A
3(43) + 6 = A
129 + 6 = A
135 = A
The measure of angle A is 135 degrees.
Hope this helps =)
The answer is m∠A= 135°
Red and gray bricks were used to build a decorative wall. The number of red bricks number of gray bricks was Start Fraction 5 over 2 End Fraction . There were 175 bricks used in all. How many red bricks were used?
Answers
Red = 5x
Gray = 2x
The total is 175 bricks, right?
5x+2x=7x
7x=175
x=25
The value of x is 25. Now, substitute that into the expression for red bricks, or 5x
5x=5(25)=125
There were 125 red bricks used. Hope this helps!
Final answer:
To find the number of red bricks used, the ratio 5:2 is represented as 5x:2x. Solving the equation 7x = 175 gives x = 25. Multiplying this by 5, there were 125 red bricks used.
Explanation:
The question asks us to find the number of red bricks used to build a wall when the ratio of red bricks to gray bricks is 5:2 and there were 175 bricks used in total. To solve this, we set up the ratio 5x:2x where 'x' represents the multiplier for the number of bricks, and the sum of red and gray bricks which is 5x + 2x equals the total number of bricks, 175.
First, we combine like terms: 5x + 2x = 7x. Next, we solve for 'x' by dividing both sides of the equation by 7.
7x = 175
x = 175 / 7
x = 25
We then multiply this value by 5 to find the number of red bricks: 5 * 25 = 125.
Therefore, 125 red bricks were used to build the wall.
Marta is making 3 servings of fruit salad.she adds 3/8 cup blueberries for each serving.her measuring cup holds 1/8 cup.how many times must Marta measure 1/8 cup of blueberry to have enough for the fruit salad?
Answers
1. You have the following information given in the problem above:
- Marta is making 3 servings of fruit salad.
- Marta adds 3/8 cups blueberries for each serving.
- Her measuring cup holds 1/8 cup.
2. Then, you have:
1 time----1/8 cup
x----3/8 cups
x=(3/8)/(1/8)
x= 3x8/1x8
x=24/8
x=3 times
How many times must Marta measure 1/8 cup of blueberry to have enough for the fruit salad?
The answer is: 3 times
What is the ratio of x to y?
3x = 8y
Answers
3x= 8y
x 8
-- = ---
y 3
Final answer:
The ratio of x to y, given the equation 3x = 8y, is 8:3. This is found by dividing both sides of the equation by 3y and simplifying.
Explanation:
To find the ratio of x to y, given the equation 3x = 8y, you can divide both sides of the equation by 3 to solve for x in terms of y, or vice versa.
Dividing both sides by 3y yields:
x/y = (8y)/(3y)
Assuming y is not zero, the y terms cancel out on the right side of the equation, giving us:
x/y = 8/3
Method 2: Using fraction notation:
Rewrite the equation with x isolated:
x = (8/3) × y
This also shows that the ratio of x to y is 8:3.
Both methods lead to the same answer: x : y = 8 : 3.
Thus, the ratio of x to y is 8:3.
Convert 302 inches to yards
Answers
Hope this helps!
302inches/36 inches=8 yards 14 inches or
About 8.38 yards