The quadratic equation r² – 94 = 0 has two real solutions, as the discriminant is positive when applying the quadratic formula.
Explanation:The question deals with the quadratic equation r2 – 94 = 0. To determine how many real solutions this equation has, we can rearrange it into the standard quadratic form ar2 + br + c = 0, where a = 1, b = 0, and c = -94. The real solutions of a quadratic equation are found using the quadratic formula, which is r = −b ± √(b2 - 4ac) / (2a). In this case, the discriminant (b2 – 4ac) becomes (02 – 4(1)(-94)) which simplifies to 376. This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 0, and c = -94. To find the number of real solutions, we need to determine the discriminant, which is given by the formula: discriminant = b² - 4ac. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. In this case, the discriminant is: 0 - 4(1)(-94) = 376. Since the discriminant is greater than zero, the equation r² - 94 = 0 has two real solutions. Since the discriminant is positive, this equation has two real solutions.
The equation has two real solutions.
Explanation:This expression is a quadratic equation of the form where the constants are To find the number of real solutions, we can use the discriminant, which is given by . If Δ > 0, there are two real solutions. If Δ = 0, there is one real solution. If Δ < 0, there are no real solutions. Let's calculate the discriminant:
Δ = 0² - 4(1)(-94) = 376
Since Δ > 0, the equation has
Write an equation of a line that goes through point (4, -5) and is parallel to line y = 2x + 8. Show all work.
I really need help with this.
The measurement of the supplement of an angle is 7 times the measure of the complement. find the measure of the complement
Answer:
15⁰
Step-by-step explanation:
Angke = x
Complement = 90 - x
Supplement = 180 - x
Given:
180 - x = 7 (90 - x)
180 - x = 630 - 7x
6x = 450
x = 75
Complement = 90 - 75 = 15⁰
1. What is the difference between –4 and 6?
1) –10
2) –2
3) 2
4) 10
2. What is the first step in solving the equation 4.2y -5.2=18.5
1. Add 5.2 to each side of the equation.
2. Subtract 5.2 from each side of the equation.
3. Multiply each side of the equation by 4.2.
4. Divide each side of the equation by 5.2.
The cost of a classified ad is based on a daily rate plus a flat service fee. One day cost $3.50 and four days cost $800 write and solve a linear equation to find the cost of a 7-day ad.
x= 11
hope this helped :)
The linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
The cost of a 7-day ad is $12.50.
Let, the daily rate is "d" dollars and the flat service fee is "f" dollars.
We are given two pieces of information:
One day costs $3.50.
Four days cost $8.00.
Using this information, we can set up two equations:
For one day: d + f = $3.50
For four days: 4d + f = $8.00
Now, we need to solve this system of linear equations to find the values of "d" and "f."
Subtract Equation 1 from Equation 2 to eliminate "f":
(4d + f) - (d + f) = $8.00 - $3.50
3d = $4.50
Now, divide both sides by 3 to solve for "d":
d = $4.50 / 3
d = $1.50
Now that we have the value of "d," we can find the value of "f" by substituting "d" into Equation 1:
d + f = $3.50
$1.50 + f = $3.50
Now, subtract $1.50 from both sides to solve for "f":
f = $3.50 - $1.50
f = $2.00
So, the daily rate (d) is $1.50, and the flat service fee (f) is $2.00.
We get, a linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
Now, to find the cost of a 7-day ad, we can use the daily rate and multiply it by the number of days (7):
Cost of a 7-day ad = 7 * $1.50 + $2.00
Cost of a 7-day ad = $10.50+ $2.00 = $12.50
The cost of a 7-day ad is $12.50.
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This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
The graph intersects the y-axis the y-coordinate is known as the y-intercept and this can be determined by using the definition of the y-intercept.
Given :
This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
The following steps can be used in order to determine a point at which a graph intersects the y-axis:
Step 1 - According to the example (0, 5) for the equation y = x + 5.
Step 2 - When the graph intersects the y-axis the value of the x-coordinate is zero.
Step 3 - When the graph intersects the y-axis the y-coordinate is known as the y-intercept.
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How do you find the area of this triangle?
Find the value of x that makes m ∥ n
Answer:
The value of x that makes m || n is x = 20
Step-by-step explanation:
Given a line that is intersected by another two lines (for example line ''m'' and line ''n'' like in the exercise) one of the conditions that makes m || n is that the alternate interior angles must be congruent. Understanding that congruent means the same.
In the exercise, one pair of alternate interior angles are (2x+20)° and 3x°.
We need this two angles to be congruent ⇒ [tex]3x=2x+20[/tex]
Solving this for ''x'' :
[tex]3x=2x+20\\3x-2x=20\\x=20[/tex]
The value of x that makes 3x° congruent to 2x+20° (that makes the alternate interior angles congruents) is x = 20
Answer:
20
Step-by-step explanation:
Theorem:
If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
Lines m and n are cut by a transversal.
Angles 3x and 2x + 20 are alternate interior angles.
For lines m and n to be parallel, angles 3x and 2x + 20 must be congruent, so their measures must be equal.
3x = 2x + 20
x = 20
Answer: 20
Use the trapezoid rule to estimate the area under the graph of y = x2 + 2 for values of x from 0 to 3.
(1 pt) which point represents the origin? number line from minus5 to 5 with point s at minus2, t at 0, u at 1, and v at 3.
Claire and rachel plays volleyball for different teams .claire team practices seven hours every two days and rachels team practices eight hours every three days match player to the team that represents the average number of hours that they practice each day over a seven day period
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Answer:
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Step-by-step explanation:
C) Having a savings account gives individuals the ability to borrow money from members in the community
please show me how to solve ... -5x-10=10
Find measure of angle EFG
Approximately how many times greater is 8.5×108 than 3.4×105 ? A 2.5 B 250 C 2,500 D 25,000
Solution:
we have been asked to find that , how many times one number is to the other given numbers.
To do this we will divide the larger number by the smaller number and the resulting number will be the answer of the question.
Here the larger number is [tex]8.5\times10^8[/tex]
The smaller number is [tex]3.4\times 10^5[/tex]
Now lets divide as follows
[tex]\frac{8.5\times10^8}{3.4\times 10^5} =\frac{8.5}{3.4}\times 10^{8-5}\\ \\\frac{8.5\times10^8}{3.4\times 10^5} =2.5\times10^3=2500[/tex]
Hence the correct option is C.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.
A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
To determine the extent of how many times greater is the number of bacteria in petri dish A than petri dish B, we simply have to take the ratio of the two.
1.75 x 10^18 / 6.25 x 10^15 = 280
So the bacteria in petri dish A is 280 times larger.
In scientific notation:
2.8 x 10^2
Answer:
280 is the answer, I did the test.
The table below shows some values of f(x) and g(x) for different values of x.
x f(x) = 9x + 7 g(x) = 5x
-2 -11
-1 -2
0 1
1 5
2
Complete the chart and determine the solution of the equation f(x) = g(x)?
A.) x = -1
B.) x = 0
C.) x = 2
D.) x = 25
Answer:
x = -1.75 makes f(x) = g(x)
Step-by-step explanation:
See the attached for a table. You will notice that for x=-1.75, the values of f(x) and g(x) are the same. That means x = -1.75 is the solution to f(x)=g(x).
Upon calculating the values for f(x) and g(x), it's determined that f(x) = g(x) when x = -7/4. The options provided do not include this answer, suggesting a possible typo in the question or answer choices.
Completing the Values and Finding the Solution for f(x) = g(x)
To complete the given table, we need to apply the functions f(x) = 9x + 7 and g(x) = 5x to the missing x values. For x = -2, g(x) equals -10 (since 5 * -2 = -10). For x = 0, f(x) is 7 (since 9 * 0 + 7 = 7), and for x = 2, f(x) equals 25 (since 9 * 2 + 7 = 25) and g(x) equals 10 (since 5 * 2 = 10).
To determine the solution for the equation f(x) = g(x), we set the two expressions equal to each other:
9x + 7 = 5x
By subtracting 5x from both sides, we get:
4x + 7 = 0
Now, subtracting 7 from both sides, we find:
4x = -7
Finally, by dividing both sides by 4, we get:
x = -7/4
None of the given options A, B, C, or D match x = -7/4, which might indicate there could be a typo in the question or answer choices.
The length of a photograph is 1 cm less than twice the width. The area is 91cm^2. Find the width and length.
The length of the photograph is 13 cm and the width is 7 cm.
What is a rectangle?
A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Given that:-
The length of a photograph is 1 cm less than twice the widthThe area is 91 cm²The length and the width will be calculated as:-
let the width = x
length = 2x - 1
91 = x ( 2x - 1 ) = 2x² - x
2x² - x - 91 = 0
= ( 2x + 13 ) ( x - 7 )
x = - 13 / 2
x = 7 cm
Length will be = 2x - 1 = 2 x 7 - 1 = 13 cm
Therefore the length of the photograph is 13 cm and the width is 7 cm.
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What is the width of a rectangle with an area of 5/8in and the length of 10in?
Two plans for reaching a goal are given below.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
Which of the following is a true statement?
a.
Only plan A will work for achieving the goal.
b.
Only plan B will work for achieving the goal.
c.
Both plans will work for achieving the goal.
d.
Neither plan will work for achieving the goal.
Answer:
The correct option is C) Both plans will work for achieving the goal.
Step-by-step explanation:
Consider the provided information.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
For next 8 weeks by working 9 hours per week at $7.20 per hour, you will earn:
[tex]8 \times 9 \times 7.20 = 518.40[/tex]
We need to save $450 which is less than $518.40. Thus, plan A will work.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
For next 6 weeks by working 15 hours per week at $6.50 per hour, you will earn:
[tex]6 \times 15 \times 6.50 = $585.00[/tex]
We need to save $450 which is less than $585.00. Thus, plan B will work.
Hence, the correct option is C) Both plans will work for achieving the goal.
In a bag there are 13 red marbles, 5 blue marbles, and 7 green marbles. what percent of the marbles are green?
Joanna bought 1 1/2 pounds of apples, 3/4 pound of strawberries, 1/2 pound of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears. How many pounds of fruit did Joanna buy in all?
Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.
= 1 1/2 + 3/4 + 1/2 + 1 3 /4 + 1 1/4
= 3/2 + 3/4 + 1/2 + 7/4 + 5/4
= (6 + 3 + 2 + 7 + 5)/4
= 23/4
= 5 3/4
Thus, Joanna bought 5 3/4 pounds of fruit in all if Joanna bought 1 1/2 pounds of apples, 3/4 pounds of strawberries, 1/2 pounds of grapes, 1 3/4pounds of oranges, and 1 1/4 pounds of pears.
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On the first 4 quizzes of her chemistry class, nadia got an average score of 88. what does she need on the next quiz to have an overall average of 90?
What is a security deposit?
A local reader's club has a set of 12 hardback books, a set of 18 paperbacks, and a set of 36 magazines. each set can be divided equally among the club members. what is the greatest possible number of club members?
The greatest possible number of club members is the greatest common factor of 12, 18, 36 since all of these quantities of books have to be distributed evenly:
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
The greatest common factor for this three numbers is 6.
As a result, the greatest possible number of club members is 6.
When Rosina babysits for 5 hours she charges $40 and when she babysits for 6 hours she charges $48. How much does Rosina charge in one hour?
find the inverse function for f(x)=square root 2x-6
Find the slope of the line that passes through the pair of points (1/10,6) and (3/16,11/5)
Andrew took a math test with 40 questions. If he scored an 85%, how many questions did he get correct?
Answer:
34 is my answer
Rajesh wakes up at 7:00 a.m. and takes a walk for half an hour. He then spends 30 minutes bathing and eating breakfast. After watching the morning news on TV for a while, Rajesh leaves for school at 9:30 a.m. How many hours does Rajesh spend watching the news? 1 and 1/2 hours 2 hours 2 hours and 30 minutes 120 minutes 130 minutes