We are given the equation:
c = 500 + 1100 x – 100 x^2
Solve for x given the value of c = 2300
Rearrange and substitute:
- 100 x^2 + 1100 x + 500 = 2300
Divide everything by -100:
x^2 – 11 x – 5 = - 23
x^2 – 11 x = - 18
Completing the square:
(x – 11/2)^2 = - 18 + (11/2)^2
x – 11/2 = ±3.5
x = 2, 9
So x is 2 or 9
What theorem or postulate can prove a triangle to be an isosceles?
Final answer:
The Converse of the Base Angles Theorem states that if two angles of a triangle are congruent, then the triangle is isosceles.
Explanation:
In geometry, the theorem that can prove a triangle to be isosceles is the Converse of the Base Angles Theorem. It states that if two angles of a triangle are congruent, then the triangle is isosceles. In other words, if the two base angles of a triangle are equal, then the triangle is isosceles. For example, if angles A and B in triangle ABC are congruent (angle A = angle B), then triangle ABC is isosceles.
What is the probability of throwing a number greater than 4 when rolling a number cube that has sides labeled 1, 2, 3, 4, 5, 6?
The probability of rolling a number greater than 4 on a six-sided die is 1/3 or 0.33 or 33%. This is obtained by dividing the number of favourable outcomes (2, i.e., 5 and 6) by the total number of outcomes (6).
Explanation:The subject of the question is the probability in mathematics, specifically related to an experiment involving rolling a six-sided die. To answer your question, a six-sided die has numbers from 1 to 6. But you are asking about throwing a number greater than 4. There are only two outcomes that are greater than 4, the numbers 5 and 6. Therefore, the possible favorable outcomes are 2.
The total outcomes (since it's a six-sided standard die) are 6. Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, it will be 2/6 = 1/3 which is approximately 0.33 or 33%.
This means, if you roll the die, on an average, you can expect to roll a number greater than 4 about 33 times if you roll it 100 times.
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For all real numbers a and b if a not equal to 0 and b not equal to 0 then a^2 + b^2 does not equal (a+b)^2
Help please! I need to show my work
What is the value of cos 45 degrees?
(answers in picture)
The length of a rectangle is four times its width. If the perimeter is at most 100 centimeters, what is the greatest possible value for the width? Question 17 options:
Let p: The shape is a rhombus. Let q: The diagonals are perpendicular. Let r: The sides are congruent. Which represents "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”?
Answer:
C.)p ↔ (q ∧ r)
Step-by-step explanation:
I scored a 100 on my quiz
Solve the inequality
7x ≥ -7
a. x ≤ -1
b. x > -14
c. x ≥ -1
d. x ≥ 14
Answer:
A: x ≥ -1
its rightc bc
Is 81 a multiple of 3 explain why
Simplify 7t · s · 3rt.
10rst
10rst2
21rst2
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 7t · s · 3rt, when simplified will be equal to 21rst². The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 7t · s · 3rt can be written as,
7t · s · 3rt
= 7 × t × s × 3 × r × t
= 21rst²
Hence, the given expression 7t · s · 3rt, when simplified will be equal to 21rst².
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Important state labor laws and safety regulations came about as a result of the 1911 __________.
a. labor relations act
b. triangle shirtwaist factory fire
c. homestead strike
d. massachusetts child safety campaign
Answer:
Option B is correct.
Step-by-step explanation:
Important state labor laws and safety regulations came about as a result of the 1911 - Triangle shirtwaist factory fire
The Triangle shirtwaist factory fire was one of the worst industrial disasters during that time. Many people died due to a fire breakout in the factory. They could not escape the building and died due to smoke inhalation or burns.
After this incident, a Committee on Public Safety was formed that led to a legislation requiring labor laws and improved factory safety standards.
Use the graph shown to fill in the blank.
When x = -3, then y = a0.
Which term describes gross pay that is calculated based on the number of hours an employee has worked?
Answer: Hourly wage
Step-by-step explanation:
The term "hourly wage" describes the gross pay that is calculated based on the number of hours an employee has worked.
The hourly wage is the amount of money that is earned by a employee for every hour worked or it is the amount of money paid by employer for every hour worked.
Here, the gross pay is calculated by multiplying the hourly wage to the number of hours worked.
What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?
find the slope of the line given:
y = mx+b
y = -3x/2 -7/2
slope = -3/2
the slope of the perpendicular line is the negative reciprocal
so answer is 2/3
Can someone how to get the answer? Thanks! PLEASE HELPpppppppppppppppppppppppp
Rob cuts 15-foot wire into 8 equal pieces. About how long is each piece
A triangle has base 6 cm and area 42 cm^2 what is the height of the triangle
The height of the triangle is 14 cm.
Explanation:To find the height of the triangle, we can use the formula for the area of a triangle: Area = 1/2 * base * height. In this case, the base is 6 cm and the area is 42 cm^2. By rearranging the formula, we can solve for the height: Height = 2 * Area / Base. Plugging in the values, we get Height = 2 * 42 cm^2 / 6 cm = 14 cm.
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Odette deposited $3,624.40 into a savings account with an interest rate of 2.1% compounded annual. About how long will it take for the account to be worth $7,000?
A. 31 years, 9 months
B. 30 years, 9 months
C. 28 years, 4 months
7000 = 3624*(1+0.21)^x
7000 = 3624 *1.021^x
7000/3624 = 1.021^x
875/453 = 1.021^x
xlog(1.021 = log(875/453
x = 31.677
31 years 9 months
Answer:
Option A is the answer.
Step-by-step explanation:
p = 3624.40
r = 2.1% or 0.021
n = 1
t = ?
A = 7000
Compound interest formula is :
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
Substituting the values in formula:
[tex]7000=3624.40(1+\frac{0.021}{1})^{t}[/tex]
=> [tex]\frac{7000}{3624.40} =(1.021)^{t}[/tex]
=> [tex]1.93135=(1.021)^{t}[/tex]
[tex]t=\frac{log1.93135}{log1.021}[/tex]
=> t = 31.670 years.
Closest to option A.
Does a negative minus a negative equal positive
What is the equation of the line shown in this graph?
pls help
the line of the graph is vertical since both x coordinates are the same ( both are -2)
so the equation would be x = -2
I have a graphing question
What is the value of x in the parallelogram?
I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $20. Then it occurred to me that, if my nickels were dimes and my dimes were quarters, I would have $46.25. How many dimes and nickels are in the box?
There are 150 nickels and 125 dimes in the box.
Let x = the number of nickels in the box
Let y = the number of dimes in the box
Firstly, we have to convert value of nickels and dimes into cents.
Value of 1 nickel = 5 cents
Value of 1 dime = 10 cents
Value of 1 dollar = 100 cents
Thus, the equation (1) (in cents) can be written as:
x + 2y = 400 Equation (1)
If my nickels were dimes and dimes were quarters:
A quarter is worth 25 cents.
Thus, the equation (2) (in cents) can be written as:
5x+10y =2000
5(x+2y)= 2000
x+2y = 2000/5
2x + 5y = 925 Equation (2)
Multiply Equation (1) by "2", we get:
10x +25y= 4625
5(2x+5y)=4625
2x+5y=4625/5
2x + 4y = 800 Equation (1)
Subtraction Equation (1) from Equation (2):
2x +5y-2x -4y=925-800
y= 125
2x + 5y = 925
2x + 5 × 125 = 925
2x + 625 = 925
2x = 925 - 625
2x = 300
x = 150
There are 150 nickels and 125 dimes in the box.
Here, we can check it by putting the value of x and y in Equation (1):
5x + 10y = 2000
5× 150 + 10 × 125 = 2000
750 + 1250 = 2000
2000 = 2000
There are 150 nickels and 125 dimes in the box.
State a true conclusion. 1) If a ● b = 0, then a = 0 or b = 0 2) 3x = 0
Answer:
x=0
Step-by-step explanation:
Proposition 1) If a ● b = 0, then a = 0 or b = 0
Proposition 2) 3x = 0
=> 3 = 0 or x = 0
Given that 3 ≠ 0, x must be equal to 0.
Conclusion: x = 0
The expression 3x² represents
Final answer:
The expression 3x² signifies a quadratically powered variable (x) that is multiplied by the coefficient 3, commonly seen in algebraic equations.
Explanation:
The expression 3x² represents a mathematical formula where the variable x is squared (multiplied by itself) and then multiplied by 3. The squaring of a variable is a fundamental concept in algebra that symbolizes a number raised to the power of 2.
The coefficient 3 in this case indicates that the square of x is being tripled. Therefore, if x is 2, x² would be 4, and 3x² would be 12. This type of expression is essential in solving quadratic equations and appears frequently in various mathematical contexts.
The vertex of the graph of a quadratic function is (–2, –9) and the y-intercept is (0, –5). Which of the following is the equation of the function? A. y = x2 +10x + 2 B. y = x2 +10x – 2 C. y = x2 – 2x – 5 D. y = x2 + 4x – 5
Which graph represents the solution set of the system of inequalities?
a line that passes through two sides of triangles divides the sides proportionally
A. always
B. sometimes
C. never
Which pair of triangles are congruent by ASA ?
The pair of triangles that are congruent by ASA is figure C
The ASA theoremTwo triangles can be judged to be congruent using the ASA (Angle-Side-Angle) criterion. For triangles to satisfy ASA congruency:
Angle: The triangles' two matching angles have to coincide.Side: There must also be congruence on the included side that lies between the congruent angles.Put otherwise, the ASA criterion determines that two triangles are congruent if two of their angles and the included side are congruent, respectively. For this criterion, the angles and sides' order matters.
Based on the explanations, hence the pair of triangles that are congruent by ASA is figure C
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[02.05]
Solve for x: 4 − (x + 2) < −3(x + 4) (1 point)
x < −7
x > −7
x < −9
x > −9
Option A
x<-7
Given :
[tex]4 - (x + 2) < -3(x + 4)[/tex]
Explanation :
Solve the given inequality for x by applying algebraic properties
We use order of operation to simplify the left and right side of inequality
[tex]4- (x + 2) < -3(x + 4)\\4-x-2<-3x-12\\-x+2 < -3x -12\\Add\; 3x \; on \; both \; sides\\2x+2<-12\\Subtract\; 2\; from \; both \; sides\\2x<-14\\Divide \; both \; sides \; by 2\\x<-7[/tex]
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