This answer details the use of the quadratic formula to solve quadratic equations and the discriminant's role in determining the number of real solutions.
Explanation:The question involves solving quadratic equations and using the discriminant to determine the number of real solutions. The quadratic formula, \(x = \frac{-b \pm \sqrt[tex]{b^2[/tex] - 4ac}}{2a}\), is a powerful tool in finding the roots of any quadratic equation of the form \([tex]ax^2[/tex]+ bx + c = 0\). The discriminant, \(\Delta =[tex]b^2[/tex] - 4ac\), helps in understanding the nature of the roots without actually solving the equation. If \(\Delta > 0\), there are two distinct real solutions; if \(\Delta = 0\), there is exactly one real solution; and if \(\Delta < 0\), there are no real solutions and instead two complex solutions.
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
12 ⋅ x − 4
x − 4 ⋅ 12
4(x − 12)
12(x − 4)
Question 2(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "some number to the power of 5?"
5x
x5
5x
x + 5
Question 3(Multiple Choice Worth 3 points)
(06.02)
Translate the algebraic expression shown below into a verbal expression.
Fraction with variable x in numerator and 10 in the denominator.
The sum of ten and some number
The quotient of some number and ten
The product of some number and ten
The difference of ten and some number
Question 4(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "eight less than some number?"
8 − b
b − 8
Fraction 8 over b
Fraction b over 8
Question 5(Multiple Choice Worth 4 points)
(06.02)
Which verbal expression best describes the algebraic expression 4x ÷ 6?
The sum of four and some number divided by six
The quotient of four times some number and six
The product of some number and six divided by four
The quotient of four and some number times six
Question 6(Multiple Choice Worth 3 points)
(06.02)
Which of these is the algebraic expression for "seven more than the product of three and some number?"
7 + 3 + x
3 + 10 ÷ x
3x + 7
3 + 7x
I am just going to answer the first one
1. 12(x - 4)
Help! Halfway there. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 16 in and the height is 28. On the 2nd pyramid the height is 112. What is the side length of the base of the 2nd pyramid?,
A club has members from three grades. It has 36 members from sixth grade, 24 members from seventh grade, and 30 members from eighth grade. What is the ratio of the club's seventh graders to eighth graders?
Answer:
the correct answer is 4/5!
have a great day!
Factor. 25m^100 - 121n^16
What is the rule for the reflection?
Will mark brainliest!
Answer:
Option C is correct.
[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
Step-by-step explanation:
From the given figure:
Coordinate of Triangle ABC are:
A(-2, 1), B(-3, 4) and C(-4, 1)
And
Coordinate of Triangle A'B'C' are:
A'(1, -2), B'(4, -3) and C'(1, -4)
The rule of reflection across the line:
[tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
then;
Apply the given rule of reflection on coordinate of triangle ABC
[tex]A(-2, 1) \rightarrow (1, -2) =A'[/tex]
[tex]B(-3, 4) \rightarrow (4, -3) =B'[/tex]
[tex]C(-4, 1) \rightarrow (1, -4) =C'[/tex]
Therefore, the rule of reflection used here is [tex]r_{y=x} (x, y) \rightarrow (y, x)[/tex]
The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all entry tickets during the off-peak season. The Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets to the water park during the off-peak season. 78 = one-half x + (x − 6) What is the regular price of a child's ticket?
Which equation is true for the value b = 2? 2b + 24 = 30 3b − 2 = 4 b + 4 = 8 2b − 3 = 0
Answer:
3(b – 2) = 24
Step-by-step explanation:
What is the measure of ∠XBC?
1. m∠XBC = m∠BAC + m∠BCA
2. 3p – 6 = p + 4 + 84
3. 3p – 6 = p + 88
4. 2p – 6 = 88
5. 2p = 94
m∠XBC =
The measure of an exterior angle of triangle is equal to the sum of measures of two interior angles of triangle that are not supplementary with this exterior angles.
In the case of this question this fact sounds as
m∠XBC = m∠BAC + m∠BCA (option 1).
Now if
m∠XBC=(3p-6)°m∠BAC=(p+4)°m∠BCA=84°,then
3p-6=p+4+84 (option 2),
3p-6=p+88 (option 3),
3p-p-6=p-p+88,
2p-6=88 (option 4),
2p-6+6=88+6,
2p=94 (option 5),
p=47.
Then m∠XBC=(3p-6)°=(3·47-6)°=135°.
Answer: m∠XBC=135°.
the function f(x)=2^x and g(x)=f(x)+k. if k=2, what can be concluded about the graph?
the graph of g(x) is shifted vertically...
2 units to the left of the graph of f(x)...
Answer:
Its shifted verticlly 2 and to the left 2.
Step-by-step explanation:
Its verticlly because when it says 2^x its going up if it said -2^x it would go down.
It goes left because it is 2^x=? so if you put it on the other side its negative which makes it to the left.
A line passes through the point (–7, 5) and has a slope of 1/2. Which is another point that the line passes through?
(–13, 9)
(–9, 13)
(9, 13)
(13, 9)
Answer:
Option C is correct.
Another point is, (9, 13)
Step-by-step explanation:
Point slope form states the equation of a straight line in the form [tex]y-y_1=m(x-x_1)[/tex]; ......[1]
where
m is the slope of the line and
[tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.
As per the given condition we have;
[tex](x_1, y_1)[/tex] = (-7, 5)
Slope(m) = 1/2
then; substitute these in [1] we have;
[tex]y -5 = \frac{1}{2}(x-(-7))[/tex]
or
[tex]y -5 = \frac{1}{2}(x+7)[/tex]
Using distributive property; [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]
[tex]y-5= \frac{1}{2}x+\frac{7}{2}[/tex]
Add 5 on both sides we get;
[tex]y=\frac{1}{2}x+\frac{7}{2} + 5[/tex]
Simplify:
[tex]y= \frac{1}{2}x+\frac{17}{2}[/tex]
Only option which satisfy the above line equation is (9, 13).
Check:
put x = 9 and y = 13
[tex]13= \frac{1}{2}(9)+\frac{17}{2}[/tex]
[tex]13=\frac{9}{2}+\frac{17}{2} =\frac{26}{2} = 13[/tex] True.
Therefore, the another point that the line passes through is, (9, 13)
Simplify by using fractional exponents.[tex] \sqrt[3]{ x^{2} } [/tex]
Helppp!!! Will fan and Medal!!!
suppose n is an integer. select all statements below that are true:
n^2 + n is always an even integer
n^2 + n is always an even integer when n is even
n^2 + n is always an even integer when n is odd
n^2 + n is never an even integer when n is odd
n^2 + n is never an even integer
n^2 + n is sometimes an even integer
Panel 1 is the answer choice
Panel 2 is the question
The more surface area an ice cube has, the more quickly it melts to cool a beverage. mark states that the ideal ice cube would be a prism that is a perfect cube of dimensions 2 by 2 by 2. denise thinks that the prism should be more flat, with dimensions of 1 by 2 by 4. which rectangular prism gives the greatest surface area, making for a better ice cube?
Answer: D
Step-by-step explanation:
Denise Rectangular prism gives the greatest surface area, making for a better ice cube.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The surface area of a rectangular prism can be calculated by adding up the areas of all six faces.
The surface area of a prism with dimensions l, w, and h is given by:
A = 2lw + 2lh + 2wh
For Mark's prism (2 by 2 by 2), the surface area is:
A = 2(2 × 2) + 2(2 × 2) + 2(2 × 2)= 24
For Denise's prism (1 by 2 by 4), the surface area is:
A = 2 (1 × 2) + 2 (1 × 4)+ 2 (2 × 4)= 28
So both prisms have the different surface area of 24 square units and 28 square units.
Hence, Denise rectangular prism gives the greatest surface area, making for a better ice cube
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Find the amount paid for the loan.
$2400 at 10.5% for 5 years
Final answer:
$3,919.24
Explanation:
To calculate the total amount paid for a loan of $2,400 at an interest rate of 10.5% over 5 years, we will assume the interest compounds annually for simplicity. The formula to find the future value of a loan including interest is P(1 + r)^n, where P is the principal amount ($2,400), r is the annual interest rate (10.5% or 0.105), and n is the number of years (5).
Plugging the numbers into the formula gives us $2,400(1 + 0.105)^5. Calculating this gives us approximately $3,919.24. Therefore, the total amount paid for the loan over 5 years would be $3,919.24.
To find the amount paid on a $2400 loan at 10.5% interest for 5 years, calculate the simple interest and add it to the principal. The total interest is $1260, bringing the total repayment amount to $3660 over 5 years.
To find the amount paid for the loan of $2400 at 10.5% interest for 5 years, one would typically use the formula for the compound interest or an installment payment plan depending on whether the loan is paid off in a lump sum at the end of the term or through regular payments over the term. However, you have not specified the method of repayment (lump sum or installments), so let's consider a simple interest scenario which is often used for short-term loans.
The simple interest can be calculated as:
I = PRT
Where:
Using the formula:
I = $2400 × 0.105 × 5 = $1260
Therefore, the total interest paid over 5 years is $1260. To find the total amount paid for the loan, add the interest to the principal:
Total Amount Paid = Principal + Interest
Total Amount Paid = $2400 + $1260 = $3660
The borrower would have to pay a total of $3660 after 5 years.
simplify: 27k^5m^8/(4k^3)(9m^2)
If f(x)=2x-4 and g(x)=x^2 , what is f(g(x)) ?
Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?
Mr. sam's swimming pool is in the shape of a parallelogram, as shown. what is the area of his swimming pool? 189 ft² 234 ft² 279 ft² 585 ft² parallelogram a b c d with side a d parallel to side b c and side a b is parallel to side d
c. point e is on side a
b. a e is 5 feet. dc is 26 feet. a dotted segment d e runs from point d to the opposite side a b and is perpendicular to side a
b. d e is 9 feet.
PLEASE PLEASE PLEASE PLEASE HELP ME!
suppose ruth ann has 3 routes she can travel between the school to the library and 5 routes from the library to her home. how many routes are there from ruth anns school to her home with a stop at the library.
a. 9
b. 60
c. 15
d. 25
Write an equation in slope intercept form for the line that passes through (-2,3) and is parellel to the line whose equation 3x+2y=6
MATH hw help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
leon made 4 liters of lemonade for the party, but it was too strong, it was 14% lemon juice. How much 8% lemonade should he add to make a mixture that is 10% lemon juice? can someone show me how to solve this using the table or bucket method? thanks
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The scatterplot below shows the distances and times spent traveling for 22 trips by a driver. What is the time, in hours, of the trip represented by the data point farthest from the line of best fit (not shown)
A. 4
B. 6
C. 8
D. 10
Write a pair of integers whose sum gives
(a) a negative integer (b) zero
(c) an integer smaller than both the integers. (d) an
integer smaller than only one of the integers.
(e) an integer greater than both the integers,
Answer:
The pairs below satisfy the five questions. A) -2 & 1. -2 + 1 = -1 B) -2 & 2. -2 + 2 = 0 C) -1 & - 2. -1+ -2 = -3 D) -3 & 1. -3 + 1 = -2 E) 1 & 2. 1 + 2 = 3.
Step-by-step explanation:
hope this helps have an amazing day
Compare the fraction by using the symbol < , <, or =. a. 4⁄9 _____ 5⁄9 b. 4⁄5 _____ 8⁄10 c. 7⁄12 _____ 7⁄15 d. 3⁄4 _____ 6⁄7
Final answer:
To compare fractions, evaluate if they are equal or if one is greater by comparing the numerators and denominators.
a. 4/9 < 5/9
b. 4/5 = 8/10
c.7/12 > 7/15
d.3⁄4 < 6⁄7
Explanation:
In fractions, to compare two fractions, check if the fractions are equal, or if one is greater than the other by comparing the numerators and denominators.
a. 4/9 vs. 5/9: 4/9 < 5/9 since 5 is greater than 4.
b. 4/5 vs. 8/10: 4/5 = 8/10 since they are both equivalent fractions.
c. 7/12 vs. 7/15: 7/12 > 7/15 since 12 is greater than 15.
d. 3/4 vs. 6/7: 3⁄4 < 6⁄7 because converting to decimals, 3⁄4 is 0.75 and 6⁄7 is approximately 0.857, making 6⁄7 larger.
Using a directrix of y = −2 and a focus of (2, 6), what quadratic function is created?
Charlie wants to order lunch for his friends. He'll order 5 sandwiches and a $3 kid's meal for his little brother. Charlie has $28. How much can he spend on each sandwich if they are all the same price? Choose two answers: one for the inequality that models this situation and one for the correct answer.
The inequality 5x + 3 ≤ 28 represents the situation and each sandwich cost is $5.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
Let x be the cost of each sandwich.
5 sandwich costs = 5x
$3 kid's meal for his little brother.
Total cost = 5x + 3
5x + 3 = 28
5x = 25
x = $5
The inequality:
5x + 3 ≤ 28
Thus, the inequality 5x + 3 ≤ 28 represents the situation and each sandwich cost is $5.
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What is the first step in solving 12 (9+5) - 6 (3)?
On a map, 2 inches represents 60 miles. What part of an inch represents 12 miles? Please show how you get you answer.
A. 1/10in.
B. 1/5in.
C. 2/5in.
D. 1/2in.
Which equations are true for x = –2 and x = 2? Check all that apply.
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0
Answer:
x2 – 4 = 0
4x2 = 16
Step-by-step explanation: