A value in the interval (-∞,-2√5] ∪[2√5,∞) will give the two real number solutions.
Given quadratic equation is:
[tex]x^{2} +bx+5=0[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where a≠0.
To have two real number solutions the discriminant of a quadratic equation should be greater than or equal to zero.
[tex]b^{2} -4(1)(5)\geq 0[/tex]
[tex]b^{2} -20\geq 0[/tex]
[tex]b^{2} -(2\sqrt{5} )^2\geq 0[/tex]
[tex](b+2\sqrt{5} )(b-2\sqrt{5} )\geq 0[/tex]
[tex]b\in(-\infty,-2\sqrt{5} ]\cup [2\sqrt{5} ,\infty)[/tex]
Hence, a value in the interval (-∞,-2√5] ∪[2√5,∞) will give the two real number solutions.
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The price of an item has been reduced by 80% . The original price was $85. What is the price of the item now?
and fast pls it is due today and thx u!.
Let the price be x
x=85-80% of 85x=85-0.8(85)x=85-68x=$17Price is $17 now
Rectangle A'B'C'D' was created by dilation Rectangle ABCD using D as the center of dilation.
What is the scale factor of the dilation?
Based on the scale factor, how many copies of ABCD, including the original, should fit inside A'B'C'D?
In Rectangle , 16 copies of ABCD fit inside A'B'C'D'.
What is a rectangle, exactly?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
DA = 3
D'A' = 12
Scale factor DA/D'A' = 3/12 = 1/4
The scale factor = 1/4
The scale factor = 1/4
area ratio = 1/16
16 copies of ABCD fit inside A'B'C'D'.
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dont mind the answer that I picked on accident and pls dont send no PDF or a image to download
Answer:
I guess that X measures 50° because X and 50 are vertically opposite angles...
help me please im getting tired of getting no answers!
Answer:
The picture isnt popping up fix it and ill answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
change in time: 2
change in distance: 5.5
2:5.5
what expression is equivalent to 2x+9-x+3? show your answer is correct by substituting a value for x.
Answer:
Step-by-step explanation:
Given
2x + 9 - x + 3
What's equivalent
Solution
2x - x + 9 + 3 The terms have been rearranged. Combine
x + 12
Test.
x = 5
2(5) + 9 - 5 + 3
10 + 9 - 5 + 3
19 - 5 + 3
14 + 3
17
x + 12
5 + 12 = 17
What is the Pythagorean Theorem and when can you use it?
Step-by-step explanation:
The Pythagorean Theorem is a useful tool that shows how the sum of the areas of three intersecting squares can determine the side lengths of a right triangle.
You use the Pythagorean Theorem when you know the lengths of two sides of a right triangle and you want to figure out the length of the third side.
Answer number 9 please thanks
Solve the system of equations (1 point)
y = 2x(squared) – 3
y = 3x - 1
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
════════════════════
1.
[tex]y = {2x}^{2} - 3[/tex]
[tex] {2x}^{2} - 3 = y[/tex]
[tex] {2x}^{2} = y + 3[/tex]
[tex]\frac{2x^{2}} {2} = \frac{y + 3}{2}[/tex]
[tex] {x}^{2} = \frac{y + 3}{2} [/tex]
[tex]x = \sqrt \frac{2y + 6}{2}[/tex]
───────────────────
2.
[tex]y = 3x - 1[/tex]
[tex]3x - 1 = y[/tex]
[tex]3x = y + 1[/tex]
[tex] \frac{3x}{3} = \frac{y+1}{3}[/tex]
[tex]x = \frac{y + 1}{3}[/tex]
═══════════════════
Explanation:
#Carry on learning
If 2/5 of the judges were wearing their powdered wigs, what fraction of the judges were not wearing their powdered wigs?
Answer: [tex]\frac{3}{5}[/tex] of the judges were not wearing their powdered wigs.
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] out of the whole [tex]\frac{5}{5}[/tex] were wearing a wig. So subtract [tex]\frac{2}{5}[/tex] from [tex]\frac{5}{5}[/tex] to see the fraction that wasn't wearing a wig.
[tex]\frac{5}{5} -\frac{2}{5} =\frac{3}{5}[/tex]
Which statements are correct? check all that apply. the angles in the smaller prism measure 90 degrees. the perimeter of the rectangular bases changes by a factor of 2. the surface area changes by a factor of 8. the larger prism has twice the volume of the smaller prism. the area of the rectangular bases changes by a factor of 4.
Answer:
1st, 2nd, and 5th one
Step-by-step explanation:
I got an 100 on the assignment! hope this help <3
A store sells an 8-pound bag of flour for $18.80. If larry can buy a 2-pound bag of flour at the same rate, what would be the price of the 2-pound bag?
Answer:
$4.70
Step-by-step explanation:
First, you need to divide 18.80 by 8.
18.80/8 = 2.35
2.35 is the unit price for one (1) pound bag of flour,
Multiply by 2 to find the price of a two (2) pound bag.
2.35 * 2 = 4.7
$4.70 is the price of a two-pound bag.
hope this helps :)
Given X(4, -7). what are
the coordinates of X" 1EX - R,ax(R, axi, (X)),
A
(4,7)
B
(0,9)
C
(-4, -7)
D
(-4, 7)
See the picture for my question.
Which number is the best estimate of 2.3 x 3.6?
O A. 6
OB. 8
O c. 9
OD. 12
Answer:
B. 8
Step-by-step explanation:
Explanation: 2.3x3.6 is 8.28, and we round down to 8 because 8.28 is closer to 8 than 9.
(3 9/13 * 2 1/6 -5)^3-(9-5*2)^5+0.4(29.51+90.49)
Answer:
76
Step-by-step explanation:
All steps are in the pic attached :
5) WILL GIVE BRAINIEST TO BEST ANSWER
find the equations use to solve
Graphing!
Answer:
A: y= 3x-4
B: y= -2/4x+3
Step-by-step explanation:
slope intercept form: y=mx+b
m = slope
slope = rise/run
b = y-intercept
Answer:
A: y = 3x - 4
B: y = -1/2x +3
Step-by-step explanation:
First, lets find the slope of line B. We need to find two coordinates on the line that coincide with points on the grid. We see that (2, 2) and (4, 1) are two points that match the criteria, so we can use both points. You can use any two points, I just randomly chose these two. Slope is nothing but the Y coordinate of the first point subtracted from the Y coordinate of the second point. We do 2 - 4 and get -2. Next, we do the same thing but with the X coordinates to get 2 - 1, which is 1. We do 1 over -2 to get negative 1/2 for our slope. The last variable in the equation is just where the line hits the Y axis, which is 3. So, the final equation is y = -1/2x + 3. Rinse and repeat for the next question.
Which equation is equivalent to log subscript 3 baseline (x 5) = 2? 3 squared = left-bracket log subscript 3 baseline (x 5) right-bracket cubed 2 cubed = left-bracket log subscript 3 baseline (x 5) right-bracket squared 3 squared = x 5 2 cubed = x 5
The equation that is equivalent to the considered equation of log is given by: Option E: 2^3 = x+5
What is logarithm and some of its useful properties?When you raise a number with an exponent, there comes a result.
Lets say you get [tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
The equation given is:
[tex]\log_3(x+5) = 2[/tex]
By using the definition of log, which says [tex]a^b = c \leftrightarrow \log_a(c) = b[/tex], we get:
[tex](x+5) = 2^3[/tex] or [tex]2^3 = x+5[/tex]
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
(we used the fact that the question is asked in a way that expresses that there is only one equivalent equation. Plus we used the fact that as option E is a sure equivalent version, so it is correct option).
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
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Which situation does NOT yield variability?
Select one:
How many days are in a leap year?
How many siblings does each person in your class have?
How many miles do you travel in your car each day?
Options A and B situation does NOT yield variability that is A. How many days are in a leap year? B. How many siblings does each person in your class have?
What is statistical data?Statistics deals with the study of variability. The statement is said to be statistical if there would be variability in that data.
A. How many days are in a leap year?
This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.
B. How many siblings does each person in your class have?
This situation does NOT yield variability because the question is answered by a single value. It does not need any collecting data that vary.
C. How many miles do you travel in your car each day?
This situation yield variability because the question is answered by collecting data.
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Is the function F(x)=5x2
Im trying to help my sis but i cant remember :/
428.5oz (total amount she had to put out)÷ 5(amount of bowls she wanted to use) = 85.7oz
Please help!! Will mark brainlyest.
C
Step-by-step explanation:Line symmetry is when a shape can be folded over an imaginary axis and have both sides be a mirror of the other. This axis is called the line of symmetry.
Letter C
In this case, if you draw a horizontal line across the middle of the letter "C" and fold the letter, each half would be the same. The top half of "C" mirrors the lower half.
Other Examples
The lowercase letter "l" also has 2 lines of symmetry. You can draw both a horizontal and vertical line across the letter and each side will mirror the other.
What is the slope of the line that contains the points (13, -2) and (3, -2)?
Answer:
the slope = 0
Step-by-step explanation:
we notice that the points (13, -2) and (3, -2) have the same y-coordinate -2
Then
the slope = 0
o Watch help video
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=
Given that f(x) = x2 - 6x + 8 and g(x) = X – 2, find (fºg)(x) and express
the result in standard form.
Answer: [tex]x^{2} -7x+10[/tex]
Explanation:
Get the result ⇒ [tex]f(x)-g(x)=(x^{2} -6x+8)-(x-2)[/tex]
Remove the parentheses ⇒ [tex]x^{2} -6x+8-x+2[/tex]
Reorder and gather like terms ⇒ [tex]x^{2} +(-6x-x)(8+2)[/tex]
Collect the coefficients for the like terms ⇒ [tex]x^{2} +(-6-1)*x+(8+2)[/tex]
Calculate the sum or difference ⇒ [tex]x^{2} -7x+(8+2)[/tex]
Calculate the sum or difference ⇒ [tex]x^{2} -7x+10[/tex]
Convert to required form ⇒ [tex]x^{2} -7x+10[/tex]
Answer ⇒ [tex]x^{2} -7x+10[/tex]
Please help!! 50 points!!!!
Jim walks 3 miles per hour slower than his friend Steve runs. Steve runs 4 miles per hour slower than his friend Matt rides his bike. Jim walks 25 miles in the same time Matt rides his bike 60 miles. Steve runs 16 miles in the same time Matt rides his bike 24 miles.
Part A: Write an equation to calculate Jim's speed.
Part B: Write an equation to calculate Steve's speed.
Part C: Write two equations that can be used to calculate Matt's speed.
Answer:
Jim=S-3
Steve=M-4
U figure out the last part. I helped
Step-by-step explanation:
Answer:
See below ~
Step-by-step explanation:
Let Jim, Steve, and Matt have speeds of j, s, and m respectivelyFrom the problem :j = s - 3 [Jim]s = m - 4 [Steve]Jim takes same time to walk 25 miles at it takes Matt to ride 60 milesj = 25/t₁ and m = 60/t₁Steve runs 16 miles in the same time Matt rides his bike 24 miless = 16/t₂ and m = 24/t₂Equating Matt's Speed in both cases
60/t₁ = 24/t₂t₁/t₂ = 5/2 = 2.5t₁ = 2.5t₂Now, taking Equation 1 :
j = s - 325/t₁ = 16/t₂ - 325/(2.5t₂) = 16/t₂ - 310/t₂ = 16/t₂ - 36/t₂ = 3t₂ = 2 st₁ = 2.5(2) = 5 secondsEq.1) m = 60/5 [Matt]Now, taking Equation 2 :
s = m - 416/t₂ = 24/t₂ - 48/t₂ = 4t₂ = 2 secondsEq.2) m = 24/2 [Matt]Round 5.78575184279 to the nearest whole number.
Answer:
6
Step-by-step explanation:
5.7 is already immediately 6 because if a number after the whole number is 5 or more you round up.
6
Step-by-step explanation:
let p be a polynomial function where p(x)=x4- dx3 + 8x2 - 10x + 4 if (x-2) is a factor of the polynomial, what is the value of d?
Answer:
d = 4
Step-by-step explanation:
If (x -2) is a factor of polynomial p(x), then the remainder will be zero.
⇒ p(2) = 0
[tex]\sf \bf 2^4-d*2^3 + 8*2^2 -10*2 + 4 = 0\\\\[/tex]
16 - 8d + 8*4 - 20 + 4 = 0
16 - 8d + 32 - 20 + 4 = 0
-8d + 32 = 0
-8d = - 32
d = -32/(-8)
[tex]\boxed{d = 4}[/tex]
What is the solution to 4|x – 6| ≤ 16?
x ≤ 2 or x ≥ 10
2 ≤ x ≤ 10
–10 ≤ x ≤ 2
x ≤ –10 or x ≥ 2
Answer:
2 ≤ x ≤ 10
Step-by-step explanation:
4|x – 6| ≤ 16
|x – 6| ≤ 4
-4 ≤ x – 6 ≤ 4
2 ≤ x ≤ 10
The solution to 4|x – 6| ≤ 16 is 2 ≤ x ≤ 10
What are polynomials?
A polynomial expression is an expression that can be built from constants and symbols.
Polynomials are algebraic expressions that comprise exponents which can be added, subtracted, or multiplied. Polynomials are of different types. Monomial- Linear equations (A monomial is a polynomial with one term)Binomia l- quadratic equation (A binomial is a polynomial with two, unlike terms).
calculation:-
⇒4|x – 6| ≤ 16
⇒|x – 6| ≤ 4
⇒-4 ≤ x – 6 ≤ 4
⇒2≤ x ≤ 10
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URGENT!!
Find the solutions by completing the square x^2-5x+4=y
Answer:
y=x^2-5x+4 i am not sure but a im try
I urgently need help!! Please!!
Answer: f= [tex]x^2+4x+8+(7/3x-4)[/tex]
Step-by-step explanation:
Careful with simplifying every step.
Suppose a normal distribution has a mean of 98 and a standard deviation of
6. What is P(x s 110)?
A. 0.975
B. 0.84
O C. 0.025
OD. 0.16
The probability (x s 110) is 0.975, the correct option is A.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that;
Mean=98
Now,
To find the probability that x is less than or equal to 110 for a normal distribution with mean 98 and standard deviation 6, we need to use the standard normal table or a calculator.
Using the standard normal table, we first need to convert x to a z-score using the formula:
z = (x - mean) / standard deviation
Plugging in x = 110, mean = 98 and standard deviation = 6, we get:
z = (110 - 98) / 6
z = 2
This means that x = 110 is equivalent to z = 2 on the standard normal distribution.
Now we look up the value of z = 2 on the table and find that it corresponds to an area of 0.9772. This means that P(z ≤ 2) = 0.9772.
However, this is not the answer we want. We want P(x ≤ 110), which is the same as P(z ≤ 2). The table gives us the area to the left of z, but we need to subtract it from 1 to get the area to the right of z. This is because P(x ≤ 110) = P(z ≤ 2) + P(z > 2) = 1.
Therefore,
P(x ≤ 110) = P(z ≤ 2)
P(x ≤ 110) = 1 - P(z > 2)
P(x ≤ 110) = 1 - (1 - P(z ≤ 2))
P(x ≤ 110) = P(z ≤ 2)
P(x ≤ 110) ≈0.9772
Therefore, by the given mean the answer will be 0.975.
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