Answers
Answer:
The range of values of x for which the function is < 0 is:
2<x<3.
Step-by-step explanation:
x²-5x+6<0
First find the critical points:
x^2 - 5x + 6 = 0
(x - 2)(x - 3) = 0.
x = 2, 3.
The critical points are 2 and 3.
Make a table of values:
x x<2 2<x<3 x >3
x -2 < 0 >0 >0
x -3 <0 <0 >0
(x - 2)(x - 3) >0 <0 >0
Related Questions
Find the missing rational expression.382x + 6(x-3)(x + 1)X-332x + 6(x-3)(x + 1)(Simplify your answer.)X-3
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Hi, can you help me answer this question please, thank you!
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From the problem we have
[tex]\begin{gathered} n_1=50 \\ n_2=30 \\ \bar{x_1}=2.31 \\ \bar{x_2}=2.02 \\ s_1=0.89 \\ s_2=0.61 \end{gathered}[/tex]We replace in t
[tex]\begin{gathered} t=\frac{(2.31-2.02)}{\sqrt[]{\frac{(0.89)^2_{}}{50_{}}+\frac{(0.61)^2_{}}{30_{}}_{}}} \\ t=\frac{0.29}{\sqrt[]{0.028245_{}_{}}} \\ t=1.725 \\ t=1.73 \end{gathered}[/tex]The answer is t=1.73helppppppppppppppppppppppppppppppp
Answers
Answer:
b=4
I believe this is correct.
Step-by-step explanation:
-(2)^3+7(2)^2-2(2)+12=
-8+28-16
-8+12
4
The product of two consecutive positive even integers is 48. Find the greatest positive integer.
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From that statement we can create the following equation,
[tex]n\cdot \left(n+2\right)=48[/tex]solving for n,
[tex]\begin{gathered} n^2+2n=48 \\ n^2+2n-48=0 \\ n_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-48\right)}}{2\cdot \:1} \\ n_{1,\:2}=\frac{-2\pm \:14}{2\cdot \:1} \\ n_1=\frac{-2+14}{2\cdot \:1},\:n_2=\frac{-2-14}{2\cdot \:1} \\ n=6,\:n=-8 \end{gathered}[/tex]We can only use the positive number for this problem, therefore n = 6
From the above, the set of numbers is 6 and 6+2=8, since 6*8=48.
Answer: the greatest integer is 8
im not sure the steps to this math problem, from step one to step three
Answers
The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]I NEED HELP WITH THIS ASAP ILL MARK YOU BRAINLIEST Put each set of numbers from greatest to least
Answers
Every number is equivalent to:
[tex]\begin{gathered} 7.18\times10^{-3}=0.00718 \\ \sqrt{\frac{25}{49}}=\frac{5}{7}=0.7143 \\ \frac{7}{10}=0.7 \\ 0.\bar{8}=0.8888 \\ \frac{3}{4}=0.75 \\ 80\text{ \% = 0.8} \end{gathered}[/tex]So, each number from greatest to least is:
[tex]0.\bar{8},80\text{ \%, }\frac{3}{4},\sqrt{\frac{25}{49}},\frac{7}{10},7.18\times10^{-3}[/tex]Bella competed in the 5,000 m race at the Olympics she finished in the race 14.2 minutes after the race Bella wrote the equation c equals 18.1 m to model the relationship between the number of calories she burned c and the number of minutes she ran m.how many calories did Bella burn in the first 10 minutes of the 5,000 meter race.
Answers
Answer
She burnt 181 calories in that first 10 minutes of the 5,000 meter race.
Explanation
Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as
c = 18.1m
The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.
That is, find c when m = 10 minutes
Recall,
c = 18.1m
c = 18.1 (10)
c = 181 calories.
Hope this Helps!!!
What is the length of the arc ? ( Precalc )
Answers
We're going to use the following formula:
[tex]L=2\cdot\pi\cdot r\cdot\frac{\theta}{360}[/tex]If we replace our values:
[tex]L=2\cdot\pi\cdot3\cdot\frac{60}{360}=\pi[/tex]Therefore, the length is pi.
the length of a rectangle is two more than the width. if the perimeter is 28, find the length and the width of the rectangle, let w represent the width and l represent the length.
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You have that the perimeter of a rectangle is 28. In order to find the values of length and width of the rectangle, you take into account the following formula for the perimeter of a rectangle:
[tex]P=2w+2l[/tex]where w is the width and l is the length. You have that the length l is twice the width w of the rectangle, that is l=2w. By replacing this expression for l into theformula for the calculation of the perimeter you obtain:
[tex]P=2w+2(2w)=2w+4w=6w[/tex]Thus, you have that P = 6w. You solve this equation for w, and also replace the value of P, just as follow:
[tex]\begin{gathered} P=6w \\ w=\frac{P}{6}=\frac{28}{6}=\frac{14}{3}=4.66 \end{gathered}[/tex]Then, the width is 4.66. The length is:
[tex]l=2w=2(4.66)=9.33[/tex]length = 9.33
When interest rates are low, some automobile dealers offer loans at 0% APR, as indicated in a 2016 advertisement by a prominent car dealership, offering zero percent financing or cash back deals on some models.Zero percent financing means the obvious thing—that no interest is being charged on the loan. So if we borrow $1,200 at 0% interest and pay it off over 12 months, our monthly payment will be $1,200/12 = $100.Suppose you are buying a new truck at a price of $26,000. You plan to finance your purchase with a loan you will repay over two years. The dealer offers two options: either dealer financing with 0% interest, or a $2,600 rebate on the purchase price. If you take the rebate, you will have to go to the local bank for a loan (of $23,400) at an APR of 6.5%.What would your monthly payment be if you took the rebate? (Round your answer to the nearest cent.)
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Which choice could be used in proving that the given triangles are similar? A) PO 6 DE 4 II B) PO 4 EF 9 PO 4 DE 6 D) PR 6 DE 6 allo
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For each situation, an inequality is written. Which one has an incorrect inequality?АThree less than a number is greater than negative four and less than negative one; - 4 75DAll real numbers that are greater than or equal to - 7 1/2or less than or equal to zerox < 0 or x>-7 1/2
Answers
Option D has an incorrect inequality.
Since option D Says:
"All real numbers that are greater than or equal to - 7 1/2 or less than or equal to zero"
Greater than or equal is represented with the symbol ≤ or ≥.
So the correct inequality is for this statement is:
x ≤0 or x>-7 1/2
Not
x < 0 or x>-7 1/2
Note that the x and 0 part doesn't have an equal sign.
hello, while doing the question please don't put A decimal Answer ( ex: 1.5) because my teacher told me that's incorrect, you can add or subtract depending on the question, or check if you need to simplify! Thank you:)
Answers
Notice that the unit segment is divided in 8 parts. Then, each mark is equal to 1/8.
The kitten that weighs the most is placed over the 5ft mark. Then, its weight is:
[tex]\frac{5}{8}[/tex]The kitten that weighs the least is placed over the third mark. Then, its weight is:
[tex]\frac{3}{8}[/tex]Substract 3/8 from 5/8 to find the difference on their weights:
[tex]\frac{5}{8}-\frac{3}{8}[/tex]Since both fractions have the same denominator, we can substract their numerators:
[tex]\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{2/2}{8/2}=\frac{1}{4}[/tex]Therefore, the difference in pounds between the heaviest and the lightest kittens, is:
[tex]\frac{1}{4}[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer:
translated 8 units down and then reflected across the y-axis
Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Let R represent the number of additional rolls that Sofia orders.
1) Which inequality describes this scenario?
Choose 1 answer:
B
12 + 24R ≤ 100
12+24R 100
24+12R 100
24+12R 100
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Answer:
24 + 12R ≥ 100Step-by-step explanation:
List the conditions as per question:
Number of pieces of sushi ordered = 24,Number of pieces required in total at least 100,Number of rolls to be ordered = R,Each roll contains = 12 pieces.Inequality to represent the total number of pieces of sushi is:
24 pieces and R rolls of 12 pieces to get at least 100 pieces, or 24 + 12R ≥ 100Solve the inequality: y-5-20Which of the following is the graph of the solution?
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Given the inequality:
[tex]y-5>-20[/tex]Let's select the graph which represents the solution.
Let's solve the inequality.
Add 5 to both sides of the inequality:
[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.
Therefore, the graph of the solution is:
ANSWER:
A
Find the interest earned on a $50,000 deposited for six years at 1 1/8 % interest, compounded continuously
Answers
To calculate the interest earned, we can use the following equation:
[tex]I=P((1+i)^n-1)[/tex]Where P is the value of the deposit, i is the interest rate and n is the number of periods of time.
First, we need to calculate the equivalent value of 1 1/8 % as:
[tex]1\frac{1}{8}\text{ \% = }\frac{1\cdot8+1}{8}\text{ \% = }\frac{9}{8}\text{ \% = 1.125\% = 0.01125}[/tex]So, replacing P by $50,000, i by 0.01125, and n by 6, we get:
[tex]\begin{gathered} I=50,000((1+0.01125)^6-1) \\ I=50,000(0.694) \\ I=3,471.3577 \end{gathered}[/tex]Answer: $ 3,471.3577
is this right triangle shown a right triangle? 50 cm2 40mc2 20cm2 Explain your reasoning.
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Solution:
Note that :
[tex]2500=50^2\ne\text{ }40^2+20^2=2000[/tex]and If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. In this case, this statement is not true. We can conclude that it is not a right triangle.
5 6 7 8. One times a number equals 4 1
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hello
to solve this problem, we need to find the property of equality
let the unknown number be represented by x
[tex]4=1\times x[/tex]to solve for x, divide both sides of the equation by 1
[tex]\begin{gathered} 4=1x \\ \frac{4}{1}=\frac{1x}{1} \\ x=4 \end{gathered}[/tex]the number here is 4
the property used to get the answer is division property of equality
Watch help videoA group of friends wants to go to the amusement park. They have no more than $305to spend on parking and admission. Parking is $19, and tickets cost $26 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.<
Answers
p = number of people who can go to amusement park
Amount they want to spend is no more than $305. This means there expenses will be less than or equals to $305.
parking = $19
cost per person = $26
Therefore,
[tex]19+26p\leq305[/tex][tex]\begin{gathered} 26p\leq305-19 \\ 26p\leq286 \\ p\leq\frac{286}{26} \\ p\leq11 \end{gathered}[/tex]Gretchen is planting a rectangular garden. she wants to use 9 square feet for tulips.if garden has length of 8 feet by 3 feet, how much room will she have left for rest of her flowers
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Given: the garden has a shape of a rectangle
The garden has a length of 8 feet by 3 feet
So, the area of the garden =
[tex]8\cdot3=24ft^2[/tex]she wants to use 9 square feet for tulips.
So, the remaining for rest of her flowers = 24 - 9 = 15 square feet
In exercises 1 and 2 , identify the bisector of ST then find ST
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Given: The line segment ST as shown in the image
To Determine: The bisector of ST and the value of ST
Solution
It can be observed from the first image, the bisector of ST is line MW
[tex]\begin{gathered} ST=SM+MT \\ SM=MT(given) \\ MT=19(given) \\ Therefore \\ ST=19+19 \\ ST=38 \end{gathered}[/tex]For the second image, the bisector of ST is line LM
[tex]\begin{gathered} ST=SM+MT \\ SM=3x-6 \\ MT=x+8 \\ SM=MT(given) \\ Therefore \\ 3x-6=x+8 \\ 3x-x=8+6 \\ 2x=14 \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} SM=3(7)-6=21-6=15 \\ MT=7+8=15 \\ ST=SM+MT \\ ST=15+15 \\ ST=30 \end{gathered}[/tex]For first exercise, the bisector is MW, ST = 38
For the second exercise, the bisector is LM, ST = 30r
A
Y
+
B
X
Z
Given the diagram shown with AB|| XZ
AY = 7
AX = 6
AB= 14
find XZ.
Answers
Step-by-step explanation:
due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.
therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.
so,
AY / XY = AB / XZ
XY = AY + AX = 7 + 6 = 13
7/13 = 14/XZ
XZ×7/13 = 14
XZ×7 = 14×13
XZ = 14×13/7 = 2×13 = 26
Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
Answers
Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
HELP PLEASE will give BRAINLIEST!!! You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is
y = 3/2x +6. There is a tree in your yard at the point (6, 2). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the
tree from the zip line? Round your answer to the nearest tenth.
Answers
Answer:
Hello lovely. Assume that the attached graph represents your situation, with the red line representing the zip line and the blue dot representing the tree. The tree is at point (6, 2). You will need to choose a reference point to calculate the distance between the tree and the zip line. We'll use the point (0, 6), or the y intercept
To calculate the distance between two points, we use the formula d=√((x2 – x1)² + (y2 – y1)²).
Substitute
d=√((0 – 6)² + (6 – 2)²).
Simplify
d=√((-6)² + (4)²).
d=√(36 + 16).
d = √52
The distance is approximately equal to 7.2 feet
2x-y+4=0
d=15/2.24
d=6.70
Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Answers
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
Answers
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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in the diagram of BED below, FC||ED,BF=6,FE=18, and BC=22. What is the length of BD
Answers
we know that
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally
so
18/6=DC/11
solve for DC
DC=3*11
DC=33
Find the length of BD
BD=BC+DC
BD=11+33=44 units
therefore
the answer is 44 units
Evaluate the expression when m=9 and n=7.
5m +n
Correction: m = 7 and n = 9
Answers
We have the expression:
[tex]5m+n\text{.}[/tex]We must evaluate the expression for:
• m = 7,
,• n = 9.
Replacing the values of m and n in the expression above, we get:
[tex]5\cdot7+9=35+9=44.[/tex]Answer
44
[tex]4\sqrt[3]{16} /2\sqrt[3]{2}[/tex]
Answers
The expression 4∛16/2∛2 has a value of 4when simplified
How to evaluate the expression?From the question, the expression is given as
4∛16/2∛2
From the above parameter, we can see that the factors of the expression uses the cube root symbol
This means that the expression is a radical expression
Next, we have
4∛16/2∛2 = 4∛16/2∛2
Divide 4 by 2 in the equation
So, we have
4∛16/2∛2 = 2∛16/∛2
Solving further, we combine the cube roots (or radicals)
This is represented as
4∛16/2∛2 = 2∛(16/2)
Evaluate the quotient of 16 and 2
So, we have the following equation
4∛16/2∛2 = 2∛8
Take the cube root of 8
4∛16/2∛2 = 2 x 2
Evaluate the product
4∛16/2∛2 = 4
The expression cannot be further simplified
Hence, the solution to the expression 4∛16/2∛2 is 4
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