What is the sum of the zeros of the function y = x² - 9x-10?
Answer: 9
Step-by-step explanation:
Finding the zeros is the same as solving. Then, we will add the two solutions together.
Given:
y = x² - 9x - 10
Solving by Quadradic Formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(-10)} }{2(1)}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{81+40} }{2}[/tex]
[tex]\displaystyle x=\frac{9\pm\sqrt{121} }{2}[/tex]
[tex]\displaystyle x=\frac{9+11}{2},\;\;x=\frac{9-11}{2}[/tex]
x = 10, -1
Adding them together:
10 + -1 = 9
Tony is decorating a ballroom ceiling with garland. If the rectangular ceiling is 5 meters by 12 meters, how much garland will Tony need to reach from one corner of the ceiling to the opposite corner?
Answer: 13
Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.
Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.
The ceiling of the ballroom is rectangular in structure.
The dimensions of the rectangle are 12 by 5 meters.
So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.
We will use Pythagoras theorem to calculate the length of the diagonal.
12² +5 ² = D²
or, D² = 144 + 25
or, D =√169
or, D = 13
Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.
Hence Tony will need 13 meters of garland.
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HELP MEEEEE PLEASEEEE
You want to buy some noodles. A 9-ounce package costs $3.15. A 12-ounce package costs $4.44 A 22-ounce package costs $7.26. Which package is the best buy?
Answer: A 22-ounce package costs $7.26 is best to buy
Step-by-step explanation:
A 9-ounce package costs $3.15 = 35 cents an ounce
A 12-ounce package costs $4.44 = 37 cents an ounce
A 22-ounce package costs $7.26 = 33 cents an ounce making it the cheapest by ounce
Need help lol for this
In the given rectangle, the values of f and g are the same that is 2√6cm.
What are rectangles?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.Therefore, a particular case of a square is a rectangle. To put it another way, a rectangle can also be a square (when all sides to are equal).So, the values of f and g are:
We know that APQD is a square and its area is 24 cm².Now, calculate the sides as follows:
Formula: A = s²
24 = s²s = √24s = √2×2×2×3s = 2√6So, each side of APQD measures 2√6cm.
So, DQ (g) = 2√6cmNow, we know that ABCD is a rectangle and we know that AD || CB and AD = CD.Then,
AD = CB = 2√6cmSo, CB (f) = 2√6cmTherefore, in the given rectangle, the values of f and g are the same that is 2√6cm.
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at the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. the difference was statistically significant. what can be concluded from the study?
The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH
The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.
1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.
Total cost includes initial charge for printer set up and material cost.
C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.Part 1Average cost per T-shirt is
C(x)/ x = (4.25x + 35)/x = 4.25 + 35/xPart 2Average cost to print 25 T-shirts
4.25 + 35/25 = $5.65Average cost to print 100 T-shirts
4.25 + 35/100 = $4.60Part 3The average cost 4.25 + 35/x depends on the number of T-shirts printed.
The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.
can someone please help me solve this paper
the given expressions solved by using factorization.
What is factorization of the expression ?
To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.
Here
4) [tex]x^4-36[/tex]
=> [tex](x^2)^2 -6^2[/tex]
=> [tex](x^2-6)(x^2+6)[/tex]
5)64[tex]c^3+1[/tex]
=> [tex](4c)^3+1^3[/tex]
=> (4c+1)([tex](16c^2+4c+1)[/tex]
6)[tex]k^3-27[/tex]
=> [tex]k^3-3^3[/tex]
=>(k-3)([tex]k^2+3k+9[/tex])
7)[tex]54x^3+250y^3[/tex]
=> 2([tex]27x^3+125y^3[/tex])
=> 2([tex](3x)^3+(5y)^3[/tex])
=> 2 ( 3x+5y)([tex]9x^2+15xy+25y^2[/tex])
8)[tex]3m^4-48n^2[/tex]
=> 3([tex](m^2)^2-(4n)^2[/tex])
=> 3[tex](m^2-4n)(m^2+4n)[/tex]
9)[tex]a^7b^2-ab^2[/tex]
=> [tex]ab^2(a^6-1)\\[/tex]
=>[tex]ab^2(a^3-1)(a^3+1)[/tex]
=> [tex]ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)[/tex]
10)[tex]x^3y^2-343y^5[/tex]
=> [tex]y^2(x^3-(7y)^3)[/tex]
=>[tex]y^2(x-7y)(x^2-7xy+49y^2)[/tex]
11)[tex]9y^7-144y[/tex]
[tex]= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)[/tex]
Hence we can solve by using factorization formula.
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The graph shows how many bottles a machine caps in a certain number of seconds.
(shown in the picture below)
Part A
What is the constant of proportionality, and what does it mean in this situation?
Use the drop-down menus to show and explain your answer.
The constant of proportionality is __ (Choices: 15, 30, 20) ; the machine caps __ (Choices: 30, 20, 15) bottles in ____________ (Choices: 1 second, 1 minute, 15 seconds)
Part B
Which of the following is an ordered pair on the graph? What does it represent in this situation?
A. ) (45, 90); the machine caps 45 bottles in 90 seconds.
B. ) (45, 900); the machine caps 45 bottles in 900 seconds.
C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
D. ) (900, 45); the machine caps 900 bottles in 45 seconds.
Considering the proportional relationship graphed, it is found that:
A. The constant is of 20.
B. A pair on the graph is given as follows: C. ) (45, 900); the machine caps 900 bottles in 45 seconds.
What is a proportional relationship?A proportional relationship is a linear function with intercept zero in which the output variable y is given by the multiplication of the input variable x and the constant k, as follows:
y = kx.
Considering point (15, 300) on the graph presented, the constant is calculated as follows:
300 = 15k
15k = 300
k = 300/15
k = 20.
The input and the output are given as follows:
Input: number of seconds.Output: number of bottles capped.Hence option C is the correct option for item 2.
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an old-model machine can stamp 1000 parts in four hours. a newmodel machine can stamp 1000 parts in just two hours. how long will it take one old-model and one new-model machine to stamp 1000 parts working together?
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
Given that;
Finding the hourly cost of stamping parts for each machine is one way to approach this issue.
In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).
If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.
By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;
250t + 500t = 1000
750t = 1000
t = 1000/750
t = 1.333
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
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A dilation with scale factor 0.25 is performed on triangle 1 to produce triangle 2. Which statement MUST be true about the two triangles?
O Their corresponding sides have equal lengths, and their corresponding angles have equal measures.
• Their corresponding sides are parallel, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
O Their corresponding sides are parallel, and their corresponding angles have equal measures.
O Their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
What is property of similar triangle?
If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.
They have parallel corresponding sides, and they have angles with the same measure.
hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.
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Please Help!
Solve the inequality and graph it’s solution.
I”M GIVING BRAINLIEIST OR WHATEVER TO WHO EBER EXPLAINS THE BEST
Answer:-3
Step-by-step explanation:
a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion is called
The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .
A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.
Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.
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Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job. How much total money would Taub have after 7 weeks of saving? Also, write an expression that represents the amount of money Taub would have saved in w weeks.
Total savings after 7 weeks:
Total savings after w weeks:
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.
Taub will have a total of -
70 + 7 x 10 = $140
The expression that represents the amount of money Taub would have saved in [w] weeks is -
y = 70 + 10w
Therefore -
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
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Aaliyah was given a gift card for a coffee shop. Each morning, Aaliyah uses the card to
buy one cup of coffee. The original amount of money on the gift card was $30 and
each
сир of coffee costs $2. Make a table of values and then write an equation for A,
in terms of x, representing the amount money remaining on the card after buying a
cups of coffee.
The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x dollars.
Define the term equation?A single mathematical phrase is referred to as a term. It could be a single number (negatively or positively), a single variable (a letter), or a combination of variables multiplied but still never added or eliminated. Variables with such a number ahead of them are used in some words. A coefficient is the number that appears ahead of a phrase.The original value of the gift card was $30.
Coffee costs $2 per cup.
Let 'x' be the number of cup of coffee purchased by Aaliyah.
Total cost be 'A' be paid by her.
Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;
A = 30 - 2x dollars.
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Dados os polinomios:
X-2=
X-3=
X+1=
X+5=
Answer:
X-2=1
X-3=2
X+1=2
X+5=6
I need help to solve this please!!
Answer:
Adult is 10$ and Child is 7$.
Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.
Hope this helps!
Step-by-step explanation:
2x + 4y = 48
5x + 2y = 64
2x + 4y = 48
10x + 4y = 128
( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )
8x = 80
x = 10
2 ( 10 ) + 4y = 48
20 + 4y = 48
4y = 48 - 20
4y = 28
y = 7
having driven a hybrid car for 4.5 years, a driver believes the car gets more than 33 miles per gallon (mpg). the driver kept records of all car fill-ups and taking a sample of 15 found a sample average of 32.84 mpg and sample standard deviation of 1.86 mpg. assuming that the underlying distribution is normal, what can be concluded at the 0.05 level of significance?
By probability, There is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.p value is calculated using online p value calculator (you will find it by searching online).
p value interpretation: if the null hypothesis is true then the probability that the sample average is greater than 33 mpg is 0.373143.
[ the p value associated with a test is the probability that we obtain the observed value of the test statistic or a value that is more extreme in the direction given by the alternative hypothesis, when H0 is true ].
decision: accept H0 at 5% level of significance as p value >0.05
[level of significance is chosen as 5 %= 0.05]
conclusion : there is insufficient evidence to conclude that the gas mileage is greater than 33 mpg.
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Deshaun works as a busboy making $9 per hour and as a theater usher making $10 per hour. Let b be the number of hours he works as a busboy this
month, and let u be the number of hours he works as an usher.
His goal this month is to earn more than $1400 total
Answer:
[tex]9b + 10u > 1400[/tex]
Guys, what is the answer to 5-x=12?
Answer:
x= -7
Step-by-step explanation:
here you go.....
please mark brainliest
A box is put on a table. The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25m. The pressure on the table due to the box is 42 newtons/m² Work out the force exerted by the box on the table.
Answer:
105 N
Step-by-step explanation:
You want the force exerted on an area 2 m by 1.25 m by a pressure of 42 N/m².
AreaThe area is ...
A = LW
A = (2 m)(1.25 m) = 2.50 m²
ForceThe force is the product of the pressure and the area:
F = PA
F = (42 N/m²)(2.5 m²) = 105 N
The box exerts a force of 105 N on the table.
Describe the end behavior of each fund f(x) = x4 - x2 - x
Answer:
[tex]\lim_{x \to -\infty} f(x) = \infty[/tex] and [tex]\lim_{x \to \infty} f(x) = \infty[/tex]
Hope this helps!
Step-by-step explanation:
The equation of line s is y=3/5x2/5 Line t, which is parallel to line s, includes the point
(2, 1). What is the equation of line t?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
8
The equation of line t in slope intercept form is 5y - 3x = -1
The equation of line s is y=3/5x + 2/5
This is in the slope intercept form
y = mx + c
where m represents the slope of the line
The slope of the line y=3/5x + 2/5 is 3/5
The slope of two parallel line is same
The slope of line t is 3/5, it passes through the points (2, 1)
The equation of the line is
y - y₁ = m(x - x₁)
y - 1 = 3/5 (x - 2)
5y - 5 = 3x - 6
5y - 3x = -6 + 5
5y = 3x -1
y = 3/5 x - 1/5
Therefore, the equation of line t in slope intercept form is 5y - 3x = -1
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Determine the length of the line segment shown.
line segment from negative 5 comma 5 to 3 comma negative 1
6 units
8 units
10 units
36 units
The length of the line segment from negative 5 comma 5 to 3 comma negative 1 is 10 Units.
How to find the length of a line segment?
A line segment is defined as a line bounded by two points on a line.
The line segment from negative 5 comma 5 to 3 comma negative 1
is found by using the formula
square root of (x2-x1)² +(y2-y1)²
[tex]\sqrt{(3+5)^{2} +(-1-5)^{2} }^[/tex]
[tex]\sqrt{8^{2}+6^{2} }[/tex]
[tex]\sqrt{100}[/tex]
=10 units
therefore the length of the line segment is 10 units
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An uber charge a flat rate of $20 plu $2 per mile. Lyft charge a flat rate of $15 plu $4 per mile. Write an equation to find the number of mile m for which uber and lyft would cot the ame amount
The required equation is 20 + 2m = 15 + 4m. The number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
Uber charges a flat rate of $20 plus $2 per mile. Lyft charges a flat rate of $15 plus $4 per mile. We need to find out the equation and the number of miles for which Uber and Lyft would charge the same amount for the ride.
Let the charge of Uber and Lyft be represented by the variables C1 and C2. We can write the equations given below.
C1 = 20 + 2m
C2 = 15 + 4m
We need the charge for both companies to be equal.
C1 = C2
20 + 2m = 15 + 4m
Hence, the required equation is 20 + 2m = 15 + 4m. Now we will solve this equation to find the number of miles.
2m = 5
m = 2.5
Hence, the number of miles for which Uber and Lyft would charge the same amount for the ride is 2.5 miles.
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Screams Halloween Theme Park
reduced their admission rates by 10% this
year to try and increase their attendance. If
last year’s admission price was $35 per
person, what is this year’s admission price?
Answer:
$32.50
Step-by-step explanation:
10% of 35$ is $3.50 if ur decreasing $35 by 10% it will be $3.50-$35=$32.50
rearrange the formula below to make 'a' the new subject:
[tex]c + \frac{1}{2}a^{2}b = d[/tex]
is the bottom answer correct for this question? :
[tex]a = \sqrt{2(\frac{d-c}{b} )}[/tex]
Step-by-step explanation:
c + 1/2 × a²b = d | - c on both sides
1/2 × a²b = d - c | ×2 on both sides
a²b = 2(d - c) | /b on both sides
a² = (2/b) × (d - c) | sqrt on both sides
a = sqrt(2(d - c)/b)
yes, the given answer is correct.
PLEASE HELP!!!!!!! A warehouse store sells 5.5-ounce cans of tuna in packages of 5. A package of 5 cans costs $10.45. The store also sells 4.5-ounce cans of the same tuna in packages of 8. A package of 8 cans costs $12.96. The store sells 3.5-ounce cans in packages of 4 cans for $4.76. Which package is the best buy? find the one with the smallest unit rate!!!
Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
A discount store sells 5.5 - ounce jars of fish in bundles of 5. A bundle of 5 jars costs $10.45. Then the unit rate is given as,
⇒ ($10.45 x 5) / (5.5 x 5 x 5)
⇒ $0.38 per ounce
The store likewise sells 4.5-ounce jars of similar fish in bundles of 8. A bundle of 8 jars costs $12.96. Then the unit rate is given as,
⇒ ($12.96 x 8) / (4.5 x 8 x 8)
⇒ $0.36 per ounce
The store sells 3.5 - ounce jars in bundles of 4 jars for $4.76. Then the unit rate is given as,
⇒ ($4.76) / (3.5 x 4)
⇒ $0.34 per ounce
Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.
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quick help me please
Answer:
calculate the difference ere
(3-22)+5
remove unnecessary parentheses
-19+5
calculate the sum
= -14
