Answer:
(1) B
(2) D
Step-by-step explanation:
(1)
Let the quadratic function be:
[tex]y = ax^{2} + bx + c[/tex]
For the point, (0,-1),
[tex]y = ax^{2} + bx + c[/tex]
[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]
Then the equation is:
[tex]y = ax^{2} + bx -1[/tex]
For the point (-1, -8) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]
For the point (1, 2) ,
[tex]y = ax^{2} + bx -1[/tex]
[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]
Add the two equations and solve for a as follows:
[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]
Substitute a = -2 in (i) and solve for b as follows:
[tex]a-b=-7\\-2-b=-7\\b=5[/tex]
Thus, the quadratic function is:
[tex]f(x)=-2x^{2}+5x-1[/tex]
The correct option is (b).
(2)
The ordered pairs are:
(5, 7), (7, 11), (9, 14), (11, 18)
Represent them in an XY table as follows:
X : 5 | 7 | 9 | 11
Y : 7 | 11 | 14 | 18
Compute the difference between the Y values as follows:
Diff = 11 - 7 = 4
Diff = 14 - 11 = 3
Diff = 18 - 14 = 4
Now compute the difference between the Diff values:
d = 3 - 4 = -1
d = 4 - 3 = 1
Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.
The correct option is D.
A Water flows through a pipe at a rate of 10 milliliters every 8.5 seconds. Express this
rate of flow in liters per minute. Round your answer to the nearest hundredth
Answer:
The answer to the nearest hundredth is 0.07 liters per minute
Step-by-step explanation:
In this question, we are told to express the given metric in liters per minute.
The key to answering this question, is to
have the given measurements in the metric in which we want to have the answer.
Hence, we do this by converting milliliters to liters and seconds to minute.
Let’s start with milliliters;
Mathematically;
1000 milliliters = 1 liters
10 milliliters = x liters
x * 1000 = 10 * 1
x = 10/1000
x = 1/100
x = 0.01 liters
For the seconds;
We need to convert the seconds to minutes;
Mathematically;
60 seconds = 1 minute
8.5 seconds = y minutes
60 * y = 8.5 * 1
y = 8.5/60
y = 0.14167 minutes
Now, our rate of flow is liters per minute, that means we have to divide the volume by the time;
Hence, we have ;
0.01/0.14167 = 0.070588235294
Which to the nearest hundredth is 0.07
What is the correct prime factorization of 24
2^3 * 3^1
Go step by step. 24 = 2 x 12. 12 = 2 x 6. 6 = 2 x 3. We can't factor any more.
Therefore, we have 12 = 2 x 6, and since 6 = 2 x 3, we get 12 = 2 x 2 x 3.
Then 24 = 2 x 12, and 12 = 2 x 2 x 3, so 24 = 2 x 2 x 2 x 3.
There are 3 2's and 1 3's, so it's 2^3 * 3^1.
Hope that helped,
-sirswagger21
Answer:
24=2*12=2*6=2*3
Step-by-step explanation:
I could not draw the tree diagram
to do it you take a prime number it is divisible by and a composite number it is divisible by and you prime factorise the composite number and repeat until you get prime numbers
Simplify the expression in simplest form (3x - 5)x4 +2
Answer:
12x-8
Step-by-step explanation:
We can use PEMDAS to solve this expression.
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
The first step to do is use the distribute property to simplify the parenthesis.
The second step will be to simplify the exponent, but there aren't any so we can skip that step.
The third is to multiply but we can skip that and division while we are at it because there isn't any we can do to simplify.
The fourth step will be to add -20 with 2. We then get -18.
And finally, we have our answer
(3x - 5)x4 +2
12x-20+2
12x-18
Help !!! Thank you a lot!!
Answer:
E) 45
Step-by-step explanation:
Since b is 90 degrees, and lines CB and BA are equal (as seeen with the 2 lines across them) we can assume that this angle is 45 degrees, half or 90 degrees.
Angle C is also equal to angle A
Answer:
E
Step-by-step explanation:
Using the fact that the sum of angles in a triangle is 180 degrees, we can write the following equation to solve for 3x:
3x + 3x + 90 = 180
3x + 3x = 90
2 * 3x = 90
3x = 45°
19) Caculate the unit rate. Driving 95 miles on 3 gallons of
gas. How many miles are driven on 1 gallon of gas?
Answer:
31.6666666 miles / gallon
Step-by-step explanation:
Take the miles and divide by the gallons
95 miles / 3 gallons
31.6666666 miles / gallon
Write the ratio as a fraction in simplest form.
0.65 to 0.15
Answer:
13/3
Step-by-step explanation:
Write as a fraction first,
0.65/0.15
convert decimal to fractions,
13/20/3/20 = 13/3
a hotel manager wants miriam to tile their lobby using the dame design she created for Mr.Rivera.The lobby measures 45 feet by 45 feet. he wants the outer edge to be the same color as the center tile. will this occur ? justify your answer
Answer:
Yes it will occur
Step-by-step explanation:
The lobby measures 45 feet by 45 feet
Area of the lobby = 45 * 45
=2025 ft^2
So, the lobby has 2025 tiles
subtract 1 black tile in the center
2025 tiles - 1 black tile =2024 tiles
The number of blue tiles and black tiles is 2024 tiles
He wants the outer edge to be the same color as the center tile so, divide by 2
2024/2 = 1012 tiles
The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles
Please help At a party of 102 people, 72 lb of potato salad is served. Write and solve and equation to find how many people each pound of potato salad serves.
Answer:
1.417
Step-by-step explanation:
102/72=1.417
Find the edge length of a cube if the surface area is 565.7 m².
0 9.71 m
9.48 m
0 10.31 m
10.97 m
None of the above
Answer:
9.71 m
Step-by-step explanation:
Surface area of cube is given by 6a^2 where a is the edge length.
Given
Surface area =565.7 m²
let a be the edge length of required cube
then
6a^2 = 565.7 m²
=> a^2 = 565.7 /6 m² = 94.28
=> a = [tex]\sqrt{94.28}[/tex] = 9.71
Thus, first option 9.71 m is correct choice.
Lucy reads 450 words in 3 minutes.
This is an equation that can be used to
find w, the number of words Lucy can
read in 20 minutes if she continues to
read at the same rate?
Answer:
3000 words
Step-by-step explanation:
450 words in 3 minutes is 150 words in 1 minute. 20 minutes = 1 times 20.
1 minute = 150 words so 150 words times 20 minutes = 3000 words.
George goes to the supermarket to buy some canned tomatoes to make salsa for a party. The cans are on sale for $0.95 each. He has $4.75. Let x represent the number of cans that he can buy. Which equation models this situation?
Answer:
see below
Step-by-step explanation:
Take the price of each can and multiply by the cost of the cans
.95x
This must be less than or equal to 4.75
.95x ≤ 4.75
They may choose to use an equals sign, since they asked for an equation
.95x = 4.75
Answer: 0.95x = 4.75
Step-by-step explanation:
Since we do not know how much George can buy, we will put x as 0.95x
If you solve 0.95x=4.75 by dividing 0.95 on both sides you will get the number of cans he can buy which is 5.
Use the Law of Sines to find the missing angle of the triangle.
Find m < C to the nearest tenth if the c= 102, a = 71 and m < A=40
Answer:
66.9 degrees
Step-by-step explanation:
The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:
71/sin40 = 102/sinC
Cross multiplying, we get:
102(sin40deg) = 71(sinC)
Now, we simplify the left side and get:
65.56 = 71(sinC)
Next, we divide 65.56 by 71 to get:
0.92 = sinC
Taking the inverse sign we get:
C = 66.9 degrees
Below are a list of costs and discounts for groceries. Round to the nearest dollar to estimate the total cost
+ $12.34
+ $5.07
- $0.73
+ $2.84
- $1.50
Answer:
$18
Step-by-step explanation:
$18.02 rounds to $18
Answer:
$17
Step-by-step explanation:
Rounded, the listed numbers are ...
12 + 5 -1 +3 -2 = 17
The estimate of total cost is $17.
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II
Answer:
The error made here is a Type I error.
Step-by-step explanation:
A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.
A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.
The hypothesis in this case is defined as follows:
H₀: The product does not change the height of the plant.
Hₐ: The product makes the plant grow taller.
The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.
Thus, the error made here is a Type I error.
I need help super fast
Answer:
The last option
Step-by-step explanation:
When you have a fraction as a power, the denominator goes to the root, so in this case, it becomes root 4. The base, 5, goes to the outside, and the numerator 1, goes beside the x.
Hope this helps!
About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.
183 meters
250 meters
366 meters
683 meters
Answer:
A. 183 meters
Step-by-step explanation:
Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number. A) 183 meters B) 250 meters C) 366 meters D) 683 meters
Find distance BC
Cos (60°)=BC / AB (Adjacent divided by the hypotenuse)
Cos (60°)=1/2
BC=a
AB=500
Cos (60°)=BC / AB
1/2=a/500
1/2 * 500=a
250=a
a=250m
Find distance AC
Sin(60°)=AC/AB (opposite side divided by hypotenuse)
Sin(60°)=√3/2
AC=b
AB=500
Sin(60°)=AC/AB
√3/2=b/500
√3/2 * 500=b
250√3=b
b=433m
Distance AC and BC=AC+BC
433m+250m=683m
Subtract the distance AB from AC+BC
= 683m - 500m
=183m
Answer is A. 183 meters
Answer:
A. 183 meters
Step-by-step explanation:
sin(60) = x/500
= 433
tan(60) = 433/x
= 250
This is the driving distance. 433+250= 683. Directly walking (using hypotenuse distance) is 500.
683-500=183!
A circle has a circumference of 153.86153.86153, point, 86 units.
What is the radius of the circle?
Answer:
Step-by-step explanation:
C=153.86153...
100000C=15386153.86153...
subtract
99999C=15386000
C=15386000/99999
2 π r=15386000/99999
r=7693000/99999π≈24.5
I need a lot of help
To add fractions with different denominators you must find the highest common factor (the highest number they both go into).
For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8
now, whatever you do to the bottom, you must do to the top.
So:
3 x 2 = 6 and 5 x 4 = 20
Therefore, your answer would be 6/8 + 20/8
You do that for the rest of them as well, do you get it?
Answer:
3/4 + 5/2 = 3/4 + 10/4 = (3+10)/4 = 13/43. 4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15
5. 2/3 + 7/10 = 20/30 + 21/30 = (20+21)/30 = 41/30
Can someone answer this please? Okay so it says that something is made 3 times than the other item. The other item uses 13 beads. So, what is 13 times 3?
Answer:
13x3= 39
Step-by-step explanation:
10x3=30
3x3=9
30+9=39
Hope it helps!
What is the solution to
Ax+ bx + C=0
Answer:
x = -C / (A + b)
Step-by-step explanation:
Without given values for the constants A, b, and C (Assuming they are constants), the best we can do is to isolate the variable x. Let's proceed to solve for x.
Ax + bx + C = 0
x (A + b) + C = 0
x (A + b) = -C
x = -C / (A + b)
So now, when you get the values of the constants A, b, and C, you can plug those in to solve for variable x.
Cheers.
help asap will give 10 points
Answer:
False
Step-by-step explanation:
[tex]( {9}^{9} ) \times ( {9}^{ - 20} ) \\ = {9}^{9 + ( - 20)} \\ = {9}^{ - 11} [/tex]
Answer:
I'm pretty sure its false
find the midpoint of the line segment whose endpoints are
(5,9) (2,-1)?
Answer:
(3.5,4)
Step by step explanation:x coordinate =
[tex] \frac{5 + 2}{2} [/tex]
= 3.5
y coordinate =
[tex] \frac{ - 1 + 9}{2} [/tex]
= 4
midpoint = (3.5,4)
Answer:
( 3.5,4)
Step-by-step explanation:
To find the midpoint
Add the x coordinates together and divide by 2
(5+2)/2 = 7/2 = 3.5
Add the y coordinates together and divide by 2
(9+-1)/2 = 8/2 = 4
( 3.5,4)
Joaquin used two types of flour in a muffin recipe. How much flour did he use in all? Solve any way you choose.
Answer:
3 1/6 cups of flour.
Step-by-step explanation
Scores on the Mathematics section of the SAT Reasoning Test form a normal distribution with a mean of μ = 500 and a standard deviation of 100. What is the minimum score necessary to be in the top 10% of the distribution?
Answer:
The minimum score necessary to be in the top 10% of the distribution is 628.
Step-by-step explanation:
Given that a normal distribution has a mean of μ = 500 and a standard deviation = σ= 100
The Significance level for this test = 10 % = 0.1
For one tailed test ∝= 0.1 the value of Z∝= ±1.28
Since it a normal distribution the test statistic used is
Z= X= u / σ/√n ( taking n= 1)
1.28 = X- 500/100/√1
128 + 500 = X
or X = 628
The minimum score necessary to be in the top 10% of the distribution is 628.
Which of the following would cause an increase in heat? freezing compression stirring friction
Answer:
Compression, stirring, and friction all increase heat
Step-by-step explanation:
I did a lesson on it and got it right
Write the expression 12^-2 in simplest form?
Answer:
12 to the power of -2 is 0.00694444444
Step-by-step explanation:
When ever doing a number to the power of a negative number, the result will always be a fraction of a number.
Or
Fraction:
1/12^2
which is
1 / 144
Percentage:
0.00694444444 * 100 = 0.694444444%
Hope this helps, have a good day :)
(brainliest would be appreciated?)
The simplest form of the given expression [tex]12^{-2}[/tex] is 1/144.
The given expression is,
[tex]12^{-2}[/tex]
Here we can see that 12 has inverse power of 2.
Simplify it using basic rules of exponents.
To do so, we need to understand that a negative exponent indicates that the base should be inverted.
In other words, [tex]12^{-2}[/tex] is the same as 1/12²
To simplify this further,
Evaluate 12², which is,
12² = 12 x 12
= 144
Therefore, 1/12² can be expressed as 1/144.
Hence,
In the simplest form, we can write [tex]12^{-2}[/tex] as 1/144.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
Shape 1 and shape 2 are plotted on a coordinate plane which statement about the shapes is true?
DA Shape 1 and shape 2 are not congruent.
B A translation will prove that shape 2 is congruent to shape 1.
C. A rotation and a translation will prove that shape 2 is congruent to shape 1
OD. A reflection a rotation, and a translation will prove that shape 2 is congruent to shape 1
Answer:
The answer is D. A reflection, a rotation and a translation will prove that shape 2 is congruent to shape 1.
Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline. Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline. Approximately how many gallons of gasoline are saved on a 300-mile trip if the car is driven at a rate of 45 miles per hour instead of at 70 miles per hour?
A) 2
B) 3
C) 12
D) 20
Answer:
B) 3
Step-by-step explanation:
Traveling at a rate of 70 miles per hour, a car travels 26 miles per gallon of gasoline.
In 300 miles journey the gallon of gasoline consumed will be
300/26= 11.54 gallons
Traveling at a rate of 45 miles per hour, the same car travels 36 miles per gallon of gasoline.
In 300 miles journey the gallon of gasoline consumed will be
300/36= 8.33 gallons
The amount of gasoline saved= 11.54-8.33
The amount of gasoline saved= 3.21
approximately 3 gallons of gasoline
Haley is at the store buying some supplies for an art project. She decides to buy some colored pencils for $3.95 and a drawing tablet. The total cost of the supplies before sales tax is $6.94. What is the cost of the drawing tablet? $2.99 $1.76 $10.89 $3.01
Its $2.99 because 6.94-3.95=2.99 so $2.99
Answer:
$2.99
Step-by-step explanation:
To find the value of the drawing tablet, we can use the known total cost and the cost of the pencils. Let's build an equation, where x represents the cost of the drawing tablet:
x + 3.95 = 6.94
Now let's solve the equation for x to find the cost of the tablet.
x + 3.95 = 6.94
x + 3.95 - 3.95 = 6.94 - 3.95
x = 2.99
So the cost of the drawing tablet is $2.99.
Cheers.
Help please, I would really appreciate it. :)
Answer:
9, 13, 17, 21
Step-by-step explanation:
If x=2,
y=1+4(2)
y=9
This goes on, like a pattern. If x increases by 1, y inreases by 4. So, if y=3, x=13. If x=4, y=17, and so on.
