Answers
Answer:
(- 5, 0 ), (7, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 108 ), thus
y = a(x - 1)² - 108
To find a substitute (0, - 105 ) into the equation
- 105 = a(- 1)² - 108 ( add 108 to both sides )
3 = a
y = 3(x - 1)² - 108 ← equation in vertex form
To find the x- intercepts, let y = 0, that is
3(x - 1)² - 108 = 0 ( add 108 to both sides )
3(x - 1)² = 108 ( divide both sides by 3 )
(x - 1)² = 36 ( take the square root of both sides )
x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )
x = 1 ± 6, so
x = 1 - 6 = - 5
x = 1 + 6 = 7
x- intercepts are (- 5, 0), (7, 0)
Related Questions
Can someone please help me I don’t understand how to do it
10) A rectangular patio measures 3x+4 meters by
2x-1 metres. If the perimeter of the patio measures 96
meters. Find the area of the patio.
Answers
This problem requires multiple steps, so please read through the whole answer to get a good understanding on how to solve this problem
Step 1: Create an equation for the perimeter respect to x
The equation for the perimeter p is:
[tex]p=2w+2l[/tex] where w is the width and l is the length
The length is 3x+4 and the width is 2x-1, so substitute these values into the equation:
[tex]p=2(3x+4)+2(2x-1)[/tex]
[tex]=6x+8+4x-2[/tex]
[tex]=10x+6[/tex]
This is the equation for the perimeter
Step 2: Solve for x since we are given the perimeter
We are given that the perimeter is 96, thus we can create the equation:
[tex]10x+6=96[/tex]
Subtract 6 from both sides
[tex]10x=90[/tex]
Divide both sides by 10
[tex]x=9[/tex]
We have now found the value of x
Step 3: Find the length and width now that we know x
Plug the value of x into the expressions for the length and the width that we are given
[tex]\text{Length}=3x+4=3(9)+4=31[/tex]
[tex]\text{Width}=2x-1=2(9)-1=17[/tex]
Step 4: Solve for the area now that we know the dimensions
This is probably the easiest step. Multiply the length and width to find the area:
[tex]31 \times 17=527[/tex]
The area of the patio is 527.
I've double- and triple-checked that this is the correct answer, so do not worry about any errors.
Let me know if you need any clarifications, thanks!
(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
Answer:
Padoru Deserves a brainliest
Step-by-step explanation:
So i wrote this answer so she could have one please give them a brainliest
can someone help with number 1? i’ll give brainliest ;)
Answers
Answer:
Hey there!
She wants an 93, so we write the equation: [tex]\frac{87+96+98+90+92+x}{6}=93[/tex]
Multiply both sides by 6 to get: [tex]87+96+98+90+92+x=558\\[/tex]
Simplify: 463+x=558
Subtract 463 to get that x=95.
Thus, she must score a 95 to get a A as a final grade.
Hope this helps :)
Answer:
Sally must get 95% in her sixth test!
Step-by-step explanation:
To get an average of 93 over 6 tests, the total must be
6*93 = 558
Therefore the sixth test she must get
S = 6*93 - 87 -96 -98 -90 -92 = 95
Suppose the function ƒ(t) = et describes the growth of a colony of bacteria, where t is hours. Find the number of bacteria present at 5 hours. Question 11 options: A) 79.432 B) 8.155 C) 59.598 D) 148.413
Answers
Answer:
The number of bacteria present at 5 hours is 148.413
Step-by-step explanation:
Function: [tex]f(t)=e^t[/tex]
This function describes the growth of a colony of bacteria, where t is hours.
We are supposed to find the number of bacteria present at 5 hours.
So, Substitute t = 5
So, the number of bacteria present at 5 hours =[tex]e^5[/tex]
The number of bacteria present at 5 hours = 148.413
So, Option D is true
Hence the number of bacteria present at 5 hours is 148.413
Factor the trinomial and enter the factorization below. Write each factor as a
polynomial in descending order.
x^2+6x-27
Answers
Answer:
( x - 3 )( x + 9 )
Step-by-step explanation:
The first thing we want to do here is to break the expression into groups. This will help us factor out common terms, that will later be grouped - our resulting, factored expression.
x² + 6x - 27 - Break the expression into groups,
( x² - 3x ) + ( 9x - 27 ) - Factor out x from the expression " x² - 3x. " Respectively factor out 9 from the expression " 9x - 27. "
x( x - 3 ) + 9( x - 3 ) - Now this contains the shared expression " x - 3, " and hence can be broken down further through grouping.
Factored Expression: ( x - 3 )( x + 9 )
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
Answers
Answer:
Y=12x
If Y represents the Cost and X represents the number of books purchased.
WORD FORM:
Cost equals 12 times as many books that are purchased.
A sheep breeding farm counted a total of 40 sheep on their grounds. After one year, the number of sheep doubled. Then in the next year, the number of sheep doubled again. If this trend continues, which of the following options represents the number of sheep on the farm by the end of each year?
Answers
Answer:
Step-by-step explanation:
It is comes under geometric sequence;
40 , 80 , 160 ,320 , ........
First term = a = 40
Common ratio = r = 2
nth term = [tex]ar^{n-1}\\[/tex]
Number of sheep on the farm by the end of each year = [tex]40*(2)^{n-1}\\[/tex]
If the public debt in 2006 was $6,783,231,062,743.62 and the budget
for 2007 was in deficit by $595,821,633,586.70, what was the public
debt in 2007? (Include commas.)
Answers
Answer:
677,727,284,640,775 ?
for a certain sequence of numbers the sum of the first n numbers in the sequence is given by n^3 + 4n for all positive integers n. what is the tenth number in the sequence
Answers
Answer:
1040
Step-by-step explanation:
10^3+4(10)=
1000+40=
1040
Tenth number in the sequence is 1040.
What is sequence?A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. Sequences often have specific ways they relate and can be analyzed using products and sums to identify and work with sequences.
Given
Sequence is [tex]n^{3} +4n[/tex] for all positive integers n.
Tenth number in the sequence:
n(10) = [tex]10^{3} +4(10)[/tex]
Tenth number = 1040
Hence, Tenth number in the sequence is 1040.
Find out more information about sequence here
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Convert the following numbers of calories or
kilocalories into joules or kilojoules.
a. 7845 cal
b. 4.55 x 104 cal
C. 62.142 kcal
d. 43,024 cal
Answers
Answer:
32.823 kJ190.4 kJ260.00 kJ180.012 kJStep-by-step explanation:
The conversion factor for food energy or thermochemical calorimetry* is ...
1 calorie = 4.184 J
1000 calorie = 4.184 kJ
__
a. 7845 cal = 7845·4.184 J = 32,823 J = 32.823 kJ
b. 4.55·10^4 cal = 4.55·10^4·4.184 J = 1.904·10^5 J = 190.4 kJ
c. 62.142 kcal = 62.142·4.184 kJ = 260.00 kJ
d. 43,024 cal = 43,024·4.184 J = 180,012 J = 180.012 kJ
_____
* The thermochemical calorie is defined in terms of the heat capacity of water. An international calorie of 4.1868 J is defined in terms of energy, without respect to the heat capacity of water.
The slope is the rate of change for temperature. If the temperature increases (gets hotter) as the distance from the surface increases, then the slope is positive. If the temperature decreases (gets colder) as the distance from the surface increases, then the slope is negative. What is the slope of your equation?
Answers
Answer:
add pic
Step-by-step explanation:
Answer:
m=6.5
Step-by-step explanation:
thats what you type in
Please help me with this question! I will give the brainliest to the one with the right answer!!!
Answers
Answer:
x =4
Step-by-step explanation:
hope this is the correct answer
Answer: B
Step-by-step explanation: B: 5^2-3^2 = 25-9 = 16. the square root of 16 is 4, so x=4
1. The perimeter of a rectangle is 230 cm. If the length of the rectangle is 70 cm, find its breadth and area.
Answers
Answer:
Step-by-step explanation:
Feel pleasure to help u...
Answer:
Breadth: 45 cm.
Area: 3,150 cm^2.
Step-by-step explanation:
The perimeter is 230. Since the length of the rectangle is 70 cm, and 70 * 2 = 140, the sum of the two breadths will be 230 - 140 = 90. That means that the breadth is 90 / 2 = 45 cm.
If the breadth is 45, and the length is 70, then the area is 45 * 70 = 3,150 cm^2.
Hope this helps!
Here are the shopping times in minutes) of a sample of 19 shoppers at a local grocery store.
45, 22, 34, 30, 28, 27, 33, 35, 40, 26, 41, 29, 42, 44, 25, 46, 32, 38, 36
Draw the histogram for these data.
Frequency
Х
6
?
6-
5-
4
3
0
0
0
0
0
0-
22-26
37-41
42-46
27-31 32-36
Times (in minutes)
Answers
Answer:
22-26: frequency = 3
27-31: frequency = 4
32-36: frequency = 5
37-41: frequency = 3
42-46: frequency = 4
100,000 people are currently sick with disease. If that disease spreads at rate of 50% per week, how many weeks will it be until 1,000,000 people are infected?
Answers
Answer:
If you mean it speads at the amount of 100,000 it would be only 10 weeks before 1,000,000 people are effected
or If you mean 50% percent of 100,000 which is 50,000 it would take a total of 20 weeks before 1,000,000 people are infected
Hope this answered your question.
What is the quotient?
x-1/7x2-3x-9
Answers
=2x-10
HALPP The number of sets of two or more consecutive positive integers whose sum is 100 is ~~~~~~~ (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Answers
Answer:
E.5
Step-by-step explanation:
Answer:
E
Step-by-step explanation:
Luis and Darcy are required to write essays for their English class. The table shows the number of words they wrote for 10 randomly chosen essays. Complete the steps below to compare the number of words in Luis’s and Darcy's essays using the mean and the median. Luis Darcy 178 231 213 210 198 245 245 259 236 286 198 245 221 231 253 244 189 236 177 228 Part A What is the mean number of words in Luis’s essays?
Answers
Answer:
210.8
Step-by-step explanation:
Destiny and Guadalupe are shopping. Destiny buys 2 pairs of pants and 6 bracelets and pays $178.Guadalupe buys 3 pairs of pants and 2 bracelets and pays $155. Solve for the price of each item.
Answers
For the entirety of this problem, p will represent a pair of pants and b will represent a bracelet.
Step 1) Set up equations for Destiny and Guadalupe
Destiny: 178 = 2p + 6b
Guadalupe: 155 = 3p + 2b
I will be using substitution to solve this problem, but elimination can also be used.
Step 2) Solve Destiny's equation for p
178 = 2p + 6b
178 - 6b = 2p
89 - 3b = p
Step 3) Substitute the found value of p from Destiny's equation into Guadalupe's equation and solve for b
155 = 3(89 - 3b) + 2b
155 = 267 - 9b + 2b
155 = 267 - 7b
-7b = -112
b = 16
Step 4) Use the value of b found in step 3, plug that back into our equation from step 2 and solve for p
89 - 3(16) = p
89 - 48 = p
p = 41
one pair of pants = $16
one bracelet = $41
Hope this helps!! :)
EARTH SCIENCE The order of magnitude of the mass of Earth's
atmosphere is 1018 kilograms. The order of magnitude of the mass of
Earth's oceans is 109 times greater. What is the order of magnitude of the
mass of Earth's oceans?
Answers
Answer:
1021
Step-by-step explanation:
1018×103=1018+3=1021
If f(x) = square root of x+3, what is the equation for f–1(x)? f–1(x) = x2 - 3 f–1(x) = x2 + 3 f–1(x) = (x - 3) 2 f–1(x) = (x + 3) 2
Answers
Answer:
[tex]\Large \boxed{\sf \ \ f^{-1}(x)=x^2-3 \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]\text{For }x+3\geq 0\\\\f(x)=\sqrt{x+3}\\\\x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)+3}\\\\\text{*** take the square ***}\\\\f^{-1}(x)+3=x^2\\\\\text{*** subtract 3 from both sides ***}\\\\\large \boxed{\sf \ \ f^{-1}(x)=x^2-3 \ \ }\\[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
HELP PLZZ!! Joe performed an experiment with a spinner. He spun the spinner and recorded the results in the frequency table. The spinner and the frequency table are given below. Find the experimental probability of the spinner landing on yellow or orange.
Answers
Answer:
7/13
Step-by-step explanation:
add all outcomes: 8 + 6 + 5 + 7 = 26
landing yellow or orange: 8 + 6 = 14
14/26 simplified 7/13
The Experimental probability of the spinner landing on yellow or orange is 7/13.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Yellow= 8
Orange = 6
Red= 5
Blue = 7
Total = 8+6+5+7= 26
So, the Experimental probability of the spinner landing on yellow or orange.
= 8/26 + 6/16
= 14/16
= 7/13
Learn more about Probability here:
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find the sum of even numbers between 1001 and 10,000 (Arithmetic progressions) DO STEP BY STEP PLEASE
Answers
Step-by-step explanation:
arithmetic progression
even numbers between 1001 and 10000
1002,1004,.......9998
Tn=a+(n-1)d
Tn = 9998 last term in the progression of even numbers
a = 1002 first term
d = 2 distance
9998=1002+(n-1)(2)
8996=2n-2
8998=2n
n = 4499 the number of terms
sum = n/2 (a+Tn) = 4499/2(1002+9998)
= (4499/2)(11000) = 24744500
Logic:
notice what happens when you add the first and last terms
1002+9998=11000
1004+9996=11000
.......
The figure shows two triangles on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4. What set of transformations is performed on triangle ABC to form triangle A'B'C'? A translation 5 units up, followed by a 270-degree counterclockwise rotation about the origin A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin
Answers
Answer:
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units to the right
Step-by-step explanation:
Answer:
translation down 5, rotation 180°
Step-by-step explanation:
help I need the answer
Answers
Answer:
18.9 ft²
Step-by-step explanation:
Surface area of this cylinder = area of the bottom and top circles + area of the curved surface.
Area of the two circles = 2πr² , where r is the radius.
Area of the curved surface = 2πrh , where r is the radius and h is the height.
Radius = [tex]\frac{1}{2}[/tex] × diameter
Area of the two circles = 2 × π × ([tex]\frac{2}{2}[/tex])² = 6.3 ft² (answer rounded up to nearest tenth)
Area of the curved surface = π × diameter × h = π × 2ft × 2ft = 12.6 ft² (answer rounded up to nearest tenth)
The surface area of the cylinder = 6.3 ft² + 12.6 ft² = 18.9 ft²
Answer:
18.85 to be exact
Step-by-step explanation:
pls mark brainliest
please help- my final is timed! xx Identify the graph of the triangle with vertices P(1,4), Q(1,1), R(3,1). Then identify the image that represents ΔPQR rotated 90° counterclockwise around vertex Q and the resulting image reflected across the x-axis.
Answers
Answer:
Since it is a negative degree it’s a counter clockwise meaning the fourth picture or D with the vertexs being p’(-2,-1),q’(1,-1),r’(1,-3)
Step-by-step explanation:
can somewon help me plzzzzz if u get it right i will mark brainlest
Answers
Answer: 4
Step-by-step explanation:
Because the equation says at least 45, we know the sign is [tex]\leq[/tex]. Because she has already run 6 rounds, the equation must have + 6.
Hope it helps <3
Can some help please with this MATH! Thanks
Answers
Answer:
19.6 ft
Step-by-step explanation:
4²+x²=20²
16+x²=400
384 = x²
x = 19.6 ft
Answer:
19.6 feet
Step-by-step explanation:
We know that
The hypotenuse is 20 feet, and the bottom leg is 4 feet.
We also know that Pythagorean theorem is used when there is one missing side to a triangle.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
Substitute in a for 4 and c for 20. The hypotenuse is always the variable c.
4^2 + b^2 = 20^2
16 + b^2 = 400
b^2=384
[tex]\sqrt{384}[/tex] = 19.6
Which expression is equivalent to ...
Answers
Answer:
[tex] \sqrt{6} [/tex]Step-by-step explanation:
[tex]3 \sqrt{54} - 4 \sqrt{24} [/tex]
Simplify the radical expression
[tex]3 \sqrt{2 \times 3 \times 3 \times 3} - 4 \sqrt{2 \times 2 \times 2 \times 3} [/tex]
[tex]3 \times 3 \sqrt{2 \times 3} - 4 \times 2 \sqrt{2 \times 3} [/tex]
[tex]9 \sqrt{6} - 8 \sqrt{6} [/tex]
collect the like terms
[tex]9 - 8 \sqrt{6} [/tex]
[tex]1 \sqrt{6} [/tex]
[tex] \sqrt{6} [/tex]
Hope this helps...
good luck on your assignment..
The pair of points is on the graph of an inverse variation. Find the missing value.
(2, 8) and (x, 3)
Answers
Hi
An inverse variation is of the form : f(x) = k/x where k is a number and x the variable.
In a inverse variation , the product of x*y is for all point always the same which is K
so 2*8 = 16 so K = 16 and f(x) = 16/x
if x = 3 then f(x) = 3 so : 16/x = 3 ; 3x = 16 ; x ⇒ 16/3
I have no clue. Somebody help plz!
Answers
Answer:
arithmetic, finite
Step-by-step explanation:
Each term is 1 more than the previous term, so there is a common difference of 1. That means the series is arithmetic.
The entire series consists of the 10 terms shown, so the series is finite.
_____
If each term were multiplied by some number to get the next, then it would be a geometric series. If it went on forever, it would be an infinite series.