The equation that represents this number sentence is 1/5n - 3 = 28
Translating word problemsLet the unknown number be "n". One-fifth of a number is expressed as 1/5n
Three less than one-fifth of a number is expressed as 1/5n - 3
Finally, if three less than one-fifth of a number is equal to 28, then the final expression will be 1/5n - 3 = 28
The equation that represents this number sentence is 1/5n - 3 = 28
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There are boys and girls in a class in the ratio 1: 12 there are 77 more girls than boys. how many boys are there?
Let's set up some variables:
b: # of boysg: # of girlsLet's set up some equations based on the informative given:
boys to girls ratio ⇒ 1: 12(Mathematical form) g = 12b
77 more girls than boys(Mathematical form) g = b + 77
Let's put the equation together:
g = 12b -- equation 1
g = b + 77 -- equation 2
(equation 2)'s value of g into (equation 1)
12b = b + 77
11b = 77
b = 7
There are 7 boys.
Answer: 7 boys
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The graphs of f(x) and g(x) are shown below: graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 7, negative 2. If f(x) = (x + 7)2, which of the following is g(x) based on the translation? (5 points) a g(x) = (x + 9)2 b g(x) = (x + 5)2 c g(x) = (x + 7)2 + 2 d g(x) = (x + 7)2 − 2
The equation of the function is g(x)=(x+7)² -2 , Option D is the correct answer.
What is a Function ?A function is a mathematical statement that defines relation between two variables.
The f(x) = (x+7)²
The equation for g(x) is ?
graph of function f of x open upward and has its vertex at (-7,0).
Graph of function g of x opens upward and has its vertex at (-7,2).
g(x) is formed by the translation of the function f(x) such that it's vertex is (-7,-2)
Therefore the equation of the function is
g(x)=(x+7)² -2
Therefore , the translation is a shift of the function f(x) 2 units down
Option D is the correct answer.
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Simplify the expression when j = 5 and k = 3
*
1 point
Captionless Image
3
-9/5
41/3
6
Answer:
1 7
_
8
Step-by-step explanation:
5 x 3 = 15
5 + 3 = 8
=1 7
_
8
Solve the equation 4 sin x - cosec x =cot x for 0° < x < 360°.
For this question, I will be writing 'csc' instead of 'cosec'
[tex]4\sin x-\csc x=\cot x\\\\4\sin x-\frac{1}{\sin x}=\frac{\cos x}{\sin x}\\\\4\sin^{2} x-1=\cos x\\\\4(1-\cos^{2} x)-1=\cos x\\\\4-4\cos^{2} x-1-\cos x=0\\\\4\cos^{2} x+\cos x-3=0\\\\ (4\cos x-3)(\cos x+1)=0\\\\\cos x=\frac{3}{4}, 1\\\\\therefore \boxed{\cos^{-1} \left(\frac{3}{4} \right), 180^{\circ}, 360^{\circ}-\cos^{-1} \left(\frac{3}{4} \right)}[/tex]
HELP ASAP PLS ILL MARK YOU BRAINLIEST
Answer:
c is the answer.
f(x) = 3x+2
What is f(5)?
Answer:
the answer will be 17.
Step-by-step explanation:
if, f (x) = 3x + 2
f (5) = 3 × 5 + 2 = 17.
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Determine whether each set of ordered pairs shown below is from a geometric sequence or from an arithmetic sequence.
{(-3, 7.5) , (-2, 10) , (-1, 12.5)}
Write the equation of the graph for the set of ordered pairs.
{(1, 150) , (2, 112.5) , (3, 84.375)}
Write the equation of the graph for the set of ordered pairs.
Using sequences concepts, it is found that:
The set of ordered pairs {(-3, 7.5) , (-2, 10) , (-1, 12.5)} is an arithmetic sequence with equation a(n) = 15 + 2.5d.The set of ordered pairs {(1, 150) , (2, 112.5) , (3, 84.375)} is a geometric sequence with [tex]a_n = 150(0.75)^{n-1}[/tex].What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a(n) = a(0) + nd[/tex]
The sequence {(-3, 7.5) , (-2, 10) , (-1, 12.5)} continues with points (0, 15), (1, 17.5), and so on, hence the first term and the common ratio are given, respectively, by:
a(0) = 15, d = 2.5.
Hence the equation is:
a(n) = 15 + 2.5n.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
For the sequence {(1, 150) , (2, 112.5) , (3, 84.375)}, the first term and the common ratio are given, respectively, by:
[tex]a_1 = 150, q = \frac{112.5}{150} = \frac{84.375}{112.5} = 0.75[/tex]
Hence the equation is given by:
[tex]a_n = 150(0.75)^{n-1}[/tex]
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PLEASE HELP (PRE-ALGEBRA) MULTIPLE CHOICE! WILL GIVE BRAINLEIST! (photo attached!)
If the triangle on the grid below is translated by using the rule (x,y) → (x−2.y+2), what will be the coordinates of A'?
(4,0)
(0,4)
(0,0)
(-2.2)
Answer:
(-4, 0)
Step-by-step explanation:
x-2 means ur gonna take coordinate A and move it back 2 places along the x axis, (-4,-2) and then y+2 means ur gonna go up to places alomg the y axis which brings coordinate A' to (-4,0)
Answer:
A'(-4, 0)
Step-by-step explanation:
(x, y) → (x - 2, y + 2)
A(-2,-2 )→ A'(-2-2,-2+2)
= A'(-4,0)
Can you help find m<1
Answer:
69 degrees
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
<1 = 39+ 30
<1 = 69
Pls help 25 points!!
diane started a hike with 24 ounces of water in her backpack. what fraction of a gallon of water did she start the hike with? show your work.
Your question was incomplete. Please check below the full content.
There are 8 ounces in 1 cup and 16 cups in 1 gallon.
(a) Diane brought 4.5 gallons of water to a campout. How many ounces of water did she bring? Show your work.
(b) Diane started a hike with 24 ounces of water in her backpack. What fraction of a gallon of water did she start the hike with? Show your work.
a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
The cost price per ounce is the amount of money needed to buy one ounce of goods.To find cost price per ounce, divide the total of cost of the goods by total number of goods.Given that there are 8 ounces in 1 cup and 16 cups in 1 gallon.
a) Amount of water diana brought for campout = 4.5 gallons Ounce of water she brought = 4.5×16×8
= 576ounces
b) Diane started a hike with 24 ounces of water in her backpack.
The fraction of gallons in 24 ounces is calculated as follows:
The fraction of gallons in 24 ounces = 24 / (8×16)
= 3/16
Hence, a) 576 ounces of water Diane brought.
b) 3/16 of a gallon of water did she start the hike with.
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To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.
Is Shayla applying the vertical line test correctly?
No, because the y-axis is a horizontal line.
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0.
Yes, because the y-axis represents all vertical lines of the x-values.
Answer: Choice B
No, because using the y-axis tests only whether x = 0 is mapped to multiple values.
===================================================
Further Explanation:
Shayla stating that the y axis being used to conduct a vertical line test is part of the process. But she needs to move the vertical line around and not have it fixed in place.
If it is possible to have a vertical line (on the y axis or not) pass through more than one point on the curve, then we don't have a function. It is said the curve fails the vertical line test.
Otherwise, the graph passes the vertical line test and we have a function.
Menna is traveling in a country that measures its temperature in degrees Celsius. If the high temperature for tomorrow will be 25
∘
C, what is the equivalent temperature in
∘
F?
a. 102.6∘
F
b. 57∘
F
c. 77∘
F
d. 45.9∘
F
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Temp = 77° F[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f = \bigg (c \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[ convert 25° C to °F ]
[tex]\qquad \tt \rightarrow \: \bigg (25 \sdot \cfrac{9}{5} \bigg) + 32[/tex]
[tex]\qquad \tt \rightarrow \: (5 \sdot9) + 32[/tex]
[tex]\qquad \tt \rightarrow \: 45 + 32[/tex]
[tex]\qquad \tt \rightarrow \: 77 \degree \: \: f[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
77
Step-by-step explanation:
took the quiz
Ben, Tara and Liam are playing hide and seek. They start playing at quarter past 11. They play for 45 minutes, before stopping for a drink and a cookie. They continued to play for 45 minutes and head inside at 10 minutes past 1.
How long did they stop for a drink and a cookie. Explain your reasoning.
Answer:
25 minutes
Step-by-step explanation:
they started at a quarter past 11, which is 11:15
they then played for 45 minutes, which would be until 12:00
you also know that they stopped playing at 10 minutes past 1, at 1:10.
before 1:10, they had been playing for 45 minutes, which means they started playing for the second time at 12:25.
all that's left is the time between 12:00 and 12:25, which is 25 minutes, so they spent 25 minutes stopping for a drink and a cookie.
Using the basic identities, find the value of cosΘ if cotΘ = -12/5.
Step-by-step explanation:
please mark me as brainlest
Given that x is an even number, express, in terms of x, the product of the next two odd numbers.
Answer:
Odd is the answer.
Step-by-step explanation:
An even number can be written in the form 2x, where x is an integer.
An odd number can be written in the form 2x + 1, where x is an integer.
So two odd numbers can be represented by 2a +1 and 2b +1, the product would be:
(2a + 1)(2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2(2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.
So (2a + 1)(2b + 1) = 2(2ab + a + b ) + 1 = 2x +1 which is odd.
Someone please help with this !!!
Answer:
[tex]\dfrac 5{13}[/tex]
Step-by-step explanation:
[tex]\sin \theta =\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{5}{\sqrt{5^2 +12^2}} = \dfrac 5{\sqrt{169}} = \dfrac 5{13}[/tex]
Can someone help me please?
Answer:
B. <TSN and <ISW
C. <KSW and <NST
Answer:
D. ∠ISN and ∠TSW
Step-by-step explanation:
The meaning of vertical angles is each of the pairs of opposite angles made by two intersecting lines.
The angles ∠ISN and ∠TSW are made by two intersecting lines. This means that these angles are vertical angles.
Hope this helps!
If not, I am sorry.
The members of a golf team contributed a total of $14.30 for a party to be held after their practice. Each member contributed the same amount of money in dimes only. How many members are in the team and how much money did everyone contribute? Give all possible answers. I NEED FULL ANSWER!!!!!!!!!!!!!!!!!!
Answer:
each teammate contributed 1.43 sorry but i do not know how many members they have because my head hurts
Two towns that are 32 km apart are 8 cm on a map. What is the scale of the map?
This question is urgent, I have grade 8 final exams tomorrow and I'm struggling with this type of question.
If two towns that are 32 km apart are 8 cm on a map. Then the scale factor will be 1 cm = 4 km.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
Two towns that are 32 km apart are 8 cm on a map.
Then the scale factor will be
8 cm = 32 km
1 cm = 4 km
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(6, -5) reflected aross the y axis
Answer:
Then the new point is (-6,-5)
Step-by-step explanation:
f(x)= x - 1. Find the inverse of f(x).
O A. f¹(x) = x
OB. f¹(x) = x + 1
O c. f¹(x) = x − 1
-
O D. f¹(x)=1-x
help please asap
Step-by-step explanation:
The right answer is d because inverse means power in minus
A company makes 130 bags.
28 of the bags have buttons but no zips.
33 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?
Please answer in fraction form
Answer:
33 bags or 33/110 (which can be expressed as about 30%)
Step-by-step explanation:
BUTTONS ZIPS
28 Y N
33 N Y
49 N N
The only bags with zips is the second group of 33 bags. There are 110 bags in total, so the fraction would be (33/110)
Susan makes purple paint by mixing red and blue paint in the ratio 2:3
She has 12ml of red and 15ml of blue
What is the maximum amount of purple she can make?
Solve x+ 2y = -2 I’m really confused
Answer:
y=−1/2x−1
Step-by-step explanation:
I put it in slope intercept form as I assume that is what the question is asking.
1. A comfortable ambient temperature is called room temperature. Approximately,
how hot or cold is it?
A. 20 OC B. 20 OF C. 40 OC D. 40 OF
2. Convert: 5da = _______hr
A. 300 B. 240 C. 120 D. 60
3. Pasig river can discharge a maximum of 56 m3 per second of water. How many
liters per second can it discaharge?
A. 56 B. 560 C. 5 600 D. 56 000
4. A snail moves at a constant rate of 25 cm per minute. At this rate, how many
hours will it take the snail to crawl 75 m?
A. 3 B. 4 C. 5 D. 6
5. The human body can normally endure a temperature of 105 0F but for a short
period of time only, otherwise, there will be permanent damage to the brain and
vital organs. What is the equivalent temperature in 0C?
A. 37 B. 37.5 C. 40.56 D. 45.56
Answer:
Using the simple mathematical relations and formulas we get the following correct answers.
1. Option A
2. Option C
3. Option D
4. Option C
5. Option D
Step-by-step explanation:
1. The approximate room temperature is 20°C. Option A is correct.
2. 1 day has 24 hrs. 5 days will have 5×24 = 120 hrs. Option C is correct.
3. The discharge is 56m³/sec. 1m³ has 1000L. So the discharge is 56000L/sec. Option D is correct.
4. The speed is 25cm/min or (25×0.01×60)m/hrs. = 15m/hrs. For 75m the snail would take 75/15 = 5hrs. Option C is correct.
5. The relation between °C and °F is (F-32)/1.8. The equivalent temperature is (105-32)/1.8 = 40.56°C. Option D is correct.
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Question 11 of 20
What is the solution to the equation below? (Round your answer to two
decimal places.)
log₂ x = 5.6
Step-by-step explanation:
log2(x) = 5.6
so,
x = 2^5.6 ≈ 48.50293013... ≈ 48.50
What is the circumference of the circle shown below? (Round your answer to the nearest tenth.) A. 33.0 B. 66.0 C. 346.4 D. 206.2
Answer:
B. 66.0
Step-by-step explanation:
The formula for circumference is 2*π*r where r is the radius. MS and MR are both radii, so we can plug in 10.5 to the formula to get 2* π*10.5, which would be about 65.97, which rounds to 66.0. Hope this helps!
Plss help get brainiest if right!!
i have 25 coins. some of them are dimes, and some of them are
quarters. in total, i have $5.20. how many dimes and how many
quarters do i have?
Answer:
18 quarters7 dimesStep-by-step explanation:
The given relations can be used to write two equations describing the coins. One equation can express the total number of coins; the other, their total value.
__
setupLet d and q represent the numbers of dimes and quarters, respectively. The the total number of coins is ...
d + q = 25
and their total value is ...
0.10d +0.25q = 5.20
solutionUsing the first equation to write an expression for d, we can substitute that into the second equation.
d = 25 -q
0.10(25 -q) +0.25q = 5.20
0.15q = 2.70 . . . . . . . . . collect terms, subtract 2.50
q = 18 . . . . . . . . . . . divide by 0.15
d = 25 -q = 7
You have 18 quarters and 7 dimes.
_____
Additional comment
It is generally convenient to solve for the number of the higher-value coin. That way, the numbers in the equations stay positive, tending to reduce errors.
factorise:y(x+z)+z(x+y)+y^2+z^2
Answer: (x+z+y)(y+z)
Step-by-step explanation:
y(x+z)+z(x+y)+y^2+z^2
Factor out y and z from the expression
= y(x+z+y)+z(x+y+z)
Factor out x + z + y from the expression
= (x+z+y)(y+z)
Find the gradient of the line segment joining of
(1, 1) and (3, 5)
Answer:
2
Step-by-step explanation:
[tex]\text{First I'd recommend using this little equation:}\\\text{m}=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the values::}\\\text{m}=\dfrac{5-1}{3-1} \\\text{m}=\dfrac{4}{3}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{The gradient is:: }\dfrac{4}{3}[/tex]