Answer:
Step-by-step explanation:
80-35= 45
45/15=3 so three more rooms are $15 a room
Total rooms are 9. The original 6 plus the additional 3.
80≥35+15x
45≥15x
3=x
On a certain hot summer's day, 151 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $270.50 How many children and how many adults swam at the public pool that day?
Answer: 63 children and 88 adults swam at the public pool that day.
Step-by-step explanation:
Let x = Number of children
y= Number of adults
As per given , we have
x+y=151 (i)
1.50x+2y=270.50 (ii)
Multiply 2 on both sides of (i)
2x+2y = 302 (iii)
Eliminate (ii) from (iii)
0.5x=31.5
⇒ x = 63 [Divide both sides by 0.5]
Put value of x in (i) , we get
63+y= 151
⇒ y= 151-63 =88
Hence, 63 children and 88 adults swam at the public pool that day.
Solve the right triangle. Round decimal answers to the nearest tenth
Answer:
AB = 15
m∠A = 53.1°
m∠B = 36.9°
Step-by-step explanation:
From the picture attached,
By Applying Pythagoras theorem,
AB² = AC² + BC²
AB² = 9² + (12)²
AB² = 81 + 144
AB = √225
AB = 15
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{12}{9}[/tex]
= 1.3333
B = [tex]\text{tan}^{-1}(1.3333)[/tex]
= 53.13
≈ 53.1°
Since, m∠A + m∠B + m∠C = 180°
m∠A + 53.1° + 90° = 180°
m∠A = 180°- 143.1°
= 36.9°
Answer:
AB = 15
m∠A = 53.1°
m∠B = 36.9°
find the slope of the line
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The line goes up 2 units and right 3 units.
Answer:
the slope is 6/7
Step-by-step explanation:
What are the two radicals that surround /125
Answer:
[tex]+5\sqrt{5} and -5\sqrt{5}[/tex]
Step-by-step explanation:
The radicals are [tex]+5\sqrt{5} and -5\sqrt{5}[/tex]
as [tex]5\sqrt{5}* 5\sqrt{5} = 125[/tex]
also [tex]-5\sqrt{5} *-5\sqrt{5} = 125[/tex]
Find the sum of the first 8 terms of the following series, to the nearest integer.
36, 30, 25, ...
Answer:
The sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]Step-by-step explanation:
Given the sequence
[tex]36, 30, 25, ...[/tex]
A geometric sequence has a constant ratio and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
computing the common ratio
[tex]\frac{30}{36}=\frac{5}{6},\:\quad \frac{25}{30}=\frac{5}{6}[/tex]
[tex]r=\frac{5}{6}[/tex]
As the first element is
[tex]a_1=36[/tex]
so the nth term will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=36\left(\frac{5}{6}\right)^{n-1}[/tex]
Geometric sequence sum formula
[tex]a_1\frac{1-r^n}{1-r}[/tex]
Plugin the values to determine the sum of the first 8 terms
[tex]n=8,\:\spacea_1=36,\:\spacer=\frac{5}{6}[/tex]
[tex]=36\cdot \frac{1-\left(\frac{5}{6}\right)^8}{1-\frac{5}{6}}[/tex]
[tex]=\frac{\left(1-\left(\frac{5}{6}\right)^8\right)\cdot \:36}{1-\frac{5}{6}}[/tex]
[tex]=\frac{36\left(-\left(\frac{5}{6}\right)^8+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{36\left(-\frac{390625}{1679616}+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{\left(1-\frac{390625}{1679616}\right)\cdot \:36\cdot \:6}{1}[/tex]
[tex]=\frac{216\left(-\frac{390625}{1679616}+1\right)}{1}[/tex]
[tex]=\frac{216\cdot \frac{1288991}{1679616}}{1}[/tex]
[tex]=216\cdot \frac{1288991}{1679616}[/tex]
[tex]=\frac{1288991\cdot \:216}{1679616}[/tex]
[tex]=\frac{278422056}{1679616}[/tex]
[tex]=\frac{1288991}{7776}[/tex]
Therefore, the sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]how many solutions does 6 -3x = 12 - 6x have?
A. two solutions.
B. no solutions.
C. one solution.
D. infinitely many solutions.
Answer:
Step-by-step explanation:
6-3x=12-6x
Only one solution of x=2
When simplified, StartFraction tangent (40 degrees) minus tangent (10 degrees) Over 1 + (tangent (40 degrees) ) (tangent 10 degrees) ) EndFraction is equivalent to which expression?
Answer:
C. tan(30°)
Step-by-step explanation:
edge yuh yuhhhhh
The equivalent fraction is [tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex].
The given expression is tan 40°-tan 10°/1+tan 40°.tan 10°.
How do simplify the trigonometric expression?When simplifying trigonometric expressions, one approach is to change everything into sine or cosine.
Now, [tex]\frac{\frac{sin40\textdegree}{cos40\textdegree} -\frac{sin10\textdegree}{cos10\textdegree}}{1+\frac{sin40\textdegree}{cos40\textdegree} .\frac{sin10\textdegree}{cos10\textdegree} }[/tex]
=[tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex]
Therefore, the equivalent fraction is [tex]\frac{sin 40\textdegree. {cos10\textdegree} - {sin 10\textdegree}{cos40\textdegree}}{{cos 40\textdegree. {cos10\textdegree} + {sin 10\textdegree}{sin40\textdegree}}}[/tex].
To learn more about trigonometric expression visit:
https://brainly.com/question/14746686.
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Audrina goes to the mall with $50. She buys 3 shirts for $8.50 each, and 2 pairs of pants for $11 each. How much money does Audrina have left?
Answer:
2.5
Step-by-step explanation:
she has buys 3 shirts for 8.50 which = 25.5
then she buys 2 pair of pants for $22 because 2 x 11=22
so then 22 + 25.5 = 47.50
50.00- 47.50= 2.50
At a department store, the price of a freezer is marked up 15% to $450.50.
What was the price of the freezer BEFORE the mark up?
Answer:
The price was $391.30.
Step-by-step explanation:
We can answer this using algebra:-
Let the original price be $x, then:
x + 15% of x = 450
x + 0.15x = 450
1.15x = 450
x = 450/1.15
x = 391.304
Convert the following:
(a) 300 cm into metre
Answer:
3m
Step-by-step explanation:
1 meter equals 100 cmWe know that [tex]1meter=100centimeters[/tex] Now how many (100 cm)'s are in (300 cm)'s? There are 3 right?So if every 100 cm is also a meter and there are 3 of these (100cm)s then they are just the same as 3 meters[tex]100cm=1m\\300cm=(x)m[/tex] cross multiply[tex]100cm(x)m=300cm1m[/tex] divide both sides by 100cm[tex](x)m=3m[/tex]Answer:
Convert the following:
(a) 300 cm into metre
3 metres
Lionheart Ranch has bought a new herd of race horses. If there is one stable for every four horses, which equation shows the correct relationship between the number of stables (S) and the number of horses (H)?
Answer:
1S=4H
Step-by-step explanation
You play a game that involves spinning the money wheel shown. You spin the wheel twice. Find the probability that you get more than $500 on your first spin and then go bankrupt on your second spin. Round your answer to the nearest tenth.
Answer:
about 2.8%
Step-by-step explanation:
Point (x, y) lies on the perpendicular bisector of . What is the value of x?
Record your answer and fill in the bubbles on your answer document.
Answer:5
Step-by-step explanation:
HELP ASAP I HAVE TO GET IT DONE
Solve for x in the diagram below
Answer:
x = 35
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS Equality PropertiesGeometry
Definition of a Line: A line is 180°Step-by-step explanation:
Step 1: Set up equation
40° + (2x + 30)° + 40° = 180°
Step 2: Solve for x
Combine like terms: 2x + 110 = 180Subtract 110 on both sides: 2x = 70Divide 2 on both sides: x = 35Please help, I'm supposed to write an equation in slope-intercept form from the graph
Answer:
y = -1/2x + 1
~theLocoCoco
please help I'm actually crying! Find A and B if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3.
i have less sympathy for ur crying when you copy and paste this question and ask it again three times. why dont you just ask it once? everyone answers anyway
How do you write 462 in scientific notation?
x 10
Answer:
could you explain more?
Step-by-step explanation:
Pls give me the answer to this geometry problem smart people
Answer:
25
Step-by-step explanation:
Since it is a rhombus all the parallel lines are always divided by half at the intersection. Basically divide 50 by 2 because QN=50 and QS is half of that
marcys breakfast table has a square table top with an area of 36 square feet. what is the diagonal length of the table top
Answer:
√36 = 6
a^2 + b^2 = c^2
6^2 + 6^2 = c^2
36 + 36 = c^2
72 = c^2
√72 = c
2 36
2 18
2 9
3 3
6√2 = c
6√2 = (estimate rounded up, 8.49)
You bike 14 ଵ ସmiles from your house to a state park. You travel ଵ ଷof that distance in the woods. You bike along the bank of a stream for the last ଵ ଶof the woods. On how many miles of your trip do you bike along the bank of the stream?
Answer:
17 miles
Step-by-step explanation:
the area A (in square feet) of the rectangular shed is given by
6x^3+7x^2+11x+21. use polynomial long division to find an expression for the length (in feet) of the shed
This question is incomplete.
Complete Question
The area A (in square feet) of the rectangular shed is given by 6x³+7x²+11x+21.And one side of the rectangular is 2x+3. Use polynomial long division to find an expression for the length (in feet) of the shed.
Answer:
3x² - x +7
Step-by-step explanation:
Using the long division method:
We have :
Divisor : 6x³+7x²+11x+21
Dividend : 2x+3
Quotient : the length (in feet) of the shed = ???
Hence, we solve below
6x³+7x²+11x+21 ÷ 2x + 3
3x² -x + 7
______________________
2x+3 l 6x³+7x²+11x+21
6x³+9x²
__________
-2x²+11x
-2x²-3x
__________
14x+21
14x+21
_______
0
Therefore, an expression for the length (in feet) of the shed is 3x² - x +7
3. What is the decimal equivalent of each
rational number?
a. 9/11
b. 4/5
c. -17/5
d. 5/9
Answer:
a. 0.81818182
b. 0.8
c. -3.4
d. 0.55555556
Step-by-step explanation:
Are there any five-digit numbers which are reversed when multiplied by 8?
Estimate sixty-two percent of one hundred twenty-four.
estimate each quotient by rounding the dividend and the divisor to the largest place value
1. 2,756 divided by 532.
2. 22,528 divided by 98
3. 7,790 divided by 210
4. 17,658 divided by 360
5. 916 divided by 320
Answer:
5
230
3
0
3
Step-by-step explanation:
1)5.2 estimated is 5
2)229.9 estimated is 230
3)37.1 estimated is 3
4)0.0 estimated is 0
5)2.9 estimated is 3
There is a snowstorm in a certain town. In 1/2 hour, there was 7/8 inches of snow. It continues at the same rate for a total of 2 hours. Which statement is true about the amount of snow in the 2-hour period
Answer:
Since I don't know the statements, I'm gonna guess that if there is 7/8 snow in 1/2 hour then in 2 hours there is 3.5 inches of snow or 28/8 inches of snow in 2 hours.
Step-by-step explanation:
what is significant figures
Answer:
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
Step-by-step explanation:
An advertisement reads “All Books 28 Percent Off.” A best-selling novel is originally priced at $18.99. About how much money will Gio save if he buys the novel on sale?
Answer:
6dollars
Step-by-step explanation:
Answer:
the answer is B 6 dollars
Step-by-step explanation:
Qual é a soma das coordenadas do vértice de uma função do segundo grau definida por f(x) = 2x² + 10x + 12?
Answer:
???
Step-by-step explanation:
Use the distributive property to remove the
6(v+4)