Using proportions, it is found that:
Unit price for the 11.3 ounce package: $0.33 per ounce.Unit price for the 29.3 ounce package: $0.31 per ounce.The 29.3 ounce package is the better deal.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The unit price is given by the cost divided by the number of ounces, and the better deal is given by the deal with the lowest unit price.
Hence, for the 11.3 ounce package:
u = 3.68/11.3 = $0.33 per ounce.
For the 29.3 ounce package:
u = 8.98/29.3 = $0.31 per ounce.
Due to the lower unit cost, the 29.3 ounce package is the better deal.
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Question 10(Multiple Choice Worth 1 points)
(01.04 LC)
Choose the missing step in the given solution to the inequality -x-3 < 13 + 3x.
-x-3<13 + 3x
-4x< 16
X>-4
O-4x-3> 13
O
2x-3 <13
0-4x-3 <13
2x-3> 13
The missing step in the given solution to the inequality -x-3 < 13 + 3x is - 4x - 3 < 13
InequalityIncorrect steps:
- x - 3 < 13 + 3x
-4x < 16
X > -4
Correct steps:
- x- 3 < 13 + 3x
-x - 3x - 3 < 13
- 4x - 3 < 13
- 4x < 13 + 3
- 4x < 16
x < 16/-4
x > -4
Therefore, the missing step in the given solution to the inequality -x-3 < 13 + 3x is - 4x - 3 < 13
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Classify the following triangle. Check all that apply.
11.3
45
A. Scalene
B. Right
C. Isosceles
D. Acute
E. Equilateral
F. Obtuse
Answer:
It's A and C
Step-by-step explanation:
the angles are 45, which is less than 90
HELP HELP HELP HELP
HELP HELP HELP HELP
HELP HELP HELP HELP
HELP HELP HELP HELP
Answer:
19 inches
Step-by-step explanation:
So the perimeter of a triangle is the sum of the three sides. So the perimeter is [tex]\sqrt{65} + \sqrt{35} + \sqrt{26}[/tex] which is approximately 19.077 inches but in this case the answer is 19 inches
3. (05.02 LC)
The lengths of two sides of a triangle are 14 inches and 4 inches. Which of the following dimensions is the third side of this triangle? (5 points)
10 inches
O11 inches
O 8 inches
O9 inches
Please help ill give whoever answers the best the brainliest answer :0
Answer: Exponential
Step-by-step explanation:
Because every time x increases by 1, y increases by a factor of 3.
6/2 = 3
18/6 = 3
54/18 = 3
162/54 = 3
P.S.: I ANSWERED ONE OF YOUR PROBLEMS WITH EXACTLY THE DATA IN THIS TABLE BY COINCIDENCE HAHA
For the upcoming parade, Lauren needed to make her school's triangular flag into a larger, similar triangular flag. Using the information given, determine which (if any) similarity postulate she used in making her school's new flag.
In order to make the new flag, Lauren decided to triple the sides of the old flag in order to get a new one.
What is the difference between these trianglesThe old triangle is the smaller one. We can see that this triangle has increased by a factor of 3 on all sides.
We have 4 x 3= 12
2 x 3 = 6
7 x 3 = 21
The calculated values above is what produced the new larger flag.
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Find the measure of the angle indicated in bold
Answer:
60 for both
Step-by-step explanation:
Since these angles are parallel, they are equal to each other :
6x = 5x + 10
Subtracting 5x from both sides gives us :
x = 10
Substituting this value back into both angles gives us
6x = 60
5x+10 = 60
solve the following system of equations for x : y=4-x2 x-y=2
a. x= 2,-4
b. x= 2,-3
c. x= -2,4
d. x= -3
Answer:
b. x=2, -3
Step-by-step explanation:
So I'm assuming the two equations are: [tex]y=4-x^2[/tex] and [tex]x-y=2[/tex]
Since it's asking to solve to solve for x. Then we need to solve for y in one of the equations, so that's it's defined using x, then substitute that into the other equation, that way the only variable left is going to be the x variable.
So since y is already solved for in the first equation. I'll plug that into the second equation.
Original equation:
[tex]x-y=2[/tex]
Substitute 4-x^2 in as y
[tex]x-(4-x^2)=2[/tex]
Distribute the negative sign
[tex]x-4+x^2=2[/tex]
Organize it so it's in order by degree
[tex]x^2+x-4=2[/tex]
Subtract 2 from both sides
[tex]x^2+x-6=0[/tex]
So now we have a quadratic equation and we're trying to find the zeroes. You can use the quadratic equation, but since the only options are integers, we can easily factor this equation. So you need to look for factors of -6, which add up to 1. I like to think about it as find two numbers with a difference of 1, and then figure out which is going to be positive and which is going to be negative after. So knowing this you can easily see 3 and 2 have a difference of 1. Since the 1 is positive, that means the 3 has to be positive and the 2 has to be negative
Use the factors: 3 and -2 to rewrite the equation:
[tex](x+3)(x-2)[/tex]
Now set each factor equal to 0
x+3 = 0
x=-3
x-2=0
x=2
this gives you the two solutions: -3, and 2
You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. You will have no access to any electricity, but you must be able to illuminate the entire grounds. You know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. Suppose the intensity is 90 when the distance is 5 m.
a. Write an equation to model the situation.
b. Solve for the constant of variation.
c. Write the equation to model the situation using the constant () of variation.
d. You have been given lanterns with 40 light intensity. Use your equation to solve for the distance from the lantern.
e. You need to illuminate 225 km. How many meters do you need to light?
f. How many lanterns will you need?
The equation to model the situation is [tex]\mathbf{y = \dfrac{k}{x^2}}[/tex]. The constant for the variation is 2250.
What is the intensity of light?The intensity of light from a lantern varies inversely to the square of the distance from the lantern.
From the given information:
Let y be the intensity of light, andx be the distance from the lanternThen:
[tex]\mathbf{y \alpha \dfrac{1}{x^2} }[/tex]
[tex]\mathbf{y = \dfrac{k}{x^2} }[/tex] here, k = constant.
2.
If y = 90 W/m² when the distance x = 5m
Then:
[tex]\mathbf{90 = \dfrac{k}{(5)^2}}[/tex]
k = 90 × 25
k = 2250
c.
The equation to model the situation by using the constant variation is:
[tex]\mathbf{y = \dfrac{2250}{x^2}}[/tex]
d.
If the light intensity y = 40, then x is determined as:
[tex]\mathbf{40 = \dfrac{2250}{x^2}}[/tex]
[tex]\mathbf{x = \sqrt{\dfrac{2250}{40}}}[/tex]
x = 7.5 m
e.
The light is needed in (225 × 1000)m = 225000 km of illumination.
f.
The lantern required for the new light estimation is:
y = 2250/225000
y = 0.01 intensity
Therefore, we can conclude that to get an intensity of 1 W/m², we need to put 100 lanterns.
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Help Pls! I need this fast!
Answer: 36
Step-by-step explanation:
[tex]\overline{AB} \cong \overline{BC}[/tex] (Triangle ABC is isosceles)
[tex]m\angle CAB=m\angle CBA=30^{\circ}[/tex] (base angles of an isosceles triangle are congruent)
[tex]\angle MCB=90^{\circ}[/tex] (In triangle CMB, angles in a triangle add to 180 degrees)
[tex]\angle ACM=30^{\circ}[/tex] (triangle sum theorem)
[tex]MB=24[/tex] (30-60-90 triangle CMB)
[tex]AB=12[/tex] (sides opposite congruent angles in a triangle are congruent)
[tex]AB=36[/tex] (segment addition postulate)
5-|n-1|=-2
| | stands for absolute value
Answer:
n = 8 or n = −6
Explanation:
First, isolate the absolute value:
5 − |n − 1| = −2
7 − |n − 1| = 0
7 = |n − 1|
Then, split this into two equations, since the result of the absolute value could be positive or negative:
7 = n − 1 7 = −(n − 1)
8 = n 7 = −n + 1
n = −6
Answer:
[tex]\{-6\} \cup \{8\}[/tex]
Step-by-step explanation:
[tex]5 - |n - 1| = -2; \\ -|n - 1| = -2 - 5 \\ -|n - 1| = -7 \\ |n - 1| = 7 \\ \left \ [ {{n - 1 = 7} \atop {n - 1 = -7}} \right. \Leftrightarrow \left \ [ {{n = 7 + 1} \atop {n = -7 + 1}} \right. \Leftrightarrow \left \ [ {{n = 8} \atop {n = -6}} \right.[/tex]
A school laboratory has two types of conical flask. Large conical flasks can hold 1.6 litres and small conical flasks can hold 600 ml. a) Mark has f large flasks and w small flasks, all full of hydrochloric acid. Write an expression for how many millilitres (ml) of acid he has. b) Bev has 2f large flasks and 2w small flasks, all full of hydrochloric acid. Write an expression for how many millilitres (ml) of acid she has.
Answer:
[tex](a)1600f+600w\\\\(b)1600\times2f+600\times2w[/tex]
At noon, Bradley began steadily increasing the
speed of his car by 2 miles per hour every minute. At 12:15 p.m., he realized he was going
15 miles per hour over the speed limit. If his speed at noon was 40 miles per hour, what was the speed limit at 12:15 p.m.?
Please show work step by step
Answer:
25.5 mph
Step-by-step explanation:
So Bradley's speed can be modeled by the equation y=2x+40 where y=speed, x=time in hours after noon, and b=initial speed
So 12:15 is 15 minutes after noon, which is also 0.25 or 1/4 of an hour after noon. This is the x-value. Plug this into the equation to get his speed at 12:15
y=2(0.25)+40
y=0.5+40
y=40.5
So his speed was 40.5 at the time and since he was going 15 miles over the speed limit, the speed limit is 15 less than his speed
40.5 - 15 = 25.5
Answer:
25.5 mph
Step-by-step explanation:
Given information:
Bradley increases the speed of his car by 2 miles per hour. 12.00 pm: Bradley's speed = 40 mph12.15 pm: Bradley is driving at 15 miles over the speed limit.Calculate Bradley's speed at 12.15 pm:
60 minutes = 1 hour
⇒ 15 minutes = 1/4 hour
⇒ speed at 12.15 pm = speed at 12.00pm + 1/4 of 2 mph
= 40 mph + 0.5 mph
= 40.5 mph
If he was 15 miles over the speed limit at 12.15 pm then:
⇒ speed limit = speed at 12.15pm - miles over the limit
= 40.5 mph - 15
= 25.5 mph
Therefore, the speed limit was 25.5 mph.
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
The slope of the perpendicular line passes through C in GeoGebra.
What is GeoGebra?GeoGebra is the software for the mathematical question for all levels of academics.
GeoGebra brings many mathematical problem solutions like geometry, algebra, spreadsheets, graphing, statistics, and calculus in one search engine.
Display the slope of and the slope of the perpendicular line passing through C.
Hence, the slope of the perpendicular line passes through C in GeoGebra.
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A snail moves at about 3 inches per minute. How many miles per day could a
snail travel if it moved without taking a break?
0.068 mi
0.818 mi
9.818 mi
132 mi
Answer:
A. 0.068
Step-by-step explanation:
First, 3 inches to miles. 3 inches in a mile is 0.00004735.
The snail moves 0.00004735 miles per minute.
Next, search how many minutes are there in a day. There is 1440 minutes in a day.
Multiply the 1440 and 0.00004735.
1440*0.00004735=0.068
The snail can move 0.068 miles per day if it doesn't take a break.
Hope this helps!
If not, I am sorry.
Please help me!!
Find the value of x:
Answer:
x = 34 degrees
Step-by-step explanation:
Corresponding Angles Theorem: If 2 parallel lines are cut by a transversal, their corresponding angles are congruent.
Angle RNM = 78 degrees
Triangle RMN = 180 degrees
180 = 78 + 2x + x
102 = 3x
x = 34
Find x so that l || m. Show your work.
Hello,
Answer:
x = 13
Step-by-step explanation:
7x + 5 + 5x + 19 = 180
⇔ 12x + 24 = 180
⇔ 12x = 180 - 24
⇔ 12x = 156
⇔ x = 156/12
⇔ x = 13
Maribel leaves school at 3:10 to walk home. One day, she stopped at the store
n the way home and spent 20 minutes shopping. If she got home at the time
hown on the clock, how much time did she she spend walking?
Maribel leaves school at 3:10 to walk home, spent 20 minutes shopping and spent 30 minutes walking
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let us assume that Maribel reaches home at 4:00, hence:
Time spent walking = 4:00 - (3:10 + 20 minutes) = 4:00 - 3:30 = 30 minutes
Maribel leaves school at 3:10 to walk home, spent 20 minutes shopping and spent 30 minutes walking
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What are the x-intercepts for the graph below?
A. (6,0), (-3,0)
B. (-6,0), (-3,0)
C. (-6,0), (3, 0)
OD. (6,0), (3, 0)
Answer:
-6,0 & -3,0
Step-by-step explanation:
An american tourist changed us $1100 into barbados currency at the exchange rate us $1.00= bbd=$5.50. calculate the amount of bbd he received.
The amount of bbd received for the given currency exchange rate is 6050 bbd.
What is the currency exchange rate?The value of one country's currency in relation to the currencies of other countries or economic zones is known as the currency exchange rate.
The majority of currency exchange rates are free-floating and fluctuate according to market supply and demand.
There may be restrictions on some currency exchange rates since they are fixed to the value of other currencies.
According to the question,
Currency exchange rate: $1.00=5.50bbd
So, $1100=1100*5.50 bbd
=6050 bbd
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This is quadratic equations
Help asap!!
Answer:
x = - 3 ± [tex]\sqrt{2}[/tex]
Step-by-step explanation:
x² + 6x + 7 = 0 ( subtract 7 from both sides )
x² + 6x = - 7
using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = - 7 + 9
(x + 3)² = 2 ( take square root of both sides )
x + 3 = ± [tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± [tex]\sqrt{2}[/tex]
y varies directly with x. If y = -4 when x = -1, what is the constant of variation?
the constant variation, K= 4
Step-by-step explanation:
i have replace the constant variation by the letter K
First step is to write down the information
y directly proprotional to x
So, y= Kx
Replace the value given for x and y to find k
y= -4 and x = -1
Kx= y
K( -1) = -4
K = -4 ÷ -1
K= 4
Further answer
if you are asked the connecting equation between y and x just replace the value of K in the equation
y= Kx
y= 4x
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C of F = five-ninths (F minus 32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
the temperature of 76.1 degrees Celsius converted to degrees Fahrenheit
the amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius
the amount of time it takes a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit
The function is C(F) = (F-32) * 5/9
This means the function C, is using variable F to get the output.
C is Celsius, F is Fahrenheit, so the answer is "the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius"
Answer:
a
Step-by-step explanation:
Cindy works at Jurassic Park and has been tasked to design a container in the shape of a
rectangular prism for the incoming baby dinosaurs. The scaled model of the container has
dimensions 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model
by the same amount in order to produce a container with a volume of 84 times the volume of the
scale model. By what amount should Cindy increase each dimension of the scaled model?
The amount Cindy should increase for each dimension of the scaled model will be 12 meters.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.
Given that:-
The scaled model of the container has dimensions of 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model.The scale model will be solved as follows:-
Present volume = 2 x 4 x 6 = 48 cubic meters
Let the lengths be increased by x meters now the new volume will be:-
( 2 + x ) ( 4 + x ) ( 6 + x ) = 48 x 84
( x² + 6x + 8 ) ( 6 + x ) = 48 x 84
( x³ + 44x + 12x² - 3984 ) = 0
By solving the cubic equation we will get the value of x = 12 meters.
Therefore the amount Cindy should increase for each dimension of the scaled model will be 12 meters.
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Find the equation of the line shown
The equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.
What is the equation of a line passing through two given points in a 2-dimensional plane?Suppose the given points are (x_1, y_1) and (x_2, y_2), then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
The graph of the picture shows two clear points (4.5. 0) and (0, 9)
[tex](y - 0) = \dfrac{9 - 0}{0 - 4.5} (x -4.5)\\\\\\(y - 0) = \dfrac{9 }{- 4.5} (x -4.5)\\\\\\-4.5y = 9(x -4.5)\\\\-4.5y = 9x - 40.5\\\\y = -2x + 9[/tex]
Hence, the equation of line passing through points (4.5. 0) and (0, 9) is y = -2x + 9.
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Use π = 3
Calculate the area of a circle with
diameter
of 5cm
Answer:
18.75
Step-by-step explanation:
[tex]Area=\pi r^{2} \\Area=3(\frac{5}{2} )^{2} \\Area=18.75[/tex]
PLS HELP ME ILL MARK U BRAINLEST
Answer:
See below
Step-by-step explanation:
x^2 +2x -8 = (x-2)(x+4)
x^2 + 6x - 16 = (x + 8)(x-2) now you can cancel the ( x-2 ) to get
(x+4) / (x+ 8)
please help!!!!!!!!!!!!
Answer: $233
Step-by-step explanation:
- A flat fee is an amount that is charged or paid that doesn’t account for hourly use or work
- Then, you must pay by the hour for use
- So you would use the equation:
(22 • 9) + 35
- 22 is the maximum hours and 9 is the hourly rate
- 35 is your flat fee
- So, (22 • 9) + 35 = $233
hope this helps :)
Answer:
$233
Step-by-step explanation:
We can make up a linear equation. We already know that it costs $35 to rent a small auger.
Every hour there is a extra fee of 9$.
So, 9 can be the slope, while 35 can be the x intercept.
y=9x+35
x=22; maximum hours
y=9(22)+35
y=198+35
y=$233
Here is a more simple way
multiply 22 hours with 9 dollars, =$198
then add the 35 dollars; 198+35=$233
Find the first five terms of the sequence described:
a sub 1 = 3
a sub n+1 = a sub n + 5
From the given recursive definition,
[tex]a_1 = 3[/tex]
[tex]a_2 = a_1 + 5 = 3 + 5 = 8[/tex]
[tex]a_3 = a_2 + 5 = 8 + 5 = 13[/tex]
[tex]a_4 = a_3 + 5 = 13 + 5 = 18[/tex]
[tex]a_5 = a_4 + 5 = 18 + 5 = 23[/tex]
Can someone help me with these geometry questions? I can’t seem to understand them. If u find the answers, can u explain it too? It’s urgent
Question 5
Vertical angles are congruent. Therefore, [tex]3y=\boxed{150}[/tex]. The sum of two supplementary angles equals [tex]\boxed{180^{\circ}}[/tex].
Therefore, [tex]6x+150=\boxed{180}[/tex]
Question 6
[tex]\angle b-14=90-\angle b\\\\2\angle b=104\\\\\angle b=\boxed{52^{\circ}}[/tex]
Question 7
[tex]\angle d+32=180-\angle d\\\\2\angle d=146\\\\\angle d=\boxed{73^{\circ}}[/tex]
Question 8
[tex]7x-80=3x\\\\-80=-4x\\\\x=20\\\\\implies \boxed{m\angle 1=m\angle 3=60^{\circ}}[/tex]