+
Carla babysits and tutors to make extra money. She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week. She wants to go on a trip with her friend and needs to
make $95 dollars this week to cover the cost of the trip. Write a system of inequalities to represent this
situation.
The system of inequalities to represent this situation will be x + y ≤ 15 and 5x + 10y ≤ 95.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Carla babysits and tutors to make extra money.
She babysits for $5 an hour and tutors for $10 an hour.
She can only work at most 15 hours a week.
Likewise, she wants to go on a trip with her friend and needs to make 95 dollars this week to cover the cost of the trip.
Then the system of inequalities to represent this situation will be
Let x be the number of babysits hours and y be the number of tutor's hours.
x + y ≤ 15
5x + 10y ≤ 95
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
When f(a) = 227 + 32 - 3, evaluate f( - 1)
helpp
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]
[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]
[tex]f( - 1) = 2 - 3 - 3[/tex]
[tex]f( - 1) = - 4[/tex]
what is 1,000,000,000 divided by -1,000
-1000000 that is the answer
hope this helps!
What is the slope of the linear relationship shown in this table of values?
Answer:
B
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table
m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2
Select the correct answer.
Consider function f.
f(x) = 2x²
What is the value of (ƒ•ƒ)(x)₂
O A.
8x4
OB. 16x4
OC. 4x4
4x2
D.
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} [/tex]
[tex] \: [/tex]
[tex] = (f \circ f)(x)[/tex]
[tex] = f(f(x))[/tex]
[tex] = 2 {x}^{2} [/tex]
[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]
[tex] = 2(4 {x}^{4} )[/tex]
[tex] = 2.4 {x}^{4} [/tex]
[tex] = 8 {x}^{4} [/tex]
The answer is A.
Determine the period.
The period of the graphed function is T = 8.
How to get the period?For a sinusoidal function, the period is the horizontal distance between two consecutive peaks.
Here we can see the first peak at x = 1, and the second peak is at x = 9.
The horizontal distance is: 9 - 1= 8.
Then we conclude that the period of the function is T = 8.
If you want to learn more about period.
https://brainly.com/question/9565966
#SPJ1
Answer:
^ their right :)
Step-by-step explanation:
Its right on Acellus
have a great day!
Write and solve a proportion to complete the statement. Round to the nearest hundreth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
The conversion of the following units are done below.
6 km = 3.72 miles2.5 L = 0.65 gallons90 lb = 40.5 kgWhat is conversion?Conversion means to convert the same thing into different units.
We know the following unit's conversion.
1 km = 0.62 miles
6 km = 3.72 miles
1 L = 0.26 gallons
2.5 L = 0.65 gallons
1 lb = 0.45 kg
90 lb = 40.5 kg
More about the conversion link is given below.
https://brainly.com/question/9414705
#SPJ1
give me the answer
Given below is a magic square. Place the numbers
70 – 21 25 24 , ,, 95 –133 95 38
in the appropriate squares so that sum in each row, column and
diagonal is equal
The appropriate numbers to fill in the magic squares are;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
How to use magic squares?
To solve this magic square, we will follow the procedures below;
Step 1; Convert all the numbers into lowest forms.Step 2; Find the sum of any column or row which is 34/19.Step 3; Put the numbers given in such positions that the sum of each row, column and diagonal is equal.Step 4; Write the numbers in their original form.When we follow those steps above, we will arrive at the following figures;
Row 2, Column 2 = 21/133
Row 2, Column 3 = 24/38
Row 3, Column 2 = 70/95
Row 3, Column 3 = 25/95
Read more about Magic Squares at; https://brainly.com/question/16160523
#SPJ1
(PLEASE HELP!) A rectangular photograph measures 24x19 cm. It is mounted on a card of size such that there is a 2 cm border all around. For the purposes of this question take the length of the photograph to be 24 cm.
If one of the borders must be 2 cm in width, determine the width of a possible length and width so that the inner and outer rectangles are similar.
Answer: The card is 28 cm by 23 cm
Check out the diagram below
Explanation:
I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.
For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?
The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:
[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]
More can be learned about vertical asymptotes at https://brainly.com/question/27949428
#SPJ1
80 pupils in a sports centre are surveyed. the pupils can only use the swimming pool and the gym. 32 pupils use the swimming pool. 43 pupils use the gym. 19 pupils use neither the swimming pool nor the gym. find the probability to select a pupil that uses the swimming pool but not the gym.
[tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
It is given that:
Total students are 80
32 pupils use the swimming pool
43 pupils use the gym
19 pupils use neither the swimming pool nor the gym
To know the pupils who use both add 32+43 = 75
75-61= 14 pupils use both
32-14 = 18 pupils use only the swimming pool
43-18= 29 pupils use only the gym
Hence, [tex]\frac{18}{80}[/tex] is the probability of pupil that uses the swimming pool but not the gym.
To know more about probability visit: https://brainly.com/question/13604758
#SPJ4
1. y = 5 x Reflected across the x-axis 2. y = 5 –x+ 5 Reflected across the y-axis 3. y = 5 –x + 5 Translated down by 5 units 4. y = 5 –x – 5 Translated up by 5 units 5. y = –5 –x Translated left 5 units 6. y = 5 –x – 5 Translated right by 5 units
The matchup are:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣWhat is Translation and reflection?Reflection is known to be the turning over an object across a line and it is one where we do not need to change its size or shape.
While Translation is said to be sliding a figure into another direction and it is one where we do not need to change its size, shape or make.
The Translation and reflection matchup are given:
1. Translated left 5 units - y = 5⁻ ˣ ⁻ ⁵ 2. Translated right by 5 units - y= 5⁻ ˣ ⁺ ⁵3. Translated up by 5 units - y = 5⁻ˣ + 54. Translated down by 5 units - y = 5⁻ ˣ -5 5. Reflected across the x-axis - y= - 5 ⁻ ˣ6. Reflected across the y-axis -y = 5ˣSee full question below
Match each function formula with the corresponding transformation of the parent function y = 5-^x Please help ASAP!!
1. y = 5x
Translated left 5 units
2. y = 5–x + 5
Translated right by 5 units
3. y = 5–x – 5
Translated up by 5 units
4. y = 5–x+ 5
Translated down by 5 units
5. y = –5–x
Reflected across the x-axis
6. y = 5–x – 5
Reflected across the y-axis
Learn more about transformation from
https://brainly.com/question/12038181
#SPJ1
An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the amount of time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histograms below display the lap times for both Stefano and Alex, runners in the 3,000-meter race.
2 histograms. A histogram titled Alex apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 35 to 36, 1; 36 to 37, 5; 37 to 38, 4; 38 to 39, 4; 39 to 40, 1. A histogram titled Stefano apostrophe s 3,000 meter race lap times has lap times (seconds) on the x-axis, and frequency on the y-axis. 32 to 33, 1; 34 to 35, 1; 36 to 37, 1; 37 to 38, 4; 38 to 39, 5; 39 to 40, 1; 40 to 41, 2.
Using the histograms, which of the following is a correct comparison?
Neither runner had a lap time between 35 and 36 seconds.
Alex’s lap times show less variability than Stefano’s lap times.
The median lap time for both runners is in the 38–39 interval.
Both runners’ highest number of lap times in the 37–38 interval.
The true statement based on the histogram is
There were no lap times between 35 and 36 seconds.
The correct option is (A).
What is Histogram?A histogram is a graphical representation that organizes a group of data points into user-specified ranges.
Given:
indoor running track is 200 meters in length.
Also, a 3,000-meter race, runners must complete 15 laps of the track.
As, there no data for interval 35-36.
So, there were no lap times between 35 and 36 seconds.
Hence, The interval from 37 to 38 seconds saw the most lap times.
Learn more about histogram here:
brainly.com/question/16819077
#SPJ1
Answer:
B. Alex's lap times show less variability than Stefano's lap times.
Step-by-step explanation:
A can't be right because Alex has a lap time between 35 and 36 seconds.
C can't be right because the median lap time for Alex isn't 38-39.
D can't be right because both runners have a higher frequency on lap times other than 37-38.
so it has to be B.
If u(x) = -2x²+3 and v(x)=
X'
what is the range of (uv)(x)?
The answer is option D which is the range will be ( -∞, ∞ ).
What is the range?After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).
Given function is
u(x) = -2x²+3 and v(x) = ( 1 / x ).
The product of the function will give uv(x).
uv(x) = (-2x²+3 ) x [tex]\dfrac{1}{x}[/tex]
uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]
When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.
Therefore the answer is option D which is the range will be ( -∞, ∞ ).
To know more about the range follow
https://brainly.com/question/2264373
#SPJ1
can someone please help and explain its due in a littleee
[tex]f(x) = {x}^{2} - 3x + 2 [/tex]
••••••••••••••••••••••••••••••••••••••••put x = (-1)
[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (z)
[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (x+1)
[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]
•••••••••••••••••••••••••••••••••put x = (√2 + 1 )
[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]
Can someone help me with this, it’s urgent. It’s geometry.
Answer:
10. Ray ED and Ray EF (two rays)
11. DE and EF (two line segments)
Step-by-step explanation:
hope this helped
Answer:
Ray ED and Ray EF
DE and EF
Step-by-step explanation:
I’m really stuck please can someone help
Answer:
Least, Median and Greatest height of boys are all higher then Least, Median and Greatest of girls height
Step-by-step explanation:
Least height of boys: 158cm > 150cm Least height of girls
Median height of boys: 168cm > 165cm Median height of girls
Greatest height of boys: 182cm > 170cm Greatest height of girls
5(b)
Joe has a bucket containing 1370cm³ of water measured to the nearest 10 cm³.
Joe Says
"If I tip my bucket of water in the cuboid container, it will never overflow"
Is Joe correct?
You must explain your answer
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.
We find the cube root of 1370 cm³.
[tex]\sqrt[3]{1370} \approx11.11[/tex]
Then the cuboid container should have a side of length greater than 11.11 cm.
Here the statement "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.
If the side length is greater than 11.11 cm then it will not overflow.
Otherwise, it will overflow.
Learn more about volume here-
brainly.com/question/1578538
#SPJ10
-40 represents the height of a subway 40 feet below ground level. 40 represents the height of a kite 40 feet above ground level what does the zero rpresent in this situation
Answer:
0 represents the ground level
can someone help me?
Answer:
think of each T in the original equation as an empty box, like this:
P( ) = 2( )² + ( ) - 7
when it says p(some number), it means replace all Ts in the equation with that number.
P( 0 ) = 2( 0 )² + ( 0 ) - 7 = 0 + 0 - 7 = -7
do the same for the rest <:)
for the second part, it's the same concept: every T is replaced with what's inside the parentheses.
so P( -t ) = 2( -t )² + ( -t ) - 7 = 2t² - t - 7
and so on and so forth.
Simply the function f(x)=7(3Square root 54^x)
Answer:
54 = 2 × 3 × 3 × 3 = 2 × 3³
[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]
[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]
[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]
Initial value: x = 0
[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]
[tex] f(0) = 7(1) [/tex]
[tex] f(0) = 7 [/tex]
The initial value is 7.
The domain is all real numbers.
The range is all real numbers greater than zero.
can someone please help me
Answer:
-6, 14, -26, 10x -4, -8x + -2x - 6
Step-by-step explanation:
So F(x) is setting that the values before the lines are equal to x and should be applied to the problem. Dont forget PEMDAS with these tho, they'll try to trick u like that.
So for the first one, f(0) you plug 0 where the x's are.
1.) 8(0)^2 +2(0) -6
0 + 0 - 6 = -6
2.) 8(2) +2(2) - 6
16+ 4-6= 20 - 6= 14
3.) 8(-2) + 2(-2) -6
-16 + -4 -6 = -26
On the ones where they leave the x there, you just have to leave the x. But don't forget distribution tho.
4.) 8(x+1) +2(x+1) -6
8x +8 + 2x + 2 -6
10x +10 -6 = 10x -4
5.) 8(-x) + 2(-x) -6
-8x + -2x -6
Step-by-step explanation:
the given function is f(x) = 8x² + 2x -6
f(0) = 8(0)² + 2(0) -6 = -6
f(2) = 8 (2)² + 2 (2) - 6 = 30
f(-2) = 8 (-2)² + 2 (-2) - 6 = 22
f (x+1) = 8(x+1)² + 2 (x+1) -6
= 8(x² +2x +1 ) + 2x -4
8x² + 16x +8 +2x -4 = 8x² + 18x + 4
f(-x) = 8(-x)² + 2 (-x) - 6
= 8x² -2x -6
To eliminate the × terms and solve for y in the fewest steps by which constants should be equations be multiplied by before adding the equations together
To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
In this instance, you can do the following steps:
Start with the original equations:
Equation 1: 2x + 3y = 8
Equation 2: 3x - 2y = 4
To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:
Multiply Equation 1 by 2:
2(2x + 3y) = 2(8)
4x + 6y = 16
Multiply Equation 2 by 3:
3(3x - 2y) = 3(4)
9x - 6y = 12
Now, add the two modified equations together to eliminate the y terms:
(4x + 6y) + (9x - 6y) = 16 + 12
4x + 9x + 6y - 6y = 28
13x = 28
Finally, solve for x by dividing both sides of the equation by 13:
x = 28/13
Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
For more questions on: constants
https://brainly.com/question/27983400
#SPJ8
The probable question may be:
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.
BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O D 27° E 0 C Not drawn accurately BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O D 27 ° E 0 C Not drawn accurately
Answer:
Θ = 39°
Step-by-step explanation:
OA = OB ( radii of the circle ) , then
Δ AOB is isosceles with base angles congruent , that is
∠ ABO = ∠ BAO = 52°
the exterior angle of a triangle is equal to the 2 opposite interior angles.
∠ DOB is an exterior angle of the triangle , so
∠ DOB = ∠ ABO + ∠ BAO = 52° + 52° = 114°
the angle between a tangent and the radius at the point of contact is 90°, then
∠ OBC = ∠ ODE = 90°
the sum of the 4 interior angles of quadrilateral OBCD = 360°
∠ OBC + ∠ DOB + ∠ ODC + ∠ BCD = 360°
90° + 114° + (90 + 27)° + Θ = 360°
90° + 114° + 117° + Θ = 360°
321° + Θ = 360° ( subtract 321° from both sides )
Θ = 39°
Simplify the expression –3(x 3)2 – 3 3x. what is the simplified expression in standard form?
[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression
The given expression is:
[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]
This is the standard form of the given expression.
Learn more about Simplifying expression here https://brainly.com/question/723406
#SPJ4
Find the length of the missing side. Leave your answer in simplest radical form.
Answer:
[tex]\sqrt{69}[/tex]
Step-by-step explanation:
from the pythagorean theorem:
[tex]a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}[/tex]
A gas tank consists of a cylinder with a hemisphere on top. It is made of metal that is 1 cm
thick. It has an overall height of 90 cm and an external diameter of 20 cm. Calculate:
a the surface area of the tank
b the internal volume of the tank.
(Give answers correct to two significant figures)
The surface area of the cylinder is 5969.03 cm²
The internal volume is 23156.68 cm³
Given:
A gas tank consists of a cylinder with a hemisphere on top.
The thickness of the metal is 1 cm
The overall height is 90 cm
The external diameter is 20 cm
To Find
a) the surface area of the tank
We will add the area of the bottom circle of radius 10 cm (counting the 1 cm thickness in), the external surface area of cylinder of height (90 - 10) cm =80 cm and radius 10 cm, and the surface area of the hemisphere of radius 10 cm.
So, the surface area of the cylinder is
[tex]\pi\times(10)^2+2\times\pi\times 10\times 80+ 2\times \pi \times (10)^2[/tex]
= π×(100+1600+200)
= π×(1900)
= 5969.03 cm²
b) To find the internal volume of the tank we find the internal volume of the hemisphere with an internal radius (10-1)=9 cm,
the internal volume of the cylinder of radius 9 cm and height (80-1) cm
= [tex]\frac{4}{3}\times \pi \times 9^3[/tex]+[tex]\pi\times 9^2\times 79[/tex]
= 23156.68 cm³
Learn more about cylinders here-
brainly.com/question/16134180
#SPJ10
5. Use the law of Cosines to find each missing sides. Round to the nearest tenth
The measure of angle x will be 88 degrees. Then the correct option is C.
The complete question is attached below.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
2ab cos θ = a² + b² – c²
The triangle is shown below.
Then the value of the variable x will be
2 · 7 · 10 · cos x = 7² + 10² – 12²
140 · cos x = 49 + 100 – 144
cos x = (149 – 144) / 140
x = 87.95 ≈ 88°
Then the correct option is C.
Learn more about law of cosines here:
https://brainly.com/question/17289163
#SPJ1
Which of these r-values represents the strongest correlation?
A. -0.7
B. -0.8
C. -0.6
D. -0.9
Answer:
D
Step-by-step explanation: the larger abs(r value) is, (abs of r closest to 1) the better the correlation. Negative values indicate a negative correlation (negative slope)
What is the 25th term of this arithmetic sequence? 3,9,15,21,27
Answer:
75
Step-by-step explanation:
you need to divide numbers by 3
3×25=75
Answer:
147
Step-by-step explanation:
Arithmetic sequence:
a = first term = 3
d = common difference = second term - first term
= 9 - 3
d = 6
n = 25
[tex]\sf \boxed{\bf n^{th} \ term = a + (n-1) d}[/tex]
= 3 + (25 - 1)*6
= 3 + 24*6
= 3 + 144
= 147
