The attached graph represents the graph of the equation 3x + y = 10
How to determine the line graph?The given parameters are:
Budget: $10Smoothies: $3Candy bars: $1Represent the number of smoothies with x and the number of candy bears with y.
So, the equation is:
3x + 1y = 10
This gives
3x + y = 10
Next, we plot the graph of the above equation
See attachment for the graph of 3x + y = 10
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The line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
Sarah is going to the movies, and she has $10 to spend on snacks. Smoothies are $3 and candy bars are $1 each. She will be spending all of the $10.
Let's suppose the number of smoothies is x and the number of candy bars is y:
Then, we can frame a linear equation in one variable:
3x + y = 10
Drawing the above the line on the coordinate plane:
Thus, the line equation 3x + y = 10 represents the budget constraints and possible purchasing options that Sarah has with her $10, and the graph is shown in the picture.
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Which of the graphs below represents the equation 4x + y =7?
Answer:
Graph C
Step-by-step explanation:
Rearrange the terms so the equation is in slope-intercept form:
4x + y = 7
y = -4x + 7
The slope is -4, and the only graph that has a slope of -4 is graph C.
What is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}
The Range of the function is {y|y is a real number} , Option D is the correct answer
What is Range ?Range of a function is all the value a function can obtain.
From the figure it can be seen that the graph is moving slowly in either direction.
It extends from -∞ to +∞ ,
Therefore , {y|y is a real number} , Option D is the correct answer.
The complete question is
The graph shows a vertical translation of y = ³√x
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
The image of the translated function is attached.
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Find the slope of the line that goes through (2, 8) and (5, 13).
Answer:
1 (2/3) or 1.66666667
Step-by-step explanation:
The slope of a line is found by using the equation :
y2 - y 1 / x2 - x1
So all we have to do is plug in our values given.
To find which belongs with which variable (such as x2 or y1), we do the following:
We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.
(2, 8) will be x1 and y1.
(5, 13) will be x2 and y2
Plug in the values :
13 - 8 = 5
5 - 2 = 3
5 / 3 = 1 (2/3)
So, the slope of the line is 1.66666667 or 1 and (2/3)s
Hey can I have some help with this. Just the answer is fine
Step-by-step explanation:
4.500 mm³ → cm³
1 cm³ = 1.000 mm³
= 4.500 ÷ 1.000
= 4,5 cm³ IS THE ANSWER
What is the number of possible combinations of 7 objects taken 4 at a time?
OA. 5,040
OB. 840
OC. 210
OD. 35
The number of possible combinations of 7 objects taken 4 at a time is 35. Then the correct option is D.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
The number of possible combinations of 7 objects taken 4 at a time.
so, the number of the combination is given as
[tex]^7C_4 = \dfrac{7!}{4!(7-4)!} \\\\\\^7C_4 = \dfrac{7!}{4!(3)!} \\\\\\^7C_4 = \dfrac{7 \times 6\times 5\times 4!}{4!(3\times 2)} \\\\\\^7C_4 = 35[/tex]
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Answer:
D. 35
Hope this helps!
Step-by-step explanation:
Find the area of triangle DFG.
A. 5.3 square units
B. 34.3 square units
C. 420.0 square units
D. 424.2 square units
Answer:
34.3 square unit.
Step-by-step explanation:
[tex]calculate \: df \: using \: pythagoras \\ theorem \\ df {}^{2} = 8 {}^{2} + 6 {}^{2} \\ df {}^{2} = 64 + 36 \\ df {}^{2} = 100 \\ df = \sqrt{100} \\ df = 10 \\ calculating \: for \: the \: area \: of \: \\ angle \: \: dfg \\ using \: heros \: formular \\ \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{10 + 11 + 7}{2} = \frac{28}{2} = 14 \\ area = \sqrt{14(14 - 10)(14 - 11)14(14 - 7)} \\ area = \sqrt{14(4)(3)(7)} = \sqrt{14 \times 84} \\ area = \sqrt{1176} = 34.2928564 \\ to \: the \: nearest \: tenth \: = 34.3[/tex]
Here it is stated that, side DE = 8 units, side EF = 6 units, side FG = 7 units and side GD = 11 units. We have to find area of ∆DFG, here we will use heron's formula which is given by:
Area of ∆ = √[s(s – a) (s – b) (s – c)]
Here a, b, and c are sides of ∆. We have;
b = FG = 7 unitsc = GD = 11 unitsa = DF = ?s = semi - perimeter = ?So firstly lets calculate a i.e DF by using Pythagoras theorem on ∆DEF:
➸ DF² = 8² + 6²
➸ DF² = (8 × 8) + (6 × 6)
➸ DF² = 64 + 36
➸ DF² = 100
➸ DF = √(100)
➸ DF = √(10 × 10)
➸ DF = 10 units
Now, lets calculate s i.e semi - perimeter:
s = (a + b + c)/2s = (10 + 7 + 11)/2s = 28/2s = 14 unitsNow, using heron's formula on ∆DFG to calculate its area:
➸ Area(∆DFG) = √[14(14 – 10) (14 – 7) (14 – 11)]
➸ Area(∆DFG) = √[14(4) (7) (3)
➸ Area(∆DFG) = √(14 × 4 × 7 × 3)
We can write it as;
➸ Area(∆DFG) = √(2 × 2 × 2 × 7 × 7 × 3)
➸ Area(∆DFG) = 2 × 7√(2 × 3)
➸ Area(∆DFG) = 14√(6)
➸ Area(∆DFG) = 14 × 2.449
➸ Area(∆DFG) = 34.28
➸ Area(∆DFG) = 34.3 square units (approx)
Hence, area of ∆DFG is option B. 34.3 square units.PLEASE HURRY
Let p: A student plays basketball.
Let q: A student plays tennis.
How many students play both basketball and tennis?
Answer:
4
Step-by-step explanation:
4 is the intersecting point which states p intersect q giving both tennis and basketball players
Question 17 of 25
You need to solve a system of equations. You decide to use the elimination
method. Which of these is not allowed?
3x-2y=7
3x+4y=17
Equation 1
Equation 2
OA. Subtract equation 2 from equation 1.
OB. Subtract the left side of equation 2 from the left side of equation
1.
OC. Multiply equation 1 by 2. Then add the new equation to equation 2.
Answer:
The only methods allowed are
- "Subtract equation 2 from equation 1," and "Multiply equation 1 by 2. Then add the new equation to equation 2"
-
Step-by-step explanation:
Subtract Eq 2 from Eq 1:
3x-2y=7
-3x-4y=-17
-6y = -10
y = (5/3)
Use y =(5/3) to solve for x in both equations.
x=(31/9)
Subtract the left side of equation 2 from the left side of equation No, this is not a legal operation.
Multiply equation 1 by 2. Then add the new equation to equation 2 Yes, this works. Instead of solving for y first, this method solves for x, which can then be used to find y:
2(3x-2y=7)
6x-4y=14
3x+4y=17
9x = 31 (y is eliminated)
x = (31/9)
Now use this to find y in either equation:
3x-2y=7
3x-2(31/9)=7
y = (5/3)
please need help quick, trigonometry
Answer: C: 5
Step-by-step explanation:
Nick wants to save up enough money to go to Carowinds for the day with a group of his friends. He already has $50 saved up and plans to save $10 each week. Write an expression that represents the total amount Nick will have depending on the number of weeks (w) he saves for.
Answer:
a=10w +50
Step-by-step explanation:
a= amount
w= weeks
please vote brainliest
given f(x)=2x+2 and g(x) =-5x-3 find (f-g)(x)
Answer:
(f-g)(x) = 7x+5
Step-by-step explanation:
Given that,
f(x)=2x+2 and g(x) =-5x-3
To Find:
(f-g)(x)Solution:
[tex](f - g)(x)[/tex]
Re-write as:
[tex]f(x) - g(x)[/tex]Now substitute the values on the polynomial/function:
Simplify using this order:BPEMDAS
[tex]2x + 2 - ( - 5x - 3)[/tex][tex]2x + 2 + 5x + 3[/tex][tex]2x + 5x + 2 + 3[/tex][tex] \boxed{ ( f - g)(x) = 7x + 5}[/tex]Hence,(f-g)(x) = 7x+5.
Factor the expression below.
36x² - 49
A. (6x + 7)(6x - 7)
B. (4x-7)(9x - 7)
C. (4x+7) (9x-7)
D. (6x-7)(6x-7)
Answer:
A. (6x + 7)(6x - 7)
Step-by-step explanation:
use difference of squares, which says a^2 - b^2 =(a+b)(a-b)
take the square roots of the two numbers, 6x and 7, and use them as a and b
from a practice assignment:
solve the following differential equation given initial conditions
If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get
[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]
Integrate both sides:
[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]
Use the initial condition to solve for [tex]C[/tex] :
[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]
Then the particular solution to the initial value problem is
[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]
(A)
Pedro's dining room is 5 metres wide and 6 metres long. pedro wants to install a new wood floor. it will cost $2.18 per square metre. how much will pedro's new floor cost?
Answer:
65.4
Step-by-step explanation:
5 × 6 = 30 square meter
30 × 2.18 = 65.4
Does someone mind helping out with this ?
A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries. Choose a number between 80 and 96. This is the level of confidence you will use for this
The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.
The complete question is
A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.
Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?
With the confidence level you chose, construct that % confidence interval for the population proportion of voters that answered correctly that 4th graders in the U.S. are above average in overall education compared to other countries. What is the margin of error for this confidence interval?What is Margin of Error ?It is defined as the margin by which the values calculated will differ from the real values .
Let the chosen number is 95 %
95% Confidence Interval ,
[tex]\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\[/tex]
Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043
The margin of error is given by 0.4043-0.3329
= 0.0357
Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.
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There was a bag of counters. 45 were large! For every large counters 3/5 were small! The green was 300% than yellow, there were 12 small yellow counters. How many were large green counters?
Answer:
12 is the correct answer
what will be the exponent of ten in quotient
Answer: 8
Step-by-step explanation:
We know that:
[tex]\frac{10^{12}}{10^{4}}=10^{12-4}=10^{\boxed{8}}[/tex]
Find a rational number between -1/3 and 1/2
Answer:
1/6
Step-by-step explanation:
Rational numbers between two rational numbers:
First find the Least Common Denominator for 2 and 3Then find equivalent fractions with the LCD.LCD of 2 and 3 = 6
[tex]\sf \dfrac{-1}{3}=\dfrac{-1*2}{3*2}=\dfrac{-2}{6}\\\\\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}[/tex]
[tex]\sf Rational \ number \ between \ \dfrac{-2}{6} \ and \ \dfrac{3}{6} \ is \ \bf \dfrac{1}{6}[/tex]
please help guys how do i order fractions for least to greatest and greatest to least itll nean so much to me for my finals tmrw
Answer:
If the denominators are equal for all of the fractions, you can simply look at the numerator and order them. If the denominators aren't equal, you'll have to find the lcm (lowest common multiple), for example, if we have the fractions 3/6 and 1/4, we would find the lcm of 6 and 4, which is 12 and multiply the numerators accordingly. So the fractions would then become 6/12 and 3/12, this makes it easier for you to figure out their order from least to greatest.
Goodluck for your finals :)
Circle A has a diameter of 8 inches, a circumference of 25.12 inches, and an area of 50.24 square inches. The diameter of circle B is 3 inches, the circumference is 9.42 inches, and the area is 7.065 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)
Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)
Part C: What observation can you make about the value of pi for circles A and B? (2 points)
I just need the equations and answer for each part please
The value of pi determined is same when used the circumference formula and the formula of area.
What is Circle ?A circle is a round shaped figure , whose all the point lie on same plane.
It is given that
The value of pi is about 3.14, and it is the same when using both the area and circumference.
The circumference is found by
Circumference = π * diameter
For circle A:
25.12 = π * 8
π = 3.14
For circle B:
9.42 = π * 3
π = 3.14
The area is given by
Area = π * diameter² / 4
For circle A:
50.24 = π * (8²)/4
π = 3.14
For circle B:
7.065 = π * (3²)/4
π = 3.14
The value of pi is about 3.14,
The value of pi determined is same when used the circumference formula and the formula of area.
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The mass of a box of bolts is 3/4 kg and the mass of a box of screws is 3/5 kg.
a Which box has the greater mass?
b Calculate the difference in mass between the 2 boxes.
Answer:
a) The mass of a box of bolts is greater.
b) 3/20 kg
Step-by-step explanation:
a) Firstly, you have to make the denominators of the two fractions the same (by finding the LCM of the denominators).
The LCM of 4 and 5 is 20.
Converting 3/4 into denominator 20:
[tex]\frac{3 * 5}{4 * 5}[/tex]
= 15/20
Converting 3/5 into denominator 20:
[tex]\frac{3 * 4}{5 * 4}[/tex]
= 12/20
Now comparing the numerators:
15 > 12
Hence,
3/4 > 3/5
b) Difference of the boxes can be done by subtracting the numbers with the same denominator:
15/20 - 12/20
= 3/20 kg
Hope this helps and feel free to give me brainliest! :)
What is 1.2 converted into a fraction then divided by 7
algebra 2 pls help ill give brainliest
Answer:
Step-by-step explanation:
Carlos had at most 7 hours to spend in an amusement park in which he uses 1 hour for lunch and the rest of the time on park rides. What is the maximum number of rides Carlos can comete if each ride takes 15 minutes?
Answer:
24
Step-by-step explanation:
7 hours = 420 mins (7×60)
420-60=360 (time taken for lunch)
15mins=one ride
360÷15=24 rides
Please find the area of the given picture. Please as fast as possible........
Answer:
Area = 168 cm²
Step-by-step explanation:
**Please note that there is an error in the drawing of the given parallelogram. In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations. However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**
To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height. As the perpendicular height is unknown in the given parallelogram, use the following formula:
[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]
where:
a and b are the lengths of parallel sidesx is the included angleAs the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C is the anglea and b are the sides adjacent the anglec is the side opposite the angleFrom inspection of the given diagram:
C = ∠DCBa = DC = 13 cmb = CD = 14 cmc = DB = 15 cmSubstitute the given values into the cosine rule formula and solve for ∠ABC:
[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]
[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]
[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]
[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]
Substitute the found angle and the length of the parallel sides into the area formula:
[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]
Therefore, the area of the given parallelogram is 168 cm².
which numbers belong to the solution set of the equation?
22x=902
Answer:
D. 41
Step-by-step explanation:
To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:
The only solution for 22x=901 is 41
Answer: x=41
Step-by-step explanation:
Hii!
Do you need to know the solution set of 22x=902? No problem! (:
We just need to divide both sides by 22 to solve for "x".
x=41; this equation has one solution only
--
Hope that this helped! Best wishes.
--
LCM of 18 , 25 , 35, 40 ,80 81 , and 72
Answer:
the LCM of 18 25 40 80 81 and 72 is 226800
i hope this helps you
Step-by-step explanation:
by which method
prime factorization , division or defination method
lamy can paint 84 portraits in 6 weeks. at this rate , how many portraits can he paint in 2 weeks
Answer:
28 portraits
Step-by-step explanation:
Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.
In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is [tex]\frac{84 \text \: portraits}{6 \text \: weeks}[/tex] = 14 paintings per week.
Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.
Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.
Hope this helps!
I need help please help me
Answer:
It's the third one
Step-by-step explanation:
The cube root of 1/1000 is 1/10.
The cube root of c^9 is c^3.
The cube root of d^12 id d^4.
When you are doing to roots of variables, just divide :)
9/3 = 3
12/3 = 4