graphing a line through a given point with a given slope
graph the line with slope - 2 / 3 passing through the point (-1,3)
the fraction is negative
I have attached a hand drawn graph with the correct equation.Brainliest would be greatly appreciated!
If the length of the rectangle is 15 units long and the width is 11 units long, how long is the diagonal
Answer:
18.6 units
Step-by-step explanation:
A rectangle is a four sided shape with 4 perpendicular angles. It has two pairs of parallel sides which are equal in distance: width and length. A diagonal can be drawn between opposite corners that splits the triangle into two equal right triangles. The distance of this diagonal is found using the Pythagorean Theorem a² + b² = c². In the rectangle a = 11 and b = 15. Substitute these values and simplify using a square root operation.
11² + 15² = c²
121 + 225 = c²
346 = c²
√346 = c
18.6= c
What is the greatest common factor (GCF) of 80 and 50?
Answer: Choice B
Step-by-step explanation: The correct answer is 10, because 10 is the largest number that can you can divide both of these numbers by evenly.
1 4 of a pizza is split equally between 3 sisters. How much of a whole pizza will each sister get? A) 1 12 B) 1 3 C) 1 6 D) 1 7
Answer:
A. 1 12
Step-by-step explanation:
if i have 38 assignments and i do 15 of them what percentage do i have done?
Answer:
39.473%
Step-by-step explanation:
It is actually fairly simple to get the answer to this. What you can do to find any percentage, is to take the amount done, or whatever it is in the scenario, and divide it by the total. It is like turning it into a fraction, which you can do as well. Turn this into a fraction, and then convert it. 15/38, 15 divided by 38 = 39.473.
Hope this helped ^-^
To find the percentage you have done, divide the number you did by the total number you have to do:
15 / 38 = 0.3947
Multiply that by 100 to get the percentage:
0.3947 x 100 = 39.47% ( Round as needed).
Enter the system represented on the graph below. Find and explain the meaning of the point of intersection of the lines.
Answer:
y = -2x+4
y = (3/2)x -3
The point of intersection is (2, 0), or x=2 and y=0.
Step-by-step explanation:
The downward-sloping line drops 2 grid squares for each 1 it goes to the right, so its slope is -2. It intersects the y-axis at +4. In slope-intercept form, its equation is ...
y = slope · x + (y-intercept)
y = -2x + 4
Similarly, the upward-sloping line rises 3 grid squares for each 2 it goes to the right, so its slope is 3/2. It intersects the y-axis at -3. Its equation is ...
y = (3/2)x -3
The two lines intersect at the point where x=2 and y=0, so the coordinates are (2, 0). These are the values of x and y that satisfy both equations, so are the solution to the system.
Students are practicing their dance for the school play. They need to startin position 1 located at (3,5) then go to position 2 at (1,2) , to position 3 at (-1,-1) and finnaly to position 4. Describe the translation between each position, and give the location of the 4th position .
Answer:
Part a) The translation between each position is 2 units to the left and 3 units down
Part b) The location of position 4 is (-3,-4)
Step-by-step explanation:
we know that
step 1
Position 1 is located at (3,5) and then go to position 2 at (1,2)
so
The rule of the translation Position 1 to Position 2 is
(x,y)-----> (x-2,y-3)
that means-----> The translation is 2 units to the left and 3 units down
step 2
Position 2 is located at (1,2) and then go to position 3 at (-1,-1)
so
The rule of the translation Position 2 to Position 3 is
(x,y)-----> (x-2,y-3)
that means-----> The translation is 2 units to the left and 3 units down
step 3
Find the location of the 4th position
Applying the rule of the translation to position 3 at (-1,-1)
(x,y)-----> (x-2,y-3)
(-1,-1)-----> (-1-2,-1-3) -------> (-3,-4)
The position 4 is (-3,-4)
Answer:
D.
Step-by-step explanation:
(10Q) Solve the log.
Answer:
the answer is:
d. 5
Answer:
d
Step-by-step explanation:
You reason this out by saying
4^x = 4^5
Since the bases are the same, the answer is x = 5
Please help! The graph of function g(x) is a transformation of the graph of function f(x) = x^2.
g(x) = _________
A.) 2x^2+3
B.) -2x^2-3
C.) -1/2x^2-3
D.) 1/2x^2-3
Answer:
B.) -2x^2-3
Step-by-step explanation:
You only need to look at the values of the offered answers for x=1 in order to determine the correct one.
A.) for x = 1, 2·1+3 = 5
B.) for x = 1, -2·1-3 = -5 . . . . matches the graph
C.) for x = 1, -1/2·1-3 = -3 1/2
D.) for x = 1, 1/2·1-3 = -2 1/2
___
Comparing the values at x=1 to the values at x=0, you find that f(1)-f(0) = 1, while g(1)-g(0) = -2. This tells you the multiplier is -2, so matches choice B.
The fact that the vertex of g(x) is 3 units below that of f(x) tells you that -3 has been added to the product -2x^2.
_____
Comment on vertical scale factor
Since 1^2 = 1, it is often convenient to look at a point that is 1 unit away from the vertex of the function. The function value relative to the vertex value at that point will tell you the vertical scale factor.
For example, we know that the coefficient of x^2 is 1 in f(x), and we see on the graph that f(1) is 1 unit above the vertex at (0, 0). The value of g(1) is -5, which is 2 units below the vertex of g(x) at (0, -3). So, the vertical scale factor is -5-(-3) = -2.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
If the shapes are similar, the correspondent sides are in proportion:
[tex]AB\div DE = BC \div EF[/tex]
Let's plug the values and solve for x:
[tex]5x \div 5 = 4 \div x \iff \dfrac{5x}{5}=\dfrac{4}{x}\iff x = \dfrac{4}{x}[/tex]
Multiply both sides by x to get
[tex]x^2=4 \iff x=\pm2[/tex]
The only feasible solution, though, is [tex]x=2[/tex], because it wouldn't make sense to have negative lengths.
The value of x in the similar polygons in the given diagram is: B. x = 2.
What are the Sides of Similar Polygons?Similar polygons have the same shape but different size, thus, the length of their corresponding sides are proportional together and have equal ratio.
In essence, we will have the following ratio:
5x/5 = 4/x
(x)(5x) = (4)(5)
5x² = 20
5x²/5 = 20/5
x² = 4
x = √4
x = 2 (option B)
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A and B share the cost in a ratio of 3:2 . The cost is ?85; how much does A pay?
Answer:
The amount of money A pays is [tex]\$51[/tex]
Step-by-step explanation:
Let
x-----> amount of money A pays
y-----> amount of money B pays
we know that
[tex]x+y=85[/tex] ------> equation A
[tex]\frac{x}{y}=\frac{3}{2}[/tex]
so
[tex]y=\frac{2}{3}x[/tex] ------> equation B
substitute equation B in equation A and solve for x
[tex]x+(\frac{2}{3}x)=85[/tex]
[tex]\frac{5}{3}x=85[/tex]
[tex]x=85*3/5=\$51[/tex]
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of Integral b a f(x) dx. Which one of the following statements is true?
Lower sum < Trapezoidal rule Value < Upper sum
Lower sum < Upper sum < Trapezoidal rule value
Trapezoidal rule < Lower sum < Upper sum
Cannot be determined without the x-values for the partitions
The left sum would be f0+f1+f2+f3
The right sum would be f1+f2+f3+f4
The trapezoidal rule value is:
(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2
This would put the trapezoidal rule in the middle , which makes the answer:
Lower sum < Trapezoidal rule Value < Upper sum
Answer:
Step-by-step explanation:
Given function f(x) is positive, increasing and concave up on the closed interval [a, b],
it means f(x1) < f(x2) if x1 < x2
So Lower sum < Upper sum
As Trapezoidal is average of f(x1) and f(x2) = [f(x1) + f(x2)] / 2
it is average of the Lower and Upper sum.
The answer is Lower sum < Trapezoidal rule Value < Upper sum
Find the missing side length. Round your answer to the nearest tenth.
A) 4.7
B) 5.5
C) 30.8
D) 43.2
Answer:
Option B. [tex]5.5[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
Let
c------> the missing side length
[tex]c^{2}=9^{2}+6^{2} -2(9)(6)cos(37)[/tex]
[tex]c^{2}=30.747[/tex]
[tex]c=5.5[/tex]
What is the simplest form of the expression below? 2x2 ? 10x ? 28 6x × 6 x ? 7
Final answer:
To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).
Explanation:
To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).
When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x
Use the tangent radio to find the missing leg of this right triangle. Estimate your answer to two decimal places.
The answer is y = 6.43
Answer:
y = 6.43
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan47° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{6}[/tex]
Multiply both sides by 6
6 × tan47° = y
⇒ y = 6.43 ( to 2 dec. places )
This graph of a function is a translation of y=4/x. What is an equation for the function?
[tex]y = \frac{4}{x + 6} + 2 \\ [/tex]
found by:
as value of x approaches -6 from left, value of y appoaches negative infinity
as value of x approaches -6 from the right, value of y approaches infinity
(undefined solution)
therefore, the value of x = 0 is translated to x = - 6
if x = -6,
(x + 6) = 0
(x + 6) is the value of x in the equation
[tex]y = \frac{4}{x + 6} + c[/tex]
as x increases, the value of 4/x approaches 0
in the graph, it approaches 2 instead
meaning 2 units is added to the value of y,
therefore c = 2.
Answer:
[tex]y=\frac{4}{x+6} +2[/tex]
Step-by-step explanation:
rational exponents: product rule
simplify
v^2/3 x v^2/7
the fractions are exponents
Answer:
v^(20/21).
Step-by-step explanation:
v^2/3 x v^2/7
= v^(2/3 + 2/7)
= v^( 14/21 + 6/21)
= v^(20/21).
The following table gives the percentage of music downloaded from the United States and other countries by U.S. users: Country U.S. Germany Canada Italy U.K. France Japan Other Percent 45.2 16.4 6.5 6.3 4.2 3.7 2.1 15.6 (a) Verify that the table does give a probability distribution for the experiment. The sum of the percents is %, so this does give a probability distribution. (b) What is the probability that a U.S. user who downloads music, selected at random, obtained it from either the United States or Canada? (Enter your answer to three decimal places.) (c) What is the probability that a U.S. user who downloads music, selected at random, does not obtain it from Italy, the United Kingdom (U.K.), or France? (Enter your answer to three decimal places.)
Answer:
A) 100%; B) 0.517; C) 0.858
Step-by-step explanation:
For part A,
We find the sum of the probabilities:
45.2+16.4+6.5+6.3+4.2+3.7+2.1+15.6 = 100
Since they sum to 100%, this is a probability distribution.
For part B,
We add together the probabilities for the US and Canada:
45.2+6.5 = 51.7% = 51.7/100 = 0.517
For part C,
We first add together the probabilities for Italy, the UK and France:
6.3+4.2+3.7 = 14.2%
Next we subtract this from 100%:
100-14.2 = 85.8% = 85.8/100 = 0.858
Final answer:
The table gives a probability distribution. The probability that a U.S. user obtained music from the United States or Canada is 51.7%. The probability that a U.S. user does not obtain music from Italy, the U.K., or France is 85.8%.
Explanation:
To verify that the table gives a probability distribution, we need to show that the sum of the percentages is equal to 100%. Summing the percentages from the table, we get:
45.2 + 16.4 + 6.5 + 6.3 + 4.2 + 3.7 + 2.1 + 15.6 = 100%
This confirms that the table does give a probability distribution for the experiment.
To find the probability that a U.S. user obtained music from either the United States or Canada, we add the percentages for these two countries:
45.2 + 6.5 = 51.7%
Therefore, the probability is 0.517 or 51.7%.
To find the probability that a U.S. user does not obtain music from Italy, the United Kingdom (U.K.), or France, we subtract the percentages for these three countries from 100%:
100% - (6.3 + 4.2 + 3.7) = 100% - 14.2% = 85.8%
Therefore, the probability is 0.858 or 85.8%.
Mr. Spoke is a sales man at pop's cycle shop, each month he earns $800 plus 7% of his total monthly sales. How much did he earn last month if his sales totaled $9,200.00
Answer:
$1444
Step-by-step explanation:
7% of 9200 = 644
644 + 800 = 1444
:)
he earned 8,301.56 last month
f(x)=8x-7 find f(-6)
Answer to question #2
Answer:
see the attachment
Step-by-step explanation:
There are 16 ounces in 1 pound, so 96 ounces is 6 pounds. You solve this problem by making up the difference between the given amount and 6 pounds—basically, you subtract it from 6.
6 - 3 1/2 = 2 1/2 . . . . for example
A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserved for the company logo. Use the grid to identify the perimeter and area of the space reserved for the logo.
Answer:
The answer is the first answer
P = 8 + 4√13 cm
A = 36 cm²
Step-by-step explanation:
* Lets study the figure
- Its a kite with two diagonals
- The shortest one is 12 cm
- The longest one is 26 ⇒ axis of symmetry of the kite
- the shortest diagonal divides the longest into two parts
- The smallest part is 8 cm and the largest one is 18 cm
* To find the area reserved for the logo divide
the hexagonal piece into two congruent trapezium
- The length of the two parallel bases are 4 cm and 8 cm and
its height is 3 cm
- The length of non-parallel bases can calculated by Pythagoras rule
∵ The lengths of the two perpendicular sides are 2 cm and 3 cm
- 3 cm is the height of the trapezium
- 2 cm its the difference between the 2 parallel bases ÷ 2
(8 - 4)/2 = 4/2 = 2 cm
∴ The length of the non-parallel base = √(2² + 3²) = √13
* Now we can find the area of the space reserved for the logo
- The area of the trapezium = (1/2)(b1 + b2) × h
∴ The area = (1/2)(4 + 8) × 3 = (1/2)(12)(3) = 18 cm²
∵ The space reserved for the logo are 2 trapezium
∴ The area reserved for the logo = 2 × 18 = 36 cm²
* The area of the reserved space for the logo = 36 cm²
* The perimeter of the reserved space for the logo is the
perimeter of the hexagon
∵ The lengths of the sides of the hexagon are:
4 cm , 4 cm , √13 cm , √13 cm , √13 cm , √13 cm
∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm
* The perimeter of the reserved space for the logo = 8 + 4√13 cm
What is the solution to the system of equations below use elimination 2x+5y=20 6x-5y=12 (X,Y)
Answer:
(4, 2.4)
Step-by-step explanation:
(2x+5y=20)3
-
6x-5y=12
----------------------
then....
6x+15y=60
-
6x-5y=12
--------------------
0 + 20y = 48
y=2.4
plug in 2.4 into one of the equations and you get that x= 4
The high school leadership team is having a car wash. They charge $5.50 for large cars and $4.00 for small cars . They had a successful day, washed a total of 142 cars, and made $652.50. How many large cars and small cars did they wash?
Answer: 56 large cars and 86 small cars.
Step-by-step explanation:
Let's call:
[tex]l[/tex]: the number of large cars.
[tex]s[/tex]: the number of small cars.
Then, you can set up the following system of equations:
[tex]\left \{ {{l+s=142} \atop {5.50l+4.0s=652.50}} \right.[/tex]
You can use the Elimination Method:
- Multiply the first equation by -4.0
- Add both equations.
- Solve for l.
[tex]\left \{ {{-4.0l-4.0s=-568} \atop {5.50l+4.0s=652.50}} \right.\\--------\\1.5l=84.5[/tex]
[tex]l[/tex]≈[tex]56[/tex]
Substitute [tex]l=56[/tex] into one of the original equations and solve for s:
[tex]56+s=142\\s=142-56\\s=86[/tex]
Which of the following is a horizontal stretch of the parent function?
Answer:
C.
Step-by-step explanation:
Answer:
The correct option is 3.
Step-by-step explanation:
The parent function is
[tex]f(x)=|x|[/tex]
The horizontal stretch and compression is defined as
[tex]g(x)=|bx|[/tex]
If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.
Graph 1 passing thought the point (1,-1).
[tex]-1=|b(1)|[/tex]
This statement is false for any value of b, because the value of modulus can not be negative.
Graph 2 passing thought the point (1,2).
[tex]2=|b(1)|[/tex]
[tex]2=b[/tex]
Since b>1, therefore this graph represent the horizontal compression.
Graph 3 passing thought the point (2,1).
[tex]1=|b(2)|[/tex]
[tex]\frac{1}{2}=b[/tex]
Since 0<b<1, therefore this graph represent the horizontal stretch.
Thus, the correct option is 3.
Identify the area of the figure. PLEASE HELP!!
Answer:
92m²
Step-by-step explanation:
The height of the triangle is the height of the square plus the height above the square, or 4+8=12 m.
The length of the hypotenuse is 15 m. The length of the known leg is 12 m.
Substitute 12 for b, 15 for c, and solve for a.
a=√15²-12²= √225−144 = √81 = 9
The bottom leg of the right triangle is 9 m.
To find the length of the base of the large triangle multiply the length of the bottom leg of the right triangle by 2.
The length of the base of the large triangle is (9)(2)=18 m.
Use a formula for the area of a triangle, A=12bh, to find the area of the triangle.
18 is base and 12 is height
A=(1/2)(18)(12)= 108
to find the area of the square:
A= 4²=16
A=108-16= 92m²
Suppose that in the town of Springfield, RI, the number of days per year with no measurable precipitation is approximately normally distributed with a mean of 85.1 days and a standard deviation of 7.5 days. Ms. Johnson, who lives on a farm just outside of Springfield, wonders if the mean number of days with no measurable precipitation on her farm is different from in town. Her grandfather maintained meticulous weather records. She obtains a simple random sample of eight years from her grandfather's records, and determines that the mean number of days with no measurable precipitation in those years was 82.3 days. She plans to conduct a one-sample ????z ‑test, assuming that the standard deviation of days with no measurable precipitation is the same at the farm as in town. Choose the appropriate null and alternative hypotheses for such a test.
Answer:
H0: µ = 85.1
Ha: µ ≠ 85.1
Step-by-step explanation:
She wants to see if the number of days is different. It could be higher or lower, so the alternate hypothesis uses the "not equal to" sign. If she wanted to see if it rained more on the farm, her alternate hypothesis would be
Ha: µ > 85.1
If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1
The solution for the null hypothesis is given below,
H0: µ = 85.1
Ha: µ ≠ 85.1
What is the null hypothesis?When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.
She is checking to see if the number of days has changed. The alternative hypothesis utilizes the "not equal to" marker since it might be either higher or lower. Her alternate hypothesis, if she wanted to determine whether it rained more frequently on the farm, is
Ha: µ > 85.1
If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1.
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The friendly sausage factory (fsf) can produce hot dogs at a rate of 5,000 per day. fsf supplies hot dogs to local restaurants at a steady rate of 260 per day. the cost to prepare the equipment for producing hot dogs is $66. annual holding costs are 45 cents per hot dog. the factory operates 294 days a year.
a. find the optimal run size. (do not round intermediate calculations. round your answer to the nearest whole number.) optimal run size
b. find the number of runs per year. (round your answer to the nearest whole number.) number of runs
c. find the length (in days) of a run. (round your answer to the nearest whole number.)
Answer:
a. 21 327 hot dogs/run
b. 70 runs/yr
c. 4 da/run
Step-by-step explanation:
Data:
Production rate (p) = 5000/da
Usage rate (u) = 260/da
Setup cost (S) = $66
Annual carrying cost (H) = $0.45/hot dog
Production days (d) = 294 da
Calculations:
a. Optimal run size
(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)
= 1 470 000 hot dogs/yr
(ii) Economic run size
[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex]
[tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]
[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex]
[tex]= \sqrt{454852321}[/tex]
= 21 327 hot dogs/run
b. Number of runs per year
Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)
= 70 runs/yr
c. Length of a run
Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)
= 4 da/run
To find the optimal run size, use the EOQ formula and calculate the square root. Divide the annual demand by the optimal run size to find the number of runs per year. Finally, calculate the length of a run by dividing the days in a year by the number of runs per year.
Explanation:The optimal run size can be found using the Economic Order Quantity (EOQ) formula. EOQ = sqrt((2DS)/(H)) where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year.
Using the given values:
D = 260 per day * 294 days = 76,440
S = $66
H = $0.45
EOQ = sqrt((2 * 76,440 * 66) / (0.45)) ≈ 6868
The optimal run size is approximately 6868 hot dogs.
The number of runs per year can be calculated by dividing the annual demand by the optimal run size:
Number of runs = 76,440 / 6868 ≈ 11.15
Since the factory operates 294 days a year, the number of runs per year is approximately 11.
The length of a run can be calculated by dividing the days in a year by the number of runs per year:
Length of a run = 294 / 11 ≈ 26.73
The length of a run is approximately 27 days.
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Consider the data set on the number line. Determine the interquartile range.
A) 11
B) 17
C) 22
D) 25
Answer:
Step-by-step explanation:
The answer is B because if you subtract the correct way then you should get 17
Answer: B
Step-by-step explanation:
Fine the measure of the angle formed by the radius and the side of a regular dodecagon.
A.15
B.30
C.60
D.75
Answer:
Option D.75°
Step-by-step explanation:
we know that
The sum of the interior angles of a regular dodecagon is equal to
[tex]S=(n-2)*180[/tex]
where
n is the number of sides
In this problem
n=12 sides
substitute
[tex]S=(12-2)*180[/tex]
[tex]S=1,800\°[/tex]
Find the measure of each interior angle
Divide the sum of the interior angles by the number of sides
[tex]1,800\°/12=150\°[/tex]
The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle
therefore
[tex]150\°/2=75\°[/tex]