B. 3x +y = 4
Step-by-step explanation:It is perhaps easiest to simply try the equations to see which one works.
For x=0, there are two different kinds of answers:
... A and C: -y = 4
... B and D: y = 4
Since we know y=4 when x=0 (from the point (0, 4)), we can eliminate choices A and C.
___
Using the point (1, 1), you can try choices B and D to see which works:
... B: 3·1 +1 = 4 . . . . true (put 1 where x and y are in the equation)
... D: -3·1 +1 = -2 = 4 . . . . false
The appropriate choice is the equation of B: 3x +y = 4.
_____
Derive the equation from the given points
There are several ways you can derive the equation. Since you have the y-intercept (the point with x=0), you can use the slope-intercept form to start.
The slope (m) is ...
... m = (change in y)/(change in x) = (4 -1)/(0 -1)
... m = -3
We know the y-intercept (b) is 4, so the slope-intercept form of the equation is ...
... y = mx +b
... y = -3x +4
Adding 3x puts this in standard form:
... 3x +y = 4
The equation of the line passing through points (1,1) and (0,4) is y = -3x + 4 or in standard form -3x + y = 4.
Explanation:In the subject of mathematics, when it comes to identifying equations of the line in a graph, we consider the points it passes through. In this case, the line passes through the points (1, 1) and (0, 4). The equation of a line can be found using the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. The slope m between two points can be found using the formula: m = (y2 - y1) / (x2 - x1).
Let's substitute the given points into the slope formula and find the slope: m = (4 - 1) / (0 - 1) = -3. Now, using the slope and one of the points (let's use (0,4)), we substitute into the line formula: y - 4 = -3(x - 0). This simplifies to y = -3x + 4, which aligns with answer D: −3x + y = 4.
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A school purchases jars of marbles.
* Each jar contains 500 pieces of marbles.
* Each jar costs $10.
How much does the school have to charge for each piece of marbles to make a profit of $25 per
jar?
a. $0.07
b. $0.10
c. $0.14
d. $0.25
Answer:
a. $0.07
Step-by-step explanation:
Profit = Charge -Cost
We want to make a profit of 25 and the cost is 10
25 = Charge -10
Add 10 to each side
25+10 = Charge -10+10
35 = Charge
We need to charge 35 per jar.
Each jar contains 500 marbles
The cost per marble is Cost/ number of marbles
cost per marbles = $35 / 500
= $.07
Answer:
Option A : $0.07
Step-by-step explanation:
Given :
A school purchases jars of marbles.
Each jar contains 500 pieces of marbles.
Each jar costs $10.
To Find : How much does the school have to charge for each piece of marbles to make a profit of $25 per jar?
Solution :
Cost of one jar is $10
Now, school wants to make profit of $25 on each jar .
using formula : Profit = Charge - cost
⇒$25 = charge - $10
⇒$35 = charge
Thus school should charge one jar of marbles of $35.
Since each jar contains 500 marbles.
So,to calculate cost of each marble when charge of jar is $35.
Cost of 500 marbles is $35
Cost of 1 marble = 35/500 = $0.07
cost of each marble when charge of jar is $35 is $0.07
Hence , the school have to charge $0.07 for each piece of marble to make a profit of $25 per jar.
Option A is correct
Express 4 as a fraction. A) 1 1 B) 1 4 C) 4 1 D) 4 4
Answer:
C) 4/1
Step-by-step explanation:
Any integer can be expressed as a fraction by using a denominator of 1.
simplify the polynomials:5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
Simplify each term: 5x^4y + 7x^4y - 5x^5 - 5x^3z + 3x^3z
Combine like terms: -5x^5 + 12x^4y -2x^3z
That is the most simplified form.
If necessary, factor:
x^3(-5x^2+12xy-2z)
Plz help What is sum of 5.3x10^5 and 3.8x10^4 in scientific notation
A. 4.33x10^4
B. 5.68x10^5
C. 9.1x10^9
D. 9.1x10^5
Answer:
I would say your answer is B.
Step-by-step explanation:
5.3 times 10^5 + 3.8 times 10^4
Tirn them into their regular form and add them together you will get the answer
what is the best estimate of mean for this data set PLZ HLP
(1)has 0 dots
(2)has 3 dots'
(3)has 1 dot
(4)has 4 dots
(5)has 0 dots
(6)has 2 dots
(7)has 3 dots
(8) has 1 dot
(9) has 1 dot
(10) has 0 dots
(dot plot)
Answer:
Sample Response: The math club has 8 members. The youngest member is 9. The oldest member is 13. Therer is a cluster between 11 and 13, with a peak at 13. There is a gap at 10.
Marta believes that the equation of the line of best fit for the scatterplot below is
Which statement best summarizes why Marta is likely incorrect?
Answer:
Marta’s equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.
Step-by-step explanation:
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Sorry if this does not help
Answer:
A
Step-by-step explanation:
Given sin(−θ)= −1/4 and tanθ= 15√15 .
What is the value of cosθ ?
Marvin Company has a beginning inventory of 12 sets of paints at a cost of $1.50 each. During the year, the store purchased 4 sets at $1.60, 6 sets at $2.20, 6 sets at $2.50, and 10 sets at $3.00. By the end of the year, 25 sets were sold. Calculate (a) the number of paint sets in ending inventory and (b) the cost of ending inventory under the LIFO, FIFO, and weighted-average methods. Round to nearest cent for the weighted average
Answer:
(a) 13
(b) LIFO: $19.60; FIFO: $37.50; Avg: $28.26
Step-by-step explanation:
(a) The starting inventory was 12 sets. Added to that were 4, 6, 6, 10, to make a total of 38 paint sets. 25 were sold, so 13 remained at the end of the year.
(b)
LIFO
Sets purchased at the end of the year are sold first (last-in, first-out). So the sets remaining in inventory are the ones purchased at the beginning of the year. Those 13 sets cost 12@1.50 +1@1.60 = $19.60.
FIFO
Sets purchased first are sold first, so the sets remaining in inventory are the ones purchased last. Those 13 sets cost 10@3.00 +3@2.50 = $37.50.
Avg
The total cost of all inventory purchases was ...
... 12@1.50 +4@1.60 +6@2.20 +6@2.50 +10@3.00
... = 18.00 +6.40 +13.20 +15.00 +30.00 = $82.60
Then the value of the remaining 13 of the 38 items bought is ...
... (13/38)·$82.60 = $28.26.
_____
I find it convenient to let a spreadsheet do the arithmetic.
Q. P
12. 1.5. 18.00
4. 1.6. 6.40
6. 2.2. 13.20
6. 2.5. 15
10. 3. 30
__ __. ___
38. 10.8. 82.6
Sales. 25
Ending inventory 25-38=13. Answer a
B) ending inventory under LIFO
12×1.5=18
1×1.6=1.6
___
19.6 Answer
Ending inventory under FIFO
10×3=30
3×2.5=7.5
___
37.5. Answer
Ending inventory under weighted average
82.6÷38=2.17
2.17× 13=28.21 ...Answer
Hope it helps!
what are the x-intercepts of the parabola represented by the equation y = 3x2 + 6x − 10
x ≈ {-3.082, 1.082}
Step-by-step explanation:I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.
___
From vertex form
The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...
... y = (x +1)² -13/3
This has x-intercepts easily found.
... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0
... (x +1)² = 13/3 . . . . . . . add 13/3
... x +1 = ±√(13/3) . . . . . take the square root
... x = -1 ±√(13/3) . . . . . subtract 1
... x ≈ {-3.0816660, 1.0816660}
_____
Using the quadratic formula
This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.
... x = (-b±√(b²-4ac))/(2a)
... x = (-6 ±√(6² -4(3)(-10)))/(2(3))
... x = (-6 ±√156)/6 = -1 ±√(13/3) . . . or . . . -1 ±(√39)/3
Elias and Niko are polishing the silver at the heritage museum. Elias could polish all the silver himself in 40 minutes. That task would take Niko 50 minutes to complete alone. Which table is filled in correctly and could be used to determine how long it would take if Elias and Niko polished the silver together?
Answer:
should be the first table
Step-by-step explanation:
The table that can be used to determine how long it would take if Elias and Niko polished the silver together is table B
How to determine the tableYou can create a table to determine the time it would take Elias and Niko together to polish the silver based on their individual rates of completing the task.
Let's denote:
Elias's rate of polishing = 1 job / 40 minutes
Niko's rate of polishing = 1 job / 50 minutes
To find the combined rate when they work together, you can use the formula:
Combined rate = Elias's rate + Niko's rate
Elias's rate = 1 job / 40 minutes
Niko's rate = 1 job / 50 minutes
So, the combined rate when they work together will be:
Combined rate = 1/40 + 1/50
Combined rate = (5/200) + (4/200)
Combined rate = 9/200
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Given the vertices of isosceles trapezoid ABCD: A(2, 0), B(4, 0), C(5, -2), D(1, -2). If the image is reflected over the y-axis, C' = (5, 2) (-5, 2) (-5, -2) (5, -2)
Here is the image https://addenbrooke.owschools.com/media/g_geo_ccss_2016/10/q910l4.gif
Answer:
C' = (-5, -2)
Step-by-step explanation:
Reflection over the y-axis negates the x-coordinate.
C(5, -2) ⇒ C'(-5, -2)
Answer:
The correct option is 3.
Step-by-step explanation:
The vertices of isosceles trapezoid ABCD are A(2, 0), B(4, 0), C(5, -2), D(1, -2).
If a figure reflected over the y-axis, then the relation between coordinates of preimage and image is defined as
[tex](x,y)\rightarrow (-x,y)[/tex]
It is given that ABCD reflected over the y-axis and coordinates of point C are (5,-2), so the coordinates of C' are
[tex]C(5,-2)\rightarrow C'(-5,-2)[/tex]
The coordinates of C' are(-5,-2). Therefore the correct option is 3.
Triangle ABC is transformed to obtain triangle A′B′C′:
A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 2, 2, B at 2, 10, C at 8, 12. Triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 1,B prime at negative 1, negative 5, C prime at negative 4, negative 6.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
Answer:
Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees
Step-by-step explanation:
All the coordinates of A'B'C' are -1/2 times those of ABC. The dilation factor is 1/2, and rotation by 180° is indicated.
A'(-1, -1) = (-1/2) × A(2, 2)
B'(-1, -5) = (-1/2) × B(2, 10)
C'(-4, -6) = (-1/2) × C(8, 12)
___
Rotation by 180° negates both coordinates. It is equivalent to reflection across the x-axis and reflection across the y-axis, in either order.
Answer:
its basically B
Step-by-step explanation:
What is the decimal value of cos X?
(Round the answer to the nearest thousandth if necessary.)
Answer:
0.153
Step-by-step explanation:
It has been a long time since I've done this, so I hope it is correct:
cos = adjacent side / hypotenuse
cos x = 13 / 85 = 0.153
The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle.
Explanation:The decimal value of cos X can be found using a calculator or trigonometric table. Cosine is a trigonometric function that gives the ratio of the length of the adjacent side to the hypotenuse of a right triangle. For example, if cos X is equal to 0.6, this means that the adjacent side of the triangle is 0.6 times the length of the hypotenuse.
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A manufacturing company builds construction machinery. It sells 10 machines for $18,100 and 20 machines for $26,600. Which equation models the revenue, R(x), as a linear function of the number of machines built, x ?
Select one:
A. R(x)=750x−10100
B. R(x)=450x+7200
C. R(x)=1200x−4500
D. R(x)=850x+9600
Answer:
R(x) = 850x + 9600
Step-by-step explanation:
Which sequence of transformations would change two congruent figures into two similar figures that are no longer congruent ?
A) reflection and rotation
B) translation and dilation
C) reflection and translation
D) translation and reflection
Answer:
B
Step-by-step explanation:
....
The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.
Option B is the correct answer
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and size.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Two congruent figures:
If a translation is applied to the two congruent figures we get the same shape and size.
If we apply a dilation after the translation to the two congruent figures the size of the figures changes.
If translation and dilation are applied to two congruent figures this sequence would change two congruent figures into two similar figures that are no longer congruent.
Thus,
The sequence of translation and dilation of transformation would change two congruent figures into two similar figures that are no longer congruent.
Option B is the correct answer.
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Which pair of triangles is congruent by ASA? - Please help ASAP. THANKS!
Answer:
it would be c
Step-by-step explanation:
all you have to do is find the picture that maches the stament
asa means angle side angle so therefore c if im correct
Mr. Gonzales has only $42.50 to spend at a clothing store. He want to buy a shirt that costs $29, including tax and some bracelets that cost $4.50 each, including tax. Write an equation to determine x, the maximum number of bracelets Mr. Gonzales could but.
1) Equation ________________________
2) Solve the equation to determine the number of bracelets Mr. Gonzales could buy.
Show your work
Answer _____ bracelets
Answer:
Equation: 29+ 4.50x= 42.50
Answer: 3
Step-by-step explanation:
Find the measure of the acute angle x. Round your answer to the nearest tenth, if necessary.
29.1
0.01
60.9
0.03
Answer:
60.9
Step-by-step explanation:
Help meeeeeeweeeeeeee
A. y = (-6/5)x +10
Step-by-step explanation:The given line has a negative slope (downward to the right). The only equation offered with a negative slope is the one of selection A.
_____
Complete working
A parallel line will have the same slope. If there are less-obvious choices to select from, you need to know the slope of the given line. That is computed from ...
... slope = (change in y)/(change in x)
The coordinates of two points are given, so we can find the slope as ...
... slope = (-4-2)/(-1-(-6)) = -6/5
There are a number of ways to write the equation of a line, but in slope-intercept form, the slope is the coefficient of x. You will be looking for a choice that has an x-coefficient of -6/5.
1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.
The volume of the sphere is given by :
V=[tex]\frac{4}{3}\pi r^{3}[/tex]
And volume of cylinder is given as :
V=[tex]\pi r^{2}h[/tex]
So, as given to select the radius randomly and the height of the cylinder will be the diameter of the sphere.
The radius are = 3, 5, 8, 10, 12
And height will be = 6, 10, 16, 20, 24
1. Volume of sphere with radius 3 = [tex]\frac{4}{3}*3.14*3*3*3= 113.04[/tex] units
Volume of cylinder with radius 3 and height 6 = [tex]3.14*3*3*6=169.56[/tex] units
2. volume of sphere with radius 5 = 523.60 units
volume of cylinder with height 10 = 785.40 units
3. volume of sphere with radius 8 = 2144.66 units
volume of cylinder with height 16 = 3216.99 units
4. volume of sphere with radius 10 = 4188.79 units
volume of cylinder with height 20 = 6283.19 units
5. volume of sphere with radius 12 = 7238.23 units
volume of cylinder with height 24 = 10857.34 units
Ryan completed 1/8 of his test in 2/5 hour. If Ryan’s rate stayed the same, how much of his test was finished in one hour
Answer:
5/16
Step-by-step explanation:
In 5/2 the time, we expect that 5/2 × 1/8 = 5/16 of the test will be complete.
_____
5/2 × (2/5 h) = 1 h
Answer:5/16
Step-by-step explanation: In 5/2the time, we expect that 5/2 *1/8= 5:16
put the following values in order from least to greatest 3.
2^0=1
2^-2=1/4
(-2)^2=4
-2^2=-4
-2^2,2^-2,2^0,(-2)^2
Consider the following equation. 1000=5(10^2t) which of the following equations can be used to find true value of t. A.log2(1000) B.log2(200)=10t C.log10(1000)=5(2t) D.log10(200)=2t
D. log₁₀(200) = 2t
Step-by-step explanation:Dividing by 5 gives you ...
... 200 = 10^(2t)
Taking the log to the base 10 gives you ...
... log₁₀(200) = 2t . . . . . . matches selection D
The graph of y ≤ -2x + 4 is shown. Which set contains only points that satisfy the inequality? A) {(0, 0), (1, 2), (3, -3)} B) {(0, 0), (1, 2), (7, -2)} C) {(3, 3), (1, 2), (3, -3)} D) {(0, 0), (2, 1), (3, -3)}
To find out if a set satisfies the inequality, you can either plug in the points into the equation, or you can plug in the points into the graph.
Any point in the shaded area and on the line satisfy the inequality. If the inequality had a sign of < or >, then the point can not be on the line, only in the shaded area.
A.) This is a solution because they are all in the shaded area
B.) This is not a solution because (7,-2) is outside the shaded area
C.) This is not a solution because (3,3) is outside the shaded area
D.) This is not a solution because (2,1) is outside the shaded area
Answer:
A) {(0, 0), (1, 2), (3, -3)}
Step-by-step explanation:
Check by inserting values into the inequality.
y ≤ -2x + 4
Set A
(0,0): 0≤ 4 TRUE
(1,2): 2 ≤ -2×1 + 4
2 ≤ -2 + 4
2 ≤ 2 TRUE
(3,-3): -3 ≤ -2×3+4
-3 ≤ -6 + 4
-3 ≤ -2 TRUE
=====
Set B
(7, -2): -2 ≤ -2×7 + 4
-2 ≤ -14 + 4
-2 ≤ -10 FALSE
=====
Set C
(3,3): 3 ≤ -2×3 + 4
3 ≤ -6 + 4
3 ≤ -2 FALSE
=====
Set D
(2,1): 1 ≤ -2×2 + 4
1 ≤ -4 +4
1 ≤ 0 FALSE
Set A is the one that contains only points that satisfy the inequality.
What is the simplified value of the expression below?
1/3/2/3
Answer:
1/2
Step-by-step explanation:
1/3 ÷ 2/3
We will use copy dot flip
Copy the first number , change the divide to multiply, take the reciprocal of the second number.
1/3 × 3/2
1/2
please help me asap!
Answer:
Option b. 30.5
Step-by-step explanation:
Given in the picture is a triangle ABC with sides AB = 22.3 and side BC=24.1
The included angle B = 82 degrees
We have to find the third unknown side AC = b
REcollect the cosine formula for triangles.
[tex]b^{2} =a^{2} +c^{2} -2ac cos B[/tex]
substitute for a and c
We get
[tex]b^2 = 22.3^2+24.1^2-2(22.3)(24.1) cos 82\\=928.587[/tex]
b = square root of 928.587
b =30.47=30.5
Thus we get b = 30.5
At the city museum, child admission is $5.20 and adult admission is $8.80 . On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1090.80 . How many child tickets were sold that day?
Answer:
27 total child tickets sold
Step-by-step explanation:
Price of child ticket = $5.20
Price of adult admission = $8.80
Now according to given condition of the day of Monday
Let no of child tickets sold are = x
then
total no of adult tickets sold are =4 x
Total sales = $ 1090.80
Now according to given
we know that
sales of child tickets + sales of adults tickets = total sales
Putting in the values
x * (5.20) + (4x)*(8.80) = 1090.80
5.20 x + 35.2 x = 1090.80
40.4 x = 1090.80
Dividing both sides by 40.4
[tex]\frac{40.4x}{40.4}=\frac{1090.80}{40.4}[/tex]
x= 27
So total no of child tickets sold are 27
find the missing value of the sides.
Answer:
The values for both of the missing sides is 8.
Step-by-step explanation:
The hypotenuse of a right triangle = a(square root of 2)
Therefore the other two missing sides equal a.
Therefore, the other two sides equal 8.
now, recalling the pythagorean theorem a little.
the hypotenuse here is 8√2, and then we have the other two sides, BUT, the opposite angle for each is actually the same 45°, if each opposite angle is the same, the length of the side on the other end is also the same.
so we have say side "b" and side "a", but because each has an opposite angle of 45°, that means "b" and "a" are actually twins.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies (8\sqrt{2})^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{8\sqrt{2}}\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \stackrel{\textit{since we know that \underline{a = b}}}{[8^2(\sqrt{2})^2]=a^2+a^2}\implies 64(2)=2a^2\implies \cfrac{64(2)}{2}=a^2\implies 64=a^2 \\\\\\ \sqrt{64}=a\implies 8=a=b[/tex]
PLEASE DO PLEASE
Write the expressions as a square of a monomial.
64x^9
Write the expressions as a cube of a monomial.
If it helps, you can submit one answer at a time
The expression written as a square of a monomial is [tex](4x^3)^3[/tex]
Given the indices expression [tex]64x^9[/tex]
We are to express as a square of a monomial. This is expressed as shown:
[tex]=64x^9\\=(4 \times 4 \times 4)(x^3)^3\\= 4^3(x^3)^3\\=(4x^3)^3[/tex]
Hence the expression written as a square of a monomial is [tex](4x^3)^3[/tex]
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Final answer:
To write 64x^9 as a square of a monomial, we can write it as (8x^4)^2. To write it as a cube of a monomial, we can write it as (4x^3)^3.
Explanation:
To write 64x^9 as a square of a monomial, we need to find a monomial that, when squared, equals 64x^9. To do this, we need to identify the square root of 64, which is 8, and the square root of x^9, which is x^4. Therefore, 64x^9 can be written as (8x^4)^2.
To write an expression as a cube of a monomial, we need to find a monomial that, when cubed, equals the given expression. In this case, we need to find the cube root of 64, which is 4, and the cube root of x^9, which is x^3. Therefore, 64x^9 can be written as (4x^3)^3.
For which of these functions does the function value change at a constant rate per unit change in x? Explain.
Answer:
The function r(x) represents a constant rate per unit change in x.
Step-by-step explanation:
This is because when you increase in 2, it goes from 37 to 25, a decrease in 12, then when the x goes from 2 to 3, then it has to drop down by 6, or else it won't be linear. It does. 25-6 is 19. Then it goes from 3 to 5, meaning it has an increase of 2 in x, meaning it has to drop down in 12 to be linear, It does. 19-12 is 7. So it is linear, meaning it has a constant rate per unit change in x.