Answer:
[tex]\large\boxed{y-8=\dfrac{5}{7}(x-4)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope [tex]m=\dfrac{5}{7}[/tex] and the point [tex](4,\ 8)[/tex].
Substitute:
[tex]y-8=\dfrac{5}{7}(x-4)[/tex]
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common labeled AB.
A
[tex]y \leqslant - 2 + 3 \\ y \leqslant x + 3[/tex]
B
[tex]y \geqslant - 2x + 3 \\ y \geqslant x + 3[/tex]
C
[tex]y \leqslant - 3x + 2 \\ y \leqslant - x + 2[/tex]
D
[tex]y > - 2x + 3 \\ y > x + 3[/tex]
Answer:
[tex]\large\boxed{A.\ y\leq-2x+3,\ y\leq x+3}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
=============================================
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points:
(0, 3) - y-intercept → b = 3 (for both lines)
f(x)
(0, 3), (1, 1)
[tex]m=\dfrac{1-3}{1-0}=\dfrac{-2}{1}=-2[/tex]
Substitute:
[tex]f(x):\ y=-2x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq-2x+3[/tex]
g(x):
(0, 3), (2, 5)
[tex]m=\dfrac{5-3}{2-0}=\dfrac{2}{2}=1[/tex]
Substitute:
[tex]g(x):\ y=1x+3=x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq x+3[/tex]
Answer:
b
Step-by-step explanation:
what is the slope of the line shown below? (9, 1) (-3, -7)
Answer:
2/3
Step-by-step explanation:
To find the slope based off of two points, use the following formula:
[tex]\frac{y2-y1}{x2-x1}[/tex]
Plug in your values and simplify.
[tex]\frac{-7-1}{-3-9} \\\\\frac{-8}{-12}[/tex]
[tex]\frac{8}{12}[/tex]
[tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
I like the line up and subtract strategy. At the end you just put 2nd number over 1st.
This is the slope formula; just a different way to think about the formula.
(9,1)
-(-3,-7)
=======
12, 8
So the slope is 8/12=2/3.
The product of two numbers is 144 and their difference is 10. What is the sum of the two numbers
Answer:
18+8=26
Step-by-step explanation:
Their sum would be 18 and * because they have difference of ten. In order o get this you would have to multiply 1 X144 and so on.
Answer:
Step-by-step explanation:
Its 134 hope this helos
Sure would help a lot
Hello There!
X = 6
First, we would add 5 to both sides so adding 5 to -5 is 0 and adding 5 to 7 is 12 so we would get the equation 2x = 12
Next, we would divide 2x by 2 and divide 12 by 2 and we would get a quotient of 6.
Our final answer is x = 6
Answer:
x=6
Step-by-step explanation:
2x - 5 = 7
Add 5 to each side
2x-5+5= 7+5
2x = 12
Divide by 2
2x/2 = 12/2
x = 6
A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents this scenario?
PLZ HELP IM TIMED
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x -----> the number of solved puzzles
y -----> the number of solved riddles
we know that
[tex]2x+y \geq 4[/tex]
The solution of the inequality is the shaded area above the solid line [tex]2x+y=4[/tex]
The slope of the solid line is negative [tex]m=-2[/tex]
The y-intercept of the solid line is the point (0,4)
The x-intercept of the solid line is the point (2,0)
therefore
The graph in the attached figure
Answer:
The graph that representss this scenario is attached.
Explanation:
You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.
1. Determine the expression that relates the variables.
a) The name of the variables is given:
x: number of solved puzzles
y: number of solved riddles
b) Point rules:
Each solved puzzle is worth two points: 2x
Each solved riddle is worth 1 point: 1y = y
Sum of points: 2x + y
The video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .
In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.
2) Building the graph
Solve algebraically for y: y ≥ 4 - 2x
You want to draw the border line of the function, that is y = 4 - 2x
You have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.
x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)
y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).
In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.
Addtional constrains: x and y cannot be negative, so add the constrains:
x ≥ 0 and y ≥ 0
The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).
plz give brainliest
Two angles of a triangle have the same measure and the third one is 3 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
The LARGEST angle has a measure of ___ degrees.
Answer:
62 DEGREES
Step-by-step explanation:
TWO ANGLES=2A
LARGEST ANGLE=A+3
2A+A+3=180
3A=180-3=177
A=177/3=59
LARGEST ANGLE=59+3=62
Answer:
The Largest Angle angle has a measure of 62 degrees.
Step-by-step explanation:
In triangle ABC, angle ABC equals to angle ACB.
and BAC is the largest angle.
Let angle measure of ABC and ACB angles be "x" degree.
then, measure of third angle i.e BAC will be "x + 3" degrees.
Since sum of all angles of any triangle is 180 degree.
so, first angle + second angle + third angle = 180
x + x + (x + 3) = 180
3x = 180 - 3
3x = 177
x = 59 degrees
So, First angle = 59 degree
Second angle = 59 degree
Third Angle = 62 degree.
The Largest Angle angle has a measure of 62 degrees.
What is the truth value for the following conditional statement?
If the grass is red, then the snow is white.
T T → F
F T → T
F T → F
T F → T
Answer: the correct option is
(B) F T → T.
Step-by-step explanation: We are given to find the truth value of he following conditional statement :
"If the grass is red, then the snow is white."
Let us consider that
p : the grass is red. This is a false statement
and
q : the snow is white. This is a true statement.
So, we get
p → q
F → T, which is true (T).
Thus, the required answer is F T → T
Option (B) is CORRECT.
which of the following binomials below is a factor of this trinomial x(x)-13x+36
Answer:
(
x
+
4
)
(
x
+
9
)
=
0
Your answer would be x=-4 and x=-9.
Explanation::
(
x
+
4
)
(
x
+
9
)
x
times
x
=
x
2
x
(
9
)
+
x
(
4
)
=
13
x
4
times
9
=
36
=
x
2
+
13
x
+
36
Answer:
So the factors of the given are:
(x-4) and (x-9).
The factored form of the given expression is (x-4)(x-9).
Step-by-step explanation:
To factore the given quadratic with leading coefficient one, you must find two numbers that add to be and multiply to be c.
a=1
b=-13
c=36
So we need two numbers that multiply to be 36 and add to be -13.
These numbers are -4 and -9 since
(-4)(-9)=36 and -4+-9=-13.
So the factors of the given are:
(x-4) and (x-9).
The factored form of the given expression is (x-4)(x-9).
Swill sells 35 liters or milk in a day. How many liters of milk will be sold if he has to sell 125% more milk per day
Answer:
43.75 liters.
Step-by-step explanation:
125% = 1.25 as a decimal fraction.
number of liters of milk = 35 * 1.25
= 43.75 liters.
7 days left until the launch of our new product and we have $668.00 left in our promotion budget we need to spend 85.00 on the last day how many dollars can we spend on the remaining days
Answer:
$97.16 per day
Step-by-step explanation:
Total amount you have = $668.00
You have to spent $85.00 on the last day.
$668.00-85.00
=$583
It means you have $583 for the remaining 6 days in the week.
If you spend equal amount of money each day , you can calculate it by dividing remaining amount and number of days
=583/6
=$97.16
It means you can spend $97.16 per day....
An 'A' is considered 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0. If you received the following grades in your first semester, what would your grade point average be?
English: 3.0 credits, B.
Biology: 4.0 credits, B.
Communications: 3.0, F.
New student seminar: 1.0, A.
Express your answer rounded to the hundredths place.
Answer:
Your grade point average would be 2.75(B- or C+)
Step-by-step explanation:
[tex]\frac{3+4+3+1}{4} \\\frac{11}{4} \\2.75[/tex]
Final answer:
Explaining the calculation of GPA based on given grades, resulting in an approximate value rounded to the hundredths place.
Explanation:
The grade point average (GPA) for the given grades can be calculated as follows:
English: 3.0 credits, B, which is 3.0 in GPA scale
Biology: 4.0 credits, B, which is 3.0 in GPA scale
Communications: 3.0, F, which is 0.0 in GPA scale
New student seminar: 1.0, A, which is 4.0 in GPA scale
Calculating the GPA:
(3.0 + 3.0 + 0.0 + 4.0) / 11 = 10.0 / 11 = 0.91
Therefore, the grade point average would be approximately 0.91 rounded to the hundredths place.
Evaluate the following vertices for the function f(x)=x+2y
Answer:
You might want to see if I read your ordered pairs right because it was really hard to see for me:
f(2,6)=14
f(-1,3)=5
f(6,4)=14
Step-by-step explanation:
I assume they meant to write f(x,y)=x+2y.
Doing f(2,6) now. This means replace x with 2 and y with 6:
f(2,6)=2+2(6)=2+12=14
f(2,6)=14
Doing f(-1,3) now. This means replace x with -1 and y with 3:
f(-1,3)=-1+2(3)=-1+6=5
f(-1,3)=5
Doing f(6,4) now. This means replace x with 6 and y with 4:
f(6,4)=6+2(4)=6+8=14
f(6,4)=14
Tha values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively
Functions and valuesGive the function expressed as:
f(x, y) = x + 2y
If the coordinate point is (2, 6), then;
f(2, 6) = 2 + 2(6)
f(2, 6) = 2 + 12
f(2, 6) = 14
If the coordinate point is (-1, 3), then;
f(-1, 3) = -1 + 2(3)
f(-1, 3) = -1 + 6
f(-1, 3) = 5
If the coordinate point is (6, 4), then;
f(6, 4) = 6 + 2(4)
f(6, 4) = 6 + 8
f(6, 4) = 14
Hence the values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively
Learn more on function and values here: https://brainly.com/question/4934333
A researcher determined the amount of ducks that were in a pond over a four-year time span. The results are shown in the table below.
Year 1, 2, 3, 4
Ducks 64, 78, 92. 106
Year Ducks
1 64
2 78
3 92
4 106
Select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.
d= 64(1.22)^n-1
d=14n +64
d= 14n + 50
d + 50(1.14)^n-1
Answer:
Option C (d = 14n + 50).
Step-by-step explanation:
The observations for Year 1, 2, 3, and 4 are 64, 78, 92, and 106 respectively. It can be observed that the difference between second term and the first term is 78 - 64 = 14. This is also true for the third term and the second term. In fact, the difference between the terms is fixed. This means that the sequence is an arithmetic sequence, in which the difference between the terms is fixes for all the terms. The nth term in this case is defined as:
S = a + (n-1)*d; where S is the output at a given n, a is the first term, n is the position, and d is the common difference. In this question, S = ducks (d), a = 64, and d = 14. Therefore, plugging in the values in the above formula gives:
d = 64 + (n-1)*14.
d = 64 + 14n - 14.
d = 14n + 50.
Therefore, the model which best describes the amount of ducks that will be in the pond during the nth year is d = 14n + 50, i.e. Option C!!!
Answer: Third Option
[tex]a_n =14n+50[/tex]
Step-by-step explanation:
By subtracting consecutive terms from the number of ducks each year you will get a common difference of 144.
[tex]78-64 = 14\\92-78 = 14\\106-92 = 14[/tex]
This means that the data can be modeled by the equation of an arithmetic sequence
The arithmetic sequences have the following form:
[tex]a_n = a_1 + d(n-1)[/tex]
Where [tex]a_1[/tex] is the first term and d is the common difference between the consecutive terms.
So :
[tex]a_1 = 64[/tex]
[tex]d = 14[/tex]
Then the equation is:
[tex]a_n = 64 + 14(n-1)[/tex]
[tex]a_n = 64 + 14n-14[/tex]
[tex]a_n =14n+50[/tex]
Simplify the expression.
-(10)^-2
Answer:
-1/100
Step-by-step explanation:
-(10)^-2
Exponents first
We need to make the negative in the exponent positive, which means move it to the denominator
-1
--------
10^2
-1
---------
100
Answer:
-1/100
Step-by-step explanation:
10^(-2) becomes 1/100.
-(10)^(-2) is -1/100.
64 -[16 x (-3) – 2 x{17 – 25 }]
Answer:
96
Step-by-step explanation:
64 -[16 x (-3) – 2 x{17 – 25 }] I'm going to take a couple of steps that are very small and they can be combines along with other steps. Combine 16*-3
64 - [-48 - 2*(17 - 25)] Combine what is inside (17 - 25)
64 - [-48 - 2*(-8)] Combine -2*-8
64 - [-48 + 16] Combine what is in the brackets.
64 - [-32] Remove the brackets
64 + 32 Combine
96
The trick in this question is the signs.
2x^2+y^2=8xy find dy/dx
Answer:
2(x-2y)/(4x-y) = dy/dx
Step-by-step explanation:
2x^2+y^2=8xy
Take the derivative of each term, remembering that we take the 8xy as derivative by parts)
2 * 2x dx + *2y dy = 8 ( x dy + dx *y)
4x dx +2y dy = 8x dy + 8y dx
Subtract 2y dy from each side
4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx
4x dx = 8x dy - 2y dy + 8y dx
Subtract 8y dx from each side
4x dx -8y dx = 8x dy - 2y dy + 8y dx-8y dx
4x dx -8y dx = 8x dy - 2y dy
(4x-8y) dx = (8x-2y) dy
Factor out a 4 from the left side and a 2 from the right side
4(x-2y) dx = 2( 4x-y) dy
Cancel a 2
2(x-2y) dx = ( 4x-y) dy
Divide each side by (4x-y)
2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy
2(x-2y)/(4x-y) dx = dy
Divide by dx
2(x-2y)/(4x-y) dx/dx = dy/dx
2(x-2y)/(4x-y) = dy/dx
What is the value of k?
Answer:
i thought its -9
Step-by-step explanation:
x / x-2=x-k / x-4x /x=x-k/x-4+2cut x/x of first side
k=x/x-6now cut x/x
k=-63=-6-6-3-9
Ryan has 57 plastic blocks that are either yellow or green. In 57-X, what does x equal?
Answer:
the amount of green blocks = X then you'll end up with the amount of yellow blocks
Answer:
so x can be either yellow or green
Step-by-step explanation:
Ryan has total 57 blocks (total yellow and green)
if x is either of yellow or green
then 57 -x will be either green or yellow (According to x is green or yellow)
x can be either yellow or green .
Samir is trying to decide between two checking account plans. After researching plans at two banks, he finds that Unity Bank offers a monthly compounded interest rate of 0.14%, while Sunrise Banking offers 1.6% interest compounded annually. Which is the better plan? Explain.
(SHOW WORK)
Answer:
The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.
Step-by-step explanation:
Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.
Monthly compound interest rate = P(1+r/n)^nxt
n=12 (number of months in a year)
t=1 (number of years)
Annually compound interest rate = P(1+r/n)^nxt
n=1 (because it is for 1 year only)
t=1 (number of years=1)
Step 2 : Lets assume that P is $100 in both banks and time is 1 year.
Step 3 : Lets substitute the values to find out which one is better.
Monthly compound interest rate = P(1+r/n)^nxt
Monthly compound interest rate = 100(1+0.14/12)^12x1
Monthly compound interest rate = 114.93
114.93 - 100 = $14.93 per month
14.93 x 12 = $179.16 for 12 months or 1 year
Annually compound interest rate = P(1+r/n)^nxt
Annually compound interest rate = 100(1+1.6/1)^1x1
Annually compound interest rate = 260
260-100 = $160 for 1 year
Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.
!!
Answer:
The Unity Bank is offering a good plan.
Step-by-step explanation:
Unity Bank offers a monthly compounded interest rate of 0.14%
So, yearly rate will be = [tex]0.14\times12=1.68[/tex]% or 0.0168
Sunrise Banking offers 1.6% or 0.016 interest compounded annually.
Lets check an example with these two rates.
The compound interest formula is = [tex]A=P(1+r/n)^{nt}[/tex]
Lets take P = $1000 and t = 1 year
Case 1: when r = 1.68% and n = 12
Putting the values in formula we get
A = [tex]1000(1+0.0168/12)^{12}[/tex]
= [tex]1000(1.0014)^{12}[/tex]
A = $1016.92
Case 2: when r = 1.6% and n = 1
Putting the values in formula we get
A = [tex]1000(1+0.016/1)^{1}[/tex]
= [tex]1000(1.016)^{1}[/tex]
A = $1016.00
So, we can see that the first case gives more return than second one.
Therefore, the Unity Bank is offering a good plan.
Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.
Answer:
Part 1) [tex]c=21.9\ units[/tex]
Part 2) [tex]B=61.1\°[/tex]
Part 3) [tex]A=28.9\°[/tex]
Part 4) [tex]C=90\°[/tex]
Step-by-step explanation:
step 1
Find the length side c
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
substitute the given values
[tex]c^{2}=10.6^{2}+19.2^{2}[/tex]
[tex]c^{2}=481[/tex]
[tex]c=21.9\ units[/tex]
step 2
Fin the measure of angle B
we know that
In the right triangle
[tex]tan(B)=b/a[/tex]
substitute the given values
[tex]tan(B)=19.2/10.6[/tex]
[tex]B=arctan(19.2/10.6)=61.1\°[/tex]
step 3
Find the measure of angle A
we know that
The measure of interior angles in a triangle must be equal to 180 degrees
so
∠A+∠B+∠C=180°
Remember that in a right triangle the measure of angle C is 90 degrees
we have
[tex]B=61.1\°[/tex]
[tex]C=90\°[/tex]
substitute
[tex]A+61.1\°+90\°=180\°[/tex]
[tex]A=28.9\°[/tex]
Answer:
A = 28.9 degrees, B = 61.1 degrees, c = 21.9
Step-by-step explanation:
I got it correct on founders edtell
A side of a square is 8 3/2 inches. Using the area formula A = s2, determine the area of the square.
Answer:
Area=512 square inches
Step-by-step explanation:
According to the given data;
A side of a square = (8)³/² inches.
Area of a square = ?
To find the area of a square we use the formula:
Area = s²
Area=(8)³/²)²
Area = 8³
Area= 8*8*8
Area=512 square inches....
Elsie pays $8.99 for a one-pound canister of Georgia pecans. Write and solve a proportion to determine the cost of 4
ounces of the pecans she needs for a particular recipe. Round answer to the nearest cent.
(SHOW WORK)
To find the cost of 4 ounces of pecans, we set up a proportion comparing the cost to weight, resulting in $2.25 after rounding to the nearest cent.
Explanation:To determine the cost of 4 ounces of pecans when a one-pound (16 ounces) canister costs $8.99, we set up a proportion where the cost is directly proportional to the weight.
The proportion is $8.99/16 ounces = $X/4 ounces, where X represents the cost of 4 ounces of pecans.
Multiplying both sides by 4 to solve for X gives us $X = (4 ounces × $8.99) / 16 ounces.
Simplifying this, we find that $X = $2.2475, which, when rounded to the nearest cent, gives us an answer of $2.25.
Triangles ABD, CBD and ADC are all isosceles. Find the angle x.
AC = AD
Measure of angle 'x' given in the picture will be 36°.
From the picture attached,
In ΔABD,
m∠DAB = x° [Given]
AB ≅ BD [Isosceles triangle]
Therefore, opposite sides of the given triangles will measure the same.
m∠BAD = m∠BDA = x°
m∠BAD + m∠BDA + m∠ABD = 180° [By triangle sum theorem]
x° + x° + m∠ABD = 180°
m∠ABD = 180°- 2x°
m∠DBC + m∠ABD = 180° [Linear pair of angles]
m∠DBC + (180° - 2x) = 180°
m∠DBC = 2x°
In isosceles ΔBCD,
BD ≅ CD
Therefore, m∠DBC = m∠BCD = 2x°
In isosceles ΔACD,
Since, AC ≅ AD,
Therefore, m∠ACD = m∠ADC = 2x°
By applying triangle sum theorem in ΔACD,
m∠ACD + m∠DAC + m∠CDA = 180°
2x° + x° + 2x° = 180°
5x° = 180°
x = 36°
Therefore, measure of 'x' will be 36°.
Learn more,
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What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
Answer:
-.1
Step-by-step explanation:
The common difference in the arithmetic sequence can be found by doing term minus a previous term.
So 0.26-0.36=-.1
or 0.16-0.26=-.1
or 0.06-0.16=-.1
or -0.04-0.06=-.1
or -0.14-(-0.04)=-.1
Which expression can be used to determine the slope of the line that passes through the points (–7, 3) and (1, –9)?
Answer:
-9-3/1-(-7)
Step-by-step explanation:
Answer:
The slope of given line = -3/2
Step-by-step explanation:
Points to remember
slope of the line with end points (x1, y1) and (x2, y2) is given by,
Slope = (y2 - y1)/(x2 - x1)
To find the slope of the line
Here (x1, y1) = (-7, 3) and (x2, y2) = (1, -9)
Slope = (y2 - y1)/(x2 - x1)
= (-9 - 3)/(1 - -7)
= (-12)/8
= -3/2
Therefore the slope of given line = -3/2
Dimensions for an office floor plan is 15ft. By 15ft and 28ft. By 28ft. Tile runs $1 per square foot and carpeting $5 per square foot. What is the estimated total cost for the floor coverings installed
Answer:
$2520
Step-by-step explanation:
Taking the dimensions of the office floor from the plan to be;
[tex]15ft*28ft[/tex]
Area of the floor to be covered will be the product of the sides dimensions
[tex]=15*28=420ft^{2}[/tex]
Cost of putting tile on the floor
1ft²=$1
420ft²=?
=[tex]\frac{420*1}{1} =420[/tex]
=$420
Cost of putting a carpet on the floor
1ft²=$5
420ft²=?
[tex]=\frac{420*5}{1} =2100[/tex]
=$2100
Estimated cost
Total estimated cost =cost for putting tiles+cost for putting carpet
=$420+$2100=$2520
you roll a fair 6 sided die what is p (not 5)
Answer:
5/6
Step-by-step explanation:
There are 6 possible rolls
1 2 3 4 5 6
Only one of 6 is a five
Which of the following describes a triangle?
A. One-dimensional
B. Two-dimensional
C. Zero-dimensional
D. Three-dimensional
Answer:
B
Step-by-step explanation:
A triangle has both x and y values making it 2D. A 1D object is a point, a 3D object is a cube or something, and a 0D object is nothing.
14. Solve this system of equations:
4x + 2y = 22
3x – 2y = 13
Answer:
(x,y)= (5,1)
Step-by-step explanation:
4x+2y=22
3x-2y=13
2y=22-4x
3x-2y=13
3x-(22-4x)=13
x=5
3·5-2y=13
y=1
(x,y)= (5,1)
Answer:
(5, 1); x = 5 and y = 1.
Step-by-step explanation:
Step 1: Add the system of equations
4x + 2y = 22
3x - 2y = 13
-----------------------------
7x = 35
Step 2: Solve for x
x = 5
Step 3: Substitute the value of x in one of the original equations
4(5) + 2y = 22
Step 4: Solve for y
20 + 2y = 22
2y = 2
y = 1
Step 5: Write your answer as an ordered pair
(5, 1)
In the number 2010, the value represented by the digit 1 is what fraction of the value represented by the digit 2?
Answer:
Step-by-step explanation:
The two represents 2000
The one represents 10
The fraction you want is 10/2000 = 1/200 or 0.005
The value represented by the digit 1 in the number 2010 is 1/200 of the value represented by the digit 2. This is determined by comparing their place values, with 1 in the tens place and 2 in the thousands place.
To determine the value represented by the digit 1 in the number 2010, we need to understand place value.
→ The digit 1 is in the tens place, so its value is 10 (1 × 10).
→ The digit 2 is in the thousands place, so its value is 2000 (2 × 1000).
The fraction of the value represented by the digit 1 to the value represented by the digit 2 is calculated as follows:
→ Fraction = Value of digit 1 / Value of digit 2
= 10 / 2000
= 1/200
Therefore, the value represented by the digit 1 is 1/200 of the value represented by the digit 2 in the number 2010.