Answer:12
Step-by-step explanation:bcs in 1/3 it has the same denominatoor
Round 0.566 to the nearest tenth
Answer:
0.06
Step-by-step explanation:
If you round 0.566 to the nearest tenth it would be 0.06
pls rate and thank me
Answer:
To round 0.566 to the nearest tenth consider the hundredths' value of 0.566, which is 6 and equal or more than 5. Therefore, the tenths value of 0.566 increases by 1 to 6.
=0.6
Step-by-step explanation:
comment how this helps
Determine the type and number of solutions of 4x2 − 3x + 1 = 0. A two imaginary solutions B two real solutions C one real solution
Option A
The equation [tex]4x^2 - 3x + 1 = 0[/tex] has two imaginary solutions
Solution:
Given that we have to determine the type and number of solutions of given quadratic equation
[tex]4x^2 - 3x + 1 = 0[/tex]
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation
In the case of a quadratic equation [tex]ax^2 + bx + c = 0[/tex], the discriminant is [tex]b^2 -4ac[/tex]
[tex]\text{If } b^{2}-4 a c=0 ;$ then the given quadratic equation has one real root\\\\If b^{2}-4 a c>0,$ then the given quadratic equation has two real roots[/tex]
If [tex]b^2-4ac<0[/tex], then the given quadratic equation has two imaginal roots which are complex conjugates
Given quadratic equation is:
[tex]4x^2 - 3x + 1 = 0[/tex]
Here a = 4 and b = -3 and c = 1
The discriminant is given as:
[tex]b^2 - 4ac = (-3)^2 - 4(4)(1) = 9 - 16 = -7\\\\b^2 - 4ac = -7\\\\b^2-4ac < 0[/tex]
Therefore the given equation has two imaginary solutions
Answer:
two imaginary solutions
Step-by-step explanation:
Christian reads 14 book every 23 week.
How many books does Christian read per week?
16
38
223
6 ///////What percent is equivalent to 45 ?
20%
40%
60%
80% /////// Blueberries are on sale for $2.80 per pint. The regular price is $3.50 per pint.
What is the percent of decrease?
Select from the drop-down menu to correctly complete the statement.
The percent of decrease is
Picture 1: The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: 80% is equal to [tex]\frac{4}{5}[/tex].
Step-by-step explanation:
Picture 1: Veena ate lunch at a deli. She ordered turkey sandwich for $9.25 and a salad for $4.35. The tax was 7.5%. What is the amount of tax for Veena's meal.
Given,
Price of turkey sandwich = $9.25
Price of salad = $4.35
Total amount = 9.25+4.35 = $13.60
Tax = 7.5%
Amount of tax = 7.5% of total cost
Amount of tax = [tex]\frac{7.5}{100}*13.60[/tex]
Amount of tax = [tex]\frac{102}{100} = \$1.02[/tex]
The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads 1/4 book every 2/3 week. How many books does Christian read per week?
Given,
Books read every 2/3 weeks = 1/4 books
[tex]\frac{2}{3}\ weeks=\frac{1}{4}\ books\\[/tex]
For determining the number of books read per week, we will multiply both sides by [tex]\frac{3}{2}[/tex]
[tex]\frac{3}{2}*\frac{2}{3}\ week=\frac{1}{4}*\frac{3}{2}\ books\\\\1\ week = \frac{3}{8}\ books\\\\[/tex]
Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: What percent is equivalent to [tex]\frac{4}{5}[/tex]?
We will multiply the given fraction with hundred for calculating the percentage.
[tex]\frac{4}{5}*100\\\\\frac{400}{5}\\\\80\%[/tex]
Therefore,
80% is equal to [tex]\frac{4}{5}[/tex].
Keywords: percentage, division
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Jordan trolls a fair dice 216 times how many times would Jordan expect to roll a four
Answer:
36
Step-by-step explanation:
since a fair die has 6 sides (i.e 6 possible outcomes),
P (rolls a 4 on 1 roll) = 1/6
hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.
expected number of times to roll a 4
= (1/6) x 216 = 36 times.
Answer:
Answer:
36
Step-by-step explanation:
since a fair die has 6 sides (i.e 6 possible outcomes),
P (rolls a 4 on 1 roll) = 1/6
hence if he rolls the die 216 times, we would expect to roll a 4 for 1/6 of the time. I.e.
expected number of times to roll a 4
= (1/6) x 216 = 36 times.
Step-by-step explanation:
Given that V= πr^2h. Make r the subject of the formula.
Using the result from the above,find r when V = 81 cm3, π = 4 and h = 9cm
Answer:
The answer is [tex]r=\frac{3}{2}\ cm.[/tex]
Step-by-step explanation:
Given:
V= πr²h.
V = 81 cm3,
π = 4 and
h = 9cm.
Now, making r the subject of the formula using the result from the above, find r.
So, to get the value of r:
[tex]V=\pi r^2h[/tex]
[tex]81=4\times r^2\times 9[/tex]
[tex]81=36r^2[/tex]
Dividing both sides by 36 we get:
[tex]\frac{81}{36} =r^2[/tex]
Using square root on both sides we get:
[tex]\frac{9}{6} =r[/tex]
[tex]\frac{3}{2} =r[/tex]
[tex]r=\frac{3}{2}.[/tex]
Therefore, the answer is [tex]r=\frac{3}{2}\ cm.[/tex]
The 3rd term of a geometric sequence is -2 and the 7th is -32. Find the common ratio,the first term, the explicit formula, and the 10th term.
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Both a and r have to be found
Given a₃ = - 2, then
ar² = - 2 → (1)
Given a₇ = - 32, then
a[tex]r^{6}[/tex] = - 32 → (2)
Divide (2) by (1)
[tex]\frac{ar^6}{ar^2}[/tex] = [tex]\frac{-32}{-2}[/tex], that is
[tex]r^{4}[/tex] = 16 ( take the fourth root of both sides )
r = 2 ← common ratio
Substitute r = 2 into (1)
a × 2² = - 2, that is
4a = - 2 ( divide both sides by 4 )
a = - [tex]\frac{1}{2}[/tex] ← first term
Hence
[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex][tex](2)^{n-1}[/tex] ← explicit formula
and
[tex]a_{10}[/tex] = - [tex]\frac{1}{2}[/tex] × [tex]2^{9}[/tex] = - 0.5 × 512 = - 256
SHOW WORK
WILL MARK BRAINLIEST
Answer:
[tex]\large\boxed{x=\dfrac{5\pi}{4}\ \vee\ x=\dfrac{7\pi}{4}}[/tex]
Step-by-step explanation:
The first step in attachment.
[tex]\sin(x)=-\dfrac{\sqrt2}{2}\to x=-\dfrac{\pi}{4}+2k\pi\ \vee\ x=\dfrac{5\pi}{4}+2k\pi\\\\x\in[0,\ 2\pi)\\\\\text{Therefore}\\\\x=-\dfrac{\pi}{4}+2\pi=\dfrac{7\pi}{4}\ \vee\ x=\dfrac{5\pi}{4}[/tex]
Tiffany sketched a picture is a car she used the scale 2 inches:12 feet the car in her sketch is 8 inches long what is the length in feet of the actual car
Answer:
The actual length in feet of the car is 48 feet.
Step-by-step explanation:
Given:
Tiffany sketched a picture of a car she used the scale 2 inches : 12 feet.
In her sketch the car is 8 inches long.
Now, to find the length in feet of the actual car.
Let the actual length of car in feet be [tex]x\ feet.[/tex]
And the length of car in her sketch is 8 inches.
Thus, 8 inches is equivalent to [tex]x\ feet[/tex].
So, the ratio of the scale used by Tiffany as given is 2 inches : 12 feet.
Thus, 2 inches is equivalent to 12 feet.
Now, to get the actual length of car by using cross multiplication method:
[tex]\frac{2}{12} =\frac{8}{x}[/tex]
By cross multiplying we get:
⇒ [tex]2x=96[/tex]
Dividing both sides by 2 we get:
⇒ [tex]x=48[/tex]
⇒ [tex]x=48\ feet.[/tex]
Therefore, the actual length in feet of the car is 48 feet.
I need help on this problem
Answer: [tex]QR=4.04[/tex]
Step-by-step explanation:
For this exercise you must use the followinG Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case, given the right triangle PQR, you can identify that:
[tex]\alpha=60\°\\opposite=PR=7.0\\adjacent=QR[/tex]
Then, the next step is to substitute those values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]:
[tex]tan(60\°)=\frac{7.0}{QR}[/tex]
And the final step is to solve for "QR" in order to find its value.
So you get that this is:
[tex](QR)(tan(60\°))=7.0\\\\QR=\frac{7.0}{tan(60\°)}\\\\QR=4.04[/tex]
Which Expression Is Equivalent to 1/6 - 3/8 + 1/2
a) 1/6 -(-3/8) + 1/2
b) 1/6 - (-3/8) + (-1/2)
c) 1/6 + (-3/8) + (-1/2)
d) 1/6 + (-3/8) + 1/2
Answer:
d) 1/6 + (-3/8) + 1/2
Step-by-step explanation:
For equivalence, the sign of each term must match the original. Here's how the answer choices stack up:
a) wrong sign for -3/8
b) wrong sign for -3/8 and for 1/2
c) wrong sign for 1/2
d) correct choice
Final answer:
Option (c) 1/6 + (-3/8) + (-1/2) is equivalent to the original expression 1/6 - 3/8 + 1/2 because it accurately reflects the original values and operations without any alterations.
Explanation:
The student's question asks to find an expression equivalent to the arithmetic operation 1/6 - 3/8 + 1/2. To find the equivalent expression, we should look for an option that represents the same operation without any alteration to the values or their signs.
Upon review, option (c) 1/6 + (-3/8) + (-1/2) is the correct equivalent expression because it maintains the original values and their associated signs. The negative signs in front of the fractions in this option simply denote subtraction, which matches the original expression given.
The use of parentheses in the alternative expression is typical in algebra to emphasize operations, but it does not change the value of the expression. Thus, the correct option is c.
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apple weighs 160 pounds how much does the truckload of fruit weigh in total
Answer:
440 pounds
Step-by-step explanation:
Ratio is basically "parts".
We have ratio of 4:3:4, that is a total of 4 + 3 + 4 = 11 parts
The apple is 4 parts and total amount is 160 pounds. So each "part" is:
160/4 = 40 pounds
The total pounds of all 3 fruits is 11 parts * 40 pounds per part = 11 * 40 = 440 pounds
hence,
Truckload of fruits weigh at 440 pounds
What is 4(x−2)=3(2y−1) in standard form?
Answer: 4x-6y=5
Step-by-step explanation: Using the formula, Ax+By=C, write the equation in standard form.
Hope this helps you out! ☺
The equation 4(x-2) = 3(2y-1) can be converted into standard form by first expanding the equation and then rearranging it. The equation in standard form is 4x - 6y = -5.
Explanation:To convert the equation 4(x-2) = 3(2y-1) into standard form, we first expand both sides of the equation. This results in 4x - 8 = 6y - 3. We can then rearrange the equation to bring all variables to one side which yields 4x - 6y = -8 + 3 or 4x - 6y = -5.
However, in standard form, the coefficients of x and y should be integer and the coefficient of x should be positive. Additionally, the constant should be on the right side of the equation. Therefore, we multiply the whole equation by -1 to get -4x + 6y = 5. Multiplying again by -1 to make the coefficient of x positive, we get 4x - 6y = -5 which is the standard form of the given equation.
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write a x (-a)x 13 x a x (-a) x 13 in power notation
Answer:
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Step-by-step explanation:
The given expression
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
Writing a\times (-a)\times 13\times a\times (-a)\times 13 in power notation:
Let
[tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex]
= [tex][13\times13][(a\times (-a)\times a\times (-a)][/tex]
As
[tex]13\times13 = 13^{2}[/tex] , [tex]a\times a = a^{2}[/tex] , [tex](-a)\times (-a) = (-a)^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times (-a)^2][/tex]
As
[tex](-a)^2 = a^{2}[/tex]
So,
[tex]=[13^{2}][a^2\times a^2][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=[13^{2}][a^{2+2}][/tex]
As ∵[tex]a^{m} \times a^{n}=a^{m+n}[/tex]
[tex]=13^{2}\times a^{4}[/tex]
[tex]=a^{4}\times 13^{2}[/tex]
Therefore, [tex]a\times (-a)\times 13\times a\times (-a)\times 13[/tex] can be written in power notation as [tex]a^{4}\times 13^{2}[/tex]
Keywords: power notation
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Can you please help me solve questions 1 and 2
Answer:
see explanation
Step-by-step explanation:
(1)
Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is
third side
= 4x + 3y - (x - y + x + y)
= 4x + 3y - 2x ← collect like terms
= 2x + 3y
(2)
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 2x + 6 and h = x - 2, thus
A = [tex]\frac{1}{2}[/tex](2x + 6)(x - 2) ← expand factors using FOIL
= [tex]\frac{1}{2}[/tex](2x² + 2x - 12) ← distribute
= x² + x - 6 ← in standard form
3x +15=75 what is the value of x
Answer:
X=20
you subtract 15 from 75 to get 60 then divide 60 by 3 to get 20
In ΔJKL, k = 3.7 cm, ∠K=15° and ∠L=41°. Find the length of j, to the nearest 10th of a centimeter.
Answer:
The length of side j is 11.85cm
Step-by-step explanation:
Given that
In triangle JKL,
[tex]\angle k=15[/tex]
[tex]\angle l=41[/tex]
Side k=LJ=3.7cm
To find side j=KL:
By using sine rule,
We can write as
[tex]\frac{SinK}{LJ} = \frac{SinL}{JK} = \frac{SinJ}{KL} \\\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{SinJ}{KL}[/tex]
Using property of triangle,
[tex]\angle k+\angle l+\angle j=180[/tex]
[tex]15+41+\angle j=180[/tex]
[tex]\angle j=124[/tex]
[tex]\frac{Sin15}{3.7} = \frac{Sin41}{JK} = \frac{Sin124}{KL}\\\frac{Sin15}{3.7} = \frac{Sin124}{KL}\\KL=3.7\frac{Sin124}{Sin15}\\KL=3.7\frac{0.8290}{0.2588}\\KL=11.85cm[/tex]
Thus,
The length of side j is 11.85cm
Answer: 11.9
Step-by-step explanation:
nearest 10th you have to round it
KHAN GEOMETRY QUESTION!!!!!!!!!HELP!!!!!!
Answer:
Arc VU = 44°
Step-by-step explanation:
Given:
Arc SV means ∠SOV = 120°
Arc VU means ∠VOU = ?
We know that, from central angle theorem, central angle made by arc is twice the angle made the same arc at the circumference.
∴ ∠SOU = 2 × ∠STU
⇒ ∠SOU = 2(82°)
⇒ ∠SOU = 164°
Now, from angle addition theorem,
∠SOU = ∠SOV + ∠VOU
⇒ 164° = 120° + ∠VOU
⇒ 164° - 120° = ∠VOU
⇒ ∠VOU = 44°
Therefore, the measure of the arc VU is 44°.
5% tax on $1.50 What us total cost
Answer:
$1.58
Step-by-step explanation:
1.50 multiplied by 1.05
answer is 1.575
rounded is 1.58
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Answer:
2.25
Step-by-step explanation:
just multiply .05 by 1.50 so that would be .075, so then add that by original price so 2.25. Don't Quote me on this its been awile.
What is parentheses one fourth parentheses cubed three
Answer:
(1/4) ^3 = 0.0833333333
runner is compared with the world record
holder during a race. A negative number means the
runner is ahead of the time of the world record holder.
A
positive number means that the runner is behind
the time of the world record holder. The table
shows the time difference between the runner and
the world record holder for each lap. What time
difference does the runner need for the fourth lap
to match the world record?
Answer:
-0.42
Step-by-step explanation:
To match the world record, the runner needs a time difference for the fourth lap that brings the total time difference from all laps to zero. This time difference is calculated based on the sum of time differences of the first three laps.
Explanation:This question is asking about the time difference that the runner needs for the fourth lap in order to match the world record.
Assuming that the total time difference after the first three laps is provided in the table, what you'll do is add these three time differences to get the total difference for the first three laps.
Let's say, for instance, the total after three laps is +15 seconds. Since a positive number means the runner is behind the world record holder's time, we want the fourth lap to compensate for that and bring the total time difference to zero to match the world record. Therefore, the runner will need a -15 seconds time difference on the fourth lap.
Remember that a negative number means the runner ran the lap faster than the world record holder.
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Chloe is painting a room she uses 1/4 gallon of paint to cover 1/3 of a wall if the walls are all the same size how much paint will she need to cover one wall
Answer:
3/4 gallon
Step-by-step explanation:
we know that
Chloe uses 1/4 gallon of paint to cover 1/3 of a wall
so
using proportion
Find out how much paint she will need to cover one wall
Let
x ---> paint needed to cover one wall
[tex]\frac{(1/4)}{(1/3)}=\frac{x}{1}\\\\x=\frac{1}{4} :\frac{1}{3}\\\\x=\frac{3}{4}\ gal[/tex]
What is the value of h in the figure below? In this diagram BAD~CBD
Answer:
The correct option is E. 8
The value of h is 8 unit.
Step-by-step explanation:
Given:
Δ BAD ~ Δ CBD
AC = 20
DC = 4
∴ [tex]AD = AC - DC=20-4=16[/tex]
To Find:
h = ?
Solution:
Δ BAD ~ Δ CBD ................Given
If two triangles are similar then their sides are in proportion.
[tex]\frac{BD}{CD} =\frac{AD}{BD} =\frac{BA}{CB}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\dfrac{BD}{CD} =\dfrac{AD}{BD}[/tex]
[tex]\dfrac{h}{4} =\dfrac{16}{h}\\\therefore h^{2}=64\\\therefore h=8\ unit[/tex]
The value of h is 8 unit.
Answer:
8
Step-by-step explanation:
is y=5x+7 liner, nonlinear, or both
Please help!!
1. Solve the following system of equations by graphing.
x + 2y = 8
x + 2y = -4
What is the solution?
(3, 5), no solution, infinite solutions, none of the above
2. The ordered pair (4,2) is a solution to the system of inequalities below.
y>-3x+2
y<2x+1
True or False
3.When solving the system by substitution, what would you plug into the second equation for the letter x?
x+2y=4
2x+2y=6
x = 2, x = 4-2y, x = 4, x = 2y+4
4. There is no solution to the system below.
2x + 4y = 8
x + 2y = 6
True or False
Answer:
(Q.1) No solution
(Q.2) True
(Q.3) x = 4 - 2y
(Q.4) True
========================================
Step-by-step explanation:
(Q.1) As shown in the first attached figure.
By graphing. x + 2y = 8 & x + 2y = -4
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
===================================================
(Q.2) As shown in the second attached figure.
By graphing the system of inequalities y> -3x+2 & y<2x+1
The Shaded area represents the solution of the system of inequalities
And the point (4,2) is inside the shaded area
So, The ordered pair (4,2) is a solution to the system of inequalities.
====================================================
(Q.3) solving the system { x+2y=4 & 2x+2y=6 } by substitution
From the first equation x + 2y = 4
we will find x in terms of y then plug it into the second equation
So, x + 2y = 4 ⇒ x = 4 - 2y
=====================================================
(Q.4) As shown in the third attached figure.
By graphing. 2x + 4y = 8 & x + 2y = 6
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
how to do this?? give me a solution its confusing me?!!
Answer:
t = 3h
Step-by-step explanation:
Given
h = [tex]\frac{1}{3}[/tex] t
Multiply both sides by 3 to clear the fraction
3h = t
REALLY NEED HELP ASAP!!!!!!!
Answer: OPTION C
Step-by-step explanation:
There are some transformations for a function f(x). Some of them are shown below:
1. If [tex]f(x)+k[/tex], the function is shifted up "k" units.
2. If [tex]f(x)-k[/tex], the function is shifted down "k" units.
3. If [tex]f(x+k)[/tex], the function is shifted left "k" units.
4. If [tex]f(x-k)[/tex], the function is shifted right "k" units.
In this case you know that the function "g" is the transformation of the function "f".
Observe that the function "f" intersects the y-axis at:
[tex]y=2[/tex]
And the function "g" intersects the y-axis at:
[tex]y=-2[/tex]
Therefore, since both functions are 4 units apart, you can conclude that the function "f" was shifted down 4 units to get the function "g".
Then, the rule that shows that transformation is:
[tex]g(x)=f(x)-4[/tex]
Which is a factor of 144 − 49x2?
12 - 7x2
72 – 7x2
12 – 7x
72 + 7x
Answer:
(12-7x)
Step-by-step explanation:
144 − 49x²
by observation, we can see that 144 = 12² and 49 = 7²
hence we can rewrite the equation
144 − 49x²
= 12² - 7²x²
= 12² - (7x)²
recall that the expression x² - y² = (x+y)(x-y)
hence,
12² - (7x)²
= (12 + 7x)(12-7x)
(12-7x) appears in the expression above, hence 12 -7x is a factor
Answer:
Answer is C
Step-by-step explanation:
10 points!
Find the shape resulting from the cross-section of the cylinder.
Answer:
Triangle
Step-by-step explanation:
cross section through the cone perpendicular will be a triangle with the base of the cone's base diameter.
The graph of a system of inequalities is shown.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?
y > 2x
x + 2y ≤ –8
y ≥ 2x
x + 2y < –8
y < 2x
x + 2y ≥ –8
y ≤ 2x
x + 2y > –8
Answer:
The system is
[tex]x+2y \leq -8[/tex]
[tex]y> 2x[/tex]
Step-by-step explanation:
Part 1
Find the equation of the first inequality
we know that
The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)
The slope is equal to
[tex]m=(-4+1)/(0+6)\\m=-0.5[/tex]
The equation of the solid line in slope intercept form is
[tex]y=-0.5x-4[/tex]
Everything below the line is shaded
so
The inequality is
[tex]y \leq -0.5x-4[/tex]
Convert to standard form
Adds 0.5x both sides
[tex]0.5x+y \leq -4[/tex]
Multiply by 2 both sides
[tex]x+2y \leq -8[/tex] -----> First inequality
Part 2
Find the equation of the second inequality
we know that
The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)
This line represent a proportional relationship, because the line passes through the origin
The slope is equal to the constant of proportionality
[tex]k=(-4)/(-2)=2[/tex]
The equation of the dashed line is
[tex]y=2x[/tex]
Everything to the left of the line is shade
so
The inequality is
[tex]y> 2x[/tex] -----> Second inequality
see the attached figure to better understand the problem
The system of inequalities represented by the given graph is y > 2x and x + 2y ≤ –8.
Explanation:The system of inequalities represented by the given graph is:
y > 2xx + 2y ≤ –8We can determine the equations of the lines using the given points:
Line 1: y = mx + b, where m is the slope and b is the y-intercept. Using the points (–6, –1) and (0, –4), we can calculate the slope: m = (–4 – (–1)) / (0 – (–6)) = –3 / 6 = –1/2. Thus the equation of Line 1 is y = –(1/2)x – 3.
Line 2: Using the points (–2, –4) and (0, 0), we can calculate the slope: m = (0 – (–4)) / (0 – (–2)) = 4 / 2 = 2. Thus the equation of Line 2 is y = 2x – 4.
By looking at the graph, we can see that everything below Line 1 (shaded area) satisfies y > 2x, while everything below or on Line 2 (including the line itself) satisfies x + 2y ≤ –8.
Learn more about Graph of a system of inequalities here:https://brainly.com/question/35474217
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"If two lines intersect, then the intersection is a point." What is the hypothesis? Two lines intersect
Intersection is a point
Points have intersection
Intersection happens at a point
Answer:
Hypothesis is: Intersection happens at a point
Step-by-step explanation:
A hypothesis in science is a suggested explanation of something that has a consequence or leads to an occurrence. Usually it will be written in the form of an "if and then" statement.
Such statement explains what would occur, or follow if the possibility enunciated in the "if" part of the statement happens.
In this case the hypothesis is that if there is intersection of lines, it has to occur at a point. Therefore the closest to that statement among the options given in the problem is the last one: "Intersection happens at a point"
Answer:
Two Line Intersect
Step-by-step explanation:
I got it right on the test :)