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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.

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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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]

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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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

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:

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:

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.

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]

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

Answer:

0.06

Step-by-step explanation:

If you round 0.566 to the nearest tenth it would be 0.06

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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

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 :)

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°.

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.

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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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.

The system of inequalities represented by the given graph is:

We 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.

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Answer:

see explanation

Step-by-step explanation:

To graph the line, we require 2 points

Find the intercepts, that is where the graph crosses the x and y axes

To find the x- intercept let y = 0 in the equation and solve for x

x - 3 = 0 ( add 3 to both sides )

x = 3 ⇒ (3, 0 ) ← x- intercept

To find the y- intercept let x = 0 in the equation and solve for y

- y - 3 = 0 ( add 3 to both sides )

- y = 3 ( multiply both sides by - 1 )

y = - 3 ⇒ (0, - 3 ) ← y- intercept

Plot the points (3, 0) and (0, - 3) and draw a straight line through them

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:

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.

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

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.

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

Answer:

X=20

you subtract 15 from 75 to get 60 then divide 60 by 3 to get 20

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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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

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]

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:

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]

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]

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.

Answer:

(1/4) ^3 = 0.0833333333