2x²-5x-12=0 (simplify solution set)

Answer:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

Given equation: -3x + 7y = 21

Slope-Intercept Form: y = mx + b -

where:

Note: parallel lines have the same slope.

1. Rewrite the given equation in slope-intercept form:

[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]

Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.

2. Find the equation of the parallel line:

substitute the point (4, 9) into the equation to find the value of b

[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]

[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

3. Check your work:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]

[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

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Answer:

[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.

Slope intercept form

y = mx + c

Here,

m = slope

c = y-intercept

Let us write the given equation in slope-intercept form.

− 3x + 7y = 21

Add 3x to both sides.

7y = 3x + 21

Divide both sides by 7.

[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]

We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.

The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.

( 4, 9 ) → ( x , y )

m → 3/7

Let us find the value of c

[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]

And now let us write the equation of the new line.

[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Answer:

2.4 hours

Step-by-step explanation:

Because 1 hour Randy clean 1/4 of the room and Trey is 1/6. So we add both together and get that they clean 5/12 of the office in one hour. So 2.4 hours is the greatest amount of time it would take them to clean offices together

Step-by-step explanation:

F1/A1 = F2/A2

10/2=F2/4

5=F2/4

F2=5x4

F2=20

Solution 1 :-

>> -3 (3 - x) = 2x + 5

>> -3 × (3 - x) = 2x + 5

>> -9 + 3x = 2x + 5

>> 3x - 2x = 9 + 5

>> x = 14

Solution 2 :-

>> -6 - 9p = 3p

>> -9p - 3p = 6

>> -12p = 6

>> p = -1/2

Solution 3 :-

>> -5 (-4 - a) = 3a + 8

>> -5 × (-4 - a) = 3a + 8

>> 20 + 5a = 3a + 8

>> 5a - 3a = 8 - 20

>> 2a = -12

>> a = -12 / 2

>> a = -6

Solution 4 :-

>> s - 6 = -5s

>> s + 5s = 6

>> 6s = 6

>> s = 6 / 6

>> s = 1

Answer:

1) x = 14

2) p = - [tex]\frac{1}{2}[/tex]  (- 1/2)

3) a = -6

4) s = 1

work shown in image :)

hope this helps!!

Answer:

y = 4x - 12

Step-by-step explanation:

Answer:

A and B are correct

Step-by-step explanation:

The middle letter represents the vertex of an angle. For instance, angle ABC has a vertex at B. Because the letter "e" is in the middle of angle FED and angle DEF, it represents the vertex of those angles. Hope this helps

Hey there!

ASSUMING:

p = 2l + 2w

IF SO:

• We already have our perimeter (p) & our width (w), now you have to find our length (l)

160 = 2l + 2(34)

CONVERT TO:

2l + 2(34) = 160

SIMPLIFY IT:

2l + 68 = 160

SUBTRACT 68 to BOTH SIDES:

2l + 68 - 68 = 160 - 68

SIMPLIFY IT:

2l = 160 - 68

2l = 92

DIVIDE 2 to BOTH SIDES:

2l/2 = 92/2

SIMPLIFY IT:

l = 92/2

l = 46

Therefore, your answer should be:

l = 46

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

g(-0.0001) = -9

g(0.0001) = -1

g(0) = -1

g(9) undefined

Step-by-step explanation:

g(9) undefined .because the graph have an empty circle

at (9 , 0) which means g is not defined at 9.

Answer:

Step-by-step explanation:

-4(5x-3)+12

-20x+12+12

20x+24

my answer is 20x+24.

The simplified form of the given expression -4(5x-3)+12 would be 20x+24.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

-4(5x-3)+12

Open the bracket

-20x+12+12

Solve the like terms;

20x+24

Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.

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The area of the logo using the length and the width is 162 cm²

Length of logo = 16 cm

Width of logo = 12 cm

Area of logo = length × width

= 16 cm × 12 cm

= 192 cm²

Therefore, the area of the logo using the length and the width is 162 cm²

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 4x-3+5=2x+7-8x \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Simplify \ both \ sides \ of \ the \ equation. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{4x+2=-6x+7 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Add \ 6x \ to \ both \ sides.} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Subtract \ 2 \ from \ both \ sides. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Divide \ both \ sides \ by \ 10.} \end{gathered}$}[/tex]

↓

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Verification} \end{gathered}$}[/tex]

[tex]\sf{4\times\dfrac{1}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{\dfrac{4}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{2-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

Cancel 2

[tex]\sf{2-3+5=1+7-8\times\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-4 }[/tex]

[tex]\sf{-1+5=1+7-4}[/tex]

[tex]\sf{4=1+7-4}[/tex]

[tex]\sf{4=8-4}[/tex]

[tex]\sf{4=4}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Checked} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

x = 14.02 units

Step-by-step explanation:

Finding unknown value using Pythagorean theorem:

 This is an isosceles trapezium.  The two perpendiculars  divide the trapezium into two congruent triangles and a rectangle. Let the base of the triangle by 'y'. We can find the value of 'y' using Pythagorean theorem.      

In ΔABC,

                AC² = AB² + BC²

                   19² = 17 ² + y ²

                 361  = 289 + y ²

        361 - 289  = y ²

                      y ² = 72

                      y =√72

                      y = 8.49

x = 31 - 8.49 - 8.49

x = 14.02

Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.

Binomial distribution is known to be a kind of probability distribution whos models or show the probability of getting one of two outcomes in any  said number of points or parameters.

Note that:

5abc -2a² + 6abc

Add like terms

= 11abc - 2a²

5x³∙ 2x² -10x⁴ +3x⁵+ 3x∙(-2) x⁴

Simply

=5 . 2x³⁺² - -10x⁴ +3x⁵+ 3x∙ 2x⁴

=10x³⁺²  -10x⁴ +3x⁵+ 3∙ 2xx⁴

= 7x⁵ + 10x⁴

(t+2)²-4t

Simply

= (t² + 2t.2 + 2²) - 4t

=  (t² + 2t.2 + 4) - 4t

= t² + 4

The same applies for the rest. Therefore, one can say that Based on the four expressions written above (image attached) one can say that She is right about the remaining four expressions as they all can shown or expressed as binomials.

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Answer:

In the given Triangle problem, the three options are:

1.  m∠5 + m∠6 = 180°

2. ∠2+ ∠3 = ∠6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept: Consider Δ ABC with Exterior angles ∠1, ∠4 and ∠6.

Use the Exterior angle Property of Triangle which says that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior angle ∠1 we have:

∠1 = ∠5 + ∠3

Similarly, for Exterior ∠4 we have:

∠4 = ∠5 + ∠2

Similarly, for Exterior ∠6 we have:

∠6 = ∠2 + ∠3

Now, use the Triangle Sum Property which states that in a triangle sum of the measures of angles is equal to 180°

m∠2 + m∠3 + m∠5 = 180°

Linear Pair:

The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.

m∠5 + m∠6 = 180°

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Answer:

A and D

Step-by-step explanation:

Since tangent is opposite/adjacent,

Tan 40 in this case would be x/3.8 (i used x because we don't know what the value is)

So, you set it up as an algebra problem

Tan40 = x/3.8

Multiply both sides by 3.8

3.8tan40 = x, Option A

And then, angle E is 50 degrees

So tan 50 = 3.8/x

Multiply both sides by x

tan50x = 3.8

Divide both sides by tan50

x= 3.8/tan50

So, A and D are both correct

Answer:

The function is even because of symmetry over x axis

The value of the 6 is 3.

If you write 1 in word then you will write one and if you count the letter it will give you 3

Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.

counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.

So, if you write 6 in words you will write six and on counting the letter you will get 3.

Hence, 6 = 3 ans.

Therefore the value of the 6 is 3.

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The statement about using the line of best fit for the given scatter plot is; False

When we have a scatter plot, it is always best to look for the line of best fit or curve of best fit depending on the nature of the variation of the plotted points.

Now, from the scatter plot image attached, we can see that the points are already looking like a curved plot form and so what we will need her will be a curve of best fit and not a line of best fit plot and as such the statement about using a line of best fit plot is false.

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0.90 nearest tenth is 9 since there is no other number to help round it over.

Answer:

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Step-by-step explanation:

First highlight the important information from the question.

A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?

So, first she descends -128 feet, then she ascends 45 feet to swim with dolphins. So, now that we have the important information highlighted we can solve the problem.

-128+45=-83.

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Hope this helps!

If not, I am sorry.

The value of m will be; m  = (-∞ , - 15/4) ∪ ( 1 , ∞ ).

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given: line y = mx  + 3 intersects the line 3x + 4y + 12 = 0 at two distinct points.

To find the set of values of m.

The system of equations are;

y = mx  + 3

3x + 4y + 12 = 0

The intersection point are (1, −15/4)

So, the value of m will be

m  = (-∞ , - 15/4) ∪ ( 1 , ∞ )

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Answer:

£69

Step-by-step explanation:

Given information:

Cost of buying a dress and shoes:

⇒ £50 + £43 = £93

Discount:

⇒ 1/3 of £93 = 1/3 × 93 = £31

Cost of goods after discount is applied:

⇒ £93 - £31 = £62

Addition of shipping and handling:

⇒ £62 + £7 = £69

Therefore, Ruth will pay £69 if she buys a dress and shoes.

Answer: 72 cubic inches

Step-by-step explanation:

The formula for the volume of a cone: [tex]\dfrac{1}{3}\pi r^{2}h[/tex]

Formula for the volume of a cylinder: [tex]\pi r^{2}h[/tex]

We are given that a cylinder should fit exactly inside the cone

Upon comparing the two equations above, we get:

[tex]$$Volume of cone = \dfrac{1}{3}\text{Volume of cylinder}[/tex]

Since we are given the volume of cone is 24 cubic inches, we can write down the below:

[tex]24 = \dfrac{1}{3}\text{Volume of cylinder }\\ \text{Volume of cylinder = 72 cubic inches}[/tex]

Therefore, we can conclude that if the volume of the cylinder is 72 cubic inches, then the cone with volume of 24 cubic inches can fit exactly in.

Answer:

[tex]V_{cylinder}=72\:in^3[/tex]

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]

Step-by-step explanation:

θ = 41°

Hypotenuse = BC = 13.5 cm

opposite = AB = ?

We will use the trigonometric ratio of sin.

[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

a=-110

d=-102-(-110)=-102+110=8

let n be the number of terms.

74=-110+(n-1)×8

74=-110+8n-8

74+118=8n

192=8n

n=192/8=24

[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]

Answer:

5.1

Step-by-step explanation:

A rational number is any number that can be written as a fraction, or is a decimal that terminates or repeats.