which statement is true about the solution of this system of equations?

{x+3y=-4
3x+9y=-12

Answer:

The equation of the perpendicular line to y=-4*x-5 is [tex]y=\frac{1}{4}*x+\frac{7}{2}[/tex]

Step-by-step explanation:

Perpendicular lines are two or more lines that intersect at an angle of 90 degrees. Being  y = m * x + b the equation of a line, two lines, with a slope other than zero, are orthogonal or perpenducillary if and only if the product of their slopes is -1. In other words, if two lines are perpendicular, they have their slopes reversed and sign changed.

In this case, with y = -4x-5 the slope will be -4. So the slope of the perpendicular line will be [tex]\frac{1}{4}[/tex]. Then the equation of the perpendicular line will be:

[tex]y=\frac{1}{4}* x+b[/tex]

To find the value of b, you know the value of the point (-2,3). So x = -2 and y = 3. Replacing in the equation of the perpendicular line, you have:

[tex]3=\frac{1}{4}* (-2)+b[/tex]

Solving, you get:

[tex]3=-\frac{1}{2}+b[/tex]

[tex]3+\frac{1}{2}=b[/tex]

[tex]\frac{7}{2}=b[/tex]

The equation of the perpendicular line to y=-4*x-5 is [tex]y=\frac{1}{4}*x+\frac{7}{2}[/tex]

Answer:

A ray is a part of a line.

Step-by-step explanation:

yes

A ray is a part of a line - True

Answer:

thx for giving brainliest

Answer:

$3700

Step-by-step explanation:

Given that:

Initial amount = $1400

Amount deposited per week = 50

Amount after 47 weeks =?

Using the Arithmetic Progression relation :

Tn = A + (n - 1)d

Weekly deposit = d = 50

A = initial / first deposit = 1400

n = number of deposits

T47 = 1400 + (47 - 1)50

T47 = 1400 + (46)*50

T47 = 1400 + 2300

T47 = 3700

Answer:

$3750

Step-by-step explanation:

T47 = 3750

Answer: 36 tables

Step-by-step explanation: Just divide 288 by 8. I hope this helps!

The statement (B) " Its range includes all real numbers." is correct because it does not describe the cosine function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know, the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The domain of a cos function is al real numbers and the range of the cos function is [-1, 1]

The cos function is the reciprocal of the secant.

The cycle repeats every 21 radians.

Thus, the statement (B) " Its range includes all real numbers." is correct because it does not describe the cosine function.

Learn more about the function here:

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Answer:

The number of applications received is approximately 30,000 and the success rate is approximately 32%.

Step-by-step explanation:

The application curve is red in colour, on 2001 trace it the right hand side, the number of applications received is approximately 30,000.

The percentage of grants funded is equal to the success rate which is the curve green in colour. On 2001 trace the curve to the left hand side, the success rate is approximately 32%.

Answer:

D

Step-by-step explanation:

plug in the coordinates for x and y

Answer:

14/20 = 7/10 so I believe it would be 7 days out of 10

Step-by-step explanation:

Answer:

Wouldn't it be 14/20

Step-by-step explanation:

Answer:

The base and height of the solid is 5.5cm

Step-by-step explanation:

Given

[tex]Surface\ Area = 181.5cm^2[/tex]

Required

Determine the dimensions that maximizes the volume

Let the base dimension be x and the height be h

The volume is calculated as:

[tex]Volume =x^2 * h[/tex]

[tex]Volume =x^2h[/tex]

181.5 =x^2h

The surface area (S) is calculated as this:

[tex]S = 2(x^2 + xh + xh)[/tex]

[tex]S = 2(x^2 + 2xh)[/tex]

[tex]S = 2x^2 + 4xh[/tex]

Substitute 181.5 for S

[tex]181.5 = 2x^2 + 4xh[/tex]

Make h the subject:

[tex]4xh = 181.5 - 2x^2[/tex]

[tex]h = \frac{181.5 - 2x^2}{4x}[/tex]

Substitute [tex]h = \frac{181.5 - 2x^2}{4x}[/tex] in [tex]Volume =x^2h[/tex]

[tex]V = x^2(\frac{181.5 - 2x^2}{4x})[/tex]

[tex]V = x(\frac{181.5 - 2x^2}{4})[/tex]

[tex]V = \frac{1}{4}(x)(181.5 - 2x^2)[/tex]

[tex]V = \frac{181.5x}{4} - \frac{2x^3}{4}[/tex]

[tex]V = \frac{181.5x}{4} - \frac{x^3}{2}[/tex]

To get the maximum, we differentiate V with respect to t and set the differentiation to 0

[tex]dV = \frac{181.5}{4} - \frac{3x^2}{2}[/tex]

Set to 0

[tex]0 = \frac{181.5}{4} - \frac{3x^2}{2}[/tex]

[tex]\frac{3x^2}{2} = \frac{181.5}{4}[/tex]

Multiply through by 4

[tex]4 * \frac{3x^2}{2} = \frac{181.5}{4} * 4[/tex]

[tex]2*3x^2 = 181.5[/tex]

[tex]6x^2 = 181.5[/tex]

[tex]x^2 = \frac{181.5}{6}[/tex]

[tex]x^2 = 30.25[/tex]

[tex]x = \sqrt{30.25[/tex]

[tex]x = 5.5[/tex]

Recall that:

[tex]h = \frac{181.5 - 2x^2}{4x}[/tex]

[tex]h = \frac{181.5 - 2 * 5.5^2}{4 * 5.5}[/tex]

[tex]h = \frac{181.5 - 60.5}{22}[/tex]

[tex]h = \frac{121}{22}[/tex]

[tex]h = 5.5[/tex]

So, we have:

[tex]h = 5.5[/tex]

[tex]x = 5.5[/tex]

Hence, the base and height of the solid is 5.5cm

Answer:

answer Option A $9,722.36

I am 100% sure

Answer:

-⅜ is between -1 and 0

⅞ is between 0 and 1

-2½ is between -3 and -2 ( in the mid )

2½ is between 2 and 3 ( in the mid )

Answer:

x=4

Step-by-step explanation:

Answer:

7.60

0.76

0.2

0.2

hjlai

Answer:

The answer is S=D/H

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer: T= 3.54

Step-by-step explanation:

Step 1

Given that

The time period, T, s doirectly proportional  to the square root of the length, d, of the pendulum, we have that

T  ∝  [tex]\sqrt{d}[/tex]

Introducing the constant of proportionality, we have that

T= K[tex]\sqrt{d}[/tex].

Step 2

When d=6, T=5, K =?

T= K[tex]\sqrt{d}[/tex].

5 = k[tex]\sqrt{6}[/tex]

5=  k x 2.44949

k =5/2.44949

k =2.041

Therefore, when d = 3 , T= ?

T= K[tex]\sqrt{d}[/tex]

T= 2.041 x [tex]\sqrt{3}[/tex]

T= 3.53511≈ 3.54

Answer:

[tex]e^{t}+4e^{-4t}[/tex].

Step-by-step explanation:

To find the Laplace inverse of the above problem, we have to first solve the problem as a partial fraction, hence:

[tex]\frac{5s}{s^2+3s-4}=\frac{5s}{s^2+4s-s-4} \\\\=\frac{5s}{s(s+4)-1(s+4)}\\\\=\frac{5s}{(s-1)(s+4)}=\frac{A}{s-1}+\frac{B}{s+4}\\\\= \frac{A(s+4)+B(s-1)}{(s-1)(s+4)}\\\\Hence:\\\\\frac{A(s+4)+B(s-1)}{(s-1)(s+4)}=\frac{5s}{(s-1)(s+4)}\\\\A(s+4)+B(s-1)=5s\\\\to\ find \ A,put\ s=1:\\\\A(1+4)+B(1-1)=5(1)\\\\5A=5\\\\A=1\\\\to\ find \ B,put\ s=-4:\\\\A(-4+4)+B(-4-1)=5(-4)\\\\-5B=-20\\\\B=4\\\\Hence:\\\\\frac{5s}{s^2+3s-4}=\frac{1}{s-1}+ \frac{4}{s+4}\\\\[/tex]

[tex]L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]\\\\But\ L^{-1}[\frac{1}{s-a} ]=e^{at}\\\\Hence:\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]=e^{t}+4e^{-4t}\\\\=e^{t}+4e^{-4t}[/tex]

Answer:

x = 53°

Step-by-step explanation:

x + 127° = 180° (sum of angles on a straight line/supplementary angles)

Subtract 127 on both sides

x + 127 - 127 = 180 - 127 (subtraction property of equality)

x = 53°

[tex]\huge\underbrace\mathtt\blue{∆ᴀɴsᴡᴇʀ∆}[/tex]

[tex]1) \: \: \: \frac{34}{100} = 0.34[/tex]

[tex]2) \: \: \: \: \frac{23}{50} = \frac{23 \times 2}{50 \times 2} = \frac{46}{100} = 0.46[/tex]

[tex]3) \: \: \: \frac{6}{8} = \frac{6 \times 125}{8 \times 125} = \frac{750}{1000} = 0.008[/tex]

[tex]4) \: \: \: \frac{1}{3} = 0.3[/tex]

(for no. 4 check the image in the attachment)

Answer:

yehh it would be efffective

Answer:

64x^6

Step-by-step explanation:

Answer:

b or B is correct answer out of all

Answer:

I'll try my best to answer this but it could be A. and B.

Step-by-step explanation:

»(-2 is on the left side of the number line, the left side of number lines show negative numbers)

The reason why C. wouldn't be right is because -3 is on the same side where positive numbers would go, on the right side of 0. Meaning C. isn't a correct number line so it can't be the right answer..

I hope this helped!!

Answer:

Statement 1: Quadrilateral PQRT; line QSV; line PTV line QV bisects line RT, and line OR is parallel to line PV

Statement 3: angle QSR is congruent to angle VST

Statement 5: Triangle RSQ is congruent to angle TSV

Reason 1: Given

Reason 2: If a line bisects a segment, then it divides the segment into two congruent segments.

Reason 4: If two lines are parallel, then the alternate interior angles are congruent.

Step-by-step explanation:

The first statement will always be your given statements.

The given result is proved by ASA congruence criteria.

Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.

The given problem can be solved in statement and reason form as follows,

In triangles ΔQSR and ΔTSV,

Statement                                                           Reason

1. ∠QRS = ∠STV                                        Alternate interior angles for QR║PV

2. RS = TS                                                 QV bisects Line segment RT

3. ∠QRS = ∠VTS                                      Vertically opposite angles

4. ΔQSR ≅ ΔTSV                                     Triangles are congruent by ASA

Thus, QS =VS due to corresponding parts of congruent triangles.

Hence, QS = VS is proved by the ASA criteria for congruent triangles.

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Answer:

[tex]d = 17[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point (2, 8)

Point (17, 0)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

Answer:

2.5*5= 12.5

15-12.5=2.5

So in order to pay the 15 dollars in the photography club, she only has to pay 2.50