What is the equation of the line perpendicular to the line y = 3x + 2 and passing through the point (3, -4)?

Step-by-step explanation:

1: - 13= 7x + 4 - 4x

Isolate variables.

- 13= 7x + 4 - 4x

-13 = 3x + 4

-3x = 13+4

-3x = 17

x = -17/3

2: - b - 6 + 6b = 27

5b - 6 = 27

5b = 33

b = 33/5

3: - 5(5x - 2) = 65

-25x + 10 = 65

-25x = 55

x = -55/25

x = -11/5

Answer:

1). t ≥ -[tex]\frac{3}{2}[/tex]

2). k ≥ [tex]\frac{16}{3}[/tex]

3). y < -[tex]\frac{1}{2}[/tex]

4). b > [tex]\frac{250}{9}[/tex]

5). w ≤ 0

Step-by-step explanation:

1). [tex]14(\frac{1}{2}-t)\leq 28[/tex]

   [tex]\frac{14}{14}(\frac{1}{2}-t)\leq \frac{28}{14}[/tex]

   [tex]\frac{1}{2}-t\leq 2[/tex]

   [tex]-t\leq 2-\frac{1}{2}[/tex]

   [tex]-t\leq \frac{3}{2}[/tex]

   t ≥ -[tex]\frac{3}{2}[/tex]

2). 15k + 11 ≤ 18k - 5

   15k - 18k ≤ -5 - 11

   -3k ≤ - 16

   3k ≥ 16

     k ≥ [tex]\frac{16}{3}[/tex]

3). 44y > 11 + 88y - 22y

    44y > 11 + 66y

    44y - 66y > 11

    -22y > 11

    22y < -11

    [tex]\frac{22y}{22}<-\frac{11}{22}[/tex]

    y < [tex]-\frac{1}{2}[/tex]

4). [tex]\frac{7}{9}(b - 27) > \frac{49}{81}[/tex]

    [tex]\frac{7}{9}(b - 27)\times \frac{9}{7} > \frac{49}{81}\times \frac{9}{7}[/tex]

     (b - 27) > [tex]\frac{7}{9}[/tex]

     b > [tex]\frac{7}{9}+27[/tex]

    b > [tex]\frac{250}{9}[/tex]

5). 11w - 8w ≥ 14w

    3w - 14w ≥ 0

    -11w ≥ 0

    w ≤ 0

Answer:

6.4 x 10 to the power of 3

Step-by-step explanation:

always have 1 number after the decimal point and then times by ten to the power of 3.

Answer:

64x10²

Just move it to the left 2 times.

Answer:

whole number is the answer

Answer:

1084.5

Step-by-step explanation: 120.5*9 = 1084.5

Answer:

One pack = Rs 120.5

→ Multiply both the brackets and price by 9

9 packets = Rs 1084.5

Answer:

see explanation

Step-by-step explanation:

Given the ratio 30 : 12 ( divide both parts by 6 )

= 5 : 2

Given the ratio

40 : 16 ( divide both parts by 8 )

= 5 : 2

Thus the 2 ratios are equivalent and simplify to 5 : 2

Answer:

10:40

Step-by-step explanation:

3x4 = 12

4 x 4 = 16

5 x 4 = 20

so 10 x 4 = 40 (10:40)

Answer:

10:40

Step-by-step explanation:

Step 1: Reduce ratio to lowest value

3 : 12 = 1 : 4

*Divide by 3

Step 2: Solve ratio

Let 'x' represent the second number

1 : 4 = 10 : x

Multiple the left side by 10

10 : 40 = 10 : x

Therefore the second number in the ratio with 10 is 40

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Step 1: State what is given

2 hours playing games or 120 minutes

30 minutes reading email

Step 2: Put information into fraction

[tex]\frac{email}{games} = \frac{30}{120}[/tex]

Step 3: Simplify the fraction by 30

[tex]\frac{30}{120}=\frac{1}{4}[/tex]

Therefore the fraction representing how long he plays games and reads email is [tex]\frac{1}{4}[/tex]

Answer:

65

Step-by-step explanation:

TAB is an isosceles triangle by the point to tangent theorem theorem.

BAT and BAT are congruent because of the isosceles triangle definition.

CAT and ABT are right angles by the tangent theorem.  

Thus, CAB and CBA are both 90 - 65 = 25.

ACB is 130 because triangles' angles add up to 180.

APB is one half of ACB by the inscribed angles theorem.

The measure of the arc APB will be 230°. Then the correct option is D.

What is a circle?

It is the circle of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

We know that the tangents are equal.

Then triangle ΔATB is an isosceles triangle.

Then the angle ∠TAB and angle ∠TBA are congruent.

We know that the angle sum of a triangle is 180°.

∠TAB + ∠TBA + ∠ATB = 180°

               65° + 65° + z = 180°

                                  z = 50°

We know that the radius and tangent of circle make 90°.

And the angle sum of quadrilateral is 360°.

∠TAC + ∠TBC + ∠ATB + ∠ACB = 360°

                   90° + 90° + 50° + y = 180°

                                                y = 130°

Then the measure of the arc APB will be

x = 360° – 130°

x = 230°

The measure of the arc APB will be 230°.

Then the correct option is D.

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ2

Answer:

x=-1 or 5 or 2

Step-by-step explanation:

x³-6x²+3x+10=0

(x+1)(x-5)(x-2)=0

x+1=0 ⇒ x=-1

x-5=0 ⇒x=5

x-2=0 ⇒ x=2

Answer:

9^3

Step-by-step explanation:

9x9x9= 729

Answer:

[tex]T_{12} = 354294 + 354294i[/tex]

Step-by-step explanation:

Given

Geometric Sequence (GP)

[tex]T_1 = 2 + 2i[/tex]

[tex]r = 3[/tex]

Required

Determine T₁₂

The nth term of a GP is calculated as thus;

[tex]T_n = ar^{n-1}[/tex]

In this case;

[tex]n = 12[/tex];  [tex]r = 3[/tex] and [tex]a = T_1 = 2 + 2i[/tex]

Substitute these values in the above formula

[tex]T_{12} = (2 + 2i) * 3^{12-1}[/tex]

[tex]T_{12} = (2 + 2i) * 3^{11}[/tex]

[tex]T_{12} = (2 + 2i) * 177147[/tex]

Open the bracket

[tex]T_{12} = 177147 * 2 + 177147 * 2i[/tex]

[tex]T_{12} = 354294 + 354294i[/tex]

Hence, the 12th term of the sequence is [tex]T_{12} = 354294 + 354294i[/tex]

Answer:

The answer is -14/25 or - 0.56

Answer:

Following are the answer to this question:

Step-by-step explanation:

For calculating, matching, or arranging certain fractions, the benchmark fraction can be described as common fractions, that can be calculated or judged. It is most useful when measuring fractions to comparisons in a number line.

Given value:

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

         [tex]= 1+ \frac{1}{6}+\frac{1}{6}\\[/tex]

Start by setting up your two sets of parenthses.

Inside, we have the terms that compose each binomial.

Since x² breaks down into x · x, we use an x in each binomial.

The second term is the factors of -12 that add to the coefficient

of the middle term but what is the coefficient of the middle term?

If there is nothing written there, it's understood to be 1.

So factors of -12 that add to -1 are 4 and -4.

So we have (x + 4)(x - 3) which is our answer.

Answer:

x = 4 , x = -3

Step-by-step explanation:

x^2 - x - 12 = ( x - 4) ( x + 3)

x - 4 = 0 or x + 3 = 0

x = 4 or x = -3

Answer:

x = 85

Step-by-step explanation:

Step 1: Solve x

∠x = 180 - 27 - 68

∠x = 85

Therefore angle x equals 85

Answer:

85 degrees

Step-by-step explanation:

The sum of the angles of a triangle always add up to 180 degrees.

Here, we have two angles already given, so we can write:

27 + 68 + x = 180

95 + x = 180

Subtract 95 from both sides:

x = 180 - 95 = 85

The answer is thus 85 degrees.

~ an aesthetics lover

Answer: The maximum value is 35.94

Step-by-step explanation:

We have the function:

f(x) = -16*x^2 + 34*x + 20

This is a quadratic equation, and the first thing we can see is that the leading coefficient is smaller than zero, which means that the "arms" of the graph will go downwards, which means that the maximum of our function will be at the vertex.

First, we know that the vertex of a quadratic function is when f'(x) = 0.

f'(x) = 2*(-16*x) + 34 = 0.

x = -34/(-2*16) = 34/32 = 17/16.

Now we evaluate our function in the point x = 17/16.

f(17/16) = -16*(17/16)^2 + 32*(17/16) + 20 = 35.94

The maximum value is 35.94

Using the vertex, it is found that the maximum value of the function is of 36.

The function is given by:

[tex]f(x) = -16x^2 + 32x + 20[/tex]

Which is a quadratic function with coefficients [tex]a = -16, b = 32, c = 20[/tex].

The maximum value of a quadratic function with [tex]a < 0[/tex] is at the vertex, in which the value is:

[tex]f_{MAX} = -\frac{\Delta}{4a} = -\frac{b^2 - 4ac}{4a}[/tex]

Hence, in this problem:

[tex]f_{MAX} = -\frac{(32)^2 - 4(-16)(20)}{4(-16)} = 36[/tex]

The maximum value of the function is of 36.

A similar problem is given at https://brainly.com/question/16858635

Answer:

Step-by-step explanation:

First equation:  2x^2 + 6x = 0 factors into 2x(x + 3) = 0, so either x = 0 or x = -3.

Second equation:  x^2 + 9x + 14 = 0 factors into (x + 2)(x + 7) = 0.  Thus, either x = -2 or x = -7

Hi there! Hopefully this helps!

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|[tex]2x^{2} + 6x = 0[/tex]

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|First we factor out x

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[tex]x(2x+6)=0[/tex]

To find equation solutions, solve [tex]x = 0[/tex] and [tex]2x+6 = 0[/tex]

|

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[tex]x = 0[/tex]

[tex]x = -3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|

|[tex]x^{2}+ 9x + 14 = 0[/tex]

|

|To solve the equation, factor [tex]x^{2}+ 9x + 14[/tex] using formula [tex]x^{2} + (a + b)x + ab = (x+a) (x+b).[/tex] To find [tex]a[/tex] and [tex]b[/tex], set up a system to be solved.

|

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[tex]a + b = 9[/tex]

[tex]ab = 14[/tex]

|

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Since [tex]ab[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] have the same sign. Since [tex]a + b[/tex] is positive, [tex]a[/tex] and [tex]b[/tex] are both positive. List all such integer pairs that give product 14.

1, 14

2, 7

|

\/

Calculate the sum for each pair.

1 + 14 = 15

2 + 7 = 9

|

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The solution is the pair that gives sum 9.

[tex]a = 2[/tex]

[tex]b = 7[/tex].

|

\/

Rewrite factored expression [tex](x+a)(x+b)[/tex] using the obtained values.

[tex](x+2)(x+7)[/tex]

|

\/

To find equation solutions, solve [tex]x + 2 = 0[/tex] and [tex]x + 7 = 0[/tex].

|

\/

[tex]x = -2[/tex]

[tex]x = -7[/tex]

===============================================

Explanation:

If we had x^2+2x + ___, then 1 must go in the blank so that we have x^2+2x+1 = (x+1)^2

So we must add 1 to both sides to complete the square for the x terms. To find this value '1' we take half of the x coefficient 2 to get 1, then square it to get 1^2 = 1.

We have

x^2+y^2 + 2x - 20y - 20 = 0

x^2+y^2 + 2x - 20y - 20 + 1 = 0 + 1

(x^2+2x+1) + y^2 - 20y - 20 = 1

(x^2+2x+1) + y^2 - 20y = 1 + 20

(x+1)^2 + y^2 - 20y = 21

After completing the square for the x terms. Repeat for the y terms. Take half of -20 to get -10, which squares to 100. Add this to both sides

(x+1)^2 + y^2 - 20y = 21

(x+1)^2 + y^2 - 20y + 100 = 21+100

(x+1)^2 + (y - 10)^2 = 121

The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where

The center is (h, k) = (-1, 10). The radius is r = 11.

Answer:

Step-by-step explanation:

1.

[tex]4\sqrt{12}-\sqrt{50}-5\sqrt{48}\\\\4\sqrt{12}=8\sqrt{3}\\\\\sqrt{50}=5\sqrt{2}\\\\5\sqrt{48}=20\sqrt{3}\\\\=8\sqrt{3}-5\sqrt{2}-20\sqrt{3}\\\\\mathrm{Add\:similar\:elements:}\:8\sqrt{3}-20\sqrt{3}=-12\sqrt{3}\\\\=-12\sqrt{3}-5\sqrt{2}[/tex]

2.

[tex]\sqrt{8}\sqrt{5}\sqrt{10}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{a\times b}\\\\=\sqrt{8\times \:5\times \:10}\\\\=\sqrt{400}\\\\\mathrm{Factor\:the\:number:\:}\:400=20^2\\\\=\sqrt{20^2}\\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a\\\\\sqrt{20^2}=20[/tex]

3.

[tex]\sqrt{45}+\sqrt{180}+\sqrt{80}\\\\\sqrt{45}=3\sqrt{5}\\\\\sqrt{180}=6\sqrt{5}\\\\\sqrt{80}=4\sqrt{5}\\\\=3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\\mathrm{Add\:similar\:elements:}\:3\sqrt{5}+6\sqrt{5}+4\sqrt{5}\\\\=13\sqrt{5}[/tex]

Answer:

1) YTW

2) WT, TZ

3) UTZ

4) Right angle

  Acute angle

  Obtuse angle

  Right angle

5) TU

Answer:

BC = 1/2 AC

2m angle DBC = m angle ABC

Angle ABC is bisected by ray BD

m∠WUT = 38°

Step-by-step explanation:

For both questions, we use the Angle Bisector Theorem.

Question 1:

We know since ray DB bisects ABC, AB and BC are congruent. They are split into 2 equal parts. Therefore, we know that if we take half of mAC, we should get either mBC or mAB. Therefore, the 1st statement is correct.

Since it is ray DB bisecting ABC, it created 2 right angles. If angle DBC was bisected, it would create 2 new angles that were 45° each, so the 2nd statement is incorrect.

We know that line ABC is equal to 180°. So if we add m∠ABD and m∠DBC (they both are 90°, as denoted in the picture) together, we should get 180°. Also, since they are congruent angles, one angle multiplied twice would also be 180°. Therefore, the 3rd statement is correct.

The Angle Bisector Theorem doesn't state that the bisector and one segment would be congruent. The length of the bisector could be anything and is not marked congruent to the other segments. Therefore, the 4th statement is incorrect.

Since we see that there is a bisector DB bisecting line ABC, creating 2 congruent segments and angles, we know that the 5th statement is correct.

Question 2:

The Angle Bisector Theorem states that a bisector that bisects 2 angles will become 2 smaller but congruent angles. So,

Step 1: Find x

4x + 6 = 6x - 10

6 = 2x - 10

16 = 2x

x = 8

Step 2: Find m∠WUT

m∠WUT = 6x - 10

m∠WUT = 6(8) - 10

m∠WUT = 48 - 10

m∠WUT = 38°

Answer:

n^3 + 2n -2

Step-by-step explanation:

Remove the parentheses and simplify:

-8n^3 + 4n - 8 + 7n^3 - 2n + 6

n^3 + 2n -2.

Answer:

Step-by-step explanation:

We have to add the like terms. Like terms are with variables of same power.

-8n³ and 7n³  are like terms , now add the coefficient of n³ , -8 + 7 = -1

-8n³ + 7n³ = -1n³

(-8n³ + 4n - 8) + (7n³ - 2n + 6 )

Combine like terms

= -8n³ + 7n³    + 4n - 2n  - 8 + 6

= -1n³ + 2n - 2

Answer:

[tex]\large \boxed{\text{Q31, D. 6.00 F; 32. C. N21.75; Q33. A. 168.00 F}}[/tex]

Step-by-step explanation:

Your graph is hard to read, so I re-drew it as best I could.

You must first develop an equation relating francs and naira.

The line goes through the origin, so the general equation is

y = kx

One of the points is (40,240).

[tex]\begin{array}{rcl}F & = &k \times N\\240 & = &k \times 40\\k & = & \dfrac{240}{40}\\\\k&=&\textbf{6 F/N}\\\end{array}\\\text{The equation is $\large \boxed{\mathtbf{F = 6 N}}$}[/tex]

Q 31.

[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 1.00\\& = & \mathbf{6.00}\end{array}\\\text{The equivalent value of N1.00 is $\large \boxed{\textbf{6.00 F}}$}[/tex]

Q 32.

[tex]\begin{array}{rcl}F & = &6N\\130.5& = & 6 N\\N&=& \dfrac{130.5}{6}\\\\& = & \mathbf{21.75}\\\end{array}\\\text{The equivalent value of 130.5 F is $\large \boxed{\textbf{N21.75}}$}[/tex]

Q 33.

[tex]\begin{array}{rcl}F & = &6N\\& = & 6 \times 28.00\\& = & \mathbf{168.00}\end{array}\\\text{An amount of N28.00 is $\large \boxed{\textbf{168.00 F}}$}[/tex]

Answer:

The numbers i and V3 are elements of the set.

Step-by-step explanation:

The rational numbers are those which can be written as fractions. These are the numbers which can be repeating elements and terminating decimals. All integers can be set of rational numbers. The statements which is not true is statement  which states that numbers i and V3 are elements of the set.

Answer:

15,9,3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \sf{ \frac{1}{3} \times \frac{2}{5} }[/tex]

▪️To multiply one fraction by another , multiply the numerators for the numerator , and multiply the denominators for its denominator.

⇒[tex] \sf{ \frac{1 \times 2}{3 \times 5} }[/tex]

⇒[tex] \sf{ \frac{2}{15} }[/tex]

Hope I helped!

Best regards!

Answer:

Not enough tables.

Step-by-step explanation:

Circumference is 2*pi*r

The diameter is 2 times the radius or 2r, if the table diameter is 180cm. All we need to do is multiply by pi (3.14159) to get the circumference.

180*pi = 556.48cm

If each guest needs 70cm then we divide the circumference by 70

556.48/70 = 8.08 but we cant have a portion of a person so we can fit 8 people per table.

18 tables with 8 at a table is 8 x 18 = 144

If 145 guests are attending then there aren't enough tables, you are 1 table short.

Answer:

Step-by-step explanation:

Given that:

Keiko sold 3 less than three-fourths of his sister's sale.

To find:

Expression that represents what Keiko sold ?

[tex]1.\ \dfrac{3}{4} x - 3 \\2.\ \dfrac{3}{4} x + 3 \\ 3.\ 3 x + \dfrac{3}{4} \\4.\ 3x - \dfrac{3}{4}[/tex]

Solution:

First of all, let the sales done by Keiko's sister = [tex]x[/tex]

Now, let us consider the Keiko's sale word by word.

3 less than three-fourths of his sister's sale.

i.e. subtract 3 from the expression obtained in 1st line.

[tex]\dfrac{3}{4}x-3[/tex]

So, sales done by Keiko = [tex]\dfrac{3}{4}x-3[/tex]

So, correct answer is:

[tex]1.\ \dfrac{3}{4}x-3[/tex]

[tex]\frac{3}{4}x-3[/tex]

An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Let [tex]x[/tex] denotes sale of sister of Keiko.

As Keiko sold [tex]3[/tex] less than three-fourths of his sister's sales,

Sales of Keiko [tex]=\frac{3}{4}x-3[/tex]

For more information:

https://brainly.com/question/19585043?referrer=searchResults