Given f(x) = -2 ang g(x) = 4x - 8, find h(x) = f(x) + g(x)

Answer:

m ∠ UVT = 97° is the required answer.

Step-by-step explanation:

Given:

m∠WVU = 169°

m∠WVT = (2x + 20)°

m∠UVT = (3x + 19)°

To Find:

m∠UVT = ?

Solution:

Angle Addition Postulate is that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures.

So By applying this property in the diagram below we get,

m∠ WVT + m∠UVT = m∠WVU ............{Angle Addition Postulate}

[tex](2x+20) + (3x+19) = 169\\5x + 39 = 169\\5x=169-39\\5x=130\\\therefore x=\frac{130}{5} \\\therefore x=26\\[/tex]

Now,

m∠UVT = (3x + 19)°

Substituting x = 26 we get

  m∠UVT = 3 ×26 + 19

                = 78 +19

∴ m∠UVT = 97°

Answer:

no 4x and -x can be combined to form 3x, and 5y and 3y can be combned to form 8y. the correct equation should be 3x+8y-12

Step-by-step explanation:

Required number is [tex]\frac{-13}{5}[/tex] and required expression is n – 10 = 6n + 3

Given that  

Ten less than a number is three more than six times the number.

Number is represented by variable "n"

Need to determine equation and the number.

Ten less than number means subtracting 10 from the number  

As number is n so ten less than number = n – 10   ------(1)

Six times the number = number multiplied by 6 = 6n  

So three more than Six times the number = 6n + 3 --------(2)

As ten less than number is equal to  3 more than six times the number  

=> n – 10  = 6n + 3

Solving the above expression for n we get

-10-3 = 6n – n

=> 5n = -13

[tex]\Rightarrow \mathrm{n}=-\frac{13}{5}[/tex]

Hence required number is [tex]-\frac{13}{5}[/tex] and required expression is n – 10  = 6n + 3

Answer:

4 g after 30 seconds.

Step-by-step explanation:

After 10 seconds 32 * 1/2  = 16 g are present.

After 20 seconds 32 * (1/2)^2 = 8 g are present

After 30 seconds 32 * (1/2)^3 = 4 g are present.

x equals 47 degrees

Remember you must provide full questions in order to get excellent and precise answers. However, I have attached a figure in order to set the problem in context. Here we have a triangle. The most basic definition for a triangle is a polygon with three edges and three vertices, but there is something that is very important for all triangles:

By knowing this, we can write:

[tex]x^{\circ}+95^{\circ}+38^{\circ}=180^{\circ} \\ \\ Isolating \ x: \\ \\ x^{\circ}=180^{\circ}-95^{\circ}-38^{\circ} \\ \\ x^{\circ}=47^{\circ} \\ \\ \\ Where: \\ \\ \boxed{x=47}[/tex]

Area of triangles: https://brainly.com/question/12051125

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To find the roots of the polynomial equation x^3 - 5x + 5 = 2x^2 - 5, rearrange the equation to equal zero and use methods such as synthetic division or factoring to solve the cubic equation.

To find the roots of the polynomial equation x3 - 5x + 5 = 2x2 - 5, we need to set the equation equal to zero and rearrange it:

x3 - 2x2 - 5x + 5 + 5 = 0

x3 - 2x2 - 5x + 10 = 0

Now, we can use various methods to solve this cubic equation, such as synthetic division, factoring, or using a graphing calculator. On finding the roots of the equation, we can determine the values of x.

Answer:

The answers are "(f+g)(x)> 3 for all values of x" and "(f+g)(x)<6 for all values of x".

Step-by-step explanation:

Answer:

The values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].

Step-by-step explanation:

Given:

The equation to solve is given as:

[tex]5x^5+6x^4+80x^3+96x^2=0[/tex]

Factoring [tex]x^2[/tex] from all the terms, we get:

[tex]x^2(5x^3+6x^2+80x+96)=0[/tex]

Now, rearranging the terms, we get:

[tex]x^2(5x^3+80x+6x^2+96)=0[/tex]

Now, factoring [tex]5x[/tex] from the first two terms and 6 from the last two terms, we get:

[tex]x^2(5x(x^2+16)+6(x^2+16))=0\\x^2(x^2+16)(5x+6)=0[/tex]

Now, equating each factor to 0 and solving for 'x', we get:

[tex]x^2=0\\x=0\ and\ 0\\\\5x+6=0\\x=\frac{-6}{5}=1.2\\\\x^2+16=0\\x^2=-16\\x=\sqrt{-16}=\pm 4i[/tex]

There are 3 real values and 2 imaginary values. The value of 'x' as 0 is repeated twice.

Therefore, the values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].

Elena is wrong, because the two sides of equation are not equal for all values of x

Step-by-step explanation:

An equation of x is true for all values of x when the left hand side

is equal to the right hand side

To prove that an equation is true for all values of x do that

Lets check that with given equation 5(x + 2) = 5x + 10

∵ 5(x + 2) = 5x + 10

- Simplify the left hand side

∵ 5(x) + 5(2) = 5x + 10

∴ 5x + 10 = 5x + 10

- Subtract 5x from both sides

∴ 10 = 10

∵ L.H.S = R.H.S

∴ The equation is true for all values of x

Lets do that with Elena's equation

∵ 20(x + 2) = 4(5x + 10) + 31

- Simplify the two sides of the equation

∵ 20(x) + 20(2) = 4(5x) + 4(10) + 31

∴ 20x + 40 = 20x + 40 + 31

- Add like terms in the right hand side

∴ 20x + 40 = 20x + 71

- Subtract 20x from both sides

∴ 40 = 71 ⇒ and that not true

∵ L.H.S ≠ R.H.S

∴ The equation is not true for all values of x

Elena is wrong, because the two sides of equation are not equal for all values of x

Learn more:

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Elena took the original equation, multiplied both sides of it by 4 and added 31 to both sides.  Because she did the same thing to both sides of the equation, it is equal to the original equation and therefore is true for all values of `x`.

Answer:  (-7, -4)

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

Explanation:

The general equation y = a| x-h | + k has the vertex (h,k)

Rewrite the original function in this form to get f(x) = -1|x - (-7)| + (-4) and we see that h = -7 and k = -4

So that's why the vertex is (h,k) = (-7, -4)

The V shape graph opens downward meaning that the vertex (-7, -4) is at the highest point. The graph is shown below. I used GeoGebra to make the graph.

Answer:

-7,-4

Step-by-step explanation:

2,x, 26 are in A. P.

a2-a1 = a3-a2

x-2 = 26-x

2x = 26+2

2x = 28

So  x = 14.

Answer:

3:45 P.M.

Step-by-step explanation:

After I fill the tank, the content settles for 14 hours before the liquid is removed.

So, the liquid is removed after content settlement i.e. after 14 hours of filling up the tank.

If I fill the tank at 1:45 A.M. then after 14 hours i.e. at 3: 45 P.M I will remove the liquid.

If we separate the 14 hours into (12 hours + 2 hours), then by adding 12 hours the time will remain the same, only the A.M. will change to P.M i.e. 1: 45 P.M. and then by adding 2 hours more the time will be 3:45 P.M. (Answer)  

Answer:

-11

Step-by-step explanation:

The answer to the  first one sould be  -11

2x^3 +5x^2−x−6

Write 5x^2  as  4x^2 + x^2......and we have.....

2x^3 + 4x^2 + x^2 - x - 6

2x^2 ( x + 2) + ( x + 2)(x - 3)

(x + 2) [ 2x^2 + x - 3]

(x + 2) (2x +3) (x - 1)

x^3−4x^2−3x+18 = 0

Using some synthetic division, we have

3  [   1   - 4      -3      18  ]

              3      -3     -18

      _______________

       1    -1      -6       0

The remaining polynomial  is   x^2  - x  - 6    which factors as  (x - 3) ( x + 2)

So ....   the factored form is  (x - 3) ( x - 3) ( x + 2)  = ( x + 2) ( x - 3)^2 = 0

Answer:

-11 is correct for all future users.

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

ab is a x b

[tex]a \times b[/tex]

[tex]6 \times 7 = 42[/tex]

Answer:279,936

Step-by-step explanation:

i hope its helps

For this case we have that by definition, the slope of a line

is given by:

[tex]m = \frac {y_ {2} -y_{1}} {x_ {2} -x_ {1}}[/tex]

Where:

[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex] are two points through which the line passes.

According to the statement we have:

[tex](x_ {1}, y_ {1}): (3,5)\\(x_ {2}, y_ {2}): (3, -5)[/tex]

Substituting we have:

[tex]m = \frac {-5-5} {3-3}[/tex]

It is noted that the slope is undefined.

Answer:

The slope is undefined

Answer:

the ball is on the ground after 3 seconds right so it would still be on the ground

Step-by-step explanation:

Answer:50 meters

Step-by-step explanation:

Answer:

CD = 5.196 cm

Area = 31.177 sq. cm.

Step-by-step explanation:

See the attached diagram.

Given that ∠ ACB = 90° in Δ ABC.

Now, CD ⊥ AB and ∠ CDB = ∠ CDA = 90°

Given that ∠ ACD = 60° and BC = 6 cm.

We have to find the length of CD and the area of Δ ABC.

Now, ∠ CAD = 90° - ∠ ACD = 90° - 60° = 30°  

Again, ∠ CBD = 90° - ∠ CAD = 90° - 30° = 60°.

Now, from Δ BCD, [tex]\sin 60 = \frac{CD}{BC} = \frac{CD}{6}[/tex]

{Since Δ BCD is a right triangle and ∠ CDB = 90°}  

⇒ [tex]CD = 6 \times \sin 60 = 5.196[/tex] cm. (Answer)

Now, from Δ ACD, [tex]\sin 30 = \frac{CD}{AC} = \frac{5.169}{AC}[/tex]

{Since Δ ACD is a right triangle and ∠ ADC = 90°}

⇒ [tex]AC = \frac{5.196}{\sin 30} = 10.392[/tex] cm

So, the area of Δ ABC = [tex]\frac{1}{2} \times BC \times AC = \frac{10.392 \times 6}{2} = 31.177[/tex] sq. cm. (Answer)

Answer:

CD=3√3

Step-by-step explanation:

Answer: it should be "B. 73" if I'm incorrect sorry but it should be "B. 73"

Step-by-step explanation:

Answer:

General formula of slope=change in y/change in x

1:0.25

2:0

Length and width of rectangle is 15 inches and 6 inches respectively

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.  

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

The formula for area of rectangle is given as:

[tex]\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}[/tex]

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

[tex]\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}[/tex]

On solving the above expression for x we get

[tex]\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}[/tex]

[tex]\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}[/tex]

Hence length and width of rectangle is 15 inches and 6 inches.

Answer:

they have 214 grams of cheese together

Answer:

214g

Step-by-step explanation:

Sara has 84 grams of cheese.

Olivia has 130 grams of cheese.

Total amount of cheese = Sara's cheese + Olivia's cheese

Total amount of cheese = 84 + 130

214 = 84 + 130

Answer:

[tex]a_{7}[/tex] = - 160

Step-by-step explanation:

The n th term of a geometric sequence is calculated as

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Given

a₂ = - 5, then

a₁r = - 5, that is

2a₁ = - 5 ⇒ a₁ = - 2.5, thus

[tex]a_{7}[/tex] = - 2.5 × [tex](2)^{6}[/tex] = - 2.5 × 64 = - 160

12/30 = 18/45, so first you're going to cross multiply and you'll get (30)(18) = (12)(45). Then you can see that 540 = 540 same number so they're proportional...

BTW THIS WAY IS A LOT EASIER.

12/30 = 2/5

18/45 = 2/5

So yes, in summary, they're proportional to each other. Hope this helps, have a BLESSED and wonderful day! :-)

Answer:

proportional

Step-by-step explanation:

12/30 multiplied by a factor of 1.5 is 18/45 so it is proportional

Answer:

-32

Step-by-step explanation:

1/2x-9=-25

1/2x= -25+9

1/2x=-16 /multiply 2

x=-32

[tex]\text{Hello there!}\\\\\text{Solve:}\\\\\frac{1}{2}x-9=-25\\\\\text{Add 9 to both sides}\\\\\frac{1}{2}x=-16\\\\\text{Divide both sides by 1/2 or 0.5}\\\\\boxed{x=-32}[/tex]

Answer:

The measure of side BD is 8.6  and The measure of side CE is 8.4  

Step-by-step explanation:

Given as :

The Triangle is ABC with side AB , BC , CA

And The points E  and D  is on the side AB and AC

So, AED is a Triangle

And Δ AED [tex]\sim[/tex] Δ ABC

The measure of side AD = 6.9

The measure of side AE = 7.2

The measure of side ED = 5.2

The measure of side BC = 10.2

Let The The measure of side EB = x

And The measure of side DC = y

So, From similarity property

[tex]\dfrac{AB}{AE}[/tex] = [tex]\dfrac{AC}{AD}[/tex] = [tex]\dfrac{BC}{ED}[/tex]

Or,  [tex]\dfrac{AB}{AE}[/tex] = [tex]\dfrac{BC}{ED}[/tex]

So, [tex]\dfrac{7.2 + x}{7.2}[/tex] = [tex]\dfrac{10.2}{5.2}[/tex]

Or, 5.2 × ( 7.2 + x ) = 10.2 × 7.2

Or, 37.44 + 5.2 x = 73.44

Or, 73.44 - 37.44 = 5.2 x

∴ x = [tex]\frac{36}{5.2}[/tex]

I.e x = 6.9

Now in Δ BED

BE² + ED² = BD²

Or, 6.9² + 5.2² = BD²

Or, BD² = 74.65

∴  BD = [tex]\sqrt{74.65}[/tex]

I.e BD = 8.64

Or, BD = 8.6

Similarly for y

[tex]\dfrac{AC}{AD}[/tex] = [tex]\dfrac{BC}{ED}[/tex]

Or,  [tex]\dfrac{6.9+y}{6.9}[/tex] = [tex]\dfrac{10.2}{5.2}[/tex]

Or, 5.2 × ( 6.9 + y ) = 10.2 × 6.9

Or, 35.88 + 5.2 y = 70.38

or, 5.2 y = 70.8 - 35.88

Or, 5.2 y = 34.5

∴  y = [tex]\frac{34.5}{5.2}[/tex]

I.e y = 6.6

Now in Δ CED

CD² + ED² = CE²

Or, 6.6² + 5.2² = CE²

Or, CE² = 70.6

∴  CE = [tex]\sqrt{70.6}[/tex]

I.e CE = 8.40

Or, CE = 8.4

Hence The measure of side BD is 8.6  and The measure of side CE is 8.4  Answer

Answer:

By using geometric calculations,the measure of BD and CE are 6.9 and 7.4 respectively.

Answer: x=0.5

Step-by-step explanation: In order to solve this problem, you need to simplify the rest of the problem first. You can do this by dividing -7 by 2, which will result in -3.5, making the equation 3x-3.5=-5. If you add 3.5 to both sides, the equation becomes 3x = 1.5. If you divide 1.5 by 3, you are left with 0.5, so x=0.5.

Final answer:

The solution to the linear equation '3x minus 7 divided by 2 equals negative 5' is found by performing algebraic operations to isolate the variable, resulting in x = -1.

Explanation:

The question involves solving a linear equation which is a fundamental concept in mathematics. To solve the equation 3x minus 7 divided by 2 equals negative 5, you will perform algebraic operations to isolate the variable x. Here is a step-by-step process:

Applying this process, you can see that the original equation is satisfied when x = -1, which completes our solution.

The number of weeks requires is 15 weeks

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Given:

$85.00 a week just from Allowance

So, Gary have to work

=1200/85

= 15 weeks

Hence, the number of weeks requires is 15 weeks.

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The complete question is

can someone help me please?

Question : If you have a job or allowance, how much do you take home per week?

I put that I make $85.00 a week just from Allowance and my half job.

So the question is : how many weeks would you have to work to pay for Gary's $1200 mistake?

[calculate $1200 � your take home pay amount = answer in weeks]

Weeks for Laptop:

how many weeks would you have to work to pay for your little mistake with the $13 bounced check? You know, that $4300 messup? Weeks for pizza :

Help please thanks

Final answer:

Jason will have to work approximately 6.67 weeks, or about 6 weeks and 5 days, to pay off a $1200 mistake if he earns $4.50 per hour after government income reduction.

Explanation:

To calculate how many weeks a student would have to work to pay for a $1200 mistake, we will use the information provided about Jason's income and work scenario as a reference. According to the information, Jason nets $4.50 for every hour of work due to a reduction in government income. Thus, if Jason has to repay $1200, we will divide this amount by his net hourly income to find the total hours he needs to work.

$1200 ÷ $4.50 per hour = 266.67 hours

Now, to convert these hours into weeks, we assume a standard work week is 40 hours. Therefore, we divide the total hours by 40 hours per week.

266.67 hours ÷ 40 hours per week = 6.67 weeks

Jason will have to work approximately 6.67 weeks to pay off a $1200 mistake.

Answer:

The answer is definitely C. a naturally formed solid substance with a crystal structure

Answer:

2b+4 so yes there are equivalent

Step-by-step explanation:

4b-7-2b+11

4b-2b-7+11

2b+4

b+3+b+1

2b+4

Answer:

The correct answer is Helena