if f(x)=4x-7 and g(x)=2x+4 evalvate f(x)+g(x) for x=-3

Answer:

a. See Attachment 1

b. [tex]PT = 12.3\ m[/tex]

c. [tex]HT = 31.1\ m[/tex]

d. [tex]OH = 28.4\ m[/tex]

Step-by-step explanation:

Calculating PT

To calculate PT, we need to get distance OT and OP

Calculating OT;

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OT}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]

[tex]20 * tan50 = OT[/tex]

[tex]20 * 1.1918 = OT[/tex]

[tex]23.836 = OT[/tex]

[tex]OT = 23.836[/tex]

Calculating OP;

We have to consider angle 30, distance OH and distance OP

The relationship between these parameters is;

[tex]tan30 = \frac{OP}{20}[/tex]

Multiply both sides by 20

[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]

[tex]20 * tan30 = OP[/tex]

[tex]20 * 0.5774= OP[/tex]

[tex]11.548 = OP[/tex]

[tex]OP = 11.548[/tex]

[tex]PT = OT - OP[/tex]

[tex]PT = 23.836 - 11.548[/tex]

[tex]PT = 12.288[/tex]

[tex]PT = 12.3\ m[/tex] (Approximated)

--------------------------------------------------------

Calculating the distance between H and the top of the tower

This is represented by HT

HT can be calculated using Pythagoras theorem

[tex]HT^2 = OT^2 + OH^2[/tex]

Substitute 20 for OH and [tex]OT = 23.836[/tex]

[tex]HT^2 = 20^2 + 23.836^2[/tex]

[tex]HT^2 = 400 + 568.154896[/tex]

[tex]HT^2 = 968.154896[/tex]

Take Square Root of both sides

[tex]HT = \sqrt{968.154896}[/tex]

[tex]HT = 31.1\ m[/tex] (Approximated)

--------------------------------------------------------

Calculating the position of H

This is represented by OH

See Attachment 2

We have to consider angle 50, distance OH and distance OT

The relationship between these parameters is;

[tex]tan50 = \frac{OH}{OT}[/tex]

Multiply both sides by OT

[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]

[tex]OT * tan50 = {OH[/tex]

[tex]OT * 1.1918 = OH[/tex]

Substitute [tex]OT = 23.836[/tex]

[tex]23.836 * 1.1918 = OH[/tex]

[tex]28.4= OH[/tex]

[tex]OH = 28.4\ m[/tex] (Approximated)

Answer:

39 units²

Step-by-step explanation:

The figure is composed of a rectangle VEDR and Δ RMV

Area of rectangle = VE × ED = 5 × 6 = 30 units²

Area of Δ = 0.5 × RV × perpendicular from M to RV

                = 0.5 × 6 × 3 = 9 units²

Thus

Area of polygon = 30 + 9 = 39 units²

Answer:

The amount in 2001 is 8400

Step-by-step explanation:

Let x be the amount in 2001

There is an increase of 25% to get to the amount in 2002

x+ .25x = 1.25 x

1.25x = 10500

Divide each side by 1.25

1.25x / 1.25 = 10500/1.25

x =8400

The amount in 2001 is 8400

Answer:  The estimated value is:  " 2.1 " .

__________________________________

Step-by-step explanation:

__________________________________

We are asked to "estimate" :

 5 2/11  -  3/ 2/18 ;

 Note:  Consider:  " 5 2/11 " ;  

 Note that:  "2/11" is close to:  "2/10" ; which can be expressed as a decimal value:  "0.2 " ;

So, consider this value:  "5 2/11 ";  as estimated:  " 5.2 " .

Now, consider:  " 3  2/18 " ;

Note that :  "2/18" can easily be reduced to:  "1/9 ";

               Since:  "(2/18)" = "(2÷2) / (18÷2) " =  "1/9 " ;

Note that "1/9" is close to "1/10" ; which can be expressed as a decimal value:  "0.1 ".

 So, consider:  "3 2/18 " ; as estimated:  " 3.1 " .

__________________________________

So:  To estimate:  " 5 2/11  -  3 2/18 " ;

__________________________________

Use the following:  "5.2  - 3.1 " ;

__________________________________

    5.2

 -  3. 1

__________________________________

  " 2.1 "

___________________________________

The estimated value is:  " 2.1 " .

___________________________________

Hope this is helpful to you!

___________________________________

Answer:

4x+4y=1, 6x-y=1

x+y=4, x-y=2

x-y=9, x+y=6

Step-by-step explanation:

Answer:

x equals 27/5

Step-by-step explanation:

just substitute y into the first equation

Answer:

T1he values for x and y of the equations is y = 11, and x = -19/5.

Step-by-step explanation:

To solve this question, we need to rearrange the expression:

5x+4y=25 - (5x+2y=3)

Look, if we subtract one equation to the other, then:

5x+4y=25 [1]

-(5x+2y=3) [2]

Which is the same as:

5x+4y=25

-5x-2y=-3

Subtract them:

5x+4y=25

-5x-2y=-3

---------------

      2y =22

y = 22/2 = 11

Then, y = 11.

To find x, we can substitute y in either equation [1] or [2].

Let us use [1]

5x+4y=25

5x+4(11)=25

5x+44=25

5x=25-44

5x=-19

x = -19/5

Then, the values for x and y of the equations is y = 11, and x = -19/5.

We need to know the rules of congruence of triangles to solve the given problem. The required condition that is sufficient to prove that the triangles are congruent is option (C) AB≅JK.

There are three rules of congruence of triangles, if two triangles satisfy any one of these rules then we can say that the triangles are congruent.  The three rules are, SSS which means three sides are equal, ASA which means two angles and their corresponding sides are equal and SAS which means that two sides and the angle between them is equal. When two angles are said to be congruent it means they have the same measure that is they are equal. In this question we know that ∠A≅∠J and ∠B≅∠K , we can see that two angles are equal, if we can have the corresponding side of these two angles to be equal then we can say that the two triangles are congruent. The corresponding side of these angles are AB and JK.

Therefore we can see that the required condition to prove that the triangles are congruent is option (C) AB≅JK.

Learn more about congruency of triangles here:

https://brainly.com/question/2736828

#SPJ1

Answer:

D) Van: 7, Bus: 20

Step-by-step explanation:

Add the amount of students together (455 students in total)

Then I added the amount of buses and vans together (5 Vans and 21 Buses)

Then I plugged in each answer

5 x 7 = 35

455 - 35 = 420

420 / 21 = 20

Answer:

D. A reduction with a scale factor of [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We know for sure it is a reduction because the image, W'X'Y'Z', is smaller than the pre-image WXYZ. Because it is a reduction, the scale factor must be less than 1, so the only option can be D. Both B and C say enlargement and A says it is a scale factor of 2.

Hope this helps and I am sorry no one has answered your question until now.

I will be happy to answer any of your other questions if you want.

Have a good day! :)

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

When x is -2, F(x) is undefined.

When x is -1, F(x) is -3.

If we see the third option,

[tex]F(x)=\sqrt{x+1} -3[/tex]

When x is -2, we get the square root of -1, which is undefined.

When x is -1, we get the square root of 0, which is just 0, 0-3 is -3.

Answer:

5.541 gallons

Step-by-step explanation:

The fish tank is 1280 cubic inches, which equates to 5.541 US liquid gallons.

Answer:

5.54 gallons     (aprox.)

Step-by-step explanation:

volume = 16in * 10in * 8in

volume = 1280in³

Convert cubic inch to gallons is:

1 inch³ = 0.004329 gallon

then:

1280in³ = 1280*0.004329 = 5.54 gallons  (aprox.)

Answer:

Step-by-step explanation:

Given the expression

[tex]40=\frac{90^2}{16} sinxcosx\\\\Cross\ multiplying;\\\\16*40 = 90^2 sinxcosx\\\\640 = 90^2 sinxcosx\\\\\frac{640}{8100} = sinxcosx\\ from\ trig\ identity, sin2x = 2sinxcosx\\sinxcosx = sin2x/2\\[/tex]

[tex]Hence, \ \frac{640}{8100} = \frac{sin2x}{2} \\\\\frac{2*640}{8100} = sin2x\\ \\\frac{1280}{8100}=sin2x\\ \\0.158 = sin2x\\\\2x = sin^{-1} 0.158\\\\2x = 9.09\\x = 9.09/2\\x =4.545[/tex]

Answer:

No amplitude

Period is pi

Step-by-step explanation:

Answer:

A) it increases the mean value of the prizes.

Step-by-step explanation:

The median is resistant to large outliers, so it does not change if there is an especially large or small value. So, we can eliminate choices C and D.

I am actually not sure whether the data in the table count $100 as a large prize or a small one, but I am assuming it is a large prize. So, an extremely large prize would increase the mean value of the prizes.

Hope this helps!

The $100 gift card affect the measure of center of the data by increases the mean value of the prizes.

Option A is the correct answer.

It is the middles value of the given set of numbers after arranging the given set of numbers in an order.

We have,

The $100 gift card has a much larger value compared to the other prizes, and it is only given to one person.

Therefore, adding the $100 gift card to the prizes will significantly increase the total value of the prizes, which will affect the measures of center of the data.

The mean and median are two common measures of center in statistics. The mean is the sum of all the values divided by the number of values, while the median is the middle value when the data is arranged in order.

Adding the $100 gift card will increase the mean value of the prizes, but it will not affect the median value, since the median only depends on the order of the data, not the values themselves.

Therefore,

It increases the mean value of the prizes.

Learn more about median here:

https://brainly.com/question/28060453

#SPJ7

Answer:

see file attached

Step-by-step explanation:

Correct question is;

Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags. What will Kermit think of Peggy's iced tea? Choose 1 answer: (Choice A) A It is too strong.

(Choice B) B It is too weak.

(Choice C, Checked) C It is just right.

Answer:

C - It is just right

Step-by-step explanation:

We are given that;

The Number of tea bags needed to make every 2 liters of water = 15 tea bags.

Thus,

For each liter of water, the number of tea bags needed = 15/2 = 7.5 tea bags.

Now, kermit needs to make 12 liters of iced tea.

Therefore, total number of tea bags required for 12 liters of iced tea = 12 × 7.5 = 90 tea bags.

Now, Peggy also took 90 tea bags to make a 12-liter batch of iced tea.

Therefore, kermit would think that the mixture of Peggy's tea is just right.

Correct option is C

Answer:

ill help!

Step-by-step explanation:

find angle CBD

once you find that angle subtract it from 90 because that is the measure of ABC which is a right angle. Because all right angles are 90 degrees you can prove that it is the difference from angle CBD and 90.

hope it helped have good one!

Answer:

D.The distance you drive

Step-by-step explanation:

If you describe this situation as function, then it will look as:

The range of the function is the set of output values

In this case the range is the distance you drive

Correct option is D.

Answer:

The distance you drive

Step-by-step explanation:

i just took the test

Answer:

c. translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Step-by-step explanation:

The strategy is to translate B to E then reflect about the x-axis (y=0)

From B to E, the process is

(x,y) -> (x-4, y-1)

Therefore it is a translation (x,y) -> (x-4, y-1) followed by reflection about y=0

Answer:

The answer to your question is given in the attached photo.

Step-by-step explanation:

To determine the answer to the question,

First, we shall determine the value 3A.

This is obtained by multiplying matrix A by 3 as shown in the attached photo.

Next, we shall carry out the operation 3A – B as shown in the attached photo.

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

Answer:

A. Volume: 819, Surface Area: 598

B. Surface area

C. Volume

Step-by-step explanation:

Sorry I'm late, but here I go.

The volume of a rectangular prism is [tex]lwh[/tex] or [tex]bh[/tex]. (l being length, w being width, and h being height.)

So if we multiply the 3 values of 13, 9, and 7, we get 819. This is the volume.

To find the surface area, we can take note that 4 sides are the exact same, and the remaining two are the same. Let's find the area of the top/bottom of the prism.

[tex]13\cdot9=117[/tex]

Since there are two, bottom and top:

[tex]117\cdot2 = 234[/tex].

Now, there are the remaining 4 sides. Let's find the area of one then multiply it by 4.

[tex]13\cdot7=91\\91\cdot4=364[/tex]

Adding 364 and 234 gets up 598, so this is the surface area.

If we are painting something, the surface area is being painted, as we can't paint inside the box. However if we fill up the box with something (concrete in this case), it will be the volume.

Hope this helped!  

Answer:

a.

v= 819 cm3

sa= 542 cm2

b. surface area

c. volume

Step-by-step explanation:

Volume of a rectangular prism: Length x width x height

Replacing with the values given:

V = 13 x 9 x 7 = 819 cm3

Surface area = S = 2 × (W × L + L × H + H × W)

S = 2 ( [9x13]+ [13 x7] +[7x9]) = 2 ( 117+91+63)= 542 cm2

b . Surface area, because we only have to paint the exterior of the brick.

c. Volume, because is the amount of concrete that the brick has.

Answer:

We reject the students claim because the P-value is less than the significance level.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = 25,235

Alternative hypothesis;Ha; μ > 25,235

Now, let's find the test statistic. Formula is;

t = (x' - μ)/(σ/√n)

We are given;

x' = 27,524

μ = 25,235

σ = 6000

n = 100

Thus;

t = (27524 - 25235)/(6000/√100)

t = 2289/600

t = 3.815

So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.

The p-value is less than the significance level of 0.05. Thus,we reject the students claim.

Answer:

x = [ -b +- sqr root (b^2 - 4ac)] / 2a

a = 1

b = -5

c = -2

x = [- - 5 +- sqr root (-5^2 -4 * 1 * -2)] / 2 * 1

x = [5 +- sqr root (25 + 8)] / 2

x1 =  5.3723

x2 =-0.37228

Step-by-step explanation:

Exact solution for the give quadratic equation are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

Quadratic equation of the form [tex]ax^2+bx+c=0[/tex]

For any quadratic equation we get two values for x. we can find the values for x by applying quadratic formula .

Quadratic formula

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Given equation is [tex]x^2-5x-2=0[/tex]

The value of a=1, b= -5  and c=-2

Substitute all the values in the formula.

To find out exact solutions , we need to simplify the final answer.

Exact solutions are without any decimals.

[tex]x=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \left(-2\right)}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\pm \sqrt{33}}{2\cdot \:1}\\x=\frac{-\left(-5\right)\p+ \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5+\sqrt{33}}{2}\\\\x=\frac{-\left(-5\right)- \sqrt{33}}{2\cdot \:1}\\\\x=\frac{5-\sqrt{33}}{2}\\[/tex]

Exact solutions are

[tex]x=\frac{5+\sqrt{33}}{2},\:x=\frac{5-\sqrt{33}}{2}[/tex]

Learn more information about 'Quadratic formula ' here

brainly.com/question/8649555

Answer:

x=0    x=3

Step-by-step explanation:

F(x)=3x(2x-6)

Set equal to zero

0 =3x(2x-6)

Using the zero product property

3x =0   2x-6 =0

x =0     2x = 6

             x = 6/2

             x = 3

Answer:

x = 0 or x = 3

Step-by-step explanation:

Set the output to 0

0 = 3x(2x-6)

Set factors equal to 0.

3x = 0

x = 0

2x - 6 = 0

2x = 6

x = 3

angle HDG = angle HFE

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

Explanation:

We have the statement [tex]\triangle DHG \cong \triangle FHE[/tex] given to us. Note that "H" is in the middle for both sequences of three letters. For DHG, start at H and move back one space to get to D. Move back another unit to wrap around to G. So the new sequence is HDG which forms the first angle.

Follow the same pattern but for FHE now. Start at H, move backward one spot to F, then move back again to wrap around to E. We have HFE

This shows angle HDG pairs up with angle HFE. The corresponding angles are congruent due to CPCTC

CPCTC = corresponding parts of congruent triangles are congruent

Notice how angles HDG and HFE are alternate interior angles, which lead to showing DG is parallel to EF.

Answer:

The table D represents the function that will have the greatest y-values for very large values of x.

Step-by-step explanation:

The table A represents a linear function, for which each one unit increment in the "x" variable produces a three unit increment in the "y" variable. This means that the growth rate of this function is 3.

The table B also represents a linear function, for which each one unit increment in the x variable produces a 100 unit increment in the y variable. This means that the growth rate of this function is 100.

The table C also represents a linear function, for which each one unit increment in the x variable produces a 10 unit increment in the y variable. This means that the growth rate of this function is 10.

The table D on the other hand does not represent a linear function, since the growth rate is variable and increases for greater values of x. This means that as x grows larger, the growth rate of the function also grows larger, resulting in a much greater y value for very large x values if we compare it to a linear function, like the other options.

Answer:

D

Step-by-step explanation:

BIGBRAIN

Approximate what the value of [tex]7/15[/tex] is by using calculator.

[tex]7/15\approx0.47[/tex].

And now just multiply by 100 to get percentage.

[tex]100\cdot0.47=\boxed{47\%}[/tex].

Hope this helps.

Answer:

24%

Step-by-step explanation:

7\15 x 100

simplify and get=140\3

dived140\3=48\2

simplify 48\2=24%

Answer:

1: yes AB2×4

2:not possible

3:(11,2)

(20,12)

Step-by-step explanation:

1:compare the orders given which is 2×3 and 3×4 so to get if it's possible to multiply you just cancel out the same numbers if present i.e 3

2:so I took the first column of m multiply the first row of n (add values you get i.e -2×1+1×-4+0×2=-6) but on the second value of the first row I got 8 not 3 so I said not possible

3 you multiply row by column

(1×1+0×7+2×5=11. 1×4+0×2+-2×1=2)

(3×1+1×7+2×5=20. 3×4+1×2+2×-1=12)

therefore

(11,2)

(20,12)

Answer:

  0.20, 0.36 seconds

Step-by-step explanation:

We have already seen that the equation for y(t) can be written as ...

  y(t) = √29·sin(4πt +arctan(5/2))

The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...

  4πt +arctan(5/2) = 7π/6 or 11π/6

  t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds

and

  t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds

The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.