A carpenter is making a backyard deck. In the measurements, he has determined that he needs to make a support triangle with an area 46m2. He knows that the base must be 1 less than 2 times the height. If the base is represented by 2x-1 and height equals x. Find the equation that correctly shows the area of the triangle.

A Carpenter Is Making A Backyard Deck. In The Measurements, He Has Determined That He Needs To Make A

Answers

Answer 1

Answer:

base = 3x - 1

height = x

area of triangle = (1/2)bh

22 = (1/2)(3x-1)(x)

44 = (3x-1)(x)

44 = 3x^2-x

0 = 3x^2-x-44

0 = 3x^2-12x+11x-44

0 = (3x^2-12x)+(11x-44)

0 = 3x(x-4)+11(x-4)

0 = (x-4)(3x+11)

x = {-11/3, 4}

throw out the negative solution (extraneous) leaving

x = 4 m (height)

.

Base:

3x - 1 = 3(4) - 1 = 12 - 1 = 11 

Step-by-step explanation:

I hope it will help you


Related Questions

3(5-4)+2(5)-5 squared

Answers

the answer should be -12 if I did the math right.

Step-by-step explanation:

3*1+10-5^2(we subtract 5 from 4 first because it was inside bracket)

3+10-25(Square of 5 is 25)

-12(subtracting the above equation 12 comes)

Question 8(Multiple Choice Worth 5 points) (01.01 MC) Which number line best show how to solve -4 - (-8)?​

Answers

The answer to your question is A

Answer:

4

Step-by-step explanation:

-4 - (-8) Note: a negative negative equals a positive. There for it is just the same as saying -4 + 8

Please help
I am giving all my points for this (15 points)
Select all input values for which g(x)=8.
Choose all answers that apply:
(Choice A)
x=−4
(Choice B)
x=6
(Choice C)
x=9
(Choice D)
None of the above

Answers

Answer:

D. none of the above

Step-by-step explanation:

If g(x)=8 is the only equation, then none of the answers are correct. The correct answer would have been 8 because 8=8.

please help me out asap
(geometry)

Answers

Answer:

x = 30

Step-by-step explanation:

If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then

2x + 50 + 5x - 80 = 180

7x - 30 = 180 ( add 30 to both sides )

7x = 210 ( divide both sides by 7 )

x = 30

The fraction 9/7 is equivalent to?

Answers

9/7 is equivalent to 18/14 or 27/21 or 36/28 etc

Answered by Gauthmath must click thanks and mark brainliest

Can someone help me with this math homework please!

Answers

Answer:

negative

Step-by-step explanation:

Let,

x1 = 0

x2 = 1

y1 = 50

y2 = 44

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope

= ( 44 - 50 ) / ( 1 - 0 )

= - 6 / 1

= - 6

- 6 is a negative number.

So, the slope is negative.

Write an equation of the line that passes through the point (6, -9) with the given slope m = 3.

Answers

Answer:

y = 3x - 27

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (6, - 9) into the partial equation

- 9 = 18 + c ⇒ c = - 9 - 18 = - 27

y = 3x - 27 ← equation of line

Answer Y=3x - 27 step by step

9. Calculate the angle of elevation of the line of sight of a person 27.5 m away from a tree, whose
eye is 1.8 m above the ground, and is looking at the top of a 19.4 tree. (draw a diagram and
answer to the nearest degree)

Answers

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

1
Work out the area of the shape:
3cm
6cm
2cm
2cm

Answers

Answer:

24 cm

Step-by-step explanation:

6*2+3*4=?

12+12

24 cm

A stationer buys a gel pen Rs 20 and sells it at 20% profit.For what price should he buy it so that he can make 25% profit by selling for the same selling price.

Answers

Answer:

Current selling price = Rs 20 × 120 %

= Rs 24

Cost price should be [100 ÷ 125 ] × 24

= Rs 19.20

If a zero is
, then the graph of its function only touches the x–axis at that zero.

Answers

Answer:

Step-by-step explanation:

Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.

Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if:

a) there must be exactly 3 students on the committee

b) there must be at least one teacher and at least one student on the committee

Answers

Answer:

a) 11,880

b) 7,770

Step-by-step explanation:

The number of teachers that volunteer = 6 teachers

The number of students that volunteer = 12 students

The number of people in the committee = 5 people

a) The exact number of student on the committee = 3 student

Therefore, the number of teachers in the committee of 5 = 5 - 3 = 2

The number of teachers in the committee = 2 teachers

We get;

The number of committees that can be made = ₁₂C₃ × ₆C₂ = 792×15 = 11,880

b) When there is at least one teacher and at least one student on the committee, we have;

₁₂C₄ × ₆C₁ + ₁₂C₃ × ₆C₂ + ₁₂C₂ × ₆C₃ + ₁₂C₁ × ₆C₄ = 7,770

The number of committees having at least one teacher and at least one student = 7,770

which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2?

Answers

the answer is on the photo

Derek had a bill of $29 last month on he Call-a-Lot Plan. How many minutes did he use?

Answers

it depends on how much it costed per minute if it was a dollar a minute then it would be 29 minutes

Mr. Serpe started with $200. He has a hole in his pocket and he lost $2 every day for a week. He then found $150. How much money does he have?

Answers

Answer:

336

Step-by-step explanation:

2x7=14, so 200-14=186, then 186+150=336

need help with part b of the attached screenshot please

Answers

9514 1404 393

Answer:

  (b) 82.9253

Step-by-step explanation:

The first attachment shows the rectangles. The second shows the sum of their areas.

The midpoint of AB is M(1,1). If the coordinates of A are (3, 3), what are the coordinates of B?​

Answers

Answer:

The answer in (-1,-1) because it goes down by x-2 and y-2

HELP QUICK ILL GIVE BRAINLIEST

Answers

Answer:

A=35 degrees, B=55 degrees, C=110 degrees

Step-by-step explanation:

The 35 degree given angle is vertical angles with A, so they are congruent

The sum of angles in a triangle is 180, and we already have 2 angles (35 and 90) so subtract those and you get 55

angle c and the other given angle (70 degrees) are supplementary so subract 70 from 180

Find the value x ……….

Answers

Answer: 6 because it more than thd base and less than the other triangles leg

Step-by-step explanation:

Answer:

[tex]4\sqrt{5}[/tex]

Step-by-step explanation:

[tex]x^2 = y^2 + 25[/tex]

[tex]\frac{y}{11} = \frac{5}{y}[/tex]  

[tex]y^2 = 55[/tex]

[tex]x^2 = 80\\x = \sqrt{80} \\x= 4\sqrt{5}[/tex]

9. Choose the equation that represents the graph below:

Answers

Answer:

y= -4/3 x + 4

Step-by-step explanation:

i guess

1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é: a) r = 6 b) r = 7 c) r = 9 d) r = 11 e) r = 12 2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a: a) 78 b) 79 c) 80 d) 81 e) 82

Answers

Answer:

1) b) r = 7

2) e) 82

Step-by-step explanation:

Progressão aritmética:

Em uma progressão aritmética, a diferença entre termos consecutivos é sempre a mesma, chamada de razão.

O n-ésimo termo de uma PA é dado por, tomando o primeiro termo como referência:

[tex]a_n = a_1 + (n-1)r[/tex]

Tomando o m-ésimo termo como referência, tem-se que:

[tex]a_n = a_m + (n-m)r[/tex]

1) Se o 5o e o 9-o termos de uma PA são, respectivamente, 40 e 68, então a razão r da progressão é:

[tex]a_5 = 40, a_9 = 68[/tex]. Então:

[tex]a_n = a_m + (n-m)r[/tex]

[tex]68 = 40 + 4r[/tex]

[tex]4r = 28[/tex]

[tex]r = \frac{28}{4} = 7[/tex]

Então a resposta correta é dada pela alternativa b.

2) Inserindo-se 6 números entre 72 e 107, de modo que a sequência (72, a2, a3, a4, a5, a6, a7 ,107) seja uma progressão aritmética, tem-se a3 igual a:

O primeiro termo é [tex]a_1 = 72[/tex] e o oitavo termo é [tex]a_8 = 107[/tex]. Com isso, é possível encontrar a razão.

[tex]a_n = a_1 + (n-1)r[/tex]

[tex]107 = 72 + 7r[/tex]

[tex]7r = 35[/tex]

[tex]r = \frac{35}{7} = 5[/tex]

Então, o terceiro termo é:

[tex]a_3 = a_1 + 2r = 72 + 2(5) = 82[/tex]

Logo, a resposta correta é dada pela alternativa e.

Use a calculator to determine the unknown angle, to the nearest degree, in each of the following expressions.

tan A = 5/4

cos G = 0.88

Answers

Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

which point is on the line that passes through point H and is perpendicular to line FG?

Answers

Answer:

The correct answer is (-6, 10).

Step-by-step explanation:

You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.

Feel free to message me if you still have questions :)

Answer:

(–6, 10)

Step-by-step explanation:

Find Point P is the incenter of DEF . point p of concurrency of the angle bisectors . find PT

Answers

PT is 8 because since P is the incenter it's equidistant from all sides.

ASAP please help meeeeeeeeeeeeeee

Answers

Answer:

7/10

(-4×-7)/(5×8)

=28/40

=7/10

Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour. If her total traveling time was 14 hours, how far was it to the mall?

Answers

Given:

Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour.

Total traveling time was 14 hours.

To find:

The distance between Melinda's house and mall.

Solution:

Formula used:

[tex]Time=\dfrac{Distance}{Speed}[/tex]

Let x miles be the distance between Melinda's house and mall.

Melinda walked to the mall at 4 miles per hour. So, the time taken by Melinda is [tex]\dfrac{x}{4}[/tex] hours.

Speed of bus is 24 miles per hour. So, the time taken by bus is [tex]\dfrac{x}{24}[/tex] hours.

Total traveling time was 14 hours.

[tex]\dfrac{x}{4}+\dfrac{x}{24}=14[/tex]

[tex]\dfrac{6x+x}{24}=14[/tex]

[tex]7x=14\times 24[/tex]

Divide both sides by 7.

[tex]\dfrac{7x}{7}=\dfrac{14\times 24}{7}[/tex]

[tex]x=2\times 24[/tex]

[tex]x=48[/tex]

Therefore, the mall is 48 miles far from Melinda's house.

Candice bought 6 dozen eggs and broke 9 eggs how many eggs did she have left

Answers

Answer:

63

Step-by-step explanation:

12x6=72

72-9=63

the answer is 63

Answer: 63 eggs


Step 1: Find initial amount of eggs

Before we can solve for how many eggs are left, we must first find out how many eggs Candice initially had. We are told she bought six dozen eggs. Since a dozen is twelve, we can find out how many eggs she had by multiplying twelve and six. Let’s do this now.

6×12= 72

Step 2: Find solution

Now let’s solve for how many eggs Candice has left. We know that she bought 72 eggs, and that she broke 9. To find the answer, we need to subtract 9 from 72.

72-9= 63


Hope this helps! Comment below for more questions.

Find the measure of one exterior angle for the following regular polygon

Answers

72, all exterior angles of a regular polygon add up to 360, there are five exterior angles so you would do 360÷5 which is 72

given the preimage and image, find the dilation scale factor​

Answers

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

How much less is 17km than 24.6km?​

Answers

24.6-17= 7.6 (km) i think so

Answer:

[tex]7.4km[/tex]

Step-by-step explanation:

[tex]24.6km - 17km \\ = 7.4km[/tex]

hope this helps you.

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