(4x + 7)ºX[5(x – 4)]°

What is the Value of X?

Answer:

Time taken (t) = 2.67 s (Approx)

Step-by-step explanation:

Find:

Time taken (t)

Given:

Initial velocity (u) = 0 m/s

Acceleration due to gravity(a) = -9.8 m/s²

Distance (d) = -35 m

Computation:

Using 2nd equation of motion,

d = ut + (1/2)at²

-35 = (0)t + (1/2)(-9.8)t²

-35 = -4.9 (t²)

t² = 7.1428

t = 2.6726

Time taken (t) = 2.67 s (Approx)

Answer:

The angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Step-by-step explanation:

The required sketch is shown in the attachment to this answer.

Applying the appropriate trigonometric function to the question, we have;

Tan θ = [tex]\frac{Opposite side}{Adjacent side}[/tex]

         = [tex]\frac{5}{18}[/tex]

         = 0.2777777777

⇒ θ = [tex]Tan^{-1}[/tex] 0.2777777777

      = 15.5241

      = [tex]15.5^{0}[/tex]

Therefore, the angle created between the ladder and tree is [tex]15.5^{0}[/tex].

Answer:

V=11*7*9=693

Step-by-step explanation:

V=Bh ( B is the base area ( base*height) , and h is the height of the prism)

find B=base*h

B=11*7=77 in²

V=B*h=77*9=693 in³

The volume of the triangular prism is 174.25 in³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the triangular base has a base of 11 inches and height of 7 inches.

The formula for finding the volume of a triangular prism is V = (base area x height) / 2.

In this case, the base area of the triangle can be calculated using the formula A = (1/2)bh, where b is the base length and h is the height.

In this case, b = 11 inches and h = 7 inches, so the base area is A = (1/2)(11)(7) = 38.5 inches squared.

Now that we have the base area, we can calculate the volume of the triangular prism: V = (38.5 inches² x 9 inches) / 2 = 174.25 in³.

Therefore, the volume of the triangular prism is 174.25 in³.

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Answer:

5.83 ft

Step-by-step explanation:

Given that

Scale factor, n = 10

Wall in blueprint = 7 in

To find:

Length of actual wall = ?

Solution:

Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.

Here this factor is 10 times.

That means, the blueprint size is 10 times smaller than that of its actual size.

Or we can say that actual wall of building is 10 times the wall of blueprint.

So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches

Now, we know that 12 inches = 1 ft

1 inch = [tex]\frac{1}{12}\ ft[/tex]

70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]

so, the answer is Wall of building is 5.83 ft.

Answer:

33m 40cm.

Step-by-step explanation:

One side of the shed measures 8 meters and 35 centimetres, which is 800 + 35 = 835 centimetres.

Since the shed is a square, all side lengths are 835 centimetres long. So, the perimeter is 835 * 4 = 3,340 centimetres. That means that the perimeter is 33 meters and 40 centimetres.

Hope this helps!

Answer:

<BAC ≅ BCA by rule Base angle theorem

Step-by-step explanation:

What we know:

BAC = DAC

BC = BA

ΔBCA is an isosceles so ∠BCA  =  ∠DCA and ∠BAC

and we found that out by base angle theorem since

Base angle Theorem  = Two base angles of a icosceles triangle are equal.

And since ΔBCA is an isoceles then ∠A and ∠C will be equal. And so we can prove BC is a parallel to AD

The proof that BC ∥ AD from the given statements is that;

BC ∥ AD because of the definition of alternate angles

We are given;

AB = BC  

 AC is ∠ bisector of ∠BAD

Since AC is the angle bisector of ∠BAD, it means that;

∠BAC  = ∠DAC (definition of a bisected angle)

Now, since AB = BC, it means that ΔBCA is an isosceles triangle.

Thus; ∠BCA = ∠BAC  (base angle theorem)

Now, since ∠BCA = ∠BAC, and ∠BAC  = ∠DAC, we can say that;

∠BCA = ∠DAC

This means  ∠BCA and ∠DAC are alternate angles. Thus, we can say that AC is the transversal line carrying the two equal angles.

Thus, we can say that BC is parallel to AD as they are the parallel lines cut by the transversal line AC.

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Answer:

x=1.75

Step-by-step explanation:

3*2-4x+1=0 subtract 1 from both sides

3*2-4x=-1 multiply 3 and 2

6-4x=-1 Subtract 6 from both sides

-4x=-7 divide both sides by -4

x=1.75

If this helped, please consider giving me brainliest, it will help a lot :)

Have a good day

Answer:

[tex]\frac{\sqrt{3} }{4} a^2[/tex]

Step-by-step explanation:

To find the area of an equilateral triangle, we can apply a formula.

[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]

[tex]A= area\\s=side \: length[/tex]

The side length is given a.

Plug a in the formula as the side length.

[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]

Answer:

3 square root over 4 a square

Step-by-step explanation:

Answer:

4 hours

Step-by-step explanation:

Formula for volume of a cylinder is πr² · h

1. Find the volume of the pool

π(3.5²) · 1.9 = 73.1 m³

2. Divide by the amount of water pumped out per hour (17 m³)

73.1 ÷ 17 = 4.3

It would take 5 hours to completely empty the pool but 4.3 rounded to the nearest whole hour is 4 hours.

Answer:

The hours does it take to empty the pool is 4.299

Step-by-step explanation:

In order to calculate how many hours does it take to empty the pool, we would have to make the following calculation:

hours does it take to empty the pool=Volume of cylinder/rate water is pumped out of the pool

rate water is pumped out of the pool=17m∧3

Volume of cylinder=pi*r∧2*l

According to the given data:

r=3.5

l=1.9

Therefore, Volume of cylinder=3.14*3.5∧2*1.9

Volume of cylinder=73.0835 m∧3

hours does it take to empty the pool=73.0835/17

hours does it take to empty the pool=4.299

The hours does it take to empty the pool is 4.299

As x approaches infinity,

The function with the lowest output is graph A

The function with the greatest output is graph B

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

Explanation:

As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.

The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.

Answer: The function with the lowest output values as x approaches infinity is Graph A.

The function with the greatest output values as x approaches infinity is Graph B.

Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!

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

Explanation:

This is a visual example of the pythagorean theorem. We add the areas of the two squares to get

13+29.25 = 42.25

Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle

x = sqrt(42.25) = 6.5

---------

Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.

Answer:

Step-by-step explanation:

area of a square=a²

A=29.25

a=side=√29.25 first square

second square =a=√13

find x(c)

right triangle: a²+b²=c²

(√29.25 )²+(√13)²=c²

29.25+13=c²

c=√(29.25+13)=6.5 unit

Answer:

2 28ounce cans and 4 15ounce cans

Step-by-step explanation:

28+28=56 and 15+15+15+15=60

56+60=116

Answer:

your answer is the second option

Step-by-step explanation:

Answer:

Part 2:

The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points

The drawing of the angle cross section of a cylinder representing the banana is attached

Part 3:

When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle

The drawing of the perpendicular cross section of a cylinder representing the banana is

Step-by-step explanation:

Answer:

Her annual salary is approximately $41,667

Step-by-step explanation:

Hello,

This question deals with percentage of a number and it's very easy :)

First of all, get the data and understand what's required of us.

Pam spends $7500 yearly on expenses

But this amount represents 18% of her annual income.

Let her annual income be represented by x

18% = 7500 / x

18÷100 = 7500÷x

cross multiply and solve for x

18 × x = 7500 × 100

18x = 750,000

divide both sides by 18

18x / 18 = 750,000 / 18

x = $41,666.67

x = $41,667

Her annual salary is approximately $41,667

Answer:

10,000 panels

Step-by-step explanation:

A TV panel is being produced by two factory plants

Plant A produced 5000 fewer panels than plant B

Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B

a= b-5000............equation 1

5% of the panels from plant A were defective

= 5/100

= 0.05

2% of the panels from plant B were defective

= 2/100

= 0.02

The total defective panels of both plants is 450

0.05a + 0.02b= 450..............equation 2

Substitute b-5000 for a in equation 2

0.05(b-5000) + 0.02b= 450

0.05b - 250 + 0.02b= 450

Collect the like terms

0.05b+0.02b= 450+250

0.07b= 700

Divide both side by the coefficient of b which is 0.07

0.07 b/0.07= 700/0.07

b= 10,000

Hence plant B produced 10,000 panels

Answer:

Option C. 3077.2 mm³

Step-by-step explanation:

Data obtained from the question include the following:

Diameter (d) = 17 mm

Height (h) = 60 mm

Pi (π) = 3.14

Volume =?

Next, we shall determine the radius of the cone. This is illustrated below:

Diameter (d) = 17 mm

Radius (r) =.?

Radius (r) = diameter (d)/2

r = d/2

r = 14/2

r = 7 mm.

The radius therefore, is 7 mm.

To know how much frozen water

is in the icicle, we shall calculate the volume of the icicle using the formula for calculating the volume of a cone. This is illustrated below:

Height (h) = 60 mm

Pi (π) = 3.14

Radius (r) = 7 mm

Volume =..?

V = ⅓πr²h

V = ⅓ × 3.14 × 7² × 60

V = 3.14 × 49 × 20

V = 3077.2 mm³

Therefore, the amount of frozen water in the icicle is 3077.2 mm³

Answer:

C 3,077.2 mm

Step-by-step explanation:

Step-by-step explanation:

v= 4/3πr³

4/3×314/100×8×8×8

•

= 2,143.573

Answer:

Hey there!

We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.

Hope this helps :)

Answer:

7√2 cm

Step-by-step explanation:

Aquí, estamos interesados ​​en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.

Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.

Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.

Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.

Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.

Por lo tanto, tenemos;

14 ^ 2 = x ^ 2 + x ^ 2

196 = 2x ^ 2

dividir ambos lados por 2

98 = x ^ 2 x = √98

x = √ (49 * 2)

x = 7√2 cm

Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm

Answer:

the table is correct

the graph will look like:

Hi,

[tex]y=5x^{2} +12x-2\\y=x(5x+12)-\frac{46}{5} \\y=5(x+\frac{6}{5} )^{2}-\frac{46}{5} \\[/tex]

Have a good day.

Answer:

No

Step-by-step explanation:

He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.

Answer:

a^3 – 25a^2b^5 – 35b^4

He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.

Answer:

50

Step-by-step explanation:

The value of P(A|B) = 0.50 which is correct option(B)

What is independent events?

Independent events is defined as an event that is not affected by other events.

A and B are independent events.

P(A) = 0.50

P(B) = 0.20

P(A|B) = P(A∩B)/P(B)

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

Substitute the value of P(A) = 0.50,

P(A|B) = 0.50

Hence, the value of P(A|B) = 0.50

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Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Following are the description of the given points:

(a) This is a system of probability, which possibility occurs inside an intended manner whenever they choose this specific point of origin from 1 to 100 with no one reserve the possibility about who gets throughout the survey.  

(b) Its method is different from the random sampling technique with the base available. For example, two individuals whose names identical to both the list have no chance to join within the survey.  

(c) its sample is objective to its everyone can enter the test in equal measure.

Answer:

(-19 , -7)

Step-by-step explanation:

y - x = 12

y + x = -25 we sum them to get

2y = -14 , y = -7

then we put -7 instead of y in any of the equations:

-7 - x = 12

-x = 19

x = -19,

finally (x , y) is (-19 , -7)

Answer:

The quotient is 2x^2+4x+11

Step-by-step explanation:

Step-by-step explanation:

this is substitution method

Answer:

2x + y = 21

+

x - y = 6

_________

3x = 27

x = 27 ÷ 3

x= 9

x - y = 6

9 - y = 6

9 - 6 = y

3 = y

Therefore, x= 9 and y = 3

Answer:

Step-by-step explanation:

Total cookies = 12

Ate = 3 cookies

Now,

Percentage of the cookies that James are:

[tex] \frac{3}{12} \times 100 \: percent[/tex]

Calculate:

[tex] = 25 \: percent[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

answer is 25

Step-by-step explanation:

Answer:

The perimeter of the figure is: 8x + 34.

Step-by-step explanation:

The perimeter of a shape is the sum of the length of all its sides. In this case there is one side missing, we need to find its length. To do that we will have to use Pythagora's theorem, because we will create a right triangle as shown in the attached picture. Where a, b and c are the sides of the right triangle. We can determine the lengths of a and c. If we pay close attention to the figure we will realize that a is:

[tex]a = 2x + 5 - 2x = 5[/tex]

While c is:

[tex]c = 2(x + 7) - (x + 5) - (x - 3)\\c = 2x + 14 -x - 5 -x + 3\\c = 2x - 2x + 12\\c = 12[/tex]

We can now apply Pythagora's theorem:

[tex]b^2 = a^2 + c^2\\b^2 = 5^2 + 12^2\\b^2 = 25 + 144\\b = 13[/tex]

With this we can sum all the sides and calculate the perimeter of the shape.

[tex]2x + 5 + x - 3 + 2x + x + 5 + 13 + 2(x + 7)\\2x + x + 2x + x + 2x + 5 - 3 + 5 + 13 + 14\\8x + 34[/tex]

Answer:

0.0015 km².

Step-by-step explanation:

It is given that a map is drawn to a scale of 1 cm to 250 cm.

[tex]1\ cm\times 1\ cm=250\ cm\times 250\ cm[/tex]

[tex]1\ cm^2=62500\ cm^2[/tex]

It is given that an airport has an area of 240 cm² on the map. So, its actual area is

[tex]Area=240\times 62500\ cm^2[/tex]

[tex]Area=15000000\ cm^2[/tex]

[tex]Area=\dfrac{15000000}{10000000000}\ km^2[/tex]

[tex]Area=0.0015\ cm^2[/tex]        [tex][\because 1\ km^2=10000000000\ cm^2][/tex]

Therefore, the area of airport is 0.0015 km².