Solve without calculator log54 base 10​

Answer: The required ratio is PT:TR  = 1:2.

Step-by-step explanation:

Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².

To find : PT:TR

.i.e. Ratio of PT to TR.

Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]

[tex]=\dfrac{4\ cm}{8\ cm}[/tex]

Divide numerator and denominator by 4 , we get

[tex]\dfrac{1}{2}[/tex]

Therefore, the required ratio is PT:TR  = 1:2.

Answer:

Step-by-step explanation:

- 2(5y - 1) - y = - 4(y - 3)

Expand the terms in the bracket

That's

-10y + 2 - y = - 4y + 12

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

That's

- 10y - y + 4y = 12 - 2

- 7y = 10

Divide both sides by - 7

We have the final answer as

Hope this helps you

Answer:

Proof in the explanation.

Step-by-step explanation:

I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)

This means we want to show the following:

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].

After this I played with only the left hand side to get it to match the right hand side.

One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]

Distribute:

[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

Combine like terms and reorder left side to organize it based on right side:

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Combined like terms while keeping the same organization as the right:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]

Combine like terms:

[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]

Reorder again to fit right side:

[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]

This does match the other side.

The proof is done.

Note: Reordering was done by commutative property.

Step-by-step explanation: The first rectangle to the right is 24 because 10+14 equals 24. The rectangle to the left is 19 because 10+9 equals 19. Finally the rectangle on the bottom is 23 because 14+9 is 23

Step-by-step explanation:

x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x

(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator

(x+3)4=4×+3

(1-x)(4x-8)

1(4x-8)-x(4x-8)

4x-8-4x^2-8x=4x

Answer:

488

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

=(-5)+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4 ans.....

Answer:

6x + 3 + 2y

Step-by-step explanation:

The GCF is 6 as thats the largest factor, so you divide the numbers by 6.

6x + 3 + 2y

Answer:

1533

Step-by-step explanation:

73x21= 1533

Answer:

73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73+73

=73x21=1533

Step-by-step explanation:

Answer:

5.2 inches

Step-by-step explanation:

Let a be the side of the square poster.

The area of it is:

● A = a^2

● 27 = a^2

● a = √27

● a = √(9×3)

● a = 3√3

● a = 5.19

Round it to the nearest tenth

● a = 5.2 inches

The length of one side of the poster is approximately 5 inches rounded to nearest tenth.

We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.

According to the given question the area of a square poster is 27inch².

We have to determine the length of one side of the poster.

We know area of a square is (side)².

∴ (side)² = 27.

side = [tex]\sqrt{27}[/tex].

We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.

learn more about rounding of numbers here :

https://brainly.com/question/15235224

#SPJ2

Answer:

umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...

Step-by-step explanation:

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Answer:

Area= 452.23 ft²

Step-by-step explanation:

Angle at U = 180-48-20

Angle at U = 112°

UT/sin 112=46/sin 48

UT= 0.9272*46/0.7431

UT=57.4 ft

UV= sin 20*46/sin48

UV= 0.3420*46/0.7431

UV= 21.2 ft

S=( 21.2+57.4+46)/2

S=124.6/2

S= 62.3

Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))

Area= √((62.3)(41.1)(4.9)(16.3))

Area= √204509.5311

Area= 452.23 ft²

Intersection point of graph of function is known as solution of the function.

Graph is attached below, in which solution is shown.

1. Here, given that  [tex]3x^2-3x+2=2[/tex]

It can be written as,   [tex]y=3x^2-3x+2\\\\y=2[/tex]

Intersection point of graph of above two equation will be the solution of given function,

Solutions are (1, 2) and (0, 2)

2. Given that , [tex]3x^2-3x-1=x+1[/tex]

It can be written as

                [tex]y=3x^2-3x-1\\\\y=x+1[/tex]

Intersection of graph of above two equation will be the solution of given equation.

Solutions are  (1.721, 2.721) and (- 0.387, 0.613)

Both graph attached below,

Learn more:

https://brainly.com/question/13713063

Answer:

AE = 18 units

Step-by-step explanation:

Δ AEB and Δ DEC are similar , then corresponding sides are in proportion, that is

[tex]\frac{AE}{DE}[/tex] = [tex]\frac{AB}{DC}[/tex] , substitute values

[tex]\frac{2x+4}{x+8}[/tex] = [tex]\frac{12}{10}[/tex] ( cross- multiply )

10(2x + 4) = 12(x + 8) ← distribute parenthesis on both sides

20x + 40 = 12x + 96 ( subtract 12x from both sides )

8x + 40 = 96 ( subtract 40 from both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Then

AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18 units

Answer:

f(x) = 4sin(x) - 3

Step-by-step explanation:

Answer:

$10.48

Step-by-step explanation:

To the nearest cent, your answer would be 10.48

Answer: the answer is P

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

3/2 * (-22/33)

Simplify by dividing the second fraction by 11

3/2 * (-2/3)

Rewriting

3/3 * (-2/2)

-1/1

Answer:

-1

Step-by-step explanation:

(a/b)(c/d) = (a*c)(

(3/2)(-22/33)

(3*-22)/(2*33) = -66/66 = -1

Answer:

To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.

The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.

1) y  = -3x^2 -12x -10

the derivative of y is y' = -6x -12 = -6(x+2)

y'=0 <=>  -6(x+2) = 0 <=> x+2=0 <=> x=-2

y(-2) = -3(-2)^2 -12*(-2) -10 = 2

So the vertex is the point (-2,2) .

Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .

To find another 4 points you just have to pick values of x and replace them in the equation y  = -3x^2 -12x -10  to find y.

2) y = -2x^2 -12x -16

Do the same thing we did in point 1

y'= -4x-12 = -4(x+3)

y'=0 <=>  -4(x+3) = 0 <=> x+3=0 <=> x=-3

y(-3) = -2(-3)^2 -12*(-3) -16 = 2

So the vertex is the point (-3,2) .

Answer:

95%

Step by step explanation:

z = 17-21 / 2 and z = 25-21/2

z=-2 (2.28%) z=2 (97.72%)

97.72 - 2.28 = 5.44

100% - 5.44% is about equal to 95%

You can use any calculator in Maths.

Answer:

The answer to your question is 7 lbs.

Step-by-step explanation:

Data

angle = 70°

force = 20 lb

horizontal component

Process

To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.

1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.

                  cos Ф = adjacent side / hypotenuse

- Solve for the adjacent side

                  adjacent side = hypotenuse x cosФ

- Substitution

                  adjacent side = 20 x cos 70

- Simplification

                  adjacent side = 20 x 0.342

- Result

                  adjacent side = 6.84 ≈ 7 lb  

Answer:

The distribution is positively skewed.

Step-by-step explanation:

It's not symmetric because the distribution in the chart isn't equally shown or marked. It's not negative skewed either because for it to be negative the graph would have to go down in a negative direction, usually the left, but in the picture you posted the graph is going down in the right direction. Lastly, positively skewed graphs or charts look like the one you posted. They go down in the right direction, hence why they're called "positively" skewed. The right tail of the distribution is longer in positively skewed graphs or charts.

Answer:

76 degrees

Step-by-step explanation:

Let the angles be x, y and z

As per given:

Considering the first 2 equations in the third one:

So the third angle is:

Answer:

When two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°

Step-by-step explanation:

Based on the Inscribed Angles Theorem, the measure of an intercepted arc is twice the measure of the inscribed angle that intercepts it in a circle.

Consequently, the theorem also Holds that the measure of two inscribed angles intercepting the same arc, are congruent. In other words, both angles together are the same, and their sum would give you the measure of the arc they both intercept.

In the diagram shown in the attachment below, we have 2 inscribed angles, angle A and B. They both intercept the same arc of 75°.

Therefore, we can conclude that the measure of both angles equal 75°, which is the same as the measure of the arc they intercept.

Angle A = Angle B

m<A + m<B = measure of intercepted arc = 75°

Answer:

135

Step-by-step explanation:

The equation is 135+90+x=360. x=360-(225)=135

Answer:

31.5cm²

Step-by-step explanation:

area of a triangle =1/2 b h

b= 7cm

h=9cm

1/2×7×9

= 1/2×63

= 31.5cm²

hypotenuse is unknown so,

c²=a²+b²

c²= 7² + 9²

= 49 + 81

c²= 130

c= 11.4cm

perimeter= 7 +9+11.4

=27.4cm

pls note that no unit was stated

Answer:

[tex]\Large \boxed{11.08}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

AD/DC = BE/EC

Let the length of EC be x.

6/14 = 4.75/x

Solve for x.

Cross multiply.

6 × x = 14 × 4.75

6x = 66.5

Divide both sides by 6.

(6x)/6 = (66.5)/6

x = 11.083333...

Greetings from Brasil...

Here we can use similarities of triangles

AC/DC = BC/EC

20/14 = (4.75 + X)/X

X ≅ 11.1

see attachment