What are the solutions to the system of equations?
y = 2x² + 6x - 10
\ y =
y = -x + 5

Answer:

x = 3, x = 0

Given expression:

[tex]3^{2x-2}-28\left(3^{x-2}\right)+3=0[/tex]

rewrite expression

[tex]3^{2x} \times 3^{-2}-28\left(3^{x} \times 3^{-2}\right)+3=0[/tex]

treat [tex]\sf \s3^{x}\:as\:u[/tex], then expression

[tex]u^2 \times 3^{-2}-28\left(u \times 3^{-2}\right)+3=0[/tex]

multiply both sides by [tex]\sf 3^{2}[/tex]

[tex]u^2-28\left u+27=0[/tex]

factor expression

[tex]u^2-27\left u - u + 27=0[/tex]

factor out common terms

[tex]u(u-27) -1( u - 27)=0[/tex]

collect into groups

[tex](u-1)( u - 27)=0[/tex]

set to zero

[tex]u =1, \ u=27[/tex]

Substitute [tex]\sf 3^x = u[/tex], to find x

[tex]3^x = 1, \ 3^x = 27[/tex]

[tex]3^x = 3^0, \ 3^x =3^3[/tex]

[tex]x= 0, \ x = 3[/tex]

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Answer:

5/12

Step-by-step explanation:

A ratio of 3:4 means that red counters make up 3/7 of the sum of red and blue counters and blue counters make up 4/7 of the total sum of red and blue counters.

If there is 20 blue counters, then 20 is 4/7 of the sum of the total red and blue counters.

So we need to solve for the total sum.

[tex] \frac{4}{7} x = 20[/tex]

[tex]4x = 140[/tex]

[tex]x = 35[/tex]

So the total amount of red and blue counters are 35,

So this means the amount of red counters is 15.

The amount of yellow counters is 25.

So the total number of counters are 60.

So P(Yellow counters)= 25/60= 5/12

a. Distance moved by effort = 1 meter

b. Work done by effort = 80 Joules

c. Losses in energy = 18 Joules

a. Note that velocity ratio is defined as the ratio of a distance through which any part of a machine moves to the distance moved by its parts

Velocity ratio = distance moved by the effort/distance moved by the body

Where velocity ratio = 5

vertical distance = 20cm

Distance moved by effort = 5 × 0. 20 = 1 meter

b. Formula for work done is given as ;

Work done = Effort × distance moved by effort

Work done = 80 × 1

Work done = 80 Newtons

c. First, let's find the work output

Work output = m g h

Work output = 50 × 9.8 × 0. 20

Work output = 98 Joules

Losses in energy = Work output - work done

Losses in energy = 98 - 80

Losses in energy = 18 Joules

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Answer:

The third picture

Step-by-step explanation:

Solve for x in both equations

2x<6

Divide both sides by 2:

x<3

3x+2>-4

Subtract 2 from both sides:

3x>-6

Divide both sides by 3:

x>-2

There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.

When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.

The circles are not filled in because the symbol is < and > rather than [tex]\leq and \geq[/tex]. When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.

Answer:

5:12

Step-by-step explanation:

because of the new wife

The line which has a gradient of 6 is A. line A

To answer the question, we need to know what the gradient of a line is.

The gradient of a line is its slope. It is given by m = Δy/Δx where

Now, to find the line that has the gradient of 6, we see that the gradient

So, for a high value of gradient, we need

Also, since 6 is positive, the gradient for the line will be positive.

The only line that meets these criteria is line A.

So, the line which has a gradient of 6 is A. line A

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The probability that the person uses exactly one of the facilities is 0.64

Probability is the likelihood of an event happening or an event not happening.

When it is certain an event would happen the probability is 1.

Probability can be independent or mutually exclusive.

Analysis:

Find analysis in the attached file.

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From the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2

the answers are -2.1 and 0.2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two systems of the equation:

y = log (−5.6x + 1.3)

y  = −1 − x

After plotting the above equation on the graph we will see two intersections point:

(-2.12, 1.12) and (0.221, -1.221)

So the least value is x = -2.12 ≈ -2.1

The greatest value is x = 0.221 ≈ 0.2

Thus, from the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2

the answers are -2.1 and 0.2.

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The measure of ∠A is 115˚.

Given that, ∠A and ∠B are supplementary angles. ∠A=(7x + 24)˚ and ∠B=(7x − 26)°.

Two angles are Supplementary when they add up to 180 degrees.

Now, ∠A+∠B=180°

⇒(7x + 24)˚+(7x − 26)°=180°

⇒14x− 2°=180°

⇒14x=182°

⇒14x=182°

⇒x=13°

Now, ∠A=7×13 + 24˚

⇒∠A=91˚+ 24˚=115˚

Therefore, the measure of ∠A is 115˚.

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Hello,

We have A(3, 5) and B(5, 6)

[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]  

We know the line contain the point (3, 5)

    y = 1/2x + b

⇔ 5 = 1/2 × 3 + b

⇔ 5 = 3/2 + b

⇔ 5 - 3/2 = b

⇔ b = 10/2 - 3/2

⇔ b = (10 - 3)/2

⇔ b = 7/2

[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]

Answer:

7.6 units

Step-by-step explanation:

   Use law of sines

12 / sin C = b / sin B

sin B  * 12 / sin C = b

sin (32) * 12 / sin(57) = b = 7.6

The distance between the initial position and the final position is 72.1ft

The initial position is (0ft, 0ft). Where the notation used is:

(horizontal position, vertical position).

Martha climbs 40 steps, then the final position is:

(40*1ft, 40*1.5ft) = (40ft, 60ft)

The distance between the initial position and the final position is:

[tex]d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft[/tex]

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Answer: If for every independent unit(aka x), you multiply the dependent unit by the same amount(aka y).

Step-by-step explanation:

EXAMPLE:

(0,2) (1,6) (2,18) (3,54) (4,162)

As you can see, each time x increases by unit, you multiply the y unit by 3.

As an example, if you increase x by 4, you multiply the y unit by 3^4 = 81.

If this pattern is consistent with your whole table, you have an exponential function.

Hope this is useful.

Answer:

Step-by-step explanation:

Arithmetic sequence:

   a = first term = 4

   d = common difference =  second term - first term

       = 9 - 4

   d  = 5

[tex]\sf t_n =a +(n -1)*d[/tex]

   = 4 + (n - 1) *5

   = 4 + 5n - 5

    = 5n -1

Check; n= 1 ,  first term = 5*1 - 1 = 5 - 1 = 4

           n = 2,  second term = 5*2 - 1 = 10 -1 = 9

           n = 3, third term = 5*3 - 1 = 15 - 1 = 1

The next term, fifth term  = 5*5 - 1

                                          = 25 - 1

                                          = 24

Answer:

There are 4 red counters

Step-by-step explanation:

1. Add the known decimals

    [tex]0.25+0.35+0.3=0.9[/tex]

2. Subtract that amount from one

      [tex]1-0.9=0.1[/tex]

3. multiply the result by 40

    [tex](40)(0.1)=4[/tex]

Hope this helps

Step-by-step explanation:

a probability is always desired cases / total cases.

from the table and given information we know :

there are 40 blue counters.

0.25 = 40/x

x being the total number of counters in the box.

x = 40 / 0.25 = 160

the sum of all probabilities must be 1 (the always true probability), as there are only counters in the box, and one of the 4 colors is always the result.

so,

1 = 0.25 + 0.35 + 0.3 + red-probability

1 = 0.9 + red-probability

red-probability = 1 - 0.9 = 0.1

0.1 = red counters / 160

red counters = 0.1 × 160 = 16

there are 16 red counters in the box.

Answer: its 7

Step-by-step explanation: hope it helps

Answer: X = 5.0

Step-by-step explanation:

- since these are right triangles you can use trigonometry to solve this pretty easily

- for this situation, you only have to use sine/sin

__________________________________________________________

- to start you just need to identify which side is which:

- so, for this problem the equation is: [tex]10xSin(45) = 7.071067812[/tex]

__________________________________________________________

- so 7.071067812 is the hypotenuse of the smaller triangle so you just do the same thing again

- start with identifying which side is which:

- so for this part, the equation is: [tex]7.071067812xSin(45) = 5.0[/tex]

- so X = 5.0

__________________________________________________________

hope this helps :)

Answer:

x = 5

Step-by-step explanation:

Check the file for detailed solution.

This involves SOH-CAH-TOA method, always remember that the opposite of the 90 degree mark is always the hypotenuse. Meanwhile, the position of the given angle (theta) is dependent on which side it is placed. It give either an adjacent or opposite side.

Last option. The sequence that can be used to to get the figure A'B'C'D' is Reflection about the y-axis followed by a translation to the right by 1 unit.

We have an opposite orientation in this question. This based on the fact that (ABCD)' is counterclockwise. While its reflection ABCD is clockwise.

The reflection has to go over a vertical line given that (CD)' and CD are at the bottom. Hence this reflection has to go over  a vertical line.

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Step-by-step explanation:

We gujra weeeeeeee

We gujra weeeeeeee

We gujra weeeeeeee

We gujra weeeeeeee

The value of GX is 13 and m ∠ABX is 22°

With the information, we have

EX = 4z + 1  and XF = 2z + 7

It is important to note that  EX = XF = GX are congruent, that is, they are equal

Equate EX = XF to determine z

4z + 1 = 2z + 7

Collect like terms

2z = 6

z = 3

We know that  EX = XF = GX and x = 3, substitute into the value of any one

EX = 4(3) + 1

EX = 13

EX = GX

GX = 13

To determine m ∠ABX, we divide m ∠ABC by 2

We have

m ∠ABX  = 44/2

m ∠ABX = 22°

Therefore, the value of GX is 13 and m ∠ABX is 22°

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Answer:  13, 22°  

Step-by-step explanation:  Trust Me!  

Answer is correct on Edge. Good Luck!  :)

GX = 13

mABX = 22°

The expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

The area of the rectangle is the product of its length and its width. Therefore, the area of the given rectangle is,

Area = (2x-4)(x+5)

       = 2x² + 10x - 4x - 20

       = 2x² +6x - 20

Hence, the expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.

The complete question is:

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

The image of the rectangle is given below.

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Answer:

9000000001

Step-by-step explanation:

.....................

Answer:

6210001000

Hope This Helps!!!

The distance travelled by the object in meters is 65 meters.

using the formula,

s = 1 / 2 (u + v)t

where

Therefore, the distance can be found as follows;

s = 1 / 2 (6 + 20)5

s = 1 / 2 (26)5

s = 13(5)

s = 65 m

Therefore, the distance travelled by the object in meters is 65 meters.

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Answer:

D.

Step-by-step explanation:

I had the same question

use the 3rd icon to measure 30 and 60 degrees, Then connect them with a line and add a right angle.

Answer:

Not Possible

Step-by-step explanation:

It is not possible. While it does add up to 180, if one is 90 degrees, the rest must be 45 and 45, or your not getting anything.

Let me know if this helped !!

Answer:

m = 0.875

Step-by-step explanation:

the 3 angles lie on a straight line and sum to 180° , that is

4m + 83 + 4m + 90 = 180

8m + 173 = 180 ( subtract 173 from both sides )

8m = 7 ( divide both sides by 8 )

m = [tex]\frac{7}{8}[/tex] = 0.875

Answer:

20 vegetable plants

Step-by-step explanation:

In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!

Point Y is the centre of the circle that passes through points D, E, and F.So option A is correct.

If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.

And the circumcenter is the centre point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.

Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the centre of the circle that passes through points D, E, and F.

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Answer:

A

Step-by-step explanation:

Answer:

180%

Step-by-step explanation:

Given:

The rectangle on the left is fully shaded in meaning that is 1 whole (100%)

The rectangle on the right is 4 / 5 shaded, 4 / 5 = 0.8 (80%)

Combining these will be 100 + 80 = 180%

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Step-by-step explanation:

Using statistical concepts, it is found that it is an experimental study, as the music played corresponds to an experiment.

It is an study where an intervention is applied to a sample, and the effect of this intervention is studied.

In this problem, the music played is the intervention, and it's effect on the time that it takes for the infants to be asleep, hence it is an experimental study.

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The volume of the cone is 1, 139. 49 cm³

Height of cone = 17cm

Base of cone = 16cm

Diameter = 16cm

Radius = diameter/2 = 16/2 = 8cm

Formula for volume of a cone = [tex]\pi r^{2} \frac{h}{3}[/tex]

Substitute the values

Volume = [tex]3. 142[/tex] × [tex]8[/tex] × [tex]8[/tex] × [tex]\frac{17}{3}[/tex]

Volume = [tex]201. 088[/tex] × [tex]5. 67[/tex]

Volume = 1, 139. 49 cm³

Thus, the volume of the cone is 1, 139. 49 cm³

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