The best answer gets 100 points. A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
Infinitely many solutions exist because the two situations describe the same line.
Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.

Solution:

Given:

Let's represent the number of oranges and grapefruits by the letters o and g.

This means that...

Now, let's solve the expression to find out how much does Dion has to pay.

Substituting o and g with the given values:

We also know that Dion gave a $20. To find the change, subtract the money Dion gave with the money required to pay for the fruits.

Thus, Dion got $13.85 as change.

Answer:

True, 52-2 equals 50, 50 is greater than 6.

Step-by-step explanation:

Answer:

[tex]\large{\boxed{\sf Chord = 8cm }}[/tex]

Step-by-step explanation:

First see figure in attachment . As we know that ,Perpendicular from centre of the circle bisects the chord . Hence here ,

[tex]\sf\qquad\longrightarrow AB = 2AC = 2x [/tex]

Now in ∆OAC , by Pythagoras Theorem , we have ;

[tex]\sf\qquad\longrightarrow (5cm)^2= x^2+(3cm)^2\\ [/tex]

[tex]\sf\qquad\longrightarrow 25cm^2=x^2+9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=25cm^2-9cm^2\\[/tex]

[tex]\sf\qquad\longrightarrow x^2=16cm^2\\ [/tex]

[tex]\sf\qquad\longrightarrow \pink{ x = 4cm } [/tex]

Therefore , the length of chord will be ,

[tex]\sf\qquad\longrightarrow AB = 2x \\ [/tex]

[tex]\sf\qquad\longrightarrow AB = 2(4cm)\\[/tex]

[tex]\sf\qquad\longrightarrow \pink{ AB = 8cm } [/tex]

Hence the length of chord is 8cm .

Answer:

2 2/3

Step-by-step explanation:

Since we only know how much milk we have we will disregard the flour. That leaves us with 4 cups of milk total and 1 1/2 cups of milk per serving. Simply divide 4 by 1 1/2 to get your answer of 2 2/3. Now, if they only want full servings, then the answer would be 2.

Answer: x=27.44

Step-by-step explanation:

i had this already and i got it correct so here is your answer for this question your answer will be x=27.44

Answer:

y = 4

Step-by-step explanation:

Answer:

A.600

B.980

C.350

D.210

Step-by-step explanation:

just see what the arrow

Answer:

2 time greater

Step-by-step explanation:

5x20=100

10x20=200

100x2=200

so its 2 times greater

The true statements about Marcus graph are:

From the complete question, we have the following parameters:

Phone service 1

Phone service 2

By comparing the above parameters:

The above statements represent the true statements about the Marcus' graph

Read more about graphs at:

https://brainly.com/question/14323743

Answer:

The area of the circular park is about 1017.88

Step-by-step explanation:

First, we recall the area of a circle.

A=  πr^2

Next, we plug in the radius

A=  π*18^2

A=  π*324

A= 1017.88

To conclude, that is how you find the area of a circular park.

Answer:

D

Step-by-step explanation:

(7+8)*3

i hope my answers are ✅.......

Answer:

1+1/4

Step-by-step explanation:

Subtract 7/8 from both sides of the equation

so 2-3/4=5/4

Answer:

Which fractions

Step-by-step explanation:

Answer:     4

Step-by-step explanation:

That should be your answer

The factors of the polynomial equation by complete the statements about factoring by grouping are,

[tex](2x-1)\\(7x+3)[/tex]

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.

To find the factor of a polynomial, make the groups of the equation, and equate them equal to zero.

The provided polynomial equation is,

[tex]14x^2+ 6x - 7x - 3[/tex]

Rearrange the equation,

[tex]14x^2- 7x + 6x - 3[/tex]

Take out the common terms 7x from the first two terms and 3 from the last two terms.

[tex]7x(2x- 1) + 3(2x - 1)\\(2x-1)(7x+3)[/tex]

Thus, the factors of the polynomial equation by complete the statements about factoring by grouping are,

[tex](2x-1)\\(7x+3)[/tex]

Learn more about factor of polynomial here;

https://brainly.com/question/24380382

Answer:

Step-by-step explanation:

Here it's given that a 6m ladder is leaned against a house, and the base of ladder is 2m away from the foot of the house. Here I am assuming x to be the height of the house.

Diagram :-

[tex] \begin{picture}(3,3)\setlength{\unitlength}{1cm} \linethickness{.6mm}\put(0,0){\line(1,0){4}}\put(0.01,0){\line(4,3){4}}\put(4,0){\line(0,1){3}}\put(4.3,1){$\bf x $} \put(2,-0.5){$\bf 2m$}\put(1,1.5){$\bf 6m$}\put(.9,0.2){$\bf\theta $}\put(2,4){$\boxed{\sf - RISH4BH }$}\end{picture} [/tex]

Using, Pythagoras theorem ,

[tex]\longrightarrow h^2=p^2+b^2 [/tex]

Substitute,

[tex]\longrightarrow (6m)^2=x^2+(2m)^2[/tex]

Simplify,

[tex]\longrightarrow 36m^2= x^2+4m^2 [/tex]

Subtracting 4m² on both sides,

[tex]\longrightarrow x^2 = 36m^2 -4m^2=32m^2 [/tex]

Put square root on both sides,

[tex]\longrightarrow x =\sqrt{32m^2}[/tex]

Simplify,

[tex]\longrightarrow \underline{\underline{ x = 5.65\ m}}[/tex]

Again in order to find out the angle of elevation,

[tex]\longrightarrow cos\theta =\dfrac{b}{h} [/tex]

Substitute,

[tex]\longrightarrow cos\theta =\dfrac{2m}{6m}[/tex]

Simplify,

[tex]\longrightarrow cos\theta =\dfrac{1}{3} [/tex]

Take cos inverse both sides,

[tex]\longrightarrow \underline{\underline{\theta =cos^{-1}\bigg(\dfrac{1}{3}\bigg)}}[/tex]

The length of the wall is 5.66m and the angle of elevation is 70.56°

Data;

To calculate the length of the wall or side of the house, we have to use Pythagorean theorem which is given as

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

Let's substitute the values and solve for the length of the wall

[tex]x^2 = y^2 + z^2 \\6^2 = 2^2 + z^2 \\36 = 4 - z^2\\z^2 = 36 - 4\\z^2 = 32\\z = \sqrt{32} \\z = 5.66m[/tex]

The length of the wall is 5.66m.

To calculate the angle of elevation, we can use trigonometric ratio SOHCAHTOA

since we have the value of all the sides, we can decide to use any of the ratios.

I will use sine angle to solve for the angle of elevation.

[tex]sin \theta = \frac{opposite}{hypothenuse} \\sin \theta = \frac{5.66}{6} \\sin \theta = 0.943\\\theta = sin^-^1 (0.943)\\\theta = 70.56^0[/tex]

The angle of elevation is 70.56°

Learn more on Pythagorean theorem and trigonometric ratio here;

https://brainly.com/question/6241673

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

Explanation:

Use the distance formula to calculate the distance from R to S. This is identical to the length of segment RS.

[tex]R = (x_1,y_1) = (-3,-1) \text{ and } S = (x_2, y_2) = (0,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-0)^2 + (-1-3)^2}\\\\d = \sqrt{(-3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment RS is exactly 5 units long.

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

Repeat similar steps to find the length of segment ST

[tex]S = (x_1,y_1) = (0,3) \text{ and } T = (x_2, y_2) = (3,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-3)^2 + (3-0)^2}\\\\d = \sqrt{(-3)^2 + (3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d \approx 4.2426\\\\[/tex]

ST is roughly 4.2426 units long.

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

Lastly, let's calculate the length of segment TR.

[tex]T = (x_1,y_1) = (3,0) \text{ and } R = (x_2, y_2) = (-3,-1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-3))^2 + (0-(-1))^2}\\\\d = \sqrt{(3+3)^2 + (0+1)^2}\\\\d = \sqrt{(6)^2 + (1)^2}\\\\d = \sqrt{36 + 1}\\\\d = \sqrt{37}\\\\d \approx 6.0828\\\\[/tex]

TR is about 6.0828 units long.

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

Summary of the segment lengths:

The three sides are different lengths.

Therefore, the triangle is scalene.

The annual rate of decay is r = 0.87

We know that if a quantity has a half-life of T, then the rate of decay must be such that:

r^T = 0.5

This means that when a time T passes, the original quantity becomes half of what it originally was.

In this case we know that the half-life is T = 5 years, then we have:

r^5 = 0.5

r = 0.5^(1/5) = 0.87

Then the annual rate of decay is r = 0.87, and if the initial quantity is 18 grams, we can write the exponential decay as:

f(t) = 18g*(0.87)^t

If you want to learn more about exponential decays, you can read:

https://brainly.com/question/11464095

Answer:

13%

Step-by-step explanation:

I took the test on edge and got it right

Answer: D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

5+4=9

Answer:

4 possibly

Step-by-step explanation:

Answer:

I think x=[tex]\sqrt[6]{1}[/tex] , possibly

Step-by-step explanation:

19 3/5

yeah..

Answer:

x=41

Step-by-step explanation:

supplementary angles add to 180

3x + (2x-25) = 180

5x = 205

x= 41

 angle1          3x41 = 123

angle 2 (2x41) -25 = 57

 123 +57 = 180

Answer:

  x = 1 +√5

Step-by-step explanation:

There are different formulas for the area of a triangle available, depending on the given information.

When two sides and the angle between them are given, the relevant area formula is ...

  Area = 1/2(ab)sin(C)

When the base and height of a triangle are given, the relevant area formula is ...

  Area = 1/2bh

The problem statement tells us the two triangles shown have equal areas. That means the two formulas will give the same result.

  Area from angle = Area from base/height

  1/2(x·x)sin(30°) = 1/2(x-2)(x+1)

  x² = 2(x² -x -2) . . . . . . . . . . . use sin(30°) = 1/2, multiply by 4

  x² -2x -4 = 0 . . . . . . . . subtract x², eliminate parentheses

  (x -1)² = 5 . . . . . . . . . add 4+1 to complete the square

  x = 1 ± √5 . . . . . . take the square root, add 1

The value of x must be greater than 2 in order for the triangle side lengths to be positive. (x-2 > 0) This means x = 1-√5 is an extraneous solution.

The value of x is 1 +√5.

Answer:

Step-by-step explanation:

Let Kayla made number of 2 points shots = x

and the number of 3 points shots = y

Since she made total nine shots so the equation will be

x + y = 9 --------(1)

She scores a total of 22 points so the equation will be

2x + 3y = 22 --------(2)

Now we multiply equation (1) by 2 and subtract it from equation (2)

(2x + 3y) - 2(x + y) = 22 - 18

2x + 3y - 2x - 2y = 4

y = 4

from equation (1)

x + 4 = 9

x = 5

Therefore, number of 2 shots are 5 and number of 3 shots are 4.