Use the graph of the function y = (x + 3)(x − 2) to find the solutions of the quadratic equation 0 = (x + 3)(x − 2). The solutions of the quadratic equation 0 = (x + 3)(x − 2) are –6 and 0. –4 and 3. –3 and 2. –2 and 1.

Answer:

-7

Step-by-step explanation:

Use slope equation m=y2-y1/x2-x1 aka m=rise/run.

Insert in the correct values.

-1-(-3)=2=run

-8-6=-14=rise

SO, -14/2=m

Simplify:-14/2=-7

m=-7

The given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

An angle is formed when two rays have the same end point. The common end point is called vertex.

Given is to identify the positive angle.

Any angle measured clockwise with respect to + x axis is negative. Similarly, any angle measured anti - clockwise with respect to + x axis is negative.

Since only one angle is shown in the image, we will describe about it. It can be seen that the angle is measured clockwise with respect to + x axis. Hence, it is negative.

Therefore, the given angle is measured clockwise with respect to {+x} axis. So, it has negative measure.

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Answer:

I would say 49 is your answer

Step-by-step explanation:

53 plus 78 qould equal 131

subtract 131 from 180 and you get 49

add up all your numbers including x then they should all equal 180

Answer:

45=5t

Step-by-step explanation:

im doing it right now and got it right

Answer:

The $3485.52 money did Meg have at the end of the account term.

Step-by-step explanation:

Formula for compounded monthly

[tex]Amount = P(1+\frac{r}{365})^{365n}[/tex]

Where P is the principle , r is the rate of interest in the decimal form and n is the number of years.

As given

Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years.

Principle = $3000

3% is written in the decimal form

[tex]= \frac{3}{100}[/tex]

= 0.03

Time = 5 years

Put in the formula

[tex]Amount = 3000(1+\frac{0.03}{365})^{365\times 5}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+\frac{0.03}{365})^{1825}[/tex]

[tex]Amount = 3000(1+ 0.0000822)^{1825}[/tex]

[tex]Amount = 3000(1.0000822)^{1825}[/tex]

[tex]Amount = 3000\times 1.16184[/tex]

Amount = $ 3485.52

Therefore the  $ 3485.52  money did Meg have at the end of the account term.

Answer:

The Answer is $3,485 btw

Step-by-step explanation:

Answer C

Answer:

[tex]x^{\circ}=56^{\circ};[/tex]

The exterior angle has measure [tex]116^{\circ}.[/tex]

Step-by-step explanation:

Angle QRP and angle with measure of (2x+4)° are supplementary, then

[tex]m\angle QRP+(2x+4)^{\circ}=180^{\circ},\\ \\m\angle QRP=180^{\circ}-(2x+4)^{\circ}.[/tex]

The sum of the measures of all interior angles of the triangle is equal to 180°, then

[tex]m\angle PQR+m\angle QRP+m\angle RPQ=180^{\circ},\\ \\x^{\circ}+180^{\circ}-(2x+4)^{\circ}+60^{\circ}=180^{\circ},\\ \\x^{\circ}-2x^{\circ}=-60^{\circ}+4^{\circ},\\ \\-x^{\circ}=-56^{\circ},\\ \\x^{\circ}=56^{\circ}.[/tex]

The exterior angle has measure

[tex](2\cdot 56+4)^{\circ}=116^{\circ}.[/tex]

Answer:

x=56 and the exterior angle is 116

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +4) form a straight line so they make 180 degrees.

y + 2x+4 =180

Solve for y by subtracting 2x+4 from each side.

y + 2x+4 - (2x+4) =180 - (2x+4)

y = 180-2x-4

y = 176-2x

The three angles of a triangle add to 180 degrees

x+ y+ 60 = 180

x+ (176-2x)+60 = 180

Combine like terms

-x +236=180

Subtract 236 from each side

-x+236-236 = 180-236

-x = -56

Multiply each side by -1

-1*-x = -56*-1

x=56

The exterior angle is 2x+4.  Substitute x=56 into the equation.

2(56)+4

112+4

116

Answer:

The correct option is C.

Step-by-step explanation:

In a triangle, then sum of two smaller sides is greater than the length of third greatest side.

Let, in a triangle ABC, If the length of sides are [tex]a<b<c[/tex], then

[tex]c<a+b[/tex]

In option A,

[tex]8\nless 2+4[/tex]

Therefore option A is incorrect.

In option B,

[tex]6\nless 2+4[/tex]

Therefore option B is incorrect.

In option C,

[tex]7<3+5[/tex]

Therefore option C is correct.

In option D,

[tex]9\nless 3+5[/tex]

Therefore option D is incorrect.

Answer:

C. 3, 5, 7

Step-by-step explanation:

We know that in a triangle, 'the sum of lengths of two sides is always greater than the length of the third side'.

So, according to our options:

A. In 2, 4, 8. We have 2 + 4 = 6 < 8

B. In 2, 4, 6. We see that, 2 + 4 = 6

C. In 3, 5, 7. We see that, 3 + 5 = 8 > 7

D. In 3, 5, 9. We see that, 3 + 5 = 8 < 9.

Therefore, only option C satisfies the property of the triangle stated above.

Hence, 3, 5, 7 are the side lengths of a triangle.

This is true.  The slope of the perpendicular line is equal to the negative reciprocal.  This means that you "flip" the fraction and multiply by negative 1.  Since the reciprocal is also the multiplicative inverse (something you multiply by a number to get 1), and the signs are different (one is positive, one is negative) it equals -1.

Hope this helps!

The statement is true that the product of the slopes of perpendicular lines, excluding vertical lines, always equals -1. This is a basic rule in geometry, where two lines are perpendicular if their slopes multiply to -1.

The statement that 'the product of the slopes of perpendicular lines (excluding vertical lines) always equals -1' is true.

In the coordinate system, two lines are perpendicular if the product of their slopes is -1. This is because the slope is a measure of the steepness of a line. Imagine you have two lines with slopes m1 and m2. If these lines are perpendicular to each other, then m1 * m2 = -1.

For example, if one line has a slope of 2 (m1 = 2), the line perpendicular to it will have a slope of -1/2 (since 2 * -1/2 = -1).

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Answer:

x = 1/6

Step-by-step explanation:

2(3x+1)=3

Distribute.

6x + 2 = 3

Subtract 2 from both sides.

6x = 1

Divide by 6 on both sides.

x = 1/6

Hello there!

Question:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto2(3x+1)=3[/tex]

Distribute:-

[tex]\sf \longmapsto \: (2)(3x)+(2)(1)=3[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 6x + 2 = 3[/tex]

Subtract 2 from both sides :-

[tex]\sf \longmapsto 6x+2 - 2=3 - 2[/tex]

On Simplification:-

[tex]\sf \longmapsto6x + 0 = 3 - 2[/tex]

[tex]\sf \longmapsto6x = 1[/tex]

Divide the two sides by 6:-

[tex]\sf \longmapsto \: \dfrac{6x}{6} = \dfrac{1}{6} [/tex]

Cancel 6/6, leave x, answer is 1x. 1/6 can't be cancelled.

[tex]\sf \longmapsto \: \dfrac{ \cancel6x}{ \cancel6} = \dfrac{1}{6} [/tex]

[tex]\sf \longmapsto \: x = \dfrac{1}{6} [/tex]

In Decimal:-

[tex]\sf \longmapsto \: x = 0.16[/tex]

______________________________________

Henceforth,the value of x is :-

[tex]\boxed{\huge\tt x = \dfrac{1}{6}} [/tex]

[tex] \bold{OR,}[/tex]

[tex]\boxed{\huge\tt x = 0.16}[/tex]

_____________________________________

Please let me know if you have any questions.

~MisterBrian

Answers:

The sign is 4 ft on a side

The poster is 2 ft on a side

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

Explanation:

s = side length of the sign

p = side length of the poster

The poster "has sides measuring 2 ft less than the sides of the square sign", so p = s-2. Whatever the value of 's' is, we subtract off 2 to get the value of p. For example, if the sign has side lengths of s = 10 ft, then p = s-2 = 10-2 = 8 ft is the side length of the poster

We don't know s or p right now, so they are simply placeholders for some numbers.

If s is the side length of the sign, then s*s = s^2 is the area

If p is the side length of the poster, then p*p = p^2 is the area of the poster. We can replace p with s-2 since p = s-2. So we end up with p^2 = (s-2)^2 = s^2 - 4s + 4 after using the FOIL rule

Now subtract the two areas and set that difference equal to 12. Solve for s

(area of sign) - (area of poster) = 12

(s^2) - (s^2 - 4s + 4) = 12

s^2 - s^2 + 4s - 4 = 12

4s - 4 = 12

4s - 4+4 = 12+4

4s = 16

4s/4 = 16/4

s = 4

The sign's side length is 4, so its area is 4^2 = 16

If s = 4, then p is

p = s-2

p = 4-2

p = 2

The poster's side length is 2, so its area is 2^2 = 4

Subtract the areas: 16 - 4 = 12

The answer is confirmed

The question about the height of a tree on a scale drawing did not provide enough information for a certain answer. However, given a hypothetical height for the drawn tree, the actual height can be determined by multiplying this by the scale factor.

The subject of this question is mathematics, specifically dealing with ratios and proportions related to scale drawings. Given that the scale of the drawing is 1 in: 5 ft, this means that 1 inch on the drawing corresponds to 5 feet in real life. However, the specific height of the tree on the drawing in inches is not provided in the question, making it impossible to give a definite answer.

As an example to further explain, if the tree is drawn as 2 inches on the scale drawing, you would simply multiply by 5 (since the scale is 1 in: 5 ft) to find the actual height of the tree. So, for a 2 inch drawn tree, the actual tree would be 2 in * 5 ft/in = 10 ft tall.

But given the current information, a definite height cannot be provided. Please provide the height of the tree in inches on the scale drawing.

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Answer:

- 405

Step-by-step explanation:

the recursive formula given allows us to find the next term in the sequence by multiplying the previous term by - 3

[tex]b_{2}[/tex] = [tex]b_{1}[/tex](- 3) = 15 × - 3 = - 45

[tex]b_{3}[/tex] = [tex]b_{2}[/tex](- 3) = - 45 × - 3 = 135

[tex]b_{4}[/tex] = [tex]b_{3}[/tex](- 3) = 135 × - 3 = - 405

35kg - a mass of sugar syrup

30% of 35kg it's a mass of sugar

30% = 30 : 100 = 0.3

30% of 35kg = 0.3 · 35kg = 10.5kg - a mass of sugar

Add xkg water. Then we have (35 + x)kg of sugar syrup and still 10.5kg of sugar.

10.5kg is 25% of (35 + x)kg .

(35 + x) -- 100%

10.5  -- 25%     multiply both sides by 4

42   -- 100%

Therefore we have the equation:

35 + x = 42      subtract 35 from both sides

x = 7

Answer:

Step-by-step explanation: sec^2A-tan^2A+1

=1+1

=2

Answer:

Hello :

secA= 1/cosA

tanA = sinA / cosA

- tan²A + 1 + sec²A  = - (sinA / cosA)² + 1 + ( 1/cosA)²

                                 = - sin²A / cos²A  + 1 + 1 /cos²A

                                 = ( - sin²A  + cos²A +1)/cos²A

                                = ( 1 - sin²A + cos²A ) / cos²A

but : 1 - sin²A = cos²A   because : sin²A + cos²A = 1

so : - tan²A + 1 + sec²A  = ( 2 cos²A) / (cos²A)

- tan²A + 1 + sec²A  = 2

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

we use points (0,5) (1,9)

[tex]slope = \frac{9-5}{1-0}=4[/tex]

slope m= 5

Now we use y=mx+b equation

m= slope and b= y intercept, plug in (0,5)  and find out b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function

Answer:

5 is the initial value

Step-by-step explanation:

From the table we can see that the values of y are increasing by 4

Lets use two points and find out slope

formula of slope

slope=m=[tex]\frac{y2-y1}{x2-x1}[/tex]

putting points (0,5) (1,9) in equation of slope

m=[tex]\frac{9-5}{1-0}[/tex]

slope m= 4

we know y=mx+b

m= slope and b= y intercept, plug in (0,5)  and find out b

b=?

x=0

m=4

y=5

putting these values in y=mx+b

y=4x+b

5= 4(0) +b

so b= 5

b=5 is the initial value of the function

Answer:

B

Step-by-step explanation:

It's B.

Answer:

Step-by-step explanation:

its b

Answer:

Step-by-step explanation: to covert improper fractions to normal fractions.

29/6 would be 4 wholes and 5/6

You count how much 6’s are in the 29 which is 4. And then the left over would be 5 so 5/6

Answer:

Estimate is 150 and actual product is 138.

Step-by-step explanation:

To estimate products, we round the numbers to nearest unit place, 10th, 100th, 1000th, and so on.

Given are the numbers 3 and 46.

We can round 46 ≈ 50.

So Estimation would be 3 x 46 ≈ 3 x 50

3 times 5 is 15 and we can add zeros after it.  

So estimation is 3 x 46 ≈ 150.

Now actual product would be...

3 times 6 is 18, so we note down 8 and 1 goes to carry over 4.

3 times 4 is 12 and carry 1 will be added in it, so 12 + 1 = 13.

It means the actual product is 3 x 48 = 138.

Answer:

y + 2 = 23(x - 3)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = 23 and (a, b) = (3, - 2), hence

y + 2 = 23(x - 3) ← equation in point-slope form

Answer:

60%

Step-by-step explanation:

first do 28+32.

Next it equals 60. So change 60 to percentage form. It would be 60%

Answer:

C  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

4.20 ÷ 60 = 0.07

sales tax is 7% and this is your constant of variation

The answer is 0.07 hope this helps you ! :)

Answer:

$1453.2

Step-by-step explanation:

I assume you mean the accumulated value on a principal of $1400 with 3.8% interest in 1 year.

1400 * (100%+3.8%) = 1400 * 1.038 = 1453.2

Answer:

Step-by-step explanation:

There are several ways in which you could do this.  

One involves finding the x- and y-intercepts, plotting them and drawing a straight line through them.  Starting with 4x + 2y = 16, let x = 0 to find the y-intercept:  2y = 16, or y = 8.  The y-intercept is (0,8).  Next, let y = 0 in 4x + 2y = 16 and solve for x; this leads to the x-intercept.  4x = 16, so x = 4.  The x-intercept is then (4, 0).  Plot (4,0) and (0, 8) and draw a straight line through these two points.

Another involves solving 4x+2y=16 for y, obtaining the equivalent in slope-intercept form of this equation.  Subtracting 4x from both sides, we get 2y = 16 - 4x.  Dividing all terms by 2 results in y = -2x + 8.

As before, the y-intercept is (0,8).  Plot this point.  Now use the slope, m = -2, to find another point on this line:  Starting at (0,8), move 1 unit to the right (increasing x by 1) and then move 2 units down, arriving at (1, 6).  Plot this point.  Now draw a straight line through (1,6) and (0,8).  Your result should look the same as the previous graph you drew.

Answer: x < 3

Step-by-step explanation:

NOTE: [tex]\sqrt{(x+5)^2} = |x + 5|[/tex]

Rewrite the equation:

| x + 5 | < | x + 1 |

Remember that absolute value makes the "inside" value positive, so we need to solve for 2 case of x + 5 (inside is positive or negative) and 2 cases of x + 1.

± (x + 5) < ± (x + 1)

Case 1: +  +

x + 5 < x + 1

    5 < 1

  FALSE

Case 2: - -

-(x + 5) < -(x + 1)

 x + 5 > x + 1   divided both sides by -1

      5 > 1

     TRUE so this works when both "insides" are negative

⇒   x + 5 < 0     and      x + 1 < 0

          x < -5     and           x < -1

since it has to satisfy both, x < -5

Case 3: + -

x + 5 < -(x + 1)

x + 5 < -x - 1     distributed -1 on right side

2x + 5 < -1

2x       < -6

 x       < -3

Case 4: - +

-(x + 5) < x + 1

-x - 5 < x + 1     distributed -1 on left side

   -5 < 2x + 1

   -6 < 2x

   -3 < x

     x > -3

This is a contradiction of Case 3 so need to choose a test point.

TEST POINTS (I choose -6, -4, and -2)

 | -6 + 5 | < | -6 + 1 |

 |    -1     | < |    -5   |

          1   <   5

        TRUE so x < -5 is valid

 | -4 + 5 | < | -4 + 1 |

 |     1     | < |    -3   |

          1   <   3

        TRUE so x < -3 is valid

 | -2 + 5 | < | -2 + 1 |

 |     3     | < |    -1   |

          3   <   1

        FALSE so x > 3 is NOT valid

Note that x < -3 includes all the values of x < -5, so x < -3 is the answer.

*******************************************************************************

This is a faster way to solve it. Thank you @proner26 !

| x + 5 | < | x + 1 |

(| x + 5 |)² < (| x + 1 |)²

x² + 10x + 25 < x² + 2x + 1

       10x + 25 <       2x + 1

        8x + 25 <                1

        8x         <             -24

          x         <              -3

Answer: x < -3

Answer:

These fractions are not equivalent.

Step-by-step explanation:

To tell whether the fractions are equivalent, get a common denominator.

The common denominator is 10

1/2 *5/5 = 5/10

2/5 *2/2 = 4/10

5/10 ≠4/10

These fractions are not equivalent.

Answer:

The annual percentage yield is 6.609%

Step-by-step explanation:

Let's assume

amount invested=$1

so, P=1

APR of 6.4% compounded daily

so, r=6.4%=0.064

n=365

t=1

now, we can use formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

now, we ca plug values

[tex]A=1(1+\frac{0.064}{365})^{365\times 1}[/tex]

we get

[tex]A=1.06609[/tex]

now, we can find APY

[tex]APY=\frac{A-P}{P}\times 100[/tex]

now, we can plug values

[tex]APY=\frac{1.06609-1}{1}\times 100[/tex]

we get

APY is 6.609%

Answer:

The annual percentage yield is 6.609%.

Step-by-step explanation:

The annual percentage yield is calculated by:

APY = [tex](1+\frac{r}{n} )^{n} -1[/tex]

where r is the percentage rate and n refers to the number of times compounded.

So, r = [tex]\frac{6.4}{100}[/tex] = 0.064

Since the APR is compounded daily,

n = 365

Now,

APY = [tex](1+\frac{0.064}{365} )^{365} -1[/tex]

= 6.609% approximately

Answer:

Tony

Step-by-step explanation:

Tony:

3 Packs = 12 dollars

1 Pencil Box = 7 dollars

Mario:

4 Binders = 24 dollars

-6.

12+7= 19

24-6=18

Tony spent more money.

Answer:

The height of aquarium is [tex]\frac{3}{5}[/tex] of its length

Step-by-step explanation:

It is given that the length of rectangular aquarium is 5 decimeter

width of aquarium = [tex]\frac{4}{5}[/tex] of length

                              = [tex]\frac{4}{5} (5) = 4[/tex] decimeter

so we have

width of aquarium = 4 decimeter

Let us assume the height of aquarium be x decimeter

so the volume of the aquarium = length × width × height

Volume of aquarium = 5(4)(x)= 20x decimeter³

it is given that 40 liters of water is [tex]\frac{2}{3}[/tex] of volume of aquarium

also

1 liter = 1 decimeter³

Therefore, 40 liters = 40 decimeter³

now we have

[tex]\frac{2}{3}[/tex] of volume of aquarium = 40

[tex]\frac{2}{3}(20x)=40[/tex]

[tex]\frac{40x}{3} =40[/tex]

multiply both side by 3

[tex]40x= 3(40)[/tex]

[tex]40x=120[/tex]

divide both side by 40

[tex]x=\frac{120}{40}[/tex]

x = 3 decimeter

height of aquarium = 3 decimeter

comparing height and length

[tex]\frac{height }{length} =\frac{3}{5}[/tex]

[tex]height = \frac{3}{5} length[/tex]

hence the height of aquarium is [tex]\frac{3}{5}[/tex] of its length

Answer: 1

Step-by-step explanation:

Only one line segment can be drawn between two points. Any other line segments would be overlapping and the same segment

Answer:

-2b/(a-b)

Step-by-step explanation:

1− (a+b/a−b)

We need to get a common denominator of a-b

1 = (a-b)/(a-b)

Replace 1 with (a-b)/(a-b)

(a-b)/(a-b) - (a+b)/(a-b)

Put over the common denominator

(a-b) - (a+b)

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

(a-b)

Distribute the minus sign.

(a-b) - a-b)

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

(a-b)

a-a-b-b

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

a-b

-2b

----------

a-b