Plot the function
y = (x + 1)(x - 3) by following these steps:
4
Step 1: Plot the x-intercepts of the function.

Answer:

78.4 ft

Step-by-step explanation:

Part I:

Missing angle = 180° - (130 + 30) (sum of angles in a triangle)

= 180° - 160°

Missing angle = 20°

Part II: distance (d) from Swanson to the boat

Law of Sines is given as:

[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} [/tex]

Where,

a = d

A = 130°

b = 35 ft

B = 20°

Plug in the values and solve for d

[tex] \frac{d}{sin(130)} = \frac{35}{sin(20)} [/tex]

Multiply both sides by sin(130) to make d the subject of the formula

[tex] \frac{d}{sin(130)}*sin(130) = \frac{35}{sin(20)}*sin(130) [/tex]

[tex] d = \frac{35*sin(130)}{sin(20)} [/tex]

[tex] d = 78.4 ft [/tex]

Answer:

-3/4

Step-by-step explanation:

slope is rise over run so you go down 3 first is is -3, and then right 4 times which  means the slope is -3/4

Answer:

1.x=-5 2.t=1/2 3.x=20

Step-by-step explanation:

all simple algebra first and second is simple subtraction

the third involves division as  well

Answer:

Here are the answers:

1) -5

2) 1/2

3) 20

Hope I helped)))

Pls mark brainliest

Answer:I beleive it is (5,-2)

Step-by-step explanation:

Answer:

i think the answer is a. 25

Answer:it is 5/7

Step-by-step explanation: the formula for slope is rise/run divide and you get 5/7

Answer:

slope = [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 2) and (x₂, y₂ ) = (9, 3)

m = [tex]\frac{3+2}{9-2}[/tex] = [tex]\frac{5}{7}[/tex]

Answer:

d

Step-by-step explanation:

Answer:

[tex]-1\frac{1}{4}[/tex]

option 2

Step-by-step explanation:

In this number line, each interval equals 1/4.

P represents 1 1/4

So, opposite of number P is   ( [tex]-1\frac{1}{4}[/tex] )

Answer:

6a+10= 3a+55

6a-3a= 55-10

3a= 45

a= 45/3

a= 15

The answer is (A) 15

Hope this helps^°^

Answer:

A. 15

Step-by-step explanation:

The angles are vertical angles, therefore they are congruent. We can set the two measures equal to each other.

[tex]6a+10=3a+55[/tex]

Now, solve for a. We must get a by itself on one side of the equation.

First, subtract 3a from both sides of the equation.

[tex]6a-3a+10=3a-3a+55[/tex]

[tex](6a-3a)+10=55[/tex]

[tex]3a+10=55[/tex]

Next, subtraction 10 to both sides of the equation. We subtract because 10 is being added to 3a. The inverse of addition is subtraction.

[tex]3a+10-10=55-10[/tex]

[tex]3a=55-10[/tex]

[tex]3a=45[/tex]

3 and a are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 3

[tex]3a/3=45/3[/tex]

[tex]a=45/3[/tex]

[tex]a=15[/tex]

The value of a is 15 and choice A is correct.

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

Explanation:

A graph is a nice addition (and it will likely help us see the vertex directly), but it isn't necessary because we can use the equation given to us. Though I recommend using a graphing calculator to confirm the answer.

The original function is the same as y = 1x^2+8x + (-2). We see that it is in the form y = ax^2+bx+c where

a = 1

b = 8

c = -2

Use the values of 'a' and b to get the value of h, which is the x coordinate of the vertex.

h = -b/(2a)

h = -8/(2*1)

h = -4

The x coordinate of the vertex is x = -4. Plug this into the original equation to get

f(x) = x^2+8x-2

f(-4) = (-4)^2 + 8(-4) - 2

f(-4) = -18

Plugging x = -4 into f(x) leads to y = -18. The point (-4, -18) is on the parabola. Furthermore, this is the vertex (h,k)

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

Alternatively, you can complete the square as shown below

y = x^2 + 8x - 2

y = (x^2 + 8x) - 2

y = (x^2 + 8x + 0) - 2

y = (x^2 + 8x + 16 - 16) - 2

y = (x^2 + 8x + 16) - 16 - 2

y = (x+4)^2 - 18

y = 1(x+4)^2 - 18

y = 1(x-(-4))^2 - 18

The last equation is in the form y = a(x-h)^2 + k with (h,k) = (-4,-18) being the vertex. The 16 is the result of taking half of 8 and squaring that result. We have 16-16 = 0 to make sure that we don't change the equation and keep things balanced. This is the same as adding 16 to both sides. All of this is done so we can end up with the (x+4)^2 perfect square portion.You can expand out (x+4)^2 - 18 and you should get x^2+8x-2 again.

Answer:

i think it is the third one but dont know just an educational geuss

Step-by-step explanation:

The given steps from the derivation of the quadratic formula are:

Step 3:  [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.

The quadratic formula is as follows:

x = [-b ± (√b²+4ac)]/2a

This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].

The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]

Step 1: [tex]ax^2+bx=-c[/tex]

Step 2: Taking 'a' as common

[tex]a(x^2+\frac{b}{a}x)=-c[/tex]

Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides

[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]

⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]

Step 4a: Factoring the polynomial

[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 4b: Converting to a common denominator

[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]

⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]

Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)

⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]

⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]

⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides

⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

⇒ x = [-b ± (√b²+4ac)]/2a

Thus, step 4b best explains or justifies the property "Converting to a common denominator".

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Answer:

1. 1.3778  2. 0.0089

Step-by-step explanation:

to find the volume of the whole rectangle prism you would have to do the volume formula since it is a 3d shape. VOLUME FORMULA, LxWxH.

so 1x0.83x1.66= 1.3778

you can always convert the fraction into decimal to help you calculate the problem.

i don't know if this is correct but i give it a try, so if the whole volume of the triangle is 1.3378 than you can divide that by the the number of small cubes it has inside.

it is 5 by 10 so there are 150 cubes in total.

1.3378 divided by 150=0.0089

im confident about the 1st but not so much with the second

The volume of the rectangular prism is: 1.39 ft³

The volume of one of the small cubes is: 0.0046 ft³

Volume of rectangular prism = length × width × height

Given the following:

Length = 1 ft

Width = 5/6 ft

Height = 1⅔ ft

Volume of the rectangular prism = 1 × 5/6 × 1⅔ = 1 × 5/6 × 5/3

Volume of the rectangular prism = 25/18 = 1 7/18 ft = 1.39 ft³

Length of the edge of 1 cube = 1/6 ft

Volume of the 1 cube = (1/6)³ = 1/216 = 0.0046 ft³

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Answer: I dont know if this is right but the is 8 Ive never done this before.

Step-by-step explanation:

1 =

4 =

1 =

4 =

r− 5 ⋅ 2 = 1 = r = 11

8 = r = 11

Answer:

x = -4

Step-by-step explanation:

16 + x = 12

16 - 16 + x = 12 - 16

x = -4

Answer:

22.95×1.055≈$24.21

Answer:

1.4a > 5+a

Step-by-step explanation:

If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.

On the right side of the equation, if the number is increased by 5, then the equation is a + 5.

Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a

Answer:

To justify a solution, students will need to be able to use appropriate mathematical language to give reasons for the particular approach used to solve a problem. Any time that a student produces a 'solution' in an attempt to solve a problem, that 'solution' needs to be justified.

Step-by-step explanation:

Answer:

1,-1,4,-3 so D

Step-by-step explanation:

0 = x^4 - x^3 -13x^2 + x + 12

x = 1,-1,4,-3

The final answer is -3,-1,1 and 4

The biquadratic equation is of the form ax⁴+bx³+cx²+dx+e and hence

The sum of roots is -b/a, the sum of the product of two roots is c/a, the sum of the product of three roots is -d/a, and the product of all four roots is e/a.

There is no specific method of solving a biquadratic equation, hence we use the trial and error method and also some form of the root.

So finding f(1) = 1-1-13+1+12 = 0 hence 1 is a root.

finding f(-1) = 1-(-1)-13-1+12 = 0 hence -1 is also a root.

So let other roots be p,q

Now we can use sum of roots formula which is p+q+1-1= 1, hence p+q=1

product of roots p*q*1*-1=12, pq= -12 substituting p = -12/q

-12/q+q = 1, multiplying q on both sides

q²-12=q, q²-q-12=0, q²-4q+3q-12 = 0, q(q-4q)+3(q-4)=0

(q-4)(q+3) = 0 hence the roots are 4,-3 also

Hence 1,-1,4, and -3 are the roots of the equation.

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▹ Answer

X = 24

m = 13/7 or about 1.86

▹ Step-by-Step Explanation

X/3 + 7 = 15

X + 3 * 7/3 = 15

X + 21/3 = 15

X = 24

3.5m - 1.5 = 5

35/10m - 15/10 = 5

5 * 7/2 * 5m - 3 * 5/2 * 5 = 5

m = 13/7 or about 1.86

Hope this helps!

CloutAnswers ❁

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Answer:

[tex]5\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]4*1\frac{2}{5} = 4 * \frac{7}{5} = \frac{28}{5} = 5\frac{3}{5}[/tex]

Answer:

[tex]\boxed{ 5\frac{3}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle 4 \times 1\frac{2}{5}[/tex]

[tex]\sf Convert \ mixed \ fraction \ into \ improper \ fraction.[/tex]

[tex]\displaystyle 4 \times \frac{7}{5}[/tex]

[tex]\sf Multiply.[/tex]

[tex]\displaystyle \frac{28}{5}[/tex]

[tex]\sf Convert \ improper \ fraction \ into \ mixed \ fraction.[/tex]

[tex]\displaystyle 5\frac{3}{5}[/tex]

Answer:

48 ÷ 65

Step-by-step explanation:

hope it helps you

Answer:

[tex]\frac{48}{65}[/tex]

Step-by-step explanation:

Step 1: Find LCM for denominators

13(5) = 65

So we need to convert our fractions to add them

Step 2: Convert [tex]\frac{7}{13}[/tex] by multiplying both top-bottom by 5

[tex]\frac{7}{13} (\frac{5}{5} ) = \frac{35}{65}[/tex]

Step 3: Convert [tex]\frac{1}{5}[/tex] by multiplying both top-bottom by 13

[tex]\frac{1}{5} (\frac{13}{13} ) = \frac{13}{65}[/tex]

Step 4: Add the converted fractions

[tex]\frac{13}{65} +\frac{35}{65} =\frac{48}{65}[/tex]

And we have our answer!

Answer:

16$ per shirt

Step-by-step explanation:

60% of 10 is 6

10 + 6 = 16

Answer:

Time it takes to count the coins in your pocket

Step-by-step explanation:

35m is the answer to the problom        

Answer:

the correct answer is 13

Step-by-step explanation:

i got it correct on the test, hope this helps:)) !

The triangle is shifted 4 units downwards and then is rotated about the origin.

Given are triangles A and B.

Transformation 1 : The triangle is shifted 4 units downwards.

Transformation 2 : The figure is rotated about the origin.

Therefore, the triangle is shifted 4 units downwards and then is rotated about the origin.

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Answer:

errror

Step-by-step explanation:

Answer:

Step-by-step explanation:

All inscribed angles intercepting the same arc have the same measure.

If you slide the vertex of angle y clockwise around the circle until it coincides with the vertex of the angle marked 65°, you see that those two inscribed angles (y and 65°) intercept the same arc, so have the same measure:

  y = 65°.

The measure of an inscribed angle is half the measure of the intercepted arc, so the arc marked x is double the angle 65°.

  x = 130°.

The required ways of the combination to display the flowers on the dinner is  20.

There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner to determiined.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Examples of permutation and combination, Managing people, numbers, numerals, alphabets, letters , and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.

Since, the total number of flower in vases is 6
3 of them to be selected for the dinner table tonight.
The combination is given as.
= C( 6 , 3)
= 6!/3!(6 - 3)!
= 6!/3!3!
= 20

Thus, the required ways of combination to display the flowers on dinner is  20.

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Answer:C

Step-by-step explanation: