n⃗ =〈−2,−1〉 and D=[−4 4 2 3].

What is D⋅n⃗ ?

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Answer:

 Numbers are 5 , 7

Step-by-step explanation:

  Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

         Their product = 35

(2x + 1)(2x + 3) = 35

Use FOIL method.

       2x*2x + 2x*3  + 1*2x + 1*3 = 35

              4x² + 6x  + 2x + 3       = 35

      Combine like terms

                            4x² + 8x  + 3    = 35

                         4x² + 8x + 3 - 35 = 0

                            4x² + 8x  - 32   = 0

 Solving:

                 4x² + 8x - 32 = 0

Divide the entire equation by 2

                [tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]

                  2x² + 4x - 16 = 0

Sum = 4

Product = -32

Factors = 8 , (-4)

When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.

Rewrite the middle term

2x² + 8x - 4x  - 16 = 0

 2x(x + 4) - 4(x + 4) = 0

   (x + 4) (2x - 4) = 0

2x - 4 = 0   {Ignore x +4 = 0  as it gives negative number}

2x = 4

   x = 4/2

   x= 2

2x + 1 = 2*2 + 1 = 5

2x + 3 = 2*2 +3 = 7

   The numbers are 5 , 7

Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

Answer:

6x - 2

Step-by-step explanation:

Edge

[tex]~~~~~~~\cos^2 \left(34^{\circ}\right) - \sin^2 \left( 34^{\circ} \right)=\cos A\\\\\implies \cos \left( 2 \cdot 34^{\circ} \right) = \cos A~~~~~~~~~~~~~;[\cos 2x = \cos^2 x -\sin^2 x]\\\\\implies \cos \left(68^{\circ}\right) = \cos A\\\\\implies A = 68^{\circ}[/tex]

Step-by-step explanation:

we are missing the inequality sign in step 3.

step 1 and step 2 are correct.

step 4 is wrong.

the correct step 3 looks like

3x <= -3

if your original step 3 says the same, then the first wrong step is step 4.

if your original step 3 does not say the same, then the first wrong step is step 3.

Answer:

The answer is C: (2x +3, 2y)

Step-by-step explanation:

When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.

Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.

(x, y) -----> (2x, 2y)

Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.

Translation 2 units right:

(2x, 2y) -----> (2x +3, 2y)

By solving a quadratic equation, we will see that the length is 10m and the width is 6.5m

For a rectangle of width W and length L, the area is:

A = W*L

In this case, we know that the area is 65m² and that the length is 3 meters less than 2 times the width, so:

L = 2*W - 3m

Then we can write:

65m² = (2*W - 3m)*W = 2*W² - 3m*W

This is a quadratic equation:

2*W² - 3m*W - 65m² = 0.

The solutions are given by the Bhaskara's formula:

[tex]W = \frac{3 \pm \sqrt{(-3)^2 - 4*2*(-65)} }{2*2} \\\\W = \frac{3 \pm 23 }{4}[/tex]

We only care for the positive solution, which is:

W = (3m + 23m)/4 = 26m/4 = 6.5m

Then the length is:

L = 2*6.5m - 3m = 10m

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To solve these types of problems:

 ⇒ just solve like a regular algebraic equation

     ⇒ with an inequality sign in the middle

Let's solve:

           [tex]-3p + 2 > 5\\-3p > 3[/tex]

                ⇒ must change the inequality sign to face the other direction

            [tex]-3p > 3\\p < -1[/tex]

Answer: p < -1

Hope that helps!

Answer:

p < -1

Step-by-step explanation:

-3p + 2 > 5

subtract 2 from both sides

-3p + 2 - 2 > 5 - 2

-3p > 3

divided both sides by -3 to get p alone

-3p / -3 > 3 / -3           reverse the inequality

p > -1

The correct function shown in the graph is,

⇒ log₁₀ (ax) = 1

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:

⇒ log₁₀ (ax) = 1

or , ax = 10¹ = 10

Thus, x  = 10/a

So, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option D, that is, when a = 3. That will make x = 3.33 and thus, .

⇒ log (3 × 3.33) = 0.99 ≈ 1

Thus, out of the given options only Option D seems to be the most probable answer.

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Reason:

Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.

You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.

Using proportions, it is found that the number of chaperones that the school needs is given by:

B. 8.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 2 chaperones are needed for every 25 students. How many are needed for 100 students? The rule of three is given by:

2 chaperones - 25 students

n chaperones - 100 students

Applying cross multiplication:

25n = 2 x 100

n = 200/25

n = 8.

Hence option B is correct.

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Answer: Commutative property

The original height  of the water in a pool is 5 ft , Option B is the correct answer.

An equation can be defined as a mathematical statement when two algebraic expressions are equated using an equal sign.

It is given in the question that

A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours.

the height of the water is 4.75 feet.

The equation

4.75 = x + (negative 0.25)

can be used to find x, the original height of the water in a pool.

4.75 = x - 0.25

x = 5

Therefore the original height  of the water in a pool is 5 ft , Option B is the correct answer.

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Answer:

B

Step-by-step explanation:

Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,

sin²(x) + cos²(x) = 1

we always take the positive square root when solving for either sin(x) or cos(x).

Given that cos(α) = √11/7 and sin(β) = √11/4, we find

sin(α) = √(1 - cos²(α)) = √38/7

cos(β) = √(1 - sin²(β)) = √5/4

Now, recall the sum identity for cosine,

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

It follows that

cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28

Answer:

x = 6, -3

Step-by-step explanation:

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

Answer:

4x^2 - 4x - 3

Step-by-step explanation:

f(x) = 2x - 1

g(x) = x^2 - 4

g(f(x)) = ?

[substitute the x of g(x) with f(x)]

g(x) = x^2 - 4

g(f(x)) = (2x - 1)^2 - 4

[solve]

[binomial * binomial = quadratic equation]

[use FOIL method (first, outer, inner, last)]

g(f(x)) = (2x - 1)(2x - 1) - 4

g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4

[combine like terms]

g(f(x)) = 4x^2 - 2x - 2x + 1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

[tex]p = 3\\\\q= 1[/tex]

Step-by-step explanation:

[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]

Answer: C

Step-by-step explanation:

[tex]16x+8 \geq 12x+20\\ \\ 4x+8 \geq 20\\ \\ 4x \geq 12\\ \\ \boxed{x \geq 3}[/tex]

(4)

1. 11.444 repeater

2. 0.58333 repeater

3. 6.7333 repeater

4. 27.5454 repeater (on both 5 and 4)

5. 1.482517482517 (482517 repeater)

6. 2.285714285714 (285714 repeater)

7. 7.5666 repeater

8. 60.60606060 (60 repeater)

(5)

1. 0.666 (repeater)

2. 0.3666 (repeater)

3. 1.1818181818 (18 repeater)

4. 0.418181818 (18 repeater)

Answer:

The bottom right line plot.

Step-by-step explanation:

In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.

Answer:

$43

Step-by-step explanation:

$72.45 can be rounded down to $72.00

$28.98 can be rounded up to $29.00

$72-$29= $43

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

Pythagorean Theorem

[tex]c^2 = a^2 + b^2[/tex]

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]

Now let's factorize to get solutions for x.

[tex]0 = x(x-20)[/tex]

First solution:

[tex]x = 0[/tex]

Second solution:

[tex]x - 20 = 0\\x = 20[/tex]

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

−9x^4−18x^4y+27x^2y^2

Answer:

=−18x^4y−9x^4+27x^2y^2

Step-by-step explanation:

(−9x^2)(x^2+2x^2y−3y^2)

=(−9x^2)(x^2+2x^2y+−3y^2)

=(−9x^2)(x^2)+(−9x^2)(2x^2y)+(−9x^2)(−3y^2)

=−9x^4−18x^4y+27x^2y^2

=−18x^4y−9x^4+27x^2y^2

---

Hope I helped! Have a great day :)

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

Answer:

[tex]x=5\\[/tex]

Step-by-step explanation:

First, put your equations into a system.

[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]

Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.

[tex]4x=20[/tex]

Lastly, divide by 4 on both sides to get x by itself.

[tex]x=5\\[/tex]

The theorem that verifies that the two right angled triangles are similar is HA.

Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.

Analysis:

From the diagrams KL = OQ ( hypotenuse)

∠L is equal to ∠Q which are acute.

so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.

In conclusion, the HA theorem verifies that the two triangles are similar.

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Answer:

your answer is 4 my friend

Step-by-step explanation:

The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.

From the information, we are told to convert 2 litres into ml. This will be:

= 1000 × 2

= 2000ml

The number of eggs that will be bought to make 500 muffins will be:

= 500 × 2

= 1000 eggs.

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