Algebra 1 A Adaptive CR (JL22) 1/Tools Of The Trade
2. Simplify and write in exponential form. (4³)(3) = ?
O
O (4³) (¹)
521

Answer: (3,-2)

Step-by-step explanation:

[tex]-3x-7y=5\\15x+6y=33[/tex]

[tex]5(-3x-7y)=5(5)\\-15x-35y=25[/tex]

new system:

[tex]-15x-35y=25\\15x+6y=33[/tex]

add.

[tex]-29y=58\\y=-2[/tex]

plug in -2 for y

[tex]-3x-7(-2)=5\\-3x+14=5\\-3x=-9\\x=3[/tex]

system:

[tex](3,-2)[/tex]

Answer:

(3, - 2 )

Step-by-step explanation:

- 3x - 7y = 5 → (1)

15x + 6y = 33 → (2)

multiplying (1) by 5 and adding to (2) will eliminate x

- 15x - 35y = 25 → (3)

add (2) and (3) term by term to eliminate x

0 - 29y = 58

- 29y = 58 ( divide both sides by - 29 )

y = - 2

substitute y = - 2 into either of the 2 equations and solve for x

substituting into (2)

15x + 6(- 2) = 33

15x - 12 = 33 ( add 12 to both sides )

15x = 45 ( divide both sides by 15 )

x = 3

solution is (3, - 2 )

Answer:

[tex]cotA=\frac{2x}{5}[/tex]

Step-by-step explanation:

Answer:

[tex]\text{cotA} =\frac{2x}{5}[/tex]

Step-by-step explanation:

cotA = (Adjacent side) ÷ (Opposite side)

The measure of the Adjacent side = 2x

The measure of the Opposite side = 5

Then

[tex]\text{cotA} =\frac{2x}{5}[/tex]

Answer:

factor polynomial is x+q so x=-q

putting the value of x in both equations

eqn 1)a^2+p(-a)+q=0

a^2 -ap+q=0

eqn 2)a^2+m(-a)+n=0

a^2-am+n=0

Since both are equal to zero,we can write:

a^2-ap+q=a^2-am+n

-ap+am=n-q

a(-p+m)=n-q

a=(n-q)/(m-p)

Explanation:

Since (x + a) is a factor of the two polynomials, when x = -a, the polynomials should both equal 0 (this is known as the factor theorem).

• First equation:

[tex]x^{2} + px + q[/tex]

When x = -a:

[tex](-a)^{2} + p(-a) + q = 0\\\\a^{2} -pa + q = 0[/tex]

• Second equation:

[tex]x^{2} + mx + n[/tex]

When x = -a:

[tex](-a)^{2} + m(-a) + n = 0\\\\a^{2} -ma + n = 0[/tex]

• As both equations equal 0, we can equate them:

[tex]a^{2} -pa + q = a^{2} -ma + n \\\\-pa + ma = n - q\\\\a(m - p) =n -q\\\\a = (n - q)/ (m - n)[/tex][proven]

The coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

The linear equation is given as:

-3x + 4y= 19

Set x = 0

So, we have:

-3(0) + 4y = 19

Evaluate

4y = 19

Divide by 4

y = 19/4

Hence, the coordinate pair that is a solution of the linear equation -3x+4y=19 is (0, 19)

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The arithmetic sequences are as follow:

An arithmetic sequence in algebra is a sequence of numbers where the difference between every two consecutive terms is the same.

1) t(n) = 5n + 4

t(1) = 9, t(2) = 14, t(3) = 19

So,

9,14,19,...

d= 14-9 = 5

d= 19-14 =5

Hence, it is an AP

2) 1, 2, 4, 8 , 16

Hence, it is not an AP

3) 3, 6, 9 ,...

It is an AP

4)It is given that it is an AP

5) tn =  2*3^n

 t1= 6, t2= 18, t3= 54

So, 6, 18, 54,...

Hence, it is not an AP

6) 3 , 1, 1/3,...

It is not an AP

7) t(n+1)= 6*t(n)

t(1) = -1

t(2)=-6

t(3)= -36

Hence, it is not an AP

8) -3, 1, 5, 9

Hence, it is an AP.

9) 1, 4, 9,...

Hence, it not an AP

10) 2,1,0,1,2,...

It is not an AP

11) t(n)= -2n-5

t(1)= -7, t(2)= -9, t(3)= -11

Hence, it is an AP

12) tn= (1/2)^n

 t1= 1/2, t2= 1/4, t3= 1/8

It is not an AP

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Distribute [tex]50[/tex] to every term inside the parentheses.

[tex]50\cdotx^2+50\cdot7x+50\cdot6[/tex]

Simplify with multiplication.

[tex]\huge\boxed{50^2+350x+300}[/tex]

You can't simplify further by adding, so leave the answer as-is.

Answer:

50x^2 + 350x + 300

Step-by-step explanation:

Original Equation:

50(x^2+7x+6)

Distribute 50 to all 3 #'s:

50x^2 + 350x + 300

Answer:

x = 15° , y = 125°

I hope this helps u

The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66

What is a linear equation?

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.

We have:

0.1x + 0.25y = 19.9 and

x + y = 100

Let x = number of dimes

y = number of quarters

After solving the above system of equations by substitution method.

[tex]\rm \dfrac{398-5y}{2}+y=100[/tex]

y = 66

[tex]\rm x=\dfrac{398-5\cdot \:66}{2}[/tex]

x = 34

Thus, the statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66

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Answer:

You didn't include any choices.....see below

Step-by-step explanation:

Answer:

The required linear equation satisfying the given points (2,4) and (4,10) is y=3x-2

Step-by-step explanation:

Two points are given in question, (2,4) and (4,10).

It is required to find out a linear equation satisfying the points (2,4) and (4,10).

To find it out, find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]

Step 1 of 3

The slope of a line passing through the points (2,4) and (4,10) is given by

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{10-4}{4-2} \\m &=\frac{6}{2} \\m &=3\end{aligned}$$[/tex]

Step 2 of 3

Now use the slope m=3 and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-4)=3(x-2)$$[/tex]

Distribute 3 ,

[tex]$$\begin{aligned}&y-4=3 x-3 \times 2 \\&y-4=3 x-6\end{aligned}$$[/tex]

Step 3 of 3

This linear function can be written in the slope-intercept form by adding 4 on both sides,

[tex]$$\begin{aligned}&y-4+4=3 x-6+4 \\&y=3 x-2\end{aligned}$$[/tex]

So, this is the required linear equation.

Answer:

I hope this is the right answer

Answer:

Hello! The answer is x ≥ [tex]\frac{7}{2}[/tex].

Step-by-step explanation:

To solve this inequality, we have to get x by itself. To do so, we will rearrange the inequality. To do so, we will subtract 6x from both sides and add 3 to both sides:

8x - 3 ≥ 6x + 4

-6x +3  -6x  +3

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

2x ≥ 7

Now, we have to get x by itself and divide both sides by 2 to do so:

2x ≥ 7

--     --

2      2

This leaves us with:

x ≥ [tex]\frac{7}{2}[/tex]

The required solution to the inequality 8x - 3 ≥6x + 4 is x ≥ 3.5.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To solve the inequality, we want to isolate the variable x on one side of the inequality symbol.

8x - 3 ≥ 6x + 4

Subtract 6x from both sides:

2x - 3 ≥ 4

Add 3 to both sides:

2x ≥ 7

Divide both sides by 2:

x ≥ 7/2

Therefore, the solution to the inequality is x ≥ 3.5.

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Total length of iron edging needed to create the square frame is 43.5 inches

Important properties of square:

All four interior angles are equal to 90°

All four sides of the square are congruent or equal to each other.

The opposite sides of the square are parallel to each other.

The diagonals of the square bisect each other at 90°

The two diagonals of the square are equal to each other.

Diagonal of square = [tex]\sqrt{2}[/tex]a

9 = [tex]\sqrt{2}[/tex]a

a = [tex]\frac{9}{\sqrt{2}}[/tex]

a = 6.36 inches

Iron edging needed to create the square frame = 4*6.36 = 25.44 inches

iron edging needed to create two diagonals = 2*9 = 18 inches

total length = 18 + 25.44

                   = 43.44 ~ 43.5 inches

Thus, Total length required is 43.5 inches

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Answer:

Step-by-step explanation:

no, you don't have the measure of at least one side, so having the same angles is similar but not congruent

The error that Bryan has done in this inequality is that he included –14 in his solution set.

What Bryan has to do would be to write this inequality in such a way that the variable would appear on the left.

But the symbol that he has chosen does not move in this same direction as the graph.

The -14 should not be inclusive in the graph because it is not a part of the graph solution.

He used the wrong number in this inequality.

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Answer:

its c

Step-by-step explanation:

on edge

The order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

From the question, we are to order the given numbers from the greatest to the least in magnitude

The given numbers are

|-20|, |-4|, |-6|, |8|, |2 3/10|, |12.3|

Since the modulo sign is included, the negative signs do not take effect.

Hence, the order of the numbers from the greatest to the least is

|-20| > |12.3| > |8| > |-6| > |-4| > |2 3/10|

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m∠x+m∠r+m∠y=180° (angles in a triangle add to 180°)

m∠r+m∠s=180° (angles that form a linear pair add to 180°)

m∠x+m∠r+m∠y=m∠r+m∠s (Transitive property of equality)

m∠x+m∠y=m∠s (subtraction property of equality)

m∠s=m∠x+m∠y (symmetric property of equality)

The percentage given shows that the amount is decreasing by 8%.

From the information given, the function is f(x) = 9,628(0.92)x. This illustrates that the amount is decreasing by 8% she compared to the previous year. This was computed as:

= 1 - 0.92

= 0.08

= 8%

For part B, the percentage change will be:

= (8,972 - 8,074.80)/8972 × 10

= 10%

Therefore, the account recorded a greater percentage change in amount of money over the previous year is account B as 20% is lore than 8%.

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Answer:

The two numbers are 56 and 23.

Step-by-step explanation:

Let the two numbers be A and B.

We are told that:

A+B = 79, and

2)  3A + 5B = 283

Rearrange the first expression to isolate A:

A = 79-B

Now use this value of B in the second expression:

3A + 5B = 283

3(79-B) + 5B = 283

237-3B + 5B = 283

2B = 46

B = 23

If B=23, we can find A from (1):  

A+B = 79

A+23 = 79

A = 56

CHECK:

Does A+B = 79?

56 + 23 = 79?  YES

Does 3A + 5B = 283?

  3(56) + 5(23) = 283?

 168 + 115 = 283?  YES

Answer:

1.875 liters

Step-by-step explanation:

x=1.25×32=3.752=1.875 liters

Answer:

y=49x

Step-by-step explanation:

As you can see from the graph, the distance from home increases by 49 miles per hour driven.

Therefore the distance driven for any given time in hours is 49x

Therefore y = 49x

Answer:

Yes, it's a rational number

Step-by-step explanation:

based on the options given, one thing that isn't true of the box plot is that d. Half the data lies between 51 and 68.

the box plot has a range of 67:

= 90 - 23

= 67

the data point 5 lies outside the data set.

3/4 of the data is less than 68 which is the 3rd quartile.

this means that the false statement is that half of the data is between 57 and 68.

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Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

When the function is translated down, the slope remains constant, while when the function is reflected over the y-axis, the slope is multiplied by -1, hence both lines will have a slope of 3, and since they have the same slope, they are parallel.

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Answer:

[tex]x^2 - 10x + 25[/tex]

Step-by-step explanation:

Hello!

Expand the square using the Distributive Property.

Distributive x - 5 to each factor

The answer is [tex]x^2 - 10x + 25[/tex].

We can also use a special binomial product formula.

Formula: [tex](a - b)^2 = a^2 - 2ab + b^2[/tex]

We get the same answer both ways.

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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Answer:

Everything in the box currently is correct but the bottom two numbers are just -3 and -4

Step-by-step explanation:

The equation which could be used to find the value of x is; (x+10) +(x-6) = 10.

According to the task content, it follows that the lines WX and WY both amount to the line XY which joins points X and Y.

Hence, it follows that the equation which can be used to find the value of x is; (x+10) +(x-6) = 10.

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