Scalar and Matrix Multiplication

Answer:

[tex]3^x=5[/tex]

Step-by-step explanation:

Given:

[tex]9^x=25[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^x=25[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2x}=25[/tex]

Apply the same exponent rule:

[tex]\implies (3^x)^2=25[/tex]

Square root both sides:

[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]

[tex]\implies 3^x=5[/tex]

2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.

3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]

4) [tex]X[/tex]

Answer:

[tex]b + n = 18[/tex]

[tex]6b + 5n = 101[/tex]

Answer:

m∠M=98º

Step-by-step explanation

Sum of interior angles;

  3x-16+x+6+x = 180

                   5x = 180-6+16

                   5x = 190

                      x = 38º

Angle M;

      m<M= 3x - 16 = 3(38)-16= 98º

      m∠M=98º

Answer:

<M = 98

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

< M + < N + < O = 180

3x-16 + x + x+6 = 180

Combine like terms

5x - 10 = 180

Add 10 to each side

5x-10 + 10 = 180+10

5x = 190

Divide by 5

5x/5 = 190/5

x=38

We want to find <M

<M = 3x-16  = 3*38 -16 = 114-16 =98

Answer:

$20 × 14 days = $280

&30 × 3 = $90

&280 + $90 = $370

Answer:

For car she owes=

$20 x 14 = $280

For tank she owes=

$30 x 3 = $90

Therfore in total she owes,

$280 + $90 = $370

Factor the rational function,

.

.

.

.

Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.

.

.

So our domain can be all reals except 1.

Range: First factor out the x-1. We will be left with

.

Since 1 isn't in the domain, plug in 1 to find the what won't be in the range

.

So 7 isn't in the range,

End Behavior:

Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.

Answer:

BODMAS

[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]

Answer: Answer is 226

Step-by-step explanation: Do math

Answer: [tex]\frac{4}{3}[/tex] or about 1.333

Step-by-step explanation:

    We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.

[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]

Answer: 4/3

Step-by-step explanation:

find the reciprocal of the divisor

15/32

32/15

Now multiply it with the dividend

5/8

15/32

=5/8

32/15

=5/32

8/15

=160/120

after reducing the fraction the answer is 4/3

in mix form 1 1/3

Answer:

[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]

Step-by-step explanation:

θ = 41°

Hypotenuse = BC = 13.5 cm

opposite = AB = ?

We will use the trigonometric ratio of sin.

[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]

Answer:

Length of pipe = 21 cm

Internal diameter = 4 cm

Internal radius = \frac{4}{2} = 2 cm24=2cm

Thickness = 0.5 cm

Outer radius = 2+0.5=2.5 cm

Volume of pipe =\pi R^2 h - \pi r^2 hπR2h−πr2h

Volume of pipe =\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3

=\frac{22}{7} (2.5)^2 (21)-\frac{22}{7}(2)^2(21)=148.5 cm^3722(2.5)2(21)−722(2)2(21)=148.5cm3

Hence The volume is 148.5 cubic cm.

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The thickness of a metal pipe is 1.5cm. The inner diameter is 21cm. What is the volume of metal required for a pipe of length 7cm

Answer:

?

Step-by-step explanation:

because there is no picture or option

The time that the bus arrived Busia is given as 1.00 pm

The formula with which to solve for the time is given as

D/s = distance / by the speed.

Distance = 400km

Speed = 80km/hr

Time = 400/80

= 5 hours

Therefore the time of arrival from 8.00 am would be 1.00pm

A bus left Nairobi at 8.00am and traveled towards Busia at an average speed of 80km / hr . At 8.30 am a car left Busia for Nairobi at an average speed of 120km / hr . Given that the distance between Nairobi and Busia is 400km ​

Calculate The time the car arrived in Busia

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Answer:

Do you like having a pet? - statistcal question

Step-by-step explanation:

^^^^

Answer:

each one is double the one before it so in year 5...

3912*2=7824

Hope This Helps!!!

Answer:

7824

Step-by-step explanation:

Answer: 62.5%

Step-by-step explanation:

First, you must simplify 5/8 into a decimal and then multiply that by 100 to get the percentage of the fraction.

[tex]\frac{5}{8}=0.625[/tex]     [tex]0.625*100=62.5[/tex]%

I hope this helps!! Pls give brainliest :)

Answer:

[tex]x(x^2+2)[/tex]

Step-by-step explanation:

Since x is the only common term, you factor that part out using the distributive property.

Solution:

Detailed explanation:

Hii! Let's factorise this expression!

Did you see that both terms, x^3 and 2x, have an x in common? That's what we are going to factor out, by dividing x^3 and 2x by x.

x^2+2 is what we obtain.

Now, this can't be the end of the process. We also need to put parentheses around x^2+2.

(x^2+2)

Next we put that x we factored out a short while ago outside the parentheses.

x(x^2+2). Did you get it?

________

Hope I helped, best wishes & happy studies!
Please reach out if any queries arise. Thankyou!!

_______

Answer:

10

Step-by-step explanation:

First, divide 192 by 12, you get a unit rate of Rs. 16 per egg, then divide Rs. 160 by 16 and you get 10

The number of eggs that can be purchased at Rs. 160 is 10.

The division operator ( / ) has the quotient of its operands where the left operand exists the dividend and the right operand exists the divisor.

The cost of 12 eggs = Rs. 192

The cost of 1 egg = 192/12 = Rs. 16.

The number of eggs that can be purchased is Rs. 160 = 160/16 = 10.

Therefore, the number of eggs that can be purchased at Rs. 160 is 10.

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The graph is shown below

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, the equation x² + y² < 25 represents equation of circle.

So, the graph will be of the form circle.

and,  y² <6x is the equation to represent parabola

So, the graph will represent a parabola.

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Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequalities, the graph can be plotted as shown below. Now when the coordinates have been plotted the point that will satisfy both the inequalities is (-2,2).

Hence, the correct option is B.

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Answer:

65/8

Step-by-step explanation:

1) Turn all numbers into improper fractions: 17/2 - 3/8 = ?

2) Make all denominators the same number by finding the least common factor, which is 8. Multiply the denominator in 17/2, which is 2, by 4 to match the other denominator. And then multiply the numerator (17) by 4 as well so that the fraction still has the same value: 68/8 - 3/8 = 65/8

3) Can not simplify since there are no common factors between 65 and 8.

Answer:

what?????????????????

Answer:

x= -7, y= -5 and

x= 2, y= 13

This may also be written as (-7, -5) and (2, 13).

Step-by-step explanation:

Start by labelling the two given equations:

y= x² +7x -5 -----(1)

2x -y= -9 -----(2)

Let's solve by substitution!

Making y the subject of formula in equation (2):

From (2): y= 2x +9 -----(3)

Substitute (3) into (1):

2x +9= x² +7x -5

x² +7x -5 -2x -9= 0

x² +5x -14= 0

Factorise:

(x +7)(x -2)= 0

x +7= 0 or x -2= 0

x= -7 or x= 2

Find the respective values of y.

Substitute into (1):

y= (-7)² +7(-7) -5 or y= (2)² +7(2) -5

y= 49 -49 -5 or y= 4 +14 -5

y= -5 or y= 13

Thus, the solutions are (-7, -5) and (2, 13).

Answer:

(1,2.5)

Step-by-step explanation:

On the graph, the (-1,7) lies in the top right grid. The (3,-2) lies in the bottom left grid. If you use a graphing calculator, the middle is hard to find but you will find (1, 2.5) or (1, 5/2).

The answer is y=|x|-13.

Answer:

y=|x|-13

Step-by-step explanation:

Answer:

[tex]\fbox {DF = 20}[/tex]

Step-by-step explanation:

Given :

Step 1 : Find RT

Step 2 : Find SF

Step 3 : Find RY

Step 4 : Find TY

Step 5 : Find DF

Answer:

DF = 20

Step-by-step explanation:

Triangle SDF has side lengths SD, DF, SF.

Triangle RTY has side lengths

RT = (9/4)SD

RY = (9/4)SF

TY = (9/4)DF

"SF is 2 less than RT" Given

SF = RT - 2

SF = (9/4)SD - 2

"SD = 8" Given

SF = (9/4)(8) - 2

SF = 16

"TY is 9 more than RY" Given

TY = RY + 9

(9/4)DF = (9/4)SF + 9

(9/4)DF = (9/4)(16) + 9

(9/4)DF = 45

DF = 45 × 4/9

DF = 20

It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.

A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.

It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.

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Answer:

2

Step-by-step explanation:

the additive inverse of - 2 is 2 , since

- 2 + 2 = 0

The student made an error in step 3. To correct this error, he should define side AY in terms of angle X. Pythagorean theorem relates sides x, y, z, and angle X

In Trigonometry, law of cosine (cos) is given by this mathematical expression:

cosθ = Opp/Hyp

Where:

In this scenario, we can logically deduce that the student made an error in step 3. To correct this error, he should define side AY in terms of angle X.

After correcting this error, the student can use the Pythagorean theorem to relate sides x, y, z, and angle X.

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