For the equations given below, which statement is true?
-21 = 14
6.1 = -42
A. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -3.
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by 3.
C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -4.
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value.

Answer:

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Step-by-step explanation:

Given

[tex]A = \left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

Required

2A - 4B

To solve 2A - 4B, we first multiply matrix A by 2 and matrix B by 4

So, if

[tex]A = \left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]2A = 2 *\left[\begin{array}{ccc}-1&9&2\\10&-10&2\\-5&6&-5\end{array}\right][/tex]

[tex]2A = \left[\begin{array}{ccc}-2&18&4\\20&-20&4\\-10&12&-10\end{array}\right][/tex]

If

[tex]B = \left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

then

[tex]4B = 4*\left[\begin{array}{ccc}7&-1&-1\\6&-4&-3\\-10&10&-7\end{array}\right][/tex]

[tex]4B = \left[\begin{array}{ccc}28&-4&-4\\24&-16&-12\\-40&40&-28\end{array}\right][/tex]

So; 2A - 4B becomes

[tex]\left[\begin{array}{ccc}-2&18&4\\20&-20&4\\-10&12&-10\end{array}\right] - \left[\begin{array}{ccc}28&-4&-4\\24&-16&-12\\-40&40&-28\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-2-28&18-(-4)&4-(-4)\\20-24&-20-(-16)&4-(-12)\\-10-(-40)&12-40&-10-(-28)\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-30&18+4&4+4\\20-24&-20+16&4+12\\-10+40&12-40&-10+28\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Hence, 2A - 4B is equivalent to

[tex]\left[\begin{array}{ccc}-30&22&8\\-4&-4&16\\30&-28&18\end{array}\right][/tex]

Answer:

[tex]3(3x +2y)[/tex] and [tex]9x +6y[/tex] are equivalent to [tex]3(x + 3y + 2x - y)[/tex]

Step-by-step explanation:

Given

[tex]3(x + 3y + 2x - y)[/tex]

Required

Possible Equivalents

To start with; we need to simplify the expression in the bracket;

[tex]3(x + 3y + 2x - y)[/tex]

Collect like terms

[tex]3(x + 2x + 3y - y)[/tex]

[tex]3(3x +2y)[/tex]

At this point; we can conclude that [tex]3(3x +2y)[/tex] is equivalent to [tex]3(x + 3y + 2x - y)[/tex]

Solving further, by expanding the bracket

[tex]3(3x +2y)[/tex]

[tex]3*3x +3*2y[/tex]

[tex]9x +6y[/tex]

At this point; we can also conclude that [tex]9x +6y[/tex] is equivalent to [tex]3(x + 3y + 2x - y)[/tex]

Hence,

[tex]3(3x +2y)[/tex] and [tex]9x +6y[/tex] are equivalent to [tex]3(x + 3y + 2x - y)[/tex]

Answer:

Hi, please provide a photo or options to pick from. I will answer then.

Step-by-step explanation:

Answer:

Check Explanation.

Step-by-step explanation:

Although, the density curve for this question is missing and isn't available online, I would use an example of another density curve to explain how this could be easily done.

From the density curve attached to this question, the total area under the curve is the are of the triangular shape formed by this curve with the x-axis.

Total Area under the curve = ½×base×height

= ½ × (5-1) × 0.5 = 1 square unit

Area under the density curve where x is less than 4 is a trapezium.

Area of a trapezium = ½ (a+b) h

For the area under the density curve where x is less than 4,

a = 0.5, b = (0.5/4) = 0.125, h = (4-1) = 3

Area under the density curve where x is less than 4 = ½ (0.5+0.125) × 3 = 0.9375 square unit

In terms of the total area, Area under the density curve where x is less than 4 covers

(0.9375/1) × 100% = 93.75%

Hope this Helps!!!

Answer:

Qu.3 a = 70 degree.

Qu 4. a = 6  b= 4 c = 15  d =9

Step-by-step explanation:

Rules of parallelogram show that diagonal adjacent angles are equal

Then 110 = 110 and 110+110 = 220

Then as angles equal 360 degree we subtract.

a * 2 = 360-220 = 140 degree

Where there are two angles we divide by 2 to find one of them = a as both measures equal double;

a = 140/2 = 70 degree.

Qu 4. a = 6  b= 4 c = 15  d =9

without calculator we simplify

a= 3/4 x 8 = 1 x 8 - 1/4 = 6     = 3/4 +1/4 = 1  then 1 *8 = 8 then 8 -1/4 = 6 or go decimal 0.75 * 8 = 0.40 + 5.60 + total = 6

b = 2/6 x 12 = 1/6 x 12 (2) = 2 (2) = 4       = 1/6 *2 is the same as 2/6 we then *12

c =  3/2 x 10 = 1/2 x 10 (3) = 5 (3) = 15    = 1/2 *3 is the same as 3/2 we then *10

d =  3/12 x 36 = 1/4 x 36 = 9  = decimal 0.25 x 36 = 1.50  |  + 7.5 = 9  

Answer:

sin23° can be written as x / 17 or 0.39. That means we can write x / 17 = 0.39 which gives us x = 6.63.

Answer:

I know that (A) is correct for the fisrt one.

Step-by-step explanation:

Answer:

Not possible

Step-by-step explanation:

a + b = c = d         Substitute

30 + 30 = 7 = 24  Add

60 = 7 = 24          This is not possible because these numbers aren't equal.

Answer:

1

Step-by-step explanation:

a + b - c

Let's solve for the first triangle.

1 + 3 - 4

4 - 4 = 0

Now for the second triangle.

2 + 5 - 6

7 - 6 = 1

Add 0 and 1.

0 + 1 = 1

Answer:

1

Step-by-step explanation:

1+3=4-4=0

2+5=7-6=1

0+1=1

Answer:

Step-1: the x-intercept and the y-intercept

2x - 4y = 6

For y = 0, we get the x-intercept.

2x - 4(0) = 6

2x = 6, and then divide by two on both sides.

Hence, the x-intercept is

For x = 0, we get the y-intercept.

2(0) - 4y = 6

-4y = 6, and then divide by -4 on both sides.

Hence, the y-intercept is y = -3/2 = ( 0, -3/2)

The graph of the inequality 2x - 4y > 6 is the same as y < 0.5x - 1.5

The inequality is given as:

2x - 4y > 6

Divide through by 2

x - 2y > 3

Subtract x from both sides

- 2y > -x + 3

Divide both sides by -2

y < 0.5x - 1.5

See attachment for the graph of the inequality 2x - 4y > 6

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Answer:

6 and 2

Step-by-step explanation:

6+6=12

2+2=4

12+4=16

Answer:

D. 15x^2 + 8x - 12

Step-by-step explanation:

To solve this problem, simply expand the factorization and find the polynomial.

5x * 3x = 15x2

5x * -2 = -10x

6 * 3x = 18x

6 * -2 = -12

You are left with 15x2 - 10x +18x - 12, but you need to combine like terms, leaving you with the correct answer: 15x2 + 8x - 12.

Answer:

D.

Step-by-step explanation:

(5x+6)(3x-2)=5x*3x-5x*2+6*3x-6*2=15x^2-10x+18x-12=15x^2+8x-12

Answer:

the answer is C:x=20 I used a calculator

Step-by-step explanation: To make a line paralle to another, the slope has to be the same such as the "m" in "y=mx+b" the y-intercept or "b" could be different. In this case, the slope is -7. So the question mark should be -7.

Answer:

The correct answer is

[tex]y = -7x -3[/tex]

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula [tex]y-y1= m (x-x1)[/tex] to find the line parallel to [tex]y= -7x+2[/tex]

[tex]y=-7x-3[/tex]

Hope this helps!

- Quinn <3

Answer:

C.

Step-by-step explanation:

First find the pattern. The pattern is you multiply the number before by -3.

Just start with x as the first number.

x, -3x, 9x, -27x, 81x, -243x, 729x, -2187x, 6561x, -19683x

Add them all up: -14762

Now multiply by -3:

44286

The required sum of the first 10 terms in the series is given as 44286. Option C is correct.

Given that,
The sum of the first 10 terms in the series: -3, 9, -27, 81... is to be determined.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

here,
For Geometric progression,
a = -3
r = 9/-3 = -3

The sum of the 10 terms of GP is given as,
S = a[rⁿ - 1] / [r - 1]
Substitute the value in the above equation,
S = -3[{-3}¹⁰ - 1]/[-3-1]
S = 3/4 [3¹⁰ - 1]
S = 44286

Thus, the required sum of the first 10 terms in the series is given as 44286. Option C is correct.

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Answer:

0.58 is where the blue dot on the number line is

Answer:

The blue dot is at -0.58

Answer:

Distance = 162.5 to 2dp.

Step-by-step explanation:

Alex car drives 65km = 40mins we round up to 1hr

= 1/2 x 65 + 65 = 32.5 +65 = 97.5  km p/h

Roy is 1/4 faster (As Alex speed is 3/4 of Roy)

To find 3/4 we divide by 3  then, add the 97.5  km etc..

97.5/3 =  + 32.5km = 130 km/ph

To check we only have to divide by 4

130 / 4  = 32.5

We know 32.5 is 1/4 we can add this on as 15minutes.

130 km = 1hr +

32.5 km = 15 mins

Distance = 162.5 km

Answer:

162.50 km

Step-by-step explanation:

Alex: 40 minutes for 65 km

speed = distance/time = (65 km)/(40 min) * (60 min)/(1 hr) = 97.5 km/h

Alex's speed = 3/4 of Roy's speed

Roy's speed = (Alex's speed)/(3/4) = (97.5 km/h)/(0.75) = 130 km/h

speed = distance/time

distance = speed * time

time = 1 hour + 15 minutes = 1 hour + 15/60 hour = 1.25 hour

distance = 130 km/h * 1.25 hour = 162.50 km

Answer:

5 faces

Step-by-step explanation:

Faces:

=> 1 rectangular face+4 triangular face = 5 faces

Answer:

a pyramid has has 5 Faces.

Step-by-step explanation:

The 4 Side Faces are Triangles. The Base is a Square. It has 5 Vertices

a net with a rectanguler base and 4 triangles will form a rectanguler pyramid

Answer:

The circumference is 6908 miles.

Step-by-step explanation:

C=πd

C=π*2200

C=3.14*2200

C=6908

Option B is correct.

Answer:

b

Step-by-step explanation:

Answer:

             [tex]\dfrac{13}{17}[/tex]

Step-by-step explanation:

all headbands:   20+32+16 = 68

headbands that aren't black:   68-16 = 52

the probability:   [tex]\frac{52}{68}=\frac{13}{17}[/tex]

Answer:

I would think it is supplementary.

Step-by-step explanation:

If 2 angles equal 180 degrees, then they are supplementary.

Answer:

Step-by-step explanation:

Answer:43/10

Step-by-step explanation:

in grade school i was taught the “MAD” method which stands for multiply add divide, so you would take 10 times 4, add 3, which will give you your fraction which could also be used to divide. the answer is 43 over 10.

Answer:

No, she has not bought enough dog food to feed her 4 dogs for 5 days.

Step-by-step explanation:

She has 4 dogs which each eat 3/4 of a tin each day, so during each day 3/4 *  = 3 tins of food are eaten. She has 12 tins, and 12/3 is 4 days without running out. She has therefore not bought enough dog food to feed her 4 dogs for 5 days.

No, she has not purchased enough dog food to last five days and feeds her four dogs.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Each of her four dogs consumes 3/4 of a tin of food every day, making a total of 3 tins of food consumed daily. She has 12 tins, therefore she has 4 days before running out as of 12/3. She hasn't purchased enough dog food as a result to feed her four dogs for five days.

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Answer: 98 is your answer

Step-by-step explanation:

Answer:

-9

y= x + 3

2

2

Step-by-step explanation:

its simple just follow my steps

Answer:

Step-by-step explanation:

[tex]g^{-1} (-3)=7\\[/tex]

let h(x)=y

y=2x-3

flip x and y

x=2y-3

2y=x+3

[tex]y=\frac{1}{2}(x+3)\\or~h^{-1}(x)=\frac{1}{2}(x+3)\\(h^{-1} oh)(x)=h^{-1}(h(x))=h^{-1}(2x-3)=\frac{1}{2}(2x-3+3)=\frac{1}{2}(2x)=x\\(h^{-1}oh)(1)=1[/tex]

Answer:

It's (B) [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Hope this helped you!

Answer:

f^-1(8) = 3/2

Step-by-step explanation:

f(x) = 2x + 5

y = 2x + 5

x = 2y + 5

2y = x - 5

y = (x - 5)/2

f^-1(x) = (x - 5)/2

f^-1(8) = (8 - 5)/2

f^-1(8) = 3/2