-7/9 x 144 vbnbvcrxecvbnbvtcrxercvb

Answers

Answer 1

Answer: The first step to solving this expression is to reduce the numbers with 9.
-7 × 16
Now we need to multiply the two numbers together using the Rules of Signs for Multiplication. They state that multiplying a negative and a positive equals a negative: (-) × (+) - (-). Keeping this in mind,, when you multiply the two numbers together you should get -112.
Let me know if you have any further questions
:)

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Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has verticesX'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?

Answers

Answer:

Rotation about 90° counter clockwise (x , y) →→ ( -y, x ).

Step-by-step explanation:

Given : Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices X'(–3, 1), Y'(0, 0), and Z'(–2, –1).

To find : Which rule describes the transformation.

Solution : We have given

vertices X(1, 3) →→ X'(–3, 1)

Y(0, 0) →→ Y'(0, 0),

Z(–1, 2) →→ Z'(–2, –1).

Here , we can see in each coordinates value of y become -x and x become y.

(x , y) →→ ( -y, x ) this the rule of rotation about 90° counter clockwise.

Therefore, rotation about 90° counter clockwise (x , y) →→ ( -y, x ).

the rule is (x - 3, y - 3).

The ages of two sisters are 11 years and 14 years.In how many years time will the product of their age be 304?

Answers

x - the number of years in which the product of their ages will be 304
In x years one sister will be 11+x years old, and the other sister will be 14+x years old.

$(11+x)(14+x)=304 \n154+11x+14x+x^2=304 \nx^2+25x+154=304 \nx^2+25x-150=0 \nx^2-5x+30x-150=0 \nx(x-5)+30(x-5)=0 \n(x+30)(x-5)=0 \nx+30=0 \ \lor \ x-5=0 \nx=-30 \ \lor \ x=5$

The number of years must be a positive number, so x=5.

The product of their ages will be 304 in 5 years.

X+y=0 and x-y=10 solve by substitution.. How do I figure out the problem!

Answers

$x+y=0 \n x-y=10 \n\nx=-y\nx-y=10\n\n-y-y=10\n-2y=10\ny=-5\n\nx-5=0\nx=5\n\n\boxed{(x,y)=(5,-5)}$

x+y=0
- x-y=10
--------------
(0)+2y=-10 [x and -x cancel each other out. y minus -y is the same as y+y]
y=-5
now substitute -5 in for y in either problem:

x+-5=0
x=5

How do I write the equations of lines through the given point parallel to the given line and perpendicular to the given line?

Answers

first we find the slope of the original equation
4x - 2y = 3
-2y = -4x + 3
y = -4/-2x - 3/2
y = 2x - 3/2......slope here is 2

for a parallel line, we use the same slope
y = mx + b
slope(m) = 2
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = 2(2) + b
1 = 4 + b
1 - 4 = b
-3 = b
so ur parallel equation is : y = 2x - 3

for a perpendicular slope, we need the negative reciprocal. All that means is flip the slope and change the sign. So we have a slope of 2...the negative reciprocal we need is -1/2
y = mx + b
slope(m) = -1/2
(2,1)...x = 2 and y = 1
now we sub again
1 = -1/2(2) + b
1 = -1 + b
1 + 1 = b
2 = b
ur perpendicular line is : y = -1/2x + 2
=========================
x + 4 = 0
x = -4....this is a vertical line with an undefined slope....sorry but I am not sure about this one

Sin78 ×cos42+cos78×sin42 evaluate without the use of a calculator

Answers

sin a * cos b + cos a * sin b=sin (a+b)

sin 78 * cos 42 + cos 78* sin 42=sin (78+42)=sin 120=sin(180-120)=
sin 60=√3 / 2

Answer: sin 78 * cos 42 + cos 78* sin 42=√3 / 2

I need help with this

Answers

Answer:

a)7x - 10

b) 70 g

Step-by-step explanation:

Mass of 1st chemical which was mixed = 10g

Mass of 2nd chemical which was mixed = 2x

Mass of 3rd chemical which was mixed = 5x-20

So total mass of the the mixture which was formed after mixing all the 3 chemicals are =

10 + 2x + 5x - 20

=> 7x - 10

Mass of the mixture = 235 g

From (a) , we know that

7x - 10 = 235

=> 7x = 235 + 10 = 245

=> x = 245 / 7 = 35

Hence x = 35

We also know that mass of the 2nd chemical was = 2x.

So putting the value of x gives :-

2 × 35 = 70 g

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