Simplify the scalar multiplication on the matrix.

[tex]x+y=12\\\dfrac{x}{y+3}=\dfrac{1}{2}\\\\x=12-y\\2x=y+3\\\\2(12-y)=y+3\\24-2y=y+3\\3y=21\\y=7\\\\x=12-7=5\\\\\dfrac{x}{y}=\dfrac{5}{7}[/tex]

Answer:

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Step-by-step explanation:

Given equation is:

[tex]15sin^2 x+11cosx-17=0[/tex]

To find:

Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].

Solution:

First of all, let us recall one identity of square of sine and square of cosine.

Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.

[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]

So

Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.

[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]

So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Answer: [tex]x=\dfrac{25}{21}[/tex]

Step-by-step explanation:

Area of parallelogram = Base x height

If two parallelograms are similar, then their corresponding sides are proportional.

That means, [tex]\dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}[/tex]

[tex]\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}[/tex]

Hence, [tex]x=\dfrac{25}{21}[/tex]

Answer:

4 x 3

Step-by-step explanation:

The order of a matrix is given by stating the number of rows followed by the number of columns.

The matrix here has 4 rows and 3 columns thus order is

4 x 3

Answer:

The function is not one-to-one

Step-by-step explanation:

This is a quadratic function.

[tex]f(x)=x^2-2[/tex]

A function is one-to-one

[tex]\text{if } f(x_1)=f(x_2) \Leftrightarrow x_1=x_2[/tex]

The function given is not one-to-one because there are values of the input [tex]x[/tex], which leads to the same output.

For example.

[tex]y=f(2)=2^2-2=\boxed{2}[/tex]

[tex]y=f(-2)=(-2)^2-2=\boxed{2}[/tex]

Answer:

4.  m_LON + m_MON = m_LON; m_JKL + m_IKH = m_HKJ

Step-by-step explanation:

Both interior angles of each add up to m_LON:m_HKJ

To prove this we show the interior angles add + sign to each prove LON angle, and : colon separates from the proof of m_JKL+m_IKH= m_HKJ.

Answer:

Parallelogram

Step-by-step explanation:

Answer:

Parallelogram

Step-by-step explanation

Answer:

91

Step-by-step explanation:

Let x be the smallest one:

● x is the first number

● x+1 is the second number

● x+2 is the third number

The sum of these numbers is 276

● x+(x+1)+(x+2) =276

● x+x+1+x+2 = 276

● 3x + 3 = 276

Substract 3 from both sides:

● 3x+3-3 = 276-3

● 3x = 273

Divide both sides by 3

● (3x)/3 = 273/3

● x = 91

So the smallest one is 91

Answer:

x = [tex]\frac{29}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3}{5}[/tex] = [tex]\frac{x-1}{8}[/tex] ( cross- multiply )

5(x - 1) = 24 ← distribute parenthesis on left side

5x - 5 = 24 ( add 5 to both sides )

5x = 29 ( divide both sides by 5 )

x = [tex]\frac{29}{5}[/tex]

Answer:

8 10 12 14 16

Step-by-step explanation:

8+2=10, 10+2=12, 12+2=14, 14+2=16

Answer:

0.45p

Step-by-step explanation:

4 chocolates = £1.80

1 chocolate =  x

x= 1.80× 1 = 1.80÷4 = 0.45p

1 = 0.45p

I HOPE THIS HELPED :)

Answer:

[tex]\huge\boxed{\sf y = 2x -4}[/tex]

Step-by-step explanation:

The given equation is:

y = 2x + 3

Where Slope = m = 2 , Y-intercept = b = 3

Parallel lines have equal slopes

So, Slope of new line = m = 2

Now, Finding y-intercept:

Given Point = (x,y) = (1,-2)

So, x = 1 , y = -2

Putting m, x and y in standard form of equation to get b:

[tex]\sf y = mx+b[/tex]

[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]

Subtracting 2 to both sides

[tex]\sf b = -2-2\\[/tex]

b = -4

So, the standard form og equation for the new line is :

[tex]\sf y = mx+b[/tex]

[tex]\sf y = 2x -4[/tex]

Answer:

y = 2x - 4

Step-by-step explanation:

the problem is called (slope-intercept form)

the equation of the line is y = mx + b

the equation of a line is given as y = 2x + 3

slope = 2

b = y-intercept is where the line crosses the y-axis = 3

so point (x1, y1)  = (1, -2)

by using the equation.

y = mx + b

-2 = 2 (1) + b

-2 -2 = b

therefore b = -4

writing the new equation using the slope intercept form

y = mx + b  would be y = 2x + 4

so the equation parallel to the equation y = 2x + 3 is y = 2x - 4

Answer:

y=x-1

Step-by-step explanation:

Answer:

-3.5

Step-by-step explanation:

The problem you have stated is (y-z)/z where y=-2 and z = 4/5. To solve, substitute the values of y and z into the problem. Then, you have (-2-4/5)/4/5. (-2-4/5) simplifies to -14/5 so then you have (-14/5)/4/5. To divide, multiply -14/5 by 5/4 {multiplying by the reciprocal}. That equals -70/20 which is equal to -3.5

Answer:

[tex]\large\boxed{-3.5}[/tex]

Step-by-step explanation:

(y - z) ÷ z          y = -2 and z = 4/5

Substitute in the given values for y and z into the equation

(y - z) ÷ z  

(-2 - 4/5) ÷ 4/5

Subtract inside the parenthesis (-2 - 4/5)

-2.8 ÷ 4/5

Convert 4/5 into a decimal (in this case that can be done by multiplying both the numerator and denominator by 20)

4/5 = (4 * 20) / (5 * 20) = 80 / 100

80 / 100

Divide numerator and denominator by 10

8/10 = 0.8

Substitute into previous equation

-2.8 ÷ 4/5 = -2.8 ÷ 0.8

Divide

[tex]\large\boxed{-3.5}[/tex]

Hope this helps :)

Answer: [tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Step-by-step explanation:

Let x =  Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

[tex]x+y=45\\\\1000 x + 500y = $2500[/tex]

Answer:

1,000x + 500y = 45

x + y =45

Step-by-step explanation:

So that means answer b is the correct answer, also I took the test.

Answer:

(1) B

(2) D

Step-by-step explanation:

(1)

Let the quadratic function be:

[tex]y = ax^{2} + bx + c[/tex]

For the point, (0,-1),

[tex]y = ax^{2} + bx + c[/tex]

[tex]-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1[/tex]

Then the equation is:

[tex]y = ax^{2} + bx -1[/tex]

For the point (-1, -8) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)[/tex]

For the point (1, 2) ,

[tex]y = ax^{2} + bx -1[/tex]

[tex]2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)[/tex]

Add the two equations and solve for a as follows:

[tex]a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2[/tex]

Substitute a = -2 in (i) and solve for b as follows:

[tex]a-b=-7\\-2-b=-7\\b=5[/tex]

Thus, the quadratic function is:

[tex]f(x)=-2x^{2}+5x-1[/tex]

The correct option is (b).

(2)

The ordered pairs are:

(5, 7), (7, 11), (9, 14), (11, 18)

Represent them in an XY table as follows:

X : 5 | 7 | 9 | 11

Y : 7 | 11 | 14 | 18

Compute the difference between the Y values as follows:

Diff = 11 - 7 = 4

Diff = 14 - 11 = 3

Diff = 18 - 14 = 4

Now compute the difference between the Diff values:

d = 3 - 4 = -1

d = 4 - 3 = 1

Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.

The correct option is D.

Answer:

5/14, 7/10, 11/15, 5/6, 19/21.

Step-by-step explanation:

Covert the fractions to decimal form:

5/14 = 0.357

7/10 = 0.7

5/6 = 0.833

11/15 = 0.733

19/21 = 0.905.

So in ascending order this is:

5/14, 7/10, 11/15, 5/6, 19/21.

Answer:

Step-by-step explanation:

to arrange in ascending order, we need to convert them into like fractions

to convert them into like fractions, we need to find the LCM of the denominators

the LCM of the denominators ( 14, 10, 6, 15 and 21 ) is 210

5/14 × 15/15 = 75/210

7/10 × 21/21 = 147/210

5/6 × 35/35 = 175/210

11/15 × 14/14 =154/210

19/21 × 10/10 = 190/210

75/210 < 147/210 < 154/210 < 175/201 < 190/210

∴ 5/14 < 7/10 < 11/15 < 5/6 < 19/21

Hope this helps

plz mark as brainliest!!!!!!!

Answer:

1,080 meters squared.

Step-by-step explanation:

Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.

The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.

2(x) + 2(6/5x) = 132

2x + 12/5x = 132

10/5x + 12/5x = 132

22/5x = 132

22x = 660

x = 30.

That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.

The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.

Hope this helps!

Answer:

70

Step-by-step explanation:

8 choose 4

= (8!)/(4!*4!)

=(8*7*6*5)/(4*3*2*1)

=1680/24

=70

Answer:

4/8 simplified=1/2

Step-by-step explanation:

i hope this is right sorry if not

Answer:

Step-by-step explanation:

f(x) = x - 7

h(x) = 2x + 3

To find h(f(x)) substitute f(x) into h(x) that's replace every x in h(x) by f(x)

That's

h(f(x)) = 2(x - 7) + 3

h(f(x)) = 2x - 14 + 3

We have the final answer as

Hope this helps you

Answer:

Isabelle spent $52.50 more on Erasers than rulers.

Step-by-step explanation:

Step 1

Find the quantity of each stationery bought in fraction

Let us represent the total fraction of what Isabelle bought as: x

1/3x = quantity of pencils bought

5/8 of the remainder = quantity of erasers bought

The remainder = x - 1/3x = 2/3x

5/8 of 2/3x = 5/8 × 2/3x = 5/12x

Hence, 5/12x = quantity of erasers bought

The rest is rulers

1 - (1/3 + 5/12)

1 - (4 + 5/12)

1 - 9/12

1 - 3/4

= 1/4x

Hence, 1/4 = quantity of rulers bought.

Step 2

We find the number of stationeries that Isabelle bought.

The cost of the stationery is

a Pencil: $1.20

an eraser: $1

a ruler: $0.50.

Total amount spent on stationery = 169.50

We have this equation

1.20 × 1/3x + 1 × 5/12x + 0.50 × 1/4x = 169.50

0.4x + 0.4166666667x + 0.125x =

169.50

0.9416666667x = 169.50

x = 169.50 /0.9416666667

x = 179.99999999

Approximately , the number of stationeries that Isabelle bought = x = 180

Step 3

Find the number and the amount spent on each stationery that Isabelle bought

a) i) Quantity of pencils bought = 1/3 x

x = 180

= 1/3 × 180

= 60 pencils

ii) Amount spent on pencils

If 1 pencil = $1.20

60 pencils =

60 × 1.20 = $72

b) i) Quantity of Erasers bought = 5/12x

x = 180

= 5/12 × 180

= 75 pencils

ii) Amount spent on Eraser

If 1 pencil = $1

75 pencils =

75 × 1 = $75

c) i) Quantity of rulers bought = 1/4 x

x = 180

= 1/4 × 180

= 45 pencils

ii) Amount spent on pencils

If 1 pencil = $0.50

45 pencils =

45 × 0.50 = $22.50

Step 4

We were asked to calculate how much more did she spend on erasers than rulers.

In step 3, the amount spent on Erasers = $75

the amount spent on ruler = $22.5

The difference in the amount spent = $75 - $22.5

= $52.5

Therefore, Isabelle spent $52.50 more on Erasers than rulers.

Answer:

the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.

Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.

17, 99, 267, 8107 and 999999999 are examples of whole numbers.

A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333

A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.

Example: π is an irrational number.

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.

Included within the irrationals are the transcendental numbers, such as π

Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

Answer:

1471.15

Step-by-step explanation:

Answer:

£ 87.00

Step-by-step explanation:

52.20*2/3=52.20/3*2=17.4*2=34.8

52.20+34.80=87.00

Answer:

7/8 =s

Step-by-step explanation:

1/8=s-3/4

Add 3/4

1/8 + 3/4 = s -3/4 +3/4

1/8 + 3/4 = s

Get a common denominator

1/8 + 3/4 *2/2 = s

1/8 + 6/8 =s

7/8 =s

1/8 = s - 3/4

1/8 = s -6/8 ( * 2/2)

7/8 = s

s = 7/8

Answer: 20 is the width and 27 is length

Answer:

(5*7)-f

Step-by-step explanation:

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Algebraic expression is the combination of terms that consists of numbers  and variables connected by arithmetic operators.

Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.

We need to write it in an algebraic expression

5 times a quantity. for product we use multiplication sign

For addition we use + sign and for difference we use minus sign .

5 times the quantity 7 means 5 multiplied by 7

[tex]5 \cdot 7[/tex]

5 times the quantity 7 minus a number f  

subtract f from the expression we got

[tex]5 \cdot 7 -f[/tex]

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Learn more information about 'Algebraic expression ' here:

brainly.com/question/2193741

Answer:

6.5<3rd side <19.9

Step-by-step explanation:

Extremely easy. All you have to do to get the first answer is minus 13.2-6.7 which is 6.5. Then add 13.2+6.7 to get 19.9 for the other answer. So the two answers would be 6.5 and 19.9.

Your welcome

Answer:

x = 5/2          x=1/3

Step-by-step explanation:

(2x – 5)(3x – 1) = 0

Using the zero product property

2x-5 =0    3x-1 =0

2x=5         3x =1

x = 5/2          x=1/3

Answer:

C on edg 2021

Step-by-step explanation: