56 = h/9
k/5 - 10 = 3
3t + 5 =2

Answer:

x = 1, y = 5

x = 5, y = 13

Step-by-step explanation:

y = x² − 4x + 8 .......(1)

y = 2x + 3 .......(2)

Substitute the value of y in equation 2 into equation 1

y = x² − 4x + 8

y = 2x + 3

x² − 4x + 8 = 2x + 3

Rearrange

x² − 4x − 2x + 8 − 3 = 0

x² − 6x + 5 = 0

Solve by factorization

Find the product you x² and 5. The result is 5x²

Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.

Replace −6x in the equation above with −x and −5x. This is illustrated below:

x² − x − 5x + 5 = 0

x(x − 1) − 5(x − 1) = 0

(x − 1)(x − 5) = 0

x − 1 = 0 or x − 5 = 0

x = 1 or x = 5

Substitute the value of x into equation 2 to obtain the value of y.

y = 2x + 3

x = 1

y = 2(1) + 3

y = 2 + 3

y = 5

x = 5

y = 2x + 3

y = 2(5) + 3

y = 10 + 3

y = 13

SUMMARY:

x = 1, y = 5

x = 5, y = 13

Answer:

Samuel had RM8 previously

Step-by-step explanation:

24÷3=8

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{pq+1}{9}[/tex]

= [tex]\frac{(3x+1)(3x-1)+1}{9}[/tex]

= [tex]\frac{9x^2- 1+1}{9}[/tex]

= [tex]\frac{9x^2}{9}[/tex]

= x²

Answer:

Hello,

Step-by-step explanation:

[tex]Using\ the\ formula\ (a+b)(a-b)=a^2-b^2\\p=3x+1\\q=3x-1\\\\p*q=(3x+1)*(3x-1)=9x²-1\\\\p*q+1=9x^2\\\\x^2=\dfrac{p*q+1}{9} \\[/tex]

9514 1404 393

Answer:

  138.77

Step-by-step explanation:

Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.

The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.

You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.

__

We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.

_____

Additional comment

There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.

The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.

Answer: (a): Good course, (b): Bad course

Step-by-step explanation:

Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.

Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.

Answer:

C

Step-by-step explanation:

degree 1 ( linear function

Answer:

D

Step-by-step explanation:

The function you need to use is the Tan(39).

Tan(x) = opposite / adjacent.

The opposite side does not make up the reference angle.

In this case, the opposite side = x

The adjacent side is not the hypotenuse and does make up the reference angle (which is not the right angle).

opposite = x

adjacent = 68

Tan(39) = x / 68              Multiply by 68

68*Tan(39) = x               Divide by Tan(39)

Tan(39) = 0.9098

68*.9098 = x

x = 55.07

Answer:

all have "bases" less than one which is a decay...

only "C" is greater than 1 (1.01)

"C" is the answer

Step-by-step explanation:

Answer:

3×5×7×11=1155

a.1155 the answer

3×5×7×11=1155

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth.

Given

3×5×7×11=1155

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Answer:

b:25

Step-by-step explanation:

77 degrees Fahrenheit is 25 degrees Celsius. So, the correct answer for the given equation is the second option.

An equation is a combination of two or more expressions separated by an equal sign(=), indicating that the expressions are equal to each other. The expressions, though, are a group of numbers, variables, mathematical operations, etcetera. An equation can be represented on the Cartesian plane.

The relation between Celsius and Fahrenheit is given by the following equation:

[tex]C =\dfrac{5}{9}(F-32)[/tex],

Substitute F = 77 to convert 77 degrees Fahrenheit to Celsius.

[tex]C =\dfrac{5}{9}(77-32)[/tex]

   [tex]=\dfrac{5}{9}(77-32)\\=\dfrac{5}{9}\times45\\= 25[/tex]

Thus, the second option is correct.

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Respuesta:

9 años

Explicación paso a paso:

Dado :

Capital = Principal, P = 8500 €

Rendimiento, tasa, r = 3,75%

Intereses, i = 2868,75 €

Para obtener el plazo, número de años que se necesitarán para devengar un interés de 2868,75 € sobre un capital de 8500 € al tipo del 3,75%;

Interés = principal * tasa * tiempo

2868,75 € = 8500 € * 0,0375 * t

2868,75 € = 318,75 billones €

t = 2868,75 € / 318,75 €

t = 9

Por lo tanto, tomará un período de 9 años.

Answer:

i think it the measured of the indicated angle is 55

Answer:

Step-by-step explanation:

The answer is C.

That's another way of using the vertical line test. Put a ruler perpendicular to the x axis and going through a point. If the ruler hits only one point, then then if all the points plotted do the same thing, then the points make a function.

C says the same thing. Only 1 element in the domain (x) can be associated with 1 y value (the range). If there is more than 1 y value, then you do not have a function.

Answer:

€520=£442.83

=£442.83-£260

=£182.83 into dollars=$251.52

Therefore he receives $251.52

Answer:

you guess any value of x and then you substitute any three values for example for the first equation you can guess the value of x to be 1 or 2 or 3

Answer:

7x = 42

Step-by-step explanation:

"Product" refers to multiplication and "is" refers to equal to.

Hi! I'm happy to help!

This equation will be written like this

x×7=42

To make this easier to solve, we can use the inverse operation, division.

42÷7=x

42 divided by 7 is 6, so the answer is 6.

I hope this was helpful, keep learning! :D

Answer:

x ≈ 55.5°

Step-by-step explanation:

Using the Sine rule in the triangle

[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )

5.7 sinx = 5 sin70° ( divide both sides by 5.7 )

sin x = [tex]\frac{5sin70}{5.7}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )

Answer:

[tex]x =55[/tex]°

Step-by-step explanation:

An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):

[tex]x + x + 70 = 180[/tex]

Simplify,

[tex]2x + 70 =180[/tex]

Inverse operations,

[tex]2x + 70 =180[/tex]

[tex]2x = 110[/tex]

[tex]x =55[/tex]

Hi!

[tex]|15x+2|=8\\\\\\15x+2=8\\15x=8-2\\15x=6 \ \ |:15\\\boxed{x_1=0,4}\\\\\\15x+2=-8\\15x=-8-2\\15x=-10 \ \ |:15\\\boxed{x_2=-\frac{2}{3}}[/tex]

Answer:

x = 2/5      x = -2/3

Step-by-step explanation:

|15x + 2 |= 8

There are two solutions, one positive and one negative

15x + 2 = 8  and 15x + 2 = -8

Subtract 2 from each side

15x + 2-2 = 8-2  and 15x + 2-2 = -8-2

15x = 6                             15x = -10

Divide by 15

15x/15 = 6/15                   15x /15 = -10/15

x = 2/5                               x = -2/3

Answer:

There are no like terms

Step-by-step explanation:

×^2+9

=ײ+9

1 - 580squaredcm

2 - 540

Answer:

(a): x is 3 and ky is -1

(b): k is -2

Step-by-step explanation:

Let: 3x + ky = 8 be equation (a)

x - 2 ky = 5 be equation (b)

Then multiply equation (a) by 2:

→ 6x + 2ky = 16, let it be equation (c)

Then equation (c) + equation (b):

[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]

Then ky :

[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]

[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]

Simultaneous equations are used to represent a system of related equations.

The value of k when [tex]y = \frac 12[/tex] is -2

Given that:

[tex]3x + ky = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]y = \frac 12[/tex]

Substitute [tex]y = \frac 12[/tex] in both equations

[tex]3x + ky = 8[/tex]

[tex]3x + k \times \frac 12 = 8[/tex]

[tex]3x + \frac k2 = 8[/tex]

[tex]x - 2ky = 5[/tex]

[tex]x - 2k \times \frac 12 = 5[/tex]

[tex]x - k = 5[/tex]

Make x the subject in [tex]x - k = 5[/tex]

[tex]x = 5 + k[/tex]

Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]

[tex]3(5 + k) + \frac k2 = 8[/tex]

Open bracket

[tex]15 + 3k + \frac k2 = 8[/tex]

Multiply through by 2

[tex]30 + 6k + k = 16[/tex]

[tex]30 + 7k = 16[/tex]

Collect like terms

[tex]7k = 16 - 30[/tex]

[tex]7k = - 14[/tex]

Divide both sides by 7

[tex]k = -2[/tex]

Hence, the value of constant k is -2.

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Answer:

7^2+2ab - 4b^2

Step-by-step explanation:

A² + b² = 7b

b² + (2b-a) ²= 7²

FOIL

b^2 +4b^2-4ba+a^2= 7^2

Rewriting

a^2 -2ab + b^2    +4b^2 -2ab = 7^2

Add 2ab and subtract 4b^2 from each side

a^2 -2ab + b^2    +4b^2 - 4b^2 -2ab+2ab = 7^2+2ab - 4b^2

a^2 -2ab + b^2    = 7^2+2ab - 4b^2

(a-b)^2 = 7^2+2ab - 4b^2

Answer:

Value of ∠ BFG = 135°

Step-by-step explanation:

Given:

AB || CD

∠ AFG = (3x + 15)°

∠ FGD = (5x - 5)°

Find:

∠ BFG

Computation:

We know that;

∠ AFG = ∠ FGD

3x + 15 = 5x - 5

3x - 5x = - 5 - 15

- 2x = - 20

2x = 20

x = 10

Value of ∠ AFG = 3x + 15

Value of ∠ AFG = 3(10) + 15

Value of ∠ AFG = 45°

∠ BFG = 180° - Value of ∠ AFG

∠ BFG = 180° - 45°

∠ BFG = 135°

Value of ∠ BFG = 135°

Answer:

m <1 = 147

m <2 = 90

Step-by-step explanation:

In rhombus diagonals are perpendicular to each other so

m <2 = 90

m < 1 = 180- 33

= 147

Answered by Gauthmath

The required angle of the rhombus m∠1 = 57° and m∠2 = 90°.

Given that,
A figure of a rhombus is shown,
An angle of 33° is given,
m∠1 and m∠2 is to be determined.

The triangle is a geometric shape that includes 3 sides and sum of the interior angle should not greater than 180°.

The angle can be defined as the one line inclined over another line.

Here, the rhombus has been shown with an angle of 33° of the side with one of the diagonal.

Since the diagonal of the rhombus bisect each other at an angle of 90 so the angle m∠2 = 90  and the sum of the interior angle of a triangle is 180. So,
m∠1 + 33 + 90 = 180
m∠1 = 180 - 123
m∠1 = 57

Thus, the required angle of the rhombus m∠1 = 57° and m∠2 = 90°.

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Answer:

A = 120

Step-by-step explanation:

Angle A is a vertical angle to 120 and vertical angles are equal

A = 120

[tex]\Large\rm\underbrace{{\green{ \: Angle \: A \: = \: 120 \degree}}}[/tex]

Because vertically opposite angles are always equal.

Given:

Amplitude = 21

Vertical shift = 19 units down

To find:

The maximum and the minimum value.

Solution:

The general form of sine function is:

[tex]y=A\sin (Bx+C)+D[/tex]

Where, |A| is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is the vertical shift.

Here,

[tex]Maximum=D+A[/tex]

[tex]Minimum=D-A[/tex]

We have,

Amplitude: [tex]A = 21[/tex]

Vertical shift: [tex]D=-19[/tex]

Negative sign means shifts downwards.

Now,

[tex]Maximum=D+A[/tex]

[tex]Maximum=-19+21[/tex]

[tex]Maximum=2[/tex]

And,

[tex]Minimum=D-A[/tex]

[tex]Minimum=-19-21[/tex]

[tex]Minimum=-40[/tex]

Therefore, the minimum value is -40 and the maximum value is 2.

Answer:

Y = 2x - 4

(2,-4)

gradient= 2

y-intersept = -4

Step-by-step explanation:

The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.

Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are

±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).

Trying out a few roots until we get one that works using synthetic division, we can try

x+1 (the root is x=-1)

-1  |     1       1        -6         -14         -12

    |            -1          0          6           8

    __________________________

          1     0        -6            -8         -4

the remainder is -4, so this does not work

x+2 (the root is x=-2)

-2 |     1       1        -6         -14         -12

    |            -2          2          8          12

    __________________________

          1      -1       -4           -6         0

Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is

-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6

Using the rational roots theorem, the possible roots of x³-x²-4x-6 are

±(1,2,3,6)

Starting with

x-1 (root is x=1), we have

1 |     1       -1        -4         -6      

    |            1          0         -4        

    _____________________

          1      0       -4           -10

there is a remainder, so this is not a root

next, x-2 (root is x=2)

2 |     1       -1        -4         -6      

    |            2         2         -4        

    _____________________

          1      1       -2           -10      

there is a remainder, so this is not a root

next, x-3 (root is x=3)

3|     1       -1        -4         -6      

    |            3         6         6        

    _____________________

          1      2      2          0

x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2