2x = 4y + 8, x - 2y = 4
System of Equations

Answer:

Gradient of A: 2

Gradient of B: -1

Step-by-step explanation:

Gradient = change in y/change in x

✔️Gradient of A using two points on line A, (2, 5) and (0, 1):

Gradient = (1 - 5)/(0 - 2) = -4/-2

Simplify

Gradient of A = 2

✔️Gradient of B using two points on line B, (0, 5) and (5, 0):

Gradient = (0 - 5)/(5 - 0) = -5/5

Simplify

Gradient of B = -1

Answer:

ok so lets divide 90 by 15 to get 6 so she gets paid 6 per student and that means lisa gets paid 12 so lets just multiply

6*20=120 so mary gets paid 120

and lisa gets paid doable that so 420

but i don't know there base pay so the i can't answer this problem

Hope This Helps!!!

Answer:

0.4 or 0.40

Step-by-step explanation:

There are 10 total numbers. 4 of them are in set B.

So, 4/10 are in set B.

The probability is 0.4 because 4 divided by 10 is 0.4.

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

Answer:

13.97%

Step-by-step explanation:

Find her percent increase in pay by dividing 95 by 680:

95/680

= 0.1397

Multiply this by 100:

= 13.97

So, her percent increase in pay is approximately 13.97%

Answer:

i believe its 162

Step-by-step explanation:

hope it helped :>

Answer:

1/2

8

Step-by-step explanation:

When its talking about the result or output, look at the range, and then follow the line(s) back to the number(s) in the domain. Do the opposite when it's talking about the function of a certain number, e.g. f(4).

Answer: No, it's not possible.

Explanation: An angle must only be opposite exactly one side.

Answer:

D

Step-by-step explanation:

Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect

Answer:

The system has two solutions, but only one is viable because the other results in negative side lengths.

Step-by-step explanation:

correct on edmentum or plato

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.

Answer:

x = [tex]\frac{3}{20}[/tex]

Step-by-step explanation:

Given

x + [tex]\frac{3}{2}[/tex] + (x - 1) = [tex]\frac{4}{5}[/tex]

Multiply through by 10 ( the LCM of 2 and 5 ) to clear the fractions

10x + 15 + 10(x - 1) = 8

10x + 15 + 10x - 10 = 8

20x + 5 = 8 ( subtract 5 from both sides )

20x = 3 ( divide both sides by 20 )

x = [tex]\frac{3}{20}[/tex]

x + 3/2 + x - 1 = 4/5

Collect the same terms

x + x + 3/2 - 1 = 4/5

2x + 3/2 - 2/2 = 4/5

2x + (3 - 2)/2 = 4/5

2x + 1/2 = 4/5

2x + 0.5 = 0.8

Subtract both sides 0.5

2x + 0.5 - 0.5 = 0.8 - 0.5

2x + 0 = 0.3

2x = 3/10

Divide both sides by 2

2x ÷ 2 = ( 3/10 ) ÷ 2

x = 3/10 × 1/2

x = 3/20

_________________________________

3/20 + 3/2 + ( 3/20 - 1 ) = 4/5

3/20 + 30/20 + ( 3/20 - 20/20 ) = 4/5

(3 + 30)/20 + (3 - 20)/20 = 4/5

33/20 - 17/20 = 4/5

(33 - 17)/20 = 4/5

16/20 = 4/5

4 × 4 / 4 × 5 = 4/5

4/5 = 4/5

Thus we found the correct value of x .

And we're done...

Answer:

Step-by-step explanation:

=  [tex]\int\limits^1_0 {5x\sqrt{x} } \, dx[/tex]

=  [tex]\int\limits^1_0 {5xx^{1/2} } \, dx[/tex]

= [tex]\int\limits^1_0 {5x^{3/2} } \, dx[/tex]

= 5 [tex]\int\limits^1_0 {x^{3/2} } \, dx[/tex]

= 5*[tex]\frac{2}{5}[/tex]*[tex]x^{5/2}[/tex]  |[tex]\left[\begin{array}{ccc}1\\0\\\end{array}\right] \left[/tex]

= 5*[tex]\frac{2}{5}[/tex]*[tex]1^{5/2}[/tex]

= 2

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

9514 1404 393

Answer:

  (a) ∠SPR = 70°

  (b) ∠SRP = 30°

Step-by-step explanation:

The applicable relationships are ...

__

QR is subtended by 35° inscribed angle QPR, so is 2×35° = 70°.

PQ is subtended by 45° inscribed angle PSQ, so is 2×45° = 90°.

RS is 2×QR, so is 2×70° = 140°.

(a) Inscribed angle SPR is half the measure of arc RS, so is 140°/2 = 70°.

__

(b) Arc SP is the remaining arc in the circle, so is ...

  arc SP = 360° -arc PQ -arc QR -arc RS = 360° -90° -70° -140° = 60°.

Inscribed angle SRP is half the measure of arc SP, so is 60°/2 = 30°

Answer:

Probably 10

Step-by-step explanation:

10/5=2

Answer:

you divide a 8000÷ 5.5 yor answer is it

Hi!

[tex]3x^3-2y^3-6x^2y^2+xy=\\\\=3\cdot(\frac{2}{3})^3-2\cdot(\frac{1}{2})^3-6\cdot(\frac{2}{3})^2\cdot(\frac{1}{2})^2+\frac{2}{3}\cdot\frac{1}{2}=\\\\=3\cdot\frac{8}{27}-2\cdot\frac{1}{8}-6\cdot\frac{4}{9}\cdot\frac{1}{4}+\frac{1}{3}=\\\\=\frac{8}{9}-\frac{1}{4}-\frac{2}{3}+\frac{1}{3}=\frac{8}{9}-\frac{1}{4}-\frac{1}{3}=\frac{32}{36}-\frac{9}{36}-\frac{12}{36}=\boxed{\frac{11}{36}}[/tex]

Answer:

ones

Step-by-step explanation:

Step-by-step explanation:We have to graph the function g(x) which is given as:

g(x)=  x when x<2

and -3 when x ≥2.

Clearly after looking at the function we see that the function is not continuous since we find the continuity at x=2 as follows.

Left hand limitat 2:

g(2-h)=lim h→0 2-h

       =2-0=2

Also right hand limit at x=2 is:

g(2+h)=lim h→0 (2+h)

         = 2+0=2

Also g(2)= -3.

As:

Left hand limit= Right hand limit but is not equal to function's value at that point.

Hence, the function is discontinuous at x=2.

so for x<2 we will get a graph of a line y=x.

and for x≥2 we will get a straight line y=-3 parallel to the domain.

Answer:

5% = 1/20

15% = 3/20

6.5% = 0.065

25% = 0.25

7% = 0.07

Step-by-step explanation:

I hope this helps! Just ask me if you have any questions.

Have a nice dayy! :)

Answer:

.05  25%  .15  7% .065  100% 2000% .25

Step-by-step explanation:

Percentages to decimals :

example  

5% = .05

First remove the % sign: 5

Where is the decimal? Here : 5.00

Now move the decimal to the left two places. Fill the gaps with zeros : .05

Another way to do it is by divide the number by 100. Use a calculator if necessary.

Example 2: 6.5%

Move decimal two places to left: .065

Example 3: .56%

Move decimal to places to the left:  .0056

Decimals to percentages. Do the exact opposite. Move decimal to places to the right then add the % sign.

Example: .25 becomes 25%

                .07 becomes 07% or just 7%

Answer:

[tex](13)\ 1 <x < 15[/tex]

[tex](14)\ 6 <x < 18[/tex]

Step-by-step explanation:

Question 13:

[tex]a,b = 8,7[/tex] -- the two sides

Using triangle inequality theorem, we have:

[tex]a + b > x[/tex]

[tex]a + x > b[/tex]

[tex]x + b > a[/tex]

So, we have:

[tex]a + b > x[/tex]

[tex]8 + 7 > x[/tex]

This gives:

[tex]15 > x[/tex]

[tex]a + x > b[/tex]

[tex]8 + x > 7[/tex]

Collect and evaluate like terms

[tex]x > -1[/tex]

[tex]x + b > a[/tex]

[tex]x + 7 > 8[/tex]

Collect and evaluate like terms

[tex]x > 1[/tex]

Ignore the inequality with a negative value.

So, we have:

[tex]x > 1[/tex] and [tex]15 > x[/tex]

Rewrite as:

[tex]1< x[/tex] and [tex]x < 15[/tex]

Merge

[tex]1 <x < 15[/tex]

Question 14:

[tex]a,b = 12,6[/tex] -- the two sides

Using triangle inequality theorem, we have:

[tex]a + b > x[/tex]

[tex]a + x > b[/tex]

[tex]x + b > a[/tex]

So, we have:

[tex]a + b > x[/tex]

[tex]12 + 6 > x[/tex]

This gives:

[tex]18 > x[/tex]

[tex]a + x > b[/tex]

[tex]12 + x > 6[/tex]

Collect and evaluate like terms

[tex]x > -6[/tex]

[tex]x + b > a[/tex]

[tex]x + 6 > 12[/tex]

Collect and evaluate like terms

[tex]x > 6[/tex]

Ignore the inequality with a negative value.

So, we have:

[tex]x > 6[/tex] and [tex]18 > x[/tex]

Rewrite as:

[tex]6< x[/tex] and [tex]x < 18[/tex]

Merge

[tex]6 <x < 18[/tex]

Answer:

slope-inercept form: y = 3x + 3        point-slope form: y - 9 = 3(x - 2)

Step-by-step explanation:

slope-intercept form:

y2 - y1 / x2 - x1        

9 - (-6)/ 2 - (-3)      

= 3

y = 3x + b

9 = 3(2) + b

9 = 6 + b

3 = b

y = 3x + 3

point-slope form:

y - 9 = 3(x - 2)

Answer:

ok

What do you want me to answer ?

Answer:

x = 6

HI = 29

Step-by-step explanation:

✔️HI = ½(AB) => Triangle Mid-segment Theorem

HI = 5x - 1

AB = 58

Plug in the values and solve for x

5x - 1 = ½(58)

5x - 1 = 29

Add 1 to both sides

5x - 1 + 1 = 29 + 1

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

✔️HI = 5x - 1

Plug in the value of x

HI = 5(6) - 1

HI = 30 - 1

HI = 29

Answer: 8

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

complementary angles equal 90° and 34+56 is 90°

Answer:

True

Step-by-step explanation:

Complement angle means that the two angles add up to 90 degrees. We can check this by adding the two given angles together:

34+56=90

90=90

This means that this is true.

I hope this helps and have a great day!

Answer:

Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify.

Step-by-step explanation:

Answer:

3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]

Step-by-step explanation:

(f · g )(x) = 3[tex]x^{2}[/tex] · (x + 2) = 3[tex]x^{3}[/tex] + 6[tex]x^{2}[/tex]  (Multiply the two terms by distributing)