Use the Substitution method to solve the system of equations

3x+4y=10

y=x-1

Answer:

(5) The perpendicular height of the triangle is 8.48 mm.

(6) The 1184.86 cm far up the wall the ladder reach.

Step-by-step explanation:

Part (5):

When a perpendicular is drawn in an isosceles triangle then the perpendicular divided the base into 2 equal parts.

The figures is shown below.

In ΔABC,

CB = 6 mm

So,

CD = BD = 3 mm

Now calculating the perpendicular height of the triangle.

Using Pythagoras theorem in ΔADC:

[tex](AC)^2=(CD)^2+(AD)^2\\\\(9)^2=(3)^2+(AD)^2\\\\81=9+(AD)^2\\\\(AD)^2=81-9\\\\(AD)^2=72\\\\AD=8.48mm[/tex]

Thus, the perpendicular height of the triangle is 8.48 mm.

Part (6):

The figure is shown below.

Converting meter to centimeter:

1 m = 100 cm

So,

12 m = 1200 cm

Using Pythagoras theorem in ΔXYZ:

[tex](XZ)^2=(YZ)^2+(XY)^2\\\\(1200)^2=(190)^2+(XY)^2\\\\1440000=36100+(XY)^2\\\\(XY)^2=1440000-36100\\\\(XY)^2=1403900\\\\XY=1184.86cm[/tex]

Thus, 1184.86 cm far up the wall the ladder reach.

Answer:

x= -8y  / 5 +107

y = 535 - 5x / 8

Step-by-step explanation:

5x+8y=535

Subtract 8y from both sides.

5x=535−8y

Divide both sides by 5.

5x / 5 = 535 - 8y / 5

Dividing by 5 undoes the multiplication by 5.

x=  535−8y / 5

​ Divide 535−8y by 5.

x= -8y  / 5 +107

5x+8y=535

Subtract 5x from both sides.

8y=535−5x

Divide both sides by 8

8y / 8 = 535 - 5x / 8

Dividing by 8 undoes the multiplication by 8.

y = 535 - 5x / 8

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

The answer is 84 cubic feet.

Step-by-step explanation:

3 x 4 = 12.  12 x 6 = 72. 72 + 12 = 84

Given:

The length of field is n yards.

The length of a field in feet is a function f(n).

To find:

The function rule for this situation.

Solution:

We know that,

1 yard = 3 feet

Using this conversion, we get

n yard = 3n feet

The length of field is n yards. So, the length of the field is 3n feets.

The length of a field in feet is a function f(n). So,

[tex]f(n)=3n[/tex]

Therefore, the required function rule for this situation is [tex]f(n)=3n[/tex].

Answer:

Step-by-step explanation:

Answer:

An equation is needed to evaluate h(0).

When you evaluate h(0), you find the y-intercept of the graph because the independent variable inside the brackets, probably x or t, equates to 0.

The problem is needed for its context to be explained.

Although in most math problems, when h(x) form is used, h usually represents height.

I assume h(0) is the initial height, maybe the height that the rocket was launched or the height that the person who threw the ball is.

Answer:

postive

Step-by-step explanation:

positive collums so it's positive

Answer:

D

Step-by-step explanation:

[tex]\sqrt{17} = 4.123[/tex]

So we can see that 4.123 lie between 4 and 5

Therefore, option (D) is correct

Answer:

35x

Step-by-step explanation:

Start with parentheses, 2 x 1/2 = 1

9 x 4 = 36

36 - 1 = 35

Answer:

Y = -1/2 - 2

Step-by-step explanation:

Y - intercept (b value in y = mx + b) equals -2.

Slope is -1/2

Answer:

the equation of the line in the following graph:​ y = -1/2x - 2

Step-by-step explanation:

floor = 12*10= 120 sq ft

rug = r² = 9 Пr2

120-9π = 91.74 sq ft

Answer:

I'll do it for the equation, then you can try to solve the second one. Of your not able to, just comment and I'll answer the second one

Step-by-step explanation:

y = -3x+4

When

___x__l  _y____

   0          l    4

   1           l     1

   2          l     -2

   3          l     -5

   4          l     -8

Answer:it has to be A

Step-by-step explanation:

Answer:d

Step-by-step explanation:

Answer:

b is 3 pythagorean theorem

Step-by-step explanation:

Answer:

your answer for B is 3

Step-by-step explanation:

this is easy its a Pythagorean Triple (with triples u dont have to do much work all u have to do is know ur Triples and its that easy)

so the Triples are

p.s you might want to write these down for the future

so if we look at this picture of the triangle we can tell its a 3,4,5 triple

and there is one missing side which is 3.

Answer:

Step-by-step explanation:

Number of pupils can play either instrument:

Number of those can play both:

Answer:

the answer is 20

Step-by-step explanation:

5×12 = 60

which means he had 60 points feom hitting the target

60-20=40

therefor he lost 40 points miing the target

40÷2=20

therefor he missed the target 20 times

Answer:

I looks like it's anwser D

Answer:

$460.80

Step-by-step explanation:

with we us our formula equation I=prt we now cam solve for our depreciated value

with we substitute our varibles with the correct numerals we now get

I= 960 x 0.12 x 4

we turn our 12% into a decimal to be Simplified into our equation.

If we now solve we will get

I = 960 x 0.12 x 4

I = 460.8

Answer:

Rida is 10 years old and her father is 40 years old.

Step-by-step explanation:

Given:

Present age

Present age of Rida = x

Present age of Rida's father = 4x

Age after 5 years

Age of Radi after 5 years = x + 5

Age of Radi's father after 5 years = 3(x + 5)

What To Find:

The present age of Rida and Rida's father.

Solution:

According to the statement the equation will be,

⇒ 4x + 5 = 3(x + 5)

Remove and solve the brackets,

⇒ 4x + 5 = 3x + 15

Take numbers to RHS and variable to LHS,

⇒ 4x - 3x = 15 - 5

Subtract 3x from 4x and 5 from 15,

⇒ x = 10

Now substitute the values of Rida's age and Rida's father's age,

Rida's age = x = 10 years

Rida's father's age = 4x = 4(10) = 40 years

Answer:

7 is ur answer

Step-by-step explanation:

Answer:Its the last one to the left up

Step-by-step explanation:

Answer:

9:25

hope this helps

have a good day ;)

Step-by-step explanation:

3/4 of an hour=45 minutes so add 8:40 + 45 min

Answer:

9 : 25

Step-by-step explanation:

It shows 8 : 40

After 3/4 hour or 45 minutes.

8 : 40 + 20 minutes + 25 minutes

9 : 00 + 25 minutes = 9 : 25

Answer:

y=1/3x

Step-by-step explanation:

the slope (rise/run) is 1/3 and the y-intercept ("b" in y=mx+b) is just 0, so you dont have to write it

Answer:

the answer of this question is = 6x + 18

Answer:

15

Step-by-step explanation:

Since, triangle ABC is the enlargement of triangle XYZ.

[tex] \therefore \triangle ABC \sim \triangle XYZ[/tex]

So, corresponding sides of both the triangles would be in proportion.

[tex] \therefore \frac{x}{6}=\frac{25}{10}[/tex]

[tex] \therefore x= \frac{6\times 25}{10}[/tex]

[tex] \therefore x =\frac{150}{10}[/tex]

[tex] \therefore x = 15[/tex]

Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

Step-by-step explanation:

Answer:

n + 10

Step-by-step explanation:

im pretty sure thats right, im sorry if not but have a great day!

Answer:

I'm not tryna be a but do u know how to ask questions in the app

Step-by-step explanation:

pls

Answer:

24

Step-by-step explanation:

use a calculator for these type of problems next time!

the answer to this equation would be 24x

Answer:

[tex]9th=31[/tex]

Step-by-step explanation:

From the question we are told that:

Seventh term [tex]7th= 21[/tex]

Common difference [tex]d= 5[/tex]

Generally Equation for seventh term

[tex]7th=a+(7-1)d[/tex]

Therefore the  First Term is given as

[tex]a=7th-(7-1)d[/tex]

[tex]a=21-6*5\\a=-9[/tex]

Generally the equation for 9th term is mathematically given by

[tex]9th=a+8d[/tex]

[tex]9th=-9+8(5)[/tex]

[tex]9th=31[/tex]