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3 years ago

Miguel has 1 foot of string. He cuts the string into fourths. How many inches is each piece of string?

Mathematics

2 answers:

ra1l [238]3 years ago

6 0

3 inches is how long each piece of string is

Vikentia [17]3 years ago

5 0

Each piece of string has 3 inches each

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Number 1d please help me analytical geometry

lesantik [10]

For a) is just the distance formula

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ x}}\quad ,&{{ 1}})\quad 
% (c,d)
B&({{ -4}}\quad ,&{{ 1}})
\end{array}\qquad 
% distance value
\begin{array}{llll}

d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
\sqrt{8} = \sqrt{({{ -4}}-{{ x}})^2 + (1-1)^2}
\end{array}$
-----------------------------------------------------------------------------------------
for b) is also the distance formula, just different coordinates and distance

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ -7}}\quad ,&{{ y}})\quad 
% (c,d)
B&({{ -3}}\quad ,&{{ 4}})
\end{array}\ \ 
\begin{array}{llll}

d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
4\sqrt{2} = \sqrt{(-3-(-7))^2+(4-y)^2}
\end{array}$
--------------------------------------------------------------------------
for c) well... we know AB = BC.... we do have the coordinates for A and B
so... find the distance for AB, that is $\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ -3}}\quad ,&{{ 0}})\quad 
% (c,d)
B&({{ 5}}\quad ,&{{ -2}})
\end{array}\qquad 
% distance value
\begin{array}{llll}

d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\
d=\boxed{?}

\end{array}$

now.. whatever that is, is = BC, so the distance for BC is

$\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 5}}\quad ,&{{ -2}})\quad 
% (c,d)
C&({{ -13}}\quad ,&{{ y}})
\end{array}\qquad 
% distance value
\begin{array}{llll}

d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\
d=BC\\\\
BC=\boxed{?}

\end{array}$

so... whatever distance you get for AB, set it equals to BC, BC will be in "y-terms" since the C point has a variable in its ordered points

so.. .solve AB = BC for "y"
------------------------------------------------------------------------------------

now d) we know M and N are equidistant to P, that simply means that P is the midpoint of the segment MN

so use the midpoint formula

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
M&({{-2}}\quad ,&{{ 1}})\quad 
% (c,d)
N&({{ x}}\quad ,&{{ 1}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)=P
\\\\\\
$

$\bf \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)=(1,4)\implies 
\begin{cases}
\cfrac{{{ x_2}} + {{ x_1}}}{2}=1\leftarrow \textit{solve for "x"}\\\\
\cfrac{{{ y_2}} + {{ y_1}}}{2}=4
\end{cases}$

now, for d), you can also just use the distance formula, find the distance for MP, then since MP = PN, find the distance for PN in x-terms and then set it to equal to MP and solve for "x"

7 0

3 years ago

Given that 7x - 3y = 23

Triss [41]

7x - 3(-2) = 23
7x - - 6 = 23 (two minuses make a plus)
so it’s gonna be 7x + 6 = 23
Now you have isolate you x, so move everything else to the other side, but remember to change your sign when transferring to the other side

7x = 23 - 6
7x = 17
To isolate x in this multiple, you divide by 7 (because the inverse of multiplication is division)
x = 17/7

7 0

3 years ago

PLEASE HELP!!!!! explain too please

ale4655 [162]

Answer:

8. Not similar

9. Similar

Step-by-step explanation:

8. You could try to us the AA theorem which means that two angles in the triangle are equal, which would mean that the triangles are similar. But 46+58=104 and 180-104=76 so there are not two similar angled between the triangles.

9. You can use the same theorem for this problem (AA). So 106+31=137 and then 180-137=43 which is one of the angles in the second triangle. Since at least two of the angles are equal, you can use AA theorem yo prove they are similar.

Hope this helps!

4 0

3 years ago

Read 2 more answers

A ladder is leaning against the top of

Dafna11 [192]

Answer:

Step-by-step explanation:

Discussion

You are working with the Cosine of the angle.

Hypotenuse = 12.5

Base = 3

Theta = ?

Solution

Cos(theta) = base / hypotenuse Substitute values

Cos(theta) = 3 / 12.5 Divide

Cos(theta) = 0.24 Tale the inverse cos

theta = cos-1(0.24)

theta = 76.11 degrees

6 0

2 years ago

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Plz help ASAP! I URGENTLY NEED HELP!

Greeley [361]

Yes is the answer click it

5 0

4 years ago