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3 years ago

In the figure, what is m∠ABE? What is m∠DBE?

Mathematics

2 answers:

Dafna11 [192]3 years ago

7 0

Answer:

abe= 115.5 dbe= 25.5

Step-by-step explanation:

seropon [69]3 years ago

4 0

Yes, the above is correct

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Solve for x, y, and z

zloy xaker [14]

Answer:

The solution is x=1,y=2,z=3

Step-by-step explanation:

The given system of equations is ;\

2x−3y+4z=8...(1)

3x+4y−5z=−4...(2)

4x−5y+6z=12...(3)

Make x the subject in equation (1)

$x=\frac{8+3y-4z}{2}...(4)$

Put equation (4) into equation (2) and (3)

$3(\frac{8+3y-4z}{2})+4y-5z=-4$

Multiply through by;

$3(8+3y-4z)+8y-10z=-8$

Expand;

$24+9y-12z+8y-10z=-8$

Simplify;

$17y-22z=-32...(5)$

Equation (4) in (3)

$4(\frac{8+3y-4z}{2})-5y+6z=12$

$2(8+3y-4z)-5y+6z=12$

$16+6y-8z-5y+6z=12$

$y-2z=-4$

$y=2z-4...(6)$

Put equation (6) into equation (5)

$17(2z-4)-22z=-32$

$34z-68-22z=-32$

$34z-22z=-32+68$

$12z=36$

z=3

Put z=3 into equation (6)

y=2(3)-4=2

Put y=2 and z=3 into equation 4

$x=\frac{8+3(2)-4(3)}{2}=1$

The solution is x=1,y=2,z=3

3 0

3 years ago

Write an absolute value equation for the graph shown below

BabaBlast [244]

So, hmmm keeping in mind that, an absolute value expression is in effect a piece-wise function, let's find its "slopes", the negarive slope on the left-side and the positive slope on the right side, and let's use the vertex point as our first point

what is the slope of a line that passes through (2, -1) and (0,7)

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 0}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{7-(-1)}{0-2}\implies \cfrac{7+1}{-2}\implies -4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=-4(x-2)
\\\\\\
\boxed{y+1=-4(x-2)}$

now, what is the slope of a line that passes through (2, -1) and (4,7)

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
% (c,d)
&({{ 4}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{7-(-1)}{4-2}\implies \cfrac{7+1}{2}\implies 4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=4(x-2)
\\\\\\
\boxed{y+1=4(x-2)}$

since an absolute value expression is just a piece-wise with a +/- versions, then we can just combine those two.

$\bf \begin{cases}
y+1=-4(x-2)\\
y+1=4(x-2)
\end{cases}\implies y+1=\pm 4(x-2)
\\\\\\
y+1=|4(x-2)|\implies y=|4(x-2)|-1$

7 0

3 years ago

Which of the following expressions are equivalent to 12x+20? Select all that apply.

GalinKa [24]

Answer:

Step-by-step explanation:

4(3x+5) = 12x+20

7 0

3 years ago

Hurry: Only 5 mins to answer! When Prachisha checked out they charged her sales tax of 7.25%. How much did she pay for the items

ella [17]

101.15

Explanation:

140 x 7.25% = 10.15

140 x 35% = 49

Then we add the tax and subtract the sale :

140 + 10.15 - 49 = 101.15$

Hope it’s right
Best luck with your studying

6 0

3 years ago

Write the number 347.85 in expanded form. a 3 + 100 + 4 x 10 + 7 x 1 x 8 x (1/100) + 5 x (1/100) b 3 x 100 + 4 + 10 + 7 x 1 + 8

SVEN [57.7K]

The answer will be C

8 0

3 years ago

Read 2 more answers