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3 years ago

How to factor -10x^2+18+36

Mathematics

1 answer:

Goryan [66]3 years ago

7 0

May this help you!!!!!!!!!!!

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Mr. Wong cuts a coil of wire into two pieces in the ratio of 3:4. The length of the longer piece is 32 centimeters. What is the

zheka24 [161]

Answer:

56 cm

Step-by-step explanation:

The ratio of the lengths of the pieces is 3:4.

The longer piece is 32 cm.

We set up a proportion to find the length of the smaller piece.

Let the length of the smaller piece be x.

3 is to 4 as x is to 32

3/4 = x/32

4x = 3 * 32

4x = 96

x = 24

The smaller piece is 24 cm.

24 cm + 32 cm = 56 cm

6 0

3 years ago

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Y+9÷2=y-3÷4-(y/3)<br>pls help

Ann [662]

Answer:

y = - $\frac{63}{4}$ or - 15.75

Step-by-step explanation:

Order of operations.

y + $\frac{9}{2}$ = y - $\frac{3}{4}$ - $\frac{y}{3}$ Subtract y from each side.

y - y + $\frac{9}{2}$ = y - y - $\frac{3}{4}$ - $\frac{y}{3}$

$\frac{9}{2}$ = - $\frac{3}{4}$ - $\frac{y}{3}$ Add $\frac{3}{4}$ to each side

$\frac{9}{2}$ + $\frac{3}{4}$ = - $\frac{3}{4}$ + $\frac{3}{4}$ - $\frac{y}{3}$

$\frac{9}{2}$ + $\frac{3}{4}$ = - $\frac{y}{3}$ Find the common denominator for $\frac{9}{2}$ and $\frac{3}{4}$ , which is 4

$\frac{9}{2}$ * $\frac{2}{2}$ + $\frac{3}{4}$ = - $\frac{y}{3}$

$\frac{18}{4}$ + $\frac{3}{4}$ = - $\frac{y}{3}$

$\frac{21}{4}$ = - $\frac{y}{3}$ Multiply each side by 3

$\frac{21}{4}$ * 3 = - $\frac{y}{3}$ * 3

$\frac{63}{4}$ = - y Divide each side by -1

y = - $\frac{63}{4}$ = - 15 $\frac{3}{4}$

y = - 15.75

3 0

3 years ago

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PLEASE ANSWER!!!

valkas [14]

Answer:

Step-by-step explanation:

3 0

2 years ago

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What is the remainder of 6728 divided by 70

yanalaym [24]

The remainder of 6728 divided by 70 is 8, This is because when 6728 is divided by 70, 70 goes into 6728, 96 times evenly. And there is only 8 left.

3 0

3 years ago

The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago