Solve for m: m – 4.2 = 5.1

Select the correct answer from each drop-down menu. Which system of equations is represented by this graph? Graph shows system o

AleksandrR [38]

The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

The equation of the line going through (-6, 0) and (0, -3) is:

y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))

y = -(1/2)x - 3

The equation of the line going through (0, 3) and (-4, -5) is:

y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)

y = 2x + 3

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7 0

2 years ago

Alan and Margot each drive from City A to City B, a distance of 147 miles. They take the same route and drive at constant speeds

Westkost [7]

Answer:

Margot gets from A to B faster

Step-by-step explanation:

Alan takes 2 hr and 35 min = 2. 58... hr

Margot takes 147/64 hr = 2.296.. hr

7 0

3 years ago

Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.

Jlenok [28]

Answer:

Step-by-step explanation:

Properties of a circumcenter;

1). Circumcenter of a triangle is a point which is equidistant from all vertices.

2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.

From the picture attached,

9). AG = GB = GC = 21

10). BC = 2(DC)

= 2×16

= 32

11). By applying Pythagoras Theorem in ΔGFB,

GB² = GF² + FB²

(21)² = GF² + (19)²

441 = GF² + 361

GF² = 441 - 361

GF = $\sqrt{80}$

GF = 8.9

12). By applying Pythagoras theorem in ΔGDB,

GB² = DG² + BD²

(21)² = (DG)² + (16)² [BD = DC = 16]

DG² = 441 - 256

DG = √185

DG = 13.6

7 0

3 years ago

Triangle R Q S is cut by line segment T U. Line segment T U goes from side Q R to side Q S. The length of Q T is 32, the length

Marizza181 [45]

The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

<h3>What is the line segment about?</h3>

The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those given sides proportionally.

So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.

Thus;

$\frac{QT}{TR}$ = $\frac{32}{36} = \frac{8}{9}\\\\ \\$

$\\\frac{QU}{US} =\frac{40}{45} = \frac{8}{9}\\$

Therefore, the ratios are equal and as such TU is parallel to RS

Hence, The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

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5 0

2 years ago

The figure is made up of a hemisphere and a cylinder.

Goryan [66]

Data: (Cylinder)
h (height) = 8 cm
r (radius) = 5 cm
Adopting: $\pi \approx 3.14$
V (volume) = ?

Solving:(<span>Cylinder volume)
</span> $V = h* \pi *r^2$
$V = 8*3.14*5^2$
$V = 8*3.14*25$
$\boxed{ V_{cylinder} = 628\:cm^3}$

<span>Note: Now, let's find the volume of a hemisphere.
</span>
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 5 cm
Adopting: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4 * \pi * \frac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3} 
$

Formula: (<span>Volume of the hemisphere)
</span> $V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}$

Solving:
$V = \frac{1}{2} * 4 * \pi * \frac{r^3}{3}$
$V = \frac{1}{2} * 4 * 3.14 * \frac{5^3}{3}$
$V = \frac{1}{2} * 4 * 3.14 * \frac{125}{3}$
$V = \frac{1570}{6}$
$\boxed{V_{hemisphere}\approx 261.6\:cm^3}$

<span>Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
</span>
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 628 cm³ + 261.6 cm³
$\boxed{\boxed{Volume\:of\:the\:figure = 1517.6\:cm^3}}\end{array}}\qquad\quad\checkmark$

3 0

3 years ago

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