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4 years ago

Find the value of x. Round the answer to the nearest tenth, if needed.

Mathematics

2 answers:

lara31 [8.8K]4 years ago

8 0

Answer: x=9.5

Step-by-step explanation:

hypotenuse/leg=hypotenuse/leg

13/x=x/7

x*x=13*7

x^2=91

x=sqrt 91

x=9.5

Hope this helps, have a BLESSED and wonderful day! :-)

-Cutiepatutie

zepelin [54]4 years ago

7 0

Answer:

Step-by-step explanation:

The diagram is composed of one large right triangle and inside it it's divided into 2 small right triangles. Since these triangles all have the same shape but not the same size, they are similar triangles. Using similar triangles, create a proportion of side lengths. A proportion is an equation with equal ratios from the large triangle to a small. Notice the large triangle has a hypotenuse of 6+7 = 13 and a leg of x. The small triangle has a hypotenuse of x and a leg of 7.

$\frac{hypotenuse}{leg}=\frac{hypotenuse}{leg}$

$\frac{13}{x}=\frac{x}{7}$

To solve for x, cross multiply the numerator with the denominator.

$x*x = 13*7\\x^2 = 91\\x=\sqrt{91} \\x=9.5$

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Write the equation of a line with slope m that passes through the origin

Nastasia [14]

This is the negative reciprocal of the slope. The solution can be obtained by solving y=−0.5x+b using the information given. It is also worth knowing that if the line passes through the origin, the y intercept is already determined (it is 0 since the linewill pass through the y axis at 0)

5 0

3 years ago

Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2?

MA_775_DIABLO [31]

Answer:

A (0,3)

Step-by-step explanation:

The given trapezoid has vertices:

(0,6), (7,12), (7,9) and (0,12).

We want to choose from the given options, a point that is a vertex for the image produced by a dilation about the origin with a scale factor of 1/2.

Note that the mapping for such a dilation is:

$(x,y)\to( \frac{1}{2} x, \frac{1}{2} y)$

This implies that:

$(0,6)\to(0,3)$

$(7,12)\to(3.5,6)$

$(7,9)\to(3.5,4.5)$

$(0,12)\to(0,6)$

Therefore correct choice is (0,3)

8 0

4 years ago

THIS IS REALLY IMPORTANT 7TH GRADE MATH:

Oksana_A [137]

Rectangle perimeter is 53 meters.

L = W + 2.3

To find the options of a perimeter, divide by 4.

= 13.25

So if this was a square, it would be 13.25 for both L and W but it's not.

Since the W has 2.3 meters more then the L, we do this.

13.25 + 2.3 = 15.55

13.25 - 2.3 = 10.95

Two of your sides equal 15.55, and the other two equal 10.95.

Hope this helps!

3 0

4 years ago

A rhombus has a side length equal to one of the diagonals. The other diagonal is 4cm longer. Find the area of the rhombus.

klasskru [66]

Answer:

The area of the rhombus is 25.83 cm².

Step-by-step explanation:

The area of a rhombus is given by:

$A = \frac{d_{1} \times d_{2}}{2}$

Where:

d₁: is one diagonal

d₂: is the other diagonal = d₁ + 4 cm

We know that one side length of the rhombus is equal to d₁. We can imagine a right triangle inside the rhombus, with the following dimensions:

h: hypotenuse of the right triangle

a: one side of the right triangle

b: is the other side of the right triangle

From the above we know that:

h = d₁

$a = \frac{d_{2}}{2} = \frac{d_{1} + 4}{2}$

$b = \frac{d_{1}}{2}$

We can find d₁ with Pitagoras:

$h^{2} = a^{2} + b^{2}$

$d_{1}^{2} = (\frac{d_{1} + 4}{2})^{2} + (\frac{d_{1}}{2})^{2}$

$d_{1}^{2} = \frac{1}{4}(d_{1}^{2} + 8d_{1} + 16 + d_{1}^{2})$

By solving the above quadratic equation for d₁ and taking the positive solution we have:

$d_{1} = 5.46 cm$

So, d₂ is:

$d_{2} = d_{1} + 4 = 5.46 cm + 4 cm = 9.46 cm$

Now, we can find the area:

$A = \frac{d_{1} \times d_{2}}{2} = \frac{5.46 cm \times 9.46 cm}{2} = 25.83 cm^{2}$

Therefore, the area of the rhombus is 25.83 cm².

I hope it helps you!

3 0

3 years ago

25 points! Answer both! please leave explanation!

aliya0001 [1]

1) To solve for x you'll use the sine formula

sin 27 = 34/x
x = 34/sin27
x = 74.89

2) to find the value of x you'll use the tangent formula

tan 49 = x/55
55(tan49) = x
63.270

4 0

3 years ago