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Ulleksa [173]
3 years ago
13

If

Mathematics
1 answer:
dsp733 years ago
8 0

Answer:

\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}

Step-by-step explanation:

\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)

\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}

q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}

t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}

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Length of the median CP
ehidna [41]

Given:

ΔABC \sim ΔDEF

To find:

The length of median CP

Solution:

In ΔABC,

AP = 12, BP = 12 and PC = 3x - 12

In ΔDEF,

DQ = 16, QE = 16 and FQ = 2x + 8

If two triangles are similar, then their median is proportional to the corresponding sides.

$\Rightarrow \frac{AP}{DQ} =\frac{PC}{FQ}

$\Rightarrow \frac{12}{16} =\frac{3x-12}{2x+8}

Do cross multiplication.

$\Rightarrow 12(2x+8)=16(3x-12)

$\Rightarrow 24x+96=48x-192

Add 192 on both sides.

$\Rightarrow 24x+96+192=48x-192+192

$\Rightarrow 24x+288=48x

Subtract 24x from both sides.

$\Rightarrow 24x+288- 24x=48x- 24x

$\Rightarrow 288=24x

Divide by 24 on both sides.

⇒ 12 = x

Substitute x = 12 in CP.

CP = 3(12) - 12

     = 36 - 12

     = 24

The length of median CP is 24.

7 0
3 years ago
What are three 2-digit numbers that divide into 1520?
vlada-n [284]
1520 ÷ 10 = 152

1520 ÷ 20 = 76

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3 years ago
Write an algebraic expression for the perimeter of a rectangular garden with a width of 3 metres and a length of 2y metres. Simp
anyanavicka [17]

Answer:

P = 2(2y+3)

P = 30

Step-by-step explanation:

P = 2 (L+W) or P = L + L + W + W

P = 2 (2y+3)

P = 4y+6

Plug in 6 for y.

P = 24+6

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5 0
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Read 2 more answers
A square pyramid is shown sitting on its base.
allochka39001 [22]

Answer:

Area of Pyramid = 384 cm²

Step-by-step explanation:

Given

Shape: Square Pyramid

Base: 12 cm

Height: 10 cm

Required

The Surface area.

The surface area of the pyramid is calculated by

1. Calculating the area of the base square

2. Calculating the area of the triangles

3. Adding (1) and (2) above

Having highlighted these points,

Step 1: First we calculate the area of the base square

The dimension of the square is 12cm x 12cm

Let L represent the length of the square (L = 12 cm)

So, Area = L * L

Area = 12 cm * 12 cm

Area = 144 cm²

Step 2: There are four triangles in the above pyramid (because the base is a square; and a square has four sides)

The dimension of each triangle is

Base: 12 cm

Height: 10 cm

First, we calculate the area of one triangle

Area = 0.5 * base * height

Area = 0.5 * 12 cm * 10 cm

Area = 60 cm²

If the area of 1 triangle is 60 cm², the area of 4 triangles would be

Area = 4 * 60 cm²

Area = 240 cm²

Step 3: Adding (1) and (2) above

Area of Pyramid = Area of base square + Area of triangles

Area of Pyramid = 144 cm² + 240 cm²

Area of Pyramid = 384 cm²

Hence, the surface area of the pyramid is 384 cm²

5 0
3 years ago
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