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2 years ago

ABCD is a trapezoid. Find y

Mathematics

2 answers:

aleksandrvk [35]2 years ago

5 0

Y = 105 degrees

Angle A = Angle B
Angle C = Angle D
Trapezoid: 360 degrees

75+75= 150
360 - 150 = 210
210/2 = 105

babunello [35]2 years ago

4 0

Answer:

Step-by-step explanation:

$\angle A + \angle D = 180$

$\angle A + y = 180$

$180 = 75 + y$

$y = 180 - 75 = 105$

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If f x is a linear function, f(-1)=3, and f(1)=5, find an equation for f(x)

BartSMP [9]

The equation of f(x) is f(x) = x + 4

<h3>How to determine the equation?</h3>

The given parameters are

f(-1) = 3 and f(1) = 5

Start by calculating the slope (m) using:

$m = \frac{f(1) - f(-1)}{1 - -1}$

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$m = \frac{5 - 3}{1 + 1}$

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f(x) = 1(x + 1) + 3

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1 year ago

The cake store is having a 25% off sale on all of its cakes. If the cake you want regularly costs $9 how much would you save wit

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3 years ago

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

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3 years ago

Consider the volume of a rectangular pyramid, one whose base is not square. Does changing one of the three variables (length, wi

user100 [1]

Let

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we know that

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the three variables are going to have the same influence on the volume

example

case a) let's change the variable L (we reduce the variable by half)

L=(1/2)*L

the new volume is equal to

V new=(1/3)*[(L/2)*W]*H-----> V new=(1/2)*V

the new volume is half the original volume

case b) let's change the variable W (we reduce the variable by half)

W=(1/2)*W

the new volume is equal to

V new=(1/3)*[(W/2)*L]*H-----> V new=(1/2)*V

the new volume is half the original volume

case c) let's change the variable H (we reduce the variable by half)

H=(1/2)*H

the new volume is equal to

V new=(1/3)*[L*W]*H/2-----> V new=(1/2)*V

the new volume is half the original volume

therefore

the answer is

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