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Advocard [28]
3 years ago
12

In pauls bicycle shop, 40 bicycles are inspected. If 20 needed new tires and 30 needed gear reports, answer the following: a) wh

at is the greatest number of bikes that could have needed both. B) least number that could have needed both . C) what is the greatest number of bikes that could have needed neither.
Mathematics
1 answer:
Arisa [49]3 years ago
7 0
<span>There are three possibilities. 1. Of the 30 bikes that needed gear repairs, 20 also needed tires. 2. Of the 30 bikes that needed gear repairs, 10 also needed tires. 3. Of the 30 bikes that needed gear repairs, between 10 and 20 also needed tires.</span>
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Quadrilateral QRST is a square. If the measure of angle RQT is 3x - 6. Find the value of x.
trapecia [35]

Given that quadrilateral QRST is a square.

Each angle of a square is of 90 degrees.

Angle <RQT is also an angle of 90 degrees.

We also given angle RQT = 3x - 6.

So, we can setup an equation as 3x-6 =90.

Now, we need to solve the equation for x.

6 is being subtracted from left side.

We always apply reverse operation. Reverse operation of subtraction is addition.

So, adding 6 on both sides of the equation, we get

3x-6+6 =90+6.

3x = 96.

3 is being multipied with x, in order to remove that 3, we need to apply reverse operation of multiplication.

So, dividing both sides by 3.

\frac{3x}{3} = \frac{96}{3}

x=32 (final answer).

3 0
3 years ago
It takes a boat going upstream 5 hours to cover the same distance, as it would cover in 3 hours going downstream. What is the sp
Vaselesa [24]

Answer: 15 kilometers per hour

Step-by-step explanation:

8 0
3 years ago
Evaluate the summation of negative 2 n minus 3, from n equals 2 to 10..
Alisiya [41]
\bf \sum\limits_{n=2}^{10}~-2n-3

so, let's first change the bounds from 1 to 9, so we'll be dropping the indices by 1, in order to do the variable "n".

however, let's use a variable hmmm say "k", where "k" is the value of "n" beginning at 1, thus k = n - 1.

however, if k = n - 1, then k + 1 = n.  So let's use those fellows then,

\bf \sum\limits_{n=2}^{10}~-2n-3\qquad &#10;\begin{cases}&#10;k=n-1\\&#10;k+1=n&#10;\end{cases}\implies \sum\limits_{k=1}^{9}~-2\stackrel{n}{(k+1)}-3&#10;\\\\\\&#10;\sum\limits_{k=1}^{9}~-2k-2-3\implies \sum\limits_{k=1}^{9}~-2k-5\implies \sum\limits_{k=1}^{9}~-2k-\sum\limits_{k=1}^{9}~5&#10;\\\\\\&#10;-2\sum\limits_{k=1}^{9}~k-\sum\limits_{k=1}^{9}~5\implies -2\left( \cfrac{9(9+1)}{2} \right)\qquad -\qquad (9\cdot 5)&#10;\\\\\\&#10;-2(45)-45\implies -90-45\implies -135
5 0
3 years ago
Solve the proportion for x.
BabaBlast [244]
The answer for the question is x=1
3 0
3 years ago
Consider parent function f(x)=e^x and the transformes function g(x)= -1/2e^3x+4, quantitatively explain the transformations to t
kolezko [41]

Answer:  reflection across the x-axis

               vertical shrink by a factor of 1/2

               horizontal shrink by a factor of 1/3

               vertical shift up 4 units      

<u>Step-by-step explanation:</u>

\text{Note:}\ g(x) = -Ae^{Bx-C}+D\\\bullet \quad \text{- represents a reflection across the x-axis}\\\\\bullet \quad \text{A represent a vertical stretch by a factor of A (shrink if}\ |A| < 1)\\\\\bullet \quad \text{B represents a horizontal stretch by a factor of}\ \dfrac{1}{B}\ (\text{shrink if}\ |B| >1)  \\\\\bullet \quad \text{C represents a horizontal shift of C units}\ (\text{+ is right, - is left}) \\\\\bullet \quad \text{D represents a vertical shift of D units}\ (\text{+ is up, - is down})

\text{Parent function:}\ f(x)=e^x\\\text{Transformed function:}\ g(x)=-\dfrac{1}{2}e^{3x}+4\\

The transformed function has the following:

Negative:    reflection across the x-axis

A = 1/2         vertical shrink by a factor of 1/2

B = 3            horizontal shrink by a factor of 1/3

C = 0            no horizontal shift

D = 4            vertical shift of 4 units up

6 0
3 years ago
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