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2 years ago

Which angles are shown in the diagram?

Mathematics

2 answers:

mixas84 [53]2 years ago

8 0

Answer:

see below

Step-by-step explanation:

We have 3 angles

BCA which is also called ACB

ACD which is also called DCA

and BCD which is also called DCB

aleksklad [387]2 years ago

6 0

Answer:

<ACB and <ACD (You can count <BCD if you want)

Step-by-step explanation:

as all these have a common intersection point of C

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4 gallons of gasoline at QT cost $16.80. What was the price per gallon at QT?

lidiya [134]

It would be 4 dollars and 20 cents a gallon

6 0

2 years ago

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What is the length of side PR? Look at pic to see. PLSSS helpp it’s for a test!!

mrs_skeptik [129]

Answer:

Step-by-step explanation:

Pythagoras theorem

the square of the hypotenuse= (adjacent) square +(opposite) square

7 0

2 years ago

the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

RideAnS [48]

Well, first off, let's find what is the slope of BC

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 2}}\quad ,&{{ -3}})\quad 
% (c,d)
C&({{ 10}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2}
\\\\\\
\cfrac{4}{8}\implies \cfrac{1}{2}$

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\
slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}$

now, we know the slope "m" of AB is -2 then, thus

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ a}}\quad ,&{{ 3}})\quad 
% (c,d)
B&({{ 2}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2}
\\\\\\
\cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a
\\\\\\
-1=a$

6 0

2 years ago

The product of two consecutive odd integers is 72. Write a quadratic equation to find the integers,

zimovet [89]

Answer:

$x^2 + x - 72 = 0$

Explanation:

We are given product of two consecutive odd integers is equal to 72.

Let one integer be x , then since these are consecutive and odd so the other integer will be equal to x + 1.

Their product is equal to 72. So,

x * (x + 1) = 72

=> $x^2 + x = 72$

=> $x^2 + x - 72 = 0$ is the required quadratic equation.

5 0

3 years ago

Neil drives at an average speed of 60 miles/hour to reach his destination 480 miles away. On the way back, he decides to increas

daser333 [38]

Answer:

480/(x+60) ≤ 7

Step-by-step explanation:

We can use the relations ...

time = distance/speed

distance = speed×time

speed = distance/time

to write the required inequality any of several ways.

Since the problem is posed in terms of time (7 hours) and an increase in speed (x), we can write the time inequality as ...

480/(60+x) ≤ 7

Multiplying this by the denominator gives us a distance inequality:

7(60+x) ≥ 480 . . . . . . at his desired speed, Neil will go no less than 480 miles in 7 hours

Or, we can write an inequality for the increase in speed directly:

480/7 -60 ≤ x . . . . . . x is at least the difference between the speed of 480 miles in 7 hours and the speed of 60 miles per hour

___

Any of the above inequalities will give the desired value of x.

4 0

3 years ago