MATHEMATICS MIDDLE SCHOOL

Where is the vertex of the equation?y = x2 – 18x + 80

Answers

Answer 1

Answer:

Answer:

vertex = (9, - 1 )

Step-by-step explanation:

Given a quadratic in standard form, y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

$x_(vertex)$ = - $(b)/(2a)$

y = x² - 18x + 80 ← is in standard form

with a = 1 and b = - 18, thus

$x_(vertex)$ = - $(-18)/(2)$ = 9

Substitute x = 9 into the function for corresponding value of y

y = 9² - 18(9) + 80 = 81 - 162 + 80 = - 1

Vertex = (9, - 1 )

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Solve for t d=(1/2) at^2
Mr. Anderson drove 168 miles in 3.5 hours. He then drove the next 2.25 hours at a rate of 5 miles an hour faster than the first rate. How many miles did Mr. Anderson drive during the 5.75 hours?
A van is traveling 1.5 kilometers per minute. Approximately how fast is the van traveling in miles per hour?

Carla made a scale drawing of a classroom. The length of the classroom in the drawing is 5in. The actual length is 40ft. What scale did Carla use for her drawing?

Answers

Answer:

1/96

Step-by-step explanation:

scale is

a model cannot be as same size as that of actual object ,

hence objects are scales down to some value so that its model can be comfortably made.

scale is generally ratio of length of drawing and actual length of object

scale = length of drawing / actual length of object.

Given

length of classroom drawing = 5in

actual length of classroom = 40 ft

as unit of drawing and actual classroom is different lets make unit of class smilar to that of drawing that is in inches

we know

1 feet = 12 inches

thus 40 feet = 12*40 inches = 480 inches

thus,

actual length of classroom in inches = 480 inches

scale used by Carla = length of drawing / actual length of classroom

= 5 inches/480 inches = 1/96 (answer)

The number of tomato plants (t) is twice the number of pepper plant (p) A. t=2+p
B. +t=p
C.2t=p
D. t=2p

Answers

the number of tomato plants (t) is (=) twice (2 times) the number of pepper plants (p)
t=2(p)

so the anser is t=2p or D

D. T=2p

This is because the number of tomato plants (t) is (=) twice (2) the number of pepper plants (p)

X^-2+4x^-1+3=0 solve by making appropriate substitution

Answers

ANSWER

$x = - 1 \: or \: x = - (1)/( 3)$

EXPLANATION

The given equation is:

${x}^( - 2) + 4 {x}^( - 1) + 3 = 0$

Recall that:

${a}^( - m) = \frac{1}{ {a}^(m) }$

$\frac{1}{ {x}^(2) } + (4)/(x) + 3 = 0$

${( (1)/(x) )}^(2) + 4( (1)/(x) ) + 3 = 0$

Let

$u = (1)/(x)$

Our equation then becomes:

${u}^(2) + 4u + 3 = 0$

The factors of 3 that add up to 4 are:

${u}^(2) + 3u + u + 3$

$u(u + 3) + 1(u + 3) = 0$

$(u + 1)(u + 3) = 0$

$u + 1 = 0 \: or \: u + 3 = 0$

$u = - 1 \: or \: u = - 3$

This implies that:

$(1)/(x) = - 1 \: or \: (1)/(x) = - 3$

$x = - 1 \: or \: x = - (1)/( 3)$

Kevin drove 22 1/2 miles in 1/3 hour. What was his average speed in miles per hour

Answers

Answer=67.5 mph

22 1/2 miles 1/3hours

(22 1/2)/(1/3)=67.5miles per hour

____________________________
another way to solve this would be....

1/3 1
_______=________
22 1/2 x

cross multiply
(1/3)x=22 1/2
divide both sides by 1/3
x=67.5miles per hour

Translate the phrase into an algebraic expression. 3 more than h h−3 3×h 3÷h h+3

Answers

3 MORE than h
"more" indicated addition.

Which statements about the pattern are true?Rule: Multiply by 10 and then subtract 5.

5, 45, 445, 4445, . . .

Choose all answers that are correct.

A.
Every term has a 5 in the ones place.

B.
Every term is a multiple of 5.

C.
Every term has 1 more digit than the previous term.

D.
Every term is a multiple of 10.

btw there are more then one

Answers

IT IS A AND C.
It is A because every term has a 5 in ones place.
For Example,
5, 45, 445, 4445
And will keep being 5 in the ones place.
It is C because every term has 1 more digit than the previous term.
For Example,
5, 45, 445, 4445
THE NUMBERS I UNDERLINED IS ONE MORE THAN THE PREVIOUS TERM.

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