MATHEMATICS
MIDDLE SCHOOL

Answer:

Sam is using an industrial kitchen to make several batches of his famous chocolate chip granola bars. He needs to weight out 78 ounces of chocolate chips, plus or minus 2.5 ounces. The equation that can be used to find the minimum or maximum amount,c, of chocolate chips that he can weigh out is-

Absolute value equation is = |c-2.5| = 78

HIGH SCHOOL

two trains, train a and train b, simultaneously depart station a and station b. station a and station b are 252.5 miles apart from each other. train a is moving at 124.7mph towards station b, and train b is moving at 253.5mph towards station a. if both trains departed at 10:00am and it is now 10:08, how much longer until both trains pass each other? [a] 31.054 minutes [b] 16.232 minutes [c] 32.049 minutes [d] 32.058 minutes

Ok

first find how far they have traveled so we will know how much more they need to cover

remmeber distance=speed times time

after 8 mins (from 10 to 10:08) or 8/60 or 4/30 or 2/15 or 1/7 hours

train a traveled 124.7 times 1/7=124.7/7 miles aprox 16.62666666666 miles

train b traveld 253.5 times 1/7=253.5/7 miles aprox 36.2142857143 miles

so subtract that from total distance

252.5-16.626666666-36.2142857143= about 202 miles

use fractions

3031.1/15 miles apart

how long till they pass

means that how long will they together make up that distance

it is 't' time

distance=speed time time

total distance=d1+d2

d1=124.7 times t

d2=235.5 times t

total distance=3031.1/15

3031.1/15=124.7t+253.5t

3031.1/15=378.2t

times both sides by 15

3031.1=5673t

divide both sides by 5673

0.534302838=t

about 32.05817028 mins

answer is D

first find how far they have traveled so we will know how much more they need to cover

remmeber distance=speed times time

after 8 mins (from 10 to 10:08) or 8/60 or 4/30 or 2/15 or 1/7 hours

train a traveled 124.7 times 1/7=124.7/7 miles aprox 16.62666666666 miles

train b traveld 253.5 times 1/7=253.5/7 miles aprox 36.2142857143 miles

so subtract that from total distance

252.5-16.626666666-36.2142857143= about 202 miles

use fractions

3031.1/15 miles apart

how long till they pass

means that how long will they together make up that distance

it is 't' time

distance=speed time time

total distance=d1+d2

d1=124.7 times t

d2=235.5 times t

total distance=3031.1/15

3031.1/15=124.7t+253.5t

3031.1/15=378.2t

times both sides by 15

3031.1=5673t

divide both sides by 5673

0.534302838=t

about 32.05817028 mins

answer is D

MIDDLE SCHOOL

What is the length of the line segment that is graphed from (3, 1) to (8, 1)? A.

4 units

B.

5 units

C.

8 units

D.

9 units

A.4 units

D.9 units

id go with 9 units hope this helps

D.9 units

id go with 9 units hope this helps

The answer is D because 8-3 is 5 and that is the answer.

HIGH SCHOOL

Derive the equation of the parabola with a focus at (6,2) and a directrix of y=1

Answer:

equation of parabola

Step-by-step explanation:

Focus is (h,k+p)=(6,2)

And directrix y=k-p=1

When comparing the values we get

h=6 and

k+p=2 (a)

k-p=1 (b)

For solving (a) and (b) we substitute k=2-p in (b) we get:

Hence, put in k=2-p we get:

Now, we have general equation as:

On substituting the values in general equation we get:

Distance from focus to vertex=distance from vertex to directix

from (6,2) to y=1, the distance is 1

the focus is 1/2 higher than the vertex

vertex=(6,1.5)

for

(x-h)^2=4p(y-k)

vertex=(h,k)

p=distance from vertex to directix

vertex=(6,1.5)

ditance=0.5

(x-6)^2=4(0.5)(y-1.5)

(x-6)^2=2(y-1.5) is the equation

or

y=0.5x^2-6x+19.5 or

y=0.5(x-6)^2+1.5

from (6,2) to y=1, the distance is 1

the focus is 1/2 higher than the vertex

vertex=(6,1.5)

for

(x-h)^2=4p(y-k)

vertex=(h,k)

p=distance from vertex to directix

vertex=(6,1.5)

ditance=0.5

(x-6)^2=4(0.5)(y-1.5)

(x-6)^2=2(y-1.5) is the equation

or

y=0.5x^2-6x+19.5 or

y=0.5(x-6)^2+1.5

HIGH SCHOOL

Which of the following is the solution to the inequality below -6(4-x)<-4(x+1) A) x>2

B) x<2

C) x>10

D) x<10

MIDDLE SCHOOL

Find the value of x if GH and JH are both 13 units long. Justify your answer. (7x + 5)º

(x+ 47)º

This is Geometry

Angles of a triangle.

Answer:

Step-by-step explanation:

we have the triangle GHJ

If the segment side GH is equal to the segment JH

then

The triangle GHJ is an isosceles triangle

Remember that

An isosceles triangle has two equal interior angles and two equal sides

so

m∠G=m∠J

we have

m∠G=(7x+5)°

m∠J=(x+47)°

equate the equations

(7x+5)°=(x+47)°

Solve for x

MIDDLE SCHOOL

El caracol de granja se desplaza a una velocidad media de 5,8 m/h, mientras que el caracol común de jardín lo hace a 13,9 mm/s. ¿Cuál de los dos es más rápido?

Answer:

The common garden snail is faster than the farm snail

Step-by-step explanation:

The question in English is

The farm snail moves at an average speed of 5.8 m/h, while the common garden snail moves at 13.9 mm/sec. Which of the two is faster?

we have

The farm snail moves at an average speed of 5.8 m/h

The common garden snail moves at an average speed of 13.9 mm/sec

Remember that

Convert m/h to mm/sec

Compare the values

1.61\frac{mm}{sec}" alt="13.9\frac{mm}{sec} > 1.61\frac{mm}{sec}" align="absmiddle" class="latex-formula">

therefore

The common garden snail is faster than the farm snail

MIDDLE SCHOOL

Century is to decade as dollar is to penny,nickel,dime,quarter

Century= 10 decades a decade is ten years. A dollar=10 dimes a dime is ten cents. ANSWER: DIME

MIDDLE SCHOOL

The weather forecaster says that there is a 51% chance of rain today. Which statement describes the likelihood that it will rain today?

Answer:

It is neither likely nor unlikely that it will rain today.

Step-by-step explanation:

HIGH SCHOOL

In a mixture of concrete, there are four lb of cement mix for each pound of gravel. if the mixture contains a total of 115 lb of these two ingredients, how many pounds of gravel are there

For this case, the first thing we must do is define variables:

x: pounds of gravel

y: pounds of cement

We now write the system of equations:

x + y = 115

y = 4x

Solving the system of equations we have:

x = 23

y = 92

Answer:

there are 23 pounds of gravel

x: pounds of gravel

y: pounds of cement

We now write the system of equations:

x + y = 115

y = 4x

Solving the system of equations we have:

x = 23

y = 92

Answer:

there are 23 pounds of gravel