Applications and Problem Solving

Samantha is 80 cm.tall. Nora's height is 4cm less twice the height of Samantha.
How tall is Nora?
Understand: What is asked? HEb. What
are the given facts?
Plan: Express in algebraic expression. a. Solve and check:
d. Show your computation below. (You can use extra sheet if needed) Answer:​

Consider the inequality first ;

[tex]{:\implies \quad \sf 2x-2\> 2x+4}[/tex]

Subtracting 2x from both sides ;

[tex]{:\implies \quad \sf \cancel{2x}-2-\cancel{2x}\> \cancel{2x}+4-\cancel{2x}}[/tex]

[tex]{:\implies \quad \sf -2\> 4}[/tex]

But , as the given situation isn't possible in mathematics , so the inequality have no solutions . Or [tex]{\bf{x\in \phi}}[/tex] , where [tex]\bf \phi[/tex] is the empty set.

Find x-intercept

The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.

3x + y = 16

3x + 1(0) = 16

x1 = 5.333 y1 = 0

Find y-intercept

The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.

3x + y = 16

3(0) + y = 16

y2 = 16 x2 = 0

Answer:

[tex]\frac{13}{15}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}+\frac{1}{5}=\frac{10}{15}+\frac{3}{15}=\frac{13}{15}[/tex]

Answer:

The answer is that image below. If it isn't correct, I'm sorry.

Answer:

His pattern is 42cm long.

Step-by-step explanation:

Each repetition of the pattern is 8 cm (4 colors time 2cm each)

If the last color is red and he painted 6 red strips in total, then he repeated the pattern 5 times and ended on an extra red strip.

So 8cm times 5 repetitions equals 40, plus 2cm for the extra red strip.

Answer: 40.82

Step-by-step explanation:

Use pythagoras theorem to solve

Root 35 squared + 21 squared = 40.82

Answer:

2.9m

Step-by-step explanation:

Hope this helps! Have a great day!

P.S. Brainliest helps me reach more people and shows that I have reliable answers :D

Answer:

Length of the rectangular lot = 60 meters

Width of the rectangular lot = 30 meters

Step-by-step explanation:

Let the width of the rectangular lot be x meters.

So, Length of the same = 2x metres.

[tex]A(rectangular \:lot) = (2x)(x)[/tex]

[tex]\implies A(rectangular \:lot) = 2x^2[/tex]

When length is increasEd by 40 m and width by 6 m. Then....

New length = [tex](2x + 40) \:m[/tex]

New width =[tex](x + 6) \:m[/tex]

According to the question:

[tex](2x + 40)(x + 6) = 2(2x^2)[/tex]

[tex]\implies 2x(x + 6) + 40(x + 6) - 4x^2=0[/tex]

[tex]\implies 2x^2+12x + 40x + 240 - 4x^2=0[/tex]

[tex]\implies 2x^2- 4x^2+12x + 40x + 240 =0[/tex]

[tex]\implies -2x^2+52x + 240 =0[/tex]

[tex]\implies 2(x^2-26x - 120) =0[/tex]

[tex]\implies x^2-26x - 120=0[/tex]

[tex]\implies x^2-30x+4x - 120=0[/tex]

[tex]\implies x(x-30)+4(x - 30)=0[/tex]

[tex]\implies (x-30)(x+4)=0[/tex]

[tex]\implies x-30=0,\: x+4=0[/tex]

[tex]\implies x=30,\: x=-4[/tex]

Since, x represents the side length, so its value can't be negative.

[tex]\implies x=30[/tex]

[tex]\implies 2x=2(30)=60[/tex]

Thus,

Length of the rectangular lot = 60 meters

Width of the rectangular lot = 30 meters

Answer:

y=3/2 x + 1/2

Step-by-step explanation:

please see attached picture

Hey there!

7/8÷6/8=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

7/8×8/6=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

7×8/8×6=56/48

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 56 and 48 using

GCF(56,48) = 8

56÷8/48÷8=76

The fraction

7/6

is the same as

7÷6

Convert to a mixed number using

long division for 7 ÷ 6 = 1R1, so

7/6= [tex]1 \frac{1}{6} [/tex]

Therefore:

7/8÷6/8= 1 1/6

Let's do

[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\div \dfrac{6}{8}[/tex]

[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\times \dfrac{8}{6}[/tex]

[tex]\\ \bf\hookrightarrow \dfrac{7}{8}\times \dfrac{4}{3}[/tex]

[tex]\\ \bf\hookrightarrow \dfrac{7}{2}\times \dfrac{1}{3}[/tex]

[tex]\\ \bf\hookrightarrow \dfrac{7}{6}[/tex]

Answer: 10 rows of 10

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

if he divides (7/8) / (2/5)

he will get x bottles of honey if each bottle weighs 2/5 pound

Answer:

23.9894949495cm is the depth of the container.

Step-by-step explanation:

Cylindrical container:

height: 28

radius: 9 (or 18/2)

pi * 9² = 254.4690049408

254.4690049408 * 28 = 7,125.1321383424 cm²

cylidrical container area: 7,125.1321383424cm²

Container:

length: 27cm

width: 11cm

27 * 11 = 297

7,125.1321383424 / 297 = 23.9894949495cm

I assume that the container with rectangular base is precisely full when tou pour the water into it.

And that your question was how deep the container was.

Answer:

2 over 1

Step-by-step explanation:

step 1

multiply the denominator by the whole number

5×1=5

step 2

add the answer from step 1 to the numerator

5+5=10

step 3

write answer from step 2 over the denominator

10/5

10÷5=2 so,the answer is 2 over 1

5÷5=1

Answer:

C) 6 units

E) 8 units

Step-by-step explanation:

Kosi traced a rectangle on a coordinate grid. The rectangle had the following vertices: (−6, 5), (2, 5), (2, –1), and (–6, –1). Which of the following numbers are dimensions of the rectangle? Select each correct answer. A. 4 units B. 5 units C. 6 units D. 7 units E. 8 units F. 9 units. help, please!.

When given vertices for a geometric shapes we find the lengths of the side by using the formula:

When(x1, y1) and (x2, y2)

= √(x2 - x1)² + (y2 - y1)²

A= (−6, 5),B = (2, 5), C = (2, –1), and D = (–6, –1).

For AB

A= (−6, 5),B = (2, 5),

= √(2 -(-6)² + (5 - 5)²

= √8² + 0

= √64

= 8 units

For BC

B = (2, 5), C = (2, –1),.

√(2 - 2)² +(-1 - 5)²

= √0 + -6²

= √36

= 6 units

For CD

C = (2, –1), and D = (–6, –1).

= √(-6 -2)² + (-1 -(-1))²

= √-8² + 0²

= √64

= 8 units

For AD

A= (−6, 5), D = (–6, –1).

= √(-6 -(-6))² + (-1 - 5)²

= √0² + -6²

= √36

= 6 units

Therefore, the following numbers that are dimensions of the rectangle is

C) 6 units

E) 8 units

Answer:

Step 1: Add 2 to both sides.

7x−2+2=−9+2

7x=−7

Step 2: Divide both sides by 7.

7x/7  =  -7/7

Answer:  x=−1

Answer:

x=-1

Step-by-step explanation:

7x-2=-9 (Given)

7x=-7 (Add 2 on both sides to eliminate he -2 on the left side)

x=-1 (Divide both sides with 7 to eliminate the 7 in 7x)

Answer: x=-1

Step-by-step explanation:

[tex]4\cdot \:11-x+4=33[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:11=44[/tex]

[tex]44-x+4=33[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]-x+44+4=33[/tex]

[tex]\mathrm{Add\:the\:numbers:}\:44+4=48[/tex]

[tex]-x+48=33[/tex]

[tex]\mathrm{Subtract\:}48\mathrm{\:from\:both\:sides}[/tex]

[tex]-x+48-48=33-48[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-x=-15[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{-15}{-1}[/tex]

[tex]Simplify[/tex]

[tex]x=15[/tex]

Answer:

Okay so yes the answer is 15

Step-by-step explanation:

It begins with 4X11 which is 44

So the equation becomes 44-x+4=33

Then I add 44 plus 4 which is me adding all the available terms which is 48

Then I subtracted 33 from 48 to find the value of x

And 48-33=15

So there you pretty much have it.

To be sure you can plug the answer in.

4x11=44

44-(x) which is 15 so 44-15=29

29+4=33

There ya have it!

Answer:

C

Step-by-step explanation:

Rotates then reflects over the y axis.

Answer:

C) rotation, then reflection

Step-by-step explanation:

1. rotates to spot 2. then reflects to spot 3.

Answer:

t=2

Step-by-step explanation:

Start by subtracting 9 from both sides. You'll get 7-2t=3/2t. I made 3/2 a mixed number, so 1 1/2. You should have 7-2t=1 1/2t. Add 2t to both sides, because the 2t is negative. You should have 7=3 1/2t. Last step is to divide     3 1/2 into both sides. 7 divided by 3 1/2 is equal to 2, so t=2

Answer:

480 eggs

Step-by-step explanation:

Given;

A crate of egg cartons holds 8 cartons of eggs.

Each carton has a dozen eggs.

To Find;

How many eggs are in 5 crates?

Note;

Dozen eggs = 12 egg

Solve;

Thus, Dozen eggs × Carton of eggs × many eggs are in crates

→ 12 × 8 × 5

→ 96 × 5

→ = 480

[RevyBreeze]

Answer:

80 tools in one day

Step-by-step explanation:

30 = 2400

÷ 30

1 = 80

Answer:

  3(5h - 2g)

= 3×5h - 3×2g  

= 15h - 6g

  5(12g - 4f)

= 5×12g - 5×4f

= 60g - 20f

  2(h - 3g)

= 2×h - 2×3g

= 2h - 6g

  4(3x - g) + 4x

= 4×3x - 4×g + 4x

= 12x - 4g + 4x

= 16x - 4g

  9(4g + 1) - 5g

= 9×4g + 9×1 - 5g

= 36g + 9 - 5g

= 31g + 9

Answer:

Step-by-step explanation:

24/12 = 2

72/(8 - 9)  Be sure and use brackets when you post a question. 8 - 9 = - 1

72/-1 = - 72

2 - 72 = - 70

Answer:

I think it's 12 bro, I'm not sure

Using the normal distribution and the central limit theorem, it is found that:

a) The mean is of 0.15.

b) The standard deviation is of 0.0326.

c) There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.

d) 0.1774 of incoming kindergarteners are nearsighted.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

[tex]\mu = p = 0.15[/tex]

The mean is of 0.15.

Item b:

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.15(0.85)}{120}} = 0.0326[/tex]

The standard deviation is of 0.0326.

Item c:

The probability is the p-value of Z when X = 0.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.1 - 0.15}{0.0326}[/tex]

[tex]Z = -1.53[/tex]

[tex]Z = -1.53[/tex] has a p-value of 0.063.

There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.

Item d:

The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]0.84 = \frac{X - 0.15}{0.0326}[/tex]

[tex]X - 0.15 = 0.84(0.0326)[/tex]

[tex]X = 0.1774[/tex]

0.1774 of incoming kindergarteners are nearsighted.

To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213

Answer:

100

Step-by-step explanation:

1 out of 10, or [tex]\frac{1}{10}[/tex]. It is unlikely to occur.