The ratio of the dimensions of a rectangular patio are 4:7. if the shorter
dimension is 10 feet, What are the area and perimeter of the patio?

Answer:

Part A: [tex]x^2-30x+224\geq 0[/tex]

Part B: Jessica has at least 2 cookies more than Martha

Step-by-step explanation:

Since there are 2 question-

Let,

How many more cookies will Jessica have than Martha?If x represents the number of cookies Jessica started with, complete the statements below. Be Part A:

Let,

The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0 Jessica has at least _ cookies more than Martha.

Be Part B:

Hint:

J=Jessica

30-J=Martha

(J-6)*((30-J)-6)<=80

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve:

Starting with Part A: Find the inequality that describes the relationship between the number of cookies each one of them has

Let,

"x" be the number of cookies when Jessica started

"30-x" be the number of cookies when Martha started

Given us that:

Each of them ate 6 cookies from their bag

Therefore,  

Cookie left in each bag are:

(x-6) which is - Jessica

30 - x - 6 = (24 - x) - Martha

Solution - (x-6)(24-x)

The product of the number of cookies left in each bag is not more than 80.

Thus,

[tex](x-6)(24-x\leq 80[/tex]

[tex]24x-x^2-144+6x\leq 80[/tex]

[tex]-x^2+30x-144-80\leq 0[/tex]

[tex]-x^2+30x-244\leq 0[/tex]

[tex]\mathrm{Multiply\;by\;-1\;both\;sides}[/tex]

[tex]x^2-30x+224\leq 0[/tex]

Hence, Answer = [tex]x^2-30x+224\leq 0[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve:

Part B: Solve the quadratic equation:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:14\le \:x\le \:16\:\\ \:\mathrm{Interval\:Notation:}&\:\left[14,\:16\right]\end{bmatrix}[/tex]

[tex]\left(x-14\right)\left(x-16\right)\le \:0[/tex]

[tex]14\le \:x\le \:16[/tex]

The solution is x=16 cookies

Thus, (30-x)=30-16=14 cookies

Now we know that;

The number of cookies when Jessica started was 16 cookies

The number of cookies when Martha started was 14 cookies

So,

The number of cookies left in each bag  is equal to

Jessica:

16-6=10 cookies

Martha:

14-6=8 cookies

10 > 8

As a result, Jessica has at least 2 cookies more than Martha.

Fill in blank for:

The inequality that describes the relationship between the number of cookies each one of them has is x^2 - __30__ x +224 >= 0.

Jessica has at least __2__ cookies more than Martha.​

~Lenvy~

Answer:

C. 200 hours

Step-by-step explanation:

According to the given Question ,

It means that the aeroplane covers 400 miles in 60 minutes.

and it is asked for 30 minutes , so

We know that 30 minutes is equal to 0.5 hours

By the formula ,

Distance = Speed × Time

putting the values given , we get

= 400×0.5

Distance = 200 miles

10.9

[tex]According\ to\ the\ question,\ we\ con\ spe\ that[/tex]

             [tex]\sin{40}[/tex]° [tex]=\frac{7}{x}[/tex]

                  [tex]x=\frac{7}{\sin{40degrees}}\\ x\approx 10.9[/tex]

I hope this helps you

:)

Answer:

c=5

Step-by-step explanation:

4(c-3)=8 Distribute

4c-12=8 Add 12 to both sides

4c=20 Divide by 4 on both sides

c=5

Answer:

Step-by-step explanation:

METHOD 1:

4(c - 3) = 8    |divide both sides by 4

4(c - 3)/4 = 8/4

c - 3 = 2     |add 3 to both sides

c - 3 + 3 = 2 + 3

c = 5

METHOD 2:

4(c - 3) = 8     |use the distributive property: a(b - c) = ab - ac

4 · c - 4 · 3 = 8

4c - 12 = 8      |add 12 to both sides

4c - 12 + 12 = 8 + 12

4c = 20     |divide both sides by 4

4c/4 = 20/4

c = 5

John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the shoe cost $100, he spins the spinner and gets a discount of 25%, hence:

Money paid = 100 - 25% of 100

Money paid = 100 - 25 = $75

John paid $75 for a pair of shoe that cost $100 at a discount of 25 percent.

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Answer:

each notebook would cost $4

Step-by-step explanation:

21-13=8.    8/2=4

Answer:

27.25

Step-by-step explanation:

we find the mean by adding all the values and dividing by the number of values.

0.007 kg

[tex]1000\ grams=1\ kg\\ 7\ grams=0.007\ kg\\ Check\ conversion[/tex]

I hope this helps you

:)

Answer:

Can you please give us figure of following ?

Answer:

its the last one 212°

212°

212°

212°

212°

212°

Step-by-step explanation:

212°

The value of net asset to be in order for Nezzie to sell all of her shares when she can profit $5,000 is $33.66.

The net asset value is the difference of total asset value of the company to the total liabilities value of that company.

Nezzie invests in 300 shares of stock in the fund shown below. Name of fund nav offer price lkit mid-cap $16.58 $16.99.

Nezzie plans to sell all of her 300 shares of stock when she can profit $5,000.

To find the net asset for this case, divide the profit with the number of shares and the higher price in that.

[tex]\rm Net Asset=\dfrac{5000}{300}+16.99\\\rm Net Asset=33.66\\[/tex]

Thus, the value of net asset to be in order for Nezzie to sell all of her shares when she can profit $5,000 is $33.66.

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Answer:

is there a picture of the answers?

Step-by-step explanation:

also can u help me with my question pls

Answer:

C and D :)

Step-by-step explanation:

Answer:

c and d

Step-by-step explanation:

Answer:

Slope formula;

y2(second y coordinate) - y1(first y coordinate)

____________________________________

x2(second x coordinate) - x1(first x coordinate)

Plug in values:

  2 - 1                 1

_______ = ________, your slope is -1/14.

-17 - (-3)            -14

Answer:

LCM of 3 and 2 is 6

so, firstly we had to make the denominator same:-

[tex] \frac{2(2a + 1) + 3(3a - 1)} {6} [/tex]

[tex] \frac{4a + 2 + 9a - 3}{6} [/tex]

[tex] \frac{13a - 1}{6} [/tex]

Step-by-step explanation:

hope this helps you!!!

XxITSCHOCOLOVERxX

The simplified equation of [tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex] is [tex]\frac{13a-1}{6}[/tex]

[tex]\frac{2a+1}{3}+\frac{3a-1}{2}[/tex]

[tex]\frac{2a+1}{3}+\frac{3a-1}{2} = \frac{2(2a+1)+3(3a-1)}{6}[/tex]

open the bracket in the numerator

Therefore,

[tex]\frac{2(2a+1)+3(3a-1)}{6}=\frac{4a+2 + 9a-3}{6}[/tex]

combine like terms in the numerator

[tex]\frac{4a+2 + 9a-3}{6}=\frac{4a+9a+2-3}{6}[/tex]

Hence,

[tex]\frac{4a+9a+2-3}{6}=\frac{13a-1}{6}[/tex]

Therefore, the final equation is as follows

[tex]\frac{2a+1}{3}+\frac{3a-1}{2}=\frac{13a-1}{6}[/tex]

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#SPJ5

x + 10 = - 6x - 18

7x = - 28

x = - 4

and y = - 4 + 10 = - 6

Answer:

Step-by-step explanation:

x - 30 = 14 - 3x

    4x = 44

      x = 11

Let's call the unknown number x

Now let's decrease it by 30, that is x-30

Now let's write out "14 decreased by three times the number", that is 14 - 3x

The problem says these are the same, that is x - 30 = 14 - 3x

We now want to isolate, or solve for, x

Move the x to one side of the equation by adding 3x to both sides

3x + x -30 = 14 - 3x + 3x

4x -30 = 14

Now move the 30 to the right hand side by adding 30 to both sides

4x - 30 + 30 = 14 + 30

4x = 44

Now all we have to do to get x is divide both sides by 4

4x/4 = 44/4

x = 11

Answer:

⠀

Step-by-step explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

⠀

⠀

We know that,

⠀

So, According to the question :

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]

⠀

Therefore,

Answer:

(2,0) is not a point on the graph of the function y=x+2

Step-by-step explanation:

Go to the TI-84 plus calculator and go to the y= button and then type in x+2 and then press the 2nd button and then the graph button and then you should get your answer.

The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm

Dilation is the increase or decrease in the size of an figure or object.

A dilation with a scale factor of 2 is applied to the three line segments shown to form P'Q', A'B', and M'N'.

Hence:

P'Q' = scale factor * PQ = 2 * 2 = 4 cm

A'B' = 2 * 1.5 = 3 cm

M'N' = 2 * MN = 2 * 3 = 6 cm

The value of the dilated line segments P'Q', A'B' and M'N' are 4 cm. 3 cm and 6 cm

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Answer:

4.61

Step-by-step explanation:

Step-by-step explanation:

[tex] = 4 \frac{2}{4} + \frac{1}{9} \\ = \frac{4 \times 4 + 2}{4} + \frac{1}{9} \\ = \frac{18}{4} + \frac{1}{9} [/tex]

Find the LCM

[tex] = \frac{18}{4} \times \frac{9}{9} + \frac{1}{9} \times \frac{4}{4} \\ = \frac{162}{36} + \frac{4}{36} \\ = \frac{166}{36} [/tex]

Convert into lowest term

[tex] \frac{83}{16} \\ [/tex]

Applying the trigonometry ratios, we have:

a. CD = 63.6

b. CD = 33.8

c. CD = 16.1

d. CD = 15.9

The trigonometry ratios are used to find a length or angle in any right triangle. They are:

a. ∅ = 32°

hyp = 75

adj = CD

Apply CAH:

cos 32 = CD/75

CD = cos 32 × 75

CD = 63.6

b. ∅ = 56°

opp = 28

hyp = CD

Apply SOH:

sin 56 = 28/CD

CD = 28/sin 56

CD = 33.8

c.  ∅ = 43°

opp = 15

adj = CD

Apply TOA:

tan 43 = 15/CD

CD = 15/tan 43

CD = 16.1

d.  ∅ = 27°

hyp = 35

opp = CD

Apply SOH:

sin 27 = CD/35

CD = sin 27 × 35

CD = 15.9

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Answer:

The answer is 3 buses

Step-by-step explanation:

40 divided by 14 is 2.85714285714 buses well you cant have 3/4 of a bus so you round it up to 3 buses

Answer:

4/12 and 3/8

Step-by-step explanation:

Answer: 42.0

Step-by-step explanation:

Answer:

[tex]2m[/tex]

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

[tex]A = \frac{1}{2}bh[/tex]

They give us the area as [tex]6m^2[/tex], so let's include it in the equation.

[tex]6 = \frac{1}{2}bh[/tex]

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that [tex]h = b-4[/tex]

So replace [tex]h[/tex] in the equation with [tex]b-4[/tex].

You will now get:

[tex]6 = \frac{1}{2}b(b-4)[/tex]

Now we can work towards solving. Let's get simplifying.

[tex]12 = b(b-4)\\12 = b^2 - 4b\\[/tex]

bring everything to one side so we can make a quadratic and factor:

[tex]0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2[/tex]

We get that [tex]b=6[/tex].

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that [tex]h = b - 4[/tex], so to find h, we just sub in our b value into that.

[tex]h = (6) - 4 = 2[/tex]

We find that [tex]h=2[/tex]