1 A rectangular picture frame has perimeter
70 cm.
a The width of the frame is x cm. Find an
expression, in terms of x, for the height
of the frame.
b Find an equation for the area of the
frame, Acm?, in terms of x.
c Plot the graph which shows how A
varies with x. Use a suitable domain and
range. Hence sketch the graph on paper.
d Find the x-intercepts of the graph in part c.
e State what these two values of x represent.
f Hence find the equation of the graph's
line of symmetry, and state what this
tells you in the context of the problem.

Answer:

54

Step-by-step explanation:

Answer:

Contains two 6x6 triangles, contains one 12x3 rectangle, four 2x2 triangles, and two 2x2 squares.

88

Step-by-step explanation:

You only need the area of one side of this shape to find the total area.

((6*6)/2+(3*6)+(2*2)+(2*2))2 = 88. What's inside the parenthesis is the area for one side of the shape, then you can multiply that by two to get the entire area.

Answer: 873.76

First find 1% of 2302 which will be 2302/100=23.02

to find 43% of 2302 multiply 1% of 2302 with 43

43*23.02 = 873.76

Answer:

2

Step-by-step explanation:

Answer:

D: 50% on car payment and college savings

Step-by-step explanation:

225+375 = 600

50% of 1200 is 600

Answer:

$2,989.12

Step-by-step explanation:

The correct answer to the given question is $2,989.12. The monthly net pay is $2,989.12, when the gross monthly income is $3,750.

The deduction from the gross income is almost 20.29%.

The gross income is multiplied by 20.29% and then the answer is deducted from the gross income which gives monthly net pay as a result

$3,750 * 20.29% = $760.875

$3,750 - $760.875 = $2,989.12

Your monthly net pay is $2,989.12

Answer:

the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Step-by-step explanation:

Given the points on the graph

Here:

(x₁, y₁) = (4, 4)

(x₂, y₂) = (9, 1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [1 - 4] / [9 - 4]

               = -3 / 5

Thus, the slope of the line passing through (4, 4)  and (9, 1)   is:

Slope = -3/5

Answer:

DB = 26

Step-by-step explanation:

Remember:

☆The equation in finding the value of x would be 3x - 2 = 2x + 3.

☆Let's solve the equation.

[tex] \: \: \: \: \: \: \: \: \: 3x - 2 = 2x + 3 \\ \frac{ - 2x \: \: \: \ = - 2x}{x - 2 = 3} \\ \frac{ \: \: \: \: \: + 2 = + 2}{x = 5} [/tex]

☆Now that we found the value of x, we are going to plug in for AE and EC.

[tex]AE ; \\ 3x - 2 \\ 3(5) - 2 \\ 15 - 2 \\ 13 \\ \\ \\ \\ and \\ \\ \\ \\ \\ EC; \\ 2x + 3 \\ 2(5) + 3 \\ 10 + 3 \\ 13[/tex]

☆AE and EC each measure 13. To find the length of AC, you will have to add AE and EC. [tex]13 + 13 = 26[/tex]

The length of AC is 26. And since we know that AC is congruent (equal) to DB, meaning they measure the same. DB length is also 26.

Answer:

The ranges of value of k are values larger than 0 and lower than 16.

Step-by-step explanation:

Suppose we have a second order polynomial in the following format:

[tex]ax^2 + bx + c = 0, a \neq 0[/tex]

It will have no roots if:

[tex]\Delta = b^2 - 4ac < 0[/tex]

In this question, we have that:

[tex]hx^2 + hx - 4 = 0[/tex]

So, the coefficients are:

[tex]a = h, b = h, c = -4[/tex]

Then

[tex]\Delta < 0[/tex]

[tex]b^2 - 4ac < 0[/tex]

[tex]h^2 - 16h < 0[/tex]

A quadratic function, with a positive(as is 1 in this inequality), will be negative between it's roots.

The roots are:

[tex]h^2 - 16h = 0[/tex]

[tex]h(h - 16) = 0[/tex]

So

h = 0 or h = 16.

The ranes of value of k are values larger than 0 and lower than 16.

Answer: $11.25

Step-by-step explanation:

Answer:

$11.25

Step-by-step explanation:

I assume that x = the 5 videos streamed

5*1.25=6.25

6.25+5 =11.25

y=$11.25

Answer:

There are 473 millimeters in 1 pint.

Step-by-step explanation:

946 ml in 1 quart.

2 pints in 1 quart

hence,

946 ml in 2 pints

hence in 1 pint we have 946/2 ml

i.e. 473 ml in 1 pint.

:)

Answer:

473 milliliters

Step-by-step explanation:

If there are 946 mL in a quart and there are 2 pints in a quart, divide 946 by 2 to find how many mL are in one pint.

Here's an equation you can set up to solve the problem.

— 946 = 2x

— 946 / 2 = 2x / 2

— 473 = x

So, if we let x stand for the amount of mL in a pint, then 473 = x means there are 473 mL in a pint.

Answer:

3

Step-by-step explanation:

Answer:

it will be 6

Step-by-step explanation:

The standard deviation is 83 – 80 = 3.  Since margin of error is two times the standard deviation, it must equal 6.

Answer:

the answer is D.

Step-by-step explanation:

Since the square: (3√15) is common in both of them, you only focus on 21 and 9. if you subtract 9 from 21, it will give you 12. so, just add (3√15) to 12, which will give you: 12^3sqrt15

Answer:

yes

no

yes

no

hope this helps

Answer:

1. Yes

2. No

3.Yes

4.No

Step-by-step explanation:

I did the test and got it right!

Answer:

The village market is better than Sam's Club

Step-by-step explanation:

If you buy 5 more cans of green beans at the village, it will cost $4.40 in total. Therefore if you go buy the beans at Sam's club, the village one will be cheaper.

Answer:

348 ignore this eoendndisiwjd

Answer:

Retail price = $5.20

Percentage of mark up price = 30%

Step-by-step explanation:

Company sells $4.00 each wholesale.

Now the local store which is the retailer has a markup of $1.20.

This means that the retail price is;

Retail price = wholesale price + mark up = $4.00 + $1.20

Retail price = $5.20

To find the percentage of the markup, it is the fraction of the wholesale price multiplied by 100%.

Thus;

Percentage of Markup is;

1.2/4 × 100% = 30%

Answer:

A

Step-by-step explanation:

(x-4)^2 = x^2 -4x -4x + (-4)*(-4)

= x^2-8x+16 as required

Answer:

$32.10  

Step-by-step explanation:

The amount to be accumulated in 15 years is the future value of the sinking fund, hence, using the future value formula below, we can determine the required weekly payment as appropriate:

Future value=weekly payment*(1+r)^n-1/r

Future value=$35,000

weekly payment is the unknown

r=weekly interest rate=4.25%/52=0.08173077% ( I use 8 decimal places in order to achieve accuracy)

n=number of weekly payments in 15 years=15*52=780

35000=weekly payment*(1+0.08173077% )^780-1/0.08173077%

35000=weekly payment*(1.89125311 -1)/0.000817308

35000=weekly payment*0.89125311 /0.000817308

weekly payment=35,000*0.000817308 /0.89125311

weekly payment=$32.10

Answer:

9 hours im not really good at this but i hope i did my best ^.^ :)

It would take 31.5 hours for Dan to complete the same job.

Work is the effort applied to produce a deliverable or accomplish a task. A certain amount of time (T) is taken to complete a certain work (W).

Work Done = Time Taken × Rate of Work.

Rate of Work = 1 / Time Taken.

Time Taken = 1 / Rate of Work.

According to the question

Dan and Joan were able to clean the attic in 7 hours together

i.e

Rate of Dan = D

Rate of Joan = J

now,

Rate of Work = 1 / Time Taken.

D + J = [tex]\frac{1}{7}[/tex]

It takes Joan 9 hours to complete the same job alone

i.e

J = [tex]\frac{1}{9}[/tex]

Rate of Dan :

D + J = [tex]\frac{1}{7}[/tex]

D +  [tex]\frac{1}{9}[/tex] =  [tex]\frac{1}{7}[/tex]

D =   [tex]\frac{1}{7}[/tex] -  [tex]\frac{1}{9}[/tex]

D = [tex]\frac{2}{63}[/tex]

Therefore , Time taken by Dan  to complete the same job

As,

Time Taken = 1 / Rate of Work.  

Time taken by Dan = [tex]\frac{63}{2}[/tex]

                                 = 31.5 hr

Hence,  It would take 31.5 hours for Dan to complete the same job.

To know more about work and time relationship here:

https://brainly.com/question/3854047

#SPJ2

Answer:

The identity is proved below.

Step-by-step explanation:

The tangent of an angle [tex]\theta[/tex] is given by:

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]

In this question, we are given the following trigonometric identity:

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\tan{\theta}}{1+\tan{\theta}}[/tex]

Applying the tangent

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{1+\frac{\sin{\theta}}{\cos{\theta}}}[/tex]

Now, we apply the least common multiple on the denominator. So

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\frac{\sin{\theta}}{\cos{\theta}}}{\frac{\cos{\theta}+\sin{\theta}}{\cos{\theta}}}[/tex]

SImplifying the cosine:

[tex]\frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}} = \frac{\sin{\theta}}{\sin{\theta}+\cos{\theta}}[/tex]

Which means that the identity is proved.

Answer:

24

Step-by-step explanation:

simplify 8/10 into 2/5 then 2/5 of 30 is 24

Answer:

Total cost= $141.75

Step-by-step explanation:

Giving the following information:

Bernie's Bargains 6 DVDs for $56.70

Greg's Giveaways 10 DVDs for $99.70

Stan's Steals 8 DVDs for $79.68

First, we need to determine the unitary price of each and choose the lowest one:

Bernie= 56.7/6= $9.45

Greg= 99.7/10= $9.7

Stan= 79.68/8= $9.96

The lowest price is $9.45.

Now, the total cost of 15 DVDs:

Total cost= 9.45*15

Total cost= $141.75

Answer:

149.25

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

0.26?

0.3

Answer:

There was 20 questions on the test.

She got 3 wrong.

Step-by-step explanation:

[tex]\frac{85}{100} = \frac{17}{20}[/tex]

20 - 17 = 3

There was 20 questions on the test.

She got 3 wrong.