the legnth of rectangular sheet decreases by 34.5 cm its width decreases proportionally that is by the same percentage. if the sheets original width was half of the legnth and the new (smaller) area was 1.2 m^2 what was original sheet's width

Answer:

B, C, D

Step-by-step explanation:

if tan theta = 15/8 then the hypotenuse is 17

therefore the correct answers are B, C, D

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

G(x) = (1 - x)/4

is the inverse function required.

Step-by-step explanation:

Given F(x) = -4x + 1

Let y = F(x)

Then y = -4x + 1

=> y - 1 = -4x

4x = 1 - y

x = (1 - y)/4

That is, the inverse is (1 - x)/4

Therefore, G(x) has to be (1 - x)/4

Answer:

The value of x is 35

Step-by-step explanation:

In order to calculate the value of x in the  following parallelogram:  2x - 10  

2x + 50, we would have to calculate the following formula:

m<QPS+m<PQR=180°

According to the given data we have the following:

m<QPS=2x - 10  

m<PQR=2x + 50

Therefore, 2x - 10+2x + 50=180

4x+40=180

x=140/4

x=35

Answer:

288 in²

Step-by-step explanation:

The formula used to solve this question is :

Lateral Surface Area = s( P1 + P2)

Where s = slant height = 2 inches

P1 and P2 = Perimeter of the bases

Perimeter of base 1 = 4 × length of the end of the small square

4 × 17 inches = 68 inches

Perimeter of base 2 = 4 × length of the end of the large square

4 × 19 inches = 76 inches

Lateral Surface Area = 2 × (68 + 76)

= 2 × 144

= 288 in²

Answer:

y = -5x - 9.

Step-by-step explanation:

(-2, 1)

(0, -9)

(1 - -9) / (-2 - 0) = (1 + 9) / (-2) = 10 / (-2) = 5 / (-1) = -5

Since -5 is the slope, and the y-intercept is at (0, -9), we have an equation of y = -5x - 9.

Hope this helps!

Answer:

y=-5x-9

Step-by-step explanation:

Change in x = +2

Change in y=-10

-10/2=-5

m=-5

plug in an point

example:

1=-5(2)+B

B=-9

To check your answer:

y=-5x-9

plug in an point for x given on the chart:

-5(0)-9=-9

Answer:

Triangle klm

Step-by-step explanation:

edg 2020

Answer:

25°

Step-by-step explanation:

Since ∠DBC = 130°, ∠DBC + ∠ABD = 180° (sum of angles on a straight line is 180°). Solving for ∠ABD:

∠DBC + ∠ABD = 180°

130 + ∠ABD  = 180°

∠ABD = 180° - 130°

∠ABD = 50°

∠ABD  is bisected by line BE, therefore ∠ABD = ∠EBA + ∠DBE (angle addition postulate).

The angle addition postulate states that if w is the interior of xyz then ∠XYZ = ∠XYW + ∠ZYW

Since E is the interior of ∠ABD, then:

∠ABD = ∠EBA + ∠DBE

But ∠EBA = ∠DBE

∠ABD = 2∠EBA

50 = 2∠EBA

∠EBA = 25°

Answer:

Answer:

3 cups

Step-by-step explanation:

We can use a proportion to find how many cups of chocolate chips she needs for 30 servings. Assuming c = cups of chocolate chips and b = batches

[tex]\frac{c}{b}[/tex]

[tex]\frac{1}{10} = \frac{c}{30}[/tex]

We can now multiply the diagonal values that don't include the missing variable (30 and 1) and then divide it by the value that is diagonal to the variable (10)

[tex]30 \cdot 1 = 30\\30 \div 10 = 3[/tex]

Therefore, she needs 3 cups of chocolate chips to make 30 servings.

Answer:

3 cups

Step-by-step explanation:

We can use ratios to solve

1 cup               x cups

---------------- = ----------------

10 servings     30 servings

Using cross products

1*30 = 10x

Divide by 10

30/10 = x

3 =x

3 cups

hey mate, here is ur answer in the attachment!

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Step-by-step explanation:

c^2( c^2-10c+25)

=c^4 - 10c^3 + 25c^2

Answer:

5/6π.

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 12 cm

Area (A) = 60π cm²

Centre angle in radian (∅) =...?

Since we are to look for the centre angle in radian, the area of the sector will be given by:

A = ½r²∅

Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:

A = ½r²∅

60π = ½ × 12² × ∅

60π = ½ × 144 × ∅

60π = 72 × ∅

Divide both side by 72

∅ = 60π/72

∅ = 5/6π

Therefore, the centre angle measured in radian is 5/6π.

Answer:

Step-by-step explanation: wjbsgstexrczlkcidgxtftwdcwdkfmw,d,f

━━━━━━━☆☆━━━━━━━

▹ Answer

You can use a graphing calculator. Attached is a picture of it graphed.

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

  927 cubic inches

Step-by-step explanation:

The area of the octagonal base is ...

  A = (1/2)Pa

where P is the perimeter, and 'a' is the apothem. Using the given numbers, the base area is ...

  A = (1/2)(8·4)(4.83) = 77.28 . . . square inches

The volume of the prism is given by ...

  V = Bh

where B represents the area of the base, and h is the height.

  V = (77.28 in^2)(12 in) = 927.36 in^3

The volume of the prism is about 927 cubic inches.

the answer on edg is 927

Answer:

Correct Option: B

Step-by-step explanation:

Linear functions are the type of functions that are applied to model occurrences that rise or fall at a constant proportion. These sorts of functions are polynomial functions with a maximum exponent of one on the variable. The graphs of these kind of functions are in the form of a line.

Exponential functions are the type of functions that have the variable in exponent form. The growth rate or decline rate is either slow than quick or quick than slow.

Quadratic functions are of the form f (x) = ax² + bx + c. The graph of this function is in the form of a parabola. The graph first increases, hit a maximum, then decreases or decreases, hit a minimum, then increases.

From the provided graphs it can be seen that, the exponential function grows at approximately the same rate over the interval 0 ≤ x ≤ 1 as the quadratic function.

Answer:

bbb

Step-by-step explanation:

Answer:

<B = 32°

c = 9.43

Step-by-step explanation:

To find the measure of <B, add up the measures of the two angles that you know and subtract from 180°.

58° + 90° = 148°

180° - 148° = 32°

The measure of <B is 32°.

To find the length of side c, use the Pythagorean Theorem.

a² + b² = c²

5² + 8² = c²

25 + 64 = c²

89 = c²

c = √89

c = 9.433981132 ⇒ 9.43 (rounded to two decimal places)

The length of side c = 9.43.

Hope that helps.

Answer:

6:00 p.m.

hope this helps :)

Answer:

Option B

Step-by-step explanation:

Hope it is right

The value of equation describes the line graphed is,

⇒ y = -1/5x - 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, -4) and (5, -5).

Now,

Since, The equation of line passes through the points (0, -4) and (5, -5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 5 - (-4)) / (5 - 0)

m = - 1 / 5

Thus, The equation of line with slope - 1/5 is,

⇒ y - (-4) = -1/5 (x - 0)

⇒ y + 4 = -1/5x

⇒ y = -1/5x - 4

Therefore, The equation of line passes through the points (0, -4) and

(5, -5). will be;

⇒ y = -1/5x - 4

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ7

Answer:

720 ways

Step-by-step explanation:

At first their are six books, that means that there are six different positions to put them. The first book to be placed would have 6 position, when the first book is placed, to place the second book there would be 5 position since one position has been used by the first book. After placing the second book, to place the third book there would 4 available position, and it follows this manner i.e for the fourth book 3 available position, for the fifth book 2 available position and for the sixth book, one available position.

Therefore the number of ways to arrange the books on the shelf from left to right = 6 × 5 × 4 × 3 × 2 × 1 = 6! = 720 ways

Answer:

[tex]\overline{DF}[/tex] could be a midsegment of ∠ABC.

Step-by-step explanation:

A midsegment of a triangle must be two things:

1. Parallel to the 3rd side, in this case, [tex]\overline{AD}[/tex].

2. Half the length of the 3rd side, in this case, [tex]\overline{AD}[/tex].

Since we don't know the lengths, we can only go off of 1. There is only one line that is parallel to  [tex]\overline{AD}[/tex] and it is [tex]\overline{DF}[/tex].

Hope this helped!

Answer:

7.5 jars

Step-by-step explanation:

There are 25 students in the art class.

Mr Jones is planning that for the project, each of the 25 students will need 0.3 jar of paint.

The amount of paint Mr Jones needs for this project is therefore the product of the number of students in the class by the amount of paint each student needs.

That is:

25 * 0.3 = 7.5 jars of paint

Mr Jones needs 7.5 jars of paint for the art project.

Answer:

2 - bedroom apartment = 4

3 - bedroom apartment = 2

Step-by-step explanation:

Given the following :

2 - bedroom apartment = $700 / month

3 - bedroom apartment = $900 / month

Last month:

Number of vacant apartment = 6

Amount of Lost rent = $4600

Let a = 2 - bedroom apartment and b = 3 - bedroom apartment

Vacant apartment :

a + b = 6 - - - (1)

Lost rent :

700a + 900b = 4600 - - - (2)

From (1),, a = 6 - b

Substitute a = 6 - b into (2)

700(6 - b) + 900b = 4600

4200 - 700b + 900b = 4600

4200 + 200b = 4600

200b = 4600 - 4200

200b = 400

b = 400/200

b = 2

From (1) ;

a + b = 6

a + 2 = 6

a = 6 - 2

a = 4

a = 2 - bedroom apartment = 4

b = 3 - bedroom apartment = 2

Answer:

25 children

So , each child will get 25 pens and 7 pencils

You have to find the highest common factor of 125 and 175 which is 25 and then you have to multiply it by those two numbers to find how may pens and pencils will be given to 1 child

Hope this helps and pls mark as brianliest :)

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

2(y + 4) = 4y

Distribute

2y + 8 = 4y

Step 2 is incorrect because the added instead of multiplied

Continuing on to correct the problem

Subtract 2y from each side

2y+8-2y = 4y-2y

8 = 2y

Divide by 2

8/2 = 2y/2

4 =y

Answer:

2 should be distributed as 2y + 8; y = 4

Step-by-step explanation:

Step 2 is wrong.

2(y + 4) = 4y

The step to solve is to expand brackets or distribute 2, not divide both sides by 2.

2y + 8 = 4y

Subtract both sides by 2y.

8 = 2y

Divide both sides by 2.

4 = y

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Answer:

$191,340.80

Step-by-step explanation:

Step 1

We find the amount that is paid monthly by the Lee's

We are told in the question that:

Cost of the house =$360,000

Down payment = $50,000

We are also told, the balance left after the down payment was made = Mortgage that is amortized at an

Interest rate of 5.25%

Time = 20 years

Hence, Mortgage amount = $360,000 - $50,000 = $310,000

Formula for monthly payment =

M= P[r(1+r)^n/((1+r)^n)-1)]

M = the total monthly mortgage payment.

P = the principal loan amount.

r = your monthly interest rate.

= rate/12

=5.25%/12 = 0.0525/12

= 0.004375

n = number of payments

= number of years × number of months

= 20 × 12 = 240 payments

Formula for monthly payment =

M= P[r(1+r)^n/((1+r)^n)-1)]

M = 310,000[0.004375(1 + 0.004375)^240/((1 + 0.004375)^240 ) - 1]

M = $2,088.92

Therefore, the monthly payment by the Lee's is $2,088.92

Step 2

We calculate the Total Amount paid by the Lee's in 20years because we are told in the question that they paid off their mortgage after 20 years

Total Amount paid = Monthly payments × Number of payments

= $2,088.92 × 240

= $501,340.80

Step 3

The third and final step is to calculate the Total interest paid for 20 years

Total Interest = Total amount paid - Mortgage amount

= $501,340.80 - $310,000

Total Interest: $191,340.80

Therefore,the interest will they have paid in total is $191,340.80