What is the following sum?

Answer:

x = 70

Step-by-step explanation:

The sum of the angles of a triangle add to 180

65+45+x = 180

Combine like terms

110+x = 180

Subtract 110 from each side

x = 180-110

x = 70

Check the picture below.

Answer:

Area of the shades region = 244.6 ft²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

                                    = 29.8 × 13

                                    = 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                        = [tex]\frac{1}{2}(10.2)(28)[/tex]

                        = 142.8 ft²

Area of the shades region = 387.4 - 142.8

                                             = 244.6 ft²

Answer:

I think the answer is the blue box

Answer:

C=20° a=10.8 c= 4.3

Step-by-step explanation:

first we need to find the value of angle C by subtracting the sum of angle A and B from 180°.

to find c and a we need to use sin rule which states that sinB/b=sinA/a=sinC/c respectively

Answer:

1 : 64

Step-by-step explanation:

We require the dimensions to be the same units

1 foot = 12 inches , then

85 [tex]\frac{1}{3}[/tex] feet = [tex]\frac{256}{3}[/tex] × 12 = 256 × 4 = 1024 inches

Scale is then

16 in : 1024 in ( divide both parts by 16 )

= 1 : 64

Answer:

The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].

Step-by-step explanation:

Point P:

The coordinates of point P are (x,y).

AP=3/7 AB

So

[tex]P - A = \frac{3}{7}(B-A)[/tex]

We apply this both for coordinate x and coordinate y.

Coordinate x:

[tex]x - (-2) = \frac{3}{7}(2 - (-2))[/tex]

[tex]x + 2 = \frac{12}{7}[/tex]

[tex]x = \frac{12}{7} - 2 = \frac{12}{7} - \frac{14}{7} = -\frac{2}{7}[/tex]

Coordinate y:

[tex]y - (-2) = \frac{3}{7}(-4 - (-2))[/tex]

[tex]y + 2 = -\frac{6}{7}[/tex]

[tex]y = -\frac{6}{7} - 2 = -\frac{6}{7} - \frac{14}{7} = -\frac{20}{7}[/tex]

The coordinates of point P are [tex](-\frac{2}{7}, -\frac{20}{7})[/tex].

Answer:

8

Step-by-step explanation:

Divide 30 by 3.75 to get 8.

Hope that this helps!

Answer:

A

Step-by-step explanation:

sin θ=3/8

θ=sin ^{-1}(3/8)

≈22.02 °

Answer:

About 22 degrees

Step-by-step explanation:

Since we are given the opposite side measurement to the angle we wish to find and the hypotenuse measurement, we will want to use sine.

sin(theta)=3/8

theta=arcsin(3/8)

theta=22.024 approximately

Answer:

Multiply x by 4 and make x negative if it's positive or make x positive if it's negative.

Step-by-step explanation:

Multiplying x by a number greater than 1 will stretch the parabola.

Changing x from positive to negative and vice versa reflects the parabola over the x-axis.

Answer: 5

Step-by-step explanation:

Step-by-step explanation:

A=P(1+0.084) ^n;

=5500(1

The payment now is $4561.7450, 15 months later $5061.28, 27 months later $5500.00595 and 36 months later $5853.83.

Interest rate = 8.4/4 =2.1% = 0.021 every 3 months

The debt of $5500 is due in 27 months.

The formula to find the compound interest is  [tex]FV=PV(1+r)^{n}[/tex].

Now, [tex]PV=FV(1+r)^{-n}[/tex].

The payment now:

5500*(1.021)^-9 = $4561.7450

So if $5500 is due in 27 months its current value is $4561.7450.

( b) 15 months from now? 5 quarters  

FV(15months)= 4561.75*1.021^5

4561.75*1.021^5 = $5061.28

(c) 27 months from now? 9 quarters

FV(15 months)= $5500  that was given in the question

Verification:

FV(27months)=4561.75*1.021^9

4561.75*1.021^9 = $5500.00595

(d) 36 months from now?   12 quarters

FV(36months)=4561.75*1.021^12

4561.75*1.021^12 = $5853.83

Therefore, the payment now is $4561.7450, 15 months later $5061.28, 27 months later $5500.00595 and 36 months later $5853.83.

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Answer:

80

Step-by-step explanation:

10*8=80

Answer:

Step-by-step explanation:

to find height use pythagoras theorem

height be x

a^2+b^2=c^2

x^2+8^2=10^2

x^2+64=100

xx^2=100-64

x^2=36

x=[tex]\sqrt{36[/tex]

x=6

area of the triangle =base*height/2

=8*6/2

=48/2

=24 square units.

Answer:

0

Step-by-step explanation:

duh

Answer:

D.16.5m

because circumference=21/7×5.25

=16.5m

Answer:

56.25 cm

Step-by-step explanation:

your teacher wrote the approach already : the law of sines.

in our example we have

sin(28)/27 = sin(102)/c

c×sin(28)/27 = sin(102)

c×sin(28) = 27×sin(102)

c = 27×sin(102)/sin(28) = 27×0.98/0.47 = 56.25 cm

Answer:

x = all real numbers

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

x + 6 = 2(x + 3) - x

Step 2: Solve for x

Here we see that both sides are identical.

∴ our solution is all real numbers.

Answer:

Step-by-step explanation:

First we need to calculate how many total students there are. Once we have the total we have to divide the number in the category that we want by the total number of students to calculate the probability of randomly getting a student in that category.

Total Students = 3 + 12 + 2 + 7 = 24 students

Probabilities:

does not have a sister = [tex]\frac{2 + 7}{24}[/tex] = 0.375 or 37.5%  (multiply decimal by 100 to get percentage.

Has a brother = [tex]\frac{3 + 2}{24}[/tex] = 0.208 or 20.8%

Does not have a brother = [tex]\frac{12 + 7}{24}[/tex] = 0.7916 or 79.2%

Has a sister = [tex]\frac{3 + 12}{24}[/tex] = 0.625 or 62.5%

Answer:

B2--> the answer is 121 degrees.This is because due to alternate interior angles, the triangle

Answer:

£1350 & £3150

Step-by-step explanation:

[tex]3x+7x=4500\\10x=4500\\x=450\\\\3(450)=1350\\7(450)=3150[/tex]

Answer:

x = 27.5

Step-by-step explanation:

x/55 = 4/8 (ratio between the two polygons); cross multiply.

220 = 8x; divide 8 on both sides

x = 27.5

Answer:

y=5x-9

Step-by-step explanation:

-5(-3)+b=6

15+b=6

B=-9

[tex] \boxed{ \mathfrak{\huge \: \underline{ \underline{A nswer} }: }}[/tex]

Given terms :

[tex]\hookrightarrow \: length = 8 \: in[/tex]

[tex]\hookrightarrow \: width = 2 \: in[/tex]

[tex] \hookrightarrow \: height = 12 \: in[/tex]

we know,

[tex] \large\boxed{ \mathrm{surface \: \: area \: (a) = 2(lw + wh + lh)}}[/tex]

[tex]\hookrightarrow \mathrm{\: a = 2 \times \bigg [(8 \times 2) + (2 \times 12) + (8 \times 12) \biggr]}[/tex]

[tex]\hookrightarrow a = 2 \times \biggr[16 + 24 + 96 \biggr][/tex]

[tex]\hookrightarrow \: a = \bigg [\: 2 \times 136\bigg ][/tex]

[tex]\hookrightarrow \large \boxed{ \mathrm{a = 272 \: \: in {}^{3} }}[/tex]

____________________________________

[tex] \mathrm{✌TeeNForeveR✌}[/tex]

Answer:

d 180 miles

Step-by-step explanation:

4.5×40= 180 miles

The actual distance to college Lisa and Susan going together is 180 miles.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The map scale is 1 in. = 40 mi.

Lisa and Susan are driving to college together, On the map, Lisa measures the distance to be 4.5 inches.

Therefore,

The actual distance to college is,

= (4.5×40) miles.

= 180 miles.

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