Triangles ABC and CDE are mathematically similar.
a) Work out the length of DE.
b) Work out the length of AB.

Answer:

It was a gain, specifically 16

Step-by-step explanation:

14 + (-7) = 7

7 + 9 = 16

Please tell me if I'm wrong.

Answer:

(8a+b-16)/4

Step-by-step explanation:

1/4×3(8a-5b-4)-(4a+1)+4b

Simplify:

-4a-1+4b+1/4×3×8a-1/4×3×5b-1/4×3×4

=1/4xax24-4a-1/4bx15+4b-1/4×12-1

=1ax24/4 -4a - 1bx15/4 +4b -1×12/4 -1

=ax24/4 -4a -bx15/4 + 4b -12/4 -1

= -4a + 24a/4 + 4b - 15b/4 -1 -3

= -4a + 6a + 4b - 15b/4 - 4

= 2a + 4b - 15b/4 - 4

= 8a + 16b - 15b - 16 / 4

= (8a + b - 16) / 4

= 8a + b - 16 / 4

I hope this helps you

Answer:

see below

Step-by-step explanation:

We know that the center is (0,0) and the radius is |3 - 0| = 3.

Standard form of a circle: (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. Plugging in h = 0, k = 0 and r = 3 gives us x² + y² = 9.

Answer:

See below.

Step-by-step explanation:

The equation for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h,k) is the center and r is the radius.

From the graph, we can see that (0,0) is the center.

Thus, h=0 and k=0:

[tex]x^2+y^2=r^2[/tex]

From the graph, we can also see that the radius is 3 as (-3,0) and (3,0) are points on the circle.

Thus, r=3, and r^2=9.

The equation is:

[tex]x^2+y^2=9[/tex]

Answer:

The solution to the question is g = 52

Step-by-step explanation:

Here, we want to find the solution to the equation ;

98 + g = 150

Apparently, we want to find the value of g.

To get the value of g, what we simply need is to bring 98 over the equal sign and this gives

g = 150-98

g = 52

Answer: B or how some people say it the second question. EDGE-MATHMATICS 2022

THE ANSWER IS B

step-by-step explanation: it is the second option  because when you find out what number g is (52) you can take 98-98= 0 + g/52 and get 52.

and then the second part of it says 150-98 which is 52! so  your answer is B hope this helps! have a wonderful day!

Answer:

The equation of the tangent is [tex]y=-\frac{8}{15}x+\frac{289}{15}[/tex].

Step-by-step explanation:

Center = (0, 0). Point on the circle = (8, 15).

OP is a radius. The slope of the radius = [tex]\frac{15-0}{8-0}=\frac{15}{8}[/tex].

The tangent is perpendicular to the radius.

So, its slope is = [tex]-\frac{8}{15}[/tex].

The tangent passes through (8, 15).

So, the equation is:

[tex]y-15=-\frac{8}{15}\left(x-8\right)\\y-15=-\frac{8}{15}x+\frac{64}{15}\\y=-\frac{8}{15}x+\frac{289}{15}[/tex]

Learn more: https://brainly.com/question/1594198

Answer:

The 3rd one is correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The attachment will help you with your question:

Answer: 15 sides

Step-by-step explanation: Because the sum of the outer angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equivalent outer angles and therefore 15 vertices and sides to the polygon

Answer: angle is 24 degrees meaning that a regular polygon has more than 6 sides hope this is helpful

Step-by-step explanation:

Answer:

First Option

Step-by-step explanation:

When we graph the expression, we should see that an infinite amount of y-values work. Since the domain comprises of all working x-values, we have (negative infinity, positive infinity) or all real numbers as our range, since we have an infinite amount of y-value outputs.

Answer:

17.5 units

Step-by-step explanation:

a² + b²= c²

9² + 15² = c²

81 + 225 = c²

c² = 306

c = √306

c = 17.5

Answer:

End points of the this segment are (9,1) and (2,3).

Step-by-step explanation:

The given function is

[tex]y=h(x)[/tex]

End points of the this segment are (1,9) and (3,2).

If a function is defined as

[tex]f=\{(a,b),a\in R,b\in R\}[/tex] then

[tex]f^{-1}=\{(b,a),a\in R,b\in R\}[/tex]

It means, we have to interchange x and y-coordinates of the end points.

So, end points of the this segment are (9,1) and (2,3).

Plot these point and join them by a line segment.

The inverse of the function will be a line segment joining the points (9,1) and (2,3). See the graph.

Given information:

The function y=h(x) is a line segment joining the points (1,9) and (3,2).

So, the endpoints of the function y=h(x) can be written as,

[tex]y=h(x)=\{(1,9),(3,2)\}[/tex]

The inverse of a function is simply the opposite relation. In the inverse, the range and domain interchange themselves.

So, the inverse of the given function can be written as,

[tex]y=h^{-1}(x)=\{(9,1),(2,3)\}[/tex]

Refer to the graph of the function for more details.

For more details, refer to the link:

https://brainly.com/question/10300045

Answer:

[tex]c=2\frac{1}{3}[/tex]

Step-by-step explanation:

[tex](-9c)-4=-25\\(-9c)=-21\\9c=21\\c=21/9=2\frac{1}{3}[/tex]

Answer:

95 degrees

Step-by-step explanation:

All triangles have an interior measure of 180 degrees

180-41-44=95

Answer:

95 degrees

Step-by-step explanation:

Answer:

Term to add is (3/8)^2 = 9/64

Step-by-step explanation:

Here, we want to know the value that must be added to make the equation a perfect square.

x^2 - 3/4x = 5

x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5

x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2

= (x-3/8)^2 = 5 + (3/8)^2

So the term to add is (3/8)^2 = 9/64

Answer:

[tex]\dfrac{9}{64}[/tex]

Step-by-step explanation:

Given the equation: [tex]x^2-\frac{3}{4}x=5[/tex]

To make the left hand side of the equation a perfect trinomial, we follow these steps.

Step 1: Divide the coefficient of x by 2.

Coefficient of x [tex]=-\frac{3}{4}[/tex]

[tex]-\frac{3}{4} \div 2 =-\frac{3}{8}[/tex]

Step 2: Square your result from step 1

[tex]\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}[/tex]

Therefore, to make the Left-Hand side a  perfect-square trinomial, we add 9/64.

Answer:

1.5mg

Step-by-step explanation:

From the question, we are told that the HCP prescribed 7.5 mg of PO weekly

The therapeutic dosage is given in the question as 5 - 15 mg/m² weekly.

The child's body surface area is given = 0.6m²

The mg of PO that the nurse should administer in each of the three doses given weekly is calculated as

7.5mg/ 5mg/m²

= 1.5 mg of PO

Answer:

Step-by-step explanation:

= x^2+6x+9-8=0

=x^2+6x+1=0

D=b^2-4ac

D= 36-4

D=32

x=-b±root D/2a

x=-6+4root2/2     ,    x = -6-4root2/2

simplify you get the least form...

hope it helps

Answer: The width is x-6

Step-by-step explanation:

To find the with factor out the area x^2 - 11x + 30

[tex]x^{2}[/tex] - 11x +30  to factor it find two numbers that multiply to get 30 and add up to get -11 . And that two numbers are -6 and -5 .

[tex]x^{2}[/tex] - 5x - 6x + 30   now group them

([tex]x^{2}[/tex] - 5x) (-6x+ 30)   factor them out.

x(x - 5) - 6(x -5)   Factor x-5 out  

(x-5)(x-6)  since the length is x-5 then the width is x-6.

Answer:

A

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 3, 5 ] , thus

f(b) = f(5) = - 26 ← value of y for x = 5 from table

f(a) = f(3) = - 10 ← value of y for x = 3 from table

average rate of change = [tex]\frac{-26-(-10)}{5-3}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8 → A

Answer: The missing length is 16/3

Step-by-step explanation:

First, you have to find the proportional value between the two lengths on the first figure and the two lengths on the second figure.

The first figure’s lengths are 8 and 9, so the shorter length is 8/9 of the longer length.

Now apply the same proportional value to the second figure.

6 * 8/9 = 48/9

48/9 = 16/3

Answer:

[tex]a^3+3a^2b+3ab^2+b^3[/tex]

Step-by-step explanation:

If have [tex](a+b)^3[/tex], we can solve this as:

[tex](a+b)(a+b)(a+b)[/tex]

So, applying distribution with the first two factors and simplifying, we get:

[tex](a^2+ba+ab+b^2)(a+b)\\(a^2+2ab+b^2)(a+b)[/tex]

Then, multiplying both expressions and simplifying again, we get:

[tex]a^3+a^2b+2a^2b+2ab^2+b^2a+b^3\\a^3+3a^2b+3ab^2+b^3[/tex]

Answer:

5.83units

Step-by-step explanation:

from Pythagoras theorem;

a^2=b^2+c^2

where a is the hypotenuse,b is the opposite and c is the adjacent

b=3 and c=5

a^2=3^2+5^2

a^2=9+25

a^2=34

find the square root of both sides,

√a^2=√34

a=5.83units

Answer:5.83

Step-by-step explanation:

Answer:

B and  C

Step-by-step explanation:

Since all of it's sides are unequal, it is a scalene triangle.

It has 1 obtuse angle, so it is an obtuse angled triangle.

Answer:

there are now 3.5 kilograms of grapes in the basket (the mystery number is 1.5)

Let us suppose that the number of grapes in the box is x and the number of grapes in the basket is y.

It means that the weight of the grapes in the box is x kg and that of basket is y kg.

It has been given that the box had twice as many grapes as a basket. Therefore, we have

Now when we add 2 kg to the basket then the weight of the basket is y+2 and the weight of box will remain same.

Now, we have been given that after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. Hence, we have

Substituting the value x=2y in the equation, we get

Therefore, the basket contains 1.5 kilograms of grapes.

Answer:

42=7(x+5)

42=7x+35

42-35=7x

7=7x

X=7/7=1

Answer:

1) Qs= 24.4 cm

2) Perimeter= 72.8 m

Step-by-step explanation:

1).let qs= qos

Op is the height of the the triangle

Op= ,6.8cm

Angle ops = 180-(90+50)

Angle ops = 180-140

Angle ops = 40

Os/sin ops= op/sin pso

Os/sin 40= 6.8/sin 50

Os = sin 40(6.8)/sin50

Os= 0.6428(6.8)/0.7660

Os= 5.71

Angle oqp = 180-(90+70)

Angle oqp = 180-160.

Angle oqp = 20

Oq/sin qpo = op/sin oqp

Oq/sin 70=6.8/sin 20

Oq= sin70(6.8)/sin20

Oq= 0.9397(6.8)/0.3420

Oq= 18.68

Qs= os +oq

Qs= 5.71+18.68

Qs= 24.39

Qs= 24.4 cm

2). The other angle of the triangle

=180-90-53

= 37

Sin90 = 1

Let the length and breadth be x and y

X /sin 53 = 26

X= 26(sin53)

X= 26(0.7986)

X= 20.7636

Y/sin 37 = 26

Y= 26(0.6018)

Y= 15.6468

Perimeter= 2(x+y).

Perimeter= 2( 20.7636+15.6468)

Perimeter= 2(36.4104)

Perimeter= 72.8208 m

Perimeter= 72.8 m

Answer:

The correct option is;

Marcel did not put the first and second term in the same order

Step-by-step explanation:

From the multiplication table the equivalent ratios of two numbers can be found given that the two numbers have the same factors which is true if the numbers are on the same column in the multiplication table

Therefore, having the numbers ratio presented in the form 72:24 which are on the row labelled 3 and the row labelled 9, we have that the 72 is on row 9 while the 24 is on row 3, for which on the second column, we have 6:18

However the ordering of the ratio gives the value on the 9th column first before the value on the 3rd column, so that the correct result should be 18:6

The error was that Marcel did not put the first and second term in the same order.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

Is this equality true ?

sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x

1. let 's estimate the left part of the equation

[tex]sec(x)csc(x)(tan(x) + cot(x)) =\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin(x)}{cos(x)}+\dfrac{cos(x)}{sin(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin^2(x)+cos^2(x)}{sin(x)cos(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{1}{sin(x)cos(x)})\\\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]

1. let 's estimate the right part of the equation

[tex]2+tan^2(x) + cot^2(x)=2+\dfrac{sin^2(x)}{cos^2(x)}+\dfrac{cos^2(x)}{sin^2(x)}\\\\=\dfrac{2cos^2(x)sin^2(x)+cos^4(x)+sin^4(x)}{cos^2(x)sin^2(x)}\\\\=\dfrac{(cos^2(x)+sin^2(x))^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]

This is the same expression

So

sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x

hope this helps

Answer:

  A.  All real numbers

Step-by-step explanation:

We assume that the "linear parent function" is ...

  y = x.

Its range is "all real numbers."

Answer:

all real numbers

Step-by-step explanation:

AP-EX

Answer:

k = 50

Step-by-step explanation:

The scale 1 cm represents 50m

It means that 1 cm length of pictorial representation of any obejct  is equivalent to 50m in reality.

In scale terms it can be represented in ratio form of a:b

where

a is the length of picture and b is actual length

here length of pictorial representation is 1 cm

and 50m is actual length

thus scale will be  1:50

But is given that The scale 1 cm represents 50m can be written in the form 1:k.

1:50 is same as 1:k

thus

1:50 = 1:k

we know that in ratio

if a:b = c:d

then

a= c  and b = d

Thus,

k = 50 Answer