Type the correct answer in the box. If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is

Given -

△ABC ∼ △DEF

To find -

the value of x.

Solution -

If △ABC ∼ △DEF then,

[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]

➡ [tex]x=\frac{\cancel{12}^4}{\cancel{3}_1}\times2[/tex]

➡ [tex]x=4\times2[/tex]

➡ [tex]x=8[/tex]

Hence, the value of x is equal to 8.

Answer:

Step-by-step explanation            

Answer:

5/9 = 25/45

Step-by-step explanation

multiply 5/9 by 5/5 this will turn it into 25/45

5x5=25

5x9=45

Answer:

the large boxes weigh 40 pounds and the smaller boxes weigh 30 pounds

Step-by-step explanation:

define variables:

b is the weight of large boxes and s is the weight of small boxes. you can create two equations to represent what you know:

b + s = 70 (the weight of one large box and one small box is 70 pounds)

60b+ 55s = 4050 (the total weight of the 60 large boxes and the 55 small boxes is 4050)

then by making one of the equations equal to a variable, you can use substitution to solve.

s = 70 - b

so 60b + 55s = 4050 now becomes:

60b + 55(70 - b) = 4050, and next you solve for b

60b + 3850 - 55b = 4050

5b = 200

b = 40.

now you know that the large boxes weigh 40 pounds. to solve for the small box weight, you plug in b in either equation. i am going to choose the first once since it's fewer steps

b + s = 70 -> 40 + s = 70

s = 30

and now you know that the smaller boxes weigh 30 pounds.

Answer:

x = [12]

Step-by-step explanation:

=> [tex] \frac{x}{6} = \frac{6}{3} [/tex]

=> x = 2 × 6

=> x = 12

Answer:

B

Step-by-step explanation:

The height of 3 cut the base in half and perpendicular to the base, so

[tex]x = \sqrt{(4/2)^2 + 3^2}= \sqrt{13|[/tex]

That is B

Answer:

f(x)= -5x+1 and g(x)=x^3,

(g • f)(0)=  g(f(0))

but f(0) = -5 (0)+1 = 1

(g • f)(0)= g(1) = 1^3 = 1

Step-by-step explanation:

hope this helps

Answer:

-1

Step-by-step explanation:

f(x) = 5x - 1

g(x) = x³

f(0) = 5(0) - 1

= -1

g(-1) = (-1)³

= -1

Answer:

Slope = -1/5

y-intercept = 3/4

Step-by-step explanation:

Equation of Straight Line in the Form y=mx+c

where m is the Slope and c is the y-intercept.

Answer:

 Slope = -0.400/2.000 = -0.200

 x-intercept = 15/4 = 3.75000

 y-intercept = 15/20 = 3/4 = 0.75000

Step-by-step explanation:

* BE AWARE, THIS ANSWER IS NOT TO BE PLAGERIZED AS IT IS CONSIDERED CHEATING IF THIS IS A TEST OR HOMEWORK QUESTION, MOST LIKELY IT IS* - Purpose is to help understanding of the concept.

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(3/4-1/5*x)=0

STEP 1:

simplify 1/5

Equation at the end of step 1:

y -(3/4-(1/5• x))  = 0

Step 2:

Simplify 3/4

Equation at the end of step 2:

y-)(3/4-x/5)=0

Step 3:

Calculating the Least Common Multiple :

ind the Least Common Multiple

     The left denominator is :       4

     The right denominator is :       5

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

2 2 0 2

5 0 1 1

Product of all

Prime Factors  4 5 20

     Least Common Multiple:

     20

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 5

  Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.   L. Mult. • L. Num.      3 • 5

  ——————————————————  =   —————

        L.C.M              20  

  R. Mult. • R. Num.      x • 4

  ——————————————————  =   —————

        L.C.M              20  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3 • 5 - (x • 4)     15 - 4x

———————————————  =  ———————

      20              20  

Equation at the end of step

3

:

      (15 - 4x)

 y -  —————————  = 0

         20    

STEP

4

:

Rewriting the whole as an Equivalent Fraction :

4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  20  as the denominator :

         y     y • 20

    y =  —  =  ——————

         1       20  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

y • 20 - ((15-4x))     20y + 4x - 15

——————————————————  =  —————————————

        20                  20      

Equation at the end of step

4

:

 20y + 4x - 15

 —————————————  = 0

      20      

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 20y+4x-15

 ————————— • 20 = 0 • 20

    20    

Now, on the left hand side, the  20  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  20y+4x-15  = 0

Equation of a Straight Line

5.2     Solve   20y+4x-15  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  20y+4x-15  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3/4 so this line "cuts" the y axis at y= 0.75000

 y-intercept = 15/20 = 3/4  =  0.75000

Calculate the X-Intercept :

When y = 0 the value of x is 15/4 Our line therefore "cuts" the x axis at x= 3.75000

 x-intercept = 15/4  =  3.75000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.750 and for x=2.000, the value of y is 0.350. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.350 - 0.750 = -0.400 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -0.400/2.000 = -0.200

Geometric figure: Straight Line

 Slope = -0.400/2.000 = -0.200

 x-intercept = 15/4 = 3.75000

 y-intercept = 15/20 = 3/4 = 0.75000

Answer:

[tex]\tt x=14[/tex]

Step-by-step explanation:

[tex]\tt 6x+6=90[/tex]

[tex]\tt 6x+6-6=90-6[/tex]

[tex]\tt 6x=84[/tex]

[tex]\tt \cfrac{6x}{6} =\cfrac{84}{6}[/tex]

[tex]\tt x=14[/tex]

~

Answer:

x = 14

Step-by-step explanation:

The diagonals make a perpendicular bisector at the center.

Hence, the central angle is 90°.

The value of c in the missing triangle is 39

The side c can be found using Pythagoras theorem.

Therefore,

c² = a² + b²

c² = 36² + 15²

c² = 1296 + 225

c = √1521

c = 39

learn more on right triangle here: https://brainly.com/question/278669

The sum of the square of the hypotenuse is equal to the sum of the square of the other sides.The length of the hypotenuse of the triangle is l = √14

The sum of the square of the hypotenuse is equal to the sum of the square of the other sides.

Given that one of the sides is √7, hence;

l^2 = (√7)^2 + (√7)^2
l^2 = 7 + 7
l^2 = 14
l = √14

Hence the length of the hypotenuse of the triangle is l = √14

Learn more on pythagoras theorem here: https://brainly.com/question/343682

Answer:

A polygon that has eight sides is called a Octagon

Step-by-step explanation:

Answer:

an octagon

Step-by-step explanation:

'oct' means 8 and 'gon' means sides

Hope this helps!

Answer: 4/6 = 2/32/3 = 2/3

Step-by-step explanation: hope this help

Answer:

No

Step-by-step explanation:

1 yard = 3 feet, so 3 yards = 9 feet

Hope this helps :)

Answer:

B

Step-by-step explanation:

logₓ 7 = 3

x³ = 7

Take cube root both sides

[tex]x= \sqrt[3]{7}[/tex]

Step-by-step explanation:

154 is my answer thank you

Answer:

±4i, ±3

p(x) = A(x - 4i)(x + 4i)(x - 3)(x + 3), with A = 1.

Step-by-step explanation:

±4i, ±3

p(x) = A(x - 4i)(x + 4i)(x - 3)(x + 3), with A = 1.

Answer:

Option A

Step-by-step explanation:

To find the angles, you have to subtract the opposing angle from 180

180 - 85 = 95

180 - 70 = 110

Angle 1: 95

Angle 2: 110

Answer:

[tex]y=-\frac{1}{5} x+2[/tex]

Step-by-step explanation:

f(x) = [tex]\frac{5}{x}[/tex]  ⇒ f(x) = [tex]5x^{-1[/tex]

Use the power rule to diferentiate:

f'(x) = [tex]-5x^{-2[/tex]

Plug in the value to differentiate at:

f'(5) = [tex]-5(5)^{-2[/tex] = [tex]-\frac{1}{5}[/tex] = [tex]m[/tex]

Plug into the equation of the tangent line:

[tex]y-f(5)=f'(5)(x-5)[/tex]

[tex]y=f'(5)(x-5)+f(5)[/tex]

[tex]y=-\frac{1}{5} (x-5)+1[/tex]

[tex]y=-\frac{1}{5} x+2[/tex]

Answer:

7

Step-by-step explanation:

6 + 7x = 55

7x = 55 - 6

7x = 49

x = 49/7

therefore x = 7

Answer:

Not sure if this is right but it might be something like

350,000-4%+1671m

or

3500,000-4%y/1671m

Step-by-step explanation:

The numbers we know are 350,000 4% and 1671 per month

350,000 is the full mortgage

4% is the APR or annual percentage rate like interest

and we know the monthly for the mortgage is 1671 per month

Step-by-step explanation:

just ratio and need to identify which lines are pairs.

Answer:

Hope this helps you

Step-by-step explanation:

Mean= [tex]\frac{404}{75} = 5.386666666666667[/tex]

Therefore, the mean of the given distribution =5.39 or 3.4

If you did not understand anything you can ask in the comments

Answer:

ok so use the degrees

Step-by-step explanation:

x should be 8 + 17 and then multiply the 110 degrees by 8 + 17

Answer:

x = 6

The marked angle is 110°

Step-by-step explanation:

See how there are 8 angles in this type of image. The angles either are EQUAL, or they ADD UP TO 180°. It's just two numbers for the degrees of these angles. Four of them are the same and the other four are the same.

In your question the 8 + 17x = 110°

Solve.

Subtract 8.

17x = 102

Divide by 17.

x = 6

If your question says find the measure of the angle it is 110°, if you are to find x, then x = 6.

Jfyi, four of these angles are 110°. The other four are 70°.

[tex]\boxed{\tt \pink{Given:}}[/tex]

[tex]\red\star[/tex]Diameter of base of a cylinder = 20 cm.

[tex]\red\star[/tex]Height of cylinder = 5cm.

[tex]\\\\[/tex]

[tex]\boxed{\tt \pink{To~Find:}}[/tex]

[tex]\red\star[/tex]Volume of Cylinder.

[tex]\\\\[/tex]

[tex]\boxed{\tt \pink{Solution}}[/tex]

To find volume of Cylinder first we should know radius of Cylinder. We can get radius by diameter using this formula:-

[tex]\boxed{\rm Diameter = 2 radius}[/tex]

[tex]\\\\[/tex]

[tex]\hookrightarrow\sf Diameter = 2 radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow\sf 20= 2 radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow\sf \dfrac{20}{2}= radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow\sf \dfrac{2\times10}{2}= radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow \sf \dfrac{\cancel2\times10}{\cancel2}= radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow \sf \dfrac{1\times10}{1}= radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow \sf 10= radius[/tex]

[tex]\\[/tex]

[tex]\hookrightarrow \bf radius = \pmb{\blue{10 cm}}[/tex]

[tex]\\\\[/tex]

Now Finally Let's find volume of Cylinder.

we know:-

[tex]\boxed{\rm Volume ~ of ~ Cylinder = \pi radius^2 \times height}[/tex]

[tex]\\\\[/tex]

So:-

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi radius^2\times height\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi (10)^2\times 5\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi 10\times10\times5\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi 100\times5\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \pi\times 500\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \dfrac{22}{7}\times 500\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\sf Volume ~of ~Cylinder = \dfrac{11000}{7}\\[/tex]

[tex]\\\\[/tex]

[tex]\dashrightarrow\bf Volume ~of ~Cylinder =\pmb{\blue{1,571.4~cm}}\\[/tex]

[tex]\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc}\small\underline{\sf{\pmb{ \gray{More \: Formulae}}}} \\ \\ \bigstar \: \bold{CSA_{(cylinder)} = 2\pi \: rh}\\ \\\bigstar \: \bold{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bold{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bold{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar\: \bold{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bold{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bold{Volume_{(cube)} ={(side)}^{3} }\\ \\ \bigstar \: \bold{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bold{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\\bigstar \: \bold{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bold{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bold{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered}[/tex]

Answer:

%70.83

Step-by-step explanation:

91.66 + 50 = 141.66

141.66÷2=70.83

#A

How far means measurement of perimeter or length not volume

#B

Yes

#C

Tall means length not volume

#D

Here she needs area not volume

Answer:

19 is equal or less than X

Step-by-step explanation:

I know this because wherever the arrow goes, that’s equal to X. We also know that if the dot is colored, that means it equals: 19 is equal or less than X.

Answer:

Range is [tex]\{y|y\neq 1\}[/tex]

Step-by-step explanation:

[tex]f(x)=x+1\\g(x)=\frac{1}{x}\\ \\(f\circ g)(x)=f(g(x))=f(\frac{1}{x})=\frac{1}{x}+1[/tex]

Thus, the range of the composite function is [tex]\{y|y\neq 1\}[/tex], indicated by the horizontal asymptote.

Using the combination formula, it is found that 84 different groups of 6 people are possible from the 9 remaining friends.

The order in which the friends are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 6 friends are chosen from a set of 9, hence:

[tex]C_{9,6} = \frac{9!}{6!3!} = 84[/tex]

84 different groups of 6 people are possible from the 9 remaining friends.

More can be learned about the combination formula at https://brainly.com/question/25821700

Answer:

this wrong

Step-by-step explanation: