How do I solve a system of equations using substitution?

Answer:

[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex]

Step-by-step explanation:

The given function is

[tex]y=\cos(x-\frac{\pi}{2})[/tex]

To find the inverse of this function, we interchange x and y.

[tex]x=\cos(y-\frac{\pi}{2})[/tex]

Take the inverse cosine of both sides to obtain;

[tex]\cos^{-1} x=y-\frac{\pi}{2}[/tex]

[tex]\cos^{-1} x+\frac{\pi}{2}=y[/tex]

Therefore the inverse of the given cosine function is;

[tex]f^{-1}(x)=\cos^{-1} x+\frac{\pi}{2}[/tex] where [tex]-1\le x\le 1[/tex]

Answer:

the answer is B

y=tanx- pie/2

Answer:

y = 5x+2   ,    y=x-6

Step-by-step explanation:

just by looking at the table you can see for the first one 5x + 2 satisfies the table, and x-6 satisfies the right table.

for the first table the equation is:

[tex]x(5) + 2 = y[/tex]

and for the second it's:

[tex]x - 6 = y[/tex]

20^2+21^2=29^2 can be used to determine if the triangle is a right triangle

Answer:

Step-by-step explanation:

The two smaller line lengths are squared separately and added. The square of the third line is noted. If squares of the two small ones equal the square of the largest one, you are working with a right angle triangle.

The one that puts into a formula what is stated above is B. D is close, but the longest line must be by itself.

Answer:

B) 3.5  ^_^

Step-by-step explanation:

Answer:

[tex]x^{\frac{5}{12} }[/tex]

Step-by-step explanation:

In the question given we use the law of exponents;

[tex](a^{b})^{c} = a^{bc}[/tex]

If a base a is raised to a power b and the entire expression raised to a power c, the resulting expression is simply equal to the base a raised to the product of the two exponents b and c, that is bc.

In the case given,

a = x

b = 5/8

c = 2/3

To simplify the expression we simply multiply b and c;

bc = 5/8 * 2/3

     = 5/12

The simplified expression is thus;

[tex]x^{\frac{5}{12} }[/tex]

Answer:

The correct answer is ((x⁵/⁸)²/³) = x⁵/¹²

Step-by-step explanation:

Points to remember:-

Identity

(xᵃ)ᵇ = xᵃᵇ

Here it is given that, ((x⁵/⁸)²/³)

To find the value of ((x⁵/⁸)²/³)

(5/8) * (2/3) =  (5 * 2) /(8 * 3) = 10/24 = 5/12

By using identity (xᵃ)ᵇ = xᵃᵇ we can write,

((x⁵/⁸)²/³) = x⁽⁵/⁸⁾ˣ⁽²/³⁾

= x⁵/¹²    

Therefore the correct answer is ((x⁵/⁸)²/³) = x⁵/¹²

the answer would be 4 5/12 pounds

The total weight of the two boxes will be 4 and 5/12 pounds.

Algebra is the study of mathematical symbols, and the rule is the manipulation of those symbols.

Tim mails two boxes of cookies to friends. One box weighs 1 and 3/4 pounds, and the other weighs 2 and 2/3 pounds.

Then the total weight of the two boxes will be

Total weight = 1 + 3/4 + 2 + 2/3

Total weight = 3 + 17/12

Total weight = 3 + 1 + 5/12

Total weight = 4 + 5/12

The total weight of the two boxes will be 4 and 5/12 pounds.

More about the Algebra link is given below.

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Answer:

B because there is a dot in front of the 25 which is also known as a decimal point.

For this case we have that by definition, a decimal number is a number that is composed of a whole part, which can be zero, and by another lower than the unit, separated from the whole part by a point.

Examples:

0.05

1.76

According to the options given, we have:

A. [tex]\frac {1} {2},[/tex] it is a fraction

B. 23, is a whole number

C.[tex]\frac {33} {10}[/tex], it is a fraction

D. 0.25, is a decimal number.

Answer:

Option D

Answer:

The radius is [tex]r=5\ cm[/tex]

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m<C =(1/2)[arc\ AB][/tex]

[tex]m<C =90\°[/tex]

substitute

[tex]90\°=(1/2)[arc\ AB][/tex]

[tex]arc\ AB=180\°[/tex]

That means----> The length side AB of the inscribed triangle is a diameter of the circle

Applying Pythagoras Theorem

Calculate the length side AB

[tex]AB^{2}=AC^{2}+BC^{2}[/tex]

[tex]AB^{2}=8^{2}+6^{2}[/tex]

[tex]AB^{2}=100[/tex]

[tex]AB=10\ cm[/tex] -----> is the diameter

Find the radius

[tex]r=10/2=5\ cm[/tex] -----> the radius is half the diameter

Answer:

x = 3 + i+√5

x = 3 + i-√5

OR

x= 4 - √6

x= 4 +√6

Step-by-step explanation:

(x - 3)² +6=1​

(x - 3)² + 6 = 1

        -6   -6

sq root > (x - 3)²      = -5

x-3 = i±√5     (i because neg. number)

x = 3 + i±√5

since its ±

two possible answers

x = 3 + i+√5

x = 3 + i-√5

Or

(x - 3)² +6=1​

(x-3)+  √6= √ 1

x-3 = 1 - (±)  √6

x= 4 - (±)  √6

Answers

x= 4 - √6

x= 4 +√6

Answer: 254.47

Step-by-step explanation: A=3.14*r to the power of two=3.14*9 squared=254.47

3.14*9^2=254.34 this would be the answer

Answer:

A) 14 cm^2

Step-by-step explanation:

Given

Rhombus ABCD

let the given length be diagonal 1, a= 8cm

diagonal 2,b= 3.5cm

Area of ABCD=?

Area of rhombus= ab/2

Putting the values in above :

Area of ABCD= 8(3.5)/2

                       =28/2

                       =14 !

Answer:

14cm^2

Step-by-step explanation:

Answer:

length=16, width=4

Step-by-step explanation:

Use l as length and make an equation:

64 = x*(x-12)

Solve using quadratics, x=16.

Subtract 12 and get 4.

Answer:

[tex]m<FEH=86\°[/tex]

Step-by-step explanation:

we know that

The inscribed angle measures half that of the arc comprising

step 1

Find the measure of arc EF

[tex]m<FHE=\frac{1}{2}(arc\ EF)[/tex]

we have

[tex]m<FHE=45\°[/tex]

substitute

[tex]45\°=\frac{1}{2}(arc\ EF)[/tex]

[tex]arc\ EF=90\°[/tex]

step 2

Find the measure of arc EH

[tex]m<EGH=\frac{1}{2}(arc\ EH)[/tex]

we have

[tex]m<EGH=49\°[/tex]

substitute

[tex]49\°=\frac{1}{2}(arc\ EH)[/tex]

[tex]arc\ EH=98\°[/tex]

step 3

Find the measure of arc FGH

[tex]arc\ FGH=360\°-(arc\ EH+arc\ EF)[/tex]

substitute the values

[tex]arc\ FGH=360\°-(98\°+90\°)[/tex]

[tex]arc\ FGH=172\°[/tex]

step 4

Find the measure of angle FEH

[tex]m<FEH=\frac{1}{2}(arc\ FGH)[/tex]

we have

[tex]arc\ FGH=172\°[/tex]

substitute

[tex]m<FEH=\frac{1}{2}(172\°)=86\°[/tex]

Answer:

[tex]\large\boxed{B.\ 4x^2-41x+105}[/tex]

Step-by-step explanation:

[tex]f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105[/tex]

Answer: Option B

[tex]f(g(x)) = 4x^2 -41x + 105[/tex]

Step-by-step explanation:

We have 2 functions

[tex]f(x) = 4x -\sqrt{x}[/tex]

[tex]g(x) = (x-5)^2[/tex]

We must find [tex]f(g(x))[/tex]

To find this composite function enter the function g(x) within the function f(x) as follows

[tex]f(g(x)) = 4(g(x)) -\sqrt{(g(x))}[/tex]

[tex]f(g(x)) = 4(x-5)^2 -\sqrt{(x-5)^2}[/tex]

By definition [tex]\sqrt{a^2} = |a|[/tex]

So

[tex]f(g(x)) = 4(x-5)^2 -|x-5|[/tex]

Since x is greater than 5 then the expression [tex](x-5)> 0[/tex].

Therefore we can eliminate the absolute value bars

[tex]f(g(x)) = 4(x-5)^2 -(x-5)[/tex]

[tex]f(g(x)) = 4(x^2 -10x + 25) -(x-5)[/tex]

[tex]f(g(x)) = 4x^2 -40x + 100 -x+5[/tex]

[tex]f(g(x)) = 4x^2 -41x + 105[/tex]

The answer is -2. X is -2.

I and II

When a graph has a solid line, solutions lie ON that line, whereas if it was a dotted line, solutions lie only on the shaded side of that line, not the line itself.

Answer:

y + 4 = a(x - 7)^2

Step-by-step explanation:

The standard vertex form of a parabola with vertex at (h, k) is

y - k = a(x - h)^2

and if we start with the simplest case, y = a(x)^2 and translate its graph 7 units to the right and 4 units down, we get   y - {-4] = a(x - 7)^2, or

y + 4 = a(x - 7)^2

The answer is y + 4 = a(x - 7)^2.

The standard vertex form of a parabola with vertex at (h, k) is

y - k = a(x - h)^2

And if we start with the simplest case,

y = a(x)^2 and

translate it Into 7 units to the right and 4 units down,

we get  

y - {-4] = a(x - 7)^2

then we get the equation is y + 4 = a(x - 7)^2.

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265,000

Hope this helps!

Because the number in the ten thousands place is over 4, it’s going to turn the 2 in the hundred thousands place into a 3, making the answer 300,000

Answer:

y can be any real number

Step-by-step explanation:

8(y + 7) > 8y + 3

Distribute

8y+56 > 8y+3

Subtract 8y from each side

8y-8y +56 > 8y-8y +3

56 > 3

This is always true so the inequality is always true

y can be any real number

Answer:

135.39

Step-by-step explanation:

The solid consist of 4 triangles and a 5 rectangles.

Formula to calculate area of triangle is

1/2 (height) (base)

Formula to calculate area of rectangle is

length x width

so

Total surface area of the composite solid is

2( 4(4) + 6(4) + 1/2(√13)(4) + 1/2(2√2)(6) ) + 6(4)

111.39 + 24

135.39

Answer:

Total area = 135 .39 square yard

Step-by-step explanation:

Given : composite figure.

To find : Find the surface area of the composite solid. Round the answer to the nearest hundredth.

Solution : We have given a composite figure with rectangle base and four triangles .

Base of two triangle  =  4 yd .

Height of two triangle = √13 yd .

Base of other two triangle  =  6 yd .

Height of other two triangle = 2√2 yd .

Area of rectangle  = length * width .

Area of rectangle  = 6 *4

Area of rectangle  = 24 square yard .

Area of all rectangle = 3 *24 = 72 square yard

Area of two square = 2( 4*4) = 32 square yard.

Area of triangle  = [tex]\frac{1}{2} base * height[/tex].

Area of triangle= [tex]\frac{1}{2} 4 *√13 [/tex].

Area of triangle = 2√13 .

Area of two triangle  = 2 * 2√13 .

Area of two triangle  = 4√13 square yard.

Area of other triangle  = [tex]\frac{1}{2} 6 * 2√2 [/tex].

Area of other triangle  = 3* 2√2

Area of other triangle  = 6√2.

Area of other two triangle  = 2 *6√2.

Area of other two triangle  = 12√2 square yard.

Total area = Area of  3 rectangle + Area of two triangle + Area of other two triangle + area of square

Total area =  72 + 4√13 +  12√2 + 32

Total area = 135 .39 square yard.

Therefore, Total area = 135 .39 square yard.

Answer:

Step-by-step explanation:

[tex]30\cdot\dfrac{1}{6}=\dfrac{30}{6}=5[/tex]

Answer:

5 if its a dice.

Step-by-step explanation:

On a dice, 5. The probability of it landing on 6 is 1/6

Answer:

C. 1

Step-by-step explanation:

The line containing segment BC has a slope of 1 and a y-intercept of 5 (at point B). Thus, its equation is ...

y = x + 5

For the value of x = -4, the value of y is ...

y = -4 +5 = 1

Point (-4, 1) is on the line containing segment BC.

Answer:

C. 1

Step-by-step explanation:

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

The side adjacent to W is 4.  The side opposite of W is 3.  The hypotenuse is 5.

Therefore:

Sine = 3 / 5

Cosine = 4 / 5

Tangent = 3 / 4

[tex] {x}^{2} + {y}^{2} - 10x - 6y + 18 = 0[/tex]

Answer:

[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle

Step-by-step explanation:

The circle below is centered at the point (5,3) and has a radius of length 4

To find the center  form of equation, we use formula

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

where (h,k) is the center and 'r' is the radius of the circle

given center is (5,3)

h=5  and k =3

radius r= 4, plug in all the values in the equation

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

[tex](x-5)^2 + (y-3)^2= 4^2[/tex]

[tex](x-5)^2 + (y-3)^2= 16[/tex] is the equation of a circle

Comparing the periods of the given cosine functions indicates that functions A) and C) both have the greatest period of π, which is longer than the period of function B), π/2.

To compare the periods of the given functions, let's first understand what the general form of a cosine function tells us about its period.

The general form is y = A cos(Bx + C), where A is the amplitude, B affects the period, and C is the phase shift.

The period of such a function is given by 2π / |B|.

For function A) y = 3cos(2x+1), B = 2, thus its period is π.

For function B) y=5cos(4x +8), B = 4, yielding a period of π/2.

Lastly, for function C) y=cos(2x+4) (4.3), assuming the (4.3) is an unrelated notation and focusing on the given cos component with B = 2, its period is also π.

The function with the greatest period among A, B, and C is thus A) and C), both having the same period of π, which is greater than the period of B).

Answer: Well for example two roads that are meeting with each other and they form a right angle,

Step-by-step explanation:

Answer:

1.  A Christian cross.

2. Roads that meet at intersections

3. Hospital crosses.

Step-by-step explanation:

Perpendicular lines are lines that touch each other, or are slanted in a way that they will eventually touch each other. The examples I used are all crosses, which are two line that cross.

The formula for finding the volume of a rectangular prism (the cargo area of the truck is the shape of a rectangle in 3D; a rectangular prism) is V = (l)(w)(h); where l = length, w = width, and h = height.

First, substitute the known values into the equation:

l = 8.5

w = 6

h = 10.5

V = (8.5)(6)(10.5)

(Note: .5 = 1/2)

Now, all we need to do is simplify:

V = 535.5 ft³ OR 535 1/2 ft³

(Note: ft³ is the condensed form of cubic feet)

You can pick whichever form your test directs you to use. They are both the same value though.

Hope this helps!

The volume of the cargo area of the truck is 519.75 cubic feet.

The volume of the cargo area of the truck can be calculated by multiplying its length, width, and height. Given the dimensions in feet are:

Length = 8 1/2 feet = 8.5 feet = 8 + 1/2 feet

Width = 6 feet

Height = 10 1/2 feet = 10.5 feet = 10 + 1/2 feet

To find the volume, we convert the mixed numbers to improper fractions and then multiply:

Length in fractions = 8 + 1/2 = 17/2 feet

Width in fractions = 6 = 6 * 2/2 = 12/2 feet

Height in fractions = 10 + 1/2 = 21/2 feet

Now, multiply the dimensions to find the volume:

Volume = Length * Width * Height

Volume = (17/2 feet) * (12/2 feet) * (21/2 feet)

Volume = (17 * 12 * 21) / (2 * 2 * 2) cubic feet

Volume = 4158 / 8 cubic feet

Simplifying the fraction, we get:

Volume = 519.75 cubic feet

The basketball team sold a total of 23 items (t-shirts and hats) and made $246. By setting up and solving a system of equations, it was determined that they sold 15 t-shirts and 8 hats.

To determine the number of t-shirts and hats sold by a basketball team for a fundraiser, given that they sold a total of 23 items and made a profit of $246, with a profit of $10 per t-shirt and $12 per hat sold. To solve this problem, we can set up a system of linear equations and solve for the two variables representing the number of t-shirts (T) and the number of hats (H).

Let T represent the number of t-shirts and H represent the number of hats.

We know that T + H = 23 (since 23 items were sold in total).

We also know that the profit from t-shirts is $10 per t-shirt, and the profit from hats is $12 per hat. Therefore, 10T + 12H = $246 (total profit).

We can now set up the equations:
T + H = 23
10T + 12H = $246

From the first equation, we can express H in terms of T: H = 23 - T.

Substitute H = 23 - T into the second equation:
10T + 12(23 - T) = $246

Simplify and solve for T:
10T + 276 - 12T = $246
-2T + 276 = $246
-2T = $246 - 276
-2T = -$30
T = 15 (number of t-shirts sold)

Now, we can find the number of hats by substituting T back into H = 23 - T. Since T is 15, H = 23 - 15 = 8 (number of hats sold).

Therefore, the basketball team sold 15 t-shirts and 8 hats.

Answer:

I am pretty sure the answer is square