Which expression is equivalent to (7+4i) +(8+I)?

When A, B, and C are collinear points and B is between A and C, value of AB(x) is 6. Therefore, option A is the correct answer.

If we know that points A, B, and C are collinear, with B between A and C, then we can use the given distances AB and BC to find the total distance AC.

Since AB is given as x, and BC as x+2, and we know AC is the sum of AB and BC< which is equal to 14, we can set up the equation:

AB + BC = AC

x + (x+2) = 14

Combining like terms gives us:

2x + 2 = 14

Subtracting 2 from both sides of the equation, we have:

2x = 12

Dividing both sides by 2 to isolate x:

x = 6

Therefore, the length of segment AB, which is x, is 6 units. Option A. 6 is the correct answer.

Answer:

It's the third choice.

Step-by-step explanation:

M < NKM and m < MKL both equal  61 degrees

so KM is a bisector of < NKL.

Answer:

C:ray MK is an angle bisector of angle NKL

Step-by-step explanation:

We have to find the true statement about the diagram

[tex]\angle JKN=58^{\circ}[/tex]

[tex]\angle NKM=61^{\circ}[/tex]

[tex]\angle MKL=61^{\circ}[/tex]

[tex]\angle NKM=\angle MKL=61^{\circ}[/tex]

When a ray is a bisector of any angle then the angles are equal which are made by bisection of the angle.

By using this definition

The ray MK is a bisector of angle NKL because angle NKM and MKL are equal.

Answer:C

Find the GCD (or HCF) of numerator and denominator

GCD of 18 and 20 is 2

Divide both the numerator and denominator by the GCD

18 ÷ 2

-----------

20 ÷ 2

Reduced fraction:

9

----

10

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{What's }\huge\dfrac{18}{20}\huge\text{ simplified?}[/tex]

[tex]\huge\text{Both terms have the GCF}[/tex] [tex]\huge\text{(Greatest Common Factor) of 2}[/tex]

[tex]\huge\text{So, divide both numbers by 2.}[/tex]

[tex]\huge\dfrac{18\div2}{20\div2}[/tex]

[tex]\huge\text{18}\huge\div\huge\text{2 = 9}[/tex]

[tex]\huge\text{9 is the numerator (top \#)}[/tex]

[tex]\huge\text{20}\huge\div\huge\text{2 = 10}[/tex] [tex]\huge\text{10 is the denominator (bottom \#)}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: }\huge\dfrac{9}{10}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

cos 60° = 1/2

Step-by-step explanation:

* Lets explain how to solve the question

- If angle Ф lies in the first quadrant then sin Ф , cos Ф and tan Ф

 are positive values

- The equivalent angle of angle Ф in the second quadrant is 180° - Ф

 and sin Ф is positive but cos Ф and tan Ф are negative

- The equivalent angle of angle Ф in the third quadrant is 180° + Ф

 and tan Ф is positive but cos Ф and sin Ф are negative

- The equivalent angle of angle Ф in the fourth quadrant is 360° - Ф

 and cos Ф is positive but sin Ф and tan Ф are negative

* Lets solve the problem

∵ sin x = √3/2

∵ 90° < x < 180°

∴ ∠ x lies in the second quadrant

∴ m∠ x = 180° - Ф

- Let sin Ф = √3/2

∴ Ф = sin^-1 (√3/2)

∴ Ф = 60°

∵ x = 180° - Ф

∴ x = 180° - 60°

∴ x = 120°

- To find cos(x/2) divide 120° by 2

∵ cos (120°/2) = cos (60°)

∴ cos 60° = 1/2

Answer:

[tex]\tt x^2+3xy+4y^2[/tex]

Step-by-step explanation:

[tex]\tt(x-2y)^2+7xy\\\\=x^2-4xy+4y^2+7xy\\\\=x^2+3xy+4y^2[/tex]

Answer:

[tex] x^2 + 3xy + 4y^2 [/tex]

Step-by-step explanation:

[tex] (x - 2y)^2 + 7xy = [/tex]

[tex] = (x - 2y)(x - 2y) + 7xy [/tex]

[tex] = x^2 -2xy - 2xy + 4y^2 + 7xy [/tex]

[tex] = x^2 + 3xy + 4y^2 [/tex]

Answer:

Step-by-step explanation:

[tex]4x^2+3x=24-x\qquad\text{subtract 24 from both sides}\\\\4x^2+3x-24=-x\qquad\text{add}\ x\ \text{to both sides}\\\\4x^2+4x-24=0\qquad\text{divide both sides by 4}\\\\x^2+x-6=0\\\\x^2+3x-2x-6=0\\\\x(x+3)-2(x+3)=0\\\\(x+3)(x-2)=0\iff x+3=0\ \vee\ x-2=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2[/tex]

The given equation, 4·x² + 3·x = 24 - x, can be simplified and factorized

to give the solution as; -3, 2

The solution to the given equation, 4·x² + 3·x = 24 - x, is the point of

intersection of the parabola, 4·x² + 3·x, and the line, 24 - x

The solution is therefore, found as follows;

4·x² + 3·x = 24 - x

4·x² + 3·x - (24 - x) = 0

4·x² + 4·x - 24 = 0

Dividing by 4, gives;

4·(x² + x - 6) = 0

x² + x - 6 = 0 ÷ 4 = 0

Factorizing, the above quadratic equation, we have;

(x + 3) × (x - 2) = 0

The solution of the equation is therefore;

Learn more about factorizing quadratic equations here:

https://brainly.com/question/83151

Answer:

The correct answer option is: 4.

Step-by-step explanation:

We are given the following two functions and we are to find the value of [tex] ( f - g ) ( 5 ) [/tex]:

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

[tex]g(x) = 4x - 4[/tex]

Finding [tex] ( f - g ) ( x ) [/tex]:

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

[tex]( f - g ) ( x ) = x^2-4x-1[/tex]

So, [tex]( f - g ) ( 5 ) = (5)^2-4(5)-1 = 4[/tex]

Answer:

4

Step-by-step explanation:

f(x) = x^2 - 5

g(x) = 4x - 4

(f-g) (x)= x^2 - 5   - (4x - 4)

Distribute the minus sign

           = x^2 - 5   - 4x + 4

          = x^2 -4x-1

Let x = 5

(f-g) (5) = 5^2 -4(5) -1

            =25 - 20 -1

             =5-1

              =4

Answer:

4x^2 + 8x - 12 = 0.

Step-by-step explanation:

We first write it in factor form.

4(x - 1)(x + 3) = 0

4(x^2 + 2x - 3) = 0

4x^2 + 8x - 12 = 0 (answer).

Answer:

4x^2 + 8x - 12 = 0

Step-by-step explanation:

A quadratic equation with roots a and b has the equation (x - a)(x - b) = 0.

You roots are 1 and -3.

The equation is

(x - 1)(x - (3)) = 0

(x - 1)(x + 3) = 0

We can multiply it out.

x^2 + 3x - x - 3 = 0

x^2 + 2x - 3 = 0

Since we need the leading coefficient to be 4, we multiply both sides by 4.

4x^2 + 8x - 12 = 0

The slope and y-intercept are both [tex]\bf{1}[/tex].

This equation is written in slope-intercept form, or [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

Since there is no coefficient to [tex]x[/tex], which would have been [tex]m[/tex], [tex]m=1[/tex], so the slope is [tex]1[/tex].

[tex]b=1[/tex], so the y-intercept is also [tex]1[/tex].

Answer:

Boxplot A

Step-by-step explanation:

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

58, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 14.

We will write in ascending order:

14 ,22 ,24 ,26 ,28,30 ,32 ,34, 36 ,38, 40, 42 ,44 ,46 ,48,50,58.

Since there are 17 terms in the above data.

So, Median would be 36.

As box plot shows the middle point of the data i.e. median.

In box plot A it shows the correct median at the middle i.e. 50% of the scores.

Hence, option 'A' is correct.

Answer: second option.

Step-by-step explanation:

We know that:

[tex]\sqrt[n]{a^n}=a[/tex]

[tex](a^m)(a^n)=a^{(m+n)[/tex]

Then we can simplify the radicals:

[tex]2\sqrt{8x^3}(3\sqrt{10x^4}-x\sqrt{5x^2})=(2\sqrt{2^2*2*x^2*x})(3\sqrt{10x^4}-x\sqrt{5x^2})=\\\\=2*2*x\sqrt{2x}=3x^2\sqrt{10}-x*x\sqrt{5}\\\\=4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})[/tex]

Since:

[tex](a\sqrt[n]{x})*(b\sqrt[n]{y})=ab\sqrt[n]{xy}[/tex]

We can apply Distributive property:

[tex]4x\sqrt{2x}(3x^2\sqrt{10}-x^2\sqrt{5})\\\\12x^3\sqrt{20x}-4x^3\sqrt{10x}[/tex]

Simplifying:

[tex]12x^3*2\sqrt{5x}-4x^3\sqrt{10x}\\\\24x^3\sqrt{5x}-4x^3\sqrt{10x}[/tex]

Answer:

B

Step-by-step explanation:

edg2021

Answer:

Step-by-step explanation:

1 gallon = 4 quarts

5 gallons 2 quarts 1 pint = 4 gallons 6 quarts 1 pint

(5 gallons 2 quarts 1 pint) - (1 gallon 3 quarts)

= (4 gallons 6 quarts 1 pint) - (1 gallon 3 quarts)

= 3 gallons 3 quarts 1 pint

Answer:

red apples

Step-by-step explanation:

cause for 1 pound, a red apple will cost 2 dollars, while for 1 pound, a green apple will cost less

Answer:

Red apples

Step-by-step explanation:

Since the cost of red apples is given by the equation y = 2x

where x = is number of pounds of red apples

Therefore clearly it can seen from the equation that the slope of this equation will be more steeper than the slope of the cost of the cost the green apples.

Now since the slope is more steep, therefore we can conclude that the red apples will cost more than the green apples for per pound of apples.

Thus, red apples will cost more per pound than green apples.

Answer:

y=40

Step-by-step explanation:

Step 1: Add 1 to both sides.

3y−1+1=119+1

3y=120

Step 2: Divide both sides by 3.

3y /3  =  120 /3

y=40

Answer:

The measure of the arc x is 80°

Step-by-step explanation:

we know that

The semi-inscribed angle is half that of the arc it comprises

so

40°=(1/2)[arc x]

solve for x

arc x=(2)(40°)=80°

Answer:

[tex]\large\boxed{x=\dfrac{5}{4}\ \vee\ x=-\dfrac{13}{6}}[/tex]

Step-by-step explanation:

[tex]|5x+4|=|x+9|\iff5x+4=x+9\ or\ 5x+4=-(x+9)\\\\5x+4=x+9\qquad\text{subtract 4 from both sides}\\5x=x+5\qquad\text{subtract x from both sides}\\4x=5\qquad\text{divide both sides by 4}\\x=\dfrac{5}{4}\\\\5x+4=-(x+9)\\5x+4=-x-9\qquad\text{subtract 4 from both sides}\\5x=-x-13\qquad\text{add x to both sides}\\6x=-13\qquad\text{divide both sides by 6}\\x=-\dfrac{13}{6}[/tex]

Answer: True

Step-by-step explanation: 20% can also be written as 0.2 and if you know the number then you would multiply it by 0.2, then if you needed to add 11 that is exactly how you would write that equation

Use the substitution method

-x+4x  when x=-2

-(-2)+4(-2)  Positive number * ( multiplying)Negative number=Negative number

2-8

=-6

Answer is -6

Answer:

90$

Step-by-step explanation:

45$

45*3=135

But your return was 3 times the price, so subtract a 45.

135-45=90$

Answer: $90

Step-by-step explanation:

Given : The cost of one stock = $45

And the value of that stock after 15 years is 3 times the paid price.

i.e. The value of that stock after 15 years = [tex]3\times45=\$135[/tex]

Then, the return on owning this stock = [tex]\text{Value after 15 years -Paid price}[/tex]

[tex]=\$135-\$45=\$90[/tex]

Therefore, the return on owning this stock = $90

Answer:

59

Step-by-step explanation:

a + b + C = -1

x + y + z = -8

We want 5a so multiply the first equation by 5

5(a + b + c) = -1*5

5a+5b+5c = -5

We want -8x so multiply the second equation by -8

-8(x + y + z) = -8*-8

-8x-8y-8x = 64

Add these equations together

5a+5b+5c = -5

-8x-8y-8x = 64

---------------------------

-8x -8y-8x+5a+5b+5c = 59

Rearrange the order

-8z -8x + 5a + 5c - 8y + 5b = 59

Answer:

59

Step-by-step explanation:

The first step here is to rewrite -8z -8x + 5a + 5c - 8y + 5b as

                                                    -8x - 8y - 8z + 5a + 5b + 5c.

This is the same as -8(x + y + z) + 5(a + b + c).

Subbing -8 for (x + y + z) and -1 for (a + b + c), we get -8(-8) - 5, or 59.

Answer:

B. 4

C. Log₅ 625

Step-by-step explanation:

When given the sum of two logarithms to the same base, let us say

LogₐB +LogₐC, Then, the sum is equivalent to Logₐ(B×C)

=Logₐ BC

The sum given in the question is Log₅5 + Log₅125

This is equivalent to Log₅(5×125)=Log₅625

Log₅625=4 (Since 625=5⁴, the log of 625 to base 5 is 4)

Answer:4 Log5 625 Log5(5^4)

Step-by-step explanation:

Answer:

A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.

Step-by-step explanation:

x = 19,

Putting value of x to find m∠ABC and m∠ACB

m∠ABC = (4x – 12)°

m∠ABC = (4(19) – 12)°

m∠ABC = (76 – 12)°

m∠ABC = 64°

m∠ACB = (2(19) + 26)°

m∠ACB = (38 + 26)°

m∠ACB = 64°

now we know sum of angles of triangle is 180°. We can find the measure of third angle.

180 = 64+64 +x

x= 180 - 64 - 64

x = 52°

A triangle is equilateral if all three angles are same. but here two angles are 64° but third angle is 52°. so, Yin is incorrect.

Sample Response: No, Yin is not correct. If

x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.

What did you include in your response? Check all that apply.

Yin is not correct.

The measure of the congruent base angles is 64°.

The measures of the angles in an equilateral triangle are 60°.

The math trick described allows you to figure out which hand a friend is holding a penny in by having them multiply the value of the coins in their hands by specific numbers, adding the results, and determining whether the total is even or odd.

The subject at hand pertains to a mathematical trick used to determine in which writing a friend is holding a penny. To execute the scheme, follow the procedure:

https://brainly.com/question/2273245

#SPJ3

Answer: C

Step-by-step explanation:

y2-y1/x2-x1

-9+7/5-6 = 2

Answer:

Step-by-step explanation:

the base is a square, and then there are four triangles that meet at their tip.

so you need to find the area of the base, and the four triangles.

base-l*w=7*7=49

triangles=1/2*b*h*4=1/2*7*10*4=35*4=140

140+49=189

Final answer:

The surface area of a regular pyramid with a square base of 7 units and a height of 10 units is approximately 197.26 square units. This is calculated by adding the area of the square base to the combined area of the four triangular faces.

Explanation:

To find the surface area of a regular pyramid with a square base, we need to calculate the area of the square base and the area of the four triangular faces. The formula for the area of a square is base x base. If the base is 7 (units unspecified, but assumed to be the same for both height and base), the area of the base is 7 x 7 = 49 square units. To find the area of a triangular face, we use the formula 1/2 x base x slant height.

To calculate the slant height, we need the half of the base of the triangle (which is 3.5 if the base of the square is 7), and the given perpendicular height of the pyramid, in this case, 10 units. We can use the Pythagorean theorem to find the slant height. The slant height (s) can be calculated as s = \\sqrt{(3.5)² + 10²} = \\sqrt{12.25 + 100} = \\sqrt{112.25}, which is approximately 10.59 units.

The area of one triangular face is 1/2 x 7 x 10.59 ≈ 37.065 square units. There are four triangular faces, so their total area is 37.065 x 4 ≈ 148.26 square units. Thus, the total surface area of the pyramid is the sum of the area of the base and the four triangular faces: 49 + 148.26 ≈ 197.26 square units.

Answer:

look at the picture attached

Answer:

Step-by-step explanation:

[tex]f(x)=4-x^2,\ g(x)=6x\\\\(g-f)(x)=g(x)-f(x)\\\\(g-f)(x)=6x-(4-x^2)\\\\(g-f)(3)-\text{put x = 3 to the equation}\\\\(g-f)(3)=6(3)-(4-3^2)[/tex]

Answer:

[tex]a < 0.287[/tex]

Step-by-step explanation:

we have

[tex]13^{4a} < 19[/tex]

Solve for a

Apply log both sides

[tex]log(13^{4a}) < log(19)[/tex]  

Remember the rule

㏒(a^n) = n ㏒(a)

so

[tex](4a)log(13) < log(19)[/tex]

Divide by 4 log(13) both sides

[tex]a < log(19)/[4log(13)][/tex]

[tex]a < 0.2870[/tex]

Answer:

slope: 4

Step-by-step explanation:

y = 4x-2 is in the form y = mx +b where m is the slope and b is the y intercept

4 is the slope and -2 is the y intercept

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have [tex]y=4x-2[/tex].

Therefore

the slope [tex]m=4[/tex]

the y-intercept [tex]b=-2[/tex]

Answer:

You can not break that down any further if x does not equal anything and the equation is not equal to anything.

Step-by-step explanation: