Suppose x = 7 is a solution to the equation 4x − 2(x + a) = 8. Find the value of a that makes the equation true.

Answer:

214.6

Step-by-step explanation:

214.557 -> 214.6

Two hundred fourteen and five hundred fifty-seven thousandths to the nearest tenth​ will be 214.6.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Two hundred fourteen and five hundred fifty-seven.

The expression in mathematical form thousandths to the nearest tenth​, we have

⇒ 514.557

⇒ 214.6

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10:11 A.M

11:00 A.M is 11 hours from 12 A.M (12 midnight)

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes11 hours - 2 hours 49 minutes

11:00 A.M is 11 hours from 12 A.M (12 midnight)1 hour 29 minutes + 1 hour 15 minutes= 2 hours 49 minutes11 hours - 2 hours 49 minutes= 10 hours 11 minutes = 10:11 A.M

Therefore, she can start making the cake batter from 10:11 A.M.

Hope it helps you.

9:25 am is the latest time she can start making the cake batter

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Given that Meg is going to make a cake for her mother's birthday.

The time to bake make the cake batter is 1 hour 15 minutes.

This we can take only in minutes

1 hour = 60 minutes

So 60+15 =75 minutes to make the batter.

the cake needs to bake in the oven for 1 hour and 20 minutes

60+20=80 minutes.

Meg wants the cake to be out of the oven by 11:00 A.M.

We need to find the latest time to start the cake.

Let us find the total time to make the cake

80+75=155

155 minutes means 2 hrs 35 minutes.

Now we have to remove 2 hrs 35 minutes from 11:00 am

Which 9 hours 25 minutes.

Hence, 9:25 am is the latest time she can start making the cake batter

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Answer: f(g(2))=-7

Step-by-step explanation:

STEP 1. Find g(2)

g(x)=x²-6x-7

g(2)=(2)²-6(2)-7

g(2)=4-12-7

g(2)=-15

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

STEP 2. Find f(g(2))

f(x)=x+8

f(g(2))=g(2)+8

f(-15)=-15+8

f(-15)=-7

Hope this helps!! :)

Please let me know if you have any question or need any further explanation

Answer:

The Answer is -7 .

Step-by-step explanation:

f(x)= x+8

g(x)= [tex]x^{2}[/tex]-6x-7

Now,

fog(2)=f ([tex]2^{2}[/tex]-6*2-7)

        =f (4-12-7)

        =f (-15)

        =-15+8

        = -7          

Answer:

64/7 years

9.143 years

Step-by-step explanation:

[tex]Simple Interest = \\ \frac{Principal \times Rate \times Time}{100} [/tex]

[tex]Time = \frac{simple \: interest \times 100}{Principal \times Rate} [/tex]

[tex]Principal = 400 \\ Rate = 14 \\ Time = \\ simple \: interest = 512[/tex]

Input the values

[tex]Time = \frac{512 \times 100}{400 \times 14} \\ Time = \frac{51200}{5600} \\ [/tex]

[tex]Time = \frac{64}{7} \\ Time = 9.142 \: years \\ best \: answer \: = \frac{64}{7} years[/tex]

Answer:

Solution : (- 9, - 3)

Step-by-step explanation:

Approach 1 : Imagine that this point (3, - 9) is rotated 90 degrees clockwise. We know that this point lies in the fourth quadrant, so if it is rotated 90 degrees, you can imagine the x - coordinate will be greater than the y - coordinate, if you take their absolute value(s). Remember that the new coordinates will also lie in the third quadrant. Based on these requirements we have the resulting point (- 9, - 3) or option c.

________________________________________

Approach 2 : There is another approach to this, a more exact approach.

Rotation of axis, θ : (x, y) --> (X, Y)

X = xcos(θ) + ysin(θ),

Y = - xsin(θ) + ycos(θ)

Here θ = 90 degrees. Substitute and solve for the exact coordinates.

X = 3cos(90) + - 9sin(90) = 3cos(90) - 9sin(90) = 3 * 0 - 9 * 1 = - 9,

Y = - 3sin(90) + - 9cos(90) = - 3sin(90) - 9cos(90) = - 3 * 1 - 9 * 0 = - 3

As you can see our solution is the same, (- 9, - 3), or option c.

Answer:

x= 6

Step-by-step explanation:

[tex]\frac{1}{3}x^{2}-5=7\\[/tex]

Add 5 to both sides

[tex]\frac{1}{3}x^{2}-5+5=7+5\\\\\frac{1}{3}x^{2}=12\\[/tex]

Multiply both sides by 3

[tex]3*\frac{1}{3}x^{2}=12*3\\\\x^{2}=36\\[/tex]

x² = 6*6

Take square root,

√x² =√6*6

x = 6

Answer:

7.75

Step-by-step explanation:

By Geometric mean property:

[tex] GH = \sqrt {a \times b} [/tex]

[tex] GH = \sqrt {3 \times 20} [/tex]

[tex] GH = \sqrt {60} [/tex]

[tex] GH = 7.74596669[/tex]

[tex] GH \approx 7.75[/tex]

Answer: -a

Step-by-step explanation:

Answer:

-a

Step-by-step explanation:

DONT DO SPACE just -a

Answer

Step-by-step explanation:

domain : red

range: blue

Answer:

x = 8 units.

Step-by-step explanation:

We'll begin by calculating the length of the two squares attached to the triangle.

From the question given above, the areas of the two square are the same i.e 32 units². Therefore, the length of the two square will be the same.

Now, we shall determine the length of the square as follow:

Area of square (A) = 32 units²

Length (L) =?

Area of square (A) = Length (L) × Length (L)

A = L × L

A = L²

32 = L²

Take the square root of both side

L = √32 units

Therefore, the length of the square is √32 units. This implies that the length of both side of the triangle is √32 units

Now, we shall determine the value of x using pythagoras theory.

From the diagram above we can see that x is the Hypothenus i.e the longest side. Thus, the value of x can be obtained as follow:

x² = (√32)² + (√32)²

x² = 32 + 32

x² = 64

Take the square root of both side

x = √64

x = 8 units.

Therefore, the value of x is 8 units.

Answer:

[tex] f(x) = 72 - 12x [/tex]

Step-by-step explanation:

No. of days of study = 6

Amount of food to use for the 6 days = 72 mm

Given that equal amount of food was used each day, amount used per day = [tex] \frac{72}{6} = 12 mm [/tex]

This would enable us derive a function for the amount of food remaining f(x), which can be expressed as a function of the number of days that have passed, (x).

Thus, we would have:

[tex] f(x) = 72 - 12x [/tex]

Let's check if this equation expresses the relation of the function well.

At the end of day 1, if we used, 12mm, we would have 72 - 12 = 60mm of food remaining.

If we replace x in the equation we derived, we would get the same 60mm as the amount of food remaining.

If you try 2, 3, 4, 5 days, you'd get same thing.

At the end of the study, after the 6th day, the food would remain nothing.

Replace 6 for x in the relation function derived, you'd get a value of 0.

Answer:

General conditions of congruency of triangles

Step-by-step explanation:

As no triangles are given, explaining the general rules to apply in congruency of all triangles.

Triangles are congruent on the basis of following conditions :

Answer:

6

Step-by-step explanation:

bd/2c

-3(4)/2(-1)

-12/-2

6

Answer:

6

Step-by-step explanation:

Add the given numbers into your equation.

(-3)(4)/2(-1)

Then multiply both sides.

(-12)/(-2)

Then divide.

(-12)/(-2) = 6

Step-by-step explanation:

Hey, there!!

Let's simply work with it,

Here,

In figure ABC,

let a= 14

b= 19

and c= 8.

Using cosine rule,

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab.cosc[/tex]

putting value of all we get,

[tex] {8}^{2} = {14}^{2} + {19}^{2} - 2 \times 14 \times 19 \times cosx[/tex]

Now, simplifying them we get,

[tex]64 = 196 + 361 - 532.cosx[/tex]

[tex]532cosx = 557 - 64[/tex]

[tex]or \: 532cosx = 493[/tex]

[tex]or \: cosx = \frac{493}{532} [/tex]

cosx= 0.926691

Putting cos inverse,

[tex]x = {cos}^{ - 1} (0.926691) [/tex]

Therefore, x= 22.0752°

By rounding off we get,

x= 22° { as 0 is smaller than 5 itsvalue dont change}.

Hope it helps....

y + 2 = -(x - 4)

============================================

Explanation:

The slope of this line is -1 because each time we move down 2 units, we move to the right 2 units. So slope = rise/run = -2/2 = -1

The slope formula says the same thing more or less. Let's pick the two points (0,2) and (2,0) to find the slope through them

m = (y2-y1)/(x2 - x1)

m = (0-2)/(2-0)

m = -2/2

m = -1

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

Using that slope and a point on the line, we can form the equation. We can pick any point really as long as it's on the line. However, to have it match with the answer choices, we'll have to pick the point (4,-2)

Turn to point slope form

y - y1 = m(x - x1)

y - y1 = -1(x - x1) ... plug in the slope

y  - (-2) = -(x - 4) ... plug in the point (x1,y1) = (4, -2)

y + 2 = -(x - 4)

Answer:

[tex]3 \frac{7}{9}[/tex]

Step-by-step explanation:

We know that the first digit of 3.7, 3, will just be a 3.

However, if we have [tex].\overline{77}[/tex], we have to know what gets this.

If we have a number over 9, it will be that number repeating (excluding 9 itself).

So if we have .77 repeating, it would have to be [tex]\frac{7}{9}[/tex], adding 3 to this gets us [tex]3 \frac{7}{9}[/tex].

Hope this helped!

Answer:

(2, 10)

Step-by-step explanation:

y = (x - h)² + k

vertex = (h, k)

= (2, 10)

A relation is a function if each element of the domain is paired with exactly one element of the range. ... If given a table, or a set of ordered pairs, you can look to see if any value of the domain has more than one corresponding value in the range.

tbh google

Answer:

[tex]- 2x + 3[/tex]

Step-by-step explanation:

[tex] - 3(2x -1 ) + 4x \\ - 6x + 3 + 4x \\ = - 2x + 3[/tex]

Answer: B

Step-by-step explanation:

Let's work this problem backwards. So, if he has y dollars left after spending 25% the second time or 3/4 of the money left. So, inverse it to get  [tex]\frac{4}{3}[/tex]y. Then, do the same for 20% or 4/5, then 4/3y * 5/4 = 5/3y

Answer:

repeating decimal/number

Step-by-step explanation:

If you divide 11 by 24, you get 0.458333333...

The 3 gets repeated, so 11/24 is a repeating decimal/number

If you double the amount of fluid ounces, then the amount of cups will double as well. This is a true statement.

Consider the statement "there are 8 fluid ounces in one cup" to be written as the equation

8 fluid ounces = 1 cup

We can multiply both sides by 2 to get

16 fluid ounces = 2 cups

We must multiply both sides by the same number to keep the equation the same (keep things balanced).

Answer:

You have:

2 red tins

3 white tins

This equals 5 tins of paint.

If you multiply 5 tins by 3 times it will give you 15 tins of paint.

Now: 2 red tins x 3 = 6 red tins

3 white tins x 3 = 9 white tins

6 red tins + 9 white tins = 15 tins of paint

Answer:

She will need 6 tins of Red paint

Step-by-step explanation:

Answer:

[tex]3\frac{1}{5}[/tex]

Step-by-step explanation:

there are 3 5s in 16, and 1 remainder.

So, you write the remainder in the numerator, and 3 as a whole number.

To check, you can do:

5✖️3=15+1=16

Answer:

[tex]1 \frac{1}{15}[/tex]

Step-by-step explanation:

Hey there!

Well when dividing fractions you need to use Keep, Change, Flip.

[tex]\frac{8}{6} / \frac{5}{4}[/tex]

Keep, Change, Flip

[tex]\frac{8}{6} * \frac{4}{5}[/tex]

[tex]\frac{32}{30}[/tex]

Simplified

16/15

[tex]1 \frac{1}{15}[/tex]

Hope this helps :)

Answer:

The answer is 16/15 or 1 1/15.

Step-by-step explanation:

First, you have to multiply it by converting the second fraction upside down:

[tex] \frac{8}{6} \div \frac{5}{4} [/tex]

[tex] = \frac{8}{6} \times \frac{4}{5} [/tex]

Next, you have to cut out the common terms and multiply all:

[tex] \frac{8}{6} \times \frac{4}{5} [/tex]

[tex] = \frac{8}{3} \times \frac{2}{5} [/tex]

[tex] = \frac{16}{15} \: \: or \: \: 1 \frac{1}{15} [/tex]

Answer:

702*10-4

7020-4(because first we should do multiplication)

7016

stanndard notation=7.016

Answer:

C should slot on top of A.

Then D should slot in next to C of the left.

Lastly B should be beneath D and on the left of A.

Hope that makes sense.

Answer: B: 8*1 = 8

Step-by-step explanation:

The identity property of multiplication says that:

There exist a number, called the identity, such that when we multiply any real number N by this identity, the result is the same number N.

The identity is 1.

then N*1 = N.

The option that is an example of that is:

8*1 = 8.

Option B

Answer:

6) C

8) A

Step-by-step explanation:

6) A=(base*height)/2 is the formula for a triangle.

8) yes

6. The formula that can be used to find the total amount of paint she will need if the entire space is painted is C) A= (8)(9)/2.

The area of the triangle is given as,

Area = (1/2)*(base)*(height)

Now it is given that,

Base of space = 8 feet

Height of space = 9 feet

Thus,

Area of the space = (1/2)*(base of space)*(height of space)

⇒ Area of the space = (1/2)*(8)*(9)

or, Area of the space =  (8)(9)/2

⇒ Area of the space = 36 square feet

Thus, the formula that can be used to find the total amount of paint she will need if the entire space is painted is C) A= (8)(9)/2.

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8. The properties use to solve the equation 4x + 2 = 18 is C) The inverse property of addition and then the inverse property of multiplication.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

4x + 2 = 18

To solve the equation first using inverse property of addition

4x = 18 - 2

4x = 16

Now using inverse property of multiplication we get,

4x/4 = 16/4

x = 4

this is the required value of x.

Thus, the properties use to solve the equation 4x + 2 = 18 is C) The inverse property of addition and then the inverse property of multiplication.

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