Write the expression below as a single logarithm. log7 x+ log7 8-log7 9(answer options in picture).

Answer:

-21 F

Step-by-step explanation:

it already was -14

then dropped 7

so it becomes

-14 - 7 = -12 f

Answer:

1,056 gifts

Step-by-step explanation:

If twelve relatives give gifts to one another

This means each of the twelve relatives gets gifts from the other 11 relatives

=12 relatives * 11 gifts

= 132 gifts per year

They have been doing it for 8 years

Total gifts exchanged for 8 years= 132 gifts × 8 years

=1,056 gifts

Therefore, number of gifts exchanged for 8 years among 12 relatives is 1,056 gifts

Answer:

The area of the triangle with the given measurements is 200 in²

Step-by-step explanation:

For this problem, we will need to know the formula for finding the area of a triangle.

A = 1/2(bh)

Now, let's plug in these numbers so we can find the area.

A = 1/2(bh)

A = 1/2(16*25)

A = 1/2(400)

A = 200 in.²

Answer:

32°

Step-by-step explanation:

What we have to notice here is that m∠1 and m∠2 are complementary angles. This means that their angles add up to 90°.

Since we know the measure of m∠1, we can easily find the measure of m∠2 since both add up to 90.

m∠1 is 58, so:

[tex]58 + x = 90[/tex]

[tex]x = 90-58\\\\x=32[/tex]

Hope this helped!

Answer:

11 games

Step-by-step explanation:

17+6=23

23/2=11.5

Victoria can play 11 games. You'd usually round up, but in this case you can't play half a game so she'll play 11 games and have one quarter leftover.

Answer:

Victoria can play 11 games and have 1 quarter left over.

Step-by-step explanation:

17 given quarters +6 found quarters = 23 total quarters.

Since 23 is an odd number and we want to divide by 2, we have to go down to the last even number: 22. (This gives us the left over quarter)

22 quarters/2quarters per game = 11 games

Given: The area of a square field is 841 sq.m

Since side of square = √Area

So, side of square field = [tex]\sqrt{841} =29[/tex]

Thus , side of square field = 29 m

Perimeter of square = 4( side) = 4(29) = 116 m

Let x be the breadth of rectangle then 2x be the length

Perimeter of rectangle = 2 (length+breadth) = 2(2x+x)= 2(3x)=6x

As per question, perimeter of rectangle=  Perimeter of square

[tex]\Rightarrow\ 6x=116\\\\\Rightarrow\ x=\dfrac{116}{6}=\dfrac{58}{3}\ m[/tex]

Length : [tex]2x =2\dfrac{58}{3}=\dfrac{116}{3}\ m[/tex]

Area of rectangle =  length x breadth

[tex]=\dfrac{116}{3}\times\dfrac{58}{3}=\dfrac{6728}{9}\\\\=747\dfrac{5}{9}\ m^2[/tex]

Area of rectangle = [tex]747\dfrac{5}{9}\ m^2[/tex]

Answer:

[tex]\huge \boxed{\mathrm{5^{3+2} \ \ \ \ 5^5 }}[/tex]

Step-by-step explanation:

5³ × 25

25 can be written as a base of 5.

5³ × 5²

We need expressions with fewest number of bases possible.

Apply exponent rule : [tex]a^b \times a^c = a^{b+c}[/tex]

[tex]5^{3+2}[/tex]

Add exponents.

[tex]5^5[/tex]

Answer:

The answer is easy its 53 times 2 and 52 times 2

Step-by-step explanation:

Answer:

m∠W = 125°

m∠X = 55°

m∠Z = 55°

Step-by-step explanation:

The explanation of angle measures is shown below:-

The shape which is parallelogram WXYZ. m∠Y = 125

A parallelogram represents the shape of quadrilateral in which both opposite sides and opposite angles are similar to each other. One parallelogram diagonals bisect each other. Consecutive angles are also supplementary to a parallelogram.

In WXYZ parallelogram is there

m∠Z + m∠Y = 180° is an angle of Consecutive in a parallelogram is supplementary

m ∠ Z + 125 = 180

m ∠ Z = 180 - 125

m ∠ Z = 55°

m ∠ W which equals to m∠Y where equal angles are Opposite

m∠W = 125°

m ∠ W + m ∠ X = 180°

which is the angle of Consecutive in a parallelogram called supplementary)

m ∠ X + 125 = 180

m ∠ X = 180 - 125

After solving the above equation we will get

m ∠ X = 55°

A scientific theory is a validated explanation of some aspect of the natural world, based on multiple facts that have been frequently verified through research and experimentation. Fact theories are not "guesses" but reliable accounts of the real world.

Answer:

x+3y-6=0

Step-by-step explanation:

given eqn is y=3x-2 which is 3x-y-2=0

the eqn of line perpendicular to given eqn is -x+3y+k=0

it passes through (6,4)

-6+3*4+k=0

or,. -6+12+k=0

or, k= -6

therefore, the eqn of line perpendicular to given eqn is x+3y-6=0

Answer:

The first option.

Step-by-step explanation:

Domain is anything less than or equal to 2, but anything greater than or equal to -4

Range is anything greater than or equal to -4, but also less than or equal to 4

Answer:

[tex]\Huge \boxed{\mathrm{31}}[/tex]

Step-by-step explanation:

50 percent of 62 is also one half of 62.

62 × [tex]\frac{1}{2}[/tex] = 31

Answer:

50 is 31% of 62.

Step-by-step explanation:

To solve this, we need to set up our problem like this, since percentages are written with %, and add up to 100%.

[tex]\frac{62}{x} =\frac{100}{50}[/tex]

Next, we flip the denominators with the numerators so that the x ends up on the top.

[tex]\frac{x}{62}=\frac{50}{100}[/tex]

Finally, we can see that 50/100 is 1/2, so to solve x/62, we have to divide 62 by 2 to get our answer.

62 ÷ 2 = 31

Our answer is 31%.

Answer:

Step-by-step explanation:

The SI unit of work is Joule.

Further more explanation:

▪️[tex] \blue{ \mathsf{ {What \: is \: Work \: ?}}}[/tex]

⇒Work done by a force acting on a body is defined as the product of force and displacement of the body in the direction of the force.

▪️[tex] \blue{ \bold{ \sf{What \: is \: SI \: unit \: ?}}}[/tex]

⇒The system of units which is agreed by the international convention of scientists held in France in 1960 is called SI unit.

▪️[tex] \blue{ \bold{ \sf{What \: do \: you \: mean \: by \: \: one \: joule \: work \: \: ?}}}[/tex]

⇒One joule is the amount of work done when one Newton force displaces a body through one metre in its own direction.

Hope I helped!

Best regards!

Answer:

19. Opposite of a Difference     ↔    E. -(8 - 3·m) = 3·m - 8

20. Opposite of a sum               ↔    A.  -[(-r) + 2p] = -(-r) - 2p

21. Opposite of an Opposite     ↔   F. -1[ -1(9 - 2w)] =  9 - 2w

22. Multiplication by 0               ↔   B.  160 - (3d + 2)(0) = 160 - 0

23. Multiplication by                   ↔   D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t

21. Distributive property             ↔   C.  5(2 - x) = 10 - 5x

Step-by-step explanation:

19. Opposite of a difference is the difference of the opposites

20. Opposite of a sum is the sum if the opposites

21. Opposite of an opposite is the original number

22. Multiplication by 0- The result of multiplication by 0 is 0

23. Multiplication by -1 results in the change in sign of a number

24. Distributive property - Multiplying the sum or difference of two numbers  by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.

Answer:

a= 1,2,4 b= 1,2,3,6 c=1,2,4 d=1,2,5,10 e=1,2,3,4,6,12 H.C.F of all the pairs= 2

Step-by-step explanation:

Factors of:

a. 8=1,2,4,8

12=1,2,3,4,6,12.

common factor=1,2,4

b. 12=1,2,3,4,6,12

18=1,2,3,6,9,18

common factor=1,2,3,6

c. 16=1,2,4,16

24=1,2,3,4,6,8,12,24

common factor=1,2,4

d. 20=1,2,4,5,10,20

30=1,2,3,5,6,10,15,30

common factor=1,2,5,10

e. 24=1,2,3,4,6,8,12,24

36=1,2,3,4,6,9,12,18,36

common factor=1,2,3,4,6,12

HIGHEST COMMON FACTOR (H.C.F)=

The factor common to the whole pairs

which is 1 and 2

therefore 1 multiplied by 2 which is equal to 2

(and in Mathematics means multiplication)

Answer:

£500,000.00

Step-by-step explanation:

Principal = x

Saving rate  = 2% PA simple

Time = 5 years

Final amount = £550,000

Principal amount is £500,000

Answer:

[tex]\huge \boxed{{x=500,000}}[/tex]

Step-by-step explanation:

[tex]A=P(1+rt)[/tex]

[tex]A[/tex] = amount   ⇒  550000

[tex]P[/tex] = principal amount   ⇒  x

[tex]r[/tex] = rate   ⇒  2%

[tex]t[/tex] = time   ⇒  5

[tex]\displaystyle 550000=x(1+\frac{2}{100} (5))[/tex]

Solve for the brackets.

[tex]\displaystyle 550000=\frac{11}{10}x[/tex]

Multiply both sides of the equation by [tex]\frac{10}{11}[/tex].

[tex]500000=x[/tex]

The value of x (principal amount) is 500,000.

Answer:

(-18,5)

Step-by-step explanation:

Answer:

The correct option is;

B. This equation is not considered to be a quadratic equation because it is not in the form a·x² + b·x + c = 0

Step-by-step explanation:

A. The given equation, x² - c = 0, can be presented in the form of the difference of two squares as follows;

(x + √c)·(x - √c) = 0

B. The equation x² - c = 0, is a quadratic equation because it is a polynomial equation of degree 2

C.  The equation x² - c = 0 can always be factored as (x + √c)·(x - √c) = 0

D. Where c > 0, the equation x² - c = 0 can by the square root property as follows;

x² - c = 0

x² = c

x = √c

Answer:

[tex]\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]

Step-by-step explanation:

[tex]ax+by=c\\\\ax-ax+by=c-ax\\\\by=c-ax\\\\\frac{by=c-ax}{b}\\\\\boxed{y=\frac{c}{b}-\frac{ax}{b}}[/tex]

Hope this helps.

Answer: QN = 12

Step-by-step explanation: This quadrilateral is a paralelogram because its 2 opposite sides (NP and MQ) are parallel and the other 2 (MN and PQ) are congruent.

In paralelogram, diagonals bisect each other, which means QR = RN.

If QR = RN:

QR = 6

Then,

QN = QR + RN

QN = 6 + 6

QN = 12

The diagonal QN of quadrilateral MNPQ is QN = 12.

Hey there! I'm happy to help!

To find the area of a trapezoid, you add the lengths of the two bases, divide by two, and then multiply by the height.

We add our two bases.

483+207=690

We divide by 2.

690/2=345

We multiply by the height.

345(320)=110,400

Therefore, Hien can estimate that the area of Nevada is 110,400 square miles.

Have a wonderful day! :D

The formula for area of a trapezoid is [tex](b_{1} + b_{2})*\frac{1}{2} h=A[/tex]

b=base

h=height AKA altitude.

A=area.

Base 1 is 483.

Base 2 is 405.

483+405=888

888×320 (h) = 284160

284160 × [tex]\frac{1}{2}[/tex] = 142080

The approximate area of Nevada is 142080 square miles.

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:  20 liters

Step-by-step explanation:

The mixture is 60 liters. The ratio is 2 : 1   (2 parts to one part)

60 ÷ (2 + 1) = one part

60 ÷ 3 = 20

Therefore, the ratio of 2 : 1 means 2(20) liters milk to 1(20) liters water

If we change it to a ratio of 1 : 2, then we have 1(20) liters milk to 2(20) liters water.

2:1 ratio has 20 liters water

1:2 ratio has 40 liters water

The amount of water added is 40 - 20 = 20 liters

Answer:

$6.50

Step-by-step explanation:

Create a system of equations, where s represents the price of a stuffed animal and t represents the price of a toy train:

4s + 7t = 75

6s + 5t = 74

Solve by elimination by multiplying the top equation by 3 and the bottom equation by -2:

12s + 21t = 225

-12s - 10t = -148

11t = 77

t = 7

Plug 7 in as t to find s:

4s + 7t = 75

4s + 7(7) = 75

4s + 49 = 75

4s = 26

s = 6.5

= $6.50 for a stuffed animal

Answer:

see explanation

Step-by-step explanation:

1. The angle is RST

2. The sides of the angle are SR and ST

3. The angle can be named as ∠ RST, ∠ TSR, ∠ S

Note in the 3 letter angle name the vertex of the angle is in the middle

4 The square at S indicates the angle is right, that is 90°

Answer:

x = 12; m<ABC = 76

Step-by-step explanation:

The two angles whose measures are given form a linear pair. Therefore, they are supplementary angles, and their measures add up to 180 degrees.

8x - 20 + 116 - x = 180

7x + 96 = 180

7x = 84

x = 12

The angle with measure 8x - 20 and angle ABC are vertical angles. That means that their measures are equal.

m<ABC = 8x - 20 = 8(12) - 20 = 96 - 20 = 76

Answer: x = 12; m<ABC = 76

Answer:

Component form of the vector will be (-1, 2).

Step-by-step explanation:

When [tex]P(x_1, y_1)[/tex] translates to [tex]P'(x_2,y_2)[/tex] vector V formed after the translation will be,

V = [tex]<(x_2-x_1), (y_2-y_1)>[/tex]

If we draw this vector on a graph,

Vector will start from origin and the terminal point will be at [tex][(x_2-x_1), (y_2-y_1)][/tex]

Therefore, component form of the vector that translates from P(-3, 6) and P'(-4, 8) will be,

V = [tex]<(-4+3),(8-6)>[/tex]

V = [tex]<(-1,2)>[/tex]

Translation involves changing the position of a point

The vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]

The points are given as:

[tex]\mathbf{P = (-3,6)}[/tex]

[tex]\mathbf{P' = (-4,8)}[/tex]

The translation rule is calculated as:

[tex]\mathbf{(x,y) = P' - P}[/tex]

So, we have:

[tex]\mathbf{(x,y) = (-4,8) - (-3,6)}[/tex]

Combine

[tex]\mathbf{(x,y) = (-4+3,8-6)}[/tex]

[tex]\mathbf{(x,y) = (-1,2)}[/tex]

Express as vectors

[tex]\mathbf{<x,y> = <-1,2>}[/tex]

Hence, the vector that translates P to P' is [tex]\mathbf{ <-1,2>}[/tex]

Read more about translations at:

https://brainly.com/question/12463306

Answer:

f(4) = 23

Step-by-step explanation:

[tex] f(x) = x^2 + 7[/tex]

Plug x = 4

[tex] f(4) = 4^2 + 7[/tex]

[tex] f(4) = 16 + 7[/tex]

[tex] f(4) = 23[/tex]

Answer: f(4) = 23

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(4).

We find f(4) by plugging 4 in for x, everywhere that x appears in the function.

So we have f(4) = (4)² + 7.

(4)² is 16 so we have 16 + 7 which is 23.

So f(4) is 23.

Answer:

-6

Step-by-step explanation:

We are given x=- 3 , y= 6 and z= -4.

We are also given the expression:

-15 + (-x) +y

Substitute -3 in for x and 6 in for y.

-15 + (- -3) + 6

2 negative signs creates a positive sign

-15 + (+3) +6

-15 + 3+ 6

Add -15 and 3.

(-15+3) +6

-12 +6

Add -12 and 6.  

-6

-15+(-x)+y evaluated at x= -3 and y=6 is equal to -6.