Match the system with the amounts of solutions. pls

Answer:

7 boxes of pencils and 5 boxes of erasers.

Step-by-step explanation:

The least common denominator of these two numbers are 70. 7×10 and 14×5. So she is purchasing the same quantity of both.

Answer:  1) c     2) d

Step-by-step explanation:

Use Pythagorean Theorem to find the hypotenuse (r):  x² + y² = r²

Given: x = 2, y = 6

                2² + 6² = r²

                4 + 36 = r²

                      40 = r²

                      [tex]\sqrt{40}=r[/tex]

[tex]\sin \theta=\dfrac{y}{r}\quad =\large\boxed{\dfrac{6}{\sqrt{40}}}\quad \rightarrow \dfrac{6}{2\sqrt{10}}\quad \rightarrow \dfrac{3}{\sqrt{10}}[/tex]

*******************************************************************************************

[tex]\sin \theta = \dfrac{opposite(y)}{hypotenuse(r)}\quad =\dfrac{12}{20}\quad \rightarrow \dfrac{3}{5}\quad \rightarrow \large\boxed{0.6}\\\\\\\cos \theta = \dfrac{adjacent(x)}{hypotenuse(r)}\quad =\dfrac{16}{20}\quad \rightarrow \dfrac{4}{5}\quad \rightarrow \large\boxed{0.8}[/tex]

Tick the arithmetic sequences.

In order for a sequence to be arithmetic the relations between their numbers must be the sum of a common ratio, therefore to determine which ones are arithmetic sequence we need to satisfy the following expression:

[tex]a_n - a_{n-1} = a_{n-2} - a_{n-3}[/tex]

The expression just mean that the subtraction of consecutive terms should be equal for position in the sequence.

"1, 5, 9, 13...":

[tex]13 - 9 = 5 - 1\\4 = 4[/tex]

Since the expression is valid, then this is a arithmetic sequence.

"6, 10, 15, 21...:

[tex]21 - 15 = 10 - 6\\6 = 4[/tex]

Since the expression is invalid, then this isn't a arithmetic sequence.

"2, 3, 5, 8...:

[tex]8 - 5 = 3 - 2\\3 = 1[/tex]

Since the expression is invalid, then this isn't a arithmetic sequence.

"2, -4, 8, -16...:

[tex]-16- 8 = -4 - 2\\-24 = -6[/tex]

Since the expression is invalid, then this isn't a arithmetic sequence.

"-1, 2, 5, 8...:

[tex]8 - 5 = 2 -(- 1)\\3 = 3[/tex]

Since the expression is valid, then this is a arithmetic sequence.

"73, 66, 59, 52...:

[tex]52 - 59 = 66 - 73\\-7 = -7[/tex]

Since the expression is valid, then this is a arithmetic sequence.

"6, 1, -4, -9...:

[tex]-9 - (-4) = 1 - 6\\-5 = -5[/tex]

Since the expression is valid, then this is a arithmetic sequence.

"1, 2, 4, 8...:

[tex]8 - 4 = 2 - 1\\4 = 1[/tex]

Since the expression is invalid, then this isn't a arithmetic sequence.

Find the first five terms of the patterns with these nth terms.

For [tex]3n + 3[/tex]:

[tex]3*1 + 3 = 3 + 3 = 6[/tex]

[tex]6 + 3 = 9[/tex]

[tex]9 + 3 = 12[/tex]

[tex]12 + 3 = 15[/tex]

[tex]15 + 3 = 18[/tex]

(6, 9, 12, 15, 18)

For [tex]9n - 7[/tex]:

[tex]9*1 - 7 = 9 - 7 = 2[/tex]

[tex]2 + 9 = 11[/tex]

[tex]11 + 9 = 20[/tex]

[tex]20 + 9 = 29[/tex]

[tex]29 + 9 = 38[/tex]

(2,11,20,29,38)

Write down a formula for the nth term of these patterns. The first term is n = 1.

The nth term of any arithmetic sequence is: [tex]a(n) = a(1)*(n - 1)*r[/tex]

Therefore we need to identify r in each sequence.

For (9,15,21,27,33):

[tex]r = 15 - 9 = 6[/tex]

[tex]a(n) = 1*(n - 1)*6 \\a(n) = 6*n - 6[/tex]

For (-2,-8,-14,-20,-26):

[tex]r = -8 - (-2) = -6[/tex]

[tex]a(n) = 1*(n - 1)*(-6)\\a(n) = -6*n + 6[/tex]

Answer:

[tex]\boxed{\sf x =40}[/tex]

Step-by-step explanation:

[tex]\sf 12x=34^2 - 26^2[/tex]

Solve the square.

[tex]\sf 12x=1156-676[/tex]

[tex]\sf 12x=480[/tex]

Divide both sides by 12.

[tex]\displaystyle \sf \frac{12x}{12} =\frac{480}{12}[/tex]

[tex]\sf x =40[/tex]

Answer:

it's about 106.71ft

Step-by-step explanation:

make this problem a triangle. the ramp length is 312ft, and it is the hypotenuse of the triangle. 20 is the angle between the ramp and the floor. so what I did was take the sine of 20 and get: sin(20)=x/312 then you multiply both sides by 312 to isolate the variable. multiplying sin(20) by 312 gave me 106.71 + some change idk if you're supposed to round it or not haha.

Answer:

Hey there!

FGH is congruent to FHJ because of the ASA postulate, stating that in congruent triangles, two angles and one side must be congruent.

Hope this helps :)

Answer:

Step-by-step explanation:

Give the distance covered by Vivian at the bottom of the elevation to be -9.6 feet and the distance covered by Vivian at the top of the elevation to be 12.3 feet, Vivian's change in elevation will be expressed as the difference in the elevation at the bottom and the elevation at the top.

Let the initial elevation Ei = -9.6 feet

Final elevation Ef = 12.3 feet

Change in elevation ΔE = Ef - Ei

Change in elevation ΔE =12.3 - (-9.6)

Change in elevation ΔE = 12.3 + 9.6

Change in elevation ΔE = 21.9 feet

Hence the expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at  the top is ΔE =12.3 - (-9.6) which is equivalent to 21.9 feet

Answer:

12.3 – (-9.6)

Step-by-step explanation:

Its the answer they provided

Answer:

Option (D)

Step-by-step explanation:

In the given triangle ABC,

Sum of all interior angles = 180°

m∠A + m∠B + m∠C = 180°

72° + 85° + m∠C = 180°

m∠C = 180 - 157

m∠C = 23°

By applying Sine rule in the triangle,

[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]

[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}[/tex]

[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302[/tex]

[tex]\frac{\text{Sin72}}{a}=0.06302[/tex]

a = [tex]\frac{\text{Sin72}}{0.06302}[/tex] = 15.09

[tex]\frac{\text{Sin85}}{b}=0.06302[/tex]

b = [tex]\frac{\text{Sin85}}{0.06302}[/tex]

b = 15.81

Therefore, option (D) will be the answer.

Answer:

A : quadratic trinomial

Step-by-step explanation:

Given

(3x² - 11x - 4) - (2x² - x - 6)

Distribute both parenthesis, noting the second is distributed by - 1

= 3x² - 11x - 4 - 2x² + x + 6 ← collect like terms

= x² - 10x + 2 ←  this is a quadratic with 3 terms, thus quadratic trinomial → A

Hope helped.. Mark BRAINLIEST

Thanks!!

Answer:

A. quadratic trinomial

Step-by-step explanation:

[tex](3x^2-11x-4)-(2x^2-x-6)[/tex]

Remember that polynomials are closed to subtraction, therefore, linear binomial and linear monomial can't be an option.

[tex]3x^2-11x-4-2x^2+x+6[/tex]

[tex]x^2-10x+2[/tex]

We got a quadratic equation. Once it has the c term, it is a quadratic trinomial.

Answer:

a = 26°

b = 48°

c = 26°

d = 106°

Answer:

6

Step-by-step explanation:

the value of x is 6

so the answer is 6

Answer:

answer is 8

Step-by-step explanation:

Answer: The annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.

Step-by-step explanation:

Given: Volume of Atlantic Ocean= [tex]3.1\times10^{17}[/tex] cubic meters

Annual flow of Mississippi river = [tex]6.3\times10^{11}[/tex] cubic meters.

then, the number of times the annual flow of the Mississippi river would fit in the Atlantic ocean = [tex]\dfrac{\text{ Volume of Atlantic Ocean}}{\text{Annual flow of Mississippi river}}[/tex]

[tex]=\dfrac{3.1\times10^{17}}{6.3\times10^{11}}\ \ \=0.492063492063\times10^{17-11}\ \ [\dfrac{a^m}{a^n}=a^{m-n}]\\\\=0.492063492063\times10^6\approx4.92\times10^5[/tex]

Hence,  the annual flow of the Mississippi river would fit in the Atlantic ocean [tex]4.92\times10^5[/tex] times.

Answer:

y=2/3x+5

Step-by-step explanation:

Parallel lines share the same slope so we already know the slope: 2/3.

Now we need to find the y-intercept for the equation. To do that, replace 4 with b. We have y=2/3x+b.

To find out what b is, we need to plug in the x and y values we are given into the current equation. We get 7=2/3(3)+b.

7=2+b

5=b

Now we can put all the information we have together.

y=2/3x+5

Answer:

A.  6 and 30

B.  8 and 28

Step-by-step explanation:

we know that the area of the three squares must satisfy the Pythagorean Theorem so c² = a² + b²

where

c²  is the area of the largest square

a² and b² are the areas of the smaller squares

now.. 36² = a² + b2

The sum of the areas of the smaller squares must be equal to 36

therefore

6 and 30 >>>> could be the areas of the smaller squares (6 + 30 = 36)

8 and 28 >>>> could be the areas of the smaller squares (8 + 28 = 36)

hope it clears your mind.

Please mark as the brainliest

Answer:

Amplitude of 2, midline is y=4

Answer:

y=4.

Step-by-step explanation:

I hope this helps!

Answer:

B. 6sqrt(2).

Step-by-step explanation:

Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.

In this case, x = 6.

So, the hypotenuse is B. 6sqrt(2).

Hope this helps!

Answer: The bottom right

Step-by-step explanation: Take a peek at the pic :)

Answer:

a. 46.9 m b. 56.1 m

Step-by-step explanation:

a. Width of the river

The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.

Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from

tan58° = 75.0 m/d

d = 75.0/tan58° = 46.87 m ≅ 46.9 m

b. Height of the second cliff

Now, the difference in height of the two cliffs is gotten from

tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°

h = dtan22° = 18.94 m

So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m

Answer:

20×20-4

=400-4

=396

hope it helps u....

plz mark as brainliest...

Answer:

Step-by-step explanation:

Using BODMAS rule:

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Now, let's solve:

[tex]20 \times 20 - 4[/tex]

Multiply the numbers

[tex] = 400 - 4[/tex]

Calculate the difference

[tex] = 396[/tex]

Hope this helps...

Best regards!!

Answer:

22 units.

Step-by-step explanation:

In 45- 45- 90 triangles, there is a 1 to 1 to the square root of 2 formula. Each side length measures 1x, while the hypotenuse measures x times the square root of 2.

In this case, the hypotenuse measures 22 and the square root of 2 units. To find the value of x, simply divide that by the square root of 2 units, and you get x = 22 units. Multiply that by 1, and you get 22 units, which is the length of the leg of the triangle.

Hope this helps!

Answer:

r=9⅓

Step-by-step explanation:

(10,r). (4,-3)

(x¹,y¹) (x²,y²)

gradient=y²-y¹

x²-x¹

4= -3-r

3 4-10

multiply both sides by 3(4-10)to remove the denominators.

3(4-10)× 4 = -3-r ×3(4-10)

3 4-10

(4-10)×4= (3-r)×3

16-40=9-3r

put the liketerms together

note* signs(- +) change when they cross the equal sign(=)

3r=4+40-16

3r=28

divide both sides by 3

r=28/3.

r=9⅓

Answer:

[tex]c. \: \sqrt{9} . \sqrt{4} [/tex]

[tex] \\ [/tex]

Step-by-step explanation:

[tex] \sqrt{9.4} \\ = \sqrt{9} \times \sqrt{4} [/tex]

Answer:

(∠C) ≅ (∠B)

∴ tan(∠B) = tan(∠C) and

Slope AB = Slope BC

Step-by-step explanation:

Part A:

To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;

The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)

The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)

The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal

Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C

Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)

The slope AB = tan(∠B)

Slope BC = tan(∠C)

(∠C) ≅ (∠B)

Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.

Answer:

The top of the cake is 25.12 in²

Step-by-step explanation:

Hello!

So you are dealing with a circumference question! And because the diameter is 2x the radius, we know the radius is actually 4.

Lets write out the circumference formula and use that to help us.

c = 2[tex]\\\pi[/tex] x r

pi is 3.14....

But lets use 3.14

c = 2(3.14) x 4

Plus this into a calculator and we get 25.12 as the answer.

Answer:

≈50.265 [tex]in^{2}[/tex]

Step-by-step explanation:

You first have to find the radius since the formula for the area of a circle is  A=[tex]\pi r^{2}[/tex].

Since the radius is half the diameter, just divide 8 by 2 which will give you 4.

r=4

Now plug in the radius into the formula and simplify.

A=[tex]\pi 4^{2}[/tex]

[tex]A=\pi 16[/tex]

≈50.265 [tex]in^{2}[/tex]

Answer:

3(1 - 20) + 10 = 4

3 * (-19) + 10 = 4

-57 + 10 = 4

-47 = 4

Since the two are not equal, this statement is false/invalid.

Hope this helps!

Answer:

x = -8

Step-by-step explanation:

6x - 3 = -51

Add 3 to each side

6x - 3+3 = -51+3

6x = -48

Divide each side by 6

6x/6 = -48/6

x = -8

Answer:

B. y= -x^2+50x-300

Step-by-step explanation:

A. y^2=4x^2-100

B. y= -x^2+50x-300

C. x=-y^2-400

D. x^2=-6y^2+200

we are to find profits (y) when the company sells x items

Option A can be used to calculate the profit (y) squared

Option B can be used to calculate profits (y)

Option C can be used to calculate items sold(x)

Option D can be used to calculate items sold squared(x^2)

We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B

Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is

B. y= -x^2+50x-300

Answer:

4

Step-by-step explanation:

The coordinates are: A(0,0), B(1,4), C(2,8), D(3,12), E(4,16)

Using coordinates B and D, slope = (12 - 4)/(3 - 1) = 8/2

        ∴ slope = 4

Answer:

4

Step-by-step explanation:

Answer:   [tex]y=\sqrt{x-3}-5[/tex]

Step-by-step explanation:

The vertex form of a square root equation is: [tex]y=a\sqrt{x-h}+k[/tex] where

Input: h = 3 (3 units right) and k = -5 (5 units down) into the vertex form:

[tex]y=\sqrt{x-(3)}+(-5)\\\\y=\sqrt{x-3}-5[/tex]

The resulting equation is: [tex]h(x) = \sqrt{x - 3} - 5[/tex]

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

This question is solved using the translation concept.

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

Original function:

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

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

Translated 3 units to the right

This is f(x - 3), so:

[tex]g(x) = f(x - 3) = \sqrt{x - 3}[/tex]

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

Translating 5 units down

This is g(x) - 5, so:

[tex]h(x) = g(x) - 5 = \sqrt{x - 3} - 5[/tex]

Which is the resulting equation.

The image at the end of this answer compared the graph of the original function, in red, with the translated, in blue.

A similar question is given at https://brainly.com/question/23630829.