Mathematics Middle School

## Answers

**Answer 1**

a=2 b=4 c=1

the answer the the discriminant is 8 which is positive meaning there are 2 real number solutions

**Answer 2**

**Answer:**

8

There are two real solutions

**Step-by-step explanation:**

We have the following quadratic equation

[tex]2x^2+4x+1=0[/tex]

a refers to the coefficient next to [tex]x^2[/tex]

b refers to the coefficient with [tex]x[/tex]

c refers to the number without x

This means that

[tex]a=2\\b=4\\c=1[/tex]

We now can plug these variables into the discriminant formula

[tex]b^2-4ac\\\\(4)^2-4(2)(1)\\\\16-8\\\\8[/tex]

As our answer is positive, we can determine that this quadratic equation has two real solutions.

## Related Questions

Please help. 20 points and brainliest.

### Answers

**Answer:**

choce 3

**Step-by-step explanation:**

you can add n = 1,2,3,4 ....

you will receive the values as 1, 1/2, 1/4, 1/7

........

a⁰ = 1

5⁰ = 1

I need help with this graph?!

### Answers

**Answer:**

Im pretty sure its D. all numbers greater than or equal to -3

**Step-by-step explanation:**

The answer would be D

A number was written on the board. One student increased the number by 23, but another student decreased the number by 1. The first student’s result was 7 times greater than the result of the second student. What is the number written on the board?

### Answers

**Answer:**

5

**Step-by-step explanation:**

let the number written on the board be x.

1st student's number= x +23

2nd student's number= x -1

*1**st** **student**'**s** **number**=** **7**(**t**h**a**t** **o**f** **the** **2nd** **student**)**,*

x +23= 7(x -1)

x +23= 7x -7 *(**expand**)*

7x -x= 23 +7 *(**bring** **constant** **to** **1** **side**)*

6x= 30 *(**simplify**)*

x= 30 ÷6 (÷6 on both sides)

x= **5**

Thus, the number written on the board is 5.

I need help with this problem, its on slope please help me! I will give 15 points/Thanks/Brainliest/5 Stars if you give me a correct answer with a brief summary or explanation. (If you want) Thank youuuu!

### Answers

**Answer:**

see below

**Step-by-step explanation:**

A horizontal line ( flat) has zero slope

A vertical line ( up and down) has undefined slope

The line going up 1 and over to the right one has slope 1/1 = 1

**Answer:**

**Step-by-step explanation:**

A)

first graph has a slope of 0 since it is a horizontal line

second graph has an undefined slope, since it is a vertical line,

the third graph has a slope of 1 since it represents the equation y=x

B)

I will use points (1,1) and (5,9)

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

m=(9-1)/(5-1)

m=8/4

m=2

100PTS PLS HURRY I ONLY HAVE 40 MINUTES Determine the common ratio and find the next three terms of the geometric sequence.

-7, 3.5, -1.75 ...

a.

-0.5; 0.450, -0.8655, 0.45985

c.

-1.5; 0.450, -0.8655, 0.45985

b.

-0.5; 0.875, -0.4375, 0.21875

d.

-1.5; 0.875, -0.4375, 0.21875

### Answers

**Answer:**

[tex]\Large \boxed{\mathrm{\bold{B.} \ -0.5 \ ; \ 0.875 \ , \ -0.4375 \ , \ 0.21875}}[/tex]

**Step-by-step explanation:**

The common ratio can be found by finding the quotient of a term and the previous term in the sequence.

[tex]\displaystyle \frac{3.5}{-7} =-0.5[/tex]

The common ratio is -0.5.

The rule is to multiply a term in the sequence by -0.5 to get the next term.

Next 3 terms :

[tex]-1.75 \times -0.5=0.875 \\\\ 0.875 \times -0.5 = -0.4375 \\\\ -0.4375 \times -0.5=0.21875[/tex]

The next 3 terms are 0.875, -0.4375, 0.21875.

**Answer:**

b. -0.5; 0.875, -0.4375, 0.21875

**Step-by-step explanation:**

Given GP:

-7, 3.5, -1.75 ...

Common ratio:

r = a₂/a₁r = 3.5/-7 = - 1/2 = -0.5

Next 3 terms:

-1.75* (-0.5) = 0.8750.875*(-0.5) = - 0.4375-0.4375*(-0.5) = 0.21875

Correct answer choice is:

**b. -0.5; 0.875, -0.4375, 0.21875**

Use the graph to determine the input value for

which f(x) = g(x) is true.

Ox=0.5

x = 1

OX= 1.5

Ox=2

### Answers

Answer: x=1.5

Step-by-step explanation:

The **input value **for which f(x) = g(x) is true is x= 1.5.

What is Function?

In mathematics, a **function **is an expression, rule, or law that establishes the **relationship **between an **independent** variable and a **dependent **variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

The **intersection **both **functions **is the point when f(x)=g(x).

As, the **point **of **intersection **both graphs is (5, 2)

Here for the **input **value of x= 1.5

f(1.5)= 2

g(1.5)= 2.

So, f(1.5)= g(1.5)= 2

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hi can anybody help me with this

### Answers

**Answer:**

A) Rectangle: 6 faces, 12 edges, 8 vertices

Pentagon: 7 faces, 15 edges, 10 vertices

Hexagon: 8 faces, 18 edges, 12 vertices

B) 12 edges and 8 vertices.

**Step-by-step explanation: **I'm sorry if any of these answers are wrong but i hope they helped you. Take care.

B is 12 angles and 8

PLEASE HELP. are the values of the expressions 2m−13 and m+3 equal?

### Answers

**Answer:**

yes

**Step-by-step explanation:**

m=16

**Answer:**

Change m into 16.

m = 16

**Step-by-step explanation:**

So let’s start off by changing the expression to an equation.

Well let’s see to make the values equal we have to find the value of m first.

So we can set up the following equation -> [tex]2m-13=m+3[/tex].

So we have to simplify the equation to find m.

First off we want all the m’s on one side so we subtract the m on the left onto 2m and we just get m. The equation now looks like this -> [tex]m-13=3[/tex].

Now we have to get all the whole numbers on one side so we add 13 onto 3 and we get 16. Now we have [tex]m=16[/tex], so now we have to plug 16 in on the equation to see if they are equal. So we have [tex]2(16)-13=(16)+3[/tex].

Now let’s simplify it, 2*16=32-13 is 19.

Time for the next side 16+3 is 19 so m replaced as 16 makes the expressions equal.

Jonathon is playing a game on a rectangular board that measures 60cm long and 450 mm wide. What is the perimeter of Jonathan's game board in meters

### Answers

**Answer:**

its eather B r D

**Step-by-step explanation:**

A cylinder has a base diameter of 16in and a height of 5in. What is its volume in cubic

in, to the nearest tenths place?

### Answers

**Answer:**

1004.8 in³

**Step-by-step explanation:**

d = 2r => r = d/2 = 16in/2 = 8 inches

V = Ab×h

= π·r²×h

= 3.14·(8in)²×5in

= 1004.8 in³

A cylinder is a **three-dimensional **structure. The **volume **of the **cylinder **in cubic inches to the nearest tenth place is **1,005.3 in³.**

What is a cylinder?

A cylinder is a **three-dimensional **structure formed by two parallel circular bases **connected **by a curving surface. The circular bases' **centers **overlap **each **other to form a **right cylinder.**

The **volume** of the **cylinder **is given by the formula,

[tex]\text{Volume of the cylinder} = \dfrac{\pi}{4} d^2h[/tex]

Given that the **diameter **of the cylinder is **16 inches, **while the height of the cylinder is **5 inches. **Therefore, the **volume **of the cylinder,

[tex]\rm \text{Volume of the cylinder} = \dfrac{\pi}{4} \times (16^2) \times 5 = 10005.3\ in^3[/tex]

Hence, the **volume **of the **cylinder **in cubic inches to the nearest tenth place is **1,005.3 in³.**

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Use the given information to determine which of the following

relationships can be proved and why.

Lazo

MAP

aa

O A. ALMN~ A OPQ, because of AA.

O B. We cannot prove any relationship based on these data.

C. ALMN=A OPO, because of AA.

O D. ALMNE A OPO, because of ASA.

### Answers

**Answer:**

(A). LMN ~ OPQ, because of AA

**Step-by-step explanation:**

That's the answer

The relationship which can be proved using the given information is that A. ΔLMN **similar **to ΔOPQ because of **AA**.

Given is two triangles.

ΔLMN and ΔOPQ.

Given that,

∠L ≅ ∠O and ∠M ≅ ∠P

So, we have two angles of a triangle is equal to corresponding two angles of the other triangle.

Two angles of ΔLMN is equal to** **two angles of ΔOPQ.

**AA postulate **states that if two angles of a triangle is congruent to corresponding two angles of the other triangle, then the two triangles are **similar**.

So, ΔLMN is similar to ΔOPQ by AA postulate.

Hence the correct relationship is A. ΔLMN similar to ΔOPQ because of AA.

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Find the value of the combination.

5C5

A:1

B:5

C:0

### Answers

Answer:

A:1

Step by step explanations:

C(n,r)=C(5,5)

n=5

r=5

=n! / (r!(n-r)!)

=5! / (5!(5-5)!)

=1

A backyard pool has a concrete walkway around it that is 5 feet wide on all sides. The total are of the pool and the walkway is 950 feet. If the length of the pool is 6 feet longer than the width, find the dimensions of the pool.

### Answers

**Answer:**

**Step-by-step explanation:**

**Pool:**

Width = x ft

Length = (x+6) ft

**Pool along with walkway:**

Width = x + 5 + 5 = (x + 10) ft

Length = x + 6 + 5 + 5 = (x + 16) ft

Total area of the pool with walkway = 950 sq.ft

length * width = 950

(x+16) * (x + 10) = 950

Use **FOIL **method,

x*x + x *10 + 16*x + 16 *10 = 950

x² + 10x + 16x + 160 -950 = 0 {**Add like terms}**

x² + 26x - 790 = 0

**Answer:**

29.4 length and 21.4 width.

**Step-by-step explanation:**

To fin the dimensions of the pool we need to use the total area of the pool plus the concrete walkway. Lets say that W is the width and L the length. We know that, the walkway has 3 ft wide, this means that the width and length are increased by 6ft (3ft on each side). So, the total

y = square root of x + 6

### Answers

**Answer:**

**Step-by-step explanation:**

[tex]x^{2} + 36[/tex]

**Step-by-step explanation:**

[tex]y = \sqrt{x + 6} \\ y = x ^{2} + 6 { }^{2} \\ y = x { }^{2} + 36[/tex]

PLEASE HURRY

Which equation is parallel to

5x - 10y = 6

and passes through (2, -1)

### Answers

**Answer:**

y=1/2x-2

**Step-by-step explanation:**

A family went out to dinner and the cost of the food was $80. If the tip given was 15%, what

was the total cost?

### Answers

It should be $92.00

80 • .15 = 12

so 15% of the total ($80) is 12.

add the 12 to the total 80+12= $92

I’m guessing the cost will be $92. Hope this helps !

The ratio of the number of sheep to the number of horses on a farm is 8:3. If there are 42 horses on the farm how many sheep are on the farm?

### Answers

Cross multiply and solve for x

8/3 = x/42

**Answer:**

**112 sheep**

**Step-by-step explanation:**

~ *If the ratio of sheep:horse is **8:3**, and there are **42** horses on the farm, then that means that there are **14 times** more horse than 3. Which just means that *~ *3·14 = 42 *

~ *So we just have to take 8 (The number of sheep), and multiply it by 14, like we did to the number of horse. *

~ *8 · 14 = 112*

~ *Now the new ratio of sheep:horse is ***112:42**

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability that the lock code consists of all even digits? To find the total number of outcomes for this event, find the permutation of things taken 4 at a time. The total number of outcomes is . The total number of favorable outcomes is a permutation of things taken 4 at a time. The probability that the lock code consists of all even digits is out of 3,024.

### Answers

**Answer:**

The probability is found:

**P = 24/3024 = 1/126**

**Step-by-step explanation:**

To find total number of outcomes, we have to find permutation of 9 things taken 4 at a time:

P(9,4) = 9! / (9-3)!

P(9,4) =362880/120

P(9,4) = 3024

Number of even numbers from 0 to 9 = 4

To find desirable number of outcome, find permutation of 4 things taken 4 at a time.

P(4,4) = 4! / (4-4)!

P(4,4) = 24/1

P(4,4) = 24

The probability that the lock consists of all even digits is

P = No. of desirable outcomes / No. of total outcomes

P = 24/3024

**Answer:**

1st answer 9

2nd answer 3,024

3rd answer 4

4th answer 24

**Step-by-step explanation:**

Felicity writes −2 2/5 as a fraction using the same method she knows for positive mixed numbers. Her work is shown: Multiply the whole number by the denominator: −2⋅5=−10. Add the numerator: −10+2=−8. Write this number over the original denominator: −2 2/5=−8/5. Does this method work to correctly write −2 2/5 as a fraction? Complete the statements below to answer the question.

### Answers

**Answer:**

it doesn't because she should've subtracted the numerator instead of adding it as it is also a negative number.

the answer would be -12/5

**Answer:**

**Step-by-step explanation:**

Suppose a bus arrives at a bus stop every 35 minutes

If you arrive at the bus stop at a random time, what

is the probability that you will have to wait at least 20

minutes for the bus?

а)

v16

NI

### Answers

**Answer:**

3/7

**Step-by-step explanation:**

The probability of at least is 1 - the probability of at most

P(at least x) = 1 - P(at most x)

The given is:

1. A bus arrives at a bus stop every 35 minutes

2. You arrive at the bus stop at a random time

3. You will have to wait at least 20 minutes for the bus

∵ The bus arrives at a bus stop every 35 minutes

∵ You arrive at the bus stop at a random time

∵ You will wait at most for 20 minutes for the bus

∴ P(at most 20 minutes) =

∵ P(at least 20 minutes) = 1 - P(at most 20 minutes)

∴ P(at least 20 minutes) = 1 -

∴ P(at least 20 minutes) =

- Simplify the fraction by divide up and down by 5 and you will get your answer!

please mark me brainliest!

A number cube with the numbers 1 through 6 is rolled. What is the theoretical probability, as a decimal, of the number cube showing a 1? Round the decimal to the nearest hundredth.

### Answers

**Answer:**

**The probability of the number cube showing a 3 = 0.1667**

**Step-by-step explanation:**

**A number cube with the numbers 1 through 6 is rolled.**

**So, The numbers which are marked on the cube : 1, 2, 3, 4, 5, 6**

**Total no. of numbers which are marked on the number cube = 6**

**No. of times the number cube is rolled = 1**

**We need to find the theoretical probability, as a decimal, of the number cube showing a 3.**

**Therefore, The probability of the number cube showing a 3 is given by :**

Please help. 10 points and brainliest.

(Ignore the already marked option)

### Answers

**Answer:**

B

**Step-by-step explanation:**

from 1-3:

2 values

from 4-6:

5 values

from 7-9:

3 values

from 10-12:

1 value

11 values total

the option that has all this is B

Write the equation for a parabola with a focus at (-8, -1) and a directrix at y = − 4.

### Answers

**Answer:**

**y = 1/6 x^2 + 8/3 x + 49/6**

**Step-by-step explanation:**

This is a parabola which opens upwards.

The distance of a point (x, y) from the focus is

**√[(x - -8)^2 + (y - -1)^2]** and

the distance of the point from the line y = -4

= **y - -4**

These distances are equal for a parabola so:

√[(x - -8)^2 + (y - -1)^2] = y + 4

Squaring both sides:

(x + 8)^2 + (y + 1)^2 = (y + 4)^2

x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16

x^2 + 16x + 64 + 1 - 16 = 8y - 2y

6y = x^2 + 16x + 49

y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.

The equation for the **parabola** with focus at (-8, -1) and **directrix** at y = -4 is (x + 8)² = 12(y + 2.5)

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The standard equation for a **parabola** with a vertical axis of symmetry is:

(x - h)² = 4p(y - k)

where (h, k) is the vertex of the parabola,

p is the **distance** from the vertex to the focus or directrix, and the sign of p depends on whether the focus is above or below the vertex.

The focus is located at (-8, -1), which is 3 units above the directrix y = -4. Therefore, the value of p is 3.

The vertex of the **parabola** is halfway between the focus and the directrix, so it must be at:

(h, k) = (-8, (-1 + (-4))/2) = (-8, -2.5)

Substituting these values into the **equation**, we get:

(x - (-8))² = 4(3)(y - (-2.5))

Simplifying, we get:

(x + 8)² = 12(y + 2.5)

Therefore, the equation for the **parabola** with focus at (-8, -1) and directrix at y = -4 is (x + 8)² = 12(y + 2.5)

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Where could point E be if BC = DE and D is between E and B?

A. -1

B. 0

C. 1

D. 2

### Answers

**Answer:**

The answer is D. 2

√6(√10 + √15) simplify show all work

### Answers

**Answer:**

2 sqrt(15) + 3 sqrt(10)

**Step-by-step explanation:**

sqrt(6) * ( sqrt(10)+ sqrt(15))

Distribute

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(6) sqrt(10)+ sqrt(6) sqrt(15))

sqrt(60) + sqrt( 90)

sqrt( 4*15) + sqrt(9*10)

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(4) sqrt(15) + sqrt(9) sqrt(10)

2 sqrt(15) + 3 sqrt(10)

Answer:

≈ 15.5085

Step-by-step explanation:

√6 ≈ 2.45

6 is not a perfect square so its square root is irrational, therefore the decimal form can only be estimated.

√10 ≈ 3.16

The square root of 10 is a single number. That number is irrational, which means that its decimal expansion goes on forever without repeating, and cannot be expressed as a fraction.

√15 ≈ 3.17

This is not simplifiable. But this is approximately what equalled.

2.45(3.16 + 3.17)

= 15.5085

If Jorge walks 1 mile in 1 hour. In 2 hours at the same place, How many yards can Jorge walk now

### Answers

**Answer:**

3520 yards

**Step-by-step explanation:**

1 mile in 1 hour.

In 2 hours he will cover 2×1= 2 miles

1 mile = 1760 yards

2 miles = 3520 yards

**Answer:**

1 mile = 1760 yards

1 hour = 1 mile

2 hour = 2 mile

= 2 × 1760

= 3520 yards

check 0,3 is a solution of 3x+2y=6

### Answers

Answer:

Assuming (x,y) = (0,3)

3x + 2y = 6

3(0) + 2(3) = 6

0 + 6 = 6

Plug the cordinates in

3(0)+2(3)=6

0+6=6

6=6

enter the mean of the data 9,5,7,7,12

### Answers

i believe it is 7 or 7

sorry I just needed more words to send the message

The Mean Of The Data Is 8

ABC is reflected over the y-axis. What are the vertices of

A' B' C' ?

A (0-2), B'(-2,-4). C'(-5, -1)

A(-2,0), B(-4, 2), C (-1, 5)

A' (0.2). B (-2,4), C'(-5,1)

A'(0, 2). B' (2, 4). C'(5.1)

### Answers

**Answer:**

The answer is the first option.

**Step-by-step explanation:**

**When you flip it over the y axis. A would still be the same. ANd the first one matches A.**

The nth term of a sequence is represented by [tex]\frac{2n^4+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex] . What is the limit of the nth term as x becomes increasingly large?

WILL GIVE BRAINLIEST, PLEASE ANSWER QUICKLY

### Answers

**Answer:**

2n3+8n2-32n=16

**Step-by-step explanation:**

[tex]2n3 +8n2-32n=16[/tex]