The height of a triangle is 6 m more than its base. The area of the triangle is 56 m2. Find the length of the base. 7 m 8 m 14 m 15 m

Answers

Answer 1

base = x
height = x+6

[tex] \frac{x(x+6)}{2}=56 \\ x(x+6)=56*2 \\ x^2+6x=112 \\ x^2+6x-112=0 \\ x^2+14x-8x-112=0 \\ x(x+14)-8(x+14)=0 \\ (x-8)(x+14)=0 \\ x-8=0 \ \ \ \ \ \ \ or \ \ \ \ \ \ x+14=0\\x=8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-14 \ \ \ \O[/tex]

base = 8 m

Related Questions

Newton currently has a balance of $1,716.18 in an account he has held for 29 years. He opened the account with an initial deposit of $784. What is the simple interest rate on the account?

Answers

In economics, money has a time value because it has to adjust with the inflation rate of the economy. Your $1,000 will not have the same value 20 years from now. This is accounted for by the interest. There are two types of interest: the simple interest and the compounding interest.

In simple interest, the change of your money value with time is constant. The equation to be used is : F = Pit, where F is the future worth, P is the present worth, i is the effective interest rate, and t is the time. Using this equation:

$1,716.18 = $784*i*29
i = 0.07548 or 7.548%

A tennis racket normally costs $6060. the tennis racket is on sale for 60 60% off. what is the sale price of the tennis racket?

Answers

The answer would be 24$

Which of the following shows the extraneous solution(s) to the logarithmic equation? log4 (x) + log4(x - 3) = log4 (-7x + 21)

A. x= -7
B. x= -3
C. x= 3 and x= -7
D. x=7 and x= -3

Answers

Answer: The correct option is C, i.e., x=3 and x=-7.

Explanation:

The given equation is,

[tex]log_4(x)+log_4(x-3)=log_4(-7x+21)[/tex]

Using product property of logarithm [tex]log_a(mn)=log_am+log_an[/tex]

[tex]log_4(x(x-3))=log_4(-7x+21)[/tex]

[tex]log_4(x^2-3x)=log_4(-7x+21)[/tex]

On comparing both sides,

[tex]x^2-3x=-7x+21[/tex]

[tex]x^2-3x+7x-21=0[/tex]

[tex]x^2+4x-21=0[/tex]

Using grouping method 4x can be written as (7x-3x). Because the product of 7 and -3 is equal to the constant term -21 and the addition of 7 and -3 is equal to the coefficient of x.

[tex]x^2+7x-3x-21=0[/tex]

[tex]x(x+7)-3(x+7)=0[/tex]

[tex](x-3)(x+7)=0[/tex]

Equate each factor equal to 0.

The value of x is 3 and -7. Therefore, the option C is correct.

The extraneous solutions are x=3 or x=−7.

We have the equation; log4 (x) + log4(x - 3) = log4 (-7x + 21) we can write;

log4[x(x - 3)] = log4 (-7x + 21)

log4 can be cancelled out from both sides and we have;

x^2 - 3x = -7x + 21

To have a proper quadratic equation;

x^2 + 4x -21 = 0

The solutions of the quadratic equation therefore are x=3 or x=−7.

Learn more about quadratic equations; https://brainly.com/question/4390345

10 points! I will thanks, rate, and give best answer!!

Find the 4th term if the sequend in which a 1 = 2 and a n+1 = -4a n + 2

Answers

Answer: The fourth term is -102

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

Explanation:

The term after the nth term is generated by this rule [tex]a_{n+1} = -4(a_n) + 2[/tex] which means that we first
Step 1) multiply the nth term ( [tex]a_n[/tex] ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence

Let's follow those steps above to generate the first four terms

The first term is [tex]a_1 = 2[/tex]. In short, the first term is 2

The second term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{1+1} = -4(a_1) + 2[/tex]
[tex]a_{2} = -4(2) + 2[/tex]
[tex]a_{2} = -8 + 2[/tex]
[tex]a_{2} = -6[/tex]
So the second term is -6

The third term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{2+1} = -4(a_2) + 2[/tex]
[tex]a_{3} = -4(-6) + 2[/tex]
[tex]a_{3} = 24 + 2[/tex]
[tex]a_{3} = 26[/tex]
The third term is 26

Finally, the fourth term is...
[tex]a_{n+1} = -4(a_n) + 2[/tex]
[tex]a_{3+1} = -4(a_3) + 2[/tex]
[tex]a_{4} = -4(26) + 2[/tex]
[tex]a_{4} = -104 + 2[/tex]
[tex]a_{4} = -102[/tex]
The fourth term is -102.

If 1/3 of an office staff is on vacation and 1/4 of those not on vacation are out sick, what fraction of the staff is in the office

Answers

Let x be the total number of staff in the office.

Thus,

The number of staff on vacation = [tex] \frac{1}{3} x[/tex]

Since, it says that staff out sick are among those not on vacation, we have to subtract the number of staff on vacation from the total number of staff.

The number of staff out sick = [tex] \frac{1}{4} (x - \frac{1}{3}x)[/tex]

Hence,

The number of staff in the office = [tex]x - \frac{1}{3} x - \frac{1}{4} (x- \frac{1}{3} x) = (x - \frac{1}{3} x)(1 - \frac{1}{4} ) = x(1- \frac{1}{3})(1- \frac{1}{4}) = x( \frac{2}{3})( \frac{3}{4}) [/tex] [tex]= \frac{1}{4} x[/tex]

The top of a 15-foot ladder touches the edge of the roof of a building, and the base of the ladder is 6 feet from the building. What assumptions are made about the building and the ladder when using the Pythagorean Theorem to solve real world problems like this?

Answers

building is perpendicular to ground....ladder is straight

solve the inequality -5.3≥6.7+4.3+q

Answers

remember, you can do anything to an equation as long as you do it to both sides

for inequalities, if you multiply or divide both sides by a negative number, you flip the direction of the inequality sign

-5.3≥6.7+4.3+q
add like terms
-5.3≥11+q
minus 11 both sides
-16.3≥q
q≤-16.3
das is da soltuion

-5.3 ≥6.7+4.3+q
First of all, let's combine all like terms with the side that has a variable.
So, 6.7+4.3=11. That gives us 11+q.
-5.3≥11+q
Subtract 11 on both sides.
-5.3-11≥11+q
-16.3≥q

The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6. Applying Newton's cooling model, the temperature of the tea after 2 hours will be ºF

Answers

Newton's cooling model is ΔT = ΔTo * e ^ (-k t)

ΔTo = 200°F - 70°F = 130°F

k = 0.6

t = 2 hours

=> ΔT = 130 * e ^ (-0.6 t) = 130 * e^ (-0.6 * 2) = 130 * e ^ (-1.2)

ΔT = 39.15°F

ΔT = T - Tenvironment => T = ΔT + Tenvironment = 39.15°F + 70°F = 109.15°F ≈ 109 °F.

Answer: T = 109 °F

Answer:

T = 109 degrees f

Step-by-step explanation:

Devon is trying to find the unit price on a six pack of drinks on sale for $2.99 his sister says that at that price each drink should cost over $2 is she correct and how do you know if she's not how would Devon's sister find the correct price

Answers

The sister wrote because if 6 of the drink is 2.99 then 1 drink can possibly can 2

To ring the correct answer she would have to decide 2.99 to 6

And the correct price for each drink is 0.49833333....

A new computer virus can enter the system through an email or through a webpage. there is a 30\% chance of receiving this virus through the email. there is a 40\% chance of receiving it through the webpage. also, the virus enters the system simultaneously through the email and the webpage with probability 0.15. what is the probability that the virus does not enter the system at all?

Answers

In solving this probability problem, you can use the Venn diagram to help you visualize the problem. The Venn diagram makes use of circles with their perimeter acting as the boundaries. Please see the attached picture.

The left circle stands for the probability of email virus, so it is assigned with 0.3. The right circle stands for the probability of webpage virus, so it is assigned with 0.4. The common area between the circle is probability of email and webpage virus assigned with 0.15. From there, we subtract 0.3 and 0.4 with 0.15 to differentiate which is email alone or which is webpage alone. The x outside the circles is the probability that the virus does not enter the system at all. Since these are probabilities, they add up to 1.

1 = 0.15 + 0.15 +0.25 +x
x = 0.45

Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month? (2 points)

Answers

19779 - 57(11) = 19779 - 627 = 19152

m = 19152*2/(56*57)

m = 12

she saved $12 more every month

what should be the first step in solving the equation 1.2 W -3.8 equals 12.4

Answers

1.2W - 3.8 = 12.4
1.2W = 12.4 + 3.8
1.2W = 16.2
W = 16.2 ÷ 1.2
W = 13.5

Answer:

Step 1 would be to add 3.8 on both sides.

Step-by-step explanation:

The Equation mentioned in the question is a simple Algebra Equation. We need to solve for W. To do so, we need to get the variable W alone on one side.

Initial Equation: [tex]1.2W-3.8 = 12.4[/tex]

Step 1: Add 3.8 on both sides. [tex]1.2W = 16.2[/tex]

Step 2: Divide 1.2 on both sides. [tex]W = 13.5[/tex]

This gives us the answer of W = 13.5.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The sum of the first three terms of a convergent geometric series is 19. the sum of the series is 27. find the first term and the common ratio.

Answers

1st,since this GP is convergent that means the common ratio r <1
2nd, sum of a GP = a₁(1-rⁿ)/(1-r), where a₁ = 1st term and n=number of terms
3rd, for any convergent GP, r<1 and the sum of all terms =a₁/(1-r): Why?
[since r<1 → lim rⁿ when n→∞, =0 in the formula of the 2nd)]
Now let's solve :

a) Sum = a₁(1-r³)/(1-r) = 19 (sum of the first 3 terms)
b) Σ(Sum) = a₁/(1-r) = 27 (sum of all terms of this CONVERGENT GP)

Divide a) by b):

[a₁(1-r³)/(1-r)] / [a₁/(1-r)] = 19 /27 ↔ [a₁(1-r³)/(1-r)] x [(1-r)/a₁]=19/27.
Simplify:
(1-r³) = 19/27
-r³ = 19/27 - 1
r³ = 8/27

r = ∛(8/27)

r = 2/3 and a₁ = 9 (Plug r in the Σ sum)
Hence first term a₁ = 9
and common ration r =2/3

When asked to factor the trinomial 4x2 + 20x + 25, a student gives the answer (2x - 5)(2x - 5). what is one thing wrong with this answer?

Answers

Answer:

The minus signs should be plus signs

The required factor of the given trinomial is (2x+5)(2x + 5).

Given that,
When asked to factor the trinomial 4x² + 20x + 25, a student gives the answer (2x - 5)(2x - 5). the mistakes in the solution is to be justified.

What is the factors?

factors can be defined by splitting the value into multipliable values.

Here,
Given trionomial,
= 4x² + 20x + 25,
= 4x² + 10x + 10x + 25
= 2x(2x + 5) + 5 (2x + 5)
= (2x + 5)(2x + 5)

Thus, the required factor of the given trinomial is (2x+5)(2x + 5).

Learn more about Factors here:
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You cut a 90 cm long rope into two pieces. the longer piece is 2 times as long as the shorter piece. what is length of the longer piece and the shorter piece respectively?

Answers

Total length of rope = 90 cm

Let the shorter piece be x.

Thus, the length of the longer piece = 2x.

2x + x = 90

3x = 90

x = 30.

Therefore, the shorter piece is 30 cm and the longer piece is 60 cm.

Please help me answer this math question.

Answers

all 3 angles in a triangle need to equal 180 degrees

62 +73 = 135 degrees are known

180-135 = 45

so angle B = 45 degrees

What is the equation in point-slope form of the line passing through (1, 9) and (−1, 11)?

Answers

(1,9)(-1,11)
slope = (11 - 9) / (-1 - 1) = -2/2 = -1

there can be 2 answers for this...
y - y1 = m(x - x1)
(1,9)...x1 = 1 and y1 = 9
sub
y - 9 = -(x - 1) <== here is one answer

y - y1 = m(x - x1)
(-1,11)...x1 = -1 and y1 = 11
sub
y - 11 = -(x - (-1) =
y - 11 = -(x + 1) <== here is the other answer

use the point slope formula, y-y1=m(x-x1) to find the equation of the line.
y=-x+10

What are the rules for dividing signed numbers

Answers

alright, for the guide

basically,
when you divide 2 numbers with the same sign, the result is positive
example, [tex]\frac{2}{4}=0.5[/tex] and [tex]\frac{-2}{-4}=0.5[/tex]

when you divide 2 numbers with different signs, the result is negative
example: [tex]\frac{-2}{4}=-0.5[/tex] and [tex]\frac{2}{-4}=-0.5[/tex]

Final answer:

In dividing signed numbers, the answer's sign depends on the signs of the numbers involved: same signs result in a positive answer, different signs yield a negative answer. Additionally, the final answer should have the same number of significant figures as the number with the fewest significant figures in the problem.

Explanation:

Rules for Dividing Signed Numbers

The rules for dividing signed numbers are similar to the rules for multiplication. When dividing numbers, it is important to consider both the sign of the numbers involved as well as the significant figures in the result. Here are the key rules to remember:

When two positive numbers divide, the answer has a positive sign, e.g., 6 ÷ 2 = 3.When two negative numbers divide, the answer also has a positive sign, e.g., (-6) ÷ (-2) = 3.When the numbers being divided have opposite signs, the answer has a negative sign, e.g., (-6) ÷ 2 = -3 or 6 ÷ (-2) = -3.As for the significant figures, the final answer should have the same number of significant figures as the number with the fewest significant figures before the division. For example, if you are dividing 23 by 448, limit the final reported answer to two significant figures.

Remember, when performing calculations, significant figures are important for maintaining accuracy based on the precision of the data you start with.

Jessica is baking a cake. the recipe says that she has to mix 96 grams of sugar into the flour. jessica knows that 1 cup of this particular sugar has a mass of 128 grams. she added 1/2 of a cup of sugar into the flour. should jessica add more sugar to make the exact recipe, or did she go over by what amount?

Answers

1 cup= 128
So half cup= 128÷2=64
She needed 96 grams
96-64=32
She needs 32 more grams of sugar

Answer:

she needs to add 32 grams. this is 1/4 cups

Step-by-step explanation:

Find four consecutive positive integers such that the product of the first and fourth is four less than twice the first multiplied by the fourth.

Answers

Four consecutive integers... n, n+1, n+2, n+3.

The product of the 1st and 4th is four less than twice the 1st multiplied by the 4th.

n(n+3)=2n(n+3)-4 perform indicated multiplications...

n^2+3n=2n^2+6n-4 subtract n^2 from both sides

3n=n^2+6n-4 subtract 3n from both sides

n^2+3n-4=0 factor

n^2-n+4n-4=0

n(n-1)+4(n-1)=0

(n+4)(n-1)=0, and since n>0

n=1

So the four numbers are 1, 2, 3, 4

check...

1(4)=2(1)4-4

4=8-4

4=4

which point of the following ordered pairs is represented by a point located on the y- axis
a. (1,1)
b. (-2,0)
c. (4,-4)
d. (0,3)

Answers

For a point to be on the y-axis we know that it must have x=0; that's how the y-axis is defined.

In this list only one of the choices has x=0: Point D

the length of a rectangle is 2 inches less than twice its width. If the perimeter of the rectangle is 74 inches, what is the area of the rectangle

Answers

If the width is w and the length is l, then 2w-2=l and 2w+2l=72 (using the perimeter equation). Plugging 2w-2 in for l, we get 2w+(2w-2)*2=72 and 6w-4=72. Adding 4 to both sides, we get 6w=76. After that, we divide both sides by 6 to get 74/6=w. Since l=2w-2=136/6, we get (136/6)(74/6)=656.75=area

A projectile is thrown upward so that it's distance above the ground after t seconds is h=-16t^2 +672t. After how many seconds does it reach its maximum height?

Answers

It will reach its maximum height at the vertex of the parabola. Which is always:

(-b/(2a), (4ac-b^2)/(4a))

So the time when this occurs is the x coordinate, or t in this case.

-b/(2a), and b=672 and a=-16 so

t=-672/-32

t=21 seconds

Answer: 21 seconds

Step-by-step explanation:

We know that a parabola with equation [tex]y=ax^2+bx+c[/tex] attains its maximum height at :-

[tex]x=\dfrac{-b}{2a}[/tex]

The given function: [tex]h=-16t^2 +672t[/tex]

It will attain its maximum height at :

[tex]t=\dfrac{-672}{2(-16)}=21[/tex]

Hence , after 21 seconds the projectile will reach its maximum height .

Andrea can clean a house 4 times as fast as Denise. When they work together, Andrea and Denise can clean a large house in 8 hours. How many hours would it take Denise to clean the house by herself?

20
15
40
5

Answers

hmmm

a=amount of house andrea can clean in 1 hour
d=amount of house denise can clean in 1 hour

8a+8d=1house
and
andrea can clean 4 times faster
that means in 1 hour, andrea cleans 4 times of denise
so
a=4d
sub back

8a+8d=1 house
8(4d)+8d=1 house
32d+8d=1 house
40d=1 house

takes her 40 hours

answer is 40 hours

Answer:

8 hours

Step-by-step explanation:

A&D can clean a house in 8 hours together.

Proportionally, Denise works at x. Andrea works at 4x. There is a total of 5x.

Out of the 5x, Denise accounts for x.

x/5x = 1/5 of the work over 8 hours.

1/5 ( Denise's time for cleaning the whole house) = 8 hours.

Multiply both sides by 5:

5(1/5)(Denise's time for cleaning the whole house) = 5*8

Denise's time for cleaning the whole house = 40 hours

I like this method better...

That means in ONE hour, they get 1/8 of the job done.

Let's say Denise takes x hours to clean the house.

In one hour, she would do 1/x of the job (x can't be 0 hours).

Since Andrea does the house 4 times as fast as Denise, who takes x hours to do the job, Andrea takes x/4 hours.

In one hour, Andrea does 4/x of the job.

In one hour the part of the job Andrea does, plus the part of the job Denise does, must total 1/8.

(4/x) + (1/x) = 1/8

5/x = 1/8

Cross multiply:

x = 40

So it would take Denise 40 hours to clean the house by herself. (She's not really that efficient, or the house was REALLY dirty.

Andrea takes x/4 hours or 40/4 = 10 hours to clean the house by herself.

So with a little help from Denise, Andrea decreases her time to clean the house from the 10 hours it would take by herself to 8 hours.

ASAP!!
Shortly before a 1992 mayoral election, a local radio station conducted a Internet survey of voters. Based on the results of the survey, the magazine predicted that the Democratic candidate would beat the Republican candidate by a landslide. In fact, exactly the opposite happened. The trouble with the survey was that the radio station was a largely liberal station and few Republicans visited its Web site. This is a classic example of an error in which phase of inferential statistics?
A.Data gathering
B.Data analysis
C.Probability-based inference
D.Data organization

Answers

This is a classic example of an error in data gathering phase of inferential statistics.

What is data gathering?

Data gathering is the process of collection and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes.

Learn more about data gathering here

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Find the length of EF. Round to the nearest hundredth.

Answers

to find EF multiply 31 by tan(72)

31 * tan(72) = 95.4082

rounded to nearest hundredth = 95.41

Find all solutions to the equation. cos x = sin x

Answers

if you were to draw the cosx and sinx graph there will be infinite solutions at their interceptions which are the multiple of pi/4

Need help please!!!!

Answers

I can't see the question...maybe I would be better at helping if I knew what to assist with.

;)

A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answers

A)

The discriminant (radicand) is √(b^2-4ac), let us call this "d" for the discriminant.

If:

d<0, there are no real solutions (though there are two imaginary ones)

d=0, there is one real solution

d>0, there are two real solutions.

In this case, d=12^2-4(4)9

d=144-144

d=0

So there is one real solution.

B)

9x^2-30x+25=0

9x^2-15x-15x+25=0

3x(3x-5)-5(3x-5)=0

(3x-5)(3x-5)=0

(3x-5)^2=0

x=5/3

x=1 2/3

Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root 3

Answers

Area = 6 * (0.5*16*8sqrt3)

= 6 * 64 sqrt3

= 384 sqrt3 sq units
or 665.1 sq units to nearest tenth

The area of a regular hexagon is mathematically given as

A=665.1 sq units

What is the area of a regular hexagon whose side length is 16 in.?

Question Parameter(s):

a regular hexagon whose side length is 16 in.

and the apothem is 8 square root 3

Generally, the equation for the area is mathematically given as

A=(3√3)/2 *a^2

Therefore

A = 6*(0.5*16*8√3)

A= 384√3 sq units

A=665.1 sq units

In conclusion, the area of a regular hexagon

A=665.1 sq units