the height of a triangle is 7 cm greater than the base. the area of the triangle is 147 square centimeters. find the length of the base and the height of the triangle​

Answers

Answer 1

Answer:

height is 21cm and the base is 14cm

Step-by-step explanation:

Take a look at the equation for the area of a triangle [tex]A = \frac{bh}{2}[/tex]

Write "height of a triangle is 7 cm greater than the base" as an equation:

h = b + 7

Substitute h and the area of the triangle, 147 into the equation for area.

[tex]A = \frac{bh}{2}[/tex]

[tex]147 = \frac{b(b+7)}{2}[/tex] distribute over brackets

[tex]147 = \frac{b²+7b)}{2}[/tex]  get rid of fractions

[tex]147*2 = b²+7b[/tex]

[tex]294 = b²+7b[/tex]

Rearrange to standard for for quadratic equations

0 = b²+7b - 294

standard form is 0 = ax² + bx + c

In this base, the x variable is replaced by "b".

Use the quadratic formula to solve for b. Substitute the other three values.

[tex]x = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]

[tex]x = \frac{-(7) ±\sqrt{7^{2}-4(1)(-294)} }{2(1)}[/tex] Simplify

[tex]x = \frac{-7 ±\sqrt{1225} }{2}[/tex]

[tex]x = \frac{-7 ±35 }{2}[/tex]

Split the equation at ±

[tex]x = \frac{-7 +35 }{2}[/tex]

[tex]x = \frac{28}{2}[/tex]

[tex]x = 14[/tex]  <=base

[tex]x = \frac{-7 -35 }{2}[/tex]

[tex]x = \frac{-42}{2}[/tex]

[tex]x = -21[/tex]  <=We know this number is not possible, so its inadmissible.

The base is 14 cm.

Substitute base = 14 in h = b + 7

h = b + 7

h = 14 + 7

h = 21

The height is 21cm.

Therefore, the height is 21cm and the base is 14cm.


Related Questions

Part of Eli’s job on the ranch is to feed the new calves. There are 5 new calves, and each calf eats 15 pounds of hay every day. Complete the area model to show the total number of pounds of hay Eli feeds the calves in 6 days. Then write the partial products and the total product.

Answers

Answer:

dfdssgfnfndfnfnb

Step-by-step explanation:

Which expression is equivalent to (x^27y) ^1/3

Answers

Answer:

x^9*y^1/3

Step-by-step explanation:

Because x^(27*1/3)=x^9 and y^(1/3)=y^1/3.

simplify: 3 1/2 + 1/8= 3 5/8 is that correct

Answers

Answer:

3.625

Step-by-step explanation:

I check on Google for yeah ;)

3 1/2 + 1/8
7/2 + 1/8
28/8 + 1/8= 29/8
I think that’s the answer, I’m not sure tho:)

John walks 3 miles in 5 hours
for his exercise routine. Find
the Unit rate​

Answers

John walks 0.6 miles in 1 hour.

Step-by-step explanation:

Distance walked by John = 3 miles

Time period = 5 hours

5 hours = 3 miles

Unit rate is the ratio of two measurements, in which one measurement is one, therefore,

1 hour = [tex]\frac{3}{5}\ miles[/tex]

[tex]1\ hour=0.6\ miles[/tex]

John walks 0.6 miles in 1 hour.

Keywords: ratio, distance

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after using six mushrooms to boost their speed. marcus racer has travelled 650 feet. hiw far did marcus racer travel after using three mishrooms?​

Answers

Answer: 325 ft

Step-by-step explanation:

6 mushrooms = 650 ft

divide by 2 on both sides

3 mushrooms = 325 ft

5 mushrooms = 6-1 mushrooms

5 mushrooms = 650 - (boost distance for 1 mushroom)

1 mushroom = 650/6 = 108.3 repeating

so 5 mushrooms = 650 - 108.333333333 = 542.66666666

What is the slope of y = -4?

Answers

Answer:

The slope is 0 and the y-intercept is -4

Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?

m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94

Answers

Answer:

The diagram of the question is attached here.

The measure of [tex]\angle XBC=135\ (deg)[/tex]

Step-by-step explanation:

All the options given here will be used to find the numeric value of [tex]\angle XBC[/tex]

Here it is shown systematically.

Exterior angle theorem: Sum of two interior angles are equal to the measure of opposite exterior angle in a triangle.

To find [tex]\angle XBC[/tex]

[tex]m\angle XBC = m\angle BAC + m\angle BCA[/tex]

Plugging the values.

[tex]3p-6 = p + 4 + (84)[/tex]

[tex]3p-6 = p + 88[/tex]

Subtracting [tex]p[/tex] both sides.

[tex]2p-6 = 88[/tex]

[tex]2p = 94[/tex]

Dividing [tex]2[/tex] both sides.

[tex]p=\frac{94}{2}=47[/tex]

So plugging the value of [tex]p=47[/tex] in [tex]3p-6[/tex] we will get the measure of [tex]\angle XBC[/tex].

So [tex]\angle XBC=(3p-6)=3(47)-6=135\ (deg)[/tex]

The measure of [tex]\angle XBC[/tex] is [tex]135\ degrees[/tex].

Based on the information, the measure of Angle XBC is 278 - 4p degrees.

What's the measurements?

Given that Angle ACB is 84 degrees, Angle BAC is (p + 4) degrees, and Angle XBC is (3p - 6) degrees, you can plug in these values:

(p + 4) + 84 + (3p - 6) + Angle XBC = 360

Combine the like terms involving 'p':

4p + 82 + Angle XBC = 360

Subtract 82 from both sides:

4p + Angle XBC = 278

Now, isolate Angle XBC by subtracting 4p from both sides:

Angle XBC = 278 - 4p

So, the measure of Angle XBC is 278 - 4p degrees.

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write a sentence explaining why all solutions of rational equation must be checked

Answers

Answer:

It is highly important for all solutions of rational equation to be checked to make sure you get the right answer.

In solving a rational equation, we always clear of fractions. When we clear of fractions we always multiply both sides by a variable quantity. When we multiply both sides of an equation by a variable expression, we may introduce an extraneous solution a zero of that expression we multiplied through by.

100% on edg

What is the simplified form of StartRoot StartFraction 48 Over 192 EndFraction EndRoot? One-fourth One-half 2 4

Answers

Answer:

1/2 or B on edge

Step-by-step explanation:

If one were to simplify the fraction 48 / 192, the result they would get is the fraction 1/4 or One-fourth

When taking a fraction to its simplest form, you divide both the numerator and the denominator by their greatest common factor.

The greatest common factor of both numbers is 48.

The simplest form is therefore:

= (48 ÷ 48) / (192 ÷ 48)

= 1 / 4

In conclusion, the fraction at its simplest form is 1/4.

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Which pair of ratios does
not form a true proportion?
A) 8:14 and 20:35
B) 6 to10 and 15 to 25
D) 12:15 and 30:50

Answers

Answer:

8:14

Step-by-step explanation:

just multiply

A)8:14 and 20:35 :3 xd

Whats 6x6+9-2-1=
(my mom will not let me use a calculator)

Answers

Answer:

42

Step-by-step explanation:

6*6+9-2-1

36+9-2-1

45-2-1

43-1

42

the answers for that in the calculator is 42

The average weight of a watermelon is 4.61 kg. The average weight of a coconut is 2.22 kg less than a watermelon. The total weight of an equal number of coconuts and watermelons is 140 kg. How many coconuts are there? ​

Answers

Since the average weight of a coconut is 2.22 kg less than a watermelon, its average weight is

[tex]4.61-2.22=2.39[/tex]Let n be the number of coconuts and watermelons. The total weight of n coconuts and n watermelons is

[tex]4.61n+2.39n = 7n[/tex]

If we want this total to be 140, we have

[tex]7n=140 \iff n=\dfrac{140}{7}=20[/tex]

So, you have 20 coconuts and 20 watermelons.

Final answer:

To find the number of coconuts, we can set up an equation using the given information. The average weight of a watermelon is 4.61 kg, and the average weight of a coconut is 2.22 kg less than a watermelon. By setting up the equation x(4.61 + 2.39) = 140 and solving for x, we find that there are 20 coconuts.

Explanation:

To solve this problem, we need to set up equations using the given information. Let's represent the number of coconuts as 'x'. The average weight of a watermelon is 4.61 kg, and the average weight of a coconut is 2.22 kg less than a watermelon, which means it is 4.61 - 2.22 = 2.39 kg. Since the number of coconuts and watermelons is equal, we can write the equation: x(4.61 + 2.39) = 140. Solving this equation, we get 7x = 140, which means x = 140/7 = 20.

Therefore, there are 20 coconuts.

Sofia has $1.90 worth of nickels and dimes. She has a total of 25 nickels and dimes altogether. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Sofia has. Define the variables that you use to write the system.

Answers

Answer:

The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12

Step-by-step explanation:

Given as :

The net worth of nickels and dimes = $ 1.90

The total number of nickles and dimes altogether = 25

Let The number of nickles that Sofia has = n

And The number of dimes that Sofia has = d

Now,

Since The value of 1 nickle = [tex]\frac{1}{20}[/tex] dollar

And The value of 1 dimes =  [tex]\frac{1}{10}[/tex] dollar

So, According to question

n + d = 25          ..........1

And  $ [tex]\frac{1}{20}[/tex] × n + $ [tex]\frac{1}{10}[/tex] × d = $ 1.90

Or, n + 2 d = 38        .....2

Solving Eq 1 and 2

∵  n + 2 d = 38

or, 25 - d + 2 d = 38

or, d = 38 - 25

∴ d = 13

So, The number of dimes she has = 13

And the number of nickles = n = 25 - 13

∴  n = 12

Hence The number of dimes does Sofia has is 13 , and The number of dimes does nickles does Sofia has is 12 Answer

What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(2/3x)?


A) vertical stretching

B) vertical compression

C) horizontal compression

D) horizontal stretching

Answers

Answer:

This will be an effect of vertical compression.

Step-by-step explanation:

We have to determine the change on the graph of the function f(x) = 2x when f(x) is replaced with [tex]f(\frac{2}{3}x )[/tex].

Therefore, [tex] f(\frac{2}{3} x) = 2(\frac{2}{3}x )= \frac{4}{3} x[/tex]

It is clear that for the same value of x the y-value decreased by the factor [tex]\frac{2}{3}[/tex].

Hence, this will be an effect of vertical compression. ( Answer )

Answer:it’s horizontal stretching

Step-by-step explanation:

if you’re in usa test prep, it is NOT vertical compression.

a box of cereal weighs 600 grams . how much is this weight in pounds ? explain or show your reasoning .

Answers

Answer:

600 Grams = 1.323 Pounds

Step-by-step explanation:

1 gram equals 0.0022 pounds

600 x 0.0022 = about 1.323

Answer:

the weight in pounds is 1.324 pounds

Step-by-step explanation:

Hello, i can help you with this, you can easily solve this by using a rule of three, also you need to know

1 pound = 453 grams

Step 1

establish the relation

1 pound ⇔ 453 grams

x pound ⇔ 600 grams

the relation is

[tex]\frac{1}{453} =\frac{x}{600}\\ solve\ for\ x\\x=\frac{1*600}{453}\\x=1.324\\[/tex]

so, the weight in pounds is 1.324 pounds

I really hope It helps , have a nice day.

What is the number place 2 in 582.091 rounded to

Answers

Answer:

582.091 Rounded to 2 places after the decimal point is 582.09

:)

Answer:

unit

Step-by-step explanation:

H. T. U.

5. 8. 2

5 is representing a hundred

8 is representing the tenth

2 is representing the units

A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by g(x)= -16x^2+64+80. What is the maximum height of the rocket?

A) 150 feet C) 120 feet

B) 80 feet D) 144 feet

Answers

Answer:

D

Step-by-step explanation:

At the maximum height, the value of the vertical velocity Vy equals zero. From the value of the equation, we can get the vertical velocity by its first differential.

Differentiating this, we get -32x + 64

We then equate this value to zero. This yield 32x = 64 and x = 2

We now plug the value of x back into the original expression for height.

-16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144 feet

explain why you can have different values when evaluating an algebraic expression.

please help! ​

Answers

When evaluating an algebraic expression, the domain is typically all real numbers.

What are real numbers?

Every single number (irrational, rational, natural numbers) except imaginary ones.

When you evaluate an algebraic expression, you can choose from a range of values if it is restricted. If it is not you can only use real numbers.

You can use 1, 50, 1909893, 39309202, and many more. It goes on and on.

And since each number that is being inputted into the expression is different, you may end up with different outputs.

Thank you for posting your question on Brainly. Please feel free to ask more.

what is -21=-7x help

Answers

Answer:

x=3

Step-by-step explanation:

-21=-7x

-7x=-21

x=3

This is a. Sjdjdkdjkdkd

The scale of a map is 1:1000. The actual dimensions of a rectangle is 4cm by 3cm. What is the actual area in m²?
(hint: convert 1000cm -> m)
(ans: 1200m²)

BUT HOW TO DO....​

Answers

Step-by-step explanation:

1cm:1000cm

multiply the dimensions by 1000cm

4cm--> 4000cm

3cm--> 3000cm

convert 4000cm and 3000cm to metres by dividing by 100

because 1m=100cm

4000/100=40m

3000/100=30m

40m x 30m= 1200m²

What is the slope of this line?

15

−15

5

−5

Answers

Answer:

the slope is 1/5 which is none of these. y=1/5x+3 is the equation

Step-by-step explanation:

for every single y value that the graph goes up, it travels 5 units on the x axis.

rise over run is the way i remeber slope, rise is one for every 5 run. This has a slope of positive 1/5x.

The slope of the line is [tex]\dfrac{1}{5}[/tex]. So, the correct option is A.

Given:

The graph of the line.

To find:

The slope of the given line.

Explanation:

Slope formula: If a line passes through the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the given graph it is clear that the line passes through the points [tex](0,2)[/tex] and [tex](5,3)[/tex]. So, the slope of the line is:

[tex]m=\dfrac{3-2}{5-0}[/tex]

[tex]m=\dfrac{1}{5}[/tex]

Therefore, the slope of the line is [tex]\dfrac{1}{5}[/tex] and the correct option is A.

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Which of the following is a correct interpretation of the expression 4 - (-3)


Start at 4 on the number line and move 3 to the left.

Start at 4 on the number line and move 3 to the right.

Start at -3 on the number line and move 4 to the left.

Start at -3 on the number line and move 4 to the right.

Answers

4 - (- 3) = 4 + 3

Addition moves to the right.

Subtraction moves to the left.

Start at 4 on the number line and move 3 to the right.

Please show all work cuase I don’t understand thank you

Answers

Answer:

13a. 0.92 miles

13b. C

Step-by-step explanation:

13a. The first ride costs $2.75 more than the second ride.  Each quarter mile after the first quarter mile costs $0.75, so the difference in distance is:

0.75 d = 2.75

d = 3.67

The difference is 3.67 quarter miles, or 0.92 miles.

13b. The total cost is the cost of the first quarter mile plus the cost of the rest of the quarter miles.

C(n) = 2.50 + 0.75 (n − 1)


Which system of equations has infinitely many solutions?
A)6x + 3y = 12
3x + y = 9
B)2x + 3y = 6
4x + y = 8
C)12x +9y = 6
4x + 3y = 6
D)5x + 10y = 20
2x+4y=8​

Answers

The answer is D.

Divide the first equation by 5 to get
x + 2y = 4

Divide the second equation by 2 to also get
x + 2y = 4

Since they are the same equation it results in an answer that has infinitely many solutions.
D)
If you multiply 5x+10y=20 by 2 and 2x+4y=8 by 5 that are equal

Write the equation of the line that is parallel to y=-0.75x and that passes through the point (8,0)

Answers

Final answer:

The equation of the line that is parallel to y=-0.75x and passes through the point (8,0) is y = -0.75x + 6.

Explanation:

The equation of a line in the form y = mx + b represents a linear equation, where m is the slope of the line and b is the y-intercept. Since we are looking for a line parallel to y = -0.75x, we know that the new line will have the same slope. So, the equation of the new line is y = -0.75x + b. To find the value of b, we can substitute the coordinates of the point (8,0) into the equation and solve for b.

0 = -0.75(8) + b

0 = -6 + b

b = 6

Therefore, the equation of the line that is parallel to y = -0.75x and passes through the point (8,0) is y = -0.75x + 6.

One Morning in Atlanta, Tina observed that the temperature was 72 degrees. Later the temperature rose 21 degrees and then dropped 11 degrees. She then flew to New York where the temperature was 67 degrees. What was the change in temperature from when Tina left Atlanta and arrived in New York

Answers

answer: 72+21=93-11=82                                                                                                                                                              

The change in temperature from when Tina left Atlanta and arrived in New York will be 82° and 77°.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

One Morning in Atlanta, Tina observed that the temperature was 72 degrees.

Later the temperature rose 21 degrees and then dropped 11 degrees.

Then the final temperature in Atlanta will be

⇒ 72° + 21° - 11°

⇒ 82°

She then flew to New York where the temperature was 67 degrees.

Then the final temperature in New York will be

⇒ 67° + 21° - 11°

⇒ 77°

Then the change in temperature from when Tina left Atlanta and arrived in New York will be 82° and 77°.

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Find the largest number. 16.3, 15.7, 16.9, 15.8

Answers

Answer:

16.9

Step-by-step explanation:

A wooden plank is 19 feet long.Mrs Dambra cuts 3 feet off the wooden plank. She then cuts the remaining piece of wood into equal pieces,each 1/5 long. how many pieces does mrs.dambra cut

Answers

Answer:

80 pieces

Step-by-step explanation:

Answer:

80ft.

Step-by-step explanation:

Please mark brainliest and you will get a Dino Nuggie :)

How to solve : 16=2t + 0.25 t``squar​

Answers

Answer:

The solutions of the equation are t = 4(√5 + 1) or 4(√5 - 1).

Step-by-step explanation:

We have to solve the given quadratic equation of single variable t.

The equation is 16 = 2t + 0.25t²

⇒ 0.25t² + 2t - 16 = 0

⇒ 25t² + 200t - 1600 = 0 {Multiplying both sides with 100}

⇒ 25t² + 200t + 400 - 400 - 1600 = 0

(5t + 20)² - 2000 = 0

⇒ (5t + 20)² - (20√5)² = 0

⇒ (5t + 20 + 20√5)(5t + 20 - 20√5) = 0

So, (5t + 20 + 20√5) = 0 or, (5t + 20 - 20√5) = 0

(t + 4 + 4√5) = 0 or, (t + 4 - 4√5) = 0

t = - 4(1 + √5) or, t = 4(√5 - 1) (Answer)

Choose all the examples that describe volume.

A. the amount of shampoo in a bottle
✓ B. the amount of soap in a bar of soap
c. the amount of border around a chalkboard
D. the amount of wrapping paper covering a gift

Answers

Answer:

A, B

Step-by-step explanation:

Volume: the measure of the amount of space that a substance (such as liquid, gas, or solid) occupies in an enclosed environment (such as a container).

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