This isosceles triangle has two sides of equal length , a, that are longer than the length of the base , b. The perimeter of the triangle is 15.7 cm. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 cm, which equation can be used to find the length of the base ?

Answers

Answer 1

We are give the equation of the perimeter of the triangle as follows:
2a + b = 15.7
where b represents the base.

Now, if we want to calculate the length of the base, all we have to do is isolate the b in one side of the equation as follows:
b = 15.7 - 2a

We know that a = 6.3 cm, therefore, the length of the base can be calculated as follows:
b = 15.7 - 2(6.3) = 3.1 cm

Related Questions

Two angles are complementary. the measure of one angle is 21 more than the measure of the other angle. find the measures of the angles

Answers

The angles would be 34.5 degrees and 55.5 degrees

What is the y-intercept of the line? y +6x - 4y-intercept =?

Answers

Slope intercept form is always y=mx+b where your m is your slope and your b is your y-intercept. Knowing this we first need to put your equation into slope intercept form. to do this all we have to do is subtract everything except why across an equal sign to get y=-6x+4. Now all you have to do is figure out what the 'b' is to know that the y-intercept is 4

Answer:

[tex]\huge\boxed{\boxed{\tt{the \ y-intercept \ is \ -4}}}[/tex]

Step-by-step explanation:

Hello.

The equation is written in slope-intercept form (y-mx+b, where m stands for the slope of the line and b stands for the y-intercept)

Let's write the equation and see if we can identify its y-intercept (the point where the graph touches the y-axis)

Equation:

[tex]{\boxed{\boxed{\bf{y=6x-4}}}[/tex]

Y-intercept:

[tex]\boxed{\boxed{-4}}[/tex]

And we're done!

Note: The slope of the line is 6.

I hope it helps & have an outstanding day!

~ST2710

A company plans to enclose three parallel rectangular areas for sorting returned goods. the three areas are within one large rectangular area and 10641064 yd of fencing is available. what is the largest total area that can be enclosed?

Answers

First get the perimeter

Perimeter: 2l + 2w = 1064 yd

The region inside the fence is the area

Area: A = lw

We need to solve the perimeter formula for either length or width.

2l + 2w = 1064 yd

2w = 1064 yd – 2l

W = 1064– 2l / 2

W = 532 – l

Now substitute than to the area formula

A = lw

A = l (532 – l)

A = 532 – l^2

Since the equation A represents a quadratic expression, rewritte the expression with the exponents in descending order

A(l) = -l^2 + 532l

Then look for the value of the x coordinate

l = -b/2a

l = -532/2(-1)

l = -532/-2

l = 266 yards

Plugging in the value into our calculation for area:

A(l) = -l^2 + 532

A(266) = -(266)^2 + 532 (266)

A(266) = 70756+ 141512

= 70756 square yards.

Thus the largest area that could encompass would be a square where each side has a length of 266 yards and a width of:

W = 532 – l

= 532 – 266

= 266

It should be noted that the largest total area that can be enclosed will be 70756 yards².

How to calculate the area.

Firstly, we have to calculate the perimeter. This will be:

2l + 2w = 1064 yd

Area: A = length × width

2l + 2w = 1064 yd

2w = 1064 yd – 2l

W = 1064– 2l / 2

W = 532 – l

Since Area = lw

A = l(532 – l)

A = 532 – l²

A(l) = -l² + 532l

l = -b/2a

l = -532/2(-1)

l = -532/-2

l = 266 yards

The length is 266 yards.

Area = -l² + 532

A( = -(266)² + 532 (266)

Area = 70756+ 141512

Area = 70756 yards²

Learn more about areas on:

https://brainly.com/question/25292087

Help please !!!!!!!!!!!!!!

Answers

To start, we're given the range that x lies in: from -1 to 4. We know from the fact that [tex]-1 \leq x[/tex] that -1 will be included in that range, so we mark -1 on the number line with a solid circle. We also know from [tex]x\ \textless \ 4[/tex] that, while x can be any value up to 4, it does not include 4. We indicate this by drawing a hollow circle around 4 on the number line. Since x can be any value within this range, we make that fact clear by drawing a bold line between the points -1 and 4 on the number line. I've attached an image of what our final graph would look like.

Can you find a shortcut in doing two translations in geometry

Answers

You can. I am pretty sure

nick bought a pet lizard and enjoys the responsibility of taking care of it . every week , the lizard will eat 60 grasshoppers. nick pays $1 for 20 grasshoppers . how many dollars will a year’s worth of food cost for the lizard

Answers

60*52 = 3120 per year

3120/20 = 156

it will cost $156 a year

Find the length of the diagonal of this rectangle.

Answers

cos 32 = 10 / AC
AC = 10 / cos 32

= 11.79 m ( to nearest hundredth)

Answer:

The length of the diagonal of the given Rectangle is, 11.80 m (Approx.)

Step-by-step explanation:

In Rectangle:

* It is a four sided shape where every angle is a right angle.

* The alternative sides are equal.

*Two axes of symmetry bisect each other.

* Diagonals are equal in length.

The figure of rectangle has given the length [tex]l[/tex] = 10m

In right angle triangle ADC.

DC = 10 m ( as alternative sides are equal )

Note that we are given here the adjacent and we have to find the length of hypotenuse, then we use trigonometric ratio that contains both sides adjacent and hypotenuse.

Use: [tex]Cosine = \frac{Adjacent}{hypotenuse}[/tex]

then,

[tex]\cos 32^{\circ} = \frac{10}{AC}[/tex] or

[tex]Ac = \frac{10}{\cos 32^{\circ}} =\frac{10}{0.8480481}[/tex]

On simplify we get;

AC = 11.791784 m

therefore, the length of the diagonal of this rectangle (AC) is, 11.80 m (Approx)

What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?

Enter your answer in the box.

Answers

we know that

A method for calculating the area of a triangle when you know the lengths of all three sides is the Heron's Formula.

The Heron's Formula states that

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

where

a,b.c are the length sides of the triangle

p is half the perimeter of the triangle

Let

[tex]A(-4,1)\\B(-7,5)\\C(0,1)[/tex]

Step 1

Find the distance AB

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(-4,1)\\B(-7,5)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(5-1)^{2}+(-7+4)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]dAB=5\ units[/tex]

Step 2

Find the distance BC

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]B(-7,5)\\C(0,1)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(1-5)^{2}+(0+7)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(7)^{2}}[/tex]

[tex]d=\sqrt{65}[/tex]

[tex]dBC=8.06\ units[/tex]

Step 3

Find the distance AC

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex]A(-4,1)\\C(0,1)[/tex]

substitute the values in the formula

[tex]d=\sqrt{(1-1)^{2}+(0+4)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]

[tex]d=\sqrt{16}[/tex]

[tex]dAC=4\ units[/tex]

Step 4

Find half the perimeter

[tex]p=\frac{1}{2}(AB+BC+AC)[/tex]

substitute the values

[tex]p=\frac{1}{2}(5+8.06+4)[/tex]

[tex]p=8.53\ units[/tex]

Step 5

Find the area

Applying the Heron's Formula

[tex]A=\sqrt{8.53(8.53-5)(8.53-8.06)(8.53-4)}[/tex]

[tex]A=\sqrt{8.53(3.53)(0.47)(4.53)}[/tex]

[tex]A=\sqrt{64.11}[/tex]

[tex]A=8\ units^{2}[/tex]

therefore

the answer is

the area of the triangle is [tex]8\ units^{2}[/tex]

The area of a shape is the amount of space it occupies.

The area of the triangle is 8 unit square.

The vertices are given as:

[tex]\mathbf{A = (-4,1)}[/tex]

[tex]\mathbf{B = (-7,5)}[/tex]

[tex]\mathbf{C = (0,1)}[/tex]

The area of the triangle is:

[tex]\mathbf{A= \frac{1}{2} \times |A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}[/tex]

So, we have:

[tex]\mathbf{A= \frac{1}{2} \times |-4(5 - 1) -7(1 - 1) + 0(1 - 5)|}[/tex]

[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -7(0) + 0|}[/tex]

[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -0 + 0|}[/tex]

[tex]\mathbf{A= \frac{1}{2} \times |-16|}[/tex]

Remove absolute brackets

[tex]\mathbf{A= \frac{1}{2} \times 16}[/tex]

[tex]\mathbf{A= 8}[/tex]

Hence, the area of the triangle is 8 unit square.

Answers

1.) Twenty five minus six

Answer:

Step-by-step explanation:

1)Twenty five minus sixty percent times a number.

If a share of stock costs $32.63, what would it cost to buy 1,000 shares of the stock?

Answers

Here is your answer: If a share of the stock cost 32.63 and you wanted to buy 1,000 shares of the stock you just need to multiply 1,000 and 32.63 32.63*1,000=32,630 Your answer is: 32,630$

answer is: $32,630

you just multiply the 2 intergers

brainliest plz:)

What is the angle of elevation from jim to the top of the waterfall

Answers

Answer: <7

Step-by-step explanation:

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The angle of elevation from Jim to the top of the waterfall is ∠5. The correct option is B.

What is an angle?

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The angle of elevation is an imaginary angle that is assumed between the horizontal line and the line through which an object at a height is been seen.

In the given image the angle of elevation from Jim to the top of the waterfall is the angle formed by the line parallel to the horizontal plane and the line that connects Jim's eyesight to the top of the waterfall.

Hence, the angle of elevation from Jim to the top of the waterfall is ∠5.

Learn more about Angle:

https://brainly.com/question/7116550

#SPJ5

How to solve for a side of a right triangle when you only know one side?

Answers

Well if you know the area of the triangle you can use that to find the other lengths or else just use the Pythagorean Theroem.

Hope I helped :)

If you only know one side, then that's not enough information to solve for any other part of a triangle. You also need to know the measures of the angles at each end of it. In a right triangle, that means you need to know one of the acute angles (since you already know the right angle).

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 780-meter head start. When the start gun is fired the hare begins running at a constant speed of 10 meters per second and the tortoise begins crawling at a constant speed of 5.3 meters per second.

Answers

I am presuming that the question is who won or by how much did the winner win.

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)

The tortoise wins. The tortoise takes 154.7 seconds to finish the race. The hare takes 160 seconds to finish the race. There really isn't a question here, but I'm going to assume the unasked question is one of "Who wins?" "How long does it take the tortoise to complete the race?" or "How long does it take the hare to complete the race?" And thankfully, in determining the answer to "Who wins?" will have as a side effect the answers to the other two questions. First, how many seconds does it take for the hare to complete the race. Just divide the distance by the speed and you'll have the answer. So 1600 m / 10 m/s = 160 s Now, how many seconds does it take the tortoise to finish the race? Same thing. Distance divided by speed. But there's a twist, you need to figure out the distance. And that is just the track length minus the head start. So (1600 m - 780 m) / 5.3 m/s = 820 m / 5.3 m/s = 154.717 s And since the tortoise took less time than the hare, the tortoise wins.

Pythagorean Theorem. I need help please!!!!!

Answers

The hikers started at point S.
The first hiker went 2 miles east and 1 mile north to point A.
The second hiker went 1 mile west and 3 miles south to point B.
See the figure below.

                                                              A
                                                        I
                           1 mile                       I    1 mile
                          I---------S------------------I
                          I                2 miles
                          I
                          I
            3 miles   I
                          I
                          I
                          B

Now we need to see how much east and how much north hiker B is from hiker A.

                                                            A
                                                        I
                           1 mile                       I    1 mile
                          I---------S------------------I
                          I                2 miles   I
                          I                                   I
                          I                                   I
            3 miles   I                                   I   3 miles
                          I                                   I
                          I                                   I
                          B----------------------------I
                                         3 miles

From point B go 3 miles east, then 3 + 1 = 4 miles north to point B.
The distance between the hikers is the hypotenuse of a triangle with legs of lengths 3 and 4.

3^2 + 4^2 = d^2

9 + 16 = d^2

d^2 = 25

d = 5

The distance between the hikers is 5 miles.

Can someone help me with this? 18(−8c+16)−13(6+3c) =

Answers

Hi. I am attaching a step by step image for you. Hope this helps.

Take care,
Diana

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $27 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answers

The first plan : y = 27 + 0.12x
Second plan : y = 0.16x

27 + 0.12x= 0.16x
27 = 0.04x

x = 67.5 minutes

what is the least common factor of 54 and 77

Answers

sorryyyyyyyyyyyyyyyyyyyyyyyyyyyy go see in goggle

The Scott Shop charges $27 more than the Garcia Co. for a winter jacket. If the Scott shop’s price is $77, how much does the Garcia Co. charge?

Answers

Garcia Co. charge = 77 - 27 = $50

subract 27 from 77

77 -27 =50

Garcia charges 50 dollars

The floor of a shed has an area of 99 square feet. the floor is in the shape of a rectangle whose length is 7 feet less than twice the width. find the length and the width of the floor of the shed. use the formula, area equals=length times•width.

Answers

W=width, L=length
L=2W-7
LxW=99 (now substitute)
(2W-7)xW=99 (distribute W)
2W²-7W=99
2W²-7W-99=0 (set to 0 to solve)
(W-18/2)(W+9/2)=0
(W-9)(2W+9)=0
W-9=0; W=9
2W+9=0; 2w=(-9) not possible in real world to have a negative length
So, width = 9 ft, and length = 2(9)-7 = 11 ft

Final answer:

The width is 9 feet and the length is 11 feet.

Explanation:

The area of a shed floor is given as 99 square feet, and the floor is shaped like a rectangle. According to the problem, the length (L) of the floor is 7 feet less than twice the width (W). The relationship between length and width can be expressed as L = 2W - 7. We can use the area formula, which is Area = Length × Width.

Given the area (A) is 99 sq ft, we can set up the equation:

A = L × W
99 = (2W - 7) × W

Now we solve for W using the quadratic equation:

W2 - 7W + 99 = 0

Upon solving, we find that W = 9 feet (since the width cannot be negative). Now we can find the length L by substituting W into the length expression:

L = 2 × 9 - 7 = 11 feet

Therefore, the width is 9 feet and the length is 11 feet.

Simplify (s)(-3st)(-1/3).
A.) -3 1/3 t
B.) s^2t
C.) 3s^2t
(If this format is too weird I have added a screenshot)

Thanks in advance!

Answers

the answer is b!!!!!!

The 3 will cut off each other and the s will be squared so the answer is B..s^2.t

Consider the function
{8x-x^2 for x is less than or equal to 8
x^2+3 for x>8}

what is f(8)?

Answers

f(x) = 8x-x^2 only if x is equal to 8 or less than 8
OR
f(x) = x^2+3 only if x > 8

We can only pick one of the two paths. The function f(x) can't be both at the same time. In the case of computing f(8) we have the input x = 8. It won't fit the bottom piece as x > 8 is false when x = 8. The inequality 8 > 8 is false

So instead we pick the top piece

x = 8 ----> so "x is less than or equal to 8" is true
f(x) = 8x - x^2
f(8) = 8*8 - 8^2
f(8) = 64 - 64
f(8) = 0

The final answer is 0

What is the ratio 35 to 15 expressed as a fraction in simplest form?

Answers

35/15 = 7/3

Dividing by a factor of 5 should help.

The ratio of 35 to 15 is represented as 35:15
That is the same as 35/15
Let's use 5 to divide to its simplest form. That will be;
35 divided by 5 is 7. And 15 divided by 5 is 3. So you have;
7/3
Hope that helped. Have a nice day

a rectangle has a diagonal which is 4 times the width if the area is 15root2 what are width andperimeter of the rectangle

Answers

Let width be x
Area: 15√2
Diagonal; 4x

First, you need to find the length using pythagorean theorem.
a=x
c=4x
b=?

Solve this in terms of x and you will find the solution to be; √15x²

Knowing this, plug the number back into the area formula to find the value of x,

(x)(√15x²)=15√2
...
..
x⁴=30

Length= √(15√(30))

Do the calculations just to be sure

Hope I helped :)

if i have 64,32,16,8 what two numbers comes next

Answers

4 and 2.
(Because the pattern is that it is dividing the previous number by 2)

Sample text because sample text is sample text, which is sample text according to sample text.

4 then 2

i hope this helps and have a wonderful day!!

What? I don’t know what I’m doing???

Answers

looks like your doing it right

Complete the pairs of 's.

(triangle)FCA ~= (triangle)

DAC

EBC

GCA

Answers

I think its DAC but im not sure if you mean congruency the its most likely that one

Answer:

DAC

Step-by-step explanation:

We can write, from the figure of the question.

In ΔFCA and ΔDAC.

∠FAC=∠DCA,

AC=CA, (common)

∠FCA=∠DAC.

Hence , we can say ΔFCA ≅ ΔDAC, because here in ΔFCA and ΔDAC, the two corresponding angles and including side are same (from ASA postulate ).

Which expression is equivalent to -3.5(4x – 3)?
A. -3.9x – 3.2
B. -3.9x + 3.2
C. -14x + 10.5
D. -14x – 10.5

Answers

First, you need to solve the equation.

-3.5 * 4x = -14x
-3.5 * -3 = 10.5

C) -14x + 10.5

Hope this helps!

Answer:

The answer is c

Step-by-step explanation:

how would you graph the solution set of the system of inequalities {3y≤2x+6} { 2x+y>0}

Answers

1) Solve the first inequality

3y ≤ 2x + 6

=> y ≤ 2x/3 + 2

2) Draw the line y = 2x/3 + 2

3) Shade the region below the line y = 2x/3 + 2

4) Solve the inequality 2x + y > 0

=> y > - 2x

5) draw the line y = -2x

6) Shade the region above the line y = -2x

7) The solution is the region between the two lines shaded including the portion of the line y = 2x/3 + 2

Write an expression that is equivalent to 2/3 (4x + 9).

8/3x + 6

8/3x + 9

2/3x + 6

2/3x + 9

Answers

2/3 (4x + 9)
= 8/3x + 6

answer
8/3x + 6

2/3 of 9 = 6

2/3 *4 = 8/3

so the answer would be 8/3x +6

The legs of a right triangle measure 30cm and 40cm.what is the length of the hypotenuse

Answers

The equation to find a hypotenuse is
A^2 + b^2=c^2

Plug in the numbers

30^2 + 40^2 = c^2

900 + 1600 =c^2

2500 = c^2

The square-root of 2500 = c

50=c

The hypotenuse of the triangle is 50

Hope this helps!

a²+b²=c²
30²+40²=c²
900+1600=c²
2500=c²
√2500=√c²
c=50
The hypotenuse is 50cm long.

Hope this helps!

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