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2 years ago

The brackets for a shelf are in the shape of a triangle. Find the angles of the triangle if the

Mathematics

1 answer:

zimovet [89]2 years ago

6 0

Answer:

Step-by-step explanation:

2x+3x+5x = 180°

x = 18°

Angles: 36°, 54°, 90°

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The U.S. Senate has 100 members. After a certain election, there were 4 more Democrats than Republicans, with no other parties r

kakasveta [241]

Let x = # of Republicans

x + 4 = # of Democrats

x + x + 4 = 100

x = 48

48 + 4 = 52

There are 52 Democrats and 48 Republicans.

3 0

2 years ago

∫c x sin y ds, C is the line segment from (0, 1) to (3, 5)

Mnenie [13.5K]

Parameterize the line segment $C$ by

$\mathbf r(t)=\langle x(t),y(t)\rangle=(1-t)\langle0,1\rangle+t\langle3,5\rangle=\langle3t,1+4t\rangle$

where $t\in[0,1]$ . Then

$\mathrm ds=\|\mathbf r'(t)\|\,\mathrm dt$
$\mathrm ds=\|\langle3,4\rangle\|\,\mathrm dt$
$\mathrm ds=5\,\mathrm dt$

So the integral is

$\displaystyle\int_Cx\sin y\,\mathrm ds=5\int_0^1x(t)\sin y(t)\,\mathrm dt$
$=\displaystyle5\int_0^13t\sin(1+4t)\,\mathrm dt$
$=\dfrac{15}{16}(\sin5-\sin-4\cos5)\approx-2.7516$

3 0

2 years ago

Caitlin has 4 3/4 pounds of clay . She uses 1 1/10 pounds to make a cup ,and another 2 pounds to make a jar , how many pounds ar

Brut [27]

There are 33/20 or 1.65 pounds left.

Given:
4 3/4 pounds of clay
1 1/10 pounds of clay for a cup
2 pounds of clay for a jar

Convert the mixed fraction into fractions.
4 3/4 = (4*4+3)/4 = 19/4
1 1/10 = (1*10+1)/10 = 11/10
2 = 2/1

19/4 - 11/10 = (19/4 *5/5) - (11/10 * 2/2) = 95/20 - 22/20
= (95-22)/20 = 73/20 or 3.65 pounds after making a cup

73/20 - 2/1 = 73/20 - (2/1 * 20/20) = 73/20 - 40/20 = 73 - 40 / 20 = 33/20 OR 1.65 pounds left after making a jar.

We can also convert the fractions into decimal numbers.
19/4 = 4.75
11/10 = 1.10
2/1 = 2.00

4.75 - 1.1 - 2 = 1.65 pounds left.

5 0

2 years ago

What is 8 divided by 3/4s

d1i1m1o1n [39]

The answer is 10 2/3 because 3/4 equals .75. 8 divided by .75 equals 10 2/3

7 0

2 years ago

The graphs below have the same shape. What is the equation of the red

anyanavicka [17]

Answer:

Option B is correct .

Step-by-step explanation:

According to Question , both the graph have same shape . If we look at the the first graph it cuts x - axis at (0 , 2) and ( 0 , -2) . Hence x = 2 and -2 are the zeroes of the equation .

And ,the given function is ,

$\implies f(x) = 4 - x^2 \\\\\implies f(x) = 4-x^2=0 \\\\\implies 2^2-x^2=0\\\\\implies (2-x)(2+x) = 0 \\\\\boxed{\red{\bf \implies x = 2 , (-2) }}$

Hence ,we can can see that x = 2 and (-2) are the zeroes of graph. 

This implies that if we know the zeroes , we can frame the Equation.

On looking at second parabola , it's clear that cuts x - axis at ( 1, 0 ) and (-1,0). So , 1 and -1 are the zeroes of the quadratic equation . Let the function be g(x) . Here , a and ß are the zeroes.

$\implies g(x) = (x-\alpha)(x-\beta) \\\\\implies g(x) = (1+x)(1-x) \\\\\boxed{\pink{\bf \implies g(x) = 1 - x^2}}$

Hence option B is correct .

8 0

2 years ago

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