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3 years ago

What is the equation of a line with a slope of 7 and a point (1, 8) on the line?

Mathematics

1 answer:

Helen [10]3 years ago

7 0

Answer:

$y=7x+1$

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

In this problem we have

$m=7$

$point(1,8)$

substitute and solve for b

$8=7(1)+b$

$8=7+b$

$b=8-7=1$

The equation of the line is equal to

$y=7x+1$

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The measure of one angle is 13 less than five times The measure of another angle. The sum of the measure of the two angles is 14

kodGreya [7K]

$\huge\boxed{a=\frac{229}{2};\ \ b=\frac{51}{2}}$

In decimal form, a = 114.5; b = 25.5

We will write this as a system of equations, where $a$ and $b$ are the two angles.

$\left \{ {{a=5b-13} \atop {a+b=140}} \right$

We will use substitution to solve this system. We know what $a$ equals, so we plug that into the second equation.

$5b-13+b=140$

Combine the like terms.

$6b-13=140$

Add $13$ on both sides.

$6b=153$

Divide both sides by $6$ .

$b=\frac{153}{6}=\boxed{\frac{51}{2}}$

Now just subtract that from $140$ .

$a=140-\frac{51}{2}=\boxed{\frac{229}{2}}$

7 0

2 years ago

Solve 3x2 = −12x − 15. x = −4 ± 2i x = −4 ± i x = −2 ± 2i x = −2 ± i

diamong [38]

ANSWER

$x = - 2 \pm i$

EXPLANATION

We use the method of completing the squares.

The equation is
$3 {x}^{2} = - 12x - 15$

We rewrite the above equation to obtain;

$3 {x}^{2} + 12x = - 15$

We divide through by 3 to obtain;

${x}^{2} + 4x = - 5$

We add half the coefficient of
$x$

to both sides of the equation to get,

${x}^{2} + 4x + {2}^{2} = - 5 + {2}^{2}$

The right hand side is now a perfect square.

${(x + 2)}^{2} = - 1$

We now take square root of both sides to get;

$x + 2 = \pm \sqrt{ - 1}$

We add -2 to both sides,

$x = - 2 \pm \sqrt{ - 1}$

We simplify to obtain,

$x = - 2 \pm i$

3 0

3 years ago

Which of the following trigonometric inequalities has no solution over the interval 0 ≤ x ≤ 2pi radians?

valentinak56 [21]

Answer:

A .cos(x)<1

Step-by-step explanation:

According to the first inequality

cos(x)<1

x < arccos 1

x<0

This therefore does not have a solution within the range 0 ≤ x ≤ 2pi

x cannot be leas than 0. According to the range not value, 0≤x which is equivalent to x≥0. Thus means otvis either x = 0 or x> 0.

For the second option

.cos(x/2)<1

x/2< arccos1

x/2<0

x<0

This inequality also has solution within the range 0 ≤ x ≤ 2pi since 0 falls within the range of values.

For the inequality csc(x)<1

1/sin(x) < 1

1< sin(x)

sinx>1

x>arcsin1

x>90°

x>π/2

This inequality also has solution within the range 0 ≤ x ≤ 2pi since π/2 falls within the range of values

For the inequality csc(x/2)<1

1/sin(x/2) < 1

1< sin(x/2)

sin(x/2)> 1

x/2 > arcsin1

X/2 > 90°

x>180°

x>π

This value of x also has a solution within the range.

Therefore option A is the only inequality that does not have a solution with the range.

6 0

3 years ago

Ivan is painting 3 walls in his living room. Each wall measures 9 3/4 feet tall by 14 1/4 feet wide. Ivan needs to estimate the

Alenkinab [10]

Answer:

The estimated area is $416\frac{13}{16}\ ft^{2}$

Step-by-step explanation:

we know that

To estimate the area that Ivan will paint , calculate the area of one wall and then multiply by 3

step 1

Convert the dimensions to an improper fractions

$9\frac{3}{4}\ ft=\frac{9*4+3}{4}=\frac{39}{4}\ ft$

$14\frac{1}{4}\ ft=\frac{14*4+1}{4}=\frac{57}{4}\ ft$

step 2

Find the area of one wall

$(\frac{39}{4})*(\frac{57}{4})=\frac{2,223}{16}\ ft^{2}$

step 3

Multiply the area of one wall by 3

$(3)*\frac{2,223}{16}=\frac{6,669}{16}\ ft^{2}$

step 4

Convert to mixed number

$\frac{6,669}{16}=\frac{6,656}{16}+\frac{13}{16}=416\frac{13}{16}\ ft^{2}$

4 0

3 years ago

30 ounces = ____lb ____oz

Darina [25.2K]

The answer is C. 1 lb 14 oz.

7 0

3 years ago

Read 2 more answers