Which of the following equations represents a line that is perpendicular to
y --4x+9 and passes through the point, (4,5)?
A. y=1/4x+5
B. y=-4x+4
C. y=1/4x+4
D. y=1/4+6

Answer:

C) [tex]\sqrt{106}[/tex] units

Step-by-step explanation:

The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex] and [tex]b[/tex] are side lengths of a right triangle and [tex]c[/tex] is the hypotenuse, the longest side of the right triangle.

The distance formula is similar to that of the Pythagorean Theorem which is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points that you wish to find the distance between them in an (x,y) coordinate plane.

Here, we are given that [tex](x_1,y_1)[/tex] is [tex]P(-4,-6)[/tex] and [tex](x_2,y_2)[/tex] is [tex]Q(1,3)[/tex]. So, we can use the distance formula as described previously to find the positive distance between the two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(1-(-4))^2+(3-(-6))^2}[/tex]

[tex]d=\sqrt{(1+4)^2+(3+6)^2}[/tex]

[tex]d=\sqrt{(5)^2+(9)^2}[/tex]

[tex]d=\sqrt{25+81}[/tex]

[tex]d=\sqrt{106}[/tex]

[tex]d \approx 10.295630141[/tex]

Since all of the given answer choices are in radical form, then C is the correct answer. The distance between the two points is [tex]\sqrt{106}[/tex] units.

Answer:

Step-by-step explanation:

2x²-3=47

2x²=47+3

x²=50/2=25

x=±√25=±5

Answer:

x = ±5

Step-by-step explanation:

2x^2 - 3 = 47

Add 3 to each side

2x^2 - 3+3 = 47+3

2x^2 = 50

Divide each side by 2

2x^2 = 50/2

x^2 = 25

Take the square root of each side

sqrt(x^2) = sqrt(25)

x = ±5

Answer:

x = ⁷/₅

y = ⁻²⁹/₅

Step-by-step explanation:

4x = 3y + 23 (×3)

12x = 9y + 69

4y + 3x = -19

3x = -4y - 19 (×4)

12x = -16y - 76

∴ 9y + 69 = -16y - 76

25y = -145

y = ⁻²⁹/₅

12x = 9(⁻²⁹/₅) + 69

12x = 69 - ²⁶¹/₅

12x = ⁸⁴/₅

x = ⁷/₅

Answer:

14 cm

Step-by-step explanation:

Use the formula for the area of a square, a = s², where s is the side length of the square.

Plug in 196 as the area, then solve for s.

a = s²

196 = s²

14 = s

So, the length of the pathway is 14 cm

Answer:

18 units

Step-by-step explanation:

The base is 7-4 = 3 units

The height is 8 - 2 = 6 units

P = 2(b+h)

P = 2( 3+6)

P = 2(9)

P = 18

Answer:

isn't it 5?

by counting the lines from C to B

from C to B the length is 5 while the length of D to C is 6

Answer:

x = 21.46

Step-by-step explanation:

[tex]cos 56 = \frac{adjacent}{hypotenuse} = \frac{12}{x}\\\\x = \frac{12}{cos 56} = 21.46[/tex]

Answer:

Step-by-step explanation:

take 56 degree as reference angle

using cos rule

cos 56=adjacent/hypotenuse

0.55=12/x

x=12/0.55

x=21.81

x=21.8

Answer:

the number can be either 8 or 3.

Step-by-step explanation:

Let's define N as the "number"

We know that when the square of this number is increased by 24:

N^2 + 24

we got eleven times the original number, then:

N^2 + 24 = 11*N

We just need to solve this for N

To do it, we first move all the terms to one side of the equation:

N^2 - 11*N + 24 = 0

Now we can use the Bhaskara's formula for the zeros of a quadratic equation:

for a general quadratic equation:

a*x^2 + b*x + c = 0

the roots or zeros are given by:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

We get then:

[tex]N = \frac{-(-11) \pm \sqrt{(-11)^2 - 4*1*24} }{2*1} = \frac{11 \pm 5}{2}[/tex]

So we have two solutions:

N = (11 + 5)/2 = 16/2 = 8

N = (11 - 5)/2 = 6/2 = 3

So the number can be either 8 or 3.

Answer:

a circule

Step-by-step explanation:

Answer:

2 is in the ten thousanths place

Step-by-step explanation:

This is because 2 in 824,795 has the value of 20,000.

Answer:

7/2

Step-by-step explanation:

12 1/4 is equivalent to the improper fraction 49/4.

The square root of 49/4 is 7/2.

The squareroot of [tex]12 \frac14[/tex] is [tex]3 \frac{1}{2} [/tex].

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \sqrt{12 \frac{1}{4} } \\ \\ = \sqrt{ \frac{49}{4} } \\ \\ = \sqrt{ \frac{7 \times 7}{2 \times 2} } \\ \\ = \sqrt{ \frac{( {7})^{2} }{( {2})^{2} } } \\ \\= \frac{7}{2} \\ \\ = 3 \frac{1}{2} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

[tex] \frac{231}{4} [/tex] ✅

Step-by-step explanation:

[tex] \frac{33}{4} \times \frac{21}{3} \\ = \frac{11 \times 21}{4} \\ = \frac{231}{4} [/tex]

Note:-

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

X

Step-by-step explanation:

2x-x=x

5-5=0

Answer:

[tex]2x + (-x) + 5 + (-5) = x[/tex]

Step-by-step explanation :

Remove Parenthesis :

[tex]2x - x + 5 - 5[/tex]

Add similar elements :

[tex]x + 5 - 5[/tex]

Add them up :

[tex]5 - 5 - 0 = x[/tex]

Answer:

50

Step-by-step explanation:

Substitute.

Answer:

320

Step-by-step explanation:

(6 x 3)² - 2(12) ÷ 6

324 - 24 ÷ 6

324 - 4

= 320

Answer:

one measurement

Step-by-step explanation:

hope it's helpful for you ☺️

Answer:

Step-by-step explanation:

The standard form of an exponential function is

[tex]y=a(b)^x[/tex] where y is the value of the car after x years have gone by, a is the initial value of the car and b is the rate of depreciation. For us, that looks like this:

[tex]y=64000(.18)^{4.5[/tex] where 64000 is the initial value of the car, .18 is the depreciation rate, and 4.5 is 54 months in years. Doing the math on that gives us that the value of the car will be $51,840 4.5 years after it's purchased new.

Answer:

bh + L(S1 + S2 + h)

Step-by-step explanation:

b stands for the bottom edge of the base triangle

h is the height of the base triangle

L is the length of the prism

S1 and S2 are the two edges of the base triangle

bh is the combined area of the two triangular faces

L(S1 + S2 + h) is the area of the three rectangular side faces

Answer:

I think it´s 2.

Step-by-step explanation:

7(2) = 14

14+5=19

Pretty simple math for me, not sure about you though.

Answer:

x=2

Step-by-step explanation:

since the two angles are equivalent to each other, we also know that the legs of triangle are equal... so we set the legs equal to each other and solve for x...

7x+5=19

subtract five from both sides

7x=14

divide 7 from both sides

x=2

Answer:

The mark up is $2.20 and the new price of each T-shirt is $6.20.

Step-by-step explanation:

Before we find the new price of each T-shirt we must find the markup (by how much were raising the price).

The problem states each T-shirt costs $4.00, but then marks up the price of each by 55%.

Step 1 would be to find 55% of $4.00.

0.55 * 4 = 2.2

So that is the mark up, the price is going up by $2.20. To find the new price of each T-shirt, you take that $2.20 and add it to the original $4.00.

$4.00 + $2.20 = $6.20

So the mark up is $2.20 and the new price of each T-shirt is $6.20.

Answer:

B No if the length is 20 and the width is 11 , the perimeter is p=40+22=62 not 64

Answer:

2.05 cm

Step-by-step explanation:

3.14× (n+3)²×10 = 800

31.4(n+3)²=800

(n+3)²= 800/31.4

(n+3)²= 25.48

n+3 =√25.48

n+3= 5.05

n = 5.05 -3 = 2.05

so, the radius should be increased :

2.05 cm

The tank contains approximately 26.67 liters of water.

Use the concept of ratio defined as:

A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x: y, which is equivalent to x/y.

Where x and y are individual amounts of two quantities.

And, the Total quantity is given after combining as x + y.

Given that,

Dimensions of the tank: 50 cm by 32 cm by 20 cm

The ratio of water to sand: 5: 1

The volume of the tank: 32,000 cm³

Calculate the volume of the tank first:

Since the ratio of water to sand is 5:1,

Calculate the volume of water.

Assign the variable "x" to represent the volume of water.

According to the ratio,

The volume of sand would be 1/5th of the volume of water,

So the volume of sand would be (1/5)x.

Since the tank is full,

The combined volume of water and sand is equal to the volume of the tank.

Therefore, we have the equation

x + (1/5)x = 32,000 cm³.

Simplifying the equation,

we get (6/5)x = 32,000 cm³.

To find the volume of water (x),

Solve for x by multiplying both sides of the equation by (5/6):

x = (32,000 cm³)(5/6).

Calculating this, we get the volume of water as 26,666.67 cm³.

Now, to convert this to liters,

Divide by 1000:

26,666.67 cm³ ÷ 1000 = 26.67 liters.

Hence, there are approximately 26.67 liters of water in the tank.

Learn more about the ratio visit:

https://brainly.com/question/12024093

#SPJ4

Answer:

18 scoops is the correct answer

Step-by-step explanation:

3/4 can also be written as 6/8 (multiply both 3 and 4 by 2)

and 1 1/2 is actually 3/2 which can be written as 12/8 (multiply both 3 and 2 by 4)

thus total lentils required is 6/8 + 12/8 = 18/8 cups.

with scoop size 1/8 cup you'll need 18 scoops .

Answer:

18 1/8 scoops

Step-by-step explanation:

Soup:

6 scoops from a 1/8 cup can make a 3/4 cup

Salad:

4 scoops from a 1/8 cup can make a 1/2 cup

If 1/8 means one portion is divided into eight portions, then 8 scoops from a 1/8 cup can make 1 cup.

Answer:

38.7°

Step-by-step explanation:

∆ = Tan-1(opposite/ Adjacent)

=Tan-1(8/10)

= 38.66°

= 38.7° to n nearest tenth

Answer: D) Reflect over x-axis

=======================================================

Explanation:

When we do this type of reflection, a point like (1,2) moves to (1,-2).

As another example, something like (5,-7) moves to (5,7)

The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.

We can say that [tex](x,y) \to (x,-y)[/tex] as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.

If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.

There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.

Answer:

growth

Step-by-step explanation:

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

[tex]\displaystyle \frac{\cos y}{1-\sin y}=\frac{1+\sin y}{\cos y}[/tex]

On the left, we can multiply both layers by (1 + sin(y)):

[tex]\displaystyle \frac{\cos y}{1-\sin y}\left(\frac{1+\sin y}{1+\sin y}\right)=\frac{1+\sin y}{\cos y}[/tex]

Multiply:

[tex]\displaystyle \frac{\cos y(1+\sin y)}{1-\sin^2 y}=\frac{1+\sin y}{\cos y}[/tex]

From the Pythagorean Theorem, we know that sin²(y) + cos²(y) = 1. Hence, 1 - sin²(y) = cos²(y). Substitute:

[tex]\displaystyle \frac{\cos y(1+\sin y))}{\cos^2 y}=\frac{1+\sin y}{\cos y}[/tex]

Cancel:

[tex]\displaystyle \frac{1+\sin y}{\cos y}=\frac{1+\sin y}{\cos y}[/tex]

Hence proven.

The more accurate value is 1037.51097384802

Round that however you need to.

=======================================

Explanation:

We need the circumference of the equator. Think of the equator as the largest possible circle (or belt) to fit around the earth.

C = pi*d

C = pi*7926

C = 7926pi

C = 24,900.2633723527

In 24 hours, a person at the equator travels roughly 24,900.2633723527 miles since the earth does a full rotation in this timespan.

Divide the two quantities distance over time to get the speed

rate = distance/time

rate = (24,900.2633723527 miles)/(24 hours)

rate = ( (24,900.2633723527)/(24) ) miles per hour

rate = 1,037.51097384802

rate = 1038 mph

I'm rounding to 4 sig figs since the diameter is given to be in four sig figs.

This speed of roughly 1038 mph is a linear speed and not an angular speed.

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

Extra info (optional section)

Upon further research, I found an article from NASA JPL (jet propulsion laboratory) which states quote:

"To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr)"

Their figure of 1000 mph seems to be a rough estimate, more or less. It's fairly close to the 1038 figure we got earlier.

Answer:

52 degrees

Step-by-step explanation:

Answer:

52 degrees sorry if that's wrong