In my fish tank, the ratio of red fish to blue fish is 1:5. There are 15 blue fish. How many red fish are there?

The slope of the equation x + 2y = 4, is -1/2 and y-intercept of the equation is 2.

When any equation is represented in the y = m x +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given equation of line,

x + 2y = 4,

To find the slope,  represent the equation in slop intercept form,

Simplify the equation,

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 2

The slope of the equation is -1/2.

To find y-intercept, substitute x = 0,

y = -(1/2). 0 + 2

y = 2

The y-intercept of the equation is 2.

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[tex]A_{\triangle}=\dfrac{1}{2}bh\\\\\text{We have}\ b=7cm,\ h=4cm\\\\\text{Substitute:}\\\\A_{\triangle}=\dfrac{1}{2}(7)(4)=\dfrac{28}{2}=\boxed{14\ cm^2}[/tex]

Answer:

5y + 4 and 7y + 4 - 2y

Step-by-step explanation:

Look at  the second choice:-

5y + 4  and 7y + 4 - 2y

Simplifying the second expression:-

7y + 4 - 2y

= 5y + 4

So both expressions are equivalent . Therefore if you plug in 2 or 5 the results will be the same.

Answer:

Second option:

5y+4 and 7y+4-2y

Step-by-step explanation:

1. y=2→2y-1=2(2)-1=4-1→2y-1=3

y=2→3y-5+y→3(2)-5+2=6-5+2→3y-5+y=3

y=5→2y-1=2(5)-1=10-1→2y-1=9

y=5→3y-5+y→3(5)-5+5=15-5+5→3y-5+y=15

2y-1 is not equivalent to 3y-5+y when y=2 and y=5

2. y=2→5y+4=5(2)+4=10+4→5y+4=14

y=2→7y+4-2y→7(2)+4-2(2)=14+4-4→7y+4-2y=14

y=5→5y+4=5(5)+4=25+4→5y+4=29

y=5→7y+4-2y→7(5)+4-2(5)=35+4-10→7y+4-2y=29

5y+4 is equivalent to 7y+4-2y when y=2 and y=5

3. y=2→y+7=2+7→y+7=9

y=2→y+2+y→2+2+2→y+2+y=6

y+7 is not equivalent to y+2+y when y=2 and y=5

4. y=2→3y-4=3(2)-4=6-4→3y-4=2

y=2→3y-2+y→3(2)-2+2=6-2+2→3y-2+y=6

3y-4 is not equivalent to 3y-2+y when y=2 and y=5

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

Answer:

5. 20

6. 30

7. 22

Step-by-step explanation:

5. The median is indicated by the line (and dot) in the middle of the box.

6. The maximum value is indicated by the extreme right end of the whisker.

7, The upper quartile is indicated by the right end of the box.

Step-by-step explanation:

[tex]4csc(2x) = 2csc^2(x) tan(x)[/tex]

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

[tex]4 \frac{1}{sin(2x)}[/tex]

Also we use identity

sin(2x) = 2 sin(x) cos(x)

[tex]4 \frac{1}{2sin(x)cos(x)}[/tex]

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

[tex]2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}[/tex]

[tex]2\frac{sin(x)}{sin^2(x)cos(x)}[/tex]

[tex]2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}[/tex]

We know that sinx/ cosx = tan(x)

Also  1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

Answer

m<3  = 49°

Step-by-step explanation:

It is given that,

M∥n, m∠1 = 50°, m∠2 = 48°, and line s bisects ∠ABC

m<DEF = m<1 + m<2 = 50° + 48° = 98°

Corresponding angle of <DEF is equal to <ABC = 98°

To find m<3

< 4 = <5 = 98/2 = 49° (Since line s bisects ∠ABC)

Therefore,

m<3 = 49°  (< 4 and <3 are vertically opposite angles)

Answer:

m∠3 = 49°

Step-by-step explanation:

We are given that the angles m∠1 = 50° and m∠2 = 48° and the line s bisects ∠ABC.

If m∠1 = 50° and m∠2 = 48°, then ∠DEF = 50 + 48 = 98°

So ∠DEB will be equal to = 180 - 98 = 82°

If ∠DEB = 82°, then the angle from A to B will 180 - 82 = 98°.

We know that the line s bisects ∠ABC, therefore the measure of angle m∠3 will be half of 98 = 49°

The value of x is -101/4 or the simplified form of the expression can be given as -1/2x = 101/8

This question relates to equation in mathematics and all we need to do is solve for x. But this requires some step by step process which are

The given equation is

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\[/tex]

[tex]2(\frac{x}{2} - 5) - \frac{3}{2} (x+\frac{7}{4} )\\\\(\frac{2}{2}x-10)-(\frac{3}{2}x-\frac{21}{8}) \\x- 10 -\frac{3}{2}x-\frac{21}{8}\\[/tex]

[tex]x-\frac{3}{2}x-10-\frac{21}{8}=0\\-\frac{1}{2}x =10+\frac{21}{8}\\-\frac{1}{2}x=101/8\\[/tex]

We have to divide through by coefficient of x

[tex]-\frac{1}{2}x =\frac{101}{8}\\(-1/2x)/(-1/2)=(101/8)/(-1/2)\\x=\frac{-101}{4} \\[/tex]

from the above calculation, the value of x is -101/4. The simplified form of the expression is -1/2x = 101/8

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D

Angle 7π/6 is π/6 below the negative x-axis in the 3rd quadrant. Its cosine will be -(√3)/2.

Angle 11π/6 is π/6 below the positive x-axis in the 4th quadrant. Its cosine will be (√3)/2.

The cosines have the same magnitude, but their signs are opposite each other. Jeremy was not correct.

Answer:

Its D

Step-by-step explanation:

If p then q. If p is true then q is true.

Answer:

it's number d

Step-by-step explanation:

Answer: (2, 9)

Step-by-step explanation:

[tex]\lbrace^{y=5x-1 }_{2y=3x+12}}[/tex]

Since "y" = "5x - 1", we can replace "y" in the second equation with "5x - 1"

    2y = 3x + 12

⇒ 2(5x - 1) = 3x + 12    substituted "y" with "5x - 1"

⇒ 10x - 2 = 3x + 12     distributed 5x - 1 by 2 on left side

⇒  7x - 2 = 12              subtracted 3x from both sides

⇒  7x = 14                    added 2 to both sides

⇒ x = 2                         divided both sides by 2

Next, let's solve for y by substituting "x" with "2":

y = 5x  - 1

  = 5(2) - 1

  = 10 - 1

  = 9    

180 in² - the area

width × lenght - the area

length : width = 5 : 4 therefore length = 5x and width = 4x

(x - some unit of length)

The equation:

(5x)(4x) = 180

20x² = 180     divide both sides by 20

x² = 9 → x = √9 → x = 3 in.

The length = 5x, therefore your answer is:

Answer: sqrt(19)/10

Step-by-step explanation:

sinx=0.9

x=arcsin(0.9)

Insert x for cos(x):

cos(arcsin(0.9)=

Use identify [tex]cos(arcsin(x))=\sqrt{1-x^{2} }[/tex], so

[tex]\sqrt{1-(\frac{9}{10})^{2}} =\sqrt{\frac{19}{100} } =\frac{\sqrt{19}}{10}[/tex]

Sorry if this is confusing.

Final answer:

To find cos X given sin X = 0.9, use the Pythagorean identity, solve for cos2 X, take the square root, and round to the nearest thousandth to get cos X ≈ 0.436.

Explanation:

To calculate the value of cos X when sin X= 0.9, we can use the Pythagorean identity which states that sin2X + cos2X = 1. First, square the sine value: (sin X)2 = 0.92 = 0.81. Then, we subtract this value from 1 to find (cos X)2: 1 - 0.81 = 0.19. Finally, we take the square root of 0.19 to find the value of cos X. Since sin X is positive and assuming X is an angle in the first quadrant, cos X will also be positive. So, cos X = √0.19 ≈ 0.436.

Therefore, the value of cos X, rounded to the nearest thousandth, is 0.436.

Answer:

The true statement is UV < US < SR ⇒ 1st statement

Step-by-step explanation:

"I have added screenshot of the complete question as well as the

diagram"

* Lets revise the hinge theorem

- If two sides of one triangle are congruent to two sides of another

 triangle, and the measure of the included angle between these two

 sides of the first triangle is greater than the measure of the included

 angle of the second triangle then the length of the third side of the

 first triangle is longer than the length of the third side of the second

 triangle

* Lets solve the problem

- The figure has three triangles have a common vertex T

- m∠UTV < m∠UTS < m∠STR

- From the hinge theorem above

∵ The side opposite to ∠UTV is VU

∵ The side opposite to ∠UTS is US

∵ The side opposite to ∠STR is SR

∵ m∠UTV < m∠UTS < m∠STR

∴ UV < US < SR

* The true statement is UV < US < SR

Answer:

VU<US<SR by the hinge theorem

Step-by-step explanation:

Answer:

Judy = $5/hr

Ben = $4/hr

Step-by-step explanation:

Judy's hours at work - x

Ben's hours at work - y

8x + 10y = 80

9x + 5y = 65

Given these two equations above, we get:

10y = 80 - 8x, which means y = 8 - 0.8x.

Substitute y in the second equation with 8 - 0.8x, so we have:

9x + 5 (8 - 0.8x) = 65

9x + 40 - 4x = 65

5x = 25

x = 5

Come back to the first equation, substitute x:

8*5 + 10y = 80

10y = 80 - 40

y = 4

Final answer:

Dulcina has 26 refrigerator magnets and Hannah has 52, which is 2 times the number of Dulcina's magnets. They have 78 magnets in total.

Explanation:

The question involves a simple algebra problem. Let's say Dulcina has x refrigerator magnets. According to the problem statement, Hannah has 2 times as many refrigerator magnets as Dulcina, so she has 2x magnets. Together, they have 78 magnets, which means x + 2x = 78. To find out how many refrigerator magnets each has, we need to solve for x.

Combine like terms:
3x = 78

Divide both sides by 3 to solve for x:
x = 26

Now, to find the number of refrigerator magnets Hannah has, we multiply x by 2:
2x = 2 × 26 = 52

Set up a proportion:

17 miles in 306 minutes, write as 17/306

X miles in 162 minutes, write as X/162

Now set to equal and solve:

17/306 = x/162

Cross multiply:

17 * 162 = 306 *x

2754 = 306x

Divide both sides by 306:

x = 2754 / 306

x = 9

It will travel 9 nautical miles.

Answer:

Use point slope form, by finding the slope between two of the points given on the line you can then input it with one of the points into the formula. Then simplify to convert to slope-intercept form. You can then graph it easily. After which, you can convert to standard form by getting the variables to one side. Be sure in standard form to clear negatives x may have or any fractions x or y may have through multiplication.

Step-by-step explanation:

To write an equation for linear equations, we use one of three forms: standard, slope intercept, and point slope. Slope intercept and point slope are the most common. After we choose our form, we need to find the information required for that form. Point slope is easiest since it requires the slope/rate of change and any point on the line.

Point slope:[tex]y-y_1=m(x-x_1)[/tex]

We must find the slope using the slope formula.

Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We substitute [tex]x_1=-3\\y_1=1[/tex] and [tex]x_2=3\\y_2=5[/tex]

[tex]m=\frac{5-1}{3-(-3)}[/tex]

[tex]m=\frac{4}{3+3}=\frac{4}{6} =\frac{2}{3}[/tex]

We will substitute [tex]m=\frac{2}{3}[/tex] and [tex]x_1=-3\\y_1=1[/tex].

[tex]y-1=\frac{2}{3} (x-(-3))[/tex]

We can simplify to get slope intercept form:

[tex]y-1=\frac{2}{3} (x+3))[/tex]

[tex]y-1=\frac{2}{3}x+\frac{2}{3}(3)[/tex]

[tex]y-1=\frac{2}{3}x+2[/tex]

[tex]y-1+1=\frac{2}{3}x+2+1[/tex]

[tex]y=\frac{2}{3}x+3[/tex]

This is the slope intercept form. We can graph it by finding 3 on the y-axis. Plot a point there.  Then move up two units and to the right three units. Plot a point. Connect the points.

To convert to Standard Form, we will rearrange the equation with x and y on the same side.

[tex]y=\frac{2}{3}x+3[/tex]

[tex]-\frac{2}{3}x+y=\frac{2}{3}x-\frac{2}{3}x+3[/tex]

[tex]-\frac{2}{3}x+y=3[/tex]

[tex]-3(-\frac{2}{3}x+y=3)[/tex]

[tex] 2x-3y=-9[/tex]

This is the standard form.

See the attached picture.

Final answer:

Marcus is incorrect, not because the result may not be rational, but because of his reasoning. An integer raised to a negative integer exponent leads to the base being inverted and raised to the positive exponent, but the result is still a rational number.

Explanation:

Marcus is incorrect in stating that any time an integer is raised to an integer exponent, the result is a rational number. To understand why, we should look at the case when an integer is raised to a negative integer exponent. For example, 3-2 is equal to 1 / (32) which simplifies to 1 / 9. A negative exponent inverts the base number and raises it to the positive of that exponent, which means the result is still a rational number, as it's a quotient of two integers. Therefore, the correct statement is that the result of an integer raised to any integer exponent is indeed a rational number, as the quotient of two integers (for negative exponents) is also a rational number.

Answer:

27 muffins.

Step-by-step explanation:

We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.

To find the number of muffins sold by noon let us find 45% of 60.

[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]

[tex]\text{The number of muffins sold by noon}=27[/tex]

Therefore, 27 muffins were sold by noon.

Answer:

16

Step-by-step explanation:

sum of x and 14 is 18

x+14 = 18

Subtract 14 from each side

x+14-14 = 18-14

x = 4

product of x and 4

x*4

4*4

16

Answer:

16

18 minus 14 is 4. 4 times 4 is 16.

Answer:

Step-by-step explanation:

Start at the end and work backwards to do this one.  Mai scored 5 points.

If Noah scores three times what Mai scores, then:

Noah = 3(5) = 15

If Tyler scores 4 points less than Noah, then:

Tyler = 15 - 4 = 11

If Elena scores twice what Tyler scores, then:

Elena = 2(11) = 22

[tex]adj(x) = \frac{\sqrt{7}}{3}[/tex]

[tex]opp(y) = \frac{\sqrt{2}}{3}[/tex]

adj² + opp² = hyp²

[tex](\frac{\sqrt{7}}{3})^{2} +(\frac{\sqrt{2}}{3})^{2} = hyp^{2}[/tex]

[tex]\frac{7}{9} +\frac{2}{9} = hyp^{2}[/tex]

1 = hyp²

1 = hyp

sin = [tex]\frac{opp}{hyp} =\frac{\sqrt{2}}{3}[/tex]

cos = [tex]\frac{adj}{hyp} =\frac{\sqrt{7}}{3}[/tex]

tan = [tex]\frac{opp}{adj} =\frac{\sqrt{2}}{sqrt\{7}=\frac{\sqrt{14}}{7}}[/tex]

csc = [tex]\frac{hyp}{opp} =\frac{3}{sqrt\{2}=\frac{3\sqrt{2}}{2}}[/tex]

sec = [tex]\frac{hyp}{adj} =\frac{3}{sqrt\{7}=\frac{3\sqrt{7}}{7}}[/tex]

cot = [tex]\frac{adj}{opp} =\frac{\sqrt{7}}{sqrt\{2}=\frac{\sqrt{14}}{2}}[/tex]

****************************************************************

Answer: 8052

Step-by-step explanation:

[tex]A = Pe^{kt}[/tex]

[tex]5500 = 5000e^{k(3)}[/tex]

[tex]\frac{5500}{5000} = e^{3k}[/tex]

[tex]1.1 = e^{3k}[/tex]

[tex]ln1.1 = lne^{3k}[/tex]

ln1.1 = 3k

[tex]\frac{ln1.1}{3}=k[/tex]

0.03177 = k

[tex]A = Pe^{0.03177t}[/tex]

[tex]A = 5500e^{0.03177(12)}[/tex]

[tex]A = 5500e^{0.3812}[/tex]

[tex]A = 5500(1.4641)}[/tex]

A = 8052.55

****************************************************************

Answer: (2, 9)

Step-by-step explanation:

3x - 8y = -66   →   2(3x - 8y = -66)   →   6x - 16y = -132

2x - 7y = -59   →  -3(2x - 7y = -59)   →  -6x + 21y = 177

                                                                        5y = 45

                                                                          y  = 9

2x - 7y = -59

2x - 7(9) = -59

2x - 63 = -59

2x         = 4

x          = 2

Answer:

240 pennies occupy (2/5 minus 1/10) the penny bank volume.

2/5 - 1/10 = 3/10 = .3

240 pennies .3 * the volume

Volume = 240 / .3 = 800 pennies

Step-by-step explanation:

[tex]QR=\sqrt{68^2-60^2}\\QR=\sqrt{4624-3600}\\QR=\sqrt{1024}\\QR=32\\\\sinS=\frac{32}{68}\\sinS=\frac{8}{17}[/tex]

For this case, we have that by definition:

Be a rectangular triangle and an "x" angle.

[tex]Sine (x) = \frac {CO} {H}[/tex]

CO is the leg opposite the angle and H the hypotenuse

We want to find the Sine (S) according to the figure shown:

[tex]Sine {S} = \frac {QR} {68}[/tex]

We do not have the opposite leg, we must apply the Pythagorean theorem, which states:

[tex]H = \sqrt {(CO) ^ 2 + (CA) ^ 2}[/tex]

Where:

H: Hypotenuse

CO: Opposite leg

CA: Adjacent leg

In this case, we must find CO:

[tex]CO = \sqrt {H ^ 2- (CA) ^ 2}[/tex]

Where:

[tex]H = 68\\CA = 60[/tex]

Substituting:

[tex]CO = \sqrt {68 ^ 2-60 ^ 2}\\CO = \sqrt {4624-3600}\\CO = \sqrt {1024}\\CO = 32[/tex]

So, we have:

[tex]Sine (S) = \frac {32} {68}[/tex]

Answer:

[tex]Sine (S) = \frac {32} {68}[/tex]

[tex]Sine (S) = \frac {8} {17}[/tex]

A scale factor of 1/2 makes the triangle half the size of the original.

The original is 4 units tall, so 1/2 scale makes the new one 2 units tall.

It is 6 units long, so 1/2 would be 3 units long.

Now since the scale factor is centered at (-1,3) fine the midpoint between The top left corner of the triangle and the center point:

Midpoint ( -1-5/2 , 3+7/2)

Midpoint = (-6/2 , 10/2)

Midpoint = -3,5

This is where the top left corner of the scaled triangle would be.

See attached picture:

Answer: 12 hours

Step-by-step explanation:

1.) add 10 1/4 and 9 1/3. You’ll get 19.75

2.) divide 250 by 19.75. You’ll get something close to 12.6582278481 if you use appendix zeros.

3.) round 12.6582278481 to the nearest whole number. It will be 12. Hope this helps :)

Answer:

C

Step-by-step explanation:

The lines drawn have the following features:

Since the equation of a line has the form y=mx+b where b is y-intercept and m is the slope, we can write

y=-2x+1

y=2x-3

This is the system of equations and is answer choice C.

Answer: C

Step-by-step explanation:

Slope-Intercept form of an equation is y = mx + b

Red line:

It crosses the y-axis at -3 so b = -3

Now count the rise over run from the b (0, -3) to another point (I chose (1, -1) because it was the next point on a lattice line). The rise is 2 and the run is 1. So. rise over run is 2/1  ⇒ m = 2

Equation: y = 2x - 3

Yellow line:

Follow the same steps as the Red line to get b = 1 and m = -2

Equation: y = -2x + 1