plz help me. how many solutions

Answer:

Option (B)

Step-by-step explanation:

From the figure attached,

ΔABC is a right triangle.

Cosine and Sine ratios from the given triangle will be,

SinA = [tex]\frac{\text{Opposite side}}{Hypotenuse}[/tex]

        = [tex]\frac{a}{c}[/tex]

CosB = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{a}{c}[/tex]

Therefore, both the ratios (Sine and Cosine) will be equal as [tex]\frac{a}{c}[/tex]

Option (B) will be the correct option.

Answer:

4

Step-by-step explanation:

i dont really know how to explain i used an algebra calculator

Answer:

Jake ran 10 1/6 miles in total

Step-by-step explanation:

4 1/4 + 2 2/3 - (4 1/4-1).

                  v

6 11/12 + 3 1/4

          v

6 11/12 + 3 3/12 = 10 1/6

Jake ran 10 1/6 miles in total (Mon, Tues, Wed).

Answer:

61/6 or 10.1666666667

Step-by-step explanation:

Monday = 4  1/4

Tuesday = 2  2/3

Wednesday = Monday - 1

=> Monday = 17/4 miles

=> Tuesday = 8/3 miles

=> Wednesday = 17/4 - 4/4 = 13/4 miles.

=> (17/4 + 13/4) + 8/3

=> 30/4 + 8/3

=> Take the LCM of the denominators.

=> LCM = 12

=> 90/12 + 32/12

=> 122/12

SImplify 122/12

=> 61/6 or 10.1666666667

Answer:

a = -8

Step-by-step explanation:

-5/2 a + 5 = 25

Subtract 5 from each side

-5/2 a + 5-5 = 25-5

-5/2 a = 20

Multiply each side by -2/5

-2/5 *-5/2 a = 20*-2/5

a = -8

Answer:

Step-by-step explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or  (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.

Answer:

Step-by-step explanation:

Given the expression [tex]\large 6\cdot\frac{6+2^2}{6+2-6}[/tex], on simplification we have;

[tex]= \large 6\cdot\frac{6+2^2}{6+2-6}\\\\= \large 6\cdot\frac{6+4}{8-6}\\\\= \large 6\cdot\frac{10}{2}\\\\= 6* 5\\\\= 30[/tex]

Hence the equivalent value of the expression is 30

Answer:

A) 0.875, 87.5%

B) 0.12, 12%

C) 1.6, 160%

Step-by-step explanation:

Answer:

A) 0.875, 87.5%

B) 0.001, 0.1%

C) 1.6, 160%

Step-by-step explanation:

I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.

Answer:

12.198

Step-by-step explanation:

the thousandth is the third digit after the decimal point, so you round the next number after it, which is 5. so you round it up, ends with 12.198

We get 12.198 after rounding it to the nearest thousandth.

The rounding off decimal places is similar to the basic round-off. We check the previous number. If it is greater than or equal to 5, we increase the value up to which we are rounding by 1, or else keep it the same when the previous digit is less than 5.

The order of digits for decimal places is opposite to the normal number system.

In the number system we have units place, then tens place, then hundreds place, then thousands place, and like that.

In the decimal number system, we start from the highest and go on decreasing.

The first decimal place is the tenth place.

The second decimal place is the hundredth place.

The third decimal place is the thousandth place.

And so on.

In the question, we are asked to round 12.1975 to the nearest thousandth.

As discussed above, the nearest thousandth means rounding off up to the third decimal place.

So we round off 12.1975 up to the third decimal place, that is, we round off up to 7.

The next digit is 5, so we increase 7 by 1 to 8.

Thus, we get 12.198 after rounding it to the nearest thousandth.

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Answer:

Jess will have to spend 40% of her salary

Step-by-step explanation:

Jess salary = $15,000

Jess expenses = $6,000

what percent of Jess's money does she have to spend

Percentage of Jess expenses = Jess expenses / Total salary × 100

= 6,000 / 15,000 × 100

= 0.4 × 100

= 40%

Jess will have to spend 40% of her salary

Answer:

3 times the percent for the balance to be $221

Step-by-step explanation:

Answer:

Step-by-step explanation:

m<MON = 8x - 13°

m<LOM = 7x - 17°

To find : m <MON

First, we have to find the value of x :

Create an equation

[tex] \mathrm{8x - 13 + 7x - 17 = 180}[/tex] ( sum of angle in straight line )

Collect like terms

[tex] \mathrm{15x - 13 - 17 = 180}[/tex]

Calculate

[tex] \mathrm{15x - 30 = 180}[/tex]

Move constant to R.H.S and change its sign

[tex] \mathrm{15x = 180 + 30}[/tex]

Calculate the sum

[tex] \mathrm{15x = 210}[/tex]

Divide both sides of the equation by 15

[tex] \mathrm{ \frac{15x}{15} = \frac{210}{15} }[/tex]

Calculate

[tex] \mathrm{x = 14}[/tex]

Now, let's find the value of m<MON

[tex] \mathrm{8x - 13}[/tex]

Plug the value of x

[tex] \mathrm{ = 8 \times 14 - 13}[/tex]

Calculate the product

[tex] \mathrm{ = 112 - 13}[/tex]

Calculate the difference

[tex] \mathrm{ = 99}[/tex] °

Hope I helped!

Best regards!

Answer:

48

Step-by-step explanation:

because i say so

Answer:

4

Step-by-step explanation:

V = Lwh

the volume (given) = 24 ft^3

the height (given) = 18" = 1.5'

24 = L*w*1.5

divide both sides by 1.5

16 = Lw

You need to find the number of feet in each side of the base

since the box has a square base

L = W

AND, found above, L*w = 16

so 4*4= 16

Answer - 4

Answer:

-12°C

Step-by-step explanation:

6AM = 2°C

8AM= -2°C

10AM= -6°C

12AM= -8°C

2PM= -12°C

the temperature in degrees Celsius at 2:00 pm would be -14°C.

To find the temperature in degrees Celsius at 2:00 pm, we need to determine the number of hours that have passed from 6:00 am to 2:00 pm, and then calculate the temperature decrease accordingly.

From 6:00 am to 2:00 pm, a total of 8 hours have passed (6 hours from 6:00 am to 12:00 pm, and 2 hours from 12:00 pm to 2:00 pm).

Given that the temperature drops 2 degrees Celsius each hour, we can multiply the number of hours (8) by the rate of temperature decrease (2 degrees/hour):

Temperature decrease = 8 hours × 2 degrees/hour = 16 degrees

Starting with a temperature of 2°C at 6:00 am, if the temperature drops 16 degrees Celsius over 8 hours, we can subtract 16 from the initial temperature:

Temperature at 2:00 pm = 2°C - 16°C = -14°C

Therefore, the temperature in degrees Celsius at 2:00 pm would be -14°C.

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Answer:

x = 2

Step-by-step explanation:

6x-1=11

Add 1 to each side

6x-1+1=11+1

6x = 12

Divide by 6

6x/6 = 12/6

x = 2

Answer:

Step-by-step explanation:

[tex]6x-1=11 \\\\Collect \: like \:terms\\\\6x = 11+1\\\\Simplify\\\\6x =12\\\\Divide\:both\:sides\:by\:6\\\\\frac{6x}{6} = \frac{12}{6}\\ x = 2[/tex]

Answer:

The center of the circle is

Step-by-step explanation:

Equation of a circle is given by

where r is the radius

(h, k) is the center of the circle

The center of a circle is given by

( - h , - k)

From the question equation of the circle is

( x + 4)² + ( y - 2)² = 16

Comparing with the general equation above

( h , k) = ( 4 , - 2)

The center of the circle is

( - h , - k) = ( - 4 , -(-2))

We have the final answer as

Hope this helps you

Answer:

Option (1)

Step-by-step explanation:

The given triangle JKL is an equilateral triangle.

Therefore, all three sides of this triangle will be equal in measure.

Side JK = JL = KL = 48 units

Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.

By applying tangent rule in ΔJML,

tan(∠KJL) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

                = [tex]\frac{\text{LM}}{\text{JM}}[/tex]

                = [tex]\frac{\text{LM}}{24}[/tex]

Since, Sin(K) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Sin(60)° = [tex]\frac{\text{LM}}{48}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\text{LM}}{48}[/tex]

LM = 24√3

Now, tan(∠KJL) = [tex]\frac{\text{LM}}{24}[/tex]

                          = [tex]\frac{24\sqrt{3} }{24}[/tex]

Therefore, Option (1) will be the answer.

Answer:

a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.

For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .

Median represents the middle value of the given data when arranged in a particular order.

Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.

The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.

We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.

Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

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Answer:

[tex]\Large \boxed{\mathrm{Option \ 2}}[/tex]

Step-by-step explanation:

[tex]2x^2 =16[/tex]

The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.

The x variable should be isolated on one side of the equation. The x variable is squared so before performing the square root property where we take the square root of both sides, we divide both sides by 2, then take the square root of both sides.

Dividing both sides by 2.

[tex]\displaystyle \frac{2x^2 }{2} =\frac{16}{2}[/tex]

[tex]x^2 =8[/tex]

Taking the square root of both sides.

[tex]\sqrt{x^2 } =\pm \sqrt{8}[/tex]

[tex]x=\pm 2\sqrt{2}[/tex]

Answer:

Option 2

Step-by-step explanation:

2x² = 16

Since x is completely squared and and 2 isn't , so we need to divide both sides by 2. As to find x , we need to "isolate" x first so that is why we need to get rid of 2 with the x². We'll divide both sides by 2 in order to get rid of 2.

Dividing both sides by 2

=> x² = 8

Now , that is the x is isolated so we'll take square root on both sides

=> x = ±2√2

Answer: (2, -4) and (7, -1)

Step-by-step explanation:

Ok, the solutions of the system of inequalities are all the points that lie on the blue shaded part of the graph or in the solid line.

So, in order to see if the points are solutions of the system, then you need to locate the point in the graph and see if it is inside the shaded region or in the solid line (only in the segment that "touches" the shaded region).

Now, we want to find the equation of the solid line, we can see that it passes through the points (0, 6) and (6, 0)

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then, in this case, the slope is:

a = (0 - 6)/(6 - 0) = -1.

And to find the value of b, we have that when x = 0, y = 6.

y = 6 = -1*0 + b

6 = b

The equation is:

y = -1*x + 6

(-1, 5) is not in the blue region nor in the solid line, so this is not a solution.

(7, - 1) this point is near the solid line, let's test it:

y(7) = -1*7 + 6 = -1

So the point (7, -1) is on the solid line, and is the other solution of the system.

Answer:

f₁(x) = -3x + 2

f₂(x) = x - 4

f₃(x) = x + 8

f₄(x) = -2x - 6

f₅(x) = -3x

Step-by-step explanation:

1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)

Let the equation of the blue line is,

y = mx + b

Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{8-2}{-2-0}[/tex]

m = -3

Y-intercept 'b' = 2

Therefore, equation of the line will be,

y = -3x + 2

Linear function representing the line will be,

f₁(x) = -3x + 2

2). Let the equation of the red line passing through (0, -4) and (2, -2) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{-4+2}{0-2}[/tex]

m = 1

y-intercept 'b' = -4

Therefore, the linear function will be,

f₂(x) = x - 4

3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]

m = 1

y-intercept 'b' = 8

Therefore, linear function will be,

f₃(x) = x + 8

4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,

y = mx + b

Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]

m = -2

y-intercept of the line 'b' = -6

Therefore, function representing the line will be,

f₄(x) = -2x - 6

5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,

y = mx + b

Since the line is passing through origin, y-intercept 'b' = 0

Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]

m = -3

Therefore, equation of the linear function will be,

f₅(x) = -3x

Answer:

the mixed form is 28 [tex]19/100[/tex]

the improper form is ( 28 x 100) = 19 / 100

2819 / 00

Answer:

90°

Step-by-step explanation:

As given in the figure:

[tex]AC \perp CE\\

\therefore m\angle ACE = 90\degree \\ [/tex]

Answer:

2 pi •10•210

Step-by-step explanation:

Khan academy

Answer:

Step-by-step explanation:

Let's solve :

[tex] \mathsf{ \: people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:time \: ( \: in \: minutes)}[/tex]

[tex] \mathsf{12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \: hour \: = \: 60 \: minutes }[/tex]

[tex] \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t }[/tex]

The amount of time needed for completion is inversely proportional to the number of people working on the orchard. Let t be the amount of time ( in minutes ) needed when there are 5 people working.

[tex] \mathsf{ \frac{12}{5} = \frac{t}{60} }[/tex]

Apply cross product property

[tex] \mathsf{5t = 12 \times 60}[/tex]

Multiply the numbers

[tex] \mathsf{5t = 720}[/tex]

Divide both sides of the equation by 5

[tex] \mathsf{ \frac{5t}{5} = \frac{720}{5} }[/tex]

Calculate

[tex] \mathsf{t = 144 \: minutes}[/tex]

Hope I helped!

Best regards!!

It will take five people 144 minutes to paint the orchard.

12 people can paint the orchard in one hour, which is 60 minutes.

If there are five people, it will take them 12 × 60 / 5 = 144 minutes to paint the orchard.

So the answer is 144

Here's the explanation:

We know that the number of people and the time it takes to paint the orchard are inversely proportional. This means that if we increase the number of people, the time it takes to paint the orchard will decrease.

We can also set up a proportion to find the time it takes five people to paint the orchard. The proportion will look like this:

12 people : 5 people :: 60 minutes : x minutes

Cross-multiplying, we get:

12 × x = 5 × 60

x = 5 × 60 / 12

x = 144 minutes

Therefore, it will take five people 144 minutes to paint the orchard.

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Answer:

x=115

Step-by-step explanation:

180 - (115) =65(triangle)

65 + x = 180(on a line)

x=180-65

x = 115

Answer:

115 degrees

Step-by-step explanation:

the person above me is right, but there is an easier way.

Just add 50 and 65 degrees and boom you have your answer.

Answer:

u^18

Step-by-step explanation:

(u^3)^6

=

u^(3*6)

=

u^18

Hope this helps!

Answer:

length=4 cm

Step-by-step explanation:

Area of rectangle= length * width

48=l*12

length=48/12

length=4 cm

━━━━━━━☆☆━━━━━━━

▹ Answer

30 miles

▹ Step-by-Step Explanation

Multiply mph by hours:

15 mph * 2 hrs = 30 miles

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Yes this is a Triangle

36 degrees of any side then 41 would connct to 36 and 17 would connects to 36 and 41! If this is Khan Academy your asking out of its a Yes, it is a Triangle

Answer:

It is a triangle:

Step-by-step explanation:

b² = a² + c² - 2(a)(c)cos(B)  

b² = 41² + 20² - 2(41)(20)cos(36)

b² = 754.2121292

b = 27.46292281

b = 27.463

A = 41, B = 27.4, C = 17

Answer:

0.35, 0.359, 1

Step-by-step explanation:

0.359 = 359 thousandths

0.35 = 0.350 = 350 thousandths

1 = 1.000 = 1000 thousandths

Since 350 < 359 < 1000, then from least to greatest you get

0.35, 0.359, 1