Pencils are sold in boxes of 10 Erasers are sold in boxes of 14 A teacher wants to buy the same number of pencils and erasers work out the smallest number of boxes of each item she should buy

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Explanation:

We'll use the hinge theorem here. This says (more or less) that the larger an angle is, the side opposite of that will be longer.

Imagine that the segments with the single tickmarks represent a door swinging open/shut. The more open a door is, the further the distance it is from the handle to the frame. In terms of these triangles, the segment 25 is larger than 5x-10 because the angle 90 (opposite the 25) is larger than the angle 85 degrees (opposite the 5x-10)

In symbols we say

5x - 10 < 25

We also say 5x - 10 > 0 or 0 < 5x - 10 to ensure that the segment of length 5x-10 is not 0 or negative.

Put the two inequalities together and we get 0 < 5x - 10 < 25

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

Solve for x

0 < 5x - 10 < 25

0+10 < 5x - 10 < 25 + 10 .... adding 10 to all sides

10 < 5x < 35

10/5 < 5x/5 < 35/5 ... dividing all sides by 5

2 < x < 7

We have x between 2 and 7, and not equal to either endpoint.

Answer:

The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

The equation of a line through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is equal to:

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

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

So, the equation of the line through the points (3, 1) and (–5, –7) is:

[tex]m=\frac{-7-1}{-5-3}=1[/tex]

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

Then, we have two equations, y=x-2 and y=0.5x -1 , so solving for x, we get:

x - 2 = 0.5 x - 1

x - 0.5x = 2 - 1

x = 2

Replacing x=2 in the equation y=x-2, we get:

y =2 - 2 = 0

Finally, the solution of the system of equations is (x,y) = (2,0)

Answer:The solution of the system of equations is (x,y) = (2,0)

Step-by-step explanation:

Answer:

[tex]|w-20|\leq 0.4[/tex]

Step-by-step explanation:

The manufacturer requires that the weight differs from 20 oz in at most 0.4 oz, therefore we can write this difference (which can be either above or below 20 oz, to be smaller than or equal to 0.4 oz.

The weight can be:

1) smaller than or equal to 20 oz + 0.4 oz:  [tex]w\leq 20+0.4[/tex]  then [tex]w-20\leq 0.4[/tex]

2) larger than or equal to 20 oz - 0.4 oz:  [tex]20-0.4\leq w[/tex]  then  [tex]-0.4\leq w-20[/tex]

and which combined, can be written as a double inequality;

[tex]-0.4 \leq w-20\leq 0.4[/tex]

This double condition can also be written using the absolute value symbol as:   [tex]|w-20|\leq 0.4[/tex]

Answer:

0.897

Step-by-step explanation:

Brahmagupta formula for quadratic equation [tex]ax^2+bx=c[/tex] is

[tex]x=\dfrac{\sqrt{4ac+b^2}-b}{2a}[/tex]

It involved only one solution.

The given equation is

[tex]3x^2+4x=6[/tex]

Here, a=3, b=4 and c=6. Put these values in the above formula.

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

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

[tex]x=\dfrac{\sqrt{72+16}-4}{6}[/tex]

[tex]x=\dfrac{\sqrt{88}-4}{6}[/tex]

[tex]x\approx \dfrac{5.38}{6}[/tex]

[tex]x\approx 0.897[/tex]

Therefore, the required solution is 0.897.

Answer:

<S = 62 degrees

Step-by-step explanation:

For this problem, you need to understand two things.  A line tangent to a circle's radius creates a 90-degree angle, and the sum of the interior angles of a triangle is 180 degrees.  With that said, let's continue.

<S + <P + <Q = 180

<S + 90 + 28 = 180

<S + 118 = 180

<S = 62

Hence, <S = 62 degrees.

Cheers.

Answer:

C

Step-by-step explanation:

When you use pemdas, it gives the value of 1/32

Answer:

( x+3) ^2 + ( y-4) ^2 = 9

Step-by-step explanation:

The equation of a circle can be written as

( x-h) ^2 + ( y-k) ^2 = r^2

Where ( h,k) is the center and r is the radius

( x--3) ^2 + ( y-4) ^2 = 3^2

( x+3) ^2 + ( y-4) ^2 = 9

Answer:

True

Step-by-step explanation:

trust me, i remember this question

Answer:

We have the system:

y > 2*x

y > 3

Now, let's find the limits:

taking y > 3, we can see the limit y = 3.

Now we replace it in the first inequality:

3 > 2*x

3/2 > x.

Then we have that:

y > 3

x < 3/2

Those two inequalities define our system.

So any ordered pair where x is smaller than 3/2 and y is larger than 3, is a solution.

or example:

(1, 3.5) is a solution.

Answer:

(1,5)

Step-by-step explanation:

the other options make the system of equations wrong..

Answer:

9.42

pi x radius x radius x (height / 3) = volume

1 x 1 = 1 and 9/3 = 3

pi x 1 x 3 = volume

pi x 3 = volume

3.14 x 3 = 9.42

Hope this helps

Step-by-step explanation:

Answer:

24 cm

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

2304 pi = 4/3 pi r^3

Divide each side by pi

2304 = 4/3 r^3

Multiply each side 3/4

2304 * 3/4 = 4/3 r^3 * 3/4

1728 = r^3

Take the cube root of each side

1728 ^ 1/3 = r^3 ^ 1/3

12 = r

We want the diameter

d = 2*r

d = 2*12

d = 24

Answer:

24 centimeters

Step-by-step explanation:

A basketball is a sphere. The volume of a sphere can be found using the following formula:

V= 4/3 π r^3

We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.

2304π = 4/3 π r^3

We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.

2304π/π=4/3πr^3/π

2304π/π=4/3r^3

2304=4/3r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).

2304*3/4=4/3r^3*3/4

2304*3/4=r^3

1728=r^3

Now, take the cube root of both sides.

∛1728=∛r^3

∛1728=r

12=r

r= 12 cm

The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.

d= 2r

d= 2* 12 cm

d= 24 cm

The diameter of the basketball is 24 centimeters.

In order to solve this problem, we will need a little more information, for example, we need to know what the functions are. Let's say the problem looks like this:

Use the drawing tool(s) to form the correct answer on the provided number line. Consider the functions below.

[tex]f(x)=|3x|-3[/tex]

and

[tex]g(x)=-x^{2}+8x-5[/tex]

Represent the interval where both functions are increasing on the number line provided.

Answer:

See attached picture

Step-by-step explanation:

Since this problem is posted on the algebra section of Brainly, I assume we will need to make use of an algebraic approach to solve this. Basically, the idea is to graph the functions and find the x-values for which both functions increas. In order to graph the functions, we will need to build a table with points for each of the functions. In order to graph the functions you need to pick the x-values you wish and evaluate them in the given functions. (See attached pictures)

Once you got the desired points, you can plot them in the coordinate axis and find the x-values for which both graphs will be increasing. If we take a close look at the graphs we can see the f(x) graph increases in the interval:

(0,∞)

and the g(x) graph increases in the interval:

(-∞,4)

so the interval in which both graphs are increasing will be the region where both intervals cross each other, which will be (0,4)

so that's the interval we draw on our number line. (see attached picture.

Answer:

see photos

Step-by-step explanation:

Plato/Edmentum

Correct question :

If the perimeters of each shape are equal, which equation can be used to find the value of x? A triangle with base x + 2, height x, and side length x + 4. A rectangle with length of x + 3 and width of one-half x. (x + 4) + x + (x + 2) = one-half x + (x + 3) (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3) 2 (x) + 2 (x + 2) = 2 (one-half x) + 2 (x + 3) x + (x + 2) + (x + 4) = 2 (x + 3 and one-half)

Answer: (x + 2) + x + (x + 4) = 2 (one-half x) + 2 (x + 3)

Step-by-step explanation:

Given the following :

A triangle with base x + 2, height x, and side length x + 4 - - - -

b = x + 2 ; a = x ; c = x + 4

Perimeter (P) of a triangle :

P = a + b + c

P =( x + 2) + x + (x + 4) - - - (1)

A rectangle with length of x + 3 and width of one-half x

l = x + 3 ; w = 1/2 x

Perimeter of a rectangle (P) = 2(l+w)

P = 2(x+3) + 2(1/2x)

If perimeter of each same are the same ; then;

(1) = (2)

(x + 2) + x + (x + 4) = 2(x+3) + 2(1/2x)

Answer:

B

Step-by-step explanation:

Answer:

(x + 3)² + (y + 1)² = 100

Step-by-step explanation:

Equation of a circle is:

(x − h)² + (y − k)² = r²

where (h, k) is the center of the circle and r is the radius.

The center is on the line x − 4y = 1, so:

h − 4k = 1

h = 1 + 4k

(x − 1 − 4k)² + (y − k)² = r²

Two points on the line are (3, 7) and (5, 5), so:

(3 − 1 − 4k)² + (7 − k)² = r²

(5 − 1 − 4k)² + (5 − k)² = r²

Set the equations equal:

(3 − 1 − 4k)² + (7 − k)² = (5 − 1 − 4k)² + (5 − k)²

(2 − 4k)² + (7 − k)² = (4 − 4k)² + (5 − k)²

4 − 16k + 16k² + 49 − 14k + k² = 16 − 32k + 16k² + 25 − 10k + k²

4 − 16k + 49 − 14k = 16 − 32k + 25 − 10k

53 − 30k = 41 − 42k

12k = -12

k = -1

h = 1 + 4k

h = -3

(3 − 1 − 4k)² + (7 − k)² = r²

(3 − 1 + 4)² + (7 + 1)² = r²

6² + 8² = r²

r = 10

Therefore, the equation of the circle is:

(x + 3)² + (y + 1)² = 10²

Answer:

Relative frequencies:

Headaches = 23.55 %

Hypertension = 8.68%

Upper respiratory tract infections =24.79%

Nasopharyngitis = 21.07

Diarrhea = 21.09%

None of these adverse reactions appear to be much more common than the others.

Step-by-step explanation:

Compute frequency:

The number of adverse reactions categories:

Headaches

Hypertension

Upper respiratory tract infections

Nasopharyngitis

Diarrhea

Frequency of each adverse reaction:

Adverse reaction                                Frequency        

Headaches                                                 57                    

Hypertension                                              21

Upper respiratory tract infections             60

Nasopharyngitis                                          51

Diarrhea                                                       53

Compute total frequency

Total frequency is compute dby taking sum of all frequencies;

Sum of frequencies = 57 + 21 + 60 + 51 + 53

                                 = 242

Compute relative frequency:

In order to find if any one of these adverse reactions appear to be much more common than the others, we have to compute relative frequency using these adverse reactions.

By calculating relative frequency we are looking at the number of times a specific adverse reaction appears to be more common, compared to the others.

To calculate relative frequency, divide the frequency of each adverse reaction by the total frequency i.e. 242.

Relative frequency for Headache = 57 / 242

                                                        = 0.2355

                                                        = 23.55 %

Relative frequency for Hypertension = 21 / 242

                                                             = 0.0868

                                                             = 8.68 %

Relative frequency for Upper respiratory tract infections = 60 / 242

                                                                                              = 0.2497

                                                                                              = 24.97 %

Relative frequency for Nasopharyngitis = 51 / 242

                                                                  = 0.2107

                                                                   = 21.07 %

Relative frequency for Diarrhea    = 53 / 242

                                                        = 0.2190

                                                         = 21.90 %

If you observe the relative frequencies of all the adverse reactions, none of them appear to be much more common than the others. Relative frequencies of headaches, upper respiratory tract infections, nasopharyngitis and diarrhea are almost equally common however, relative of hypertension appears to be very less than the other three.

Answer:

42

Step-by-step explanation:

P(left) = 0.10

Expected number of lefties among high school grads of 424

= 424 * 0.10

= 42 (to the nearest person)

Answer:

you do 20% of 424

1 0% of 424 =42.4

you could round it to 42

Answer: x=25

Step-by-step explanation: There are 180 degrees in a triangle. Two of the angles (56 and 99) add up to 155. The last angle, which is x, is 180-155. Therefore, x is 25.

hope this helped you:)

Answer:

The answer is 25°.

Step-by-step explanation:

simply,

here, a triangle of measure 99° and 56° is given.

now, we have;

99°+56+ x= 180° ( sum of an interior angle of a triangle is 180°)

or, 155°+x= 180°

or, x= 180°-155°

therefore, the value of x is 25°.

hope it helps..

Answer:

the second one........the shape of the conic section os circle

Answer:

a = -6

Step-by-step explanation:

-5a-9+a=15

Combine like terms

-5a+a  -9 = 15

-4a  -9 = 15

Add 9 to each side

-4a -9+9 = 15+9

-4a = 24

Divide by -4

-4a/-4 = 24/-4

a = -6

Answer:

a = -6

Step-by-step explanation:

1. Combine like terms: -4a – 9 = 15

2. Use the additive property of equality to add 9 to both sides: -4a = 24

3. Use division property of equality to divide -4 on both sides: a = -6

Answer:

Let's put the chart into ordered pairs:

(x, y)

(2,1)

(3,4)

(3,3)

(4,2)

(5,5)

In bold, we see that there are two y-values at x=3. This means that this relation fails the vertical line test (two points on the same verticle line). This is not a function. 

The answer options may be mis-written. 

The answer is no, because one x value corresponds to more than one y-value. 

Answer:

A right scalene triangle would have a 90 degree angle and 3 non congruent sides

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

well AEB is a straight line which is 180° and we were already given the angles that made up the straight line ,so all u had to do was subtract 60° from 90°

BED =30°

Answer:

AEC=30

BED=30

Step-by-step explanation:

We know that AEC is 30 degrees because it is on line AB, along with a right angle and 60 degrees, add 90 to 60 to get 150, and subtract it from 180 to get your answer, 30

As for BED, AEC and BED are verticle angles so they are equivalent.

If you found this helpful, please consider giving me brainliest, it will help me a lot

Have a good day! :)

Answer:

49 cupboards

Step-by-step explanation:

See the steps below, it is self-explanatory:

As 14*14/4= 49, the answer is 49 cupboards

Answer:

Tamanna scored more.

Step-by-step explanation:

Bhaskar scored -60, 20 and 0. His total score is therefore:

-60 + 20 + 0 = -40

Tamanna scored 20, 0, 60. His total score is therefore:

20 + 0 + 60 = 80

Therefore, Tamanna scored more.

[tex]-4(8+y)=90\implies8+y=-22.5\implies y=-30.5[/tex].

Hope this helps.

Answer:

-30.5.

Step-by-step explanation:

-4(8 + Y) = 90

-32 - 4Y = 90

-4Y = 122

Y = -30.5.

Hope this helps!

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find an equation of a line given two points first find the slope / gradient

Slope of the line using points (-1,4) and (-2,2) is

[tex]m = \frac{2 - 4}{ - 2 + 1} = \frac{ - 2}{ - 1} = 2[/tex]

So the equation of the line using point (-1,4) is

Hope this helps you

Answer:

d is 5 units

Step-by-step explanation:

Answer:

8.4 ft

Step-by-step explanation:

Perimeter = side x 4

(Re-arrange)

Side = Perimeter / 4

34/4 = 8.4 ft

Answer:

8.5 feet

Step-by-step explanation:

Divide 34 by 4. A square has 4 sides which are all the same.

Answer:

Answer:

( x+2)^2 + (y+5)^2 = 1

Step-by-step explanation:

The equation of a circle can be written in the form

( x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

( x- -2)^2 + (y- -5)^2 = 1^2

( x+2)^2 + (y+5)^2 = 1

Answer:

[tex](x + 2)^{2} + (y + 5)^{2} = 1[/tex]

Step-by-step explanation:

The guy above is correct! I just finished the quiz and checked the answer key.