Recall the equation for a circle with center (h,k) and radius r. At what point in the first quadrant does the line with equation y=2x+5 intersect the circle with radius 5 and center (0, 5)?

Answer:

2

Step-by-step explanation:

I think the answer is 2, because 2a=4, but when simplified, you can divide both the numerator and denominator by 2, making the denominator 4/2= 2.

The missing denominator of the solution is 2.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

2x² + 10x -6 = 0

Now, using Discriminant Method

x = [ -b ± √ (b² -4ac)] / 2a

Here, a= 2, b= 10 and c=-6

So, x = [ -10 ± √(10² - 4(2)(-6)] / 2(2)

x = [ -10 ± √ 100 + 48]/ 4

x = (-10 ± 2√37)/ 4

x = (-5 ± √37)/2

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Hi there! Let’s see if I can help you <3

The Answer is: 15.81!

Here’s the step by step explication:

First we must find the difference of U and V: (7i-12j)-(-2i+j)

Distributed all out will equal: 9i-13j

We can then go ahead and use Pythagorean therm to find the magnitude: V = Square root of (9)^2 + (-13)^2

This equals Square root of 250!

Depending on the form your teacher wants to answer in it would finally be 5 square roots of 10 or in decimal form; approximately 15.8114!

HOPE IT HELPED YOUUU <3

Answer: 11.3

Step-by-step explanation:

To find the distance, we will need the distance formula.

[tex]D=\sqrt{(x_{2}-x_{1} ) ^2+(y_{2}-y_{1})^2 }[/tex]

Since we know our x and y, we can plug them into this equation.

[tex]D=\sqrt{(5-(-3))^2+(1-9)^2}[/tex]

[tex]D=\sqrt{(8)^2+(-8)^2}[/tex]

[tex]D=\sqrt{64+64}[/tex]

[tex]D=\sqrt{128}[/tex]

[tex]D=11.3[/tex]

The distance between the points is 11.3.

Answer:

Option C.

Step-by-step explanation:

Note: In option C interval should be (-1,1) instead of [-1,1].

From the given table it is clear that the value of f(x) is 0 at x=-1 and x=1.

The value of f(x) is negative over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]. So,

[tex]f(x)<0[/tex] over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]

The value of f(x) is positive over the interval [tex](-1,1)[/tex]. So,

[tex]f(x)>0[/tex] over the interval [tex](-1,1)[/tex]

Therefore, the correct option is C.

Answer:

3 boys may be answer of this question

Answer:

19/44

Step-by-step explanation:

19 boys

25 girls

19+25=44 (red hair)

19/44

Answer:

the one with 12, 18, 22

Step-by-step explanation:

in the first one, 9-3=6 and 6-3=3 so -3 is the constant of the proportionality

in the second one 3-1=2, 2-1=1 so here the constant of proprtionality is -1

in the third one 16+2=18, 18+2=20 so the constant of proportionality is 2

fourth one 4 + 0.5= 4.5 and 4.5+0.5= 5, constant of proportionality is 0.5

fifth one 12+6=18, but 18+6=24

and the rest are all proportional

Answer:

12, 18, 22

Step-by-step explanation:

Answer:

The correct option is:

14 inches

Step-by-step explanation:

The question is incomplete because the picture of the flap is not shown in the question nor the measurements are given. First lets complete the question. The figure was this question is attached below.

We can see that the bottom width of the trapezoid is 9 inches, the top width of the trapezoid is 5 inches, and it has a height of 2 inches.

The area of trapezoid is given as:

Area = ((Top width + Bottom width)/2) · h

Area = ((9+5)/2) · 2

Area = (14/2) · 2

Area = 7 · 2

Area = 14 inch²

Answer:

14

Step-by-step explanation:

a) 382 mm

b) 505 mm

c) 3162 mm

d) 3103 mm

e) 5008400 mm

f) 9046850 mm

basically, there are 10mm in a cm, so you times by ten,

1000mm in a m so multiply by 1000

1000000mm in a km

The sell price is the wholesale price plus 20%

Divide the sell price by 1.2 ( 100% + 20%)

145 / 1.2 = 120.83

The wholesale price is $120.83

Answer:

The wholesale price is $120.83

Answer:

( -3, 1)

........

Answer:

(-3, 1)

Step-by-step explanation:

The point lies on the line x = -3.

The point lies on the line y = 1.

Where both lines intersect, that is the coordinate.

(x, y)

(-3, 1)

Answer:

(-6, 0) and (3, 0).

Step-by-step explanation:

There are actually 2 x-intercepts. You will get the x-intercept when f(x) = 0.

f(x) will equal 0 when either (x + 6) = 0 or (x - 3) = 0.

x + 6 = 0

x = -6

x - 3 = 0

x = 3

So, your two x-intercepts will be at (-6, 0) and (3, 0).

Hope this helps!

Answer:

BD=7

ED=5

BE=7

AD=10

AE=5

Step-by-step explanation:

given CD = 7 you use that to find BD and BE because CD´s line length is the same as BD and BE

given BC = 5 you use that to find ED and AE and AD because BC is the same length as ED (they create the same triangle) and than given AE also equals 5 you add ED and AE to get AD

hope this helps

Answer:

a) 1/3

b) 7/9

Step-by-step explanation:

The first part asks for the probability that Matt takes the red counter.

There are 6 red counters out of total 6+4+8 = 18 counters.

6/18

Simplify the fraction.

= 1/3

The second part asks for the probability that the counter is not blue.

The counters that are blue are 4. Not blue becomes 18-4 = 14. 14 red or green counters out of total 18.

14/18

= 7/9

Answer:

Total outcome =  6 + 4 + 8 = 18

a) Probablity that the counter is red = 6/18 = 1/3

b) Probablity that the counter is blue = 14/18 = 7/9

Answer:

solution,

Let the points be A and B

A(-3,4)---->(X1,y1)

B(5,4)----->(x2,y2)

now,

Distance:

[tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {(5 - ( - 3))}^{2} + (4 - 4) ^{2} } \\ = \sqrt{ {(5 + 3)}^{2} + {(0)}^{2} } \\ = \sqrt{ {(8)}^{2} + 0} \\ = \sqrt{64} \\ = \sqrt{ {(8)}^{2} } \\ = 8 \: units[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

The answer is given below

Step-by-step explanation:

Let the number of passengers that boarded the bus at the interchange be x.

At the first  bus stop, 1/4 of the passengers alighted the bus and 6 people boarded the  bus.

Therefore The number of passengers when the bus left the first bus stop = [tex]x-\frac{1}{4}x +6=\frac{3}{4}x+6[/tex]

At the 2nd bus stop, 8/15 of the passengers alighted and 10 passengers  boarded the bus.

Therefore The number of passengers when the bus left the second bus stop

[tex]=\frac{3}{4}x+6-\frac{8}{15}( \frac{3}{4}x+6)+10=\frac{3}{4}x+6-\frac{8}{20}x-3.2+10\\\\=\frac{7}{20}x+12.8[/tex]

Given that there were 24 passengers on the bus when it left the  2nd bus stop

[tex]\frac{7}{20}x+12.8=24\\7x+256=480\\7x=480-256\\7x=224\\x=32[/tex]

Therefore 32 passengers boarded the bus at the interchange

Answer: y=1/2x−2

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

46.

Theorem:

The measure of an exterior angle of a triangle equals the sum of the measures of the remote interior angles.

The 100-deg angle is an exterior angle whose remote interior angles are angles E and F.

m<E + m<F = 110

5x + 6x = 110

11x = 110

x = 10

m<E = m<FEG = 5x = 5 * 10 deg = 50 deg

Answer: C. 50 deg

47.

A is not true since we know that 5x + 6x must equal 110, not 70.

Answer:

<FEG=50

A. is wrong

Step-by-step explanation:

For the first question, we know <F &<E are remote interior angles which add up to 110 (exterior angle)

so:

[tex]5x+6x+110\\11x=110\\x=10[/tex]

so:

[tex]5x= 5(10)\\FEG=50[/tex]

Now using what we know, we can determine that A. is wrong since 5x+6x is 110° not 70°

Hope this helps!

Answer: A

Step-by-step explanation:

it's easy

Answer:

C) 105

Step-by-step explanation:

The box plot suggests that about 50% of hight schools in orange county have more than 105 band members.

This can be inferred from the boxplotvprovided in the attachment. 50% refers to the median of the distribution which is denoted by the vertical line dividing the box into two. Tracing the vertical line to the horizontal label marked from 70 to 150, the vertical line falls on the 105 mark. Hence the value of the median or 50th percentile

Answer:

Reduce every dimension except thickness by 20%.

The requried new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.

To find the dimensions of the new candy bar after reducing the volume by 20%, we need to determine the reduction in length and width.

Let's start by calculating the original volume of the candy bar using the formula: volume = length × width × thickness.

Original volume = 13 cm × 7 cm × 2 cm = 182 cm³

Since the management wants to reduce the volume by 20%, we need to find 20% of the original volume and subtract it from the original volume.

20% of 182 cm³ = 0.2 × 182 cm³ = 36.4 cm³

Reduced volume = 182 cm³ - 36.4 cm³ = 145.6 cm³

Now, we need to determine the new dimensions while maintaining the 2 cm thickness.

Let's assume the reduction in length and width is x cm for both dimensions.

The new volume can be calculated using the formula:
volume = (length - x) × (width - x) × thickness.

Setting this equal to the reduced volume, we have:

(13 - x) × (7 - x) × 2 = 145.6

Simplifying and rearranging the equation, we get:

(91 - 20x + x²) = 72.8

x² - 20x + 18.2 = 0

Using the quadratic formula, we can solve for x:

[tex]x = \dfrac{-(-20)\pm \sqrt{(-20)^2- 4(1)(18.2)}} {2(1)}\\x = \dfrac{20 \pm \sqrt{400 - 72.8}} {2}\\x =\dfrac {20 \pm \sqrt{327.2}} {2}[/tex]

x ≈ (20 ± 18.09) / 2

Taking the positive value, we have:

x ≈ (20 + 18.09) / 2

x ≈ 19.045 / 2

x ≈ 9.5225

Since the dimensions cannot be negative, we discard the negative value.

Therefore, the reduction in length and width is approximately 9.5225 cm.

To find the new dimensions, we subtract this value from the original length and width:

New length = 13 cm - 9.5225 cm ≈ 3.4775 cm

New width = 7 cm - 9.5225 cm ≈ -2.5225 cm (discard as it is negative)

Therefore, the new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.

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Answer:

x = 8

Step-by-step explanation:

Let us take the breadth as 'x'

breadth = x

length = 3 + x

perimeter = 38m

perimeter of a rectangle = 2 ( l + b )

= 2( x + x + 3 ) = 38

4x + 6 = 38

4x = 38-6

x = 32/4

x = 8

breadth = 8

length = 11

Answer:

solution,

[tex](2 + 3 \times 2 + {3}^{2} ) - {4}^{2} \\ = (2 + 6 + 9) - 16 \\ = 17 - 16 \\ = 1[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

1

Step-by-step explanation:

Multiply  

3  by  2 . 2 + 6 + 3 2 − 4 2 Raise  3  to the power of  2 . 2 + 6 + 9 − 4 2 Raise  4 to the power of  2 . 2 + 6 + 9 − 1 ⋅ 16 Multiply  − 1  by  16 . 2 + 6 + 9 − 16

Simplify by adding and subtracting.

Add  2  and  6 . 8 + 9 − 16 Add  8  and  9 . 17 − 16  Subtract  16  from  17 .

1

Answer:

3 is not in the domain of [tex]f\circ g[/tex].

Step-by-step explanation:

The given functions are

[tex]f(x)=\sqrt{x+5}[/tex]

[tex]g(x)=-4x+4[/tex]

We need to check whether 3 is in the domain of [tex]f\circ g[/tex] or not.

[tex]f\circ g=f(g(x))[/tex]

[tex]f\circ g=f(-4x+4)[/tex]     [tex][\because g(x)=-4x+4][/tex]

[tex]f\circ g=\sqrt{(-4x+4)+5}[/tex]     [tex][\because f(x)=\sqrt{x+5}][/tex]

[tex]f\circ g=\sqrt{-4x+9}[/tex]

This function is defined if

[tex]-4x+9\geq 0[/tex]

[tex]9\geq 4x[/tex]

[tex]\dfrac{9}{4}\geq x[/tex]

It means domain of the function [tex]f\circ g[/tex] is [tex](-\infty,\dfrac{9}{4}][/tex].

[tex]3\notin (-\infty,\dfrac{9}{4}][/tex]

Therefore, 3 is not in the domain of [tex]f\circ g[/tex].

Answer:

B

Step-by-step explanation:

The option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have:

Rahim is constructing a proof to show that the opposite angles of a quadrilateral inscribed in a circle are supplementary.

From the central angle theorem:

(1/2)mQRS = ∠T because the measure of an inscribed angle is one-half the measure of its intercepted arc.

Thus, the option (A) (1/2)mQRS = ∠T is correct because the measure of an inscribed angle is one-half the measure of its intercepted arc.

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Answer:

[tex]-\frac{9}{14}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}*-\frac{6}{7}\\\\\frac{3}{2} *\frac{3}{7} \leftarrow \text{Cross Cancel Common Factor}\\\\ -\frac{3*3}{2*7}\\\\-\frac{9}{14}[/tex]

Answer:

negative 9/14

Step-by-step explanation:

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

I was taking the test and couldn't find the answer to this question anywhere so let me help you out...  

abidemiokin provided a wonderful step-by-step explanation for solving the formula, but left out the actual answer for the question which is what I'm here for. I read through abidemiokin's explanation and reviewed my options before choosing the best answer. As you see in step 5 of my edited version of abidemiokin's explanation the missing step is there. In the provided question we see steps 1,2, 3, and 4 being identical to those in the explanation below. From this, it is clear the next step (step 5) would be the next step, and as it is one of the options we can trust that it is correct.

(If you still have doubts then trust the fact that I took the test and the answer I provided above was indeed correct.)

Given the quadratic equation ax²+bx+c = 0, to derive the quadratic formula from the equation, the following steps must be followed;

ax²+bx+c = 0

Step 1: Subtract c from both sides

ax²+bx+c-c = 0-c

ax²+bx = -c

Step 2: Divide both sides of the equation by a

ax²/a + bx/a = -c/a

x² + bx/a = -c/a

Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides

x² + bx/a +  (b/2a)² = -c/a +  (b/2a)²

Step 4: Square the quantity  b/2a on the right side of the equation

x² + bx/a +  (b/2a)² =  -c/a +  b²/4a²

Step 5: Find a common denominator on the right side of the equation which is 4a²

x² + bx/a +  (b/2a)² =  -4ac/4a² +  b²/4a²

Step 6: Add the fractions together on the right side of the equation

x² + bx/a +  (b/2a)² =  (-4ac+  b²)/4a²

Note: The fraction at the right-hand side of the equation is to be added together not multiplied as shown in the question.

Step 7: The equation on the left is to be written as a perfect square as shown

(x+b/2a)² =  (-4ac+  b²)/4a²

Step 8: Take the square root of both sides

√(x+b/2a)² = √ (-4ac+  b²)/4a²

(x+b/2a) =  √(-4ac+  b²)/2a

Step 9: subtract b/2a from both sides

x+b/2a - b/2a =  -b/2a + √(-4ac+  b²)/2a

x =  -b/2a + √(-4ac+  b²)/2a

Step 10: Add the fractions together on the right-hand side

x =  -b±√(-4ac+  b²)/2a

This gives the required equation

Answer: A  Find a common denominator on the right side of the equation

Step-by-step explanation: Took the test of FLVS

Answer:

-i^5=-i

Step-by-step explanation:

rewrite the equation ;

i^4=1

I^4 *-i = 1*-i=-i

Answer:

x=5/3log(3) -1

x=2.949317

Step-by-step explanation:

reorder terms

3log(3)x(x+1)+5

distribute 3log(3)

3log(3)x+3(log)=5

Move constant to the right

3log(3)x=5-3log(3)

Divide both sides by 3log(3)

x=5/3log(3) -1

Solve 3log(3)

3log(3)= 3.949317

3.949317-1=2.949317

Answer & Step-by-step explanation:

Answer:

x=65

Step-by-step explanation:

x/5 - 2 = 11

x/5= 11+2

x/5=13

x=13×5

x=65

Answer:

Step-by-step explanation:

Question = x/5 - 2 = 11

1. Isolate the variable

x/5 - 2 = 11

    + 2   + 2

x/5 = 11

2. Remove the fraction

x/5 = 11

*5      *5

3. Simplify

x = 55

The answer is x = 55.

Hope this helped,

Kavitha