4.
Vivian has some sweets. If she shares the sweets among 4 friends, she will have
3 sweets left. If she shares the sweets among 5 friends, she will have
4 sweets left. If she shares the sweets among 9 friends, she will have
8 sweets left. What is the smallest possible number of sweets she has?


What is the solution to this question?

In the polygon QRST, the angle that is formed between sides SR and SQ is known as the angle RSQ.

In the polygon QRST, the angle included between sides SR and SQ is named as the angle RSQ. In polygons, the included angle between two sides is the angle that both sides share. Here, sides SR and SQ share vertex S, so the included angle is at S, formed by extending from R through S to Q. Hence, we denote this angle as RSQ.

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Answer:

8x + 24

Step-by-step explanation:

Given photograph length L = 7" and width W = 5"

Also that the frame is 2x" longer and 2x" wider

hence,

new length = ( 7 + 2x) inches

new width= ( 5 + 2x) inches

Hence perimeter of frame,

= 2 x ( new length + new width)

= 2 [( 7 + 2x)  + ( 5 + 2x)]

= 2 (4x + 12)

= 8x + 24 (Answer)

The standard equation of a parabola with vertex (0, 0) and focus (-2, 0) is y^2 = -8x. It opens to the left with the directrix x = 2.

To find the standard equation of a parabola with vertex (0, 0) and focus (-2, 0), we can use the definition of a parabola as the set of all points equidistant from a point (the focus) and a line (the directrix).

Since the focus is at (-2, 0), the directrix is a vertical line equidistant from the vertex on the opposite side of the focus, which is x = 2. The distance between the vertex and the focus (or the vertex and the directrix) is 2 units, so q = 2. This means that the parabola opens to the left.

The standard equation for a parabola that opens horizontally is of the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus. Here, p = -2 because the parabola opens to the left.

Therefore, the standard equation for the given parabola is y^2 = -4(2)x or y^2 = -8x.

Answer:

4(x-7)^2-(x-7)+3 (Assuming t is f)

Step-by-step explanation:

Let s(x)=x-7 and t(x)=4x^2-x+3 .

(t o s)(x)=t(s(x))=t(x-7)

Before I continue this means replace the orginal x in t with x-7.

This will then give you

4(x-7)^2-(x-7)+3

Answer:

D

Step-by-step explanation:

The area (A) of a triangle is calculated using

A = 0.5 absinC

Here a = 13 and ∠C = 65°, hence

A = 0.5 × 13 × b × sin65° = 95, that is

6.5b × sin65° = 95 ( divide both sides by 6.5sin65° )

b = [tex]\frac{95}{6.5sin65}[/tex] ≈ 16 ft ( to the nearest foot )

Given the area of 95 square feet and side AC of 13 feet, the value of side b, opposite the 65° angle, is 7 feet rounded to the nearest foot. Thus, the correct option is A.

From the image, we see that triangle ABC is a right triangle with a right angle at C. We are given that the area of the triangle is 95 square feet and that the length of side AC is 13 feet. We want to find the length of side b, which is opposite the 65° angle.

To find the area of a right triangle, we use the formula:

Area = (1/2) * base * height

In this case, the base is side b and the height is side AC. We are given that the area is 95 square feet and that AC is 13 feet, so we can plug these values into the formula to solve for b:

95 = (1/2) * b * 13

b = 95 * 2 / 13

b = 7.3 feet

Since we are asked to round the answer to the nearest foot, we round 7.3 feet up to 7 feet.

Therefore, the value of b, to the nearest foot, is 7 ft.

Answer:

All real numbers

Step-by-step explanation:

we have

f(x) = 3x +9

The linear function  has a range of all real numbers -------> (-∞, ∞)

f(x) can take any real value.

Please see attached image below, for more information

Answer:

I think its B because K is = to Y

So if K is 9 then the asymptote would be 9

Limiting the Y to the to be only greater than 9

Step-by-step explanation:

Answer:

50-4h<32

Step-by-step explanation:

If the temperature starts at 50 and the temperature is decreased by 4 per each hour, then:

1) after the first hour, the temperature is 50-4 or 46

1) after the second hour, the temperature is 46-4 or (50-4)-4 or 50-4(2).

So what I'm trying to show you that if I continue this pattern our equation for what happens h hours later is: 50-4h.

We want to know when is the temperature below 32 so less than 32.

Temperature<32

Put in our variable expression for temperature.

50-4h<32

The question is about using algebra to solve a real-life problem of temperature decrease. The correct inequality for the given problem is '50 - 4h < 32', which shows the number of hours it takes for the temperature (50 and decreasing 4 every hour) to be less than 32 degrees.

The subject matter of this question is mathematics, specifically algebra and inequalities. The question provides that the temperature in degrees Fahrenheit is reducing by 4 each hour from a starting point of 50°F and seeks to find the number of hours (h) it takes for the temperature to decrease below 32°F.

We can represent this situation as an inequality: 50 - 4h < 32. In English, this states that the temperature (50, decreasing by 4 each hour) should be less than 32 degrees. So, to answer your question, option B with '50 - 4h < 32' is the correct inequality for this problem.

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Answer:

r = 3

Step-by-step explanation:

x^2 + 6x + y^2 - 8y = - 16

Take half the linear term and square it.

x^2 + 6x + (3)^2 + y^2 - 8y + (-4)^2 = - 16

Add the squared amounts to the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = - 16 + 9 + 16  

Combine on the right.

x^2 + 6x + 9 + y^2 - 8y + 16 = 9

Represent the 2 quadratics as perfect squares.

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

The radius is the square root of 9 which is 3

Answer:

radius=3

Step-by-step explanation:

Given:

x^2 +6x +y^2 - 8y=-16

completing the squares

: x^2 +6x +9 = (x+3)^2

:y^2-8y+16 = (y-4)^2

(x+3)^2 + (y-4)^2 -9-16=-16

(x+3)^2 + (y-4)^2=-16+9+16

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

Now comparing with standard equation of circle i.e. (x-h)^2 + (y-k)^2=r^2, we get

origin(h,k)= (-3,4)

r=3 !

Answer:

2

Step-by-step explanation:

So we are going to do

(sum of parts of the secant)(part on outside)=(sum of parts of the secant)(part on outside) .

This is what you get from doing that:

(1+x+4)(x+4)=(11+x+1)(x+1)

Simplifying:

(x+5)(x+4)=(x+12)(x+1)

We could see which value of x makes both side the same.

Choice 1: Plug in 2 for x:

(2+5)(2+4)=(2+12)(2+1)

(7    )(6    )=( 14   )(3)

      42    =  42

This equation is true.

Choice 2: Plug in 3 for x:

(3+5)(3+4)=(3+12)(3+1)

(    8)(    7)=(    15)(   4)

     56     =   60

This equation is not true.

Choice 3: Plug in 6 for x:

(6+5)(6+4)=(6+12)(6+1)

( 11   )(  10 )=( 18   )(7   )

110            =   126

This equation is not true.

Choice 4: Plug in 7 for x:

(7+5)(7+4)=(7+12)(7+1)

(12  )( 11   )=( 19   )(8)

132         =152

This equation is not true.

Answer:

The answer is A or "2"

Step-by-step explanation:

Answer:

Here's what I get    

Step-by-step explanation:

∆PQR is a right triangle.

PR² = PQ² + QR² = 48² + 64² = 2304 + 4096 = 6400

PR = √6400 = 80  

PQ:QR:PR = 48:64:80 = 3:4:5

We can consider ∆PQR as a 3:4:5 triangle.

[tex]\sin \theta = \dfrac{4}{5} \\\\\cos \theta = \dfrac{3}{5}\\\\\tan \theta = \dfrac{4}{3}\\\\\cot \theta = \dfrac{3}{4} \\\\\csc \theta = \dfrac{5}{4}\\\\\sec \theta = \dfrac{5}{3}[/tex]

Answer:

The formula used for Pythagoras Theorem.

(Hypotenuse)² = (Base)² + (Perpendicular)²

We have

PQ = 48, QR = 64 and PR = ?

⇒ (PR)² = (PQ)² + (QR)²

⇒ (PR)² = (48)² + (64)²

⇒ (PR)² = 2304 - 4096 = 64 00

⇒ PR = 80

The six trigonometric functions we have are:

Answer:

B. 5 units

Step-by-step explanation:

[tex]\tt |AB|=\sqrt{(3-7)^2+(12-9)^2}=\sqrt{16+9}=\sqrt{25}=5 \ \ units[/tex]

The length of AB is 5 units.

Length is defined as the measurement or extent of something from end to end.

In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects.

Given that there are two points A = (7,9) and B = (3, 12),

So, we need to find the distance between them,

We know that the distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by,

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

D = [tex]\sqrt{(3-7)^2 + (9-12)^2}[/tex]

D = [tex]\sqrt{4^2+3^2}[/tex]

D = 5

Hence the length of AB is 5 units.

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Answer:

P(A or B) = 0.65

Step-by-step explanation:

Given that P(A) = 0.60, P(B) = 0.20, and P(A and B) = 0.15

We have to find P(A or B)

Apply the formula:

P(A or B) = P(A)+P(B)- P(A and B)

Now substitute the values in the formula:

P(A or B) = 0.60 + 0.20 - 0.15

P(A or B) = 0.80 - 0.15

P(A or B) = 0.65

Thus P(A or B) = 0.65  ....

Answer:

0.65 ~apex

Step-by-step explanation:

Answer:

9 seconds.

Step-by-step explanation:

On your graph, use a ruler and your eye to get the best fitting line.  

Then find the time in seconds (45) which is between 40 and 50 on the x axis.

Go across to the y axis. You will find it is about 9 seconds.

Based on the information depicted by the graph, the distance of the storm 45 seconds between Lightning and Thunder will be 9 miles

From the graph, we can create a proportional relationship thus :

Distance from storm = Seconds between Thunder

4 miles = 20 seconds

Let the miles traveled by Storm between 45 seconds = s

Hence, we have ;

4 miles = 20 seconds

s miles = 45 seconds

Cross multiply :

20s = 45 × 4

20s = 180

Divide both sides by 20

s = 180 / 20

s = 9 miles

Therefore, the storm will be 9 miles away.

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Answer:

y = [tex]\frac{1}{4}[/tex] x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (8, 1 ) into the partial equation

1 = 2 + c ⇒ c = 1 - 2 = - 1

y = [tex]\frac{1}{4}[/tex] x - 1 ← equation of perpendicular line

The equation 11r + 4 = 55 is equivalent to the equation 11r = 55 – 4. Then the correct option is B.

The equivalent is the expressions that are in different forms but are equal to the same value.

The equation is given below.

11r + 4 = 55

Then the equation can be written as

11r = 55 – 4

Then the correct option is B.

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Answer:

∠PRQ = 85°

Step-by-step explanation:

∠PRS and ∠TRQ are vertical angles and congruent, thus

4x + 15 = 3x + 35 ( subtract 3x from both sides )

x + 15 = 35 ( subtract 15 from both sides )

x = 20

Hence ∠PRS = (3 × 20) + 35 = 60 + 35 = 95°

∠PRQ and ∠PRS form a straight angle and are supplementary, hence

∠PRQ = 180° - 95° = 85°

Answer:

Angle QRP = 85

Step-by-step explanation:

Hopefully you can see QRS and TRP both equal 180 degrees, we will use this.  

QRS is the same as QRP and PRS added together.  Just like TRP is TRQ and QRP.  We will call QRP R for simplicities sake, and we are given a formula for PRS and TRQ.  PRS = 3x+35 and TRQ = 4x+15.

So now we have two equations.

180 = QRP + PRS = R + 3x + 35

180 = TRQ + QRP = 4x + 15 + R

So it's basically a system of equations.

180 = 35 + R + 3x

145 = R + 3x

R = 145 - 3x

180 = 4x + 15 + R

Replace R with what we found in the last  equation

180 = 4x + 15 + 145 - 3x

180 = x +160

x = 20

Now go back to the first equation and plug 20 in for x

R = 145 - 3x

R = 145 -3(20)

R = 145 - 60

R = 85

So Angle QRP = 85

Let em know if something doesn't make sense.  

Answer:

x = 21

Step-by-step explanation:

x- 12 = 9

Add 12 to each side

x- 12+12 = 9+12

x = 21

Answer:

[tex]\huge \boxed{x=21}[/tex]

Step-by-step explanation:

[tex]\Huge\textnormal{Add 12 from both sides of the equation.}[/tex]

[tex]\displaystyle x-12+12=9+12[/tex]

[tex]\Huge \textnormal{Simplify and solve to find the answer.}[/tex]

[tex]\displaystyle 9+12=21[/tex]

[tex]\huge \boxed{x=21}[/tex], which is our answer.

Answer:

the line is horizontal

Step-by-step explanation:

Note the y- coordinates of the 2 points the line passes through are equal.

This indicates that the line is horizontal and parallel to the x- axis

The equation of a horizontal line is y = c

where c is the value of the y- coordinates the line passes through.

Here the y- coordinates are 30, hence

Equation of horizontal line is y = 30

Answer:

It has a slope of zero because the change in the y-values is 0.

Step-by-step explanation:

Check the picture below.

If sides SX=5,SY=10,XU=4,YT=x then the length of ST=18.

A triangle is a two dimensional figure having three sides, three angles, three vertex. Th sum of all the angles is equal to 180°.

We have been given SX=5, XU=4,SY=10 and we are required to find the length of ST. We can write the sides as under:

SX/SU=SY/T

SX=5,SU=5+4=9,SY=10,ST=10+x

5/9=10/(10+x)

Solving this for the value of x.

5(10+x)=10*9

50+5x=90

5x=90-50

x=40/5

x=8

We know that ST=10+x.

We have to put the value of x in ST.

ST=10+8

=18

Hence if sides are SX=5,SY=10,XU=4,YT=x then the length of ST=18.

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Answer:

$30

Step-by-step explanation:

Find the cost per marker.

Given: 8 markers = $20

Divide 8 from both sides.

Let x = amount of markers.

(8x)/8 = (20)/8

x = 2.5

Each marker costs $2.50

Now, multiply 12 with $2.50

2.50 x 12 = 30

$30 is the cost of 12 markers.

~

Answer:

11

Step-by-step explanation:

It is given that:

r = 14 & s = 8

Plug in the corresponding numbers to the corresponding variables:

(3/7)(14) + (5/8)(8)

Solve. Remember to simplify. Do multiplication & division first, then add:

(3/7)(14) + (5/8)(8)

(3 * 14)/7 + (5 * 8)/8

(3 * 2) + 5

(6) + 5

11

11 is your answer.

~

Answer:

D: x = -2, x = 5

Step-by-step explanation:

To solve for a variable, you first have to isolate it on one side of the equation. Remember that whatever you do to one side, you also have to do to the other.

2x² + 2x + 12 = 3x² - x + 2   Subtract 2x² from both sides

2x + 12 = x² - x + 2   Subtract 2x from both sides

12 = x² - 3x + 2   Subtract 12 from both sides

0 = x² - 3x - 10   Using factoring, split this into two expressions

0 = (x - 5) (x + 2)   Set each expression equal to 0

x - 5 = 0 and x + 2 = 0   Solve each expression

x = 5 and x = -2

Now, you can plug in both answers to check your work

2x² + 2x + 12 = 3x² - x + 2   Plug in 5

2(5)² + 2(5) + 12 = 3(5)² - 5 + 2   Simplify

2(25) + 10 + 12 = 3(25) - 5 + 2   Simplify some more

50 + 10 + 12 = 75 - 5 + 2   Simplify one more time

72 = 72   It works!

2x² + 2x + 12 = 3x² - x + 2   Plug in -2

2(-2)² +2(-2) + 12 = 3(-2)² -(-2) + 2   Simplify

2(4) - 4 + 12 = 3(4) + 2 + 2   Simplify again

8 - 4 + 12 = 12 + 2 + 2   Simplify one more time

16 = 16   It also works!

Answer:

(see attached)

Step-by-step explanation:

Rearrange the equation in the form y (≥ or ≤) mx + c , so that you get:

y ≥ (-1/2)x - (9/20)

Graph this equation.

Test a random point on either side of the line to see which side is valid (and shade)

we try the origin (0,0)

This makes the equation :

(0) ≥ (-1/2)(0) - (9/20)

0 ≥ - (9/20)  (this inequality is valid, so that means the point we picked (0,0) falls on the valid side. Shade that side. (in this case the region above the line)

Answer:

$8.40

Step-by-step explanation:

You multiply $12 by 0.7 and get $8.40

Answer:

$8.40

Step-by-step explanation:

Since 1 Liter costs $12, you can multiply 12 by 0.7 (L) to get the answer.

Answer is 8.4, so it's $8.40

Answer:

x  ≥ 9.2

Step-by-step explanation:

If in a gymnastics competition an athletes final score is calculated by taking 75% of the average technical score and adding 25% of the artistic score all scores are out of 10 and one gymnast has a 7.6 average technical score, the gymnast needs x  ≥ 9.2 to have a final score of at least 8.0.

7.6 x 75 / 100 = 5.7

Final answer:

The gymnast requires an artistic score of at least 9.2 to achieve a final score of at least 8.0, calculated by taking 75% of their average technical score and adding 25% of their artistic score.

Explanation:

To find out what artistic score the gymnast needs to achieve a final score of at least 8.0, we use the given information that the final score is composed of 75% of the average technical score plus 25% of the artistic score. Let's represent the artistic score as A.

First, calculate 75% of the average technical score:
0.75 × 7.6 = 5.7

Now, set up the equation using the required final score (8.0) and the known technical score (5.7):
5.7 + 0.25A ≥ 8.0

To find the minimum artistic score (A), we subtract 5.7 from both sides of the equation:
0.25A ≥ 8.0 - 5.7
0.25A ≥ 2.3

Finally, divide by 0.25 to solve for A:
A ≥ ÷ 0.25
A ≥ 9.2

So, the gymnast would need an artistic score of at least 9.2 to achieve a final score of at least 8.0.

Answer:

[tex]x^{3} -12[/tex]

Step-by-step explanation:

[tex]y=\sqrt[3]{x+12}[/tex]

Replace x with y to get

[tex]x=\sqrt[3]{y+12}[/tex]

Cube both side

[tex]x^{3}=y+12[/tex]

Subract 12 from both sides

[tex]x^3-12=y[/tex]

Answer:

It is A i believe.

Step-by-step explanation:

Because, 15/100 = 0.15 and y is your regular price so;

y - 0.15

Sorry had to rewrite what i did, but i hope my answer has helped you.

Answer:

D.

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

The slope of y=4x+2 is 4.

Let's look at the choices:

A) The slope of y=-2x+3 is -2.

B) The slope of y=2x-3 is 2.

C) The slope of y=-4x+2 is -4.

D) The slope of y=4x-2 is 4.

So we are looking for a line that has the same slope as the given line which is 4.

The answer is D.

Answer:

D.

Y = mx + b is the equation for a straight line. "B" is called the y intercept. "M" is the value of the slope of the line. "X" is the value where the line intercepts the x axis.

so the reason the awnser is D is because the M=4 in both equations, meaning that they have the same slope

Check the picture below.

Answer:

i think its d

Step-by-step explanation:

Answer:

B A triangle in which no two sides are congruent is scalene

Step-by-step explanation:

A triangle that has 3 congruent sides is an equilateral triangle

A triangle in which no two sides are congruent ( no sides are the same) is a scalene triangle

A triangle that has at least two congruent sides is an isosceles triangle

Answer:

a triangle in which no two sides are congruent

Step-by-step explanation: