Matt has 12 balloons that he wants to give to 4 friends. He wants each friend to have the same number of balloons. Select the three statements that describe how Matt should give the balloons to his friends.

Answer: B: 56

Step-by-step explanation: First find f(g(x)). Where f(x) = -3x-4 and

g(x) = 2x-6. Replace X in f(x) with the equation for g(x)

f(g(x)) = -3(2x-6) -4. Then use the foil method and simplify.

= -6x+18-4

=-6x+14

Now sub. in the value of x with -7 and evaluate.

=-6(-7)+14

=42+14

=56

Answer:

1) Translation

2) Rotation

3) Reflection  

Step-by-step explanation:

To make ΔDEF ≅ ΔD'E'F' , we will carry on the following steps:

Step 1: Translate ΔD'E'F' in upward direction, the figure will remain same but it will shift a little in upwards direction.

Step 2 : Rotate ΔD'E'F' about 180°. The figure obtained will be reflection of the original image ΔDEF.

Step 3 : Reflect ΔD'E'F'.

This implies that ΔDEF≅ΔD'E'F'.  

We know that : Sin²θ + Cos²θ = 1

Given : Sinθ [tex]\bf{= \frac{4}{7}}[/tex]

[tex]\bf{\implies (\frac{4}{7})^2 + Cos^2(\theta) = 1}[/tex]

[tex]\bf{\implies Cos^2(\theta) = 1 - \frac{16}{49}}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{49 - 16}{49})}[/tex]

[tex]\bf{\implies Cos^2(\theta) =(\frac{33}{49})}[/tex]

[tex]\bf{\implies Cos(\theta) = (\pm)(\frac{\sqrt{33}}{7})}[/tex]

Given : θ lies in Quadrant II

We know that : Cosθ is Negative in Quadrant II

[tex]\bf{\implies Cos(\theta) = (-)(\frac{\sqrt{33}}{7})}[/tex]

Option 3 is the Answer

Answer:

angle(ADB)=angle(CBD)

ADC+DCB=180

AE=CE

Step-by-step explanation:

we will verify each options

option-A:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

and alternate interior angles are always equal

so,

angle(ADB)=angle(CBD)

so, this is TRUE

option-B:

we know that

ABCD is a parallelogram

so, AD and BC are parallel

so, we get

ADC+DCB=180

so, this is TRUE

option-C:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

[tex]angle(DEC)\neq angle(DEA)[/tex]

so, this is FALSE

option-D:

Since, AC is a diagonal of parallelogram

so, E is the mid-point between AC

AE=CE

so, this is TRUE

option-E:

Since, AC and DB are diagonals of parallelogram

so, they can not be equal

so, this is FALSE

Answer:

area = 6m + 51 feet²

Step-by-step explanation:

area = length × width = 3(2m + 17) = 6m + 51

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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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: C) 1

===========================================================

One way is to graph the function f(x) = ln(x)/(x-1) and you'll see the curve slowly approach y = 1 when x approaches 1 from either side. Check out the attached image labeled "figure 1" for this graph.

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You can use a table to see this in action. See figure 2 (attached below as well).

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Another alternative is to use L'Hospital's rule. This is because we get the indeterminate form 0/0 after plugging x = 1 into the original function.

if y = ln(x), then dy/dx = 1/x

If y = x-1, then dy/dx = 1

So f(x) = ln(x)/(x-1) becomes (1/x)/1 = 1/x

If you plug in x = 1, you get 1/x = 1/1 = 1.

Regardless of which method you use, the limiting value is 1

Final answer:

The blanks are filled with 'straight line' as angles on a straight line sum to 180°, which is a key concept in geometry related to the properties of angles and triangles.

Explanation:

The sum of the measures of angle 5 and angle 6 is equal to 180° and the sum of the measures of angle 2 and angle 3 is equal to 180° because angles on a straight line measure 180°. This concept is related to the geometric property that when two angles lie on the same line and add up to form a straight angle, their measures sum up to 180°.

In geometry, specifically the study of polygons and angles, we learn that a triangle is a three-sided figure lying on a plane with three angles adding up to 180°. This is called the Triangle Sum Theorem, which is fundamental to understanding the properties of triangles and other polygons.

Answer:

1. 29/4

2. 5

3. 6

4. 14/3

5. 29/27

Step-by-step explanation:

Answer: You the answer

Step-by-step explanation: cause your fine

Answer:

Perimeter = 32.44 unit

Area of triangle = 30 unit²

Step-by-step explanation:

By distance formula distance between (a,b) and (c,d) is [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]

So, we have

      [tex]AB=\sqrt{(16-2)^2+(2-8)^2}=15.23\\\\BC=\sqrt{(16-6)^2+(2-2)^2}=10\\\\AC=\sqrt{(2-6)^2+(8-2)^2}=7.21[/tex]

Perimeter = 15.23 + 10 + 7.21 = 32.44 unit

We have [tex]s=\frac{15.23+10+7.21}{2}=16.22[/tex]

Area of triangle[tex]=\sqrt{s(s-AB)(s-BC)(s-AC)}=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}=30[/tex]

Area of triangle = 30 unit²

Answer:

Let x represents the ounces of first spice.

From the given statements, you draw a table as shown below:

                           ounces of spice         Percentage           ounces of salt

First spice                 x                              3%                            0.03x

Second spice           175                            6%                          175(0.06)

Final  mixture          x+ 175                         5%                        (x+175)(0.05)

Now, to solve for x;

Final spice = First spice + second spice

[tex]0.03x+175(0.06) = (x+175)(0.05)[/tex]

[tex]0.03x + 10.5 = 0.05x + 8.75[/tex]

Subtract 10.5 on both sides we have;

[tex]0.03x + 10.5 -10.5= 0.05x + 8.75-10.5[/tex]

Simplify:

[tex]0.03x= 0.05x -1.75[/tex]

Subtract 0.05x on both sides;

[tex]0.03x - 0.05x= 0.05x -1.75-0.05x[/tex]

Simplify:

[tex]-0.02x= -1.75[/tex]

Divide both sides by -0.02, we get;

x = 87.5 ounces

Therefore, 87.5 ounces of spices i.e 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt

Answer:

None of the Above

Step-by-step explanation:

As it is given that

cosФ= 3/2

and Ф lies in quadrant 4

Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant

and sinФ is negative in 4th quadrant

also we know that by simple rules of trigonometry in a right angled triangle

cos Ф=[tex]\frac{Base}{Hypotenuse}[/tex] =[tex]\frac{3}{2}[/tex]

now from the law of trigonometry

cos²Ф+sin²Ф=1

From this we derive the value of sinФ

solving the equation

sin²Ф=1-cos²Ф

Putting in the values of cos Ф

sin²Ф=1-[tex](\frac{3}{2})^{2}[/tex]

sin²Ф=1-[tex](\frac{9}{4})[/tex]

solving the fraction

sin²Ф=[tex](\frac{4-9}{4})[/tex]

sin²Ф=[tex](\frac{-5}{4})[/tex]

so taking square root of both sides

[tex]\sqrt{sin^{2}\alpha}=\sqrt{\frac{-5}{4} }[/tex]

here

[tex]\alpha[/tex]=Ф

so it becomes

sin Ф=[tex]\frac{\sqrt{-5} }{2}[/tex]

as we know that in imaginary numbers

[tex]\sqrt{-1}[/tex] = ι

so the given becomes

sin Ф=[tex]\frac{{-5ι} }{2}[/tex]

Which is the value of sin Ф

And in the given values we can see that it is none of the values

Also seeing the question we can see that the question is absurd because

cos Ф= base / hypotenuse

in our question we can see that base =3 and hypotenuse = 2

but in real geometry this is the rule that hypotenuse can never be smaller then base either it is equal to base or greater then base

the formula for finding value of finding hypotenuse is

hypotenuse ² = base ² + perp ²

so this formula shows that if perp is 0 then hypotenuse will be equal to base

in other cases it would be greater then base

Answer:

- 1/ 2

Step-by-step explanation

-1\ 2

Use the Pythagorean identity, sin2Θ + cos2Θ = 1 to get sinΘ = ±1 - cos2Θ, then solve for sinΘ.

Joe has 8 green pepper plants and 28 red pepper plants in his garden.

Let's denote the number of green pepper plants as G and the number of red pepper plants as R.

According to the given information, the ratio of green pepper plants to red pepper plants is 2 to 7.

This can be written as G:R = 2:7.

It is also mentioned that there are 20 more red pepper plants than green pepper plants. This can be written as R = G + 20.

Now, we can substitute the value of R from the second equation into the first equation:

G:G+20 = 2:7

By cross-multiplying, we have 7G = 2(G+20).

Simplifying the equation, we get 7G = 2G + 40.

Subtracting 2G from both sides, we have 5G = 40.

Dividing both sides by 5, we get G = 8.

Therefore, there are 8 green pepper plants and 8 + 20 = 28 red pepper plants in Joe's garden.

[tex]a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}[/tex]

Answer: -1, 2, 7, 14, 23

Step-by-step explanation:

aₙ = n² - 2

for n=1

a₁ = 1² - 2 = 1-2= -1

for n=2

a₂ = 2² - 2 = 4-2 =2

for n= 3

a₃ =3² - 2 = 9-2=7

for n=4

a₄= 4² - 2 = 16-2=14

for n=5

a₅= 5² - 2=25-2=23

Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23

f(x) = 4x - 18

f(-3) - put x = -3 to the equation of the function

f(-3) = 4(-3) - 18 = -12 - 18 = -30

f(x) = -46

We have the equation:

4x - 18 = -46       add 18 to both sides

4x = -28    divide both sides by 4

x = -7

The equation of line in the slope intercept form is c = 1.5 ( t ) + 12 where t is the number of toppings and c is the total cost

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the total cost of pizza with toppings be = c

Let the number of toppings be = t

Let the initial cost of the pizza be = $ 12

Let the cost of each toppings be = $ 1.50

So , the total cost of the pizza with toppings c =  ( cost of each toppings x number of toppings ) + initial cost of the pizza

Substituting the values in the equation , we get

Total cost of the pizza with toppings c = 1.50 ( t ) + 12

Therefore , the value of A is c = 1.50 ( t ) + 12

Hence , the equation is c = 1.50 ( t ) + 12  with slope m = 1.50 and y intercept as 12

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Final answer:

The equation in slope-intercept form for the total cost C of a pizza with t toppings when a pizza costs $12 and each additional topping costs $1.50 is C = 1.50t + 12.

Explanation:

To find the equation in slope-intercept form for the total cost C of a pizza with t toppings at a pizza parlor that charges $12 for a large cheese pizza and $1.50 for each additional topping, we can establish a relationship between the number of toppings and the total cost. Let's use the slope-intercept form of the linear equation, y = mx + b where y is the total cost, m is the cost per topping, x is the number of toppings, and b represents the base price of the pizza without toppings.

The base price of the pizza is $12, which is the y-intercept, and the additional cost per topping is $1.50, which is the slope. Therefore, the equation that represents the total cost C of the pizza with t toppings is:

C = 1.50t + 12

Answer:

see below

Step-by-step explanation:

The "fundamental theorem of algebra" tells you the number of roots of a polynomial is equal to its degree. This includes real and complex roots and counts repeated roots the number of times they are repeated. (Real numbers are a subset of Complex numbers, so the choice of "complex" for this problem is appropriate.)

_____

The given quadratic can be solved using the quadratic formula:

for ax²+bx+c=0, the solutions are

... x = (-b±√(b²-4ac))/(2a)

Here, a=2, b=-4, c=-1, so ...

... x = (4 ±√(16 -4·2·(-1)))/(2·2)

... x = (2±√6)/2

Answer:

1. complex    2. 2+6      3. 2-6

Step-by-step explanation:

i took the test :)

Answer:

∠NET = 63°

Step-by-step explanation:

We are given a figure with a circle A and a line ET which is tangent to the circle at the point T. Also, the measure of the angle TNG is given to be 27° and we are to find the measure of angle NET.

If we recall the point of tangency, we will remember that the point where a tangent touches the radius of a circle is always a right angle.

That makes the angle NTE to be 90°.

Putting the sum of these angles equal to 180 to get:

90 + 27 + ∠NET = 180

∠NET = 180 - 90 - 27

∠NET = 63°

Answer:

[tex]P(x)=12.50x-150.[/tex]

Step-by-step explanation:

Let x be the number of tickets sold. If a theater group charges $12.50 per ticket for its opening play of the season, then x tickets cost $12.50x. Production costs for the play are $150. Then the profit the theater group earns from selling x tickets is

[tex]P(x)=12.50x-150.[/tex]

[tex]f(x)=4\cdot2^x\\\\y-intercept\ for\ x=0:\\\\f(0)=4\cdot2^0=4\cdot1=4[/tex]

Answer: Third option (bottom left)

Step-by-step explanation: We want to find which one of the graphs is the graph of the function f(x) = 4*2^x

Let's analyze some interesting points.

f(0) = 4*2^0 = 4*1 = 4

So we need to find the graph that passes through the point (0,4) (this means that intercepts the y-axis in the 4)

The graph that passes through the point (0,4) is the third option (bottom left one)

Answer:

60 percent

Step-by-.step explanation:

You need to convert 3/5 to a percentage.

This is 3*100 / 5

= 300 / 5

= 60 per cent

Final answer:

Roasted beans retain 3/5 of their initial weight, which is equivalent to 60% when converted to a percent.

Explanation:

To convert this fraction to a percentage, we follow the steps outlined in the explanation: dividing the numerator by the denominator to get a decimal value, and then multiplying by 100 to express it as a percentage. In this case, 3 divided by 5 equals 0.60, which when multiplied by 100 gives 60%.

The roasted beans retain approximately 3/5 of their initial weight after roasting. To determine what percentage of their initial weight they retain, we convert the fraction 3/5 to a percent. To do this:

Therefore, roasted beans retain 60% of their initial weight.

Answer:

[tex]\$164.5[/tex]

Step-by-step explanation:

Bonnie deposits $70.00 into a new savings account.

The account earns 45% simple interest per year.

She neither added or removed from the savings account for 3 years.

We know that,

[tex]i=\dfrac{P\cdot r\cdot r}{100}[/tex]

here,

i = interest,

P = principal = $70,

r = rate of interest = 45%,

t = time = 3 years,

Putting the values,

[tex]i=\dfrac{70\cdot 45\cdot 3}{100}=\$94.5[/tex]

So the total amount will be,

[tex]=\text{Principal}+\text{Interest}[/tex]

[tex]=70+94.5[/tex]

[tex]=\$164.5[/tex]

Answer:

its 4.5 not 45

Step-by-step explanation:

Answer: 27 grams

Step-by-step explanation:

m(x) = 64(0.75)ˣ

m(3) = 64(0.75)³

      = 64(.421875)

      = 27

Answer:the answer is D. All of the above

Step-by-step explanation:

Answer:

D) ALL OF THE ABOVE

Explanation:

In today's world, banks offer various variety of services at door-steps to attract customers However, some basic today's services offered by the banks to its customers are discussed below:

1. Home banking:

Home banking is the procedure of finishing financial affairs from an individual's own home as opposed to using a branch of a bank. It compromises actions such as transferring money, applying for loans, paying bills, making financial inquires and directing deposits.

2. Online banking:

Online banking is one of the famous service offered by banks nowadays that allows customers to access their account data by using the internet. Online banking is also known as “Internet banking”.

3. Priority banking:

Priority banking may include various services, but some of the famous services include online bill pay, financial consultation, free checking of account amount and information.

Answer:

F(-4) = -3313

Step-by-step explanation:

To solve this, let x=-4

f(x) = 3x^5 + 4x^3-x+11

f(-4) = 3(-4)^5 + 4(-4)^3 -(-4) +11

     = 3(-1024) +4 (-64) +4+11

    = -3072 - 256+15

     = -3313

Answer:

This means the function touches the x-axis at -1 but does not cross.

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

This means the function touches the x-axis at -1 but does not cross.

So the first thing we need to do is set up an equation (using x to represent the number). Then, we'll solve it to get the answer.

Step 1: Translate the word problem into an equation

Word problem: The sum of nine and six-tenths and a number is thirteen and two-tenths.

Equation: [tex]9 \frac{6}{10}[/tex] + x = [tex]13 \frac{2}{10}[/tex]

Step 2: Isolate x by subtracting [tex]9 \frac{6}{10}[/tex] from each side

[tex]9 \frac{6}{10}[/tex] + x -  [tex]9 \frac{6}{10}[/tex] = [tex]13 \frac{2}{10}[/tex] -  [tex]9 \frac{6}{10}[/tex]

Step 3: The numbers on the left cancel out, leaving x alone

x =  [tex]3 \frac{6}{10}[/tex]

Step 4: Convert the answer to decimals

x = 3.6

Answer:

its B

Step-by-step explanation: