If you only have a 1/10 measuring cup and a recipe calls for
4 3/10 cups of flour, how many 1/10 cups would you need to use?

Answer:

(-6, -36)

Step-by-step explanation:

The vertex [tex](h,k)[/tex] of a function of the form [tex]f(x)=ax^2+bx+c[/tex] is given by the formula:

[tex]h=\frac{-b}{2a}[/tex]

[tex]k=f(h)[/tex] in other words, we find h and then evaluate function at h to find k.

We know from our function that [tex]a=1[/tex], [tex]b=12[/tex].

Replacing values

[tex]h=\frac{-12}{2(1)}[/tex]

[tex]h=-\frac{12}{2}[/tex]

[tex]h=-6[/tex]

Now we can evaluate our function at -6 to find k:

[tex]k=f(h)=f(-6)[/tex]

[tex]k=(-6)^2+12(-6)[/tex]

[tex]k=36-72[/tex]

[tex]k=-36[/tex]

We can conclude that the vertex (h, k) of our function is (-6, -36)

Answer:

(-6,-36)

Step-by-step explanation:

The given function is

[tex]f(x)=x^2+12x[/tex]

We complete the square to write this function in the vertex form.

Add and subtract the square of half the coefficient of x.

[tex]f(x)=x^2+12x+6^2-6^2[/tex]

[tex]f(x)=x^2+12x+36-36[/tex]

The first three terms is now a perfect square trionomial

[tex]f(x)=(x+6)^2-36[/tex]

Or

[tex]f(x)=(x--6)^2-36[/tex]

The function is now in the form:

[tex]f(x)=a(x-h)^2+k[/tex]

where h=-6 and k=-36

The vertex is therefore (h,k)=(-6,-36)

Answer:

The last option (62 degrees)

Step-by-step explanation:

Angle F is the same measure as angle E, just like angle D is the same measure as G.

The measure of angle ∠E will be 62°. Then the correct option is D.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.

DEFG is an isosceles trapezoid.

Then the angle ∠E and ∠F will be congruent.

∠E = ∠F

∠E = 62°

Then the correct option is D.

More about the trapezium link is given below.

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The answer is B. I just answered this question earlier!

Answer:

i need the ansrew too

Step-by-step explanation:

hehe

For this case we have the following functions:

[tex]g (x) = 9 + 4x\\h (x) = \frac {x + 21} {5}[/tex]

We must find [tex](h * g) (x)[/tex]. By definition of composite functions we have to:

[tex](h * g) (x) = h (x) * g (x)[/tex]

So:

[tex](h * g) (x) = 9 + 4x * \frac {x + 21} {5}[/tex]

We apply distributive property:

[tex](h * g) (x) = \frac {9x + 9 * 21 + 4x ^ 2 + 4x * 21} {5}\\(h * g) (x) = \frac {9x + 189 + 4x ^ 2 + 84x} {5}\\(h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}\\[/tex]

Answer:

[tex](h * g) (x) = \frac {4x ^ 2 + 93x + 189} {5}[/tex]

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer: Option D

[tex]f(x)=(x+3)^2 -k[/tex]

Step-by-step explanation:

For a quadratic function of the form

[tex]ax ^ 2 + bx + c[/tex]

The x coordinate of the vertice is:

[tex]x =-\frac{b}{2a}[/tex]

In this case the function is:

[tex]f(x)=x^2+6x-2\\\\[/tex]

So

[tex]a=1\\b=6\\c=-2[/tex]

The x coordinate of the vertice is:

[tex]x=-\frac{6}{2*1}\\\\x=-3[/tex]

The y coordinate of the vertice is:

[tex]f(-3) = (-3)^2 +6(-3) -2\\\\f(-3)=-11[/tex]

The vertice is: (-3, -11)

The form e vertice for a quadratic equation is:

[tex]f(x)=(x-h)^2 +k[/tex]

Where

the x coordinate of the vertice is h and the y coordinate of the vertice is k.

Then h=-3 and k =-11

Finally the equation [tex]f(x)=x^2+6x-2\\\\[/tex] in vertex form is:

[tex]f(x)=(x+3)^2 -k[/tex]

Answer:

The correct answer option is D. f(x) = (x + 3)² - 11.

Step-by-step explanation:

We know that the standard form of a quadratic function is given by:

y = ax² + bx + c

The vertex form of a parabola is given by

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b / 2a and k = f(h)

In the given equation f(x) = x² + 6x - 2

a = 1, b = 6 and c = -2

Finding h:

h = -6 / (2 × 1)

h = -6/2

h = -3

Finding k:

k = 1(-3)² + 6(-3) + 3

k = 9 - 18 - 2

k = -11

Therefore, the given quadratic function in vertex form: f(x) = (x + 3)² - 11

first off let's convert the mixed fraction to improper fraction, and then do the division, since it was divided among all 6, he and 5 friends.

[tex]\bf \stackrel{mixed}{4\frac{4}{5}}\implies \cfrac{4\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{24}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{24}{5}\div 6\implies \cfrac{24}{5}\div \cfrac{6}{1}\implies \cfrac{24}{5}\cdot \cfrac{1}{6}\implies \cfrac{24}{6}\cdot \cfrac{1}{5}\implies \cfrac{4}{1}\cdot \cfrac{1}{5}\implies \cfrac{4}{5}[/tex]

Answer:

0.8 or 4/5

Step-by-step explanation:

4/5=.8 4.8/6=.8

Answer:

Do you need work shown?

Step-by-step explanation:

(I don't know where to comment here)

Answer:

x - 3

Step-by-step explanation:

Given

[tex]\frac{x^2-9}{x+3}[/tex]

Note that x² - 9 is a difference of squares and factors as

x² - 9 = (x + 3)(x - 3), thus

[tex]\frac{(x+3)(x-3)}{x+3}[/tex]

Cancel the x+ 3 factor on the numerator/ denominator leaving

x - 3 ← in simplified form

The simplified form of the given rational expression x²-9/x+3, provided x is not equal to -3, is x-3.

The given rational expression is x²-9/x+3. To simplify this expression, we can recognize that the numerator (x^2-9) is a difference of squares. In fact, we can rewrite the expression as (x+3)(x-3)/(x+3). As long as x doesn't equal -3 (to prevent division by zero), we can simplify the expression by canceling out the common factor of 'x+3' in both the numerator and denominator. Therefore, the simplified form of the rational expression is x-3 when x does not equal -3.

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Multiplying two negative numbers would always give you a positive product

Example 1) -2 * -1 = 2

Example 2) -5 * -4 = 20

Example 3) -10 * -3 = 30

Answer:

The correct answer option is -7.

Step-by-step explanation:

We are asked to determine the minimum value of y on the graph of [tex]y = sin x - 6 [/tex].

[tex]y' = cos(x) = 0[/tex]

[tex]x = arccos(0) = \pm\frac{\pi }{2} +2k\pi[/tex] where 'k' is any integer.

So, [tex] y = sin ( \frac { \pi} { 2 } ) - 6 = 1 - 6 = -5 [/tex] (it is the absolute minimum value)

and [tex]y=sin(\frac{-\pi}{2}+2\pi )-6 = sin(\frac{3\pi}{2})-6 [/tex] = -7 (absolute minimum y value)

Answer:

The correct answer option is -7.

We are asked to determine the minimum value of y on the graph of . where 'k' is any integer.

So,  (it is the absolute minimum value)and  = -7 (absolute minimum y value)

Answer:

1320

Step-by-step explanation:

This is a simple permutation.

Since you start with 12 people and there are 3 winners, after every winner the number pf people available to win decrease.

First, there are 12 people, then after the first win there are 11 people, and after the 2nd win, for the third win the there are 10 people.

Thus, to find the total number of combinations, you multiply:

12*11*10=1320

Thus, there are 1320 possible combinations

Answer:

5/48

Step-by-step explanation:

Answer:

5/48

Step-by-step explanation:

The algebraic representation of the given statement is:

[tex]n^2 + (n + 1)^2 = 85[/tex]

Expanding and simplifying:

[tex]n^2 + (n^2 + 2n + 1) = 85[/tex]

[tex]2n^2 + 2n + 1 = 85[/tex]

[tex]2n^2 + 2n + 1 - 85 = 0[/tex]

[tex]2n^2 + 2n - 84 = 0[/tex]

Dividing the equation by 2 to simplify:

[tex]n^2 + n - 42 = 0[/tex]

Now, we can solve this quadratic equation using the quadratic formula:

[tex]n = [-b ± √(b^2 - 4ac)] / (2a)[/tex]

Where a = 1, b = 1, and c = -42:

n = [-(1) ± √((1)^2 - 4(1)(-42))] / (2(1))

n = [-1 ± √(1 + 168)] / 2

n = [-1 ± √169] / 2

n = [-1 ± 13] / 2

This yields two possible values for n:

n₁ = (-1 + 13) / 2 = 12 / 2 = 6

n₂ = (-1 - 13) / 2 = -14 / 2 = -7

Since n represents the smaller of the two consecutive integers, we discard the negative value.

Therefore, the smaller integer (n) is 6.

To solve this problem algebraically, we first translate the given statement into an equation. We know that the sum of the squares of two consecutive integers can be represented as[tex]n^2 + (n + 1)^2, v[/tex]where n is the smaller integer. Setting this expression equal to 85, we get the equation [tex]n^2 + (n + 1)^2 = 85.[/tex]

We then expand and simplify this equation to get a quadratic equation in standard form: [tex]2n^2 + 2n - 84 = 0.[/tex]

Next, we use the quadratic formula to solve for n, which gives us two possible values. Since we are looking for the smaller of the two consecutive integers, we discard the negative solution.

Thus, the smaller integer is n = 6.

Complete question:

The sum of the squares of two consecutive integers is 85. Using n to represent the smaller of the two consecutive integers, express this statement in algebraic form

Answer:

D

Step-by-step explanation:

Distribute the negative 1 in the second group.

[tex]5k^4*-1=-5k^4 \\ 5k^3*-1=-5k^3 \\ -k*-1=k[/tex]

Now add by combining like terms.

[tex]3k^4-5k^4=-2k^4 \\ -2k^3-5k^3=-7k^3 \\ k+k=2k[/tex]

[tex]-2k^4-7k^3+2k[/tex]

3/6 because there are 6 sides and there are 3 numbers that you want to roll. They are even numbers so if you want to roll half of the numbers but not the other half well you have 3/6

Answer: view image. its a proof (in red)

Step-by-step explanation:

The answer is 1/2.

2r = d.

Hope this helps!

A Radius Of The Circle Is Always Half The Diameter. This Means That The Radius Is Half Way Across A Circle.

ANSWER

The train is moving 82.5mi/hr

EXPLANATION

How fast the train is going is the same as the speed of the train:

The speed of the train is calculated using the formula,

[tex]Speed = \frac{distance}{time} [/tex]

[tex]Speed = \frac{330}{4} [/tex]

[tex]Speed = 82.5[/tex]

Therefore the train is moving 82.5mi/hr

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

We have m = -1/4 and the point (4, 5). Substitute:

[tex]y-5=-\dfrac{1}{4}(x-4)[/tex]

Answer: $32.45

Step-by-step explanation:

Because....

55%  × 59 = $32.45

You could also write 55% as 0.55.

So it will look like this :

0.55 × 59 = 32.45.

It will still give you the same answer :)

* Hopefully tis helps:) Mark me the brainliest:)!!

Answer:

all real numbers

Step-by-step explanation:

Answer:

a = 15

b = 7

c = 4

Step-by-step explanation:

Given in the question an expression [tex]\sqrt[4]{15}^{7}[/tex]

This expression can be written as [tex]15^{\frac{7}{4} }[/tex]

As we know that roots are most often written using a radical sign, like this, [tex]\sqrt[n]{x}[/tex] But there is another way to represent the taking of a root.

You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. For example, [tex]\sqrt[n]{x}[/tex] can be written as [tex]x^{\frac{1}{n} }[/tex]

Secondly two powers having same base can be multiply

[tex]x^{n}(^{m})=x^{nm}[/tex]

Answer:

[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]

Step-by-step explanation:

[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]

Answer:

B. y+13=5(x+2)

Step-by-step explanation:

I personally do y=_+_(x-_) when solving these equations

Plug in -2 the x coordinate for (x- (-2) to be (x+3)

Plug in -13 for the y intercept.

5 from 5x is the slope.

Thus y=-13+5(x+3)

Then just move 13 to the other side

Answer:

120 square centimeters

Step-by-step explanation:

The question says the formula already.

Area = bh

b = base length   b = 10

h = height length   h = 12

Area = 10 · 12

Area = 120 square centimeters

Answer: B. 120 square centimeters

Step-by-step explanation:

Given : The area of a parallelogram is found using the formula [tex]bh[/tex], where b represents the length of the base and h represents the length of the height.

Then , the area of a parallelogram that has a base of 10 centimeters and a height of 12 centimeters will be:-

[tex]\text{Area}=10\times12\\\\\Rightarrow\text{Area}=120\text{ square centimeters}[/tex]

Therefore , the area of the parallelogram = 120 square centimeters

Simplify 6x/9 to 2x/3

2x/3(x + y)

Simplify

= 2x(x + y)/3

3.25 • p = t

Or

p = t/3.25

Hope this helps!

The time it takes to print a number of photos can be shown as a proportionality relationship p = (78/24) * t, with p being the number of photos printed and t being time in seconds.

The relationship between the time (t) needed to print pictures and the number of pictures (p) printed by a photo printer can be represented by a simple proportionality relationship. This means that we can express this relationship as a rate. In this case, the printer prints 78 pictures in 24 seconds, so we can write the relationship as:

p / t =78/24

Or in other words:

p = (78/24) * t

This equation suggests that for any given unit of time t, you simply multiply t by the rate (78/24) to find the number of pictures p that can be printed in that time.

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Answer:

(B) 132 in²

Step-by-step explanation:

Top Length = 3 + 8 + 3 = 14 in

Bottom Length = 8 in

Area of the trapezoid

= 1/2 (14 + 8) x 12

= 1/2 (22) (12)

= 132 in²

Answer:

B

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases.

here h = 12, a = AB = 8 and b = DC = 3+ 8 + 3 = 14

A = [tex]\frac{1}{2}[/tex] × 12 × (8 + 14) = 6 × 22 = 132 in² → B

Answer:

[tex]9 \cdot 10^6[/tex]

Step-by-step explanation:

A phone number contains 7 digits. How many different numbers can be made using the digits 0–9 if the first digit is not 0 and all of the digits can be repeated

In 7 digit phone number, the first number cannot be 0

So only 1  to 9 are used to get the first digit. 9 numbers can be used

other digits can use number from 0 to 9. 10 number can be used

So possible numbers can be made is

[tex]9 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10[/tex]

[tex]9 \cdot 10^6[/tex]

The correct option is C.[tex]\ 9 \times 10^6[/tex]

To solve the problem of finding how many different [tex]7[/tex]-digit phone numbers can be made using the digits [tex]0–9[/tex], with the first digit not being 0 and digits allowed to repeat, we can follow these steps:

1. First Digit Choices

The first digit has 9 possible choices ([tex]1[/tex] through [tex]9[/tex]) since it cannot be 0.

2. Remaining Digits Choices

Each of the remaining [tex]6[/tex] digits can be any of the [tex]10[/tex] digits ([tex]0[/tex] through [tex]9[/tex]).

So, the total number of different [tex]7[/tex]-digit phone numbers can be calculated by multiplying the number of choices for each digit:

[tex]\[9 \text{ choices for the first digit} \times 10 \text{ choices for each of the remaining 6 digits}\][/tex]

This can be represented mathematically as:

[tex]\[9 \times 10^6\][/tex]

Calculating [tex]\(10^6\)[/tex]

[tex]\[10^6 = 1,000,000\][/tex]

So,

[tex]\[9 \times 1,000,000 = 9,000,000\][/tex]