1234-4566/45.44+67*755.34

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

I recommend using guathmath

Answer:

See below ~

Step-by-step explanation:

Let the bases be x and x + 6.

Substituting the known values into the formula :

The base lengths are :

Answer:

One base is \(\large \boxed{\sf 9}\)  inches for one of the bases and \(\large \boxed{\sf 15}\) inches for the other base.

\(\large \boxed{\sf 24}=\sf(b_1+b_2)\).  Use guess and check to find two numbers that add to \(\large \boxed{\sf 24}\) with one number 6 more than the other to get

\(\large \boxed{\sf 9}\)  inches for one of the bases and \(\large \boxed{\sf 15}\) inches for the other base.

Step-by-step explanation:

\(\textsf{Area of a trapezoid}= \sf \dfrac{1}{2}(b_1+b_2)h \quad \textsf{(where b are the bases and h is the height)}\)

Given:

Substitute given values into the formula to find (b₁ + b₂) :

\(\implies \sf 48=\dfrac{1}{2}(b_1+b_2)4\)

\(\implies \sf \dfrac{48}{4}=\dfrac{1}{2}(b_1+b_2)\)

\(\implies \sf 12=\dfrac{1}{2}(b_1+b_2)\)

\(\implies \sf 12 \cdot 2=(b_1+b_2)\)

\(\implies \sf 24=(b_1+b_2)\)

Therefore:

\(\large \boxed{\sf 24}=\sf(b_1+b_2)\)

Let:

\(\implies \sf (b_1+b_2)=24\)

\(\implies \sf x+x+6=24\)

\(\implies \sf 2x+6=24\)

\(\implies \sf 2x=18\)

\(\implies \sf x=9\)

\(\sf If\:b_1=9\:in,\:then\:b_2=9+6=15\:in\)

Therefore,

Answer:

On a number line, the solution x = -10 would be located to the left of the origin (0) by a distance of 10 units. So, you would mark the point representing -10 on the number line to the left of 0.

The inequality is 30 + 7.5v ≤ 135

The number of visits Emma could make to earn her first free movie ticket is 14

From the question, we are to write and solve an inequality which can be used to determine the number of visits Emma can make to earn her first fee movie ticket

From the given information,

"She receives 30 rewards points just for signing up"

and

"She earns 7.5 points for each visit to the movie theater"

If she visits the movie theater v number of times,

Then,

She would earn

30 + 7.5v points

Also,

She needs at least 135 points for a free movie ticket.

Thus,

The inequality that could be used to determine the number of visits, v, to earn a free movies ticket is

30 + 7.5v ≤ 135

Solving the inequality

30 + 7.5v ≤ 135

Subtract 30 from both sides

30 - 30 + 7.5v ≤ 135 - 30

7.5v ≤ 105

v ≤ 105/7.5

v ≤ 14

Hence, the number of visits Emma could make to earn her first free movie ticket is 14

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Answer:

what is this??

Step-by-step explanation:

The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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Answer:

43

Step-by-step explanation:

Answer:

Factoring the expression \(76d-24\) using the GCF we get \(\mathbf{4(19d-6)}\)

Step-by-step explanation:

We need to factor the expression using the GCF : \(76d-24\)

GCF stands for greatest common divisor.

We need to find the greatest number that is divisible by both terms.

The greatest number that is divisible by both terms is 4

So, Now factoring the term:

\(76d-24\\=4(19d-6)\)

So, factoring the expression \(76d-24\) using the GCF we get \(\mathbf{4(19d-6)}\)

Answer:

Let's call the number of magazines charged at £1.90 each "x".

So, the number of magazines charged at £1.70 each is "t=70-x".

The total cost of the x magazines is x * £1.90, and the total cost of the t magazines is t * £1.70.

The total bill for all 70 magazines is £124, so we can write an equation:

x * £1.90 + t * £1.70 = £124

x * £1.90 + (70-x) * £1.70 = £124

Expanding the equation, we get:

x * £1.90 + 70 * £1.70 - x * £1.70 = £124

x * £1.90 - x * £1.70 = £124 - 70 * £1.70

x * (£1.90 - £1.70) = £124 - 70 * £1.70

x * £0.20 = £124 - 70 * £1.70

x = (£124 - 70 * £1.70) / £0.20

Now that we have an expression for x, we can use a calculator to solve for it.

x = (124 - (70 * 1.70)) / 0.20 = 40.

So, 40 magazines were charged at £1.90 each and 70 - 40 = 30 magazines were charged at £1.70 each.

The inequality that represents p, the number of people the theater can seat is p ≤ 25

From the question, we have the following parameters that can be used in our computation:

A movie theater can seat a maximum of 25 people

This means that

Maximum =  25 people

In other words, the movie theatre can allow 25 or less people to attend a movie

In inequality, 25 or less means less than or equal to 25

When represented as an inequality expression, we have

≤ 25

Using the variable p, we have

p ≤ 25

Hence, the inequality is p ≤ 25

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Hope it's helpful!!

Answer:

An Irrational number is a number that cannot be expressed as the ratio of two integers.

Example: \(\pi\)

its numbers are infinite

Answer:

ok 11.5

Step-by-step explanation:

ok

Answer:11.5

Step-by-step explanation:

9514 1404 393

Answer:

  g(x) = 1/2

Step-by-step explanation:

You want to evaluate ...

  \(g(x)=\log_b(x)=\log_b(\sqrt{b})\\\\g(x)=\log_b(b^\frac{1}{2})=\dfrac{1}{2}\log_b(b)=\dfrac{1}{2}\cdot 1\\\\\boxed{g(x)=\dfrac{1}{2}}\)

\({ \bf{ \underbrace{Given :}}}\)

Radius of the circle "\(r\)" = 9 in.

\({ \bf{ \underbrace{To\:find:}}}\)

The circumference of the circle.

\({ \bf{ \underbrace{Solution :}}}\)

\(\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in\)

Therefore, the circumference of the circle is 56.52 in.

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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Answer:

Step-by-step explanation:

3

Answer:

Associative Property of Addition

Step-by-step explanation:

Associative Property of Addition - if the grouping changes, the answer will be the same - Correct (2 + 3) + 5 = 2 + (3 + 5)

Identity Property of Addition - anything added by 0 will equal itself (5 + 0 = 0, 2.3 + 0 = 2.3, etc.)

Commutative Property of Addition - if the order changes, the answer will be the same (2 + 3 = 5 and 3 + 2 = 5 also)

Distributive Property of Addition - allows you to "distribute" a number (2(3 + 5) = 2 * 3 + 2 * 5 = 6 + 10 = 16)

The total depth of the lake is:

And we need to find how many feet are 7/8 of the depth.

To find how much is 7/8 out of 32 ft what we do is multiply 32 by 7/8:

This multiplication can also be represented as follows:

We start by solving the division:

and finally, we solve the multiplication:

-->the fish swam 28 ft.

Answer: 28 ft

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

c.

Step-by-step explanation:

Students who have chosen to attend a basketball game are more likely to like basketball.

Answer:

We know that there are total 12 marbles are not there because 48-36=12. Now, I take:

12÷48=0.25 or 25%. As a result, the percent error is 25%. Hope it helps!

Step-by-step explanation:

The percentage error is 40.9%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the estimated value is 52 and the actual value is 88.

The percent error is given

error% = (|estimated - actual|)/actual × 100 %

error% = (|52 - 88|)/88 × 100 %

error% = 40.9%

Hence, the percentage error is 40.9%.

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Answer:

56.42 minutes

Step-by-step explanation:

The initial sample= y0 = 800

After 13 minutes , amount = 320

Y= y0e-kt

320 = 800e-k(13)

320/800 = e-k13

0.4 = e-k13

In0.4 = -k13

-0.91629= -k13

0.07048= k

Y = 800e-0.07048t

Minutes when the bacterial present will be 15

15 = 800e-0.07048t

15/800= e-0.07048t

0.01875 = e-0.07048t

In 0.01875 = -0.07048t

-3.97656 = -0.07048t

-3.97656/-0.07048= t

56.42 = t

56.42 minutes

Answer:

A

Step-by-step explanation:

To answer this question, we can use the following co-function identity:

\(\sin(\theta)=\cos(90\textdegree-\theta)\)

We know that sin(21°) is 0.36. This means that:

\(0.36=\sin(21\textdegree)=\cos(90\textdegree-21\textdegree)\)

Subtract within the cosine:

\(0.36=\sin(21\textdegree)=\cos(69\textdegree)\)

We can remove our second term:

\(\cos(69\textdegree)=0.36\)

So, our answer is A.

And we're done!

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

x = 17

Step-by-step explanation:

(5x - 23) and (7x - 1) are same- side interior angles and sum to 180° , so

5x - 23 + 7x - 1 = 180

12x - 24 = 180 ( add 24 to both sides )

12x = 204 ( divide both sides by 12 )

x = 17

Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Answer:

1 m&m

Step-by-step explanation:

in order to find out how many will be left you will make the number of m&ms even causing it to have an even amount left over.