karen has 3 1/3 hours to run errands spends 1 2/3 hour at grocery store and rest at library how muh time did she spend at library

Answer:

(2, 7)

Step-by-step explanation:

(2, 7) are the coordinate which ordered pair is a solution to the following system of inequalities [tex]y \leq -x^2 + 8x \\[/tex] and [tex]y > x^2 - 3[/tex].

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

we want to find which ordered pair is a solution to the following system of inequalities.

[tex]y \leq -x^2 + 8x \\[/tex]

[tex]y > x^2 - 3[/tex]

The solution of a inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the inequality is the graph of all solutions of the system.

Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.

[tex]y \leq -x^2 + 8x \\\\y = -x^2 + 8x\\\\y > x^2 - 3\\\\[/tex]

x = 2 and y = 7

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Answer:

-3(-2) - 6

6 - 6

= 0

Answer:

0

Step-by-step explanation:

-3a-6=-3×-2-6=6-6=0

The base is 5 units and the height is 9 units.

Base:

-4 to 1

=====

1 -(-4)

5 units

Height:

-1 to 8

=====

8 -(-1)

8 + 1

9 units

[tex]~~~~y= \sec^{-1} (14x)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{1}{14x \sqrt{(14x)^2 -1}} \cdot 14\\\\\\\implies \dfrac{dy}{dx}=\dfrac{1}{x\sqrt{196x^2 -1}}\\\\\\\text{At point,}~~ (x_1,y_1) = \left(\dfrac{\sqrt2}{14}, \dfrac{\pi}4} \right), \text{slope of the tangent line,}\\\\\\m = \dfrac{dy}{dx} = \dfrac{1}{\dfrac{\sqrt 2}{14} \sqrt{196 \left(\dfrac{\sqrt 2}{14} \right)^2-1}} \\\\\\~~~~~~~~~~~=\dfrac{14}{\sqrt 2 }\\\\\\~~~~~~~~~~~=\dfrac{7\sqrt 2 \sqrt 2}{\sqrt 2}\\\\\\[/tex]

             [tex]=7\sqrt 2\\\\\\\text{Equation of tangent line,}\\\\\\~~~~~y-y_1 = m(x -x_1)\\\\\\\implies y- \dfrac{\pi}4 = 7\sqrt 2 \left(x - \dfrac{\sqrt 2}{14} \right)\\ \\\\\implies y= 7x\sqrt 2 - 1+ \dfrac{\pi}4[/tex]

Answer:

x = 3/2 or x = -5/4

Step-by-step explanation:

Solve for x over the real numbers:

8 x^2 - 2 x - 15 = 0

Using the quadratic formula, solve for x.

x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:

x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16

Simplify radicals.

sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:

x = (2 + 22)/16 or x = (2 - 22)/16

Evaluate (2 + 22)/16.

(2 + 22)/16 = 24/16 = 3/2:

x = 3/2 or x = (2 - 22)/16

Evaluate (2 - 22)/16.

(2 - 22)/16 = -20/16 = -5/4:

Answer: x = 3/2 or x = -5/4

Answer: 11

Step-by-step explanation:

Answer:

-56

Step-by-step explanation:

Formula to get determinant is::

[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]

0(0)-8(7)

0 - 56

-56

[tex]\\ \rm\Rrightarrow \left|\begin{array}{ccc}0 &8 \\ 7& 0\end{array}\right|[/tex]

[tex]\\ \rm\Rrightarrow 0-8(7)[/tex]

[tex]\\ \rm\Rrightarrow 0-56[/tex]

[tex]\\ \rm\Rrightarrow -56[/tex]

Answer:

54=x

Step-by-step explanation:

2x+2=3x-52

this is because they are opposite alternating angles so now we can re arrange the equation.

54=x

Step-by-step explanation:

The both angles are vertically opposite angle so

[tex](2x + 2) = (3x - 52)[/tex]

By moving x on left side

[tex]2x - 3x = - 52 - 2[/tex]

So

[tex] - x = - 54[/tex]

Negative sign in both side are canceled so we got

[tex]x = 54[/tex]

Answer:

660 ft³

Step-by-step explanation:

The way I'm thinking of it, we can think of it as a triangle and then extruding out from that triangle for the length.

First, the triangle:

area = base * width / 2 = 12 * 10 / 2 = 60 ft²

volume = the triangle for the length

the length is 11 feet,

so we extrude that triangle for 11 feet to get

60 ft² * 11 ft = 660 ft³

we multiply 10 ft by 12 ft by 11 ft. there are 3 instances of ft, so the corresponding exponent is therefore ³.

another way to think of the extrusion is like a rectangular prism, the formula for a rectangular prism's volume is length * width * height. we're extruding from the bottom rectangle for the whole of the height, so we multiply the area of the bottom triangle (length * width) by height.

this might be confusing so let me know if you have any questions!

Answer:

8 (none of the above)

Step-by-step explanation:

Given that,

→ x = 3

→ y = -2

Let's solve the equation,

→ 2x - y

→ 2(3) -(-2)

→ 6 + 2

→ 8 is the answer.

Answer:

2

Step-by-step explanation:

Answer:

Median

Step-by-step explanation:

In this data set, there's a huge outlier ($1,120,000) which would skew the results upwards. Using the mean to make an inference about the profits would better represent the whole data set since you'd get $150,000 which is more in line with the rest of the data point.

Answer:

1/32

Step-by-step explanation:

Basic theory: x ^ (-a) = 1 / x^ (+a)

2^(-5) = 1 / 2^(+5) = 1/ 32

Answer:

875 inches

Step-by-step explanation:

almost 73 feet!

Answer:
To find how much money Chase will get in a certain amount of years, set up the following equation:

(7440.93*0.0123)*x = y

Plug in x. "x" stands for how many years Chase keeps the money in his account while earning interest.

Keep "y" unknown, as that stands for what you are trying to solve for, which is how much interest money Chase will make.

Answer: 6 inches

Step-by-step explanation: the area of a rectangle is width times length, that is [tex]A = w.l[/tex]

In this case we have:

So to get the Lenght l we need to divide  [tex]l = \frac{A}{w}[/tex]

[tex]l = \frac{72}{12}[/tex]

[tex]l = 6[/tex]

x=1

x=2

x=3

Answer:

rea (A)  0.0682

Step-by-step explanation:

The sketch for the region enclosed by the given curves can be found in the image attached below.

From the image below;

The two curves intersect in the area of tan 9x = 2 sin 9x

Recall that:

making x the subject; then:

The subdivision of the domain is in two intervals

where;

Area (A) =

Area (A) = 0.06818

Area (A)  0.0682

Answer:

Read explanation

Step-by-step explanation:

1st city.  8.1-(-17) OR 8.1+17 which is 25.1 degrees

2nd city. 3.2+16.8 is 20

3rd city. 33.1-3.9 is 29.2

4th city. -6+29 is 23 degrees

Answer:

• no

• no

• no

• yes

Step-by-step explanation:

Let's start by solving the inequality.

-8 +5w >32

5w> 32 +8

5w> 40

Divide both sides by 5:

w> 8

This means that the value of w should be greater than 8.

Since w is not ≥8, the value of w does not include 8. -6 and -5 are smaller than 8 and are thus not the value of w either.

9, being greater than 8, is a solution to the inequality.

Answer:

23x-y=13

Step-by-step explanation:

we need to find the derivative with respect to x

In(y) =In(10^x)

In(y)=xIn(10)

now we have to take the derivative with respect to x

Therefore, y'=yIn(10)

where y'=10^xIn(10), Chain rule!

note: First derivative function always give us the gradient value when x value is substituted in

Therefore, at x=1, our gradient will be m= 10^1In(10)

Gradient m=23.0 to the nearest tenth

Finding the equation of the line

y-y1=m(x-x1)

y-10=23(x-1)

y-10=23x-23

y-23x=-23+10

y - 23x = -13

so, the equation of the line tangent line is

23x - y =13

The question is an illustration of ratio, each person will get 1.67 pounds of ground beef

The given parameters are:

Ground beef = 5 pounds

People = 3 i.e. Fred, Janice and Ralph

The amount gotten by each person is:

Share = 5 pounds/3

Evaluate the quotient

Share = 1.67 pounds

Hence, each person will get 1.67 pounds of ground beef

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Answer:

[tex]\fbox{625 \: dollars }[/tex]

Step-by-step explanation:

Given:

from circular graph,

Savings by Oliver's = 25% of Total budget

Monthly budget = $ 2500

To find:

How much money does Oliver save?

Solution:

From diagram we came to know that,

Oliver's saving is 25% of total monthly budget.

Hence the money he saves each month will be 25% of $2500(Monthly budget)

To calculate the X percent of any given real number multiply the number with X and divide it by 100.

[tex] \sf \hookrightarrow \: 25  \% \: of \: 2500 \\ \sf \hookrightarrow 2500 \times \frac{25}{100} \\ \sf \hookrightarrow 2500 \times \cancel\frac{25}{100}_4 \\ \sf \hookrightarrow \: \frac{2500}{4} \\ \sf \hookrightarrow \cancel{\frac{2500}{4}} \: ^{625} \\ \sf \hookrightarrow \fbox{625 \: dollars }[/tex]

625$ does Oliver saves each month.

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Answer:

Yes, since log(2) and log(5) both exist as valid values for the logarithm.

didnt check if ur equation is correct though

Domain: All possible x-values

Starting at the left side, the smallest value of the domain is -12. There is a break at x = -6, but there is still a closed circle, which means that there IS a value for -6. The same occurs at x = 6. The largest x-value of this graph is 10.

Therefore, the domain is -12 <= x <= 10

Hope this helps!

Answer:

addition !

Step-by-step explanation:

Answer: subtraction is the reverse operation of Addition

Step-by-step explanation: Hope this helps,

Answer:

B)   A = (-1, 0),  B = (1, 0)

Step-by-step explanation:

If the transformation of AB to A'B' is (x+4, y-3),

then the transformation of A'B to AB is the reverse: (x-4, y+3)

Given

A' = (3, -3)  →  A = (3-4, -3+3) = (-1, 0)

B' = (5, -3)  →  B = (5-4, -3+3) = (1, 0)

Therefore:

A = (-1, 0),  B = (1, 0)

Answer:

Correct option is B)

252=

2×2

​

×

3×3

​

×7

The prime factor 7 does not appear in pairs. To make 252 a perfect square we need one more 7.

Hence, the smallest number  by which 252 must be multiplied so that

the product is a perfect square is 7.

And, 252×7=

2×2

​

×

3×3

​

×

7×7

​

252×7

​

=

2×2

​

×

3×3

​

×

7×7

​

​

=2×3×7=42

Step-by-step explanation:

To find the smallest whole number by which 2268 should be multiplied to get a perfect square, we need to factorize 2268 into its prime factors. Then, we can determine which prime factors are needed to make the number a perfect square.

The prime factorization of 2268 is:

2268 = 2^2 * 3^2 * 7 * 9

To make it a perfect square, we need to include the missing factors. In this case, we are missing a factor of 2 and a factor of 3. Therefore, we need to multiply 2268 by 2 * 3 = 6.

2268 * 6 = 13608

Now, we have a perfect square number, 13608.

To find the square root of 13608, we can take the square root of each of its prime factors:

√(2^2 * 3^2 * 7 * 9)

= √2^2 * √3^2 * √7 * √9

= 2 * 3 * √7 * 3

= 6 * √7

So, the square root of the square number 13608 is 6√7.

Answer:

10 and 19

Step-by-step explanation: