carl is 7 years older than angela. the sum of five times carl's age and four times angela's age is 197. how old is each now

Answer:

[tex]9^{\frac{1}{8}x }[/tex]

Step-by-step explanation:

The function in the question

[tex]\sqrt[4]{9} ^{\frac{1}{2}x }[/tex]

is equivalent to

[tex]9^{(\frac{1}{4})(\frac{1}{2} x) }[/tex]

where you multiply the powers and get the final answer

[tex]9^{\frac{1}{8}x }[/tex]

Answer:

(i) Attached below.  You can copy what I drew

(ii) (a) 35, (b) 60, (c) 5

Step-by-step explanation:

(a) Thus, 35 students study French only.

(c) Thus, 5 students' study neither Arabic nor French

the number of students who study French only + the number of students who study both French and Arabic + the number of students who study Arabic only + the number of students who study neither Arabic nor French equals 75:

35 + 10 + 25 + 5 = 75

45 + 30 = 75

75 = 75

Thus, our numbers are correct.

(b) Also, the number of students who study only subject is 60, as 35 (number of students studying French only) + 25 (number of students studying Arabic only) = 60

For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.

We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).

First, we need to find the value of cosA and sinB:

Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:

cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61

Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:

hypotenuse = √(4² + 3²) = 5

sinB = opposite/hypotenuse = 4/5

Now we can substitute these values into the formula:

cos(A-B) = cosA cosB + sinA sinB

= (60/61)(3/5) + (11/61)(4/5)

= 180/305 + 44/305

= 224/305

To learn more about angles click on,

https://brainly.com/question/22879396

#SPJ1

Answer:

  x ≥ 5

Step-by-step explanation:

You want the domain of the equation y = √(x -5) -1.

The domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...

  x -5 ≥ 0

  x ≥ 5 . . . . . . the domain of this function

__

Additional comment

The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.

<95141404393>

k bro i gochu

the answer is 84 man,

do good on ur hw

also can i get a pizza

Answer:

B.   {1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

Step-by-step explanation:

The intersection of two sets is a set containing the elements that are present in both sets.

{1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}

The domain and the range of the graph seen in the figure are X = {- 5, - 4, - 1, 3} (or x ∈ [- 5, 3]) and Y = {- 2, 0, 2, 4} (or y ∈ [- 2, 4]).

Herein we find a graph generated by four points of the form (x, y) set on Cartesian plane. The domain of the graph consists in the set of all x-coordinates of the graph, whereas range is for the set of all y-coordinates.

Domain

X = {- 5, - 4, - 1, 3}

(Interval notation)

x ∈ [- 5, 3]

Range

Y = {- 2, 0, 2, 4}

(Interval notation)

y ∈ [- 2, 4]

To learn more on domain and range: https://brainly.com/question/32300586

#SPJ1

The size of angle  can be expressed as 130 degrees

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.

Considering the given figure, if we look at the right top triangle  we can deduced that it is an isosceles, then the supplementary angle of angle α  can be calculated as

(180 - 80)/2

= 50 degrees.

Hence,  α = 180 - 50

= 130 degrees.

Learn more about angle at:

https://brainly.com/question/25716982

#SPJ1

The fraction represented by the point between 1 and 2 on the number line is 5/3.

If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.

The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.

Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.

                              2

Thus, the point A corresponds to the mixed fraction 1 -

                                                                                     3

 2                             5

1 -  = (1*3)+2 / 3 =  -

 3                             3

So, the fraction represented by the point between 1 and 2 on the number line is 5/3.

for similar questions on fraction.

https://brainly.com/question/78672

#SPJ8

Answer:

  (e)  $13,480

Step-by-step explanation:

You want the estimated profit from selling 60 computers, if the profit from selling x computers is P = 4x² -15x -20.

Put 60 where x is in the profit equation and do the arithmetic.

The result is an estimated profit of $13,480.

__

Additional comment

To simplify evaluation, the polynomial can be written in "Horner form:"

  P = (4x -15)x -20

Evaluating it this way takes fewer math operations and generally involves smaller numbers.

<95141404393>

Answer:

Love helping people so here's the answer :)

Step-by-step explanation:

A square pyramid has 5 faces: 1 square base and 4 triangular faces. The surface area of the pyramid is the sum of the areas of all its faces.

The area of the square base is 1 * 1 = 1 square inch.

The area of each triangular face is (1/2) * base * height = (1/2) * 1 * 2 = 1 square inch.

Since there are 4 triangular faces, the total area of the triangular faces is 4 * 1 = 4 square inches.

Therefore, the surface area of the pyramid is 1 + 4 = 5 square inches.

Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

Approximately 5048 sports cars will have less than 150,000 miles on the odometer

Mean = 120,000

Standard deviation = 30,000

Total group = 6000

Total Miles = 150,0000

An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.

Calculating the Z score -

z = x - u/a

= 15,0000 - 12,0000/30000

= 30000/30000

= 1

Using the standard normal table, to determine the value -

P ( Z<1) = 0.8413

Calculating the total number of cars -

= P value x total group of cars

= 6000 x 0.8413

= 5047.7 or 5048

Read more about odometer on:

https://brainly.com/question/12819435

#SPJ1

Cos = 20/27 = 0.7407

so

angle that stream makes with the road = 42.2

answer

42 (Round only your final answer to the nearest degree)

Answer:

The third option

Step-by-step explanation:

Answer:

2x and 180 - 5x are complementary angles.

2x + 180 - 5x = 90

-3x + 180 = 90

-3x = -90

x = 30

Answer:

The distance between Garland and Mansfield on the map is 15 inches.

Step-by-step explanation:

On Giana's map of Texas, the scale is 1 inch = 3.5 miles. To determine the distance between Garland and Mansfield on the map, we can use the scale to find the corresponding measurement. Given that the actual distance between these two cities is 52.5 miles, we can set up a proportion:

1 inch / 3.5 miles = x inches / 52.5 miles

Cross-multiplying, we have:

3.5 miles * x inches = 1 inch * 52.5 miles

3.5x = 52.5

Dividing both sides by 3.5, we find:

x = 15

Therefore, the distance between Garland and Mansfield on the map is 15 inches.

For more questions on distance

https://brainly.com/question/28342342

#SPJ11

Answer:

36

Step-by-step explanation:

48/8 = 6. 6*6 = 36.

144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.

145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.

For question 144.)

Two triangles are congruent means that the angles are equal to each other. That is;

2.3x +25 = 5.8x + 11

Bring like terms together;

5.8x-2.3x = 25-11

3.5x = 14

X = 14/3.5

= 4.

For question 145.)

When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.

The two given angles are congruent;

That is;

13x -15 = 22x + 9

Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9

Learn more about congruent angles here:

https://brainly.com/question/30449822

#SPJ1

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

The contrapositive of the original conditional statement is B. If a number does not have a negative cube root, then the number is not negative.

In logic, the contrapositive of a conditional statement is a logically equivalent statement that switches the positions of the hypothesis and the conclusion, while also negating both.

The contrapositive maintains the logical validity of the original statement. If the original statement is true, then the contrapositive is also true, and vice versa.  "If a number is negative, then it has a negative cube root." The contrapositive of this statement would be: "If a number does not have a negative cube root, then the number is not negative."

Find out more on contrapositive at https://brainly.com/question/1542283

#SPJ1

The required sample size for the confidence interval and given margin of error is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

[tex]\pi = 0.5[/tex]

Then the sample size for M = 0.04 is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]

n = 1037.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

The values of x that satisfy the equation are x = (-4 + 2√6) / 5 and x = (-4 - 2√6) / 5

The values of x that satisfy the equation 5x² + 4x - 4 = 0 can be determined using the quadratic formula given below:

x = (-b ± √(b² - 4ac)) / (2a)

From the equation:

a = 5, b = 4, and c = -4.

Substituting these values into the quadratic formula:

x = (-(4) ± √((4)² - 4(5)(-4))) / (2(5))

Simplifying to solve for values of x

x = (-4 ± √(16 + 80)) / 10

x = (-4 ± √96) / 10

x = (-4 ± 4√6) / 10

x = (-4 ± 2√6) / 5

Hence, x = (-4 + 2√6) / 5 or x = (-4 - 2√6)

Learn more about quadratic equations at: https://brainly.com/question/1214333

#SPJ1

The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.

Let j represent Jayda's age.

Since Jayda is older than her 12-year-old sister, we can write the inequality:

j > 12

Thus, the inequality states that Jayda's age (j) is greater than 12.

Learn more about Inequality here:

https://brainly.com/question/20383699

#SPJ1

Answer:

3/8 = (3 + AD)/20

8(3 + AD) = 60

24 + 8AD = 60

8AD = 36

A = 4 1/2

B is the correct answer.

16800 cubic inches of concrete is needed to make the stairs

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

The given stairs can be divided into 3 rectangular prisms as shown in the image attached.

Volume of a concrete needed = Volume of A + Volume of B + Volume of C

Volume of a rectangular prism = l × w × h

where l is the length, w is the width and h is the height

For A:

l = 40, w = 10 in and h = 7 + 7 + 7 = 21 in  

For B:

l = 40, w = 10 in and h = 7 + 7 = 14 in

For C:

l = 40, w = 10 in and h = 7 in

Volume of a concrete needed = (40 * 10 * 21) * (40 * 10 * 14) + (40 * 10 * 7)

Volume of a concrete needed = 8400 + 5600 + 2800

Volume of a concrete needed = 16800 in³

Learn more about Rectangular Prisms on:

brainly.com/question/21308574

#SPJ1

The distance of the perpendicular from Q to line PR is D = 2.2135 units

Given data ,

Let the triangle be represented as ΔPQR

Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)

And , the equation of line of PR is given by

Slope m = ( 15 - 3 ) / ( 5 - 1 )

m = 3

y - 3 = 3 ( x - 1 )

Adding 3 on both sides , we get

y = 3x

y - 3x = 0

And , the point is Q(5, 4)

Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²

D = | 5 - 12 | / √10

D = 7/√10

D = 2.2135 units

Hence , the distance is 2.2135 units

To learn more about distance of point to line click :

https://brainly.com/question/21096072

#SPJ1

Answer: 2x2 + 1000 x 1000 = 1000004

Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also

Answer:

1000004

Step-by-step explanation:

First we do can separate it into the parentheses: (2*2) + (1000*1000)

= 4 + 1000000

= 1000004

The volume of the storage nook is 24 cubic feet.

To find the area of 8 puzzles, we multiply the area of one puzzle by 8:

Area of 8 puzzles = 1 square foot * 8 = 8 square feet

Now, to find the volume of the storage nook, we multiply the area of the floor by its height:

Volume of the nook = Area of the floor * Height

= 8 square feet * 3 feet

= 24 cubic feet

Hence, the volume of the storage nook is 24 cubic feet.

Learn more about volume at https://brainly.com/question/27710307

#SPJ1