37. Two numbers are such that their
difference, their sum and their
product are in the ratio 1:7: 24.
Find the product of the
number.

9514 1404 393

Answer:

  66.5 cm²

Step-by-step explanation:

A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...

  A = LW + 1/2(b1 +b2)h

  A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²

  A = 66.5 cm² . . . . area of the figure

Answer:

3x

Step-by-step explanation:

Answer:

Huh? is it triangle? and right triangle? if it is its 62^2 = 12^2 + x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution of the problem has been solved on paper and attached in the attachment section. Kindly refer to that and feel free to ask any doubt.

Answer:

#########

Step-by-step explanation:

Answer:

Problem 7) C

Problem 8) B

Step-by-step explanation:

Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

Problem 7)

We are given that y = 39 when x = 1/3. Thus:

[tex]\displaystyle 39=\frac{k}{{}^{1}\!/ \!{}_{3}}[/tex]

Solve for k:

[tex]\displaystyle k=\frac{1}{3}(39)=13[/tex]

Hence, our equation is:

[tex]\displaystyle y=\frac{13}{x}[/tex]

Then when x = 26, y equals:

[tex]\displaystyle y=\frac{13}{(26)}=\frac{1}{2}[/tex]

Problem 8)

We are given that y = 25 when x = -1/5. Thus:

[tex]\displaystyle 25=\frac{k}{-{}^{1}\!/ \!{}_{5}}[/tex]

Solve for k:

[tex]\displaystyle k=-\frac{1}{5}(25)=-5[/tex]

Hence, our equation is:

[tex]\displaystyle y=-\frac{5}{x}[/tex]

Step-by-step explanation:

If

[tex]V=\dfrac{4\pi}{3}r^3[/tex]

then we can solve for r as

[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]

If the volume of the sphere is 150 ft^3, then the radius is

[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]

The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.

Given that

the volume of a sphere = 150 cubic feet.

the radius of the sphere=????

a round solid figure, or its surface, with every point on its surface equidistant from its center.

as we know,

the volume of a sphere

[tex]V=\frac{4}{3} *\pi *r^3[/tex]

[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]

therefore, the radius of the given sphere is 2.29feet

to get more about sphere refer to the link,

https://brainly.com/question/22807400

The cordent plan of the answer is 2

Answer:

The scale factor will just be 2

Step-by-step explanation:

The length of PQ is twice as larger than the length of AB.

so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12

Answer:

It has a side that is 9 units long.

Step-by-step explanation:

Answer:

B) It has a side that is 9 units long.

Step-by-step explanation:

Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.

Answer:

17

Step-by-step explanation:

Substitute.

f(x)=3(5)+2

    =15+2

    =17

I hope this helps!

Step-by-step explanation:

if the equation if f(x) = 3x + 2, then f(5) would be equal to 3*5 + 2 = 17. 

f(0) = 56

f(2) = 42

f(-2) = 70

f(x+1) = 7|x-7|

f(x²+2) = 7|x²-6|

Answered by GAUTHMATH

Answer:

8.2 miles per minute

Step-by-step explanation:

Given

See attachment for graph

Required

The rate of Tyler's graph

This means that we calculate the slope (m) of the graph using:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

So, we have:

[tex](x_1 ,y_1) = (0,0)[/tex]

[tex](x_1 ,y_1) = (1,8.2)[/tex]

So, we have:

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]

[tex]m = \frac{-8.2}{- 1}[/tex]

[tex]m = 8.2}[/tex]

Answer:

-1

Step-by-step explanation:

1-2=-1

y=mx+b

b= y intercept

Answer:

-1

Step-by-step explanation:

Answer:

They are supplementary and their sum is 180°

w = 45 + 60 or w = 105

z = 180 - 105 or z = 75

total area =A1+A2+A3

A1=1/2b*h

A1=1/2*8mm*6mm

A1=24mmsquare

A2=1/2b*h

A2=1/2*8mm*6mm

A2=24mmsquare

A3=b*h

A3=8mm*6mm

A3=48mmsquare

Atotal=24mmsquare+24mmsquare+48mmsquare

Atotal=96mmsquare

Answer:

change inches into centimeter and then divide it

hope this help

Answer:

See Explanation

Step-by-step explanation:

Required

Proportion problems

An example is:

y is directly proportional to x such that: y=4 when x = 2;

Derive the equation

For direct proportions, we have:

[tex]y\ \alpha\ x[/tex]

This gives:

[tex]y = kx[/tex]

Make k the subject

[tex]k = y/x[/tex]

So:

[tex]k = 4/2 =2[/tex]

So, the equation is:

[tex]y = kx[/tex]

[tex]y = 2x[/tex]

Assume the above question is for inverse proportion

The variation will be:

[tex]y\ \alpha\ \frac{1}{x}[/tex]

This gives:

[tex]y\ = \frac{k}{x}[/tex]

Make k the subject

[tex]k =x*y[/tex]

[tex]k =2* 4 = 8[/tex]

So, the equation is:

[tex]y\ = \frac{k}{x}[/tex]

[tex]y = \frac{8}{x}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]y=(x-7)^2-1[/tex]

Step-by-step explanation:

We want to convert the equation:

[tex]\displaystyle y=x^2-14x+48[/tex]

Into vertex form, given by:

[tex]\displaystyle y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.

Method 1) Vertex Formulas

Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.

Recall that the vertex is given by:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:

[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]

To find the y-coordinate, substitute this value back into the equation. Hence:

[tex]y=(7)^2-14(7)+48=-1[/tex]

Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.

And since we already determined a = 1, our equation in vertex form is:

[tex]\displaystyle y=(x-7)^2-1[/tex]

Method 2) Completing the Square

We can also complete the square to acquire the vertex form. We have:

[tex]y=x^2-14x+48[/tex]

Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:

[tex]y=(x^2-14x)+48[/tex]

Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.

We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:

[tex]y=(x^2-14x+49)+48-49[/tex]

Factor using the perfect square trinomial and simplify:

[tex]y=(x-7)^2-1[/tex]

We acquire the same solution as before, with the vertex being (7, -1).

Answer:

Between 50 and 60

Step-by-step explanation:

4,346/82 is 53 which is between 50 and 60.

Hope this helps!

Answer:

Option D

Step-by-step explanation:

In the given triangles ΔABC and ΔDEF,

∠A ≅ ∠D

AB ≅ DE

By SAS property of congruence of two triangles,

Two sides and the included angle of one triangles should be congruent to corresponding two sides and the included angle of the other triangle.

Therefore, AC ≅ FD will be the desired property to prove the given triangles congruent.

Option D will be the correct option.

Answer:

Step-by-step explanation:

Answer:

y 9 5 473648

Step-by-step explanation:

Answer:

[tex]10x^{5}y \sqrt{6xy}[/tex]

Step-by-step explanation:

Answer:

The numerical values of the circumference and area of the circle are equal.

Answer:

a

Step-by-step explanation:

square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8

Answer:

Step-by-step explanation:

On the graph of two inequalities, solution of two inequalities is defined by the common shaded area.

That means all the points which lie in this area will satisfy both the inequalities.

From the graph attached,

Points given in the options (0, 0), (0, -1) and (1, 1) are not lying in the solution area.

Since, ordered pair given in 4th option is not clear in the picture, Option (4) may be the answer.

Answer:

Determine the conditional probability distribution of X given that Y = 1 and Z = 2. Round your answers to two decimal places (e.g. 98.76).

answer:

Given that Y = 1 :  2/5

Given that Z = 2 : 3/5

Step-by-step explanation:

The conditional probability distribution of X     F x | yz^( x )

Given that Y = 1

F x | yz . ( x | yz )  = 2/5

Given that z = 2

= 3/5

attached below is the detailed solution

[tex]\bar{x} = 0[/tex]

[tex]\bar{y} =\dfrac{136}{125}[/tex]

Step-by-step explanation:

Let's define our functions [tex]f(x)\:\text{and}\:g(x)[/tex] as follows:

[tex]f(x) = x^2 + 1[/tex]

[tex]g(x) = 6x^2[/tex]

The two functions intersect when [tex]f(x)=g(x)[/tex] and that occurs at [tex]x = \pm\frac{1}{5}[/tex] so they're going to be the limits of integration. To solve for the coordinates of the centroid [tex]\bar{x}\:\text{and}\:\bar{y}[/tex], we need to solve for the area A first:

[tex]\displaystyle A = \int_a^b [f(x) - g(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}[(x^2 + 1) - 6x^2]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\int_{-\frac{1}{5}}^{+\frac{1}{5}}(1 - 5x^2)dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\left(x - \frac{5}{3}x^3 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:= \dfrac{28}{75}[/tex]

The x-coordinate of the centroid [tex]\bar{x}[/tex] is given by

[tex]\displaystyle \bar{x} = \dfrac{1}{A}\int_a^b x[f(x) - g(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:= \frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} (x - 5x^3)dx[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{75}{28}\left(\dfrac{1}{2}x^2 -\dfrac{5}{4}x^4 \right)_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:= 0[/tex]

The y-coordinate of the centroid [tex]\bar{y}[/tex] is given by

[tex]\displaystyle \bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}[f^2(x) - g^2(x)]dx[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:=\frac{75}{28}\int_{-\frac{1}{5}}^{+\frac{1}{5}} \frac{1}{2}(-35x^4 + 2x^2 + 1)dx[/tex]

[tex]\:\:\:\:\:\:\:=\frac{75}{56} \left[-7x^5 + \frac{2}{3}x^3 + x \right]_{-\frac{1}{5}}^{+\frac{1}{5}}[/tex]

[tex]\:\:\:\:\:\:\:=\dfrac{136}{125}[/tex]

Step-by-step explanation:

a the rate of changes = (185-146)/30

= 1.3° /minutes.

after 45 minutes = 1.3 ×45 = 58.5°

so, the temperature = 185 - 58.5

= 126.50°F

b. the time to reach 100°F =

(185-100)/ (1.3)

= 85/(1.3) = 65.38

after 65.38 minutes

Answer:

Two sample t test

Step-by-step explanation:

The two sample t test can be used in the scenario described above, where two independent samples are obtained, we take a certain sample of children with autism and then another sample of children without autism. The number of children chosen for each sample should be random and could be of equal or unequal sizes. The mean and standard deviation of each of sample A and B are deternined and used to perform the analysis to determine if the mean of each sample are equal or not. This test is also called the WELCH T TEST

Answer:

The statements are logically equivalent.

The 6th column is:

F T F F

The 7th column is:

F T F F

Step-by-step explanation:

The 6th column is just the opposite of the 5th column

The 7th column is T only if both the 1st and 4th are T