Question 1 (1 point)
Find the missing side of the right triangle. ROUND TO THE NEAREST TENTH (one decimal place). Of 88 and 81

Answer:

A product of a number and 12 is increased by 23

Answer:

(10 *sin(81))/sin(34)=17.66>>>17.7

Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=3, b=-7

How to write the equation in slope-intercept form?

Given:

m=3(slope)

b=-7(y -intercept)

The slope-intercept form is given by,

y=mx+b

y=3x-7

Thus, y=3x-7 is the slope-intercept form.

How to rewrite the equation in standard form?

Standard form is given by,

Ax+By=C

Since, slope-intercept form is y=3x-7

⇒3x-y=7

Thus,3x-y = 7  is the standard form.

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Answer:

Step-by-step explanation: 10=-9-x > add 9 to 10 > 19=-x> divide 19 by -x> x=-19

Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.

A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Given data

The fractions can be represented as follows;

x < ½   and y < ½

The sum of both of the inequalities is;

x + y < ([tex]\frac{1}{4}[/tex]) + ([tex]\frac{1}{4}[/tex])

x + y < ½

Examples are-

[tex]\frac{1}{5}[/tex]+ [tex]\frac{2}{3}[/tex] =[tex]\frac{13}{15}[/tex]

¼ + ½ = ¾

[tex]\frac{1}{2}[/tex] +[tex]\frac{1}{3}[/tex] = [tex]\frac{5}{6}[/tex]

Therefore, Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.

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Answer:

x-int: (-12/9, 0)

y-int: (0, 6)

Step-by-step explanation:

x-int ==> on x-axis when y=0

y-int ==> on y-axis when x=0

9/4x -1/2y = -3

x-int: 9/4x -1/2(0) = -3

9/4x = -3

9x/4 = -3

9x*4/4=-3*4

9x=-12

x=-12/9 ==> x-int: (-12/9, 0)

y-int: 9/4(0) -1/2y = -3

-1/2y = -3

1/2y=3

y/2=3

y=6 ==> y-int: (0, 6)

The possible dimensions ( width and length) plot of land are 9.5 m and 19 m.

A rectangle is a confined two-dimensional structure with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal as well as parallel.

Area of a rectangle

area of rectangle = l×w

where, l = length and w = width.

Thus, the perimeter for 2 side of width and 1 side of length is;

perimeter = 2w+ l

Perimeter of river = 38 m.

38 = 2w + l

l = 38  - 2w

Hence, Put the value of l in the area.

area = w(38 - 2w)

The area of the land is 140 sq.m.

140 = 38w - 2w²

-2w² + 38w - 140 = 0

-w² + 19w - 70 = 0

The equation is in the form of quadratic. Thus use the relation of coefficients and the roots to evaluate the width.

w = - b / a

Comparing the coefficients;

where,

a = -1

b = 19

w = - 19 / 2( -1)

w = 9.5 meters

Then,

l = 38  - 2w

l = 38 - 2(9.5)

l = 19 meters

Therefore, the dimensions of the plot of land are 9.5 meters and 19 meters.

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If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

a.  0scar sits between Morgan and Phil

First step is to calculate the total distance

Total distance=2 feet+4 feet+3 feet

Total distance=9 feet

Since Morgan is 2 feet from Phil.

Hence,

P(Oscar sits between Morgan and Phil)=2/9

b. Oscar sits between Phil and Tyreese.

First step is to calculate the  distance between Phil and Tyreese

Distance= 4 feet + 3 feet

Distance =7 feet

Hence,

P(Oscar sits between Phil and Tyreese)=7/9

Therefore If Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. the probability that 0scar sits between Morgan and Phil is 2/9 and the probability that Oscar sits between Phil and Tyreese is 7/9.

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The complete question is:

Morgan, Phil, Callie, and Tyreese are sitting on the side of a pool in that order. Morgan is 2 feet from Phil. Phil is 4 feet from Callie. Callie is 3 feet from Tyreese. Oscar joins them.

a. Find the probability that 0scar sits between Morgan and Phil.

b. Find the probability that Oscar sits between Phil and Tyreese.

Answer:  x-axis

Explanation:

The point (2,3) moves to (2, -3)

The x coordinate stays the same, but the y coordinate flipped from positive to negative. Therefore, the rule used is [tex](\text{x},\text{y}) \to (\text{x}, -\text{y})[/tex] which is a reflection over the horizontal x axis.

Answer: yes it is a solution

The RHS congruency criterion showed ABD ≅ DCA.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

The diameters of a circle with an O-centered center are AOC and BOD.

To Locate:

By RHS, ABD and DCA are congruent.

Solution:

The fact that AOC and BOD are a circle's diameters is a given.

BD = CA (circle circumferences)

"BAD = CDA" [90° angles in semicircle]

AD = AD (shared by both triangles)

[Using RHS congruence criterion] ABD ≅ DCA

As a result, the RHS congruency criterion showed ABD ≅ DCA.

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Answer:

Let y = length of side parallel to the side with no fence

x = length of each of the other two sides

Then, y+2x = 64. So, y = 64-2x

Area = A = xy = x(64-2x)

The graph of the area function is a parabola opening downward with a highest point and with x-intercepts (0,0) and (32,0).

By the symmetry of the parabola, the x-coordinate of the maximum point lies halfway between the x-intercepts.

So, the area is maximized when x = 16 ft

y = 64 - 2x = 32 ft

Maximum area = xy = (16)(32) = 512 ft2

To maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.

The required value of y is 10.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx,       —-- 1

Now, find k for given x = 15 and y = 25, we need to put these values in equation 1, i.e.

25 = k(15)

k = 25 / 15

k = 5 / 3

Further calculate y for given x = 6 and constant of proportion = 5/3 i.e.

y = (6)(5 / 3)

y = 10

Hence, the required value of y is 10.

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Answer: 4 inches.

Step-by-step explanation:

Answer:

Use the formula L(x)=f(a)+f'(a)(x−a) to find the linearization.

L(x)=2

Step-by-step explanation:

Answer:

a+b= (-1)

Step-by-step explanation:

4+(-5)=

4-5= (-1)

Answer:

-1

Step-by-step explanation:

a = 4

b = -5

4 + -5 = -1 ( +- turns to -)

Answer:5/25,25, 0.3

Step-by-step explanation:

Answer:

5/25 , 25% , 0.3

Step-by-step explanation:

first let's change everything into decimals

0.3 is already a decimal

25% can be changed into 0.25

5/25 can be changed into a percentage first like 25%

so:

[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex] (you multiply both sides by 4 because you need to have the denominator as a 100 and 25 x 4 = 100)

[tex]\frac{5}{25}[/tex] × [tex]\frac{4}{4}[/tex]  = [tex]\frac{20}{100}[/tex]

this means that the percentage is 20% now lets change that into a decimal like we did with 25% earlier:

20% = 0.20

we can then order everything from least to greatest:

0.20 , 0.25 , 0.3

or

5/25 , 25% , 0.3

Answer:5

Step-by-step explanation:

Answer:

(5,15)

Step-by-step explanation:

we know that c=12 is 5 so your answer is 5,15

Answer:

Step-by-step explanation:

Point slope form:

y - y1 = m(x-x1)

y - 6 = 2(x + 2)

y - 6 = 2x + 4

y = 2x +10

In the sample that is used number of viruses were 6000 times greater than the number of protozoa.

Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population.

Given the number of protozoa in the sample as 5 × 10⁵ and the number of viruses in the sample as 3x10⁹.

This is represented in the scientific notation.

To calculate the number of times the viruses in the sample is more than the protozoa in the sample we divide the amount of virus by the amount of protozoa.

∴ (3x10⁹) ÷ (5 × 10⁵)

= 6000

Therefore in the sample that is used number of viruses were 6000 times greater than the number of protozoa.

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Answer:

f(- 2) = 14

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3(- 2)² + 2 = 3(4) + 2 = 12 + 2 = 14

Distance between the points [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex] is [tex]a[/tex]. (Option D)

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by [tex]d= \sqrt{(x^{2}-x) ^{2}+(y^{2}-y) ^{2} }[/tex]. This formula is used to find the distance between any two points on a coordinate plane or x-y plane. This formula is called distance formula.

Let A= [tex](a cos(0 +\frac{2\pi }{3} ), a sin(0+\frac{2\pi }{3}))[/tex] and B= [tex](a cos(0+\frac{\pi }{3}), a sin(0+\frac{\pi }{3}))[/tex].

Putting values in above formula:

AB=[tex]\sqrt{a^{2}[cos(0+\frac{\pi }{3})-cos(0+\frac{2\pi }{3})]^{2}+a^{2}[sin(0+\frac{\pi }{3})-sin(0+\frac{2\pi }{3})]^{2} }[/tex]

AB= [tex]a\sqrt{cos^{2}(0+\frac{\pi }{3})+sin^{2}(0+\frac{\pi }{3})+cos^{2}(0+\frac{2\pi }{3})+sin^{2}(0+\frac{2\pi }{3})}[/tex]

AB= [tex]a\sqrt{cos(0+\frac{\pi }{3})cos(0+\frac{2\pi }{3})sin(0+\frac{\pi }{3})sin(0+\frac{2\pi }{3})}[/tex]

AB=[tex]a\sqrt{1+1-2cos(0+\frac{2\pi }{3}-0-\frac{\pi }{3}) }[/tex]

AB= [tex]a\sqrt{2-2cos\frac{\pi }{3} }[/tex]

AB= [tex]a\sqrt{2-2\frac{1}{2} }[/tex]

AB= [tex]a\sqrt{2-1} =a[/tex]

Hence, the distance between the two given points is [tex]a[/tex].

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Answer:

2 laps

Step-by-step explanation:

The equation for circumference of a circle is 2πr.

We can use this equation to find how many ft are in a lap, then determine with the circumference how many laps need to be completed.

This is simple algebra

2πr

2π(50)

2(3.14)(50)

314.

One lap is 314 feet, so Sammy needs to walk 2 laps.

Answer: 2 laps

Step-by-step explanation:

Length of a circular path is 2πR (R=50ft)

Length of a circular path is:

2*3.14*50=

314 ft

628:314=

2 laps

Answer:

84 Meters^3

Step-by-step explanation:

Since this is a three dimensional object, you need to have an exponent of 3