What additional information is needed to show that triangle PQR is congruent to triangle STU by SSS

Answer:

Equation of the line is: \(x=6\)

Step-by-step explanation:

We know that , the equation of any line parallel to y axis is :

\(x=k\)    where \(k\) ia a constant

And here it is given that the line is passing through the point P(6,-3)

Therefore, it will satisfy the equation \(x=k\).

So, substitute \((6,-3)\) in equation \(x=k\), we get

\(k=6\)

Hence the equation of line will be \(x=6\)

The expression of the statement that is given above can be written as follows: 262144y³ + 27.

To determine how to express the given statement the following should be carried out.

When a number is said to be cubed, it means that the number should be times by itself three consecutive times.

That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,

= 64×64×64(y)³ + 3×3×3

= 262144y³ + 27.

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Answer:

x=5

Step-by-step explanation:

\(60+3x\leq 75\)

3x=15

x=5

movies 1.75 each

games 5.75 each

Answer: she is now 121 feet below sea level.

Step-by-step explanation:

Given, A scientist was in a submarine, 95.7 feet below sea level, studying ocean life.

Over the next ten minutes, she went down 25.3 feet.

Then, she was (95.7+25.3) feet below sea level now.  [we will add both distances ]

Then, she was 121 feet below sea level now.

Hence, she is now 121 feet below sea level.

Answer:

A

Step-by-step explanation:

The equation is V=4/3 times Pi times radius^3

Answer:

795

Step-by-step explanation:

318 x 2 (to get 12 ounces)

636 + (1/2 x318) (to get 3 ounces)

636 + 159 (to get 16 ounce)

795

The number of calories in one pound is 848 calories.

Given that, there are 318 calories in six ounces of a certain ice cream.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let x be number of calories in 1 pound = 16 ounces

Here, 318:6::x:16

⇒ 6x=318×16

⇒ 6x=5088

⇒ x=5088/6

⇒ x=848

Therefore, the number of calories in one pound is 848 calories.

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Answer:

A common factor is a whole number which is a factor of two or more numbers.

\(factors \: of \: 9 = 1 \times 3 \times 3\)

\(factors \: of \: 15 = 1 \times 3 \times 5\)

since both of the numbers have only 1 and 3 in common.

therefore ,

Option A is correct.

______________________________________

______________________________________

Additional information

★ The highest common factor (HCF) is the greatest factor that will divide into two or more numbers.

★ The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.

hope helpful :D

Answer:

3 7/12

Step-by-step explanation:

9514 1404 393

Answer:

  1173 in

Step-by-step explanation:

The measure of angle O is ...

  O = 180° -N -P = 180° -32° -97° = 51°

The law of sines tells you ...

  o/sin(O) = n/sin(N)

  o = n·sin(O)/sin(N) = (800 in)·sin(51°)/sin(32°)

  o ≈ 1173 in

The angle between the two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of the contact at the Centre are supplymentary,

So,

15.) let the unknown angle be x

=》x + 55° = 180°

=》x = 180° - 55°

=》

\( \boxed{x = 125°}\)

16. let the unknown angle be n

=》n + 80° = 180°

=》n = 180° - 80°

=》

\( \boxed{n = 100°}\)

9514 1404 393

Answer:

  15)  125°

  16  100°

Step-by-step explanation:

The short arc where two tangents intersect a circle, and the angle where the tangents meet are supplementary.

__

15) ? = 180° -55° = 125°

16) ? = 180° - 80° = 100°

_____

Additional comment

The quadrilateral formed by the tangents and the radii to the points of tangency has a total interior angle measure of 360°. The angles where the radii meet the tangents are 90°, so the sum of the external angle and the central angle is 360° -90° -90° = 180°. That is, the external angle and the central angle are supplementary.

Step-by-step explanation:

N6000×5=N30000

1)N30000-N25000=N5000

2)N5000÷N25000×100℅=20℅

Answer:

ok

Step-by-step explanation:

ok

Answer:

its 502.4 i believe

Step-by-step explanation:

Answer:

\(t=\frac{19.9-19}{\frac{4.5}{\sqrt{45}}}=1.342\)  

The degrees of freedom are given by:

\( df=n-1= 45-1=44\)

And the p value would be;

\(p_v =P(t_{44}>1.342)=0.0932\)  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 19 mph

Step-by-step explanation:

Information given

\(\bar X=19.9\) represent the sample mean

\(s=4.5\) represent the sample standard deviation

\(n=45\) sample size  

\(\mu_o =19\) represent the value to verify

\(\alpha=0.01\) represent the significance level for the hypothesis test.  

t would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to verify if the true mean is higher than 19, the system of hypothesis would be:  

Null hypothesis:\(\mu \leq 19\)  

Alternative hypothesis:\(\mu > 19\)  

The statistic would be given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)  

Replacing the info given we got:

\(t=\frac{19.9-19}{\frac{4.5}{\sqrt{45}}}=1.342\)  

The degrees of freedom are given by:

\( df=n-1= 45-1=44\)

And the p value would be;

\(p_v =P(t_{44}>1.342)=0.0932\)  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 19 mph

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer:

undefined

Step-by-step explanation:

The slope is not consistent.

6, -3, -6/5, -3/4 are not equal

Answer:

0

Step-by-step explanation:

use y2-y1/x2-x1 to find slope

-6-(-6)/8-5

0/3

0

Hopes this helps please mark brainliest

Given the coordinates of XYZ:

X(-5, -4), Y(2, -2), Z(-3, -6)

Here, triangle XYZ was rotated 270 degrees counterclockwise about the origin to get traingle X'Y'Z'.

Let's answer the following.

• Part A.

Let's determine the coordinates of triangle X'Y'Z'.

Apply the rules of roatation.

After a rotation of 270 degrees counterclockwise, the coordinates (x, y) becomes (y, -x).

Applying the rotation rule, we have the coordinates of X'Y'Z' below:

(x, y) ==> (y, -x)

X(-5, -4) ==> (-4, - -5), ==> X'(-4, 5)

Y(2, -2) ==> (-2, -2) ==> Y'(-2, -2)

Z(-3, -6) ==> (-6, - -3) ==> Z'(-6, 3)

Therefore, the coordinates of traingle X'Y'Z' are:

X'(-4, 5)

Y'(-2, -2)

Z'(-6, 3)

• Part B.

To select the general rule that describes the rotation mapping, apply the rotation rules for 270 degrees counterclockwise rotation.

We have:

(x, y) ==> (y, -x)

Therefore, the general rule that describes the rotation mapping is:

(x, y) ==> (y, -x)

ANSWER:

(a) X'(-4, 5)

Y'(-2, -2)

Z'(-6, 3)

(b) (x, y) ==> (y, -x)

all work should be in the picture, lmk if theres anything confusing

By first method, he volume of the rectangular prism is (9/32) cubic feet.

By second method, the volume of the rectangular prism is (27/64) cubic feet, which agrees with the volume calculated using the first method.

Volume is a measurement of the amount of space that an object occupies. It is the three-dimensional space occupied by an object. Volume is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, and so on.

We can determine the volume of the rectangular prism in two different ways using the formula:

Volume = Length x Width x Height

First Method:

In the first method, we simply substitute the given dimensions of the rectangular prism into the formula and calculate the volume:

Volume = (3/4) ft x (3/8) ft x (3/4) ft

Volume = (9/32) ft³

Second Method:

In the second method, we can use the fact that the rectangular prism can be divided into 4 smaller rectangular prisms, each with dimensions (3/4) ft x (3/8) ft x (3/16) ft. We can calculate the volume of one of these smaller prisms and then multiply by 4 to get the total volume:

Volume of one smaller prism = (3/4) ft x (3/8) ft x (3/16) ft

Volume of one smaller prism = (27/256) ft³

Total volume = 4 x Volume of one smaller prism

Total volume = 4 x (27/256) ft³

Total volume = (27/64) ft³

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Answer:

60 in²

Step-by-step explanation:

Area of parallelogram = base x height

= 10 in x 6 in

= 60 in²

The area of the parallelogram is 60in².

the counting number just before C5F16 is 3,072.

In the given map, the domain is the Weight.

Thus, all values in the choices that are under the table of the Weight are Domains.

Therefore, the answers (Domains) are: 110, 130, and 140.

The rest of the choices are Ranges.

Answer:

x = -4/3 and x = 5/2.

Step-by-step explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

\(\frac{-b±\sqrt{b^2 - 4ac} }{2a}\)

In this case, a = 6, b = -7, and c = -20.

\(\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}\)

= \(\frac{7±\sqrt{49 + 80 * 6} }{12}\)

= \(\frac{7±\sqrt{49 + 480} }{12}\)

= \(\frac{7±\sqrt{529} }{12}\)

= \(\frac{7±23 }{12}\)

\(\frac{7 - 23 }{12}\) = \(\frac{-16 }{12}\) = -8 / 6 = -4 / 3

\(\frac{7 + 23 }{12}\) = \(\frac{30}{12}\) = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!  

Answer:

Step-by-step explanation:

\(6 {x}^{2} - 7x = 20\)

Move constant to the left and change its sign

\( {6x}^{2} - 7x - 20 = 0\)

Write -7x as a difference

\(6 {x}^{2} + 8x - 15x - 20 = 0\)

Factor out 2x from the expression

\(2x(3x + 4) - 15x - 20 = 0\)

Factor out -5 from the expression

\(2x(3x + 4) - 5(3x + 4) = 0\)

Factor out 3x + 4 from the expression

\((3x + 4)(2x - 5) = 0\)

When the product of factors equals 0 , at least one factor is 0

\(3x + 4 = 0\)

\(2x - 5 = 0\)

Solve the equation for X1

\(3x + 4 = 0\)

Move constant to right side and change its sign

\( 3x = 0 - 4\)

Calculate the difference

\(3x = - 4\)

Divide both sides of the equation by 3

\( \frac{3x}{3} = \frac{ - 4}{3} \)

Calculate

\(x = - \frac{4}{3} \)

Again,

Solve for x2

\(2x - 5 = 0\)

Move constant to right side and change its sign

\(2x = 0 + 5\)

Calculate the sum

\(2x = 5\)

Divide both sides of the equation by 2

\( \frac{2x}{2} = \frac{5}{2} \)

Calculate

\(x = \frac{5}{2} \)

\(x1 = - \frac{4}{3} \)

\(x2 = \frac{5}{2} \)

Hope this helps...

Best regards!!

Answer:

D

Step-by-step explanation:

To reflect over the Y axis, the X values of each coordinate must be made into opposites. So a coordinate with the form (x,y) will become (-x,y) when reflected across the Y axis, which is needed here.

Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. \(\cos{\beta}\cot{\beta}\)

The cosecant of an angle is given by one divided by the sine of the angle, hence:

\(\csc{\beta} = \frac{1}{\sin{\beta}}\)

The sine and the cosine of an angle are related as follows:

\(\sin^2{\beta} + \cos^2{\beta} = 1\)

\(\cos^2{\beta} = 1 - \sin^2{\beta}\)

The cotangent of an angle is:

\(\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}\)

The expression given is:

\(\csc{\beta} - \sin{\beta}\)

Simplifying the cosecant:

\(\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}\)

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

\(\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}\)

Hence option A is correct.

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