Triangle Q S R is shown. Angle Q S R is a right angle. Altitude s is drawn from point S to point T on side Q R to form a right angle. Side Q S is labeled r and side W R is labeled q. The length of Q T is 10 and the length of R T is 4.

What is the value of q?

4 StartRoot 5 EndRoot
2 StartRoot 14 EndRoot
20 StartRoot 5 EndRoot
64 StartRoot 5 EndRoot

Answer:

[tex]65.4[/tex]

Step-by-step explanation:

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

[tex]\cos 61^{\circ}=\frac{y}{135},\\t=135\cos 61^{\circ}=65.4492987333\approx \boxed{65.4}[/tex]

9514 1404 393

Answer:

  (b)  20 1/4

Step-by-step explanation:

9(-3)^2(2^-2) = 9(9)(1/4) = 81/4 = 20 1/4

Answer:

16% of GMAT scores are 647 or higher.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

This means that [tex]\mu = 547, \sigma = 100[/tex]

What percentage of GMAT scores are 647 or higher?

The proportion is 1 subtracted by the p-value of Z when X = 647. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{647 - 547}{100}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

1 - 0.84 = 0.16

0.16*100% = 16%

16% of GMAT scores are 647 or higher.

Answer:

[tex]( - 2,1)[/tex]

Step-by-step explanation:

Hope it is helpful...

Answer:

t = 51 - 25p

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

25p + 1t = 51

Step 2: Solve for t

Answer:

17) option b

18) option b

19) option d

Step-by-step explanation:

17)

Cost of 25 burgers = $75

Therefore , cost of 1 burger:

                                          [tex]\frac{75}{25} = 3[/tex]

18)

Area of  rectangle = length x breadth

                 [tex]\frac{7}{6} = length \times \frac{5}{6}\\\\\frac{7}{6} \times \frac{6}{5} = length \\\\\frac{7}{5} = length \\\\Length = \frac{7}{5} \ km[/tex]

19)

                   14.25

                 x    6.3

             _________

                   4275

            +    8550              

             __________

                89.775

            ___________

Answer:

[tex]x \approx 2.278863[/tex]

Step-by-step explanation:

Required

The positive root of [tex]3\sin(x) = x[/tex]

Equate to 0

[tex]0 = x -3\sin(x)[/tex]

So, we have our function to be:

[tex]h(x) = x -3\sin(x)[/tex]

Differentiate the above function:

[tex]h'(x) = 1 -3\cos(x)[/tex]

Using Newton's method of approximation, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

Plot the graph of [tex]h(x) = x -3\sin(x)[/tex] to get [tex]x_1[/tex] --- see attachment for graph

From the attached graph, the first value of x is at 2.2; so:

[tex]x_1 = 2.2[/tex]

So, we have:

[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]

[tex]x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}[/tex]

[tex]x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641[/tex]

The process will be repeated until the digit in the 6th decimal place remains unchanged

[tex]x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654[/tex]

[tex]x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627[/tex]

[tex]x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627[/tex]

Hence:

[tex]x \approx 2.278863[/tex]

Answer:

Step-by-step explanation:

If x is -1, then the point on the parabol is (-1,4)

If x is 0, then the point on the parabol is (0,-2)

If x is 1, then the point on the parabol is (1,-6)

Answer:its d

Step-by-step explanation:

Answer:

y = -4x + 25

Step-by-step explanation:

[tex](x_1, y_1) = (5, 5) \ ; \ slope ,\ m = -4[/tex]

Equation of line :

 [tex](y - y_1) = m(x - x_1)[/tex]

 [tex](y - 5) = -4(x-5)\\y - 5 = -4x + 20\\y = -4x +20 + 5\\y = -4x + 25[/tex]

Answer:

0=4x+y-5

Step-by-step explanation:

slope(m)=-4

y-intercept(c)=5

now, the equation joining the straight line satisfy the equation,

y=mx+c

or, y= -4x+5

or, 4x+y-5=0

or, 0=4x+y-5

it is the required equation.

Answer:

[tex]{ \tt{(x + 3)(x - 1)}} \\ = { \tt{ {x}^{2} - x + 3x - 3 }} \\ = { \tt{ {x}^{2} + 2x - 3 }} \\ \\ { \boxed{ \bf{coefficient = 2}}}[/tex]

Answer:

eeeeeee

Step-by-step explanation:

xdddddddudjdjdjdjdjdjsjsjsjsjsjsjsjjsjsjsjsjsjsjsjsjsjsjjs

Answer:

[tex]\boxed {\boxed {\sf B. \ 324 \ cm^3}}[/tex]

Step-by-step explanation:

The volume of a triangular prism is the product of the area of the triangular cross-section (B) and the height (h).

First, let's find the area of the triangular cross-section/the end of the triangle. The area of a triangle is:

[tex]B= \frac{1}{2} b*h[/tex]

The base of the triangle base (not the prism) is 6 centimeters and the height is 9 centimeters.

[tex]B= \frac{1}{2} (6 \ cm)(9 \ cm)[/tex]

Multiply the numbers in parentheses.

[tex]B= \frac{1}{2}(54 \ cm^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]B= 27 \ cm^2[/tex]

Now we know the area of the cross-section or base is 27 square inches. The height of the prism is 12 centimeters.

Substitute the values into the volume formula for a triangular prism.

[tex]V= 27 \ cm^2 * 12 \ cm[/tex]

Multiply.

[tex]V= 324 \ cm^3[/tex]

The volume of the prism is 324 cubic centimeters and choice B is correct.

The volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

The volume of a triangular prism is determined by multiplying the area of the triangular cross-section (B) by the height (h). In this case, the base (b) of the triangular cross-section is given as 6 centimeters, and the height (h) is given as 9 centimeters.

To find the area of the triangular cross-section (B), we can use the formula for the area of a triangle: B = (1/2) * base * height.

Substituting the values:

B = (1/2) * 6 * 9 = 27 square centimeters.

Next, we multiply the area of the cross-section (B) by the height (h) to find the volume (V) of the prism:

V = B * h = 27 * 12 = 324 cubic centimeters.

Therefore, the volume of the triangular prism is 324 cubic centimeters, and choice B is correct.

To know more about triangular prism:

https://brainly.com/question/27102803

#SPJ6

Answer: 28

Step-by-step explanation:

The multiples of 7 that's less than 30 include: 7, 14 , 21 and 28.

From the numbers above,

7 isn't divisible by 4 as it gives a remainder.

14 isn't divisible by 4 as it gives a remainder.

21 isn't divisible by 4 as it gives a remainder.

28 is divisible by 4 without a remainder

Therefore, the correct answer should be 28

Answer:

At this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:

Current amount - (amount lost per year x number of years) = 237.6

586.08 - (7.92 x X) = 237.6

586.08 - 7.92X = 237.6

-7.92X = 237.6 - 586.08

-7.92X = -348.48

X = -348.48 / -7.92

X = 44

Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.

Answer:

A: -21

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic function:

[tex]g(x) = x^2 - 6x - 12[/tex]

So [tex]a = 1, b = -6, c = -12[/tex].

Minimum value:

This is the y-value of the vertex. So

[tex]\Delta = b^2-4ac = (-6)^2 - 4(1)(-12) = 36+48 = 84[/tex]

[tex]y_{v} = -\frac{\Delta}{4a} = -\frac{84}{4} = -21[/tex]

The minimum value is -21, and the correct answer is given by option A.

Answer:

(x+3)^2+(y−3)^2=9

Step-by-step explanation:

The equation for a circle is given by

(x−h)^2+(y−k)^2=r^2  where (h,k) is the center and r is the radius

(x− -3)^2+(y−3)^2=3^2

(x+3)^2+(y−3)^2=9

Answer:

5(x+2)

Step-by-step explanation:

each term, 5x and 10, have only the number 5 in common

factor out the 5 to get:

5(x+2)

Answer:

136 general admission tickets were​ purchased, and 300 upper reserved tickets were purchased.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the number of general admission tickets purchased.

y is the number of reserved tickets purchased.

There were 436 tickets purchased for a major league baseball game.

This means that [tex]x + y = 436[/tex], or also, [tex]x = 436-y[/tex]

The general admission tickets cost ​$6.50 and the upper reserved tickets cost ​$8.00. The total amount of money spent was ​$3284.00.

This means that [tex]6.5x + 8y = 3284[/tex]. Since [tex]x = 436-y[/tex]

[tex]6.5(436-y) + 8y = 3284[/tex]

[tex]1.5y = 450[/tex]

[tex]y = \frac{450}{1.5}[/tex]

[tex]y = 300[/tex]

And:

[tex]x = 436 - y = 436 - 300 = 136[/tex]

136 general admission tickets were​ purchased, and 300 upper reserved tickets were purchased.

Answer:

1. Paralleogram

2. Trapeziod

3. Square

4. Rhombus

5. Rectangle

6. I don't know

7. Rectangle

8. can't see it

9. Trapeziod

Answer: 2

Step-by-step explanation: Rate of change is also defined as slope, so using the rise over run method, you can see that the slope of the line is +2.

Answer:

why you just don't put the question up

Step-by-step explanation:

Answer:

x = 4  or x= -4

Step-by-step explanation:

2x^2 − 11 = 21

Add 11 to each side

2x^2 − 11+11 = 21+11

2x^2 = 32

Divide by 2

2x^2   /2  = 32/2

x^2 = 16

Take the square root of each side

sqrt(x^2) = sqrt(16)

x = ± 4

x = 4  or x= -4

Answer:

the answer this number ...

Answer:

a) 3/5 < 4/5

b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.

c)  [tex]\frac{7}{10} > \frac{9}{15}[/tex]  or  [tex]\frac{7}{10}<\frac{9}{15}[/tex]

Step-by-step explanation:

a) 3/5 < 4/5

Flip the sign and the placement of the fraction so 3/5 is less then 4/5.

b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.

c) We need to change the denominators to a common denominator to compare the size of the two fractions:

[tex]\frac{7}{10}[/tex] × [tex]\frac{3}{3}[/tex] = [tex]\frac{21}{30}[/tex]

[tex]\frac{9}{15}[/tex] ×  [tex]\frac{2}{2}[/tex] = [tex]\frac{18}{30}[/tex]

The common denominators of the two fractions is 30. Comparing the two fractions:

[tex]\frac{21}{30} >\frac{18}{30}[/tex]  or  [tex]\frac{18}{30}<\frac{21}{30}[/tex]

so we get:  [tex]\frac{7}{10} > \frac{9}{15}[/tex]  or  [tex]\frac{7}{10}<\frac{9}{15}[/tex]

Answer:

The grapefruit is 18% heavier than the apple.

Step-by-step explanation:

Orange defines the 100% in this situation.

We know that grapefruit is 8% heavier than an orange, so the weight of a grapefruit   (in percentage)  will be: 100% + 8% = 108%

And an apple is 10% lighter than the orange, then the weight (in percentage) of the apple will be: 100% - 10% = 90%

The difference between the two weights is then:

grapefruit - apple

108% - 90% = 18%

So the grapefruit is 18% heavier than the apple.