The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers

Answer:

The sum of the geometric sequence is: -6665

Step-by-step explanation:

By looking at the geometric sequence, we can note that each term is multiplied by -6.

So, the fourth term is going to be: -216

The fifth term is going to be: 1296

The sixth term is going to be: -7776

The sum of the geometric sequence is: 1 - 6 + 36 - 216 + 1296 - 7776 = -6665

Answer:

6√2

Step-by-step explanation:

A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)

Given: leg = 6

So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2

Answer:

x = 6√2

Answer:

B

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

and the exact value for sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]

Multiply both sides by x

x × sin45° = 6 ( divide both sides by sin45° )

x = [tex]\frac{6}{sin45}[/tex] = [tex]\frac{6}{\frac{1}{\sqrt{2} } }[/tex] = 6[tex]\sqrt{2}[/tex]

[tex]A=\pi r(r+l)\\r=4\\l=13\\\\A=\pi \cdot 4(4+13)=4\pi \cdot 17=68\pi[/tex]

The question appears to be about finding the surface area of a cone, but the provided information discusses a concave mirror instead, which is not relevant for the surface area calculation of a cone.

The question asks for the surface area of a right cone. However, the information provided pertains to the cross-sectional area of a concave mirror that is a quarter-section of a cylinder and not a cone. To find the surface area of a cone, one would use the formula A = πrs + πr^2 where r is the radius of the base and s is the slant height of the cone. In the given text, the radius of the mirror is mentioned to be 80.0 cm, and the insolation is 900 W/m².  This data seems to be mistakenly provided instead of the cone's dimensions and is irrelevant for calculating the surface area of a cone.

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Answer: 107 degrees.

Step-by-step explanation:

A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.

By definition the interior angles of a quadrilateral add up 360 degrees.

We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.

Let be "x" the measure of the fourth angle.

Then you can write this expression:

[tex]360\°=90\°+90\°+73\°+x[/tex]

And finally solve for "x":

 [tex]360\°=253\°+x[/tex]

[tex]360\°-253\°=x[/tex]

[tex]x=107\°[/tex]

Answer:

Option C.

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem triangles HEF and EGE are similar  

because

[tex]EF/GF=HF/EF[/tex]

substitute the values

[tex]\frac{\sqrt{3}}{1}=\frac{3}{\sqrt{3}}\\ \\3=3[/tex]

Is true

The sides are proportional

and

∠HFE=∠GFE

∠EHF=∠GEF

∠HEF=∠EGF

The angles are congruent

The scale factor is equal to

[tex]EF/GF[/tex]

[tex]\frac{\sqrt{3}}{1}[/tex]

Answer:

Option C

Step-by-step explanation:

Two triangles are similar if they have at least 2 equal angles

Note that the HEF triangle has angles of 90 °, 60 ° and 30 °

Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °

Then HEF and EGF are similar triangles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then

[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]

Where the constant k is known as "scale factor"

In this case

[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]

[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]

[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]

or

[tex]\sqrt{3}:1[/tex]

The answer is Option C

ANSWER

[tex]k = 17[/tex]

EXPLANATION

The given function is

[tex]f(x) = 2x + 3[/tex]

The translation that shifts this function 10 units to the right is

[tex]f(x - 10)[/tex]

This implies that

[tex]f(x - 10) = 2(x - 10) + 3[/tex]

We expand the parenthesis to get:

[tex]f(x - 10) = 2x -20+ 3[/tex]

[tex]f(x - 10) = 2x - 17[/tex]

Comparing this equation with

[tex]f(x) = 2x - k[/tex]

we have

[tex]k = 17[/tex]

k=17

The new function would be f(x)=2x-17

In the previous function when u put x=0 you got 3.

Now when the function moves 10 units to the right you still have to get y=3 for x=10. So

2x-k=3 substitute 10 for x

20-k=3 solve for k

K=17.

Answer:

The correct answer option is E. [83 + 2(79) + 4(88)] × 1/7.

Step-by-step explanation:

We are given the quiz average, test average and final average for Sabra's grades for a class.

Given that her test average counts twice as much as her quiz average and final exam counts twice as much as her test average for her overall average:

[tex](83+79+79+88+88+88+88)[/tex] ÷ [tex]7[/tex]

This can also be written as:

[83 + 2(79) + 4(88)] × 1/7

Answer:

[tex]X\leq -8[/tex]

This solution provides a step-by-step explanation to solve the inequality x – 1 ≤ -9, which results in the solution x ≤ -8. This solution indicates that all numbers x that are less than or equal to -8 will satisfy this inequality.

To solve the given inequality x – 1 ≤ – 9, you should first isolate the variable on one side of the inequality:

So, the solution to the inequality is x ≤ -8, which means all numbers x that are less than or equal to -8 will satisfy this inequality.

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Answer:7

Step-by-step explanation:since it has the rule f(n) =2n+1

Third term is when n=3

Therefore 2(3) +1=7

Answer:

A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

We are given that

The probability that a customer buys socks ,P(A)=0.15

The probability that a customer socks given that the customer buys shoes P(A\B)=0.20

The probability that a customer buys shoes,P(B)=1-0.15=0.85

By using formula P(E')=1-P(E)

Where P(E)= Probability of an event that is happened

P(E')=Probability of an event that is not happened

We have to find [tex]P(A\capB)[/tex]  for two events

[tex]P(A)\cdot P(B)[/tex]

[tex]=0.85\times 0.15=0.1275[/tex]

We know that conditional probability of an event when given that the probability of an event B is given

[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex]

[tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex]

[tex]P(A\cap B)=0.20\times 0.85=0.17[/tex]

[tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].

Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.

Therefore, option A is true.

Answer: A. Buying socks and buying shoes are dependent events.

Step-by-step explanation:

For this case we have the following function:

[tex]f (x) = - \sqrt {x + 3} -2[/tex]

By definition, the domain is given by all the values for which the function is defined.

The given function is no longer defined if the argument of the root is negative. So:

[tex]x + 3 \geq0\\x \geq-3[/tex]

Thus, the domain of the function is given by all the values of x greater than or equal to -3.

Domain: [-3, ∞)

Substituting the values of the domain, we find the range.

[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]

The function evaluated in ∞ gives -∞. So the range is given by:

(-∞, 2]

Answer:

Domain:  [-3, ∞)

Range: (-∞, 2]

The answer for this equation is C.

Answer:

The value of 8m is 2

Step-by-step explanation:

step 1

Find the value of m

we know that

[tex]m^{-3} =64[/tex]

so

[tex]\frac{1}{m^{3}}=64\\ \\m^{3}=\frac{1}{64}\\ \\ m=\frac{1}{\sqrt[3]{64}}\\ \\m=\frac{1}{4}[/tex]

step 2

Find the value of 8m

[tex]8m=8(\frac{1}{4})=2[/tex]

Answer:

15

Step-by-step explanation:

Substitute x = - 5 into f(x)

f(- 5) = 5(- 5) + 40 = - 25 + 40 = 15

Answer:  b) (2m³ - 4p⁵)(2m³ + 4p⁵)

Step-by-step explanation:

Use the difference of a square formula: a² - b² = (a - b)(a + b)

[tex]4m^6 - 16p^{10}\\\bullet a) \sqrt{4m^6}=2m^3\\\bullet b)\sqrt{16p^{10}}=4p^5[/tex]

(2m³)² - (4p⁵)² = (2m³ - 4p⁵)(2m³ + 4p⁵)

Answer:

16

Step-by-step explanation:

You need to multiply 4/5 * $20 = $16

Answer:

f(x) = -(x-4)^2 + 5

Step-by-step explanation:

The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.

Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:

[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]

The function which has a range of {y | y < 5} is f(x) = -(x – 5)² + 4​.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a range of the function, {y | y < 5}.

We want to find the corresponding function.

The range of the function contains all the values less than 5.

For the first two functions, when we substitute x = 4,

The value of the function, f(x) = 5

So this is not possible.

For the third function also, when we substitute any integers other than 5, the value of function is greater than 5.

Hence the correct option is D.

Learn more about Range of Functions here :

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Answer:

2957

Step-by-step explanation:

Instead of just giving you a formula.. I want to show you how to understand the formula

So 2200 is the initial population

After 1st year, we are going to have an increase of 3% so 1st yr gives us 2200(1.03)=2266

After 2nd year, we are going to have increase of 3% from previous year so we could do 2266(1.03) or realize this is the same as 2200(1.03)^2 .

so you are going to keep multiplying factors of 1.03 to that per year.

So at 10 years we have 2200(1.03)^10

The formula I mentioned was really this initial population times (1.03)^(number of yrs)

So answer is 2956.616

To the nearest whole number is 2957

Answer:

maybe number 2

Step-by-step explanation:

because if 2+k=18 then there is no other k there and where did the additional 2 come from ?and 2k=18 then value of k is 9 + there is balance.I may be wrong correct me but i think it is no.2

Answer:

2k = 18

k = 9

Step-by-step explanation:

First we have to look at each side of the hanger.

There are 2 k's, which can be represented as "2 times the value of k" or 2k.

On the other side, we have the value of 18. The question states that the two sides are balanced. Therefore, the correct equation that represents the image is:

2k = 18.

To find the value of k that makes the equation true, we must isolate the variable k. To do this, we divide 2 from each side of the equation.

2k ÷ 2 = 18 ÷ 2

k = 9.

The value of k that makes the equation true is 9.

Answer:

it is 2

Step-by-step explanation:

Hello There!

The slope of this line would be 3.

The slope is gradually increasing so starting from the Y intercept value, its consistently going up 3 on the Y axis and going over 1 on the X axis

77.99+7.00+9.99=96.98

96.98 times 8.75% or 0.0875=8.48575 or 8.49                    8.49+96.98=$105.47

[tex]\bf \textit{Cofunction Identities} \\\\ sin\left(90^o-\theta\right)=cos(\theta) \qquad cos\left(90^o-\theta\right)=sin(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(x)=\stackrel{90-56}{sin(\stackrel{\downarrow }{34^o})}\implies cos(\stackrel{\downarrow }{x})=sin(90^o-\stackrel{\downarrow }{56^o})\implies cos(56^o)[/tex]

There are 2 way to find value of x

cos x = sin 34°

First

Co-function identities

sin(90° -∅ ) =cos(∅)     cos(90 -∅) =sin(∅)

       90-56 ↓

cos(x)=sin(34°)⇒ cos (x) =sin(90°-56)⇒ cos(56°)

∴ value of x = 56°⇒ 0.5592

Second way to find  value x

x = cos-1(0.5592)

This is much simpler,

cos (90 - x)= sin x

So,

90 - 34 = 56

∴ x = 56

cos(56) = 0.5592

sin(34) = 0.5592.

A branch of mathematics that studies relationships between side lengths and angles of triangles.

Sin 34 degrees is the value of the sine trigonometric function for an angle equal to 34 degrees. The value of sin 34° is 0.5592

The value of cos 34

= 0.829

The value of cos 34° is equal to the x-coordinate (0.829).

∴ cos 34° = 0.829.

To learn more about the value of x, refer

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The arithmetic expression (-7 + 31) minus (2) equals 22 when you apply the order of operations, which requires us to calculate expressions within parentheses first.

To solve this arithmetic problem, let's break down the expression into two parts, working within the parentheses first. The term inside the first set of parentheses is -7 + 31 which equals 24. The term inside the second set of parentheses appears to have missing or incorrect data.

If we ignore that, we have just (2). Now we subtract the second term (2) from the first term (24). Thus, the value of (-7 + 31) – (2) is 22.

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Answer:

Third Option: $2.07

Step-by-step explanation:

Sales tax is the tax that is applied on the sales of goods by the government paid by the public. Here,

Given

Amount = $29.50

And

Sales tax rate = 7%

The formula for calculation of tax is:

Sales tax = Amount * tax rate

= 29.50 * 7/100

= 29.50*0.07

= 2.065

Rounding off will give

$2.07

So third option is correct ..

Answer:

$2.07

Step-by-step explanation:

Answer:

c- shifted 3 units right and 4 units up

Step-by-step explanation:

In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact  3 units right and 4 units up.

Answer:  The correct option is

(c) shifted 3 units right and 4 units up

Step-by-step explanation:  We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.

From the graph, we note that

the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).

And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).

So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :

A(2, 3)    ⇒   A'(5, 7) = (2+3, 3+4),

B(4, 8)    ⇒   B'(7, 12) = (4+3, 8+4),

C(6, 8)    ⇒   C'(9, 12) = (6+3, 8+4),

D(8, 3)    ⇒   D'(11, 7) = (8+3, 3+4).

Therefore, the required rule of translation from ABCD to A'B'C'D' is

(x, y)  ⇒   (x+3, y+4). That is, 3 units right and 4 units up.

Thus, the required steps applied to ABCD to obtain A'B'C'D' are

Shifted 3 units right and 4 units up.

Option (c) is CORRECT.

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (5, 3)

m = [tex]\frac{3-3}{5+4}[/tex] = [tex]\frac{0}{9}[/tex] = 0

Answer:

f(3) = 64/3

Step-by-step explanation:

f(x)=1/3•4^x

Let x = 3

f(3) = 1/3* 4^3

    = 1/3 * 64

   = 64/3

Answer:

64/3 (APEX)

Step-by-step explanation:

Answer:

The y-intercept is the point (0,5)

Step-by-step explanation:

step 1

Find the slope of the line perpendicular to the line y=(3/4)x+3

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=3/4 -----> the slope of the line y=(3/4)x+3

Find m2

substitute

(3/4)*m2=-1

m2=-4/3

step 2

Find the equation of the line into point slope form

The equation is equal to

y-y1=m(x-x1)

we have

m=-4/3

(x1,y1)=(3,1)

substitute

y-1=-(4/3)(x-3) ----> equation of the line into point slope form

step 3

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation of the line and solve for y

y-1=-(4/3)(0-3)

y-1=4

y=4+1=5

The y-intercept is the point (0,5)

Final answer:

The y-intercept of the line perpendicular to y = 3/4x+3 that includes the point (3, 1) is 5.

Explanation:

To find the y-intercept of the line perpendicular to the line y = 3/4x+3 that includes the point (3, 1), we first need to determine the slope of the perpendicular line. Since the given line has a slope of 3/4, the slope of the perpendicular line will be the negative reciprocal, which is -4/3. We then use the point-slope form of a line equation, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.

Substituting the point (3, 1) and the slope -4/3 into the equation gives us y - 1 = -4/3(x - 3). Simplifying, we get y = -4/3x + 5. The y-intercept of this line is the y-value when x is zero, which in this case is 5.

The calculated value of y in this linear system is 18

How to determine the value of y in this linear system?

From the question, we have the following parameters that can be used in our computation:

x + y + z = 62

x - y = 12

2x + y + z = 92

Subtracting the equations 1 and 2, we have

2x - x = 92 - 62

x = 30

In equation (2), we have

x - y = 12

This gives

y = x - 12

Substitute the known values into the equation

y = 30 - 12

Evaluate

y = 18

Hence, the value of y is 18

Answer:

-3

Step-by-step explanation:

Consider the geometric sequence:

[tex]b_1=-2\\ \\b_2=6\\ \\b_3=-18\\ \\b_4=54\\ \\....[/tex]

Note that

[tex]b_2=b_1\cdot q\\ \\b_3=b_2\cdot q\\ \\b_4=b_3\cdot q\\ \\...[/tex]

So,

[tex]6=-2q\\ \\-18=6q\\ \\54=-18q\\ \\...[/tex]

From all of these equalities we can state that

[tex]q=-3[/tex]

Answer:

r = - 3

Step-by-step explanation:

The sequence is geometric if a common ratio r exists between consecutive terms.

6 ÷ - 2 = - 3

- 18 ÷ 6 = - 3

54 ÷ - 18 = -3

The sequence is geometric with common ratio r = - 3

Answer:

(b - 2)(3b + 7)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term

product = 3 × - 14 = - 42 and sum = + 1

The factors are - 6 and + 7

Use these factors to split the b- term

3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )

= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term

= (b - 2)(3b + 7) ← in factored form