what is the solution to 3x + 5 > or equal to 7

Answer:

Part 1) The measure of angle A is [tex]A=80\°[/tex]

Part 2) The length side of a is equal to [tex]a=10.9\ units[/tex]

Part 3) The length side of b is equal to [tex]b=6.3\ units[/tex]

Step-by-step explanation:

step 1

Find the measure of angle A

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

[tex]A+B+C=180\°[/tex]

substitute the given values

[tex]A+35\°+65\°=180\°[/tex]

[tex]A+100\°=180\°[/tex]

[tex]A=180\°-100\°=80\°[/tex]

step 2

Find the length of side a

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]a=\frac{10}{sin(65\°)}(sin(80\°))[/tex]

[tex]a=10.9\ units[/tex]

step 3

Find the length of side b

Applying the law of sines

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

substitute the given values

[tex]\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}[/tex]

[tex]b=\frac{10}{sin(65\°)}(sin(35\°))[/tex]

[tex]b=6.3\ units[/tex]

Answer:

4(x - 5)^2 - 18.

Step-by-step explanation:

For a move 5 to the right f(x) ----> f(x - 5).

For a move of 2 down  f(x - 5) ----> f(x - 5) - 2.

For this case we have that by definition of function transformation is fulfilled:

Let h> 0:

To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph[tex]y = f (x + h),[/tex] the graph moves h units to the left.

Let k> 0:

To graph [tex]y = f (x) + k[/tex], the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

So, we have the following function:

[tex]h (x) = 4x ^ 2-16[/tex]

5 units on the right:

[tex]h (x) = 4 (x-5) ^ 2-16[/tex]

2 units down

[tex]h (x) = 4 (x-5) ^ 2-16-2\\h (x) = 4 (x-5) ^ 2-18[/tex]

Answer:

[tex]h (x) = 4 (x-5) ^ 2-18[/tex]

Answer:

The correct ans would be B, 25%+10%+10%+10%+10%

Step-by-step explanation:

When percentages are found, the best way to calculate them is to break them down to the simplest percentage form, and 10% is the simplest percentage that a person can calculate of whatever digit. So if someone wishes to find out the friendly percents, then the easiest would be to calculate the 10% of the figure, add them four times, then add them 2 times plus the half of 10%, which will become 25%, and then add them all to get the 65% of that figure.

Answer:

B.

Step-by-step explanation:

i took the test

The y-intercept would elevate up the y-axis by 3

This is because the y-intercept in y= -4x+2 is 2 and when you change it to y= -4x+5 you are moving the intercept to a y of 5.

Answer:

=14

Step-by-step explanation:

In a rhombus, opposite angles are equal.

In the one provided in the question, 5x° is opposite the angle 70°

Let us equate the two.

5x=70

x=70/5

=14°

The value of x in the figure is 14°

Answer:(7,52)

Step-by-step explanation:plug those values into the equation.

52<8(7)+3.

52<59.

Answer:

Option A) Bethany is correct because consecutive odd integers will each have a difference of two

Step-by-step explanation:

The sum of 3 consecutive odd integers is 91. Let the first odd integer is x. The next odd integer will be obtained by adding 2 in x i.e. (x + 2). The third odd integer will be obtained by adding 2 in the second odd integer i.e. (x + 2) + 2 = x + 4

So, the 3 odd integers will be:

x  , (x+2) and (x+4)

Their sum is given to be 91. So we can write:

x + (x+2) + (x+4) = 91

Hence, we can conclude that: Bethany is correct because consecutive odd integers will each have a difference of two.

Other options are not correct because consecutive odd integers always increase by 2. For example, the next odd integer after 1 is 3, which is obtained by adding two, similarly the next odd will be 5 and so on.

Answer:

a

Step-by-step explanation:

Answer:

d =12

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

Substituting what we know

36 pi = pi r^2

Divide each side by pi

36 pi/pi = pi r^2/pi

36 = r^2

Taking the square root of each side

sqrt(35) = sqrt(r^2)

6 =r

We want the diameter

d = 2r

d = 2(6)

d = 12

Answer:

y=2

Step-by-step explanation:

8 - y = 9 - 3

Combine like terms

8 - y = 6

Subtract 8 from each side

8-8 - y = 6-8

-y = -2

Multiply each side by -1

-1 * -y = -2 *-1

y =2

Answer:

x = -4 and x=1

Step-by-step explanation:

The solutions to the equation x^2 +3x -4 = 0 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x=-4 and x=1.

One of the roots is located between -4 and -3, and the other one between 0 and 1.

Answer:

(-0.75, 0.5)

or in fractions:

(-3/4, 1/2)

Step-by-step explanation:

Answer:

The HCF = 3.

Step-by-step explanation:

The prime factors of

234 = 2*3*3*13,

and of 111 = 3*37.

The only common factor is 3.

Answer:

(- 9 × 234 ) + (19 × 111 )

Step-by-step explanation:

Using the division algorithm to find the hcf

If a and b are any positive integers, then there exists unique positive integers q and r such that

a = bq + r → 0 ≤ r ≤ b

If r = 0 then b is a divisor of a

Repeated use of the algorithm allows b to be found

here a = 234 and b = 111

234 = 2 × 111 + 12 → (1)

111 = 9 × 12 + 3 → (2)

12 = 4 × 3 + 0 ← r = 0

Hence hcf = 3

We can now express the hcf (d) as

d = ax + by where x, y are integers

From (2)

3 = 1 × 111 - 9 × 12

From (1)

3 = 1 × 111 - 9( 1 × 234 - 2 × 111)

   = 1 × 111 - 9 × 234 + 18 × 111

   = - 9 × 234 + 19 × 111 ← in required form

with x = - 9 and y = 19

Answer:

15

Step-by-step explanation:

The formula for factoring a sum of cubes is:

[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

We have a=3f and b=5g here.

So a*b in this case is 3f*5g=15fg.

The ? is 15.

The value of the missing coefficient in the factored form of the sum of cubes 27f³ + 125g³ is 15, resulting in the complete factorization being (3f+5g)(9f² -15fg+25g²).

The expression 27f³ + 125g³ can be factored using the sum of cubes formula, which is a³ + b³ = (a + b)(a² - ab + b²).

Given [tex]27f^3+125g^3[/tex], we have [tex]a=3f[/tex] and [tex]b=5g[/tex]

Applying the sum of cubes formula, we get:

[tex]27f ^3+125g ^3 =(3f+5g)((3f) ^2 -(3f)(5g)+(5g)^ 2 )[/tex]

[tex]27f ^3 +125g ^3=(3f+5g)(9f ^2-15fg+25g ^2 )[/tex]

So, the missing coefficient in the factored form is 15.

Therefore, the factored form is,

[tex]27f ^3+125g ^3[/tex] is [tex](3f+5g)(9f^ 2-15fg+25g ^2 )[/tex]

The complete question is:

Find the value of the missing coefficient in the factored form of 27f³ + 125g³ .

27f³ + 125g³ =(3f+5g)(9f² -?fg+25g² )

The value of ? =

Answer:

8.4

Step-by-step explanation:

the equation 4x+8y -40 can be written as 4x-8y-40=0, this represents a line in a space of two dimensions.

solving for x when y=0.8 we have the equation below>

[tex]4x+8*0,8-40=0[/tex]

Which gives that x=42/5, or in more simpler terms, 8.4

Answer:

17.009 in

Step-by-step explanation:

For a normal distribution with mean of 15.2 in and standard deviation of 1.1 inches, we finnd that 5% are excluded when the width of the seats are greater than 17.009 inches.

Therefore, the seat should have a width of 17.009 in.

To accommodate 95% of women based on hip breadth, airline seats should be designed at least 17.015 inches wide, calculated using the given mean of 15.2 inches, a standard deviation of 1.1 inches, and the z-score for the 95th percentile.

To determine the width of airline seats that would accommodate 95% of women, the airline needs to calculate the 95th percentile of women's hip breadths, modeled by a normal distribution.

Using the provided mean of 15.2 inches and a standard deviation of 1.1 inches, we find the z-score that corresponds to the 95th percentile. In normal distribution, the z-score for the 95th percentile is approximately 1.65.

Using the z-score formula Z =(X - μ / Σ, where Z is the z-score, X is the value we seek, μ is the mean, and Σ is the standard deviation, we can set Z to 1.65 and solve for X:

1.65 = (X - 15.2) / 1.1

X = 1.65 * 1.1 + 15.2

X = approx. 1.815 + 15.2

X = approx. 17.015 inches

Therefore, to exclude only the 5% of women with the widest hips, the airline should design seats that are at least 17.015 inches wide.

Answer:

red: 9/20, 0.45, 45%

White: 15%, 0.15, 3/20

Blue: 0.4, 2/5, 40%

Step-by-step explanation:

For red: you start with 9/20. It’s best to get to a denominator of 10. So divide each number by 2. You would get 4.5/10. Then change to a percent by moving the decimal of the numerator one to the right and changing it to percent. 4.5 -> 45. -> 45%. Then for the decimal, divide 45 by 100. 45/100 = 0.45.

For white: you start with 15%. Divide by 100. 15/100=0.15. Put into a fraction with a denominator of 100. It would be 15/100. Simplify. Each number can be divided by 5, so your fraction would be 3/20.

For blue: you start with 0.4. Turn this into a fraction. Since there is one decimal place, it can have a denominator of 10. The fraction is 4/10, simplified to 2/5. Using the fraction 4/10, the percent would be 40%.

I hope this helps!

Answer:

y=2x-2

Step-by-step explanation:

in slope intercept form we need make in this formula..

y=Mx+c

Answer:

y = 2x - 2

Step-by-step explanation:

Given

y + 6 = 2(x + 2) ← distribute

y + 6 = 2x + 4 ( subtract 6 from both sides )

y = 2x - 2 ← in slope- intercept form

Answer:

[tex]A=\frac{225t^2}{\pi}[/tex] given the circumference is 30t.

Step-by-step explanation:

The circumference of a circle is [tex]C=2\pi r[/tex] and the area of a circle is [tex]A=\pi r^2[/tex] assuming the radius is [tex]r[/tex] for the circle in question.

We are given the circumference of our circle is [tex]2 \pi r=30t[/tex].

If we solve this for r we get: [tex]r=\frac{30t}{2\pi}[/tex].  To get this I just divided both sides by [tex]2\pi[/tex] since this was the thing being multiplied to [tex]r[/tex].

So now the area is [tex]A=\pi r^2=\pi (\frac{30t}{2 \pi})^2[/tex].

Simplifying this:

[tex]A=\pi (\frac{30t}{2 \pi})^2[/tex].

30/2=15 so:

[tex]A=\pi (\frac{15t}{\pi})^2[/tex].

Squaring the numerator and the denominator:

[tex]A=\pi (\frac{(15t)^2}{(\pi)^2}[/tex]

Using law of exponents or seeing that a factor of [tex]\pi[/tex] cancels:

[tex]A=\frac{(15t)^2}{\pi}[/tex]

[tex]A=\frac{15^2t^2}{\pi}[/tex]

[tex]A=\frac{225t^2}{\pi}[/tex]

Answer:

P(x) is the profit amount from selling tickets.

P(100) = $160

Step By Step Explanation:

First, plug in r(x) and c(x) into the p(x) equation:

p(x) = r(x) - c(x)

p(x) = (10x) - (8x+40)

Then simplify it:

p(x) = 10x - 8x - 40 {just distribute a +1 into the parentheses}

p(x) = 2x - 40 {combine like terms}

Now substitute 100 for x:

p(100) = 2(100) - 40

Then solve:

p(100) = 200 - 40

p(100) = 160

Without a specific equation or context, we can't find a specific value for x. If the equation were a+c=x, with a=13 and c=47, then x would equal 60.

This question appears to be missing some information to find a specific value for x. If this were an algebraic equation such as a+c=x where a and c are declared as 13 and 47 respectively, you would simply add these two numbers together. So if a=13 and c=47, then x (your answer in this case) would be 60. However, without a given equation or context, it's impossible to determine the exact value for x.

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Answer:

B.

I ignored the extra y= part in each equation.

Step-by-step explanation:

The line given is in slope-intercept form, y=mx+b where m is slope and b is y-intercept.

Parallel lines have the same slope.

So the slope of y=(2/5)x+9 is m=2/5.

So we are looking for a line with that same slope.

In slope-intercept form the line would by y=(2/5)x+b where we do not know b since we weren't given a point.

So all of the choices are written in standard form ax+by=c where a,b, and c are integers.

We want integers so we want to get rid of that fraction there.  To do that we need to multiply both sides of y=(2/5)x+b for 5.  This gives us:

5y=2x+5b

Subtract 2x on both sides:

-2x+5y=5b

Now of the coefficients of x in your choices is negative like ours is. So I'm going to multiply both sides by -1 giving us:

2x-5y=-5b

Compare

2x-5y=-5b to your equations.

A doesn't fit because it's left hand side is 5x+2y.

B fits because it's left hand side is 2x-5y.

C doesn't fit because it's left hand side is 5x-2y.

D doesn't fit because it's left hand side is 2x+5y.

I ignored all the extra y= parts in your equations.

Answer:

-7/2 ±1/2sqrt(13) = x

Step-by-step explanation:

f(x) =x^2 + 7x + 9

To find the zeros, set this equal to zero

0 = x^2 + 7x + 9

I will complete the square

Subtract 9 from each side

0-9 = x^2 + 7x + 9-9

-9 =x^2 + 7x

Take the coefficient of the x term, 7

divide by 2, 7/2

Then square it, (7/2)^2 = 49/4

Add this to both sides

-9 +49/4=x^2 + 7x + 49/4

-36/4 +49/4 = (x+7/2)^2

13/4 =  (x+7/2)^2

Take the square root of each side

±sqrt(13/4) = sqrt( (x+7/2)^2)

± sqrt(13) /sqrt(4)= (x+7/2)

± 1/2 sqrt(13) = (x+7/2)

Subtract 7/2 from each side

-7/2 ±1/2sqrt(13) = x+7/2-7/2

-7/2 ±1/2sqrt(13) = x

The function f(x) = x^2 + 7x + 9 has no real-number zeros as the discriminant is negative, indicating that the quadratic formula solution involves an imaginary number.

The student is asking to find the zeros of the quadratic function f(x) = x^2 + 7x + 9. To solve for the zeros, we need to find the values of x that make the function equal to zero. We can use the quadratic formula, which is [tex]x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}[/tex], where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, our equation is already in the correct form with a = 1, b = 7, and c = 9. Plugging these into the quadratic formula, we get:

[tex]x = \frac{{-7 \pm \sqrt{{7^2 - 4(1)(9)}}}}{{2 \cdot 1}}[/tex]

Upon further calculation, we find that the equation has no real-number solutions as the discriminant (b^2 - 4ac) is negative (49 - 36 = 13), leading to an imaginary number in the square root. Therefore, we conclude that the function does not cross the x-axis and has no zeros on the real number line.

Using the Pythagorean theorem:

a = √(c^2 - b^2)

a = √(8^2 - 5^2)

a = √(64 - 25)

a = √39 ( Exact answer )

Or √39 =  6.244997 as a decimal and you round the decimal answer as needed.

Answer:

153 units squared

Step-by-step explanation:

To solve, multiply your length by your width.

[tex]A=lw\\A=9(17)\\A=153[/tex]

Answer:

A=153

Step-by-step explanation:

The area of a rectangle with a length of 9 and a width of 17 is 153.

Formula: A=wl

A=wl=17·9=153

Answer:

c) 5,160

Step-by-step explanation:

If from a jar of pennies, 1290 are drawn, marked, and returned to the jar and after mixing,  a sample of 200 pennies is drawn and it was noticed that 50 were marked. Based on the given information there are  5,160 pennies in the jar.

1290 pennies are drawn and returned to the jar.

200 pennies were drawn.

50 pennies were marked.

1,490 is not enough.

258,000 is way too much.

5,160 makes sense.

Final answer:

Using the proportion of marked to sampled pennies, the total number of pennies in the jar is estimated to be 5160.

Explanation:

The task is to use the information given about the marked and sampled pennies to estimate the total number of pennies in the jar.

This is a classic example of using proportions in mathematics. If out of 200 sampled pennies, 50 are marked, this represents 25% of the sample.

Since 1290 pennies were marked to begin with, we assume that the sampled 25% represents a similar proportion of the total jar.

Thus, the equation to solve is 1290 / total number of pennies = 50 / 200. Simplifying the right side of the equation gives 1290 / total number of pennies = 1 / 4.

By cross-multiplication, the total number of pennies is 4 × 1290, which equals 5160.

Answer:

I only used two steps: 3) then 6) then 1).

Step-by-step explanation:

Ok, if x-5 is a factor of p(x), then p(5)=0 by factor theorem.

This also goes the other way around:

If p(5)=0 then x-5 is a factor of p(x) by factor theorem.

Let's check. I'm going to evaluate p(x) for x=5.

[tex]p(5)=5^3-5(5)^2-5+5[/tex]

[tex]p(5)=125-5(25)-5+5[/tex]

[tex]p(5)=125-125-5+5[/tex]

[tex]p(5)=0+0[/tex]

[tex]p(5)=0[/tex]

This implies x-5 is a factor since we have p(5)=0.

The first step I did was 3) evaluate p(x) for x=5.

The second step I did 6) simplify and find the remainder. I did this when I was evaluating p(5); that was a lot of simplification and then I found the remainder to be 0 after that simplification. The last step was 1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x).

To determine if x-5 is a factor of the polynomial, evaluate p(x) when x=5. If the result is 0, then the Factor Theorem implies that x-5 is a factor. If not, x-5 is not a factor.

To determine if x-5 is a factor of p(x)=x^3-5x^2-x+5, you can follow these steps:

When you evaluate p(x) for x=5, if you get 0, it demonstrates, according to the factor theorem, that x-5 is a factor of p(x) because it results in the polynomial function equaling zero. If you don't get zero, then it's not a factor.

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D. 103 12/13 or about 104

First sort the data into two sets of points, (1989,2881), (2002, 4232).

Now use the slope equation with your numbers.

(y2-y1)/(x2-x1)

(4232-2881)/(2002-1989)

1351/13=

103 12/13 or about 104

The equation of the volume of the sphere is 4/3 × 27π

The volume of a cylinder is expressed as

V = πr²h

Since the cylinder has thesame height and radius, therefore, the volume of the cylinder will now be

V = πr² × r

V = πr³

The volume of a sphere is expressed as

V = 4/3(πr³)

Therefore we can say

the volume of sphere = 4/3 × volume of the cylinder

Volume of cylinder = 27π

volume of sphere = 4/3 × 27π

= 4 × 9

= 36πft³

Answer:

B

Step-by-step explanation:

Factor the numerator, that is

x² + 6x + 8 = (x + 4)(x + 2), now

f(x) = [tex]\frac{(x+4)(x+2)}{x+4}[/tex]

Cancel the factor (x + 4) on the numerator/ denominator, leaving

f(x) = x + 2 ← simplified version

Cancelling the factor x + 4 leaves a discontinuity ( a hole ) at

x + 4 = 0 ⇒ x = - 4 and f(- 4) = x + 2 = - 4 + 2 = - 2

There is a discontinuity at (- 4, - 2 )

To find the zero let f(x) = 0, that is

x + 2 = 0 ⇒ x = - 2

The zero is (- 2, 0 )

Answer:

d=-4

Step-by-step explanation:

20 = –d + 16

Subtract 16 from each side

20-16 = –d + 16-16

4 = -d

Multiply each side by -1

-1 *4 = -1 * -d

-4 =d