Solve 5 - 2x < 7.
A) x < -1
B) x > -1
C) x < -12
D) x > -12

Check the picture below.

so the figure is really just 3 triangles and one square, we can simply get the area of each shape and sum them up, and that's the area of the composite

[tex]\bf \stackrel{\textit{green triangle}}{\cfrac{1}{2}(9)(3.5)}+\stackrel{\textit{brown triangle}}{\cfrac{1}{2}(2)(2)}+\stackrel{\textit{purple square}}{(2\cdot 2)}+\stackrel{\textit{pink triangle}}{\cfrac{1}{2}(5)(2)} \\\\\\ 15.75+2+4+5\implies 26.75[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

We have

the right traingle with the legs a = 3.5 and b = 2 + 2 + 5 = 9

the trapezoid with the bases b₁ = 2 + 2 + 5 = 9, b₂ = 5 and the height h = 2.

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

Substitute:

[tex]A=\dfrac{(3.5)(9)}{2}=15.75[/tex]

The formula of an area of a trapezoid:

[tex]A=\dfrac{(b_1+b_2)h}{2}[/tex]

Substitute:

[tex]A=\dfrac{(9+2)(2)}{2}=11[/tex]

The area of the shape:

[tex]\bold{A=15.75+11=26.75}[/tex]

1 foot = 12 inches.

The president is 6 x 12 = 72 inches tall.

54 inch model / 72 inches = 0.75 = 3/4

The model is 3/4 scale.

Answer:

1923 cm²

Step-by-step explanation:

The surface area of a sphere is A = 4πr².

The first spherical beach ball has a radius of 24 cm:

A = 4π (24)²

A ≈ 7238 cm²

The second spherical beach ball has a radius 3 cm greater, or 27 cm:

A = 4π (27)²

A ≈ 9161 cm²

So the difference in area is:

9161 - 7238

1923 cm²

Answer:

1923 cm²

Step-by-step explanation:

Equation for the surface area of a sphere is 4πr².

The surface area of the bigger ball is (27²×4×π) = 2916π

The surface area of the smaller ball is (24²×4×π) = 2304π

The difference is 2916π-2304π = 612π

This is 1923 cm²

Answer:

80%

Step-by-step explanation:

According to the given data, the numbers 0 through 6 represent students who sent a text yesterday while the numbers 7 through 9 represent students who did not send a text yesterday.

Based on this key, we will calculate the number of students who sent the text yesterday and the number of students who did not sent the text yesterday.

The given data is: 62072, 34570, 80983, 04292, 83150, 36330, 96268, 14077, 77985, 13511

For each group we will identify how many students sent the text and how many students did not. According to the key, a number from 0 to 6 will be counted as a student who sent the text and a number from 7 to 9 will be counted as a student who did not send the text. Students who did not sent the text are made bold in the groups below.

62072:  4 students sent the text, 1 did not

34570:  4 students sent the text, 1 did not

80983:  2 students sent the text, 3 did not

04292:  4 students sent the text, 1 did not

83150:   4 students sent the text, 1 did not

36330:  All 5 students sent the text

96268:  3 students sent the text, 2 did not

14077:   3 students sent the text, 2 did not

77985:  1 student sent the text, 4 did not

13511:    All 5 students sent the text

We need to find the probability that 3 or more of a group of 5 students randomly selected will send a text today.

From the given groups, the number of groups where 3 or more students sent a text = 8

This represents our number of favorable or desired outcomes.

Total number of possible outcomes is the total number of groups = 10

Since, probability is defined as the ratio of number of favorable outcomes to total number of outcomes, based on the simulated data  the probability that 3 or more of a group of 5 students randomly selected will send a text today will be = [tex]\frac{8}{10}=0.80=80\%[/tex]

Thus, based on the simulated data there is 80% probability that 3 or more of a group of 5 students randomly selected will send a text today

Answer:

The answer is 80% or 4/5(;

Step-by-step explanation:

Answer:

≈ 7.07

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (- 7, - 2)

d = [tex]\sqrt{(-7-0)^2+(-2+1)^2}[/tex]

  = [tex]\sqrt{(-7)^2+(-1)^2}[/tex]

  = [tex]\sqrt{49+1}[/tex] = [tex]\sqrt{50}[/tex] ≈ 7.07

Answer:

The correct option is D.

Step-by-step explanation:

It is given that Issouf claims that the scale factor is 1/2.

From the given figure it is clear that

[tex]CB'=C'B'=2[/tex]

[tex]B'B=6[/tex]

[tex]CB=CB'+B'B=2+4=6[/tex]

The scale factor of a figure is

[tex]k=\frac{\text{Length of any side of image}}{\text{Length of corresponding side of preimage}}[/tex]

[tex]k=\frac{C'B'}{CB}[/tex]

[tex]k=\frac{2}{6}[/tex]

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

The scale factor is 1/3 because CB is actually 2 + 4 = 6.

Therefore the correct option is D.

Answer:

x=-2.6

y=5.2

Step-by-step explanation:

The endpoint of line AB are at:

A(-4,8) and B(2,-4)

The x-coordinate of the point that divides this AB in the ratio m:n=3:10 is

[tex]x=\frac{mx_2+nx_1}{m+n}[/tex]

We substitute the given values to obtain;

[tex]x=\frac{3(2)+10(-4)}{3+10}[/tex]

We simplify to get:

[tex]x=\frac{6-40}{13}[/tex]

[tex]x=\frac{-34}{13}[/tex]

[tex]x=-2.6[/tex]

The y-coordinate of the point that divides this AB in the ratio m:n=3:10 is

[tex]y=\frac{my_2+ny_1}{m+n}[/tex]

We substitute the given values to obtain;

[tex]y=\frac{3(-4)+10(8)}{3+10}[/tex]

We simplify to get:

[tex]y=\frac{-12+80}{13}[/tex]

[tex]y=\frac{68}{13}[/tex]

[tex]y=5.2[/tex]

Answer:

x= -2.6

y= 5.2

Step-by-step explanation:

Answer:

B. -3

Step-by-step explanation:

The answer is -3

Because

Answer: The graph of g(x) is the graph of f(x) compresed vertically.

Step-by-step explanation:

Given the parent function [tex]f(x)^2[/tex], there are some transformations rules:

If [tex]f(x)=a(x^2)[/tex] when [tex]a>1[/tex], then it is stretched vertically.

If [tex]f(x)=a(x^2)[/tex] when [tex]0<a<1[/tex], then it is compresed vertically.

If [tex]f(x)=(ax)^2[/tex] when [tex]0<a<1[/tex], then it is stretched horizontally.

If [tex]f(x)=(ax)^2[/tex] when [tex]a>1[/tex], then it is compresed horizontally.

In this case for [tex]g(x)=\frac{2}{5}x^2[/tex], it has the form [tex]f(x)=a(x^2)[/tex] and [tex]0<a<1[/tex], then the graph of g(x) is the graph of f(x) compresed vertically.

The graphs of the functions f(x) = x^2 and g(x) = 2/5x^2 both represent parabolas, with g(x) being vertically compressed by a factor of 2/5 compared to f(x), which makes the g(x) graph appear narrower and less steep than the f(x) graph.

The functions f(x) = x2 and g(x) = 2/5x2 both represent parabolas, which are U-shaped curves on a graph. The significant difference between these two functions is their scaling, or how they stretch or compress vertically. The function f(x) = x2 has no scaling factor, which means it represents a standard square function with a one-to-one ratio. On the other hand, the function g(x) = 2/5x2 has a scaling factor of 2/5, meaning the graph of g(x) compared to f(x), will be vertically compressed by a factor of 2/5. This means the heights on the graph of g(x) are 2/5 times the corresponding heights on the graph of f(x). Therefore, the g(x) graph will appear narrower and less steep than the f(x) graph.

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Answer:  [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Step-by-step explanation:

The equation of the line in Point-Slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope and ([tex]x_1,y_1[/tex]) is a point on the line.

You can identify that in the equation of the line [tex]y-3=4(x+2)[/tex], the slope is:

[tex]m=4[/tex]

By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:

[tex]m=-\frac{1}{4}[/tex]

 Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation  [tex]y-y_1=m(x-x_1)[/tex] to get the equation of this line:

 [tex]y-7=-\frac{1}{4}(x-(-5))[/tex]

 [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Slope-intercept form: y= mx + b (m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y))

To find the slope, use the slope formula and plug in 2 points:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

(x₁ , y₁) = (5, 2)

(x₂ , y₂) = (10, 6)

[tex]m=\frac{6-2}{10-5} =\frac{4}{5}[/tex]

[tex]y=\frac{4}{5}x+b[/tex]    To find b, plug in a point into the equation (5, 2)

[tex]2=\frac{4}{5}(5)+b[/tex]

2 = 4 + b

-2 = b

[tex]y=\frac{4}{5}x -2[/tex]

Answer:

y = 4/5x -2

Step-by-step explanation:

equation of a line passing through two points is given by

y - y₁ = m (x - x₁), where m = (y₂ - y₁) / (x₂ - x₁)

y₂ = 6, y₁ = 2

x₂ = 10, x₁ =5

m = (6-2)/(10-5)

m = 4/5

y - 2 = 4/5 (x - 5)

multiply both sides by 5

5(y -2) = 4(x - 5)

5y -10 = 4x -20

5y = 4x -20 +10

5y = 4x -10

divide through by 5

y =4/5x -2

Answer:

6038 x 1

or

603.8 x 10

Answer:

The measure of angle B is [tex]132\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

In an inscribed quadrilateral, opposite angles are supplementary

so

[tex]x\°+(2x+36)\°=180\°[/tex]

[tex]3x=180\°-36\°[/tex]

[tex]3x=144\°[/tex]

[tex]x=48\°[/tex]

step 2

Find the measure of angle B

[tex]B=(2x+36)\°[/tex]

[tex]B=(2(48)+36)\°=132\°[/tex]

Answer:

D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or  [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]

Step-by-step explanation:

The given equation is:

[tex]3x^2+8x=5[/tex]

Divide through by 3;

[tex]x^2+\frac{8}{3}x=\frac{5}{3}[/tex]

Add the square of half the coefficient of x to both sides.

[tex]x^2+\frac{8}{3}x+(\frac{4}{3})^2=\frac{5}{3}++(\frac{4}{3})^2[/tex]

[tex]x^2+\frac{8}{3}x+\frac{16}{9}=\frac{5}{3}+\frac{16}{9}[/tex]

The left hand side is now a perfect square:

[tex](x+\frac{4}{3})^2=\frac{31}{9}[/tex]

Take square root

[tex]x+\frac{4}{3}=\pm \sqrt{ \frac{31}{9}}[/tex]

[tex]x=-\frac{4}{3}\pm \sqrt{ \frac{31}{9}}[/tex]

[tex]x=-\frac{4}{3}\pm \frac{\sqrt{31}}{3}[/tex]

D. [tex]x=\frac{-4-\sqrt{31}}{3}[/tex] or  [tex]x=\frac{-4+\sqrt{31}}{3}[/tex]

Answer:

15

Step-by-step explanation:

30 divided by 2 to find a radius. that equals 15.

The answer to that is 15!

Answer:

the equation of the perpendicular bisector of segment AB is y = -2x + 7

Step-by-step explanation:

Going from B(-1, 4) to A(3, 6), x increases by 4 and y increases by 2.  Thus, the slope of this line is m = rise / run = 2/4, or 1/2.

Any line perpendicular to the one joining A and B has a slope which is the negative reciprocal of 1/2:  that'd be -2.

                                                               3 - 1       6 + 4

The midpoint of line segment AB is ( --------- , ---------- ), or (1, 5)

                                                                  2            2

Thus, the perpendicular bisector passes through the midpoint (1, 5) and has slope -2:

Starting from y = mx + b, we get  5 = -2(1) + b, or 7 = b, and so the equation of the perpendicular bisector of segment AB is

y = -2x + 7

Answer:

a=5, b=-2

Step-by-step explanation:

If you simplify the equation, you get:

3ax +6 -4x -4b - 11x - 14 = 0 =>

3ax - 15x -4b -8 = 0

group together x's and constants:

(3a-15)x -8 -4b = 0

To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2

Answer:

it is 1500 and .97 on  

Step-by-step explanation:

Answer:

a = 1500 (initial Bone density)

b = 0.97 (remaining percentage every year)

x = x (years)

Step-by-step explanation:

The question already sets x as the "years" variable, and the function must be expressed:

[tex]f(x) = a*b^x[/tex]

Then we can set a as the initial bone density: 1,500 kg/mg3

and b as the remaining percentage after each year: 100% - 3% = 97%

In decimal notation: 97% is equivalent to 0.97

The x exponent of b represents the succesive density reduction each year.

For example, replacing for values for the first 5 years we obtain the following results:

(Note: results are limited and rounded to two decimals)

[tex]f(x) = 1500*0.97^1 = 1455[/tex]

[tex]f(x) = 1500*0.97^2 = 1411.35[/tex]

[tex]f(x) = 1500*0.97^3 = 1369,01[/tex]

[tex]f(x) = 1500*0.97^4 = 1327,94[/tex]

[tex]f(x) = 1500*0.97^5 = 1288,10[/tex]

Answer:

150°

Step-by-step explanation:

(30x+30)=2(20x-5)

x=4

AB=30×4+30=150

Answer:

150°

Step-by-step explanation:

The angle at the centre subtended by arc AB is twice the inscribed angle, that is

30x + 30 = 2(20x - 5) ← distribute

30x + 30 = 40x - 10 ( subtract 40x from both sides )

- 10x + 30 = - 10 ( subtract 30 from both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

Hence

arc AB = (30 × 4) + 30 = 120 + 30 = 150°

Answer:

BF and HG

Step-by-step explanation:

this is because skew lines are lines that are not parrallel but are never going to intercet each other.

Answer:Lines BF and HG are skew.

Step-by-step explanation:

A skew lines are two lines that lie on different planes, will never intersect, and are not parallel.

Step-by-step explanation:

1 and 2 share the same line (a line equals 180°) if 1 = 100° then 180°-100°=80°

2=80°

bc and 4 also share a straight line. if bc=30° then 180°-30°=150°

4=150°

this can be checked by adding them all together. a circle is equal to 360°.

100°+80°+30°+150°=360°

San makes up the straight line that makes up 1 and 2 (as you can see I have already answered the question a million times over) and as it is a straight line it is 180° which is backed up by all of the double checked math.

Answer:

180 is correct

Step-by-step explanation:

Answer:

The length of the new image is 3 cm

Step-by-step explanation:

we know that

To find the length of the new image, multiply the length of the original image by the scale factor

Let

A'B'-----> the length of the new image

z ----> the scale factor

we have that

AB=1.5 cm

z=2

A'B'=z*AB

A'B'=2*1.5=3 cm

Answer:

C

Step-by-step explanation:

Since you are basically interested in what the graph looks like, there is no need to go beyond a good graphing program like Desmos. The graph is provided below.

Red: y = -1/2  x + 4

Blue:2y + x = -8

Since both of them have the same slope, they never meet.

The correct answer is C: No solution

Answer:

- 121

Step-by-step explanation:

The recursive formula allows us to find the next term in a sequence from the previous term, thus

f(1) = - 3f(0) + 2 = - 3 × 5 + 2 = - 15 + 2 = - 13

f(2) = - 3f(1) = - 3 × - 13 + 2 = 39 + 2 = 41

f(3) = - 3f(2) + 2 = - 3 × 41 + 2 = - 123 + 2 = - 121

Janice should measure each wall's height and length to determine the square footage needed for painting and divide this by the coverage area of a gallon of paint to estimate the number of gallons she will need, ensuring to round up for any excess needed for touch-ups.

Janice's accuracy in estimating the amount of paint needed for her apartment is important to ensure that she neither runs out of paint before completing the job nor wastes money buying too much.

In general, paint cans are sold in one-gallon sizes, and a gallon typically covers around 350 to 400 square feet of wall space.

When calculating the paint needed, Janice should measure each wall's height and length to determine the square footage, considering any deductions for windows and doors.

Once she has the total square footage, she can divide by the coverage area of a gallon of paint to estimate the number of gallons needed. It's usually a good idea to buy a little extra for touch-ups, so round up to the nearest whole number.

As a review, understanding unit conversions is also pertinent.

For example, when converting miles to feet, ounces to pounds, or quarts to gallons, each conversion requires knowledge of the correct factors: 1 mile = 5,280 feet, 1 pound = 16 ounces, and 1 gallon = 4 quarts.

Such conversions are crucial in accurately determining quantities and can help avoid overestimating or underestimating the resources required for a task.

Final answer:

Janice needs to carefully calculate the amount of paint needed for her apartment by considering the square footage and paint coverage, possibly with a margin for extra paint. The painting job timing can be expressed with a linear equation T = 4 + 0.001S, where T is total time and S is square footage.

Explanation:

For Janice to estimate the amount of paint needed accurately, it's important that she does a careful calculation based on the square footage of her apartment walls and the coverage provided by each gallon of paint. The accuracy of this estimation will prevent the wastage of resources and ensure that the work does not halt due to the shortage of paint. However, it's also practical to consider buying an extra can to account for any unforeseen circumstances, as the estimation might have a margin of error.

Regarding the linear equation for the painting job: If it requires four hours of setup time plus one hour per 1,000 square feet, then we can express this as T = 4 + 0.001S, where T is the total time in hours and S is the square footage of the painting area. This linear equation will help to estimate the time needed for any given square footage.

Answer:

Step-by-step explanation:

The sum of the angles measures at one side of the parallelogram is 180°.

Therefore we have the equation:

x + 113 = 180             subtract 113 from both sides

x + 113 - 113 = 180 - 113

x = 67

Answer:

67

Step-by-step explanation:

Answer:

333 in^3

Step-by-step explanation:

Circumference = pi *d

27 = pi*d

Replacing d with 2*r  ( 2 times the radius)

27 = pi * 2 * r

Divide each side by 2

27/2 = pi *r

13.5 = pi *r

Divide by pi

13.5/ pi = r

We want to find the volume of a sphere

V = 4/3 pi * r^3

V = 4/3 pi (13.5/pi)^3

  = 4/3 pi * (13.5)^3 / (pi^3)

  4/3 pi/pi^3  * (13.5)^3

   4/3 * 1/ pi^2 *2460.375

 3280.5 / pi^2

Let pi be approximated by 3.14

 380.5/(3.14)^2

 332.7214086 in^3

To the nearest in^3

333 in^3

Answer:

332.384142939 cubic inch, rounded- 332 cubic inches

Step-by-step explanation:

Volume of a sphere is 4/3 pi*r^3

circumference=C = 2 π r

we can simply 27 by 2*pi to get radius-

approx 4.29718346348.

4/3 pi*4.29718346348.^3

4/3* pi*79.3508690311= about 332.384142939

Answer:

2,180 people

Step-by-step explanation:

Let

x-----> number of people at the book fair

we know that

1) 1/4 of the people bought 1 book each

(1/4)x=(5/20)x

2) 3/5 of the remaining  people bought 2 books each

The remaining people is (3/4)x

so

(3/5)(3/4)x=(9/20)x

3) the rest of the people bought 3  books each

The rest of the people is x-(5/20)x-(9/20)x=(6/20)x

The linear equation that represent this situation is

(1)*(5/20)x+(2)*(9/20)x+(3)*(6/20)x=4,469

(5/20)x+(18/20)x+(18/20)x=4,469

(41/20)x=4,469

x=4,469*20/41

x=2,180 people

Answer:

y=0.5x+3

Step-by-step explanation:

A triangle's angles always add up to a total 180º, and a right triangle always has an angle equal to 90º.

90º + 34º + xº = 180º

124º + xº = 180º

xº = 56º