As given that the every surface of the block shown will be painted, except for one of the bases.
And a block have 6 surface but one is not painted so there are 5 surface that are painted so:
The area of the painted surface is:
[tex]A=5a^2[/tex]Where a is 3.2 cm
[tex]\begin{gathered} A=5(3.2)^2 \\ A=5\times10.24 \\ A=51.2cm^2 \end{gathered}[/tex]The area of painted surface is 51.2 square cm
5.-4h + 3 + 7h 9h - 21
-4h + 3 + 7h ≥ 9h - 21
combining similar terms,
(-4h + 7h) + 3 ≥ 9h - 21
3h + 3 ≥ 9h - 21
3h is adding on the left, then it will subtract on the right.
21 is subtracting on the right, then it will add on the left.
3 + 21 ≥ 9h - 3h
24 ≥ 6h
6 is multiplying on the right, then it will divide on the left.
24/6 ≥ h
4 ≥ h
We can check the answer replacing with a value wich is a solution and another value wich is not. For example, with h = 3, we get:
-4*3 + 3 + 7*3 ≥ 9*3 - 21
-12 + 3 + 21 ≥ 27 - 21
12 ≥ 6
This result confirm that h = 3 is a solution.
Substituting with h = 5, we get:
-4*h + 3 + 7h ≥ 9h - 21
graph f(x) = 2sin x
Explanation
We are given the function:
[tex]f(x)=2\sin x[/tex]We are required to graph the function above.
- Using a graphing calculator, we have:
QuestionFind the equation of the line with slope m=1/4 that contains the point (4,5)
The standard form equation for a line is
[tex]y=mx+b[/tex]in which m represents the slope and b the y-intercept.
start putting the value of the slope into the equation
[tex]y=\frac{1}{4}x+b[/tex]although it is a fraction we repace it as if it was a whole number
then using (4,5) as (x,y) we can find b, the y-intercept
[tex]5=\frac{1}{4}(4)+b[/tex]simplify both sides of the equation
[tex]5=1+b[/tex]subtract 1 one on both sides in order to find b
[tex]\begin{gathered} 5-1=1+b-1 \\ 4=b \\ b=4 \end{gathered}[/tex]The equation of the line is
[tex]y=\frac{1}{4}x+4[/tex]A bicycle tire with a 16-inch radius has an angular speed of 328(pi) radians per minute. Find the linear speed of the tire in feet per second. Round to the nearest tenth.
SOLUTION
The relationship between linear and angular speed is given as
[tex]\begin{gathered} v=rw \\ \text{Where } \\ v=l\text{inear sp}eed=? \\ r=\text{ radius = 16-inch} \\ w=\text{ angular sp}eed\text{ = 328}\pi\text{ radians } \end{gathered}[/tex]Substituting the values into the equation we have
[tex]\begin{gathered} v=rw \\ v=16\times\text{328}\pi \\ v=16487.07825 \end{gathered}[/tex]13. SHOPPING You go to the hardware store for some building materials. You purchase 7fans (f) for a house you are remodeling and $8 worth of other materials. You return 2fans (f) that were not working properly. Write an expression that represents yourshopping. After writing your expression, simplify the expression.
The function of the situation would be:
[tex]\begin{gathered} 7\cdot f+8-2\cdot f \\ 5\cdot f+8 \end{gathered}[/tex]therefore, the expression is:
5*f + 8
An equation is shown below:5(2x − 3) = 5Part A: How many solutions does this equation have? (4 points)Part B: What are the solutions to this equation? Show your work.
Part A
The given equation is
[tex]5(2x\text{ -3\rparen=5}[/tex]as there is only one variable, the equation either has 1 solution or no solution. However, note that on the left we have a polynomial of degree 1 (a line), whenever we make it equal to a constant, we always have a solution. So in this case the solution is 1.
Part B
Now, to solve this equation first we divide both sides by 5. So we get
[tex]2x\text{ -3=1}[/tex]Then, we add 3 on both sides to get
[tex]2x=1+3=4[/tex]Finally we divide both sides by 2 to get
[tex]x=\frac{4}{2}=2[/tex]so the unique solution of the equation is x=2
The value of the expression -2xy for x = -4.7 and y = 0.2 is _____.
-1.88
-18.8
18.8
1.88
Answer:
answer: 1.88
Step-by-step explanation:
if X=4.7 and if Y=0.2 then the expression should look like this.
-2 × -4.7 × 0.2 = -1.88
the value that x and y was assigned will be used in the expression for instance if I said Y is equal to 5 then that means that Y and 5 is used to replace Y in the equation.
Example:
X•Y= ?
when
Y=5
and
X=4
that means.
4•5=20
.
Answer:
d) 1.88
Step-by-step explanation:
Given that,
→ x = -4.7
→ y = 0.2
The given expression is,
→ -2xy
Now the required value is,
→ -2xy
→ -2(-4.7) × 0.2
→ 9.4 × 0.2 = 1.88
Hence, the value is 1.88.
You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?
N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
[tex]\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}[/tex]so, the direction is
N 60° W
Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day. How many minutes does she jump rope on Thursday?
She jumped 25 minutes on Tuesday as the problem says, "Lola jumps rope for 15 minutes on Monday. She jumps rope 10 more minutes each day."
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The total amount or sum of the two whole numbers is obtained by adding them. Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation. The mathematical operation of addition is the process of adding two or more numbers together to determine the total, or sum. 5 + 11 + 3 equals 19, as an illustration of addition.
Here,
She jumped 15 minutes on Monday
On Tuesday, she will jump 10 more minutes,
=15+10
=25 minutes
As stated in the problem, she jumped 25 minutes on Tuesday "On Monday, Lola jumps rope for 15 minutes. She adds 10 more minutes of daily rope jumping."
To know more about addition,
https://brainly.com/question/875080?referrer=searchResults
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Solve for y:2x-17y=13
The given equation is:
[tex]2x-17y=13[/tex]Step 1. Add 17y to both sides:
[tex]\begin{gathered} 2x-17y+17y=13+17y \\ \\ 2x=13+17y \end{gathered}[/tex]Step 2. Subtract 13 from both sides:
[tex]\begin{gathered} 2x-13=13-13+17y \\ \\ 2x-13=17y \end{gathered}[/tex]Step 3. Isolate y by dividing both sides by 17 and simplify:
[tex]\begin{gathered} \frac{2x-13}{17}=\frac{17y}{17} \\ \\ \text{ Simplify }\frac{17}{17}=1 \\ \\ \frac{2x-13}{17}=1*y \\ \\ \text{ Reorder terms} \\ y=\frac{2x-13}{17} \end{gathered}[/tex]As we don't have an x-value, we let y in terms of x, as in the equation above.
100%Normal textCalibri11+BIUcaIE:531123461.Here are box plots that summarize the heights of 20 professional male athletes in basketball,football, hockey, and baseball.basketballfootballhockeybaseball652075808590height in inchesa.In which two sports are the players' height distributions most alike? Explain your reasoning.
From the graph shown, it can be observed that the values of the minimum heights, to the quartile, to the median, to the interquartile, and the maximum heights are as stated below:
[tex]\begin{gathered} \text{Basketball}-67,76,78,80,91 \\ \text{Football}-66,70,73,75,77 \\ \text{Hockey}-69,72,73,75,76 \\ \text{Baseball}-70,72,73,74,76 \end{gathered}[/tex]From the observed heights, it can be clearly seen that Football, Hockey and Baseball have the same median of 73 heights
[tex]\begin{gathered} \text{Range of Basketball= 91-67=24} \\ \text{Range of Football= 77-66=11} \\ \text{Range of Hockey=76-69=7} \\ \text{Range of Baseball=76-70=6} \end{gathered}[/tex]From the values of the range, it can be observed that the range of Hockey and Baseball is almost the same, 6 and 7
Hence, the two sports that most alike are Hockey and Baseball
determine the numbers of solutions that exist to the equation below 8 (j - 4) = 2(4j - 16)
Step 1: Write out the equation
[tex]8(j-4)=2(4j-16)[/tex]Step 2: Divide both sides by 2
[tex]\begin{gathered} \frac{8(j-4)}{2}=\frac{2(4j-16)}{2} \\ \text{Therefore} \\ 4(j-4)=4j-16 \end{gathered}[/tex]Step 3: Expand the left side of the equation to get
[tex]\begin{gathered} 4j-16=4j-16 \\ \text{Thus} \\ 4j-4j=-16+16 \\ 0=0 \end{gathered}[/tex]0 = 0 is always true no matter the value of j.
Hence, the number of solutions is infinite
An amusement park sold ride tickets in the ratio shown in the diagrams
as shown in the diagram.
Every 3 A tickets sold, B tickets were sold 5. Thus:
for A. it should be 8 tickets sold ----> false
for B. This is A + B = 3 + 5 = 8, so it should be 5:8 ----> false
for C. 3 A tickets sold, B tickets were sold 5, so its 3 to 5 -----> true
for D. A tickets sold, B tickets were sold 5, so -----> true
for E. 6 ride A tickets were sold, it should be 10 ride B tickets sold, so ----> false
for F. the ratio of 30 to 50 is 3 to 5 so, ----> true
answer: C, D and F
In AFGH, f = 83 inches, g=11 inches and ZH=60°. Find the length of h, to the nearest inch
Answer:
78 in
Explanation:
We can calculate the length of h using the cosine law because we have two sides and the measure of the angle between them. So, the cosine law says that h is equal to:
[tex]h^2=f^2+g^2-2fg\cos (H)[/tex]Where h, f, and g are the sides of the triangle and H is the angle between f and g. Then, replacing f by 83 in, g by 11 in, and H by 60°, we get:
[tex]\begin{gathered} h^2=83^2+11^2-2(83)(11)\cos 60 \\ h^2=6889+121-913 \\ h^2=6097 \\ h=\sqrt[]{6097} \\ h=78.08 \end{gathered}[/tex]Therefore, the answer is 78 in.
A sales person is given a choice of two salary plants plan one is a weekly salary of 800 plus 3% commission of sales. plan 2 is a straight commission of 11% of sales. how much in sales must she make in a week for both plans to result in the same salary
SOLUTION:
Let us represent the amount in sales that we are to calculate with "x".
For both plans to result in the same salary, we have;
Plan 1 = Plan 2
[tex]800\text{ + 3 \% of x = 11 \% of x}[/tex][tex]\begin{gathered} 800\text{ + 0.03x = 0.11x} \\ 800\text{ = 0.11x - 0.03x} \\ 800\text{ = 0.08x} \\ \\ \frac{0.08x}{0.08}\text{ = }\frac{800}{0.08} \\ \\ x\text{ = 10,000} \end{gathered}[/tex]The amount in sales she must make in a week for both plans to result in the same salary is 10,000
Part AWhat is the mass in grams of 17.96 mL of acetone?Express your answer to four significant figures and include the appropriate units.mass = Value and UnitsPart BWhat is the volume in milliliters of 7.40 g of acetone?Express your answer to three significant figures and include the appropriate units.V = Value and Units
Part A:
Ans: Mass=14.11 g.
Given:
The volume of acetone, V=17.96 mL.
We know, the density of acetone, D=0.7857 g/mL.
The mass in grams of acetone is,
[tex]\begin{gathered} M=VD \\ =17.96\text{ mL}\times0.7857\text{ g/mL} \\ =14.11\text{ g} \end{gathered}[/tex]Therefore, mass of acetone in grasm rounded upto four significant figures is 14.11 g.
Mass=14.11 g.
Part B:
Ans: V=9.42 mL
Given
The mass of acetone, M=7.4 g.
We know, the density of acetone, D=0.7857 g/mL.
The volume in mL of acetone is,
[tex]\begin{gathered} V=\frac{M}{D} \\ =\frac{7.40\text{ g}}{0.7857\text{ g/mL}} \\ =9.42\text{ mL} \end{gathered}[/tex]Therefore, voulme of acetone in mL rounded upto three significant figures is 9.42 mL.
Volume, V=9.42 mL
Write the slope intercept form of the equation of the line through the given points.through: (-3,4) and (0,-5)
The equation of a line that passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging the values of the points given we have:
[tex]\begin{gathered} y-4=\frac{-5-4}{0-(-3)}(x-(-3)) \\ y-4=\frac{-9}{3}(x+3) \\ y-4=-3(x+3) \\ y-4=-3x-9 \\ y=-3x-9+4 \\ y=-3x-5 \end{gathered}[/tex]Therefore, the equation of the line is:
[tex]y=-3x-5[/tex]About 102 baby boys are born for every 100 baby girls. What is the simplified ratio of girls to boys?
Answer: 51/50
Step-by-step explanation: 102/100 = 51/50
because you divide both by 2 which is the answer
reduce to lowest term.4x-24/x^2-36
Explanation
[tex]\frac{4x+24}{x^2-36}[/tex]Step 1
factorize
[tex]\begin{gathered} a)\text{ 4x+24} \\ if\text{ we rewrite 24 as a product of its factors} \\ 4x+24=4x+(6\cdot4) \\ 4x+(6\cdot4)\rightarrow4\text{ is a common factor, so }\rightarrow4(x+6) \end{gathered}[/tex]and the denominator
we have
[tex]b)x^2-36[/tex]remember:When an expression can be viewed as the difference of two perfect squares, it can be factorized this way
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \end{gathered}[/tex]so, apply this .
[tex]\begin{gathered} x^{^{}2}-36=x^2-6^2=(x+6)(x-6) \\ so,\text{ } \\ x^{^{}2}-36=(x+6)(x-6) \end{gathered}[/tex]hence, the expression would be:
[tex]\frac{4x+24}{x^2-36}=\frac{4(x+6)}{(x+6)(x-6)}[/tex]Step 2
finally, eliminate the (x+6) ,so
[tex]\begin{gathered} \frac{4(x+6)}{(x+6)(x-6)}=\frac{4}{(x-6)} \\ \frac{4}{(x-6)} \end{gathered}[/tex]therefore, the lowest term is
[tex]\frac{4}{(x-6)}[/tex]I hope this helps you
do the following which line segments with the given lengths form a right triangle9.40,4111.60,6248.55,73
From the Pythagorean Theorem, if a, b and c are the sides of a right triangle, with c being the longest side, then:
[tex]a^2+b^2=c^2[/tex]Or, equivalently:
[tex]a^2+b^2-c^2=0[/tex]Find the corresponding values of the second expression for each case. If the result is equal to 0, then those are the sides of a right triangle:
9, 40 and 41
[tex]\begin{gathered} 9^2+40^2-41^2=81+1600-1681 \\ =1681-1681 \\ =0 \end{gathered}[/tex]Then, these are the sides of a right triangle.
11, 60 and 62
[tex]\begin{gathered} 11^2+60^2-62^2=121+3600-3844 \\ =3721-3844 \\ =-123 \end{gathered}[/tex]Then, these are not the sides of a right triangle.
48, 55 and 73
[tex]\begin{gathered} 48^2+55^2-73^2=2304+3025-5329 \\ =5329-5329 \\ =0 \end{gathered}[/tex]Then, these are the sides of a right triangle.
Therefore, from the given sets of numbers, the ones that correspond to lengths of sides of a rigtr triangle, are:
[tex]\begin{gathered} 9,40,41 \\ 48,55,73 \end{gathered}[/tex]Tell whether the ordered pair is a solution of y=-2x+1.
the expression is,
y = -2x + 1
a)
the point is (-4,9)
put x = -4 and y = 9
9 = -2(-4) + 1
9 = 8 + 1
9 = 9
both values are same
so this pair is satisfying the equation.
b) the point is (0.5,0)
put x = 0.5 and y = 0
0 = -2(0.5) + 1
0 = -1 + 1
0 = 0
so this pair is satisfying the equation.
c)
the point (1,3)
put x = 1 and y = 3
3 = -2(1) + 1
3 = -2 + 1
3 = -1
so this pair is not satisfying the equation.
fly) = -2Determine whether each relation is a function.+13. {(3,-8), (-9,1), (3, 2), (-4,1), (-11,-2)}for x = -534. Evaluate the function for the given value of x and write the input x andoutput f(x) as an ordered pair.
For x= -5, you have to replace the value in the function
[tex]f(-5)=\frac{2(-5)+1}{3}=-3[/tex]This means that when x=-5, y=-3, you can write it as pair (-5,-3)
What is the value of x?
Enter your answer in the box.
Answer:
x = 12
Step-by-step explanation:
Creating an equation.
The angles shown form a straight line making them supplementary.
Supplementary angles add up to 180 degrees.
Hence, the sum of the two angles = 180
So we can say that (10x - 20) + (6x + 8) = 180
Solving for x
(10x - 20) + (6x + 8) = 180
==> remove parenthesis
10x - 20 + 6x + 8 = 180
==> combine like terms
16x - 12 = 180
==> add 12 to both sides
16x = 192
==> divide both sides by 16
x = 12
Which statements about angles ABC and angles DEF is true
First, we identify the corresponding sides in the triangles. In the following image we can see corresponding sides in the same color:
For the triangles to be similar, there must a proportion between the corresponding sides.
A proportion is a number by which you multiply the sides of 1 triangle to get the sides of the other triangle. In this case, we can see that between the red sides there is a proportion of 2:
Also, between the blue sides there is a proportion of 2:
But, between the green sides, this proportion of 2 is not true, because 6x2 will be 12 and we have 14,
thus, the answer is:
They are not similar because corresponding sides are not proportional
VINCEуf(x)2724211815129630341 2 3Time (h)MathMLXFill in the missing blanks.MathMLXQuestion 11 point)
We are given a graph of the function f(x)
Where input x is the time in hours and the output is the number of boxes packed.
We are asked to find f(1)
f(1) is the output (number of boxes packed) when we substitute the input (x = 1)
Refer to the graph below
As you can see, at time x = 1 the output is 6 (number of boxes packed)
Therefore, f(1) = 6
Water Pressure ApplicationIn certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot,60at a depth of d feet below the surface, is given by the equation P = 13+11-If a scientific team uses special equipment to measures the pressure under water andfinds it to be 427 pounds per square foot, at what depth is the team making theirmeasurements?If the pressure is 427 pounds per square feet, the team is measuring atfeet below the surface.> Next Question0
Given that the model of taking the measurement is
[tex]P=13+\frac{6d}{11}[/tex]Explanation
To get the depth at which the team is taking their measurement if the pressure is 427 pounds per square foot, we will insert the value of the pressure into the model.
[tex]\begin{gathered} 427=13+\frac{6d}{11} \\ 427-13=\frac{6d}{11} \\ 414=\frac{6d}{11} \\ swap\text{ sides} \\ \frac{6d}{11}=414 \\ cross\text{ multiply } \\ 6d=414\times11 \\ 6d=4554 \\ d=\frac{4554}{6} \\ d=759feet \end{gathered}[/tex]Answer: 759 feet
I need help on this pleasefirst blank: a geometric, an arithmetic
This is geometric sequence and the common ratio is equal to 1/10
Explanation:The sequence: 200, 20, 2, ....
For the sequence to be arithmetic, we must have a common difference
For the sequence to be geometric. we msut have a common ratio
common difference = next term - previous term
when next term = 20, previous term = 20
common difference = 20 - 200 = -180
when next term = 2, previous term = 20
common difference difference = 2 - 20 = -18
The common difference are not the same. Hence, it is not an arithmetic sequence
common ratio = next term/previous term
when next term = 20, previous term = 200
common ratio = 20/200 = 1/10
when next term = 2, previous term = 20
common ratio = 2/20 = 1/10
Common ratio is the same.
Hence, it is a geometric sequence.
Completing the statement:
This is geometric sequence and the common ratio is equal to 1/10
Write the equation of the line in slope-intercept form.M = 1/8, y-intercept (0,4)
Answer:
[tex]y=\frac{1}{8}x+4[/tex]Explanation:
The information we have about the line is:
slope
[tex]m=\frac{1}{8}[/tex]Y- intercept is (0,4) here, the y-coordinate 4 is the point where the line crosses the y-axis and is the y-intercept usually represented by the letter b:
[tex]b=4[/tex]Now, the general equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]We substitute the known values:
[tex]y=\frac{1}{8}x+4[/tex]This is the equation for the line in slope -intercept form.
In circle C with mZBCD = 66 and BC = 15 units find area of sector BCD. Round to the nearest hundredth. с B D
ANSWER:
The area of sector BCD is 129.53 square units
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the area of the circle completely. That area would be for 360 °, therefore by means of a proportion we can calculate the area for the BDC sector.
The area of circle is:
[tex]\begin{gathered} A=\pi\cdot r^2 \\ \text{replacing} \\ A=3.14\cdot15^2 \\ A=706.5 \end{gathered}[/tex]Now, we calculate the area of the BDC sector by means of the following portion
[tex]\frac{706.5}{360}=\frac{x}{66}[/tex]Solving for x:
[tex]\begin{gathered} x=66\cdot\frac{706.5}{360} \\ x=129.525\cong129.53 \end{gathered}[/tex]Find the factors of f(x), given that x = 4 is a zero.f(x) = x3 − 7x2 + 2x + 40.
Answer:
Explanation:
Here, we want to get the factors of the given polynomial
From what we have:
[tex]\begin{gathered} x\text{ = 4} \\ \text{ Then x-4 is a factor} \end{gathered}[/tex]To get other factors, we have to divide the polynomial by the first factor obtained
Mathematically, we have that as follows:
[tex]\frac{x^3-7x^2\text{ + 2x +40}}{x-4}=x^2-9x\text{ + 20}[/tex]What we finally have to do is to factorize what was obtained
We have that as:
[tex]\begin{gathered} x^2-9x+20=x^2-4x-5x+20 \\ =x(x-4)-5(x-4) \\ =\text{ (x-5)(x-4)} \end{gathered}[/tex]So, we have the factors as (x-5)(x-4)(x-4)