We can do as follow s
centimeters km
4 5
x 10
which is the same as saying that 4 centimeters are 5km, so x centimeters are 10 km. We want to find the value of x. To do so, we use the fact that this is a proportion, so it must happen that
[tex]\frac{4}{5}\text{ = }\frac{x}{10}[/tex]So if we multiply on both sides by 10, we get
[tex]x\text{ = }\frac{4_{}\cdot10}{5}\text{ = }\frac{40}{5}=8[/tex]So 8 cm represent 10 km.
Estimate a 15% tip on a dinner bill of $89.14 by first rounding the bill amount to the nearest ten dollars. 1
Let:
C = Cost of the dinner
T = Tip
r = Percentage of the tip
[tex]\begin{gathered} C=89 \\ r=0.15 \\ T=C\cdot r \\ T=89\cdot0.15 \\ T=13.35 \end{gathered}[/tex]Answer:
$13.35
base: 4 in. area: 22 in
Area of a triangle
The area of a triangle of base length b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]We are given the area as A=22 square inches and the base length b=4 inches. We are required to find the height.
Solving for h:
[tex]h=\frac{2\cdot A}{b}[/tex]Substituting:
[tex]h=\frac{2\cdot22in^2}{4in}=\frac{44in^2}{4in}=11in[/tex]The height is 11 inches
How many different ID cards can be made if there are four digits can be used more than once? What if digits can be repeated?
ANSWERS
1) 5,040
2) 10,000
EXPLANATION
1) If we have 10 numbers (from 0 to 9), the ID cards have 4 of them and the digits do not repeat, we have 10 numbers to choose from for the first digit, 9 numbers for the second digit, 8 numbers for the third digit, and 7 numbers for the fourth digit. So,
[tex]10\cdot9\cdot8\cdot7=5,040[/tex]Hence, there are 5,040 different ID cards that can be made if no digit can be used more than once.
2) In this case, the numbers can be repeated, so for each of the four digits we have 10 options to choose from,
[tex]10\cdot10\cdot10\cdot10=10^4=10,000[/tex]Hence, there are 10,000 different ID cards that can be made if digits can be repeated.
Find the circumference of the circle. Give the exact circumference and then an approximation. Use i 3.14. diamater of 17cm
To find the circumference of the circle, we will follow the steps below
Formula for the circumference of a circle is
C = 2 π r
where C = circumference of the circle
π is a constant
r is the radius of the circle
From the question, diameter is 17 cm
radius is half the diameter
That is:
radius = 17/2 = 8.5 cm
π = 3.14
Substituting the parameter in the formula given will yield
C = 2 x 3.14 x 8.5 cm
C =53.38 cm
The exact circumference is 53.38 cm
The circumference is approximately 53 cm to the nearest whole number
Solve this equation.
2/3x−1/5x=x−1
A. 1 13/15
B. 1 7/8
C. 1 7/15
D. 7/8
Answer:
your answer would be c 1 7/15 tell me if I'm wrong
Step-by-step explanation:
Answer:
B 1 7/8
Step-by-step explanation:
2/3x−1/5x=x−1
1. multiply both sides by 15
10x-3x=15x-15
2. collect like terms
7x = 15x -15
3. move the variable to the left
7x-15x=-15
4. collect like terms
-8x = -15
5. divide both sides by -8
x=15/8
or
1 7/8
A rectangular garden covers 690 square meters. The length of the garden is 1 meter more than three times its width. Find the dimensions of the gardenThe length isand the width is01(Type whole numbers.)
Ok, so
We got the situation here below:
We know that the area of the garden is 690 m².
So, we got that the height (1+3x) multiplied by the width (x), should be equal to 690.
[tex]\begin{gathered} (1+3x)(x)=690 \\ x+3x^2=690 \end{gathered}[/tex]We have to solve:
[tex]3x^2+x-690=0[/tex]If we solve this quadratic equation, we obtain two solutions.
One of both solutions is negative, so we will not use it.
The second one is positive and equals to 15. So, x=15.
Now that we know that x=15, we replace:
x, (Width) is equal to 15 meters.
1+3x (Length), is equal to 46 meters.
Therefore, these are the dimensions of the garden.
Width: 15 meters
Lenght: 46 meters.
According to the graph of H(w) below, what happens when w gets very large?H)5.6.20.00)A. H(w) gets very large.B. H(w) approaches a vertical asymptote.C. H(w) equals zero.D. H(w) gets very smallSUBMIT
Considering the graph H(w),
As w gets larger, H(w) continues to approach a horizontal asymptote.
Hence, H(w) gets very small.
Therefore, the correct option is option D
Find an equation for the line that’s passes through the following points shown in the picture. ( Please fins answer in timely answer very brief explaination :) )
The general equation of line passing through the points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passing thgrough the point (-6,-1) and (2,5).
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{2-(-6)}(x-(-6)) \\ y+1=\frac{6}{8}(x+6) \\ y+1=\frac{3}{4}x+\frac{9}{2} \\ y=\frac{3}{4}x+\frac{9}{2}-1 \\ =\frac{3}{4}x+\frac{7}{2} \end{gathered}[/tex]So equation of line is y = 3/4x + 7/2.
Would to ask question about composite shape perimeter. Having trouble sending drawing
First let's split the shape in two, like this:
As you can see, now we have a triangle on the right, the length of the base of this triangle is the length of the bottom side of the original figure minus the lenght of the top side of the original figure, we can find it like this:
b = 100 ft - 70 ft = 30 ft
The height of the triangle "h" equals the height of the rectangle, which is 50 ft, then we can find the length of the missing side a (the hypotenuse of the triangle) by means of the Pythagorean theorem, like this:
[tex]\begin{gathered} a^2=h^2+b^2 \\ a=\sqrt[]{h^2+b^2} \end{gathered}[/tex]Where "a" is the length of the hypotenuse, "h" is the height and "b" is the base. By replacing 30 for b and 50 for h, we get:
[tex]a=\sqrt[]{50^2+30^2}=\sqrt[]{2500+900}=10\sqrt[]{34}=58.3[/tex]Then the length of the missing side of the composite shape is around 58.3 ft:
Now that we know the lengths of the sides of this figure we can calculate its perimeter by summing them up, like this:
Perimeter = 70 + 50 + 100 + 58.3 = 278.3
The perimeter of this plot of land equals 278.3 ft
Can you please help me
The area for a trapezoid can be found through the fromula
[tex]A=\frac{1}{2}(B+b)\cdot h[/tex]in which B represents the major base, b the minor base and h the height of the trapezoid.
According to this the area of the trapezoid is going to be:
[tex]\begin{gathered} A=\frac{1}{2}(37+22)\cdot23 \\ A=\frac{1}{2}(59)23 \\ A=\frac{1357}{2}cm^2 \\ A=678.5cm^2 \end{gathered}[/tex]Need answer to pictured problem! The answer should be in reference to trig identities
Step 1. The expression that we have is:
[tex]cos^2(5x)[/tex]and we need to find the equivalent expression.
Step 2. The trigonometric identity we will use to solve this problem is:
[tex]cos^2A=1-sin^2A[/tex]In this case:
[tex]A=5x[/tex]Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:
[tex]cos^2(5x)=\boxed{1-sin^2(5x)}[/tex]This is shown in option d).
Answer:
[tex]\boxed{d)\text{ }1-s\imaginaryI n^2(5x)}[/tex]For the rotation -1046°, find the coterminal angle from 0° < O < 360°, the quadrant and the reference angle.
Solution
Step 1
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Step 2
The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.
Coterminal angle
[tex]\begin{gathered} Coterminal\text{ angle = -1046 + 3}\times360 \\ Coterminal\text{ angle = -1046 + 1080} \\ Coterminal\text{ angle = 34} \end{gathered}[/tex]Quadrant = 1st quadrant
Reference angle
0° to 90°: reference angle = angle
Reference angle = 34
Final answer
Find the value of r so that the line through (-4, r) and (-8, 3) has a slope of -5.
The value of r is -17.
Given,
Points (-4,r) and (-8,3)
slope=-5
Let
A(x1,y1)=(-4,r)
B(x2,y2)=(-8,3)
To find 'r' use formula,
[tex]slope=\frac{y2-y1}{x2-x1}\\ \\-5=\frac{3-r}{-8-(-4)}\\\\-5=\frac{3-r}{-8+4}\\\\-5=\frac{3-r}{-4}\\\\20=3-r\\\\20-3=-r\\\\17=-r\\\\-17=r[/tex]
Thus, the value of r is -17.
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how would I simplify 3x^3-12x÷3x^3+6x^2-24x?
To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher2025465030 35 40Salan (thousands of S)If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
Const Workers , Teachers
Median salary of const Worker =45
Median salary of teacher = 40
Then, they are making more than 100% of teachers
Answer is
100%
Translate the following into algebraic equation and solve: Twice the sum of a number and five is equal to 40.
Let:
x = Unknown number
Twice the sum of a number and five:
[tex]2(x+5)[/tex]Is equal to 40:
[tex]2(x+5)=40[/tex]Solve for x:
Expand the left hand side using distributive property:
[tex]2x+10=40[/tex]Subtract 10 from both sides:
[tex]2x=30[/tex]Divide both sides by 2:
[tex]x=15[/tex]Select the point that satisfies y≤ x²-3x+2.
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
To check for the equation, substitute each point into the inequality and check validity of solution
A (4, 4)
4 ≤ 16 - 12 + 2 ⇒ 4 ≤ 6 → True hence valid solution
B (3, 3 )
3 ≤ 9 - 9 + 2 ⇒ 3 ≤ 2 → False hence not valid
C (1, 1 )
1 ≤ 1 - 3 + 2 ⇒ 1 ≤ 0 → False hence not valid
D (2, 2 )
2 ≤ 4 - 6 + 2 ⇒ 2 ≤ 0 → False hence not valid
Therefore, the point A (4, 4) satisfies the equation y≤ x²-3x+2.
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Disclaimer: The question given by you is incomplete, the complete question is
Select the point that satisfies y ≤ x² - 3x + 2.
A. (4, 4)
B. (3, 3)
C. (1, 1)
D. (2, 2)
Answer:
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
Step-by-step explanation:
Consider the function g. 9(-) = 6() For the x-values given in the table below, determine the corresponding values of g(x) and plot each point on the graph.. -1 0 1 2 g(x) Drawing Tools Click on a tool to begin drawing * Delete Undo Reset Select Point 14 13 12 11 10 9 00 reserved.
we have the function
[tex]g(x)=6(\frac{3}{2})^x[/tex]Find out the value of function g(x) for each value of x
so
For x=-1
substitute the value of x in the function g(x)
[tex]\begin{gathered} g(-1)=6(\frac{3}{2})^{-1} \\ g(-1)=6(\frac{2}{3}) \\ g(-1)=4 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} g(0)=6(\frac{3}{2})^0 \\ g(0)=6 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} g(1)=6(\frac{3}{2})^1 \\ g(1)=9 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} g(2)=6(\frac{3}{2})^2 \\ g(2)=13.5 \end{gathered}[/tex]using a graphing tool
plot the different points
so
we have
(-1,4)
(0,6)
(1,9)
(2,13.5)
see the attached figure to better understand the problem
please wait a minute
if you shift the function F(x) = log10 x up four units, what is the new function, G(x)?*PHOTO*
Given:
The function
[tex]F(x)=log_{10}x[/tex]Required:
If you shift the function up for four units. What is the new function G(x)?
Explanation:
We have that function is shifting up for four units that is on y axis.
So, the new function will look like
[tex]G(x)=log_{10}x+4[/tex]Answer:
option A is correct.
Directons: Write each equation in slope-intercept form. Identify the slope and y-intercept.
Given:
The equation is x - y = -8.
Explanation:
The slope intercept form of linear equation is,
[tex]y=mx+c[/tex]Here, m is slope and c is y-intercept.
Simplify the given equation to obtain in slope-intercept form.
[tex]\begin{gathered} x-y=-8 \\ y=x+8 \\ y=1\cdot x+8 \end{gathered}[/tex]So slope of line is m = 1 and y-intercept is 8.
Answer:
Equation in slope ntercept form: y = x + 8
Slope: 1
Y-intercept: 8 OR (0,8)
The organizer of a conference is selecting workshops to include. She will select from 5 workshops about genetics and 8 workshops about ethics. In how many ways can she select 6 workshops if fewer than 3 must be about genetics?
We have the following:
- 5 possible about genetics and need fewer than 3 (so it can be 0, 1 or 2).
- 8 about ethics
- want to select 6 in total.
We can calculate all the possible ways by doing it in three situations:
1 - From the 6, 0 will be genetics and 6 will be ethics
2 - From the 6, 1 will be genetics and 5 will be ethics
3 - From the 6, 2 will be genetics and 4 will be ethics
All of these will have to add up to find the total number of ways.
1 - 0 genetics, 6 ethics:
Since no genetics will be chosen, we can choose any 6 from the 8 possible about ethics, that is, we have a situation of "8 choose 6"
The equation for a situation "n choose k" and the number of ways in it is:
[tex]n=\frac{n!}{k!(n-k)!}[/tex]So, if we have "8 choose 6":
[tex]n_1=\frac{8!}{6!(8-6)!}=\frac{8\cdot7\cdot6!}{6!2!}=\frac{8\cdot7}{2}=4\cdot7=28[/tex]So, in this first we have 28 ways.
2 - 1 genetics, 5 ethics:
Here, we will have one equation for each and the total number of ways will be the multiplication of both.
For genetics, we have to pick 1 from 5, so "5 choose 1":
[tex]\frac{5!}{1!(5-1)!}=\frac{5\cdot4!}{4!}=5_{}[/tex]For ethics, we have to pick 5 from 8, so "8 choose 5":
[tex]\frac{8!}{5!(8-5)!}=\frac{8\cdot7\cdot6\cdot5!}{5!3!}=\frac{8\cdot7\cdot6}{3\cdot2}=8\cdot7=56[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_2=5\cdot56=280[/tex]3 - 2 genetics, 4 ethics:
Similar to the last one.
For genetics, we have to pick 2 from 5, so "5 choose 2":
[tex]\frac{5!}{2!(5-2)!}=\frac{5\cdot4\cdot3!}{2\cdot3!}=\frac{5_{}\cdot4}{2}=5\cdot2=10[/tex]For ethics, we have to pick 4 from 8, so "8 choose 4":
[tex]\frac{8!}{4!(8-4)!}=\frac{8\cdot7\cdot6\cdot5\cdot4!}{4!4!}=\frac{8\cdot7\cdot6\cdot5}{4\cdot3\cdot2}=2\cdot7\cdot5=70[/tex]So, the total number of ways is the multiplicatinos of them:
[tex]n_3=10\cdot70=700[/tex]Now, the total number of ways is the sum of all these possibilities, so:
[tex]\begin{gathered} n=n_1+n_2+n_3 \\ n=28+280+700 \\ n=1008 \end{gathered}[/tex]So, the total number of ways is 1008.
In quadrilateral ABCD, MZA = 72, mZB = 94, and m2C = 113. What is m2D?
First, let's picture the problem
Let's label the angle D as x
Remember that the sum of angles in a quadrilateral is 360
[tex]\begin{gathered} 72^0+94^0+113^0+x=360^{\square} \\ x=81^0 \\ m\angle D=81^0 \end{gathered}[/tex]Admission to the fair costs $6.00. Each ride costs you$0.50. You have $22.00 to spend at the fair on rides and admission. Express the number of tickets you can buy as an inequality.
Let:
x = Number of rides
Total money spent = $6.00 + $0.50x
Since you have $22.00 to spend at the fair on rides and admission:
[tex]\begin{gathered} 6+0.5x\leq22 \\ \text{solving for x:} \\ 0.5x\leq22-6 \\ 0.5x\leq16 \\ x\leq\frac{16}{0.5} \\ x=32 \end{gathered}[/tex]100 POINTS!! I NEED THIS KNOWW!!!!The number line shows the distance in meters of two birds, A and B, from a worm located at point X:A horizontal number line extends from negative 3 to positive 3. The point labeled as A is at negative 2.5, the point 0 is labeled as X, and the point labeled B is at 2.5.Write an expression using subtraction to find the distance between the two birds.Show your work and solve for the distance using additive inverses.
The expression used to represent the distance between the two birds on the number line is 2.5 - (-2.5) and the distance is 5 units.
Let us represent the bird A is sitting at one point on the number line.
Bird B is sitting at another point.
Both of them are at a an equal distance from a worm which is at the position O which is the origin.
Now it is given that A and B are at the positions of the number line marked 2.5 and -2.5
Now the distance between A and B can be calculated by finding the distance between A and O and adding the additive inverse to it to get the distance between O and B using subtraction.
AO = 2.5 - 0 = 2.5 units
The additive inverse of this is -2.5 units.
Therefore the distance AB :
= AO - BO
= 2.5 -(-2.5)
=2.5 +2.5
=5 units.
Hence they are at a distance of 5 units from each other.
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what's the solution to this system
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
so
In this problem
the intersection point is (-2,2)
therefore
the solution is (-2,2)3andLet's compare38ロ<ロ>=First, write the fractions with the same denominator.х?138-138Then, use <, = , or > to compare the fractions.m 100
To rewrite the fractions as fractions with the same denominator we have to determine the minimum number greater than 8 and 3 that can be exactly divided by 8 and 3 (LCM). Notice that the LCM of 8 and 3 is
[tex]24=8\cdot3.[/tex]Because:
[tex]\begin{gathered} 8=2\cdot2\cdot2, \\ 3=3. \end{gathered}[/tex]Therefore, we rewrite the given fractions as:
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]From the above fractions, we get that:
[tex]\frac{3}{8}>\frac{1}{3}\text{.}[/tex]Answer:
a)
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]b)
[tex]\frac{1}{3}<\frac{3}{8}\text{.}[/tex]Find the future value$4013 invested for 9 years at 4.1% compounded quarterly.
We are to find the future value
The future value can be calculated using
[tex]FV=PV(1+\frac{r}{100\alpha})^{n\alpha}[/tex]From the given information
PV = $4013
r = 4.1
n = 9 years
Since the investment is compounded quarterly then
α = 4
By substituting these values we get
[tex]FV=\text{ \$4013(1 }+\frac{4.1}{100(4)})^{9(4)}[/tex]Simplifying the equation we get
[tex]\begin{gathered} FV=\text{ \$}4013(1\text{ }+\frac{4.1}{400})^{36} \\ FV=\text{ \$}4013(1\text{ }+0.01025)^{36} \\ FV=\text{ \$}4013(1.01025)^{36} \\ FV=\text{ \$}4013(1.44436) \\ FV=\text{\$}5793.17 \end{gathered}[/tex]Therefore,
The Future Value is $5793.17
IIIDECIMALSRounding decimalsRound 0.434 to the nearest hundredth.0x
Answer
Explanation
In rounding off numbers, when the number after the required level of precision is less than 5, we round it down. But if that number is 5 or more, we round it up.
the points (v,-3) and (8,5) fall on a line with a slope of -8. what is the value of v?
The slope m is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \text{Where:} \\ (x1,y1)=(v,-3) \\ (x2,y2)=(8,5) \\ m=-8 \\ so\colon \\ -8=\frac{5-(-3)}{8-v} \\ \text{solve for v:} \\ -8(8-v)=5+3 \\ -64+8v=8 \\ 8v=72 \\ v=\frac{72}{8} \\ v=9 \end{gathered}[/tex]Simplify Remove all perfectsquares from inside the square root. v52
The square root we need to simplify is:
[tex]\sqrt[]{52}[/tex]We need to find an expression equivalent to 54 which includes a perfect square number (4, 16, 25, etc,...)
In this case, we note that:
[tex]52=4\times13[/tex]We substitute this in the square root:
[tex]\sqrt[]{4\times13}[/tex]And we calculate the square root of 4 which is 2, and that goes outside the square root:
[tex]2\sqrt[]{13}[/tex]we left the number 13 inside the square root because the square root of 13 is not exact.
Answer:
[tex]2\sqrt[]{13}[/tex]