To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:
I A bar of gold is 10 cm long,5 cm wide, and 7 cm high. What is it's volume?
Assuming the bar of gold has a rectangular form, its volume would be the product between all three dimensions.
[tex]A=10\operatorname{cm}\cdot5\operatorname{cm}\cdot7\operatorname{cm}=350\operatorname{cm}^3[/tex]Therefore, the volume is 350 cubic centimeters.
Dan paid three times as much as Greg for his dinner. (Translate the given situation into an equation. Pick the variable you use according to the context.
Let d represent Dan payment and let g represent Greg payment
"Dan paid three times as much as Greg for his dinner" can be represented as
d= 3g
Number 2
Let x represent the cost of Gym A and Y represent the cost of Gym B
Since Gym B cost twice as much as Gym A
Then y=2x
Number 3
Let d represent Diana's race and let c represent Calorine's race
Diana = 3 x Calorine
d=3c
What is the equation of the line shiwn graphed below
we are given the horizontal line. To determine the equation of this line let's remember that the equation of any horizontal line is of the form:
[tex]y=k[/tex]Where "k" is the point where the line touches the y-axis, in this case, the equation of the line is:
[tex]y=4[/tex]The circumference of the hub cap of a tire is 79.63 centimeters. Find the area of this hub cap. Us3.14 for a. Use pencil and paper. If the circumference of the hub cap were smaller, explain how twould change the area of the hub cap.The area of this hub cap is about square centimeters.(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearestthousandth as needed.)
Recall that the circumference of a circle is given by the following formula:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
We are given that:
[tex]79.63cm=2\pi r,[/tex]therefore:
[tex]r=\frac{79.63}{2*\pi}cm.[/tex]Now, the area of a circle is given by the following formula:
[tex]A=\pi r^2,[/tex]Therefore, the area of the hub cap is:
[tex]A=\pi *(\frac{79.63cm}{2})^2*\frac{1}{\pi^2}\approx505cm^2.[/tex]Answer:
[tex]\begin{equation*} 505cm^2. \end{equation*}[/tex]Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34minutes of calls is $25.92, and the remaining credit after 53 minutes of calls is $23.64. What is the remaining credit after 71 minutes of calls?
The remaining credit after 71 minutes is $21.48
To solve this, we can calculate the equation of the linear function that represents the remaining credit
x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation
34 min and $25.92 => (34,25.92)
53 min and 23.64 => (53,23.64)
the formula to calculate the slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12[/tex]now we know the slope, we can get the line euqation
[tex]y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}[/tex]Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.
for x=71 min:
[tex]y=-0.12(71)+30=-8.52+30=21.48[/tex]theremaining credit is $21.48.
Find the midpoint and distance on points (5,5) and (-1,3)
Given:
Two points (5, 5) and (-1, 3).
To find the midpoint and distance:
Using the midpoint formula,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{5-1}{2},\frac{5+3}{2}) \\ =(\frac{4}{2},\frac{8}{2}) \\ =(2,4) \end{gathered}[/tex]Thus, the mid-point formula is (2, 4).
Using the distance formula,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}[/tex]Thus, the distance between the two points is,
[tex]2\sqrt[]{10}units[/tex]write an equivalent ratio in simplest form of the ratio 1852 to 3690
926/1845
Explanation:To get the equivalent ratio in its simplest form, wefind the numbers common to both numbers.
[tex]\begin{gathered} \frac{1852}{3690} \\ \end{gathered}[/tex]2 is common to both, so we divide:
[tex]\begin{gathered} 1852\div\text{ 2 = 926 } \\ 3690\div2\text{ = 1845} \\ \frac{926}{1845} \end{gathered}[/tex]We check again if there is a number common to them
No number is common to both numerator and denominator asides 1
Hence, the simplest form is 926/1845
Find the value of 4² + 6².
Answer:
Step-by-step explanation:
52
Answer: The correct answer is 52
Step-by-step explanation:
4² + 6²
4*4 + 6*6
16 + 36 = 52
Elisa's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Let's define the next variables:
x: price of one senior ticket
y: the price of one child ticket
On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:
8x + 5y = 94 (eq. 1)
The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:
4x + 10y = 152 (eq. 2)
Multiplying equation 2 by 2, we get:
2(4x + 10y) = 2*152
8x + 20y = 304 (eq. 3)
Subtracting equation 1 to equation 3, we get:
8x + 20y = 304
-
8x + 5y = 94
------------------------
15y = 210
y = 210/15
y = 14
Substituting this result into equation 1:
8x + 5(14) = 94
8x + 70 = 94
8x = 94 - 70
8x = 24
x = 24/8
x = 3
Each senior citizen ticket cost $3 and each child ticket cost $14
which choices are equivalent to the expression below? check all that apply.[tex] 4\sqrt{6} [/tex]a. [tex] \sqrt{96} [/tex]b.[tex] \sqrt{24} [/tex]c. 96d. [tex] \sqrt{4} \times \sqrt{36} [/tex]e.[tex] \sqrt{16} \times \sqrt{6} [/tex]f.[tex] \sqrt{32} \times \sqrt{3} [/tex]
To find the equivalents of this expression we can write it another way:
[tex]4\cdot\sqrt[]{6}=\sqrt[]{16\cdot6}=\sqrt[]{4\cdot4\cdot6}=\sqrt[]{2\cdot2\cdot2\cdot2\cdot2\cdot3}[/tex]We can group the 2's and 3 however we want and the expression will be the same.
If we do the multiplication of all of them (or 16 times 6, is the same) we get that it's 96, so option a is one equivalent
[tex]\sqrt[]{96}[/tex]Then from the second term we have that another equivalent is
[tex]\sqrt[]{16}\cdot\sqrt[]{6}[/tex]Because the square root can be distributed into the product. So option e is equivalent
If we multiply all the 2's we get that it's 32, so another equivalent is:
[tex]\sqrt[]{32}\cdot\sqrt[]{3}[/tex]Option f is equivalent
A Scientist uses 10 grams of carbon evrey 15 mins during an experiment. If the experiment lasted 3 hours, how many total kilograms of carbon did they use
We know that
• A scientist uses 10 grams every 15 minutes.
To find the kilograms used in 3 hours, first, we transform 10 grams into kilograms
[tex]\frac{10}{1000}kg=0.01\operatorname{kg}[/tex]Then, we use the following proportion
[tex]\frac{0.01\operatorname{kg}}{x}=\frac{15\min }{180\min }[/tex]Because 3 hours is equivalent to 180 minutes. Let's solve for x
[tex]\begin{gathered} x=\frac{180\cdot0.01}{15} \\ x=0.12 \end{gathered}[/tex]Hence, the total kilograms are 0.12.What is the parallel slope to this equation? f(x)=-5x + 6
Remember the equation of a line with slope m and y-intercept b:
[tex]y=mx+b[/tex]Which can be expressed in terms of functions by replacing y=f(x)
[tex]f(x)=mx+b[/tex]Any line with the same slope will be parallel to that equation.
By comparing with:
[tex]f(x)=-5x+6[/tex]We can know that its slope is equal to -5.
Since the "parallel slope" is just the slope, then
Which of the following is not a step in solving the equation 3/x = 8/7 (1) Divide both sides of the equation by 8(2) Use cross products to write the equation 3.7 =8x(3) Divide both sides of the equation by 3(4) Rewrite 3.7 as 21
Let's solve the equation:
3/x = 8/7
8x = 3 * 7 Cross product
8x = 21 Rewrite 3 * 7 as 21
Dividing both sides by 8:
8x/8 = 21/8
x = 2.625
As you can see, we do not follow step 3. Divide both sides of the equation by 3.
20 points 2. Krisstopher was driving to Houston from Pasadena, he drives a 2 3/4 miles and stops for a break. He then drives 5 1/2 miles to reach his destination. What distance in miles did Krisstopher travel to reach his final destination. 81/4 miles 71/2 miles 81/2 miles 6 1/3 miles Clear selection
Add 2 + 3/4 + 5 + 1/2
this gives (2+5) + ( 3/4+2/4)
7 + 5/4 = 8.25
In the figure, LMN is congruent to QRS.What is the value of x and y?
If they are congruent, then;
3x + 5 = 2x + 10
collect like term
3x - 2x = 10 - 5
x = 5
Similarly,
y + 6 = 2y - 12
collect like term
2y - y = 6 + 12
y = 18
If h(x)=-3x and g(x)=2x-1 what input value would make h(x)=12?
The question gives the function h(x) as
[tex]h(x)=-3x[/tex]To find the value that will make the function 12, we equate the function to 12, such that
[tex]-3x=12[/tex]Solving to get x, we have
[tex]\begin{gathered} x=\frac{12}{-3} \\ x=4 \end{gathered}[/tex]Therefore, h(x) = 12 when x = 4.
I would like someone to help me so I can understand what to do. Pls anyone
we have that
2 cups in a pint
2 pints in a quart
4 quarts in a gallon
so
4 cups in 2 pints
4 cups in a quart
16 cups in 4 quarts
16 cups in a gallon
and
we have
3 parts red and 5 parts yellow
3 parts +5 parts=8 parts
8 parts=1 gallon
red paint fraction is 3/8 gallon
yellow paint fraction is 5/8 gallon
Remember that
I need 16 cups for a gallon
Apply proportion
16/1=x/(3/8)
x=(3/8)16
x=6 cupsConsider the following graph. Explain why it is possible to find an Euler circuit for this graph. Then, using Fleury's algorithm, identify and draw an Euler circuit starting with point A and choosing the first edge as A to F. Show all work using the required method. Draw the graph properly. (If you choose not to draw on my graph, then draw a LARGE graph on your paper.)
The Euler circuit for the graph using Fleury's algorithm is attached below.
The following steps are to be used to form the circuit.
Of the three edges coming from vertex "2" should I choose? We avoid choosing the edge "2-3" because it is a bridge and we cannot return to "3".
Any of the two remaining edges is ours to choose. Let's say we choose "2-0." By eliminating this edge, we can travel to vertex "0."
We pick the one edge from vertex "0" that is present, remove it, and then move to vertex "1." The Euler tour changes to "2-0 0-1."
We take the lone edge from vertex "1," delete it, and then move to vertex "2." The Euler tour is now "2-0 0-1 1-2."
Once more, vertex 2 has just one edge, so we pick it, remove it, and continue on to vertex 3.
Hence we get the required circuit.
The term "Eulerian graph" has two different meanings in graph theory. One interpretation applies to a graph with an Eulerian circuit, whereas the other applies to a graph where each vertex has an even degree. These definitions apply to linked graphs.
To learn more about Euler circuit visit:
https://brainly.com/question/22089241
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Solve 9abs(3n-2) + 6 > 51 and graph on the number line
Solving the inequality,
[tex]\begin{gathered} 9\lvert3n-2\rvert+6>51 \\ \rightarrow9\lvert3n-2\rvert>45 \\ \rightarrow\lvert3n-2\rvert>5 \end{gathered}[/tex]Remember that if
[tex]\lvert u\rvert>a,a>0\Rightarrow u<-a\text{ or }u>a[/tex]This way, we get:
[tex]\begin{gathered} 3n-2<-5\rightarrow3n<-3\rightarrow n<-1 \\ 3n-2>5\rightarrow3n>7\rightarrow n>\frac{7}{3} \end{gathered}[/tex]As an interval, we get:
[tex]\: \mleft(-\infty\: ,\: -1\mright)\cup\mleft(\frac{7}{3},\: \infty\: \mright)[/tex]In the number line, we get:
Last week you worked 28 hours, and earned $266. What is your hourly pay rate? $ per hour Give your answer in dollars and cents (like 5.50)
1) Gathering the data
Last week
28 worked hours = $266
What is your hourly pay rate?
2) To find out that, let's set a proportion
Worked hours $
28------------------------ 266
1--------------------------- x
Let's use the fundamental property of a proportion that allows us to cross multiply the ratios of that proportion
So the hourly pay rate is approximately $11.08 per hour.
Can you please help me with this question D and E
Solution
Part d
T= -2ºC, V=15 km/hr
We can convert to F and mi/h like this:
T= 1.8*(-2)+ 32= 28.4ºF
Ms= As/0.62= 15 km/hr /0.62= 24.19 mi/hr
Replacing we have:
[tex]WC=35.74+0.6215\cdot(28.4)-35.75(24.19^{0.16})+0.4275(28.4)(24.19^{0.16})[/tex]Solving we got:
[tex]WC=35.74+17.651-59.519+20.213=14.08[/tex]Rounded to one decimal we got:
14.1
Part e
T= 10ºC = 1.8(10)+ 32=50ºF
Ms = 34 km/hr
Ms= As/0.62= 34 km/hr/ 0.62= 54.84 mi/hr
Replacing we got:
[tex]WC=35.74+0.6215\cdot(50)-35.75\cdot(54.84^{0.16})+0.4275(50)(54.84^{0.16})[/tex][tex]WC=35.74+31.075-67.847+40.566=39.53[/tex]Rounded to the nearest tenth we got:
39,5
Althought the reported temperature is 50 ºFahrenheit, because of wind it feels like 39.5 Fahrenheit
solve the given system of equations2y=x+93x-6y=-15
Answer:
No solutions
Explanation:
The given system of equations is
2y = x + 9
3x - 6y = -15
To solve the system, we first need to solve the first equation for x, so
2y = x + 9
2y - 9 = x + 9 - 9
2y - 9 = x
Then, replace x = 2y - 9 on the second equation
3x - 6y = -15
3(2y - 9) - 6y = -15
3(2y) + 3(-9) - 6y = -15
6y - 27 - 6y = -15
-27 = -15
Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.
Joy has $68,020 in a savings account that earns 13% annually. The interest is not compounded. How much will she have in 5 years?
A = P + I
A is the new value
P is the initial value
I is the interest
I = PRT
R is the rate in decimal
T is the time
Joy has $68020
P = 68020
The account earns 13% annually
R = 13% = 13/100 = 0.13
The time is 5 years
T = 5
Let us find I, then A
I = 68020(0.13)(5)
I = 44213
Now let us find A
A = 68020 + 44213
A = $112233
She has $112233 in 5 years
Section 1- Question 10Use the quadratic formula to solve the following equation:4m2-7m +2=57+√97A87+√17B87 + √1C87+√-63D8
The Solution:
Given:
[tex]4m^2-7m+2=5[/tex]We are required to use the Quadratic Formula to solve the equation above.
[tex]\begin{gathered} 4m^2-7m+2-5=0 \\ 4m^2-7m-3=0 \end{gathered}[/tex]The Quadratic Formula is:
[tex]m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In this case:
[tex]\begin{gathered} a=4 \\ b=-7 \\ c=-3 \end{gathered}[/tex]Substitute:
[tex]m=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-3)}}{2(4)}[/tex][tex]m=\frac{7\pm\sqrt{49+48}}{8}=\frac{7\pm\sqrt{97}}{8}[/tex]Therefore, the correct answer is [option A]
An arch is in the shape of a parabola. It has a span of 96 feet and a maximum height of 8 feet.Find the equation of the parabola. ______________Determine the distance from the center at which the height is 2 feet. ___________
We know the equation of a parabola can be written as
y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros
y = a ( x - 48) ( x - -48)
y = a ( x-48) (x+48)
Now when x = 0 y = 8
8 = a ( 0-48) ( 0+48)
8 = a (-2304)
-8/2304 = a
-1/288 = a
y = -1/288 ( x-48) (x+48)
This is the equation for the parabola
Now let y = 2
2 = -1/288 ( x-48) (x+48)
Multiply each side by -288
-576 = (x-48)(x+48)
FOIL
-576 = x^2- 2304
ADD 2304 to each side
1728=x^2
Take the square root of each side
24 sqrt(3) = x
24 sqrt(3) ft
41.569 ft
Use the graph to respond to the questions. 6a. What is the height of the ball before its thrown? b. Approximately how high in the air did the ball go? C. NWAOOOOO INW Approximately long did it take the ball to reach the max height? d. How long was the ball in the air? 34(0.3) 2 e. (-0.2.0) -2 -1 (3.0) t 3 4 What does the point (3, 0) tell us about this situation? 1 INV
Given data:
The given graph is shown.
a)
The initial height of the ball is 3 units.
b)
The maximum height of the ball is approx 12.5 units.
c)
The time taken by the ball to reach maximum height is 1.5 units.
d)
The time ball was in air is 3 units.
e)
The point (3,0) denoted the coordinate of time is 3 when height is zero.
In right triangle XYZ, the hypotenuse measures 14 inches and one leg measures 10 inches. Find the length of the other leg. Show your work and write your answer in simplest radical form.
As per given by the question,
There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.
Now,
First draw the triangle XYZ.
Now,
From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.
So,
First leg z is 10, then find the value of second leg x.
Then,
To find the value of second leg, here use pythagoras theorem.
So,
From the pythagoras theorem;
[tex]XY^2+YZ^{2^{}^{}}=XZ^2[/tex]Now,
[tex]\begin{gathered} XY^2+YZ^2=XZ^2 \\ 10^2+x^2=14^2 \\ 100+x^2=196 \\ x^2=196-100 \\ x^2=96 \end{gathered}[/tex]Then,
[tex]\begin{gathered} x^2=96 \\ x=\sqrt{96}^{} \\ x=9.79 \end{gathered}[/tex]Hence, the length of the other leg is 9.79.
a. Make a scatter plot of the data in the table below.b. Does it appear that a linear model or an exponential model is the better fit for the data?
a) Option C
b) A linear model
Explanation:To determine the correct plot from the options, we trace the x and y values given
Option A:
When x = 5, y = 1
when x = 6.6, y = 2
We see this is exact opposite of the values in the given table
Option B:
when x = 5, y = 5
when x = 6.6, y = 6.6
This is also different from the given values in the table
Option C:
when x = 1, y = 5
when x = 2, y = 6.6
when x = 3, y = 8.4
This is the same as the given values in the table.
Hence, the correct scatter plot is option C
We need to check if the points are linear:
[tex]\begin{gathered} u\sin g\text{ any two points on the table,} \\ \text{rate = }\frac{6.6\text{ - 5}}{2-1}\text{ = 1.6/1 = 1.6} \\ \text{rate = }\frac{8.4\text{ - 6.6}}{3-2}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{10.2\text{ - 8.4}}{3\text{ - 2}}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{12-10.2}{4-3}\text{ = 1.2/1 = 1.2} \end{gathered}[/tex]A linear model fit the data
A triangle has vertices on a coordinate grid at D(-5, -2), E(-5,4), andF(-1,4). What is the length, in units, of DE?
To find the length of DE,
Here D = (-5,-2) and E = (-5,4).
Hence the distance is given by
[tex]DE=\sqrt[]{(-5+5)^2+(4+2)^2}[/tex]On simplifying,
[tex]\begin{gathered} DE=\sqrt[]{6^2} \\ DE=6 \end{gathered}[/tex]Hence the length of DE is 6 units
find the percent notation for 0.376
To convert a decimal into a percentage we have to multiply the decimal by 100, as follows:
[tex]0.376\cdot100=37.6\text{ \%}[/tex]0.376 is equivalent to 37.6 %