Given:
(y) varies directly as (z) and inversely as (x):
[tex]\begin{gathered} y\propto z;y\propto\frac{1}{x} \\ \\ so,y\propto\frac{z}{x} \end{gathered}[/tex]so, the equation will be:
[tex]y=\frac{kz}{x}[/tex]Where: k is the proportionality constant
Graph the line from the table you found in (5). Remember to scale and label your axes!
We are asked to draw a line by using the values given in the table.
Let x denotes the first column of values and y denotes the second column of values
So, the (x, y) ordered pairs are
(0, 4), (2, 0), (1, 2), (3, -2), (-1, 6)
Let us plot these points on the graph then we would draw a line connecting these points.
Therefore, this is how the graph of the line looks like.
The y-intercept of the line is the point where the line intersects the y-axis.
From the above graph, we see that the line intersects the y-axis at y = 4
Therefore, the y-intercept of the line is 4
The slope of the line is given by
[tex]slope=\frac{\text{rise}}{\text{run}}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
As you can see, we selected two points on the line. (you may select any two points)
The two points are (2, 0) and (3, -2)
The vertical distance is -2 (negative because it is going down) and the horizontal distance is 1
[tex]slope=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}=-2[/tex]Therefore, the slope of the line is -2
In rectangle ABCD, the diagonals intersect at E. If m angle∠AEB= 3x and m angle∠DEC= x+80, find m angle∠AEB and m angle∠EBA.
Since the angles∠ AEB and ∠DEC are vertically opposite angles, they are congruent, so we have:
[tex]\begin{gathered} 3x=x+80 \\ 2x=80 \\ x=40 \end{gathered}[/tex]So the measure of angle ∠AEB is:
[tex]\begin{gathered} \angle\text{AEB}=3x \\ \angle\text{AEB}=3\cdot40=120\degree \end{gathered}[/tex]The diagonals of a rectangle are congruent and intersect in their middle point, so the segment AE is congruent to the segment EB, therefore the triangle AEB is isosceles, so the angle ∠BAE is congruent to ∠EBA.
The sum of the internal angles of a triangle is 180°, so in triangle AEB we have:
[tex]\begin{gathered} \angle\text{BAE}+\angle\text{EBA}+\angle\text{AEB}=180\degree \\ \angle\text{EBA}+\angle\text{EBA}+120=180 \\ 2\angle\text{EBA}=60 \\ \angle\text{EBA}=30\degree \end{gathered}[/tex]what is the intermediate in the form (x+a)^2=b as a result of completing the square for the following equation?Answer:()^2=
Step 1: Write out the equation
[tex]x^2-12x+32=4[/tex]Step 2: Subtract 32 from both sides of the equation
[tex]\begin{gathered} x^2-12x+32-32=4-32 \\ x^2-12x=-28 \end{gathered}[/tex]Step 3: Complete the square by adding 1/2 of the square of the coefficient of x to both sides
That is
[tex]x^2-12x+(-6)^2=-28+(-6)^2[/tex]This implies that
[tex](x-6)^2=-28+36=8[/tex]Hence the intermediate step is (x - 6)² = 8
Please help will mark Brainly
Answer:x=7
Step-by-step explanation:
2) The mass of a radioactive element decays at rate given by m(t) = m0e^-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay.Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? (Use e = 2.71828.]A) 28.54387 gB) 30.58254 gC) 32.14286 gD) 32.68034 g
Solution
- We are given the following formula:
[tex]\begin{gathered} m(t)=m_0e^{-rt} \\ \text{where,} \\ r=\text{decay rate} \\ t=\text{time} \\ m_0=\text{ Initial mass} \\ m=\text{mass after time t} \end{gathered}[/tex]- We are told that the Initial mass is 50g, the decay rate is .0491593745, time (t) is 10 hours, and e = 2.71828.
- With the above information, we can proceed to substitute the values given into the formula and get the mass of Uranium after 10 hours.
- This is done below:
[tex]\begin{gathered} m=50\times2.71828^{-(0.0491593745)\times10} \\ \\ m=50\times0.611651003817 \\ \\ \therefore m=30.5825\ldots\approx30.58254g \end{gathered}[/tex]Final Answer
The answer is 30.58254g (OPTION B)
Find the angle of taper on the steel bar shown if it is equal to twice.
The angle m can be found by noticing that:
cos m = 22.5/25
That's so because if we divide the triangle formed by the taper into two others, we get two right triangles.
Each right triangle has the angle m, the adjacent leg measuring 22.5 mm, and the hypotenuse measuring 25.0 mm.
So, using the formula for the cosine, we get the above relation. Then, solving this equation, we have:
cos m = 22.5/25
m = arccos 22.5/25
m ≅ 25.84º
Therefore, the angle of the taper is:
2 * m = 2 * 25.84º = 51.68º
Now, in order to convert this result using arc minutes, we need to remember that each 1º corresponds to 60' (60 arc minutes). Thus, we have:
1º --- 60'
0.68º --- x
So, cross multiplying those values, we find:
1º * x = 0.68º * 60'
x = (0.68º/1º) * 60'
x = 0.68 * 60'
x = 40.8'
x ≅ 41'
Therefore, the answer is 51º41'.
in the triangle abc a =65 b =58 identity the longest side of the triangle
We know two angles of a triangle, ∠A = 65° and ∠B = 58°, and we have to identify the longest side.
The longest side will be the one that is opposite to the widest angle. In our case, we don't know the measure of C, but we know that the sum of the three measures has to be 180°, so we can calculate it as:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 65+58+m\angle C=180 \\ m\angle C=180-65-58 \\ m\angle C=57\degree \end{gathered}[/tex]As the widest angle is at vertex A, the longest side will be its opposite, which correspond to the side formed by the other two vertices: B and C.
The longest side is BC.
I answered a problem for my prep guide, I just need to know if I’m correct or not. And I would like it to be answered as well just to make sure that I did everything correctly
Notice that,
[tex]f(x)=3^{x-1}-6=3^x\cdot3^{-1}-6=\frac{3^x}{3}-6[/tex]And there are no restrictions for the values that x can take. The domain is the whole set of real numbers.
Now, we need to check for the limits when x->+/- infinite, as follows:
[tex]\begin{gathered} \lim _{x\to\infty}3^x=\infty \\ \lim _{x\to-\infty}3^x=\lim _{x\to\infty}\frac{1}{3^x}=0 \end{gathered}[/tex]Then, the range of 3^x is (0, infinite).
Finally, we can get the range of function f(x):
[tex]\lim _{x\to\infty}f(x)=\frac{1}{3}(\lim _{x\to\infty}3^x)-6=\frac{1}{3}\infty-6=\infty[/tex][tex]\lim _{x\to-\infty}f(x)=\frac{1}{3}(\lim _{x\to-\infty}3^x)-6=\frac{1}{3}\cdot0-6=-6[/tex]Then,
[tex]\begin{gathered} The\text{ range of }f(x)\text{ is} \\ Range=(-6,\infty) \end{gathered}[/tex]Which equation can Pablo use to find p the regular price of the shirt
The final price of the shirt is given by the regular price minus the discount value. Since the final price is $28, the regular price is p, and the discount is $16, the equation is
[tex]p-16=28[/tex]If we add 16 to both sides of the equation, we have
[tex]\begin{gathered} p-16+16=28+16 \\ p=28+16 \end{gathered}[/tex]If we invert the order of the equality, we get the last option as the answer
[tex]16+28=p[/tex]???. Can you help me .???I have to find the simple interest earned to the nearest cent for each principle, interest rate, and time
Given:
Principal amount, P = $640
Time, T = 2 years
Interest rate, R = 3%
Let's find the simple interest.
To find the simple interest, apply the Simple Interest formula:
[tex]I=\frac{P\ast R\ast T}{100}[/tex]Substitute values into the formula:
[tex]\begin{gathered} I=\frac{640\ast3\ast2}{100} \\ \\ I=\frac{3840}{100} \\ \\ I=38.40 \end{gathered}[/tex]Therefore, the simple interest to the nearest cent is $38.40
ANSWER:
$38.40
5. Math home work thanks type the answer out domain and range
Answer:
Explanation:
Given the below quadratic function in vertex form;
[tex]g(x)=-0.25(x-1)^2+19[/tex]A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
When a
Michael Run 3 times last week who are the destinations human
Given the distances Michael ran each day, add them up in order to obtain the total distance, as shown below
[tex]7+16.9+8.48=32.38[/tex]Therefore, the answer is 32.38km
May I please get help with Solve for x: −3<−10(x+15)≤7
Given the compound inequality;
[tex]-3<-10(x+15)\le7[/tex]We would begin by simplifying the parenthesis as follows;
[tex]\begin{gathered} -3<-10(x+15) \\ \text{AND} \\ -10(x+15)\le7 \end{gathered}[/tex]We shall now solve each part one after the other;
[tex]\begin{gathered} -3<-10(x+15) \\ -3<-10x-150 \\ \text{Collect all like terms and we'll have;} \\ -3+150<-10x \\ 147<-10x \\ \text{Divide both sides by -10} \\ \frac{-147}{10}>x \end{gathered}[/tex]We can switch sides, and in that case the inequality sign would also "flip" over, as shown below;
[tex]\begin{gathered} \frac{-147}{10}>x \\ \text{Now becomes;} \\ x<\frac{-147}{10} \end{gathered}[/tex]For the other part of the compound inequality;
[tex]\begin{gathered} -10(x+15)\le7 \\ -10x-150\le7 \\ \text{Collect all like terms and we'll have;} \\ -10x\le7+150 \\ -10x\le157 \\ \text{Divide both sides by -10} \\ \frac{-10x}{-10}\le\frac{157}{-10} \\ x\ge-\frac{157}{10} \end{gathered}[/tex]Therefore, the values are;
[tex]\begin{gathered} x<-\frac{147}{10} \\ \text{And } \\ x\ge-\frac{157}{10} \\ \text{Hence;} \\ -\frac{157}{10}\le x<-\frac{147}{10} \end{gathered}[/tex]Written in interval notation, this now becomes;
[tex]\lbrack-\frac{157}{10},-\frac{147}{10})[/tex]Cora and Leroy went out to lunch. Leroy's billwas $8.59 less than three times Cora's bill. Iftheir combined bill total was $68.29. how muchmore did Leroy pay than Cora?
Cora and Leroy went out to lunch. Leroy's bill
was $8.59 less than three times Cora's bill. If
their combined bill total was $68.29. how much
more did Leroy pay than Cora?
Let
x -------> Leroy's bill
y -------> Cora's bill
we have
x=3y-8.59 ------> equation A
x+y=68.29 ------> equation B
solve the system
substitute equation A in equation B
(3y-8.59)+y=68.29
solve for y
4y=68.29+8.59
4y=76.88
y=19.22
Find the value of x
xc=3(19.22)-8.59
x=49.07
therefore
Leroy's bill was $49.07Cora's bill was $19.22y=9/5x+8/3That's my question
Given an equation of the form:
[tex]\begin{gathered} y=mx+b \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]For the line:
[tex]\begin{gathered} y=\frac{4}{9}x-\frac{2}{3} \\ m=\text{slope}=\frac{4}{9} \\ b=-\frac{2}{3} \end{gathered}[/tex]Mr. Crow, the head groundskeeper at High Tech Middle School, mows the lawn along the side of the gym. The lawn is rectangular, and the length is 5 feet more than twice the width. The perimeter of the lawn is 250 feet.a. Define a variable and write an equation for this problem.b. Solve the equation that you wrote in part (a) and find the dimensions of the lawn. c. Use the dimensions you calculated in part (a) to find the area of the lawn.
Given:
Length of the rectangular lawn is 5 feet more than the width.
Perimeter of the lawn is 250 feet.
The objective is,
a) To define the variables and write an equation.
b) To solve the equation in part (a) and find the dimensions of the lawn.
c) To find the area of the lawn.
a)
Consider the width of the lawn as w feet.
It is give that the length of the lawn is 5 feet more than the width of the feet.
Then, length of the law can be represented as, l = w+5.
Since, the perimeter is given as 250 feet, the equation can be represented as,
[tex]\begin{gathered} P=2(l+w) \\ P=2(w+5+w) \\ P=2(2w+5)_{} \\ P=4w+10 \end{gathered}[/tex]Hence, the required equation is P = 4w+10.
b)
Now, the dimensions of the lawn can be calculated by substituting the value of perimeter in the equation.
[tex]\begin{gathered} 250=4w+10 \\ 4w=250-10 \\ 4w=240 \\ w=\frac{240}{4} \\ w=60\text{ f}eet \end{gathered}[/tex]Since, the length of the lawnis 5 feet more than the width of the lawn.
[tex]\begin{gathered} l=w+5 \\ l=60+5 \\ l=65\text{ f}eet \end{gathered}[/tex]Hence, the width of the lawn if 60 feet and length of the lawn is 65 feet.
c)
Area of rectangluar lawn can be calculated as,
[tex]\begin{gathered} A=l\times w \\ A=65\times60 \\ A=3900ft^2 \end{gathered}[/tex]Hence, the area of the lawn is 3900 square feet.
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hourWhat is the range of this relation
Answer:
A. 3 ≤ y ≤ 5
Explanation:
The range is the set of values that the variable y can take. In this case, the variable y is the speed, so the range is the set of values of Rosalie's speed in her training.
Since the speed takes values from 3 miles per hour to 5 miles per hour, the range is
3 ≤ y ≤ 5
Determine if the expression -4c5 + c3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial. .
It is a polynomial. 5th degree (incomplete) polynomial. Binomial.
1) Considering the expression:
[tex]-4c^5+c^3[/tex]2) And the Polynomial definition as:
[tex]P(x)=a_nx^n+a^{}_{n-1}x^{n-1}+.\ldots+a_0[/tex]We can state that this is an incomplete polynomial.
About the degree, it is a 5th-degree polynomial given by its highest exponent.
Binomial since it has two terms.
3) Hence the answer is an incomplete polynomial, 5th degree.
The admission fee at an amusement park is $2.75 for children and $4.80 for adults. On a certain day, 312 people entered the park, and the admission fees collected totaled $1104. How many children and how many adults were admitted?
Let the number of children admitted be x and let the number of adults admitted be y.
It is given that the total number of 312 people were admitted, this implies that the sum of the number of children and adults is 312:
[tex]x+y=312[/tex]It is given that the admission fee for children is $2.75, this implies that the total fees collected for x children are:
[tex]x\cdot2.75=2.75x[/tex]It is also given that the admission fee for adults is $4.80, this implies that the total fees collected for y children are:
[tex]y\cdot4.80=4.80y[/tex]Since the admission fees collected totaled $1104, it follows that:
[tex]2.75x+4.80y=1104[/tex]Hence, the following system of equations is formed:
[tex]\begin{cases}x+y=312{} \\ 2.75x+4.80y={1104}\end{cases}[/tex]Solve the system of equations:
Solve the first equation for x:
[tex]x=312-y[/tex]Substitute this for x in the second equation:
[tex]\begin{gathered} 2.75\left(−y+312\right)+4.8y=1104 \\ \text{ Simplify both sides of the equation:} \\ \Rightarrow-2.75y+858+4.8y=1104 \\ \Rightarrow-2.75y+4.8y+858=1104 \\ \Rightarrow2.05y+858=1104 \\ \text{ Subtract }858\text{ from both sides:} \\ \Rightarrow2.05y+858−858=1104−858 \\ \Rightarrow2.05y=246 \\ \text{ Divide both sides by }2.05: \\ \Rightarrow\frac{2.05y}{2.05}=\frac{246}{2.05} \\ \Rightarrow y=120 \end{gathered}[/tex]It follows that the number of adults admitted is 120.
Substitute y=120 into the equation x=312-y to find the value of x:
[tex]\begin{gathered} x=312-120 \\ \Rightarrow x=192 \end{gathered}[/tex]Hence, the number of children admitted is 192.
Answer: 192 children and 120 adults were admitted.
For positive acute angles A and B, it is known that sin A= 7/25 and cos B= 21/29. Find the value of sin(A + B) in simplest form.
Answer
sin A = 7/25
cos B = 21/29
To find sin(A + B), we use double angle formula.
sin(A + B) = sin A cos B + sin B cos A
sin A = 7/25 , cos B = 21/29
From trigonometric identity, sin²θ + cos²θ = 1
cos A = √(1 - sin²A) = √(1 - (7/25)²)
cos A = √(1 - (49/25))
cos A = √(576/625)
cos A = 24/25
Also, sin B = √(1 - cos²B) = √(1 - (21/29)²)
sin B = √(1 - (441/841))
sin B = √(400/841)
sin B = 20/29
Recall that sin(A + B) = sin A cos B + sin B cos A
sin (A + B) = (7/25 x 21/29) + (20/29 x 24/25)
sin (A + B) = (147/725 + 480/725)
sin (A + B) = (147 + 480)/725
sin (A + B) = 627/725
1.). Two planes leave Dingle City at 1 PM. Plane A heads east at 450 mph and Plane B heads due west at 600 mph. How long will it be before the planes are 2100 miles apart? (No wind) but I need to do this with the Read, plan, solve, check format.
We have that the functions that describes their movement are
[tex]x=x_{0A}+v_At[/tex]And:
[tex]x=x_{0B}+v_Bt[/tex]We then proceed as follows:
[tex]x_{0A}+v_At+x_{0B}+v_Bt=2100[/tex]Then:
[tex]v_At+v_Bt=2100[/tex]That since their starting positions are the same and are 0, then:
[tex]t(v_A+v_B)=2100\Rightarrow t=\frac{2100}{v_A+v_B}[/tex]We then replace the values of vA and Vb, these are the velovities of each plane:
[tex]t=\frac{2100}{450+600}\Rightarrow t=2[/tex]The time it would take them to b 2100 miles apart is 2 hours.
* We determine the function that describes the trajectory of each plane with respect to their final position and speed, then since we know their expected distance we add both expressions (Since the total of their trajectories will give us the total distance) and solve for the time.
Write the fraction as equivalent fraction with the given denominator
Okay, here we have this:
Considering the provided fraction, we are going to rewrite it as equivalent fraction with the given denominator, so we obtain the following:
Then we will solve the following proportion to find the missing value:
[tex]\frac{3}{4}=\frac{x}{12}[/tex]Solving for x:
[tex]\begin{gathered} x=\frac{3}{4}\cdot12 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Finally we obtain the following fractions:
[tex]\frac{3}{4}=\frac{9}{12}[/tex]Answer: 9/12
Step-by-step explanation:
[tex] |4x - 5 \leqslant 7| [/tex]here's my absolute value equation
2.
The inequation is given as,
[tex]\lvert4x-5\rvert\leq7[/tex]Consider the analogy,
[tex]\lvert a\rvert\leq b\Rightarrow-b\leq a\leq b[/tex]Applying this analogy to the given inequality,
[tex]-7\leq4x-5\leq7[/tex]Now, we just need to obtain the solution set for this inequality.
Add 5 to each term,
[tex]\begin{gathered} -7+5\leq4x-5+5\leq7+5 \\ -2\leq4x\leq12 \end{gathered}[/tex]Divide by 4 each term of the inequality,
[tex]\begin{gathered} \frac{-2}{4}\leq\frac{4x}{4}\leq\frac{12}{4} \\ -0.5\leq x\leq3 \end{gathered}[/tex]Thus, the solution set to the given inequation is obtained as,
[tex]-0.5\leq x\leq3[/tex]Please help me with the equation part of this question thank you
B) As requested, let's focus on figuring out the equation. Note from the table that this is a proportional relationship, the more time goes by the more the speed increases.
2) Proportional relationships are linear equations, with the y-intercept passing through the origin. So, we can write out this equation simply:
[tex]d=60t[/tex]Note: the y-intercept is equal to zero.
Thus, this is the answer.
Since f is parallel to line g, use the diagram to the right right to answer the following question
Step 1
[tex]\begin{gathered} m\angle2=m\angle6=117^o(\text{ corresponding angles are equal)} \\ m\angle6=m\angle7=117^o(vertically\text{ opposite angles are equal)} \\ \end{gathered}[/tex]Step 2
[tex]undefined[/tex](Please reference attached photo for problem.)Show your work please. Also, What is the perimeter?
Solution:
Given the shape below:
The above shape is a combination of a semicircle and a rectangle labeled as A and B respectively.
To find the perimeter of the shape:
step 1: Evaluate the perimeter of the circle.
The perimeter of the semicircle is expressed as
[tex]\begin{gathered} perimeter\text{ of semicircle=2}\pi r \\ where\text{ r is the radius} \\ \pi\Rightarrow3.14 \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} perimeter=2\times3.14\times(\frac{10}{2}) \\ =31.4\text{ cm} \end{gathered}[/tex]step 2: Evaluate the perimeter of the rectangle.
The perimeter of the rectangle is expressed as
[tex]\begin{gathered} perimeter=2(l+w) \\ where \\ l\Rightarrow length \\ w\Rightarrow width \end{gathered}[/tex]In this case, we have
[tex]\begin{gathered} l=10\text{ cm} \\ w=4\text{ cm} \\ thus, \\ Perimeter\text{ = 2\lparen10+4\rparen} \\ =2(14) \\ =28\text{ cm} \end{gathered}[/tex]step 3: Sum up the perimeters.
Thus, we have
[tex]\begin{gathered} perimeter\text{ of shape = perimeter of circle + perimeter of rectangle} \\ =31.4+28 \\ \Rightarrow perimeter\text{ of shape = 59.4 cm} \end{gathered}[/tex]Hence, the perimeter of the shape is evaluated to be
[tex]59.4\text{ cm}[/tex]If X = 7 units, Y = 11 units, Z = 14, and H = 4 units, what is the surface area of the triangular prism ?
we know that
The surface area of a triangular prism is equal to
SA=2B+PL
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the prism
step 1
Find the area B
B=(1/2)*y*h
substitute the given values
B=(1/2)*11*4
B=22 units^2
step 2
Find teh value of P
P=X+X+y
substitute the given values
P=7+7+11
P=25 units
step 3
Find the surface area
SA=2*22+25*14
SA=394 units^2Kiera is decorating for a party. She wants balloons in 6 different locations. In each location, she will have 3 bunches of 4 balloons. How many balloons will Kiera need in all?
Shay created the table below to graph the equation r=2-sin theta (rounded to the hundredths place). Analyze the table. Did Shay make a mistake? If there is a mistake, which point is incorrect
The given equation is
[tex]r=2-sin\theta[/tex]To find the incorrect point, we will substitute the value of theta in each point and find the value of r to the nearest 2 decimal points and compare it with the value of r of the point
[tex]\begin{gathered} \theta=0 \\ r=2-sin0 \\ r=2-0 \\ r=2 \end{gathered}[/tex]Answer A is correct
[tex]\begin{gathered} \theta=\frac{\pi}{6} \\ r=2-sin\frac{\pi}{6} \\ r=2-\frac{1}{2} \\ r=1.5 \end{gathered}[/tex]Answer B is correct
[tex]\begin{gathered} \theta=\frac{\pi}{3} \\ r=2-sin\frac{\pi}{3} \\ r=1.13 \end{gathered}[/tex]Since the value of corresponding r is 2.09, then
Answer C is incorrect
The answer is C
Calculate the distance between the points G=(-2,-6) and N=(-9, 2) in the coordinate plane.Give an exact answer (not a decimal approximation).
To find the diatance between two points you use the next formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the given two points:
[tex]\begin{gathered} d=\sqrt[]{(-9-(-2))^2+(2-(-6))^2} \\ \\ d=\sqrt[]{(-7)^2+8^2} \\ \\ d=\sqrt[]{49+64} \\ \\ d=\sqrt[]{113} \end{gathered}[/tex]Then, the distance between points G and N is the square root of 113