Solution:
The heights and the shadows are in the same ratio because the sun is shining from the same angle, so the triangles formed are similar.
Notice that Anita's height is twice as long as her shadow, so the height of the flagpole will be
[tex]2\text{ x }3.5\text{ = 7m}[/tex]We can also write a direct proportion:
[tex]\frac{x}{3.5}\text{ = }\frac{1.5}{0.75}\text{ }\frac{\leftarrow\text{heights}}{\leftarrow shadows}[/tex]solving for x, we get:
[tex]x\text{ =}\frac{3.5\text{ x }1.5}{0.75}\text{ = 7m}[/tex]then, we can conclude that the correct answer is:
[tex]x\text{ = 7m}[/tex]What is the solution to the equation below?A.x = -1B.x = 0C.x = -5D.x = 3
We must solve the following equation for x:
[tex]x+3=\sqrt{3-x}[/tex]We can square both sides of the equation so we can get rid of the radical:
[tex]\begin{gathered} (x+3)^2=(\sqrt{3-x})^2 \\ (x+3)^2=3-x \end{gathered}[/tex]We expand the squared binomial on the left:
[tex]\begin{gathered} (x+3)^2=x^2+6x+9=3-x \\ x^2+6x+9=3-x \end{gathered}[/tex]Then we substract (3-x) from both sides:
[tex]\begin{gathered} x^2+6x+9-(3-x)=x-3-(3-x) \\ x^2+6x+9+x-3=0 \\ x^2+7x+6=0 \end{gathered}[/tex]Then we have to find the solutions to this last equation. Remember that the solutions to an equation of the form ax²+bx+c have the form:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In our case a=1, b=7 and c=6 so we get:
[tex]\begin{gathered} x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot6}}{2\cdot1}=\frac{-7\pm\sqrt{49-24}}{2}=\frac{-7\pm\sqrt{25}}{2}=\frac{-7\pm5}{2} \\ x=\frac{-7+5}{2}=-1\text{ and }x=\frac{-7-5}{2}=-6 \end{gathered}[/tex]So we have two potential solutions x=-1 and x=-6. However we should note something important, in the original equation we have the term:
[tex]\sqrt{3-x}[/tex]Remember that the result of the square root is always positive. Then the term in the left of the expression has to be positive or 0. Then we impose a restriction in the value of x:
[tex]x+3\ge0\rightarrow x\ge-3[/tex]From the two possible solutions only x=-1 is greater than or equal to -3 so this is the correct one.
AnswerThen the answer is option A.
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,where t is measured in seconds.(A)(i) Find the average velocity over the time interval [3,4].Average Velocity = ___ meters per second(ii) Find the average velocity over the time interval [3.5,4].Average Velocity=____meters per second(iii) Find the average velocity over the time interval [4,5].Average Velocity= ____meters per second(iv) Find the average velocity over the time interval (4,4.5] Average Velocity = ____meters per.(B) Find the instantaneous velocity when t=4.Instantaneous velocity= ____ meters per second.
Given
The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,
Question 8 According to a textbook, this is a challenging question; according to me, it is the easiestquestions, among the easy questions!Suppose that the equations ax + by = c, where a, b, and c are real numbers, describes a directvariation. What do you know about the value of c?That c is
The Solution:
Given the equation below:
[tex]ax+by=c_{}[/tex]We are asked to say what we know about the value of c.
From the above equation, it is clear that:
c is a variable that depends on the values of the variables x and y.(where a and b are possibly constants.
On number 9, you have to figure out the value of X. I attempted to solve the equation and got the answer of 46. Am I correct?
From the number line given, we have the miles increasing from x all the way to 184. Similarly, we have the hours increasing all the way from 4 to 16.
To find out the value of x, we need to set up an equation that uses the ratio of both miles and hours. This is shown below;
[tex]\frac{x}{4}=\frac{184}{16}[/tex]We now cross multiply and we have;
[tex]\begin{gathered} x=\frac{4\times184}{16} \\ x=\frac{184}{4} \\ x=46 \end{gathered}[/tex]ANSWER:
[tex]x=46[/tex]Need answer for 3a please. This is for homework :)
Given the supplementary angle below for 3a,
Supplementary angles is 180°,
To find x,
[tex]\begin{gathered} 132^0+2x^0+3=180 \\ 2x^0+135^0=180^0 \\ 2x^0=180^0-135^0 \\ 2x^0=45^0 \\ x=\frac{45^0}{2}=22.5^0 \\ x=22.5^0 \end{gathered}[/tex]Hence, x = 22.5°
Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account how much did Michael earn doing odd jobs
Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account How much did Michael earn doing odd jobs?
____________________________________
13% interest compounded quarterly
after 2 years there is 100.00
_________________________________-
interest compounded
A = P(1 + r/n)^nt
A= Final amount
P= Principal Amount
r= interest
n= number of compounding periods (year)
t= time (year)
_____________________
Data
A= 100.00
P= Principal Amount (The question)
r= interest (0.13)
n= number of compounding periods (4)
t= time (2)
_________________
Replacing
A = P(1 + r/n)nt
P = A / ((1 + r/n)^nt)
P = 100.00/ ((1 + 0.13/4)^4*5)
P= 100.00/ (1.0325^20)
P= 52
________________
Michael earns doing odd jobs 52 dollars.
A manufacturer knows that their items have a normally distributed length, with a mean of 8.4 inches, and standard deviation of 1.4 inches.If one item is chosen at random, what is the probability that it is less than 11.8 inches long?
We will make use of the z-score to calculate the probability. The z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the score, μ is the mean, and σ is the standard deviation.
From the question, we have the following parameters:
[tex]\begin{gathered} x=11.8 \\ \mu=8.4 \\ \sigma=1.4 \end{gathered}[/tex]Therefore, we have the z-score to be:
[tex]\begin{gathered} z=\frac{11.8-8.4}{1.4} \\ z=2.43 \end{gathered}[/tex]Using a calculator, we can get the probability value to be:
[tex]P=0.9925[/tex]The probability is 0.9925 or 99.25%.
Factor 6z^2 + 31z + 18
Louis and Jenny each wrote an equation to represent the graphed linear function. Louis’s answer is y=2x. Jenny’s answer is y=x+2. Which student is correct?
Concept
First, find the slope of the line, and secondly use a slope-intercept form of the equation to find the equation of the line.
Step 1: find the slope
From the graph, choose two coordinates at the intercept
( 0, 2 ) and ( -2, 0 )
x1 = 0
y1 = 2
x2 = -2
y2 = 0
Substitute the values in slope equation
[tex]\begin{gathered} \text{Slope m = }\frac{rise}{\text{run}}\text{ }=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{Slope = }\frac{0-2}{-2-\text{ 0}} \\ \text{m = 1} \end{gathered}[/tex]Step 2: Find the intercept c
The intercept on the y-axis is c = 2
Step 3: Write the equation of a line in slope-intercept form
y = mx + c
Step 4: substitute the values of m and c to find the equation
y = 1(x) + 2
y = x + 2
Final answer
y = x + 2 Jenny's is correct
Solve.Draw a rectangular fraction model to explain yourthinking.Then, write a number sentence.1/3of3/7=
We are asked to find 1/3 of 3/7 using a rectangular fraction model.
Let us draw a rectangular fraction model.
1/3 means make 3 rows
3/7 means make 7 columns
[tex]\frac{1}{3}\times\frac{3}{7}=\frac{3}{21}[/tex]Three 3 filled boxes represent the numerator and the total 21 boxes represent the denominator.
Therefore, the result is 3/21
3. Given x=2 and y=-3, evaluate the expression given below 2x - 3xy - 2y? A) -28 B) 28 C) 8 D) 44
Given:-
x=2,y=-3
[tex]2x-3xy-2y\text{?}[/tex]To find evalute the given expression,
[tex]2x-3xy-2y[/tex]
Subtitute the x and y value in above equation,
[tex]\begin{gathered} 2(2)-3(2)(-3)-2(-3) \\ =4-(6\times-3)+6 \\ =4-(-18)+6_{} \\ =4+18+6 \\ =28 \end{gathered}[/tex]So the required value is 28.
So the correct option B.
giving that -3+20=5x-4 write 3 more equations that you know are true
Answer:
Step-by-step explanation:
ft7654
Write the expression as a product of two factors. 12s + 10 + 6y
to write the expression as a product between two factors you must identify the common factor between all the terms in tis case the common factow will be 2
[tex]12s+10+6y=2\cdot(6s+5+3y)[/tex]Find the lenghts of the sides of the rectangle ABCD shown on the coordinate plane. Suppose you double the length of each side. What would be the new coordinates of point C if the coordinate of point A stay the same
Looking at the diagram,
each small box represents one unit
The number of units from A to B is 4 units
The number of units from B to C is 3 units
Thus, the length of rectangle ABCD is 4 units and its width is 3 units.
The original coordinates are
A(0, 0)
B(0, 4)
C(3, 4)
D(3, 0)
If
Find the circumference of each circle .(use 22/7 as an approximation for PI
Let us find the circumference of each circle.
The circumference of a circle is given by
[tex]C=2\pi r\: \: or\: \: C=\pi D[/tex]Where r is the radius and D is the diameter of the circle.
Circle 1:
Here we are given the diameter of the circle
D = 21 cm
[tex]C=\pi D=\frac{22}{7}\cdot21=22\cdot3=66\operatorname{cm}[/tex]So, the circumference of the circle is 66 cm.
Circle 2:
Here we are given the diameter of the circle
D = 91 ft
[tex]C=\pi D=\frac{22}{7}\cdot91=286\: ft[/tex]So, the circumference of the circle is 286 ft.
Circle 3:
g(x)= x^2+3h(x)= 4x-3Find (g-h) (1)
Given:-
[tex]g(x)=x^2+3,h(x)=4x-3[/tex]To find:-
[tex](g-h)(1)[/tex]At first we find the value of (g-h)(x), so we get,
[tex]\begin{gathered} (g-h)(x)=g(x)-h(x) \\ =x^2+3-(4x-3) \\ =x^2+3-4x+3 \\ =x^2-4x+6 \end{gathered}[/tex]So the value of,
[tex](g-h)(x)=x^2-4x+6[/tex]So the value of (g-h)(1) is,
[tex]\begin{gathered} (g-h)(x)=x^2-4x+6 \\ (g-h)(1)=1^2-4\times1+6 \\ (g-h)(1)=1-4+6 \\ (g-h)(1)=7-4 \\ (g-h)(1)=3 \end{gathered}[/tex]So the required value is,
[tex](g-h)(1)=3[/tex]Solve for w.4w²-24w=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution".W =0U08Nosolution
ANSWER
[tex]\begin{equation*} w=0,\text{ }w=6 \end{equation*}[/tex]EXPLANATION
We want to solve the given equation for w:
[tex]4w^2-24w=0[/tex]To do this, we have to factorize the equation and simplify it.
Let us do that now:
[tex]\begin{gathered} (4w*w)-(4w*6)=0 \\ \\ 4w(w-6)=0 \\ \\ \Rightarrow4w=0\text{ and }w-6=0 \\ \\ \Rightarrow w=0,\text{ }w=6 \end{gathered}[/tex]That is the answer.
the volume of a sphere is 2304pi in^3 the radius of the sphere is ___ inches.
Answer:
The radius = 12 inches.
Explanation:
Given a sphere with radius, r units:
[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]If the volume of a sphere is 2304π in³, then:
[tex]\frac{4}{3}\pi r^3=2304\pi[/tex]We solve the equation for r:
[tex]\begin{gathered} \frac{4\pi r^3}{3}=2304\pi \\ 4\pi r^3=2304\pi\times3 \\ r^3=\frac{2304\pi\times3}{4\pi} \\ r^3=1728 \end{gathered}[/tex]Next. take cube roots of both sides.
[tex]\begin{gathered} r=\sqrt[3]{1728} \\ r=12\text{ inches} \end{gathered}[/tex]The radius of the sphere is 12 inches.
Larry purchased a new combine that cost $260,500, minus a rebate of $5,500, a trade-in of $8,500, and a down payment of $7,000. He takes out a loan for the balance at 8% APR over 4 years. Find the annual payment. (Simplify your answer completely. Round your answer to the nearest cent.)
The annual payment for the loan balance is $72,310.03.
What is the periodic payment?The periodic payment is the amount that is paid per period (yearly, monthly, quarterly, or weekly) to repay a loan or a debt.
The periodic payment can be computed using an online finance calculator, making the following inputs.
N (# of periods) = 4 years
I/Y (Interest per year) = 8%
PV (Present Value) = $239,500 ($260,500 - $5,500 - $8,500 - $7,000)
FV (Future Value) = $0
Results:
PMT = $72,310.03
Sum of all periodic payments = $289,240.13
Total Interest = $49,740.13
Thus, the annual payment that Larry needs to make is $72,310.03.
Learn more about annual payments at https://brainly.com/question/14290379
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Ronald purchased a brand new phone for $450.00. Since phones are taxablehe had to pay a sales tax of 45%. much sales tax did Ronald pay for the phone ?
please help figure out this problem i’m trying to determine if the lines that appear to be tangent are tangent
Suppose that the two lines that form the missing angle are tangents to the circle. Then, the measure of the missing angle can be found using the following equation:
[tex]\measuredangle ABC=\frac{arc\text{ AEC - arc AGC}}{2}[/tex]Notice that we can complete the information about the arcs of the circle with the central angle:
then, we can find the angle x with the following expression:
[tex]\begin{gathered} \measuredangle x=\frac{243-117}{2}=\frac{126}{2}=63 \\ \Rightarrow\measuredangle x=63\degree \end{gathered}[/tex]therefore, the measure of the missing angle is 63 degrees.
Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?
Answer
• Exponential model
[tex]A(t)=13.60(1+0.25)^{t}[/tex][tex]A(8)\approx81.06[/tex]Explanation
The exponential model equation can be given by:
[tex]A(t)=C(1+r)^t[/tex]where C is the initial value, r is the rate of growth and t is the time.
We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:
[tex]A(t)=13.60(1+r)^t[/tex]Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:
[tex]26.56=13.60(1+r)^3[/tex][tex]\frac{26.56}{13.60}=(1+r)^3[/tex][tex](1+r)^3=\frac{26.56}{13.60}[/tex][tex]\sqrt[3]{(1+r)^3}=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]1+r=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]r=\sqrt[3]{\frac{26.56}{13.60}}-1\approx0.2500[/tex]Thus, our rate is 0.25, and we can add it to our equation:
[tex]A(t)=13.60(1+0.25)^t[/tex]Finally, we evaluate t = 8:
[tex]A(8)=13.60(1+0.25)^8=81.06[/tex]if f(x)=-2x-3, find f(-1)
Solve;
[tex]\begin{gathered} f(x)=-2x-3 \\ f(-1)=-2(-1)-3 \\ f(-1)=2-3 \\ f(-1)=-1 \end{gathered}[/tex]The answer is -1
That is f(-1) = -1
2) (3 pt) Write the function from the table and graph.хf(x)-10004122130.52) f(x) =
(x - h)^2 = 4p(y - k)
(-1 - 3)^2 = 4p(8 - 0.5)
(-4)^2 = 4p(7.5)
16 = 30p
p = 16/30
p = 8/15
(x - 3)^2 = 16/15(y - 0.5)
15(x^2 - 6x + 9) = 16y - 8
15x^2 - 90x + 135 = 16y - 8
16y = 15x^2 - 90x + 135 + 8
y = 15/16 x^2 - 90/16 x + 143/16
f(x) = 15/16 x^2 - 90/16x + 143/16
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
the table below shows the height of trees in a park. how many trees are more than 8m tall but not more than 16m tall?
Does the least-squares fit line always go through at least one point in the plot?
Not necessarily. The least-squares line is the best fit for all the points in the scatterplot. if it so happens that in order to get close to some point on the plot the line has to go a little further away from some other point, the line will be adjusted to accommodate that.
Hence, the least square line does not always pass through at least one point on the line.
PLEASE HURRY AND HELP I NEED THIS TODAY
Solve k over negative 1.6 is greater than negative 5.3 for k.
k > −8.48
k < −6.9
k > −6.9
k < 8.48
Answer: [tex]k < 8.48[/tex]
Step-by-step explanation:
[tex]\frac{k}{-1.6} > -5.3\\\\k < (-5.3)(-1.6)\\\\k < 8.48[/tex]
the radius of the circle is 5 inches. what is the area?give the exact answer in simplest form.
The area is 25π square inches
Explanation:Given a radius, r = 5 in.
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]Substituting the value of r, we have:
[tex]A=\pi(5^2)=25\pi[/tex]The area is 25π square inches
Point X is (3, -6). Wgich point is 10 units away from Point X
If we find the point X on the plane we can see the following:
Notice that the point D and the point X are 10 units apart with respect the x-axis, therefore, the point that is 10 units away from X is point D
