Answer:
-128/147 cm/min
Step-by-step explanation:
[tex]A=\frac{1}{2}bh \\ \\ 90=\frac{1}{2}(10.5)b \\ \\ b=\frac{120}{7} \\ \\ \\ A=\frac{1}{2} bh \\ \\ \implies \frac{dA}{dt}=\frac{b}{2} \frac{dh}{dt}+\frac{h}{2} \frac{db}{dt} \\ \\ 4=\frac{21}{4}+\frac{db}{dt}+\frac{60}{7} \\ \\ \frac{db}{dt}=-\frac{128}{147}[/tex]
What is 106/200 written as a decimal
Answer:
0.53
Step-by-step explanation:
you just take 106 and divide it by 200
Billie opened a savings account, which pays 3% intrest per year. If she had a balance of $14,935 after one year, how much was her original deposit?
Answer: 27.50
Step-by-step explanation:
How much must be doposited today into the following account in order to have $45,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%
Solution
[tex]F=p(1+\frac{r}{n})^{nt}[/tex]where:
F=future value = 45000
P=present value
r=rate (as a decimal) = 7%=0.07
n=number of compounding periods per year = 1
t=number of years = 6
[tex]\begin{gathered} F=p(1+\frac{r}{n})^{nt} \\ 45000=p(1+\frac{0.07}{1})^{1(6)} \\ 45000=P(1+0.07)^6 \end{gathered}[/tex][tex]\begin{gathered} 45000=P(1.07)^6 \\ 45000=P(1.50073) \\ P=\frac{45000}{1.50073} \\ P=29985.4 \end{gathered}[/tex]Therefore the present value deposited today = $29,985.40
You are now on your way to college and need to make some money decisions. Your parents are going to help pay for some of your necessities but they want to know what you need. You are budgeting your money for textbooks and trying to decide how many hardback and paperback textbooks you can afford. Hardback books cost $45 and paperback books cost $20. You have $440 dollars to spend on textbooks. You know you need to buy 12 textbooks for the school year. Your task is to find out how many hardback and paperback textbooks you can buy.
You can buy 8 hardbacks and 4 paperback textbooks.
What is a Simultaneous Equation?This refers to two or more algebraic equations that have common variables and are resolved at the same time.
From the question:
Hardback books cost, H =$45
paperback books cost, P = $20.
The total amount to spend on textbooks = $440.
The total amount of textbooks needed for the school year is Hardback books+ paperback books= 12.
Solving Simultaneously we have:
H + P = 12 ..............(i)
45H + 20P = 440...........(ii)
Equation (i) * -20
-20H - 20P = -240............(iii)
Add Equation (iii) and Equation (ii)
45H + 20P = 440...........(ii)
+ -20H - 20P = -240............(iii)
We have:
25H = 200
H =200/25
H = 8
Substitute H = 8 into Equation (ii)
45(8) + 20P = 440...........(ii)
360 + 20P = 440
collecting like terms:
20P =440 - 360
20P = 80
Divide both sides by the coefficient of P
20P/20 =80/20
P= 4
Hence, You can buy 8 hardbacks and 4 paperback textbooks.
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Line f passes through 4, 0) and is parallel to a line that passes through (7, -3) and (-10. -2)
A straight line can be written in the form of a two variable linear equation.
The equation of line passing through point (4,0) is y = -1 / 17 x + 4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The line is passing through the point (4,0).
It is parallel to the line passing through (7, -3) and (-10. -2).
The slope of the line passing through (7, -3) and (-10. -2) is
m₁ = (-2-(-3)) / (-10 - 7)
m₁ = - 1 / 17
Since the slope of two lines parallel to each other is equal, the slope of the line passing through point (4,0) is - 1 / 17.
Thus, the equation of line passing through point (4,0) can be written as,
(y - 4) / (x - 0) = - 1 / 17
=> y = -1 / 17 x + 4
Hence, the equation of the given line is y = -1 / 17 x + 4.
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can anyone help??????
Answer:
140
Step-by-step explanation:
triangles equal to 180
64+76+x=180
x=40
180-40=140
Answer:
140°
Step-by-step explanation:
We know that,
the exterior angle of a triangle is equal to the sum of the interior opposite angles of a triangle.
Accordingly,
k = 64 + 76
k = 140°
One spring day, Evan noted the time of day and the temperature, in degrees Fahrenheit. His findings are as follows: At 6 a.m., the temperature was 58° F. For the next 3 hours, the temperature rose 1° per hour. For the next 4 hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 62° at midnight. On the set of axes below, graph Evan's data.
The graph of the Evan's data is attached below.
Dylan noted the time of day and the temperature, in degrees Fahrenheit, and his findings are as follows: At 6 a.m., the temperature was 58° F. For the next 3 hours, the temperature rose 1° per hour. For the next 4 hours, it rose 2° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 62° at midnight. The data points are in the form of time and temperature. The data points are 6 AM = 58, 7 AM = 59, 8 AM = 60, 9 AM = 61, 10 AM = 63, 11 AM = 65, 12 PM = 67, 1 PM = 69, 6 PM = 69, 7 PM = 67, 8 PM = 65, 9 PM = 63, and 12 AM = 62.
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Identify all pairs of congruent corresponding parts.Then write another congruence statement for the polygons.AABC ~ADEF
1) Congruent parts possess the same length, or measure (if angles).
2) As we can see, by the marks on the angles notation within each triangle we can state the following:
[tex]\begin{gathered} AB\cong ED \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]Note that was possible since we could base ourselves on the measure of those angles.
3) Thus, we can state that these triangles as we can see, fall under the case of:
SSS - Side Side Side Congruence
Given that those three sides are congruent to each other.
Brian had p pencils. Then he bought 4 more.
How many does he have now? due tm pleaseeeeeeeeeeeeee help
Answer: The number of pencils Brian has is p+4
Step-by-step explanation:
Because p is the original number of the pencil ( we don't know how many are there so we keep it p). Then he bought 4 more which mean +4, so the answer is p+4
I need help with this problems please I need a huge explanation
In this case we must apply the properties of supplementary angles and opposite angles.
1 .
opposite angles
∠ 1 = 120 °
supplementary angles
∠ 1 + ∠ 2 = 180
120 + ∠ 2 = 180
∠ 2 = 180 - 120
∠ 2 = 60 °
The same properties can be applied in the other exercises to solve them.
The solution is:
∠ 1 = 120 °
∠ 2 = 60 °
Bryce wants to renovate his kitchen. The construction estimate is $28,400. He can finance through his local bank or directly through the construction company. The bank (loan A) offers a maximum 6-year loan at 8% annual interest, resulting in monthly payments of $497.94.The construction company (loan B) offers a maximum 10-year loan at 5.5% annual interest, resulting in monthly payments of $308.21.Which loan requires Bryce to pay less, and by how much?First, calculate the total payback for each loan.
ANSWER:
Loan A requires Bryce to pay less by $1,133.52
EXPLANATION:
For bank A, we're given;
Length of loan in years(t) = 6 years
Annual interest rate(r) = 8% = 8/100 = 0.08
Loan payment(PMT) = $497.94
Number of compounds per year(n) = 12
We can go ahead and determine the loan amount using the below formula as seen below;
[tex]\begin{gathered} Loan\text{ }amount,P_0=\frac{PMT(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}} \\ \\ =\frac{497.94(1-(1+\frac{0.08}{12})^{-12*6}}{\frac{0.08}{12}} \\ \\ =\text{ \$}28399.77 \end{gathered}[/tex]So we can see that Bryce will pay back;
[tex]\begin{gathered} Bank\text{ }A\text{ }Loan\text{ }Payback=497.94(12*6) \\ \\ =497.94\left(72\right) \\ \\ =\text{\$}35,851.68 \end{gathered}[/tex]For bank B, we're given;
Length of loan in years(t) = 10 years
Annual interest rate(r) = 5.5% = 5.5/100 = 0.055
Loan payment(PMT) = $308.21
Number of compounds per year(n) = 12
We can go ahead and determine the loan amount using the below formula as seen below;
[tex]\begin{gathered} Loan\text{ }amount,P_0=\frac{PMT(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}} \\ \\ =\frac{308.21(1-(1+\frac{0.055}{12})^{-12*10}}{\frac{0.055}{12}} \\ \\ =\text{ \$}28399.57 \end{gathered}[/tex]So we can see that Bryce will pay back;
[tex]\begin{gathered} Bank\text{ B }Loan\text{ }Payback=308.21(12*10) \\ \\ =308.21\left(120\right) \\ \\ =\text{\$}36985.20 \end{gathered}[/tex]We can see that Bryce will pay back $35,851.68 for Loan A and $36,985.20 for Loan B, so Loan A requires Bryce to pay less and by $1,133.52
A guy wire runs from the top of a cell tower to a metal stake in the ground. Penelope
places a 12-foot tall pole to support the guy wire. After placing the pole, Penelope
measures the distance from the stake to the pole to be 5 ft. She then measures the
distance from the pole to the tower to be 21 ft. Find the length of the guy wire, to the
nearest foot.
Answer:
68 ft
Step-by-step explanation:
You want the length of a guy wire from a stake to the top of a cell tower if the stake is 5 ft from a 12-ft pole that is 21 ft from the tower. The guy wire crosses the top of the pole.
TrianglesThe attached diagram shows the geometry. The smaller triangle is a right triangle with legs 5 and 12. Its hypotenuse is ...
c = √(5² +12²) = √169 = 13
The larger triangle is similar and has a base of 21+5 = 26 units. This means its hypotenuse, the length of the wire, will be 26/5 times the length of the hypotenuse of the smaller triangle.
guy wire length = (26/5)(13 ft) = 67.6 ft ≈ 68 ft
The length of the guy wire is about 68 feet.
Rewrite in simplest terms: -5a – 8(-8a + 1)
The expression is given as
[tex]-5a-8(-8a+1)[/tex]Step 1: Expand the parenthesis (-8a+1) by multiplying through by -8:
[tex]\begin{gathered} -5a\lbrack+64a-8\rbrack \\ \therefore-5a+64a-8 \end{gathered}[/tex]Simplify the expression by collecting and solving like terms:
[tex]\begin{gathered} -5a+64a-8\text{ } \\ =59a-8 \end{gathered}[/tex]Thus, the simplest term is 59a - 8
PLS HELP Which of the following quantities are directly proportional?
the number of pumps used to fill a tank and the time needed to fill that tank
Number of pipes to fill a tank and the time required to fill the same tank is directly proportional.
Given,
Direct proportion;
When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another. If we spend $50 on two pens, as an example. For four pens, it will cost us 100 $When the ratio x:y1 is
Here
Option d Number of pipes to fill a tank and the time required to fill the same tank is directly proportional. Because in a fixed time interval, as the speed of a vehicle increases, the distance travelled by it also increases in the same ratio.
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The given question is incomplete. Completed question is given below;
Which of the following is in direct proportion?
(a) One side of a cuboid and its volume.
(b) Speed of a vehicle and the distance travelled in a
fixed time interval.
(c) Change in weight and height among individuals.
(d) Number of pipes to fill a tank and the time required
to fill the same tank.
3. (02.02 MC)
The beginning mean bi-weekly wage in a certain industry is $2,498.00. If the mean bi-weekly wage grows by 3.25%, what is the new mean annual wage? (4 points)
$62,903.63
$64,948.00
$67,058.81
$69,079.13
If the mean bi-weekly wage grows by 3.25%, the new mean annual wage is: C. $67,058.81.
What is annual wage?Annual wage can simply be defined as the amount a person is paid annually as wages . Wages can be paid daily or weekly.
Using this formula to find the new mean annual wage
New mean annual wage = [Beginning mean bi-weekly wage × ( 1+ mean bi-weekly wage ) ]× Number of weeks per year /2
Let plug in the formula
New mean annual wage = [$2,498.00 × (1+ 0.0325)] × 52 weeks /2
New mean annual wage = [$2,498.00 × (1.0325)] × 26 weeks
New mean annual wage = $2,579.185 × 26 weeks
New mean annual wage = $67,058.81
Therefore the correct option is C.
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Graph the function h(x)=. I have a picture of the problem
Let's begin by listing out the given information
[tex]\begin{gathered} h(x)=-\frac{2}{3}x-2 \\ h(x)=y \\ y=-\frac{2}{3}x-2 \end{gathered}[/tex]We will graph the function by assuming values for the independent variable (x = -3, 0, 3
[tex]\begin{gathered} y=-\frac{2}{3}x-2 \\ x=-3 \\ y=-\frac{2}{3}(-3)-2=2-2=0 \\ (x,y)=(-3,0) \\ x=0 \\ y=-\frac{2}{3}(0)-2=0-2=-2 \\ (x,y)=(0,-2) \\ x=3 \\ y=-\frac{2}{3}(3)-2=-2-2=-4 \\ (x,y)=(3,-4) \end{gathered}[/tex]We will plot the ordered points (shown below)
QUICK ANSWERS PLEASE!37. What common angle do AACF and ABCG share?BСAFGA. ZCB. ZFC. ZAD. ZB
Explanation
as we can see in the picture, after drawing the angles, we can observe the common angles is
[tex]A)\angle C[/tex]I hope this helps you
Use the following function rule to find f(9).
f(x) = x + 6
f(9) = [
What does f(9) =
Answer:
f(9) = 15Step-by-step explanation:
In order to find f(9) we substitute the value of x that's 9 into f(X) that's where there's x we substitute it with 9 and calculate.
We have
[tex]f(x) = x + 6[/tex]
[tex]f(9) = 9 + 6 \\ = 15[/tex]
We have the final answer as
f(9) = 15Hope this helps you
Classify the four angles of the quadrilateral. A B 70° 140° 60° 90° с D ZA LB ZC ZD √ Right Acute Obtuse O X S ?
Solution:
Given the shape;
Acute angles measure less than 90 degrees.
Right angles measure 90 degrees.
Obtuse angles measure more than 90 degrees.
ANSWER:
can someone turn 5x + 20y = 500 into slope intercept form
Answer:
y=-1/4x+25
Step-by-step explanation:
Answer: y=-1/4x + 25
Step-by-step explanation: If you don't understand how i got this remember the formula
y = mx + b
Good luck!
15)The demand equation for a certain product is given by the formulap = 32-10.0001x+1where x is the number of units sold in a month and p is the price perunit. If the price is set at $14.75 for the month, how many units will be sold?
The demand equation is given to be:
[tex]p=32-\sqrt{0.0001x+1}[/tex]where p is the price and x is the number of units sold.
If the price per unit is $14.75, the number of units will be calculated as follows:
[tex]\begin{gathered} p=14.75 \\ \therefore \\ 14.75=32-\sqrt{0.0001x+1} \end{gathered}[/tex]Subtracting 32 from both sides, we have:
[tex]\begin{gathered} -\sqrt{0.0001x+1}=14.75-32 \\ -\sqrt{0.0001x+1}=-17.25 \end{gathered}[/tex]Multiply both sides by -1:
[tex]\sqrt{0.0001x+1}=17.25[/tex]Square both sides:
[tex]\begin{gathered} 0.0001x+1=17.25^2 \\ 0.0001x+1=297.5625 \end{gathered}[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 0.0001x=297.5625-1 \\ 0.0001x=296.5626 \end{gathered}[/tex]Divide both sides by 0.0001:
[tex]\begin{gathered} x=\frac{296.5625}{0.0001} \\ x=2965625 \end{gathered}[/tex]The number of units sold will be 2,965,625 units.
List all numbers from given set that are a. Natural numbers, b. Whole numbers, c. Integers, d. Rational numbers, e. Irrational numbers, f. Real numbers {-6,-3/5,0,0.25,2.4}
(a) Natural Numers: root 81 = 9
(b) Whole Numbers: 0, root 81 = 9
(c
The radius of a circle is 18 ft. Find its área un terms of pi
Answer
Area = 324π ft²
Explanation
The area of a circle is given as
Area = πr²
where
π = pi
r = radius of the circle = 18 ft.
Area = πr²
Area = π (18²)
Area = 324π ft²
Hope this Helps!!!
Which line matches the equation belowF(x)=-3^xA RedB blueC greenD purple
The function is given as,
[tex]F(x)=-3^x[/tex]The graph representing the above equation is green colour.
What is the sum of -12, 5, and -10?
0-27
0-17
O 17
O 27
Answer:
The answer is -17
Step-by-step explanation:
Add all the numbers together:
-12-10 is -22
Then -22+5= -17
a naturalist relocated 12 wild bears in 6 months. the naturalist relocated the same number of wilde bears each month how many wild bears did the naturalist relocate per month HELP SUPER URGENT
The number of wild bears the naturalist can relocate per month is 2 wild bears.
Number of wild bears relocated by the naturalist = 12 wild bears
Time taken by the naturalist to relocate these wild bears = 6 months
Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method
This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears
Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
select all pairs of ratios that form a proportion.
A. 1/6,4/20
B.7/9 ,28/36
C. 14/18 ,21/27
D. 30/80 , 6/18
All the pairs of ratios that form a proportion are;
B. 7/9, 28/36
C. 14/18, 21/27
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
All the ratio are,
A. 1/6,4/20
B.7/9 ,28/36
C. 14/18 ,21/27
D. 30/80 , 6/18
Now,
Solve the ratio in simplest form as;
A. 1/6, 4/20
1/6 = 1 / 6
And, 4 / 20 = 1 / 5
Thus, It is not form a proportion.
B. 7/9, 28/36
7 / 9 = 7 / 9
And, 28 / 36 = 7 / 9
Thus, It is form a proportion.
C. 14/18 ,21/27
14 / 18 = 7 / 9
And, 21 / 27 = 7 / 9
Thus, It is form a proportion.
D. 30/80 , 6/18
30 / 80 = 3 / 8
And, 6 / 18 = 1 / 3
Thus, It is not form a proportion.
Therefore, All the pairs of ratios that form a proportion are;
B. 7/9, 28/36
C. 14/18, 21/27
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Which equation models the line on the graph?
(-1,4)
(3,2)
O A) y-2= -1/2(x-3)
O B) y + 2 = -1/2 (x+3)
O C) y-2=-2(x-3)
OD) y + 2 = -2(x+3)
Answer:
a i
gussed
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
To the nearest tenth, the sides measure 4.5, 9.5, and 10.5 units.
Step-by-step explanation:
[tex]{x}^{2} + {(x + 5)}^{2} = {(x + 6)}^{2} [/tex]
[tex] {x}^{2} + {x}^{2} + 10x + 25 = {x}^{2} + 12x + 36[/tex]
[tex]2 {x}^{2} + 10x + 25 = {x}^{2} + 12x + 36[/tex]
[tex] {x}^{2} - 2x - 11 = 0[/tex]
x = 4.5, so x + 5 = 9.5 and x + 6 = 10.5
