Answers
Answer:
35
Step-by-step explanation:
AEC and AEB form a straight angle(180°)
180-40=140
AEV and AED are equal
140 divided by 4 = 35
Related Questions
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answers
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a population that is growing exponentially. In the year 2000, there were half as many people in B as in A. In the year 2010, the population of A was 20% more than the population of B.
When will the populations be equal? Give your answer in years after 1990.
Answers
Answer:
City A and city B will have equal population 25years after 1990
Step-by-step explanation:
Given
Let
[tex]t \to[/tex] years after 1990
[tex]A_t \to[/tex] population function of city A
[tex]B_t \to[/tex] population function of city B
City A
[tex]A_0 = 10000[/tex] ---- initial population (1990)
[tex]r_A =3\%[/tex] --- rate
City B
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010
Required
When they will have the same population
Both functions follow exponential function.
So, we have:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
Calculate the population of city A in 2000 (t = 10)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]
[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]
[tex]A_{10} = 10000 * (1.03)^{10}[/tex]
[tex]A_{10} = 13439.16[/tex]
Calculate the population of city A in 2010 (t = 20)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]
[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]
[tex]A_{20} = 10000 * (1.03)^{20}[/tex]
[tex]A_{20} = 18061.11[/tex]
From the question, we have:
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] and [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]
[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]
[tex]B_{10} = 6719.58[/tex]
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]
[tex]18061.11 = B_{20} * (1.20)[/tex]
Solve for B20
[tex]B_{20} = \frac{18061.11}{1.20}[/tex]
[tex]B_{20} = 15050.93[/tex]
[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
For: [tex]B_{10} = 6719.58[/tex]
We have:
[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
For: [tex]B_{20} = 15050.93[/tex]
We have:
[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]
[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]
Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]
[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]
Apply law of indices
[tex](1 + r_B)^{20-10} = 2.2399[/tex]
[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)
Take 10th root of both sides
[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]
[tex]1 + r_B = 1.08[/tex]
Subtract 1 from both sides
[tex]r_B = 0.08[/tex]
To calculate [tex]B_0[/tex], we have:
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]
So:
[tex]B_0 * 2.2399 = 6719.58[/tex]
[tex]B_0 = \frac{6719.58}{2.2399}[/tex]
[tex]B_0 = 3000[/tex]
Hence:
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
[tex]B_t = 3000 * (1 + 0.08)^t[/tex]
[tex]B_t = 3000 * (1.08)^t[/tex]
The question requires that we solve for t when:
[tex]A_t = B_t[/tex]
Where:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_t = 10000 * (1 + 3\%)^t[/tex]
[tex]A_t = 10000 * (1 + 0.03)^t[/tex]
[tex]A_t = 10000 * (1.03)^t[/tex]
and
[tex]B_t = 3000 * (1.08)^t[/tex]
[tex]A_t = B_t[/tex] becomes
[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]
Divide both sides by 10000
[tex](1.03)^t = 0.3 * (1.08)^t[/tex]
Divide both sides by [tex](1.08)^t[/tex]
[tex](\frac{1.03}{1.08})^t = 0.3[/tex]
[tex](0.9537)^t = 0.3[/tex]
Take natural logarithm of both sides
[tex]\ln(0.9537)^t = \ln(0.3)[/tex]
Rewrite as:
[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]
Solve for t
[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]
[tex]t = 25.397[/tex]
Approximate
[tex]t = 25[/tex]
Three lines intersect at point P, as shown in the diagram below. Find the measure of
Answers
Answer:
VPQ = 83°
Step-by-step explanation:
You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:
SPR = UPV; TPU = RPQ; TPS = VPQ
360 - SPR - UPV - RPQ - TPU = VPQ + TPS
As some of they are equal, we can just multiply they by 2:
360 - 2×SPR - 2×RPQ = 2× VPQ
360 - 2×35 - 2×62 = 2×VPQ
360 - 70 - 124 = 2×VPQ
2 VPQ = 166
VPQ = 166/2
VPQ = 83°
Find f(-2) for f(x) = 3x2^x
Answers
Is 1/2^2=1/4
3 x 1/4 is 3/4
The answer is 3/4 I think
The value of function f (- 2) would be,
⇒ f (- 2) = 3 / 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 3 × 2ˣ
Now,
At x = - 2;
The value of function f (- 2) would be,
⇒ f (x) = 3 × 2ˣ
⇒ f (- 2) = 3 × 2⁻²
⇒ f (- 2) = 3 × 1 / 4
⇒ f (- 2) = 3 / 4
Thus, The value of function f (- 2) would be,
⇒ f (- 2) = 3 / 4
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ2
The following hypothetical data represent a sample of the annual numbers of home fires started by candles for the past several years.
5640, 5090, 6590, 6380, 7165, 8440, 9980
The population has a standard deviation equal to 1210. Assuming that the data is from a distribution that is approximately normal, construct a 90 % confidence interval for the mean number of home fires started by candles each year
Answers
Answer:
(6290.678 ; 7790.742)
Step-by-step explanation:
Given the data :
5640, 5090, 6590, 6380, 7165, 8440, 9980
The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71
The 90% confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 90% confidence = 1.64
Hence,
Margin of Error = 1.64 * 1210/√7
Margin of Error = 750.032
90% confidence interval is :
7040.71 ± 750.032
Lower boundary = 7040.71 - 750.032 = 6290.678
Upper boundary = 7040.71 + 750.032 = 7790.742
(6290.678 ; 7790.742)
How far does a train travel in 12 hours at 115 miles per hour?
1,509 mi
1,265 mi
1,380 mi
Answers
Answer:1380
Step-by-step explanation: 12x115
Answer:
1,380
Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)
Hope this is helpful
Help!!!!!!!!!!! Photo attached
Answers
Answer:
option A : 25
Step-by-step explanation:
Given :
P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)
Find the length of PQ ,QR , PR.
Using distance formula to find the lengths.
[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]
[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]
Clearly , the triangle satisfies Pythagoras theorem :
Square of larger side = Sum of squares of other sides.
Therefore , PQR is a right triangle,
with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .
[tex]Area = \frac{1}{2} \times base \times height[/tex]
[tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]
Charlie (c) has 75 more pencils than Kate (k). Together, they have 135 pencils. How many pencils does Kate have? *
Answers
Answer:
60
Step-by-step explanation:
135-75 = 60
HOPE IT HELPS
In the accompanying diagram, ABC is isosceles, BC is extended to D. AB = AC. and M
Answers
Answer:
m∠ACD = 130
Step-by-step explanation:
If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.
This is because angles in a triangle adds up to 180°.
180° - 80° = 100°/2 = 50°
∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:
50° + 80° = 130°
Or
Angles on a straight line adds up to 180°.
180° - 50° = 130°
What is the surface area and volume of the sphere shown below?
Your response should show all necessary calculations and diagrams.
Answers
Answer:
ur mom
Step-by-step explanation:
doin doin
PLEASE HELP!! Please answer all if you can and show answer clearly thankyou sm if u do
Answers
Answer:
Below:
Step-by-step explanation:
A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)
B) 0.45
C) 0.40
A) the total probability has to equal 1.
To find the probability of rat subtract the other animals from1:
Rat = 1 - 0.35-0.4-0.1 = 0.15
Rat = 0.15
B) probability of cat or hamster equals the sum of their probabilities:
Cat = 0.35 + hamster = 0.1 = 0.45
Answer = 0.45
C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16
Answer = 0.16
Please help!
Geometry
10 points!
Answers
Explanation: Use the 45-45-90 theorem and solve for C, Use the 30-60-90 theorem and solve for D.
45 45 90
s s s√2
6 6 6√2
c=6√2
30-60-90
a a√3 2a
7√3 7 14
d=7√3
4th grade math question:
jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Answers
Answer:
1 gallon
Step-by-step explanation:
gallons of paint needed; 4
gallons used: (3/4)*4
= 1 gallon was used
Answer:
Answer is 3 gallons
Step-by-step explanation:
1 gallon= 25%
2 gallons=50%
3 gallons=75%
3/4 is equivalent to 75%
Hope this helped!
The net of a solid figure is shown below:
Which calculation will give the total surface area of the solid figure? (1 point)
1) 5.6.6 square inches
2) 6.5.5 square inches
3) 6.5.5.5 square inches
4) 5.6.6.6 square inches
Answers
===========================================================
Explanation:
Each square has a side length of 5 inches, so each square has area 5*5 = 25 square inches. We have 6 such squares to give a total surface area of 6*25 = 150 square inches.
Effectively, this is the same as using the formula below
S = 6x^2
S = 6*5^2
S = 6*5*5
S = 150
x = 5 refers to the side length and S is the surface area. It might help to cut the figure from the paper, and fold it up and you should find that a 3D box will form. There are 6 faces with area of 5*5 each, hence the 6*5*5
Which number line represents the solution set for the inequality -4(x + 3) S-2 – 2x?
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
+
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2:-1 0 1
2.
+
6
+
7
3 4
01
5
02
Answers
Answer:
the answer is the alphabet A at the picture
The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A
Inequality expressionGiven the inequality expression
-4(x+3) <= -2-2x
Expand the inequality
-4x - 12 <= -2-2x
Collect the like terms
-4x + 2x <= -2+12
-2x <= 10
Divide both sides by -2
-2x/-2 >= 10/-2
x >= -5
For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.
Learn more on inequality expression: https://brainly.com/question/24372553
2. How many miles the trucks will have to drive for the costs of the trucks to be equal?
Answers
Step-by-step explanation:
kayo na po bahala mag calculate
PLEASSSSSSSSSSSEEEEEEEE HELPPP IM BEGGING SOMEONE PLEASEEEEEEEE PLEASEEEEEEEEEEE HELPPPP
Answers
Answer:
20 degree
Step-by-step explanation:
x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)
2x = 110 - 70
x = 40/2
x = 20 degree
Find the perimeter of the figure.
Answers
Answer:
below
Step-by-step explanation:
p = 2( a + b)
p = 2(24 +16)
p =80 in
p semicircle
=πr
= 3.142 *8
= 25.136
p of figure
p =80 +25.136
p=105.136 in
What is the answer to this?
Answers
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
The answer is "The second choice".
Step-by-step explanation:
[tex]r=6\\\\h=13 \\\\[/tex]
Formula:
[tex]A=2\pi rh[/tex]
[tex]=2\times 3.14 \times 6 \times 13\\\\=2\times 3.14 \times 78\\\\=3.14 \times 156\\\\=3.14 \times 156\\\\=489.84 \approx 489.8 ft^2[/tex]
Evaluate the function.
f(x) = 2x2
Find f(-3)
Can anybody answer this?
Answers
Answer:
18
Step-by-step explanation:
f(x) = 2x^2
Let x = -3
f(-3) = 2 * (-3)^2
Exponents first
f(-3)=2 *9
f(3) = 18
Answer:
f ( - 3 ) = 18
Step-by-step explanation:
f ( x ) = 2x²
Find f ( - 3)
let , x = - 3
lf ( - 3 ) = 2 ( -3 )²
f ( - 3 ) = 2 × ( - 3 )²
Evaluate the power
f ( -3) = 2 × 9
multiply the numbers
f ( - 3 ) = 18
Get brainiest if right!!!
10points if right!!
Answers
Answer:
the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)
the formula is 0.3*0.5^n-1
the formula for finding the nth term of a geometric sequence preset would be
a*r^n-1
a is first term
r is common ratio
Step-by-step explanation:
Which of the following expressions are equivalent to 52n+n4n2 + 4n
5
2
n
+
n
4
n
2
+
4
n
?
Answers
Answer:
they just go straight what does it mean?
A bag has 2 yellow marbles and 16 red marbles. Half of the red marbles are made of plastic. A marble is selected at random from the ball What is the probability that it is a red, plastic marble? Write your answer as a fraction in simplest form.
Answers
Answer:
4/9
Step-by-step explanation:
2+16 = 18 total marbles
16 ÷ 2= 8 plastic marbles
Since there are 18 total marbles and 8 plastic red marbles we can say that there is a probability of 8/18.
8/18 in simplest form is 4/9.
Hope this helps! Brainliest?
Find the complement of the set given that
U = {x | x is in I and −3 ≤ x ≤ 7}.
(Enter your answers as a comma-separated list.)
{−1, 1, 3, 5, 7}
Answers
4. What is the product of (3x - 1)(x + 4)?
HELP PLEASE RIGHT NOT SHOW YOURE WORK!!!!!
Answers
[tex]3 {x}^{2} + 11x - 4[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex](3x - 1)(x + 4) \\ \\ = 3x(x + 4) - 1(x + 4) \\ \\ = 3 {x}^{2} + 12x - x - 4 \\ \\ = 3 {x}^{2} + 11x - 4[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Find the equation of a sphere if one of its diameters has endpoints: (-14. -3, -6) and (-4, 7, 4) Note that you must move everything to the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.
Answers
Answer:
[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]
Step-by-step explanation:
From the question we are told that:
Diameters has endpoints: [tex](-14. -3, -6) & (-4, 7, 4)[/tex]
Generally the equation for Center of The sphere is mathematically given by
[tex]C=(\frac{-14+(-4)}{2},\frac{-3+(7)}{2},\frac{-6+(4)}{2})[/tex]
[tex]C=(9,2,-1)[/tex]
Generally the equation for Radius of the sphere is mathematically given by
[tex]R=\sqrt{(9-2)^2+(2-9)^2+(-1-2)^2}[/tex]
[tex]R=\sqrt{107}[/tex]
Therefore the Equation of the Sphere is
[tex](x-9)^2+(y-2)^2+(z+1)^2=107[/tex]
[tex](x^2-18x+81)+(y^2-4y+4+(z^2+2z+1))=107[/tex]
[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]
Help, please
no links
Answers
9514 1404 393
Answer:
4/10 and 10/25
Step-by-step explanation:
If each of the ratios reduces to the same lowest terms, then they are a proportion. All are in lowest terms except the first pair. Reducing those gives ...
4/10 = 10/25 = 2/5
4/10 and 10/25 form a proportion
__
All of the other pairs are pairs of different ratios, so do not form a proportion.
What is the production matrix?
Answers
Answer:
[tex]\left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]
Step-by-step explanation:
Here we want to compute the product of two matrices, one 2x2, and other 2x1.
[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right][/tex]
Remember that in the product, we multiply the rows of the first one by the columns of the second one, then the product is just:
[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right] = \left[\begin{array}{ccc}0.3*4 + 0.3*6\\0.35*4 + 0.4*6\end{array}\right] = \left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]
If you leave Louisville Ky at 8:15 am and arrive in Chicago at 2:25 pm how long did you travel ?
Answers
Answer: 6 hours and 10 minutes
Step-by-step explanation: