Answers
m<B=70, and c=9 in. Which information about the triangle is given.
======================================================
Solution:
Given the following:
a = 11 in , ∠B = 70° , c = 9 in
The given information can be used in the cosine law.
Which is ⇒⇒⇒ b² = a² + c² - 2 a c * cos (B)
The correct answer is the third option.
Related Questions
The penguin exhibit at a zoo has a raised circular island that is surrounded by water. The diameter of the island is 20 meters. One penguin swims half way around the island before hopping out.
How far did the penguin swim?
Answers
Answer:
10pi
Step-by-step explanation:
The answer is 10pi
Find the lengths of the sides of the right triangle?
Answers
The lengths of the sides are:
2x = 12
2x -7 = 5
_____
You can use the Pythagorean theorem to write the relationship between the sides.
(2x)² +(2x -7)² = 13²
4x² +4x² -28x +49 = 169 . . . . . eliminate parentheses
8x² -28x -120 = 0 . . . . . . . . . . . put in standard form
4(2x² -7x -30) = 0 . . . . . . . . . . . factor out 4
(x -6)(2x +5) = 0 . . . . . . . . . . . .. divide by 4 and factor further
x = 6, -5/2 . . . . . . . . . . . . . . . . .. only the positive solution (x=6) is useful
Then 2x = 12; 2x-7 = 5.
Question 21 [t-interval] a random sample of size 18 is drawn from a population that is normally distributed. the sample mean is 58.5, and the sample standard deviation is found to be 11.5. determine a 95% confidence interval about population mean.
a. [52.78,64.22]
b. [53.78,63.22]
c. [53.18,63.81]
d. [54.04,62.96]
Answers
Answer:
Option a. [52.78,64.22]
Step-by-step explanation:
We are given that a random sample of size 18 is drawn from a population that is normally distributed.
Sample mean is 58.5, and the sample standard deviation is found to be 11.5 i.e., X bar = 58.5 and s = 11.5
The pivotal quantity for calculating 95% confidence interval is;
[tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
So, 95% confidence interval about population mean is given by;
P(-2.110 < [tex]t_1_7[/tex] < 2.110) = 0.95
P(-2.110 < [tex]\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.110) = 0.95
P(-2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]{Xbar - \mu}[/tex] < 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
P(X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] < [tex]\mu[/tex] < X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ) = 0.95
95% confidence interval about [tex]\mu[/tex] = [ X bar - 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] , X bar + 2.110 * [tex]\frac{s}{\sqrt{n} }[/tex] ]
= [ 58.5 - 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] , 58.5 + 2.110 * [tex]\frac{11.5}{\sqrt{18} }[/tex] ]
= [ 52.78 , 64.22 ]
Therefore, 95% confidence interval about population mean is [52.78 , 64.22].
What form of a quadratic function would be graphed having the vertex at the same point as the y-intercept
Answers
9514 1404 393
Answer:
a form with no horizontal translation of the parent function
Step-by-step explanation:
If the vertex is the y-intercept, then it has not moved horizontally from its position in the parent function. The form of the quadratic is one without any horizontal translation.
A quadratic function with its vertex and y-intercept at the same point would be in the form f(x) = ax². The coefficients b and c must be zero for the vertex to be at the origin (0,0), and by varying a, we can achieve a vertical stretch or shrink without altering the y-intercept.
The student's question pertains to the graph of a quadratic function with specific conditions on its vertex. If a quadratic function has its vertex at the same point as its y-intercept, then the vertex is located at the origin (0,0), because the y-intercept is the point where the graph crosses the y-axis, and at the vertex, the value of y is at its maximum or minimum depending on the direction of the parabola.
The standard form of a quadratic function is f(x) = ax² + bx + c. For the function to have its vertex at the origin, both b and c would need to be zero, making the function f(x) = ax². This represents a parabola that opens upwards if a is positive, or downwards if a is negative.
To maintain the y-intercept, we must ensure that the transformation applied to the graph, such as a vertical or horizontal shrink, does not alter the location of the vertex. A horizontal shrink is achieved by making a larger absolute value while ensuring that it remains positive or negative in accordance with the original direction of the parabola.
The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?
Answers
If we look at y = mx + b and y = 8x -b we can see the similarities
y = mx + b
y = 8x - 1
m = slope = 8
b = y-intercept = -1
Slope = 8
Answer:
8
Step-by-step explanation:
I just took the test.
6(z+2)-2(2z+5)=18 show step by step
Answers
Note:
Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)
Because you are trying to isolate the z (variable), you cannot do parenthesis. Instead, distribute 6 to z and 2, and -2 to 2z and 5
6(z + 2) = 6z + 12
-2(2z + 5) = -4z - 10
6z + 12 - 4z - 10 = 18
Next, combine like terms. Combine terms with common variables together, as well as constants.
6z - 4z = 2z
12 - 10 = 2
2z + 2 = 18
Next, isolate the z, do the opposite of PEMDAS. Note that there is an equal sign. What you do to one side, you have to do to the other.
2z + 2 = 18
subtract 2 from both sdies
2z + 2 (-2) = 18 (-2)
2z = 18 - 2
2z = 16
isolate the z, divide 2 from both sides
2z = 16
2z/2 = 16/2
z = 16/2
z = 8
8 is your answer for z
hope this helps
What is the area of the rhombus shown below? A. 110.5 square units B. 129.2 square units C. 221 square units D. 15 square units
Answers
the answer is A. 110.5
The area of the rhombus is 110.5 square units if the lengths of the diagonal of a rhombus are 13 and 17 units option (A) 110.5 square units is correct.
What is a rhombus?A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.
We have a rhombus shown in the picture with dimensions:
As we know,
The area of the rhombus is given by:
A =pq/2
p and q are the lengths of the diagonal of a rhombus.
p = MK = 13 units
q = JL = 17 units
Plug the values in the formula:
A = (13×17)/2
A = 221/2
A = 110.5 square units
Thus, the area of the rhombus is 110.5 square units if the lengths of the diagonal of a rhombus are 13 and 17 units option (A) 110.5 square units is correct.
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8.
Howmet Corporation needs $200,000 in 5 years.
Find the required quarterly payment into a sinking fund if funds are invested in an account earning 10% per year compounded quarterly.
$38,050.00
$6,716.00
$32,760.00
$7,830.00
Answers
Fv = 200,000
r = 0.1
n = 5
k = 4 (quarterly)
Pmt=200,000÷(((1+0.10÷4)^(4×5)−1)÷(0.10÷4))=7,829.43
The fraction 7/8 is a multiple of what unit fraction?
Answers
[tex]\dfrac{7}{8}=7\times\dfrac{1}{8}[/tex]
The unit fraction is 1/8.
You earn $56 for washing 8 cars. How much do you earn for washing 5 cars?
Answers
First find out how much you earn washing one car. Divide 56 with 8
56/8 = 7
You earn $7 for washing 1 car.
Now find out how much you earn washing 5 cars.
7/1 (being $7 per 1 car)
5/5 (amount of cars washed)
7/1 x 5/5 = 35/5
For 5 cars, you earn $35.
$35 is your answer
hope this helps
$56 = 8 cars
$x = 5 cars
Now we can do cross multiply
8 * x = 5 * 56
8x = 280
Now we can divide both sides by 8
8x/8 = 280/8
x = 35
Thus,
You earned $35 for washing 5 cars!
Which is the equation of an ellipse centered at the origin with foci on x-axis, x-intercepts +7, -7 and y-intercepts +2,
-2?
Answers
foci on x-axis-------> is a ellipse with horizontal major axis
the equation is
(x²/a²)+(y²/b²)=1
major axis is the x-axis with length 2a
2a=14--------> a=7
minor axis is the y-axis with length 2b
2b=4-----> b=2
the equation is
(x²/a²)+(y²/b²)=1------> (x²/7²)+(y²/2²)=1-----> (x²/49)+(y²/4)=1
the answer is
(x²/49)+(y²/4)=1
see the attached figure
Answer:
It's B on edge.
Step-by-step explanation:
Which description best describes the three-dimensional object that is formed when the segment is rotated about the axis as shown?
an oblique cylinder
a cone with an open base
a triangular prism
a hollow pyramid
Answers
Second option is correct. A cone with open base is formed when the segment is rotated about the axis as shown in figure.
What is solid revolution?A solid revolution is a three dimensional figure obtained by rotating a two-dimensional figure or (curve) around a straight line(called the axis) that lies in the same plane.
According to the question
If we see in the given figure, there is a triangle about a vertical line. As the triangle is revolved about a line, the vertices A and C remain stationary. While the vertex B which follows the path of circle. As the triangle rotates, AB creates the outline of cone.
Hence, Option second is correct i.e. a cone with an open base.
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Answer: A cone with an open base.
Step-by-step explanation:
The correct answer is a cone with an open base. When this segment is rotated around the axis as shown, the three-dimensional object formed will be a cone with no base. If you imagine mirroring the segment shown, you will create a triangle with no base. Next, if you imagine spinning this triangle around, you will be left with a cone. Since the segment does not connect to the axis at the bottom, the resulting cone will have an open base.
A visual example of a cone is attached below.
Henry cut a piece of yarn that was 11/6 into two pieces. List to different pairs of fractions that could show the lengths , in feet , of the two pieces.
Answers
hey can you please help me posted picture of question
Answers
Explanation:
Total outcomes of rolling a die = 6 (as there are six sides)Total outcomes of tossing a coin = 2 (there are two sides)
Total number of possible outcomes of both = 6*2=12 (Option A).
It represents the number of leaves required on the tree diagram.
Based on the family the graph below belongs to, which equation could represent the graph
Answers
Answer: Second option y=log(2x)+3
Solution:
Based on the family of graphs shown in the attached file, the equation could represent the graph is y=log(2x)+3
This graph is the graph of the funtion y=log(x) stretched horizontally by a factor of 2 and translated 3 units upward.
(2x3z2)3
------------------
x3y4z2 * (x-4z3)
Answers
[tex]\dfrac{(2x^{3}z^{2})^{3}}{x^{3}y^{4}z^2x^{-4}z^{3}}=2^{3}x^{(3\cdot3-3-(-4))}y^{-4}z^{(2\cdot3-2-3)}\\\\=\dfrac{8x^{10}z}{y^{4}}[/tex]
At 0°C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 225. Write an equation that represents the volume of the gas in terms of the temperature.
Answers
At temperature [tex]T=1C[/tex], the volume of the gas is (22+225) L.
This means that if we increase the temperature by [tex]k[/tex] degrees:
[tex]T=k^{\circ}C[/tex]
the volume of the gas is
[tex]V=22 + 225 k [L][/tex] (1)
Since T=k, we can rewrite eq.(1) as
[tex]V= 22 + 225 T [L][/tex]
which gives the expression for the volume of the gas in liters, as a function of the temperature T in Celsius.
Answer:
V=2/25T+22
Step-by-step explanation:
3. Jared has two ropes. Each rope is 9 inches long. How many inches of rope does he have in all?
Answers
The length of one rope = 9 in
Number of ropes Jared have = 2.
The total inches of rope does Jared have will be calculated as under -
We can add the length of two ropes as = 9 in + 9 in = 18 in
Or we can do it by other method as well.
The other method is by multiplying -
The total inches of rope does Jared have = The length of one rope × Number of ropes Jared have
The total inches of rope does Jared have = 9 in × 2 ropes = 18 in
Logarithmic Functions Question, Many Points
I got the first part of this question correct, I believe.
I was supposed to find the graph with a base of 3 (attached), but now I need to justify my answers, which I don't understand. Here are the choices:
The graph of f(x)= log_3 x+c must intersect with the line y= c+1 when x= 3.
The graph of f(x)= log_3 x+c must intersect with the line y= c when x= 3.
The graph of f(x)= log_3 x+c must intersect with the line x= c when y= 3.
The graph of f(x)= log_3 x+c must intersect with the line x= c+1 when y= 3.
Answers
The graph of [tex]f(x)=\log_{3}(x)+c[/tex] must intersect with the line y= c+1 when x= 3.
_____
See the attachment for plots of base-3 logarithms. Note that when [tex]c=1.4[/tex], the value of f(3) is 1 more than the value of [tex]c[/tex].
) 20% of computer chips from a certain manufacturer are defective. if 100 computer chips are purchased, what is the approximate probability that at least 20 of them are defective
Answers
what is a verbal expression?
Answers
A mathematical verbal expression is a translation into words of an algebraic expression that can consist of different operations, numbers and varibles ur welcome.
For example, the following is a verbal phrase: "John went to the store and bought five apples. Each apple cost $1.25. How much did John spend before tax?" To translate it to a verbal model, the problem solver represents the problem in simplified words that represent the cost of the apple times the number of apples bought. To translate it further to a mathematical phrase, the problem solver puts numbers in the problem: "$1.25 times 5."
Michelle invests $1000 at a bank offering 3% compounded quarterly. Write an equation to model the growth of the investment.
A) A = 1000(1.03)4t
B) A = 1000(1+.03
4
)t
C) A = 1000(1+.03
4
)4t
D) A = 1000((1.03)
4
)4t
Answers
is what I got
Answer:
C. [tex]1000( \frac{1+.03}{4})^{4t}[/tex]
Step-by-step explanation:
A rectangle floor is 24 feet long and 9 feet wide. what is it’s area of the floor in square yards?
Answers
The rectangle is 24 ft (length) by 9 ft (width):
Area = 24 * 9 => Area = 216 sq. yds.
Final answer:
The area of a rectangle floor that is 24 feet long and 9 feet wide is 216 square feet, which is equivalent to 24 square yards when converted using the fact that there are 9 square feet in a square yard.
Explanation:
The student is asking about the area of a rectangle when the dimensions are given in feet and the answer is required in square yards. To convert the area from square feet to square yards, we need to know the conversion factor between these two units of measurement.
It's established that 1 square yard is equal to 9 square feet. Thus, the area of the floor in square feet is calculated by multiplying the length by the width:
Area in square feet = Length in feet × Width in feet
= 24 ft × 9 ft
= 216 square feet
Next, we convert the area into square yards by dividing by 9:
Area in square yards = Area in square feet ÷ Conversion factor
= 216 sq ft ÷ 9 (sq ft/sq yd)
= 24 square yards
Therefore, the area of the floor in square yards is 24 square yards.
99 POINTS!!!: if i have a circle with a radius of 6 in and it is cut into 8 equal slices (like a pie) and the coordinates are (8, 5) then
what is the central angle,
what is the measure of the arc that 2 pieces together would intercept,
and the equation that represents
and circumference?
PLEASE HURRY!!!
Answers
coordinates of the center (8,5)
radius=6 in
is cut into 8 equal slices-----> 360°/8-----> 45° each slice
a) equation of a circumference
(x-h)²+(y-k)²=r²--------> (x-8)²+(y-5)²=6²
b) circumference=2*pi*r-----> 2*pi*6---> 37.68 in
if 360° (full circle) has a length of---------> 37.68 in
90° (2 pieces together)---------> x
x=90*37.68/360-----> x=9.42 in
the measure of the arc that 2 pieces together would intercept is 9.42 in
c) The central angle of one slice is 45 degrees
Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 4, f '(0) = 18
Answers
Answer:
f(x) = -x⁴ + 4x³ - x² + 18x + 4
Step-by-step explanation:
If we take the integral of f''(x) with respect to x, we get that f'(x)= -2x + 12x² - 4x³ + C.
Substituting in f'(0)=18, we get C=18.So, f'(x) = -2x + 12x² - 4x³ + 18.If we take the integral of f'(x) with respect to x, we get that f(x) = -x² + 4x³ - x⁴ + 18x + C.
Substituting in f(0) = 4, we get C=4.So, f(x) = -x⁴ + 4x³ - x² + 18x + 4To find the function f, we need to integrate its second derivative, then use the given initial conditions to solve for the constant of integration and find the exact function f(x).
Explanation:To find the function f, we need to integrate its second derivative. We integrate each term of the second derivative separately, using the power rule for integration. So, f''(x) = -2 + 24x - 12[tex]x^2[/tex] becomes f'(x) = -2x + 12[tex]x^2[/tex] - 4[tex]x^3[/tex] + C, where C is the constant of integration. Then, we integrate f'(x) to find f(x), again using the power rule for integration. Finally, we use the given initial conditions, f(0) = 4 and f'(0) = 18, to solve for the constant of integration and find the exact function f(x).
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In qam with 2 possible amplitudes, how many possible states
Answers
Find an equation of the line passing through the pair of points. Write the equation in the form Ax+ By=C. (3,2) and (5,8)
Answers
equation of the line is given by the formula:
a(x-x1)=y-y1
where a is the slope
a=(y-y1)/(x-x1)
thus using our values:
a=(8-2)/(5-3)=6/2=3
thus the equation of the line will be:
3(x-3)=y-2
simplifying the above and writing in the form of Ax+By=C we shall have:
3x-9=y-2
3x-y=-2+9
3x-y=7
thus 3x-y=7 is in the form of Ax+By=C where A=3, B=-1 and C=7
A jacket has a regular price of $80. It is on sale for 10% off. The sales tax is 7%. What is the total cost of the jacket including tax?
Answers
Sale Price= Cost - (Cost * Discount %)
Sale Price= $80 - (80 * 10%)
=80 - 8
=$72 sale price
STEP 2:
use sale price from step 1 in this equation
Final Price= Cost + (Cost * Tax %)
Final Price= $72 + (72 * 7%)
= 72 + 5.04
= $77.04
ANSWER: The final price after a 10% discount and 7% sale tax is $77.04.
Hope this helps! :)
Answer:
77.04
Step-by-step explanation:
Someone please help I only have enough points for one use.
Answers
b . i)6/25 ii) 4/15
I would apprectiate a 5 star review and a Brainliest
after lily's graduation party, 1/2 of of the cake was left. she shared the remaining cake equally with her sister Kayla and her brother Logan. what fraction of the original cake did each of them get?
show all your work please
Answers
1/2 = 50%
50% / 2 = 25%
25%= 1/4