Tell whether x and y show direct variation 5y=x
△BQH∼△SFN
What is FN ?
Answer:
23.4 in
Step-by-step explanation:
The only side of SFN we know the measurement of is FS, which is 18.2. We see from the similarity statement that FS corresponds to QB, which is 14. This gives us the ratio
14/18.2.
From the similarity statement, we see that FN corresponds to QH; this gives us the ratio
18/x
Together this gives us the proportion
14/18.2 = 18/x
Cross multiplying gives us
14(x) = 18.2(18)
14x = 327.6
Divide each side by 14:
14x/14 = 327.6/14
x = 23.4
You want to draw an enlargement of a design that is printed on a card that is 4 in. by 5 in. You will be drawing this design on a piece of paper that is 8one half in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
Answer:
The dimensions are
[tex]8\frac{1}{2}\ in[/tex]
[tex]10\frac{5}{8}\ in[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the scale factor is the ratio of its corresponding sides
step 1
Divide [tex]8\frac{1}{2}[/tex] by [tex]4[/tex]
[tex]8\frac{1}{2}=\frac{8*2+1}{2}=\frac{17}{2}\ in[/tex]
so
[tex]\frac{17}{2}/4=2.125[/tex]
step 2
Divide [tex]11[/tex] by [tex]5[/tex]
so
[tex]\frac{11}{5}=2.2[/tex]
step 3
Find the largest complete enlargement
The scale factor is the smaller of the two previous values
so
The scale factor is [tex]2.125[/tex]
The dimensions are
[tex]4*2.125=8.5=8\frac{1}{2}\ in[/tex]
[tex]5*2.125=10.625=10\frac{5}{8}\ in[/tex]
Answer:
8 1/2 in. by 10 5/8 in.
Step-by-step explanation:
which pair of ratios form a true proportion
a) 1/2=6/10
b) 6/8=5/20
c) 3/5=6/10
d) 3/9=7/80
What are the angle measures of the triangle 6 12 6sqrt3?
Answer:
The measure of angle A is 30 degree, measure of angle B is 90 degree and measure of angle C is 60 degree.
Step-by-step explanation:
The measures of given sides are 6, 12, [tex]6\sqrt{3}[/tex].
According to the Law of Cosine:
[tex]\cos A=\frac{b^2+c^2-a^2}{2bc}[/tex]
Using Law of Cosine, we get
[tex]\cos A=\frac{(12)^2+(6\sqrt{3})^2-(6)^2}{2(12)(6\sqrt{3})}[/tex]
[tex]\cos A=\frac{216}{144\sqrt{3}}[/tex]
[tex]\cos A=\frac{3}{2\sqrt{3}}[/tex]
[tex]\cos A=\frac{\sqrt{3}{2}[/tex]
[tex]A=30^{\circ}[/tex]
Similarly,
[tex]\cos B=\frac{a^2+c^2-b^2}{2ac}[/tex]
[tex]\cos B=\frac{(6)^2+(6\sqrt{3})^2-(12)^2}{2(6)(6\sqrt{3})}[/tex]
[tex]\cos B=\frac{0}{36\sqrt{3}}[/tex]
[tex]\cos B=0[/tex]
[tex]B=90^{\circ}[/tex]
Therefore, measure of angle A is 30 degree and measure of angle B is 90 degree.
According to angle sum property, the sum of interior angles of a triangle is 180 degree.
[tex]A+B+C=180^{\circ}[/tex]
[tex]30^{\circ}+90^{\circ}+C=180^{\circ}[/tex]
[tex]C=60^{\circ}[/tex]
Therefore the measure of angle C is 60 degree.
The triangle with sides 6, 12, and 6√3 has angles of 30 degrees, 60 degrees, and 90 degrees.
Given a triangle with sides 6, 12, and 6√3, we can find the angles using the Law of Cosines.
First, we use the formula for the Law of Cosines,
c² = a² + b² - 2ab * cos(C).
Let a = 6, b = 6√3, and c = 12.
We substitute these values into the formula to find angle C,
cos(C) = (6² + (6√3)² - 12²) / (2 * 6 * 6√3)
Compute the values inside the formula:
6² = 36
(6√3)² = 108
12² = 144
cos(C) = (36 + 108 - 144) / 72
cos(C) = 0
Therefore, angle C = 90 degrees.
To find the other angles, we use the Law of Sines,
(sin A / a) = (sin B / b) = (sin C / c).
We already know C = 90°, so (sin C / 12) = 1/12.
For angle A,
sin(A) / 6 = 1/12
sin(A) = 6/12 = 1/2
A = 30 degrees
For angle B:
B = 180° - 90° - 30° = 60 degrees
Therefore, the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees.
which statement best describes the function below?
f(x)=2x^2-3x+1
A.It is a one-to-one function.
B.It fails the vertical line function.
C.It is a many-to-one function.
D.It is not a function.
f(x)=2x^2-3x+1
the graph of the function is attached with the answer
As we can see that equation is quadratic and its graph is a parabola facing upward.
As we can see it passes the Vertical line test
As it passes the Vertical line test , So it is a function
And two values of x has one value of y
So it is a many to one function.
6 cards are drawn from a standard deck without replacement how many different 6 card hands are possible if the drawing is done without replacement
How do you make 3ln2+2ln4 a single logarithm?
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.
y=16(7/6)^t
Plz help!
Which stem-and-leaf plot represents the data 80, 81, 91, 92, 66, 55, 54, 30, 55, 79, 78?
Answer:The answer is below Hope this help and tthanjs for answer please like and vote excellent thanks and have a good day.
Step-by-step explanation
3 0
4
5 455
6 6
7 89
8 01 9 12PLEASE HELP!!
is it right??
8j -k+148j−k+148, j, minus, k, plus, 14 when j=0.25j=0.25j, equals, 0, point, 25 and k=1k=1
Answer:
15. It was right for me, not sure for anyone else
Step-by-step explanation:
Sue wakes up at 7:45
a.m. and jogs for 40 minutes. she then spends 45 minutes dressing for school before she catches the bus. at what time does sue get on the bus?
Which set does not contain –3?
the set of all whole numbers
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]
Let us find the value of cos([tex] \frac{3\pi}{4} [/tex]) and [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] cos(\frac{3\pi}{4} )=cos(\pi -\frac{\pi}{4} ) [/tex]
The angle [tex] \pi -\frac{\pi}{4} [/tex] lies in second quadrant.
So, [tex] cos(\frac{3\pi}{4} )=-cos(\frac{\pi}{4} ) =-\frac{1}{\sqrt{2}} [/tex]
[tex] So, cos(\frac{3\pi}{4} )=-\frac{1}{\sqrt{2}} [/tex]
Now, Let us find the value of [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] sin(\frac{7\pi}{6} ) =sin(\pi +\frac{\pi}{6} )=-sin(\frac{\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] sin(\frac{7\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]=2*[tex] \frac{-1}{\sqrt{2}} [/tex]-4*[tex] \frac{-1}{2} [/tex]
=[tex] \frac{-2}{\sqrt{2}} +\frac{4}{2} [/tex]
=[tex] \frac{-2\sqrt{2}}{2} +\frac{4}{2} [/tex]
=[tex] \frac{-1\sqrt{2}}{1} +\frac{2}{1} [/tex]
=[tex] -\sqrt{2} +2 [/tex]
=[tex] 2-\sqrt{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6})=2-\sqrt{2} [/tex]
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=8700(1.04)^4
Using exponential function concepts, it is found that it represents growth of 4%.
Exponential function:An exponential function is modeled by:
[tex]y(t) = y(0)(1 + r)^t[/tex]
In which:
y(0) is the initial value.r is the rate of change. If it is positive, it represents growth, and if it is negative, it represents decay.In this problem, the equation is:
[tex]y = 8700(1.04)^t[/tex]
Hence:
[tex]1 + r = 1.04[/tex]
[tex]r = 0.04[/tex]
Since r = 0.04 is positive, it represents a growth of 4%.
To learn more about exponential function concepts, you can take a look at https://brainly.com/question/24757163
Final answer:
The function y = 8700(1.04)^4 represents an exponential growth with a rate of increase of 4% per time period over four periods.
Explanation:
The given function is y = 8700(1.04)^4. This represents an exponential growth because the base of the exponent, 1.04, is greater than 1. To determine the percentage rate of increase, we observe that the base, 1.04, when written as a percentage, is 104%. This means that the amount increases by 4% over each time periodperiod. Since the exponent is 4, this growth occurs over four time periods. However, the overall increase is not simply 4% multiplied by 4, as exponential growth compounds wicompoundsth each time period.
A baker used the equation y = kx to find how many cupcakes he needs to fill 22 identical boxes. He found that he would need 176 cupcakes. How many cupcakes fit into each box?
Use the triangle pictured to calculate the following measurements.
Perimeter: p = ___ units Semiperimeter: s = ___units Area: A ≈ ___square
triangle is 8 by 12 by 10
Answer:
Step-by-step explanation:
The base of an isosceles triangle is 70 centimeters long. The altitude from the vertex angle to the base is 75 centimeters long. Find, to the nearest whole degree, the measure of the base angles of this triangle.
Four years ago, Tom’s age was 3/4 of the age he will be in 6 years. How old is he now?
1.66666666667 rounded to the tenth
A triangle has an area of 30 cm². The base and height are scaled by a factor of 4.
What is the area of the resulting triangle?
Enter your answer in the box.
Answer:
480cm². Verified by correct test results.
Noah was asked to find the median of the following numbers.
115, 109, 117, 136, 127, 131
Noah’s work is shown below.
109, 115, 117, 127, 131, 136
mc006-1.jpg
What error, if any, did Noah make?
A)He forgot to put the numbers in order first.
B)He crossed off the high/low number pairs incorrectly.
C)He left out a number when putting the numbers in order.
D)He did not make any error.
Write an numerical expression to show the product of the difference of 12 and 4 and the sum of 3 and 2.
the length of a rectangular prism is 4 feet, and the width is 3 feet. The volume of the prism is 9 cubic feet. In inches, what is the height of the prism?
A) 6 inches
B) 8 inches
C) 9 inches
D) 10 inches
Answer:
C 9 inches
Step-by-step explanation:
Let d represent the number of degrees in one angle of a regular polygon, and n represent the number of sides of the polygon to tessellate. which equation can be used to determine if the polygon will tessellate? 360° · n = d 360° · d = n 360° ÷ d = n n + d = 360° brainly
Answer:
360°/d = kn.
Step-by-step explanation:
To know if a regular polygon can tessellate, we divide 360 by the interior angle of the polygon and the result needs to be an integer, but not in all cases you get the number of sides of the polygon, you get a multiple of the number of sides. So, none of the options are correct, the correct would be
360/d = kn, where k is an integer.
Find the retail price of a backpack that has a wholesale price of $25 and is marked up 40%. Multiply $25 and 40% in decimal form to find the markup amount. 25(0.40) = $10 Add the wholesale price to the markup amount. What is the selling price? $10 $15 $35 $65
Answer:
35 35 35 35
Step-by-step explanation:
it 35
Given that f(x) = x2 − 3x + 3 and g(x) = the quantity of x minus one, over four , solve for f(g(x)) when x = 5. (1 point)
Answer:
The answer is 1
Step-by-step explanation:
If BE is parallel to CD, the. The value of x is:
A. 10
B. 6
C. 9
A cylindrical container holding sugar has a height of 15 inches and a diameter of 4 inches. Which of the following is the closest to the volume of the sugar container?
A.
707 cubic inches
B.
94 cubic inches
C.
754 cubic inches
D.
188 cubic inches
Using the formula V = πr²h, the volume of the cylinder is calculated as 188.4954 cubic inches, which can be rounded to 188 cubic inches, corresponding to answer choice D.
To calculate the volume of the cylindrical container holding sugar, we can use the formula for the volume of a cylinder, which is V = πr²h. Here, π is a constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.
The diameter of the container is given as 4 inches, so the radius (r) is half of the diameter, which is 2 inches. The height (h) is given as 15 inches. Plugging these values into the volume formula, we get:
V = π(2 inches)²(15 inches)
= π(4 square inches)(15 inches)
= 60π cubic inches
Using 3.14159 as the value for π, the volume calculates to:
V = 60 * 3.14159 cubic inches = 188.4954 cubic inches
So, the closest estimate to the volume of the sugar container would be 188 cubic inches, which corresponds to answer choice D.