Answer:
Hmm... None of these choices seem to be correct.
Step-by-step explanation:
In 30-60-90 triangles, the length of the shorter leg is half the length of the hypotenuse. In this case, the hypotenuse is the diagonal. So half of 28 is 14. Therefore, the width of the TV is 14 inches. This eliminates answer choices A and C, that would imply the answer is either B or D, but.....In 30-60-90 triangles, the length of the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg. So if we were being exact, the length of the TV is [tex]14\sqrt{3}[/tex] . And if we rounded, the length would be about 24.25. There is no choice in your options that is similar to our conclusions. Maybe you should contact your teacher about this. Have a nice day! :)The exact dimensions of the TV are approximately 14 inches by [tex]14\sqrt{3}[/tex] inches, which simplifies to 14 inches by 142 inches
The correct answer is:
B. 14 inches by 142 inches.
To find the exact length and width of the TV, we can use the properties of a 30-60-90 right triangle. In such a triangle, the side lengths are related as follows: the length of the side opposite the 30-degree angle is [tex]\( \frac{1}{2} \)[/tex] times the length of the hypotenuse, and the length of the side opposite the 60-degree angle is [tex]\( \frac{\sqrt{3}}{2} \)[/tex] times the length of the hypotenuse.
Given that the diagonal of the TV forms the hypotenuse of two 30-60-90 right triangles, let's denote the length and width of the TV as [tex]\( L \)[/tex] and [tex]\( W \)[/tex] respectively, and the length of the diagonal as [tex]\( D \).[/tex]
We have the following equations:
[tex]\[ L = \frac{1}{2}D \][/tex]
[tex]\[ W = \frac{\sqrt{3}}{2}D \][/tex]
Given that the diagonal [tex]\( D = 28 \)[/tex] inches, we can substitute this value into the equations to find the exact length and width:
[tex]\[ L = \frac{1}{2} \times 28 = 14 \text{ inches} \][/tex]
[tex]\[ W = \frac{\sqrt{3}}{2} \times 28 \approx 14\sqrt{3} \text{ inches} \][/tex]
Now, we need to rationalize the denominator for the width:
[tex]\[ W = 14\sqrt{3} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{42}{\sqrt{3}} \][/tex]
To rationalize the denominator, multiply both numerator and denominator by[tex]\( \sqrt{3} \):[/tex]
[tex]\[ W = \frac{42\sqrt{3}}{3} = 14\sqrt{3} \text{ inches} \][/tex]
So, the exact dimensions of the TV are approximately 14 inches by [tex]14\sqrt{3}[/tex] inches, which simplifies to 14 inches by 142 inches. Therefore, the correct answer is B.
Complete question:
The diagonal of a TV is 28 inches long. Assuming that the diagonal form a pair of 30-60-90 right triangles, what are the exact length and width of the TV?
A. 55 inches by 568 inches
B. 14 inches by 142 inches
C. 56 inches by 56.5 inches
D. 14 inches by 14.5 inches
A dilation produces a smaller figure. Which is a possible scale factor?
A dilation producing a smaller figure requires a scale factor less than 1. If the scale factor is 1/2, the model size is half the actual size. By setting up and solving a proportion, actual dimensions can be calculated.
Explanation:When a dilation results in a smaller figure, the scale factor used is less than 1. Think of the scale factor as a fraction where the actual size is the denominator and the model size is the numerator. For instance, a scale factor of 1/2 would mean that the model is half the size of the actual figure.
For a practical example: if we have a scale factor of 1:4 and the scale measurement is 4, the actual dimension can be found by setting up a proportion as 1/4=4/x, solving for x would give us the actual dimension, which in this case would be 16.
Please answer.
The table represents the function f(x) = 2x+1
Which value goes in the empty cell?
A)3
B)5
C)8
D)23
Replace the x in the equation with the x value in tha table for the missing f(x) and calculate:
f(x) = 2x +1 = 2(2) +1 = 4 +1 = 5
The answer is B) 5
The table represents the function f(x) = 2x +1. The value goes in the empty cell is 5. The answer is B) 5.
What is a function?A function is a type of relation, or rule, that maps one input to specific single output.
The table represents the function
f(x) = 2x +1
Replace the x in the equation with the x value in the table for the missing f(x)
F( 2) = 2(2) +1
F( 2) = 4 +1
F( 2) = 5
The answer is B) 5
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What is the midpoint between (-2, -3) and (1, 0.5)
Answer:
(-1/2,-1.25)
Step-by-step explanation:
Once you plot the points, you should be able to find the midpoint formula.
The midpoint between the points (-2, -3) and (1, 0.5) is (-0.5, -1.25).
To find the midpoint between two points, you average the x-values and the y-values of the given points separately. The formula for the midpoint M between two points P1(x1, y1) and P2(x2, y2) is
M = ((x1 + x2) / 2, (y1 + y2) / 2)
Applying this to the given points (-2, -3) and (1, 0.5), we calculate the midpoint as follows:
Average the x-values:
(-2 + 1) / 2 = -0.5
Average the y-values:
(-3 + 0.5) / 2 = -1.25
The two right scalene triangles shown are similar , but not congruent. Which statement about the triangles is not true
Answer:
Third choice.
The right correspondence is [tex]\angle CDB \cong \angle ECD[/tex]
Step-by-step explanation:
The third choice is not true, that is
[tex]\angle CDB[/tex] NOT corresponds to [tex]\angle ECD[/tex]
If [tex]\triangle CBD \sim \triangle CDE[/tex], then corresponding sides are proportional, and corresponding angles are congruent. The corresponding angle of [tex]\angle CDB[/tex] is
[tex]\angle CDB \cong \angle ECD[/tex]
Therefore, the third option shows a wrong correspondence, that's the right choice in this case, because it doesn't express a valid correspondence.
Ed decides to include more fruit in his diet he go to the grocery store over the weekend and buy six apples six oranges and six avocados the total cost is $19.50 write an equation
A=apple o=orange a=avocado
6A+6o+6a=19.50
Happy To Help! :D
Answer:
x + y + z = 3.25
Step-by-step explanation:
We are given that Ed buys six apples, six oranges and six avocados and their total cost is $19.50.
We are to write an equation representing this.
Assuming apples to be x, oranges to be y and avocados to be z, we can write it as:
[tex] 6 x + 6 y + 6 z = 1 9 . 5 0 [/tex]
Simplifying it by taking the common out to get:
[tex]x+y+z=3.25[/tex]
will mark brainliest!!
Solve the system of equations. x2 = y + x + 8
y = -x + 2
A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
B) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 - radical 10 )
C) ( radical 10 , 2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
D) ( radical 10 , -2 - radical 10 ) and (- radical 10 , 2 + radical 10 )
Answer:
the answer is A) ( radical 10 , 2 - radical 10 ) and ( radical 10 , 2 + radical 10 )
Step-by-step explanation:
Find the missing exponent. Explain 5^11/5^?=5^4
Answer:
The missing exponent is 5^7
Step-by-step explanation:
5^11/5^?=5^4
1. Subtract the exponents from each other.
11-4=7
2. Plug 7 in as the exponent.
5^11/5^7
3. 11-7=4 therefore, 5^11/5^7 equals 5^4.
Answer:
? = 7Step-by-step explanation:
[tex]\text{We know:}\ \dfrac{a^n}{a^m}=a^{n-m}.\\\\\dfrac{5^{11}}{5^{?}}=5^4\\\\5^{11-?}=5^4\to?=7\ \text{because}\ 11-7=4[/tex]
Jon drove 365 on 20 gallons of gas. How many miles did he get per gallon?
Answer:
18.25
Step-by-step explanation:
365 ÷ 20 = 18.25
Jon drove 365 miles on 20 gallons of gas, so to find out how many miles he got per gallon, you divide 365 miles by 20 gallons. The result is 18.25 miles per gallon.
Explanation:To solve this problem, you need to divide the total number of miles that Jon drove by the number of gallons of gas he used. This is because the miles per gallon is calculated by dividing the total miles driven by the amount of gas used.
So, in this case, you would do the following calculation: 365 miles ÷ 20 gallons = 18.25 miles per gallon
This means that Jon got 18.25 miles per gallon of gas.
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an outcome or set of outcomes of an experiment or situation
Answer: Probability theory would be my best guess, but I would need more information to be able to fully answer this question.
Step-by-step explanation:
What the equation of the quadratic function in standard form represented by the graph
Answer:
x^2 +6x +8
Step-by-step explanation:
The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).
The standard form of the function with zeros p and q is ...
(x -p)(x -q) = x^2 -(p+q)x +pq
So, for zeros p=-4, q=-2, the standard form is ...
x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8
We can check to make sure the above vertex point satisfies this function:
(-3)^2 +6(-3) +8 = 9 -18 +8 = -1
The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.
The function is ...
y = x^2 +6x +8
Sam worked 26 hours so far this week. He normally works a 40 hour week What fraction and percent represents the portion of hours he has worked? Simplify the fraction
Answer:
13/20, 65%
Step-by-step explanation:
So he has worked 26 hours out of 40 so that becomes 26/40 that is equal to 13/20 so that is your fraction and to convert to a percentage times 100 go that equals 65 so 65%
Please answer right away
Answer:
$29000 with a margin of error of $5000
Step-by-step explanation:
We have that the midpoint between the given values is
(X1+X2) / 2 = ($34000+$24000)/2 = $29000
We have that the midpoint between the given values would be
(X2-X1)/2=($34000-$24000)/2=$10000/2=$5000
So I can write that approach as $29000 with a margin of error of $5000
Done
Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models the situation as well as the correct solution for the situation. An isosceles right triangle has sides that are x + 2 units long and a hypotenuse that is 8 units long. What is the length of the missing sides of the triangle?
Answer:
2(x^2 + 4x - 28) = 0.
The length of the missing sides are:
4√2 units.
or 5.66 units ( to the nearest hundredth).
Step-by-step explanation:
Applying the Pythagoras Theorem:
8^2 = (x + 2)^2 + (x + 2)^2
2(x^2 + 4x + 4) = 64
2x^2 + 8x + 8 - 64 = 0
2x^2 + 8x - 56 = 0
2(x^2 + 4x - 28) = 0 models the situation.
Solving:
x = [- 4 +/- √(4^2-4*1*-28)] / 2
= (-4 +/- √128) / 2
= (-4 + 8√2) / 2 , (-4 - 8√2) / 2 (we ignore this negative root).
= -2 + 4√2.
This is 3.66 to the nearest hundredth.
So the length of the 2 equal sides is 2 + (- 2 + 4√2) = 4√2.
or 5.66 to the nearest hundredth.
Sal wants to build a robot. He puts a sphere on top of a cylinder.what will probably happen?
Answer:
It depends on which side of the cylinder. If she puts it on the curved side, it will roll off. If she puts it on the flat side and stabalizes it, it will stay in place if no further force is acted on it.
Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 points. In the last 4 innings, her team scored the same number of points per inning, and the other team did not score any more points. Kim's team won with the most points.
Write an inequality to determine the number of points per inning, ppp, Kim's team could have scored.
Answer:
The required inequality is [tex]6+4p>17[/tex].
Step-by-step explanation:
Let p represent the number of runs per inning.
It is given that the team scores the same number of runs per inning and the other team did not score any more points. So, the total score of other team after last four inning is 17.
Kim's team total score in last four inning is 4p. So, the total score of Kim's team after last four inning is
[tex]6+4p[/tex]
Kim's team win if the total score of other team after last four inning is less than the Kim's team.
[tex]6+4p>17[/tex]
Therefore the required inequality is [tex]6+4p>17[/tex].
Answer:
6+4p>17
Step-by-step explanation:
3 per inning
Given f(x) = e^x and g(x) = x – 2, what is the range of (g*f)(x)
The range of (g * f)(x) is all real numbers (ℝ).
Explanation:Composing functions: We first need to understand that (g * f)(x) refers to the composition of g and f, where f is evaluated first and then its output is used as the input for g. So, (g * f)(x) = g(f(x)) = g(e^x).
Analyzing g(e^x): The function g(x) simply subtracts 2 from its input. Since e^x is a real number for all real values of x, g(e^x) will also be a real number for all real values of x.
Range of the composed function: Therefore, as g(e^x) can take any real value, the range of (g * f)(x) will be all possible outputs of g(e^x), which is all real numbers (ℝ).
In simpler terms, no matter what real number you input into f(x), the final output after applying g(x) will always be a real number. This is because the subtraction in g(x) doesn't restrict the output in any way.
36+4x=x^2+15
What is x?
X = -3 or X = 7
Step 1: Simplify both sides of the equation.
Step 2: Subtract x^2+15 from both sides.
Step 3: Factor left side of equation.
Step 4: Set factors equal to 0.
Answer:
x=7 or x=-3
Step-by-step explanation:
36+4x=x^2+15
36-15+4x=x^2
21+4x=x^2
0=x^2-4x-21
0=x^2-(7-3)x-21
0= x^2-7x+3x-21
0= x(x-7)+3(x-7)
0= (x-7)(x+3)
so either
x-7=0
x=7
or x+3=0
x=-3
A squirrel runs across a road in 3 seconds. The road was more than 34 feet wide. Which inequality can be used to determine the squirrel’s speed?
3r is greater than 34
3r is less than 34
r/3 is greater than 34
r/3 is less than 34
What is the solution to the inequality? Round to the nearest tenth, if necessary.
r less than 11.3
r greater than 11.3
r less than 102
r greater than 102
How can you interpret the solution?
The squirrel can run at least 11.3
The squirrel can run faster than 11.3
The squirrel can run no faster than 102
The squirrel can run slower than 102
Answer:
Step-by-step explanation:
squirrel speed (r) x seconds (3) has to be more than 34 feet
3r is greater than 34
r is greater than 11.3
34 / 3 = 11.333
11.3 (squirrels speed) x 3 (seconds) = 33.9 feet
the squirrel can run faster than 11.3
Answer:
A). Option A
B). Option B
C). Option B
Step-by-step explanation:
A). A squirrel runs across a road in 3 seconds.
Width of the road is more than 34 feet.
We have to calculate the squirrel speed.
Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
= [tex]\frac{34}{3}[/tex]
Since distance is more that 34 so the speed will be more than [tex]\frac{34}{3}[/tex]
This is because Speed ∝ Distance.
Let r is the speed of squirrel.
r > [tex]\frac{34}{3}[/tex]
3r > 34
Option A is the correct option.
B). Inequality is 3r > 34
r > [tex]\frac{34}{3}[/tex]
r > 11.3
Option B is the answer.
C). The squirrel can run at faster than 11.3 feet per second.
Option B.
The Roosevelts and the Jaspers live in the same city and pay the same sales
tax rate, and both families made $16,000 in taxable purchases last year, if the
Roosevelts made $91.000 and the Jaspers made 37000 last year, is the
sales tax in their city an example of a regressive tax?
Answer:
Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.
Step-by-step explanation:
Regressive tax is a constant, instead of a percentage of income. Those with a lower income would pay a higher percentage of their income. Both families, irregardless of income, paid $16,000 in taxes.
APEX
Answer:
Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.
Step-by-step explanation:
A regressive tax is one that collects a smaller percentage of the income as the person earns more. That is to say that at higher profit or higher income, the percentage of taxes that must be paid on the total tax base is lower.
In this way the poor are relatively more affected than the rich.
The Roosevelts made $91.000 (high income)
The Jaspers made $37.000 (low income)
But both paid the same sales tax rate of $16,000.
This type of tax does not have a redistribution effect of wealth. On the contrary, if it is a very high tax, it can accentuate inequality in a society.
whats is pemdas in math
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
What PEMDAS stands for is that in a mathematical equation, parentheses has the priority of being solved. The second priority goes to exponents, then Multiplication and Division, and then finally Addition and Subtraction.
[tex]\text{Hey there!}[/tex]
[tex]\text{The P stands for parentheses}[/tex]
[tex]\text{The E stands for exponents}[/tex]
[tex]\text{The M stands for multiplication/multiply}[/tex]
[tex]\text{The D stands for division/divide}[/tex]
[tex]\text{The A stands for Addition/Add}[/tex]
[tex]\text{The S stands for Subtraction/Subtract}[/tex]
[tex]\text{Some people refer to it as: (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally}[/tex] [tex]\text{method for the abbreviations}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
A rectangular block measures 3 cm x 4 cm x 3 cm how much water would it displace?
Answer:
36c^3m^3x^2
Step-by-step explanation:
you first multiply 3 cm by 4 cm by 3 cm to get 36 cm.its mass in air and its effective mass when submerged in water (density = 1 gram per cubic centimeter).1.0 g/cm3then you get the answer 36c^3m^3x^2If a data set has 20 data values, the number of values in the upper quartile is ?
Answer:
the answer is 5.5
explanation:
just did the test
Answer: The uper quatile Q3=15.75
Step-by-step explanation:
Q3=3/4(N+1)
Q3=3/4(20+1)
Q3=3/4(21)
Q3=63/4
Q3=15.75
PLEASE HURRY!! VW is parallel to YZ in the map below. Which proportion solves for the distance between Y and Z?
Answer:
[tex]\frac{3}{9}=\frac{4}{x}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
Triangle XVW is similar to triangle XZY
therefore
[tex]\frac{YZ}{VW}=\frac{XZ}{XV}[/tex]
substitute the given values
[tex]\frac{x}{4}=\frac{9}{3}[/tex]
[tex]x=3*4=12\ miles[/tex]
Answer:
A
Step-by-step explanation:
A circle has a radius of 5ft and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which equation gives the measures of the central angle q?
Answer:
[tex]\frac{q}{360}[/tex] × π10 = 7
Explanation:
The formula to find arc length is [tex]\frac{x}{360}[/tex] × [tex]\pi r^{2}[/tex]
Simply plug in radius and arc length to get your equation.
Answer:
Central angle = 80.21°
Step-by-step explanation:
The arc length in circle is the product of radius and central angle made by the arc in radians.
That is
l = rθ
Here given the values r = 5 ft and l = 7 ft
Substituting
7 = 5 x θ
θ = 1.4 radians
[tex]\theta =1.4\times \frac{180}{\pi }=80.21^0[/tex]
Central angle = 80.21°
solve for X
x + 53 = 231
Answer:
x=178
Step-by-step explanation:
Since 53 is being added to x, you will subtract 53 from both sides. 231-53 equals 178, therefore x=178
25. Find the area of the trapezoid. Leave your answer in simplest radical form. The figure is not drawn to scale.
please answer ASAP if you have the answers for the whole exam I'll take them to please
A.48cm^2
B.40cm^2
C.32cm^2
D.44cm^2
Answer:
Option D. [tex]44\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]h[/tex]
we have
[tex]b1=8\ cm[/tex]
[tex]b2=(4+8+2)=14\ cm[/tex]
[tex]h=4\ cm[/tex]
substitute the values
[tex]A=\frac{1}{2}[8+14](4)=44\ cm^{2}[/tex]
Answer:
D. 44cm^2
Step-by-step explanation:
Which equation is graphed here?
Answer:
The third one or the first one
Step-by-step explanation:
Can't be +4 or -4
Answer:
The equation of the line on the graph is y - 4 = -3(x+1)
Having trouble to find the answer help plssssss
Answer:
it is 20
Step-by-step explanation:
5 * 20 = 100
100 - 10 = 90 which equals a angle in a right angle triangle
Answer:
The value of x is 11 ⇒ answer B
Step-by-step explanation:
* lets check the properties of the square
- Its four aides are equal
- Its four angles are equal and the measure of each one is 90°
- Its diagonals bisect its vertices
∵ BD is a diagonal of the square
∴ BD bisects angle B
∴ m∠ABD = m∠CBD
∵ B is a vertex of the square
∴ m∠B = 90°
∴ m∠ABD = m∠CBD = 90 ÷ 2 = 45°
∵ m∠ABD = (5x - 10)°
∴ (5x - 10)° = 45° ⇒ add 10 to each side
∴ 5x = 55 ⇒ divide both sides by 5
∴ x = 11
* The value of x is 11
what is the range of the function on the graph
Answer:
All real numbers greater than or equal to -2.
Step-by-step explanation:
The range is the set of values of the y-coordinates of the points on the graph.
The smallest y-coordinate is -2. All real numbers greater than equal to -2 are the range.
Answer: All real numbers greater than or equal to -2.
on Saturday morning Owen earned $29. By the end of the afternoon he had earned a total of $67. Enter an equation, using x as your variable to determine whether Owen earned $38 or $34 on Saturday afternoon
Answer:
$67 = $29 + $ x
Step-by-step explanation:
Given that on Saturday morning Owen earned= $29
End of afternoon amount total earned was= $67
Let's find the amount earned in the afternoon=?
Let's take the amount earned in the afternoon to be =$ x
Equation for total amount earned by the end of afternoon= $29 + $x
But we know total amount earned by end of afternoon was=$67 hence
the equation to determine afternoon amount will be;
$67 = $29 + $ x ----------------------------go ahead and solve for x
$67-$29 = $ x
$ 38 = x