Answer:
3 < x < 13
Step-by-step explanation:
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let x be the length of the unknown side.
Therefore, x will either be the longest side or one of the shorter sides.
Therefore:
x < 5 + 8
⇒ x < 13
And:
8 < 5 + x
⇒ 3 < x
So the range of possible values of the third side is greater than 3 and less than 13: 3 < x < 13
One-third of the class grew peas, one-third grew carrots, and one-third grew beans. The class consisted of 63 students of which five-sevenths were girls. The teacher chose the three groups to be as equal in their boy-girl composition as possible. How many boys and girls were assigned to each team?
The number of boys and girls assigned to each team is 6 and 15 respectively.
FractionNumber of students in class = 63 Number of students who grows peas = 1/3 × 63= 63/3
= 21 students
Number of students who grows carrots = 21Number of students who grows beans = 21Number of girls = 5/7 × 63
= 315/7
Number of girls = 45 students
Number of boys = 63 - 45 = 18 students
If the three groups have equal composition of boys and girls, then,
Number of boys and girls in each group is 6 and 15 respectively.
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IN
A graph of two functions is shown below:
g(x)
f(x)
Ox=1
Which of the following is an approximate solution for f(x) = g(x)?
Ox=-1
Ox=-4
Ox=2
62.5
45
37.5
30
225
15
-15
225-
-30
Hello,
Answer: We have f(x) = g(x) when x ≈ 1
(a) x = 1, is an approximate solution for f(x) = g(x).
Here, we have,
given that,
A graph of two functions is shown
f(x) and, g(x)
now, we have,
The graph has two functions, which are f(x) and g(x) and a graph.
In the graph, we can follow their intersections.
Those would be the parts of the line that would make the functions to have the same value.
The first intersection is really close to 1,
and second is very unclear, most likely beyond -2.5.
Since the highest number is 1 and the intersection is very close to 1,
we have to go with the approximate answer.
We have f(x) = g(x) when x ≈ 1.
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Is this right or wrong
Answer:
∠C and ∠F are right angles
Step-by-step explanation:
To prove that two triangles are congruent using HL, one must have:
a right angle congruent,a leg congruent, and the hypotenuse (the side across from the right angle) congruent.For this problem, there are two sides of the triangle already congruent: one could be the hypotenuse (if the right angle were across from it), and the other congruent side could be a leg. So, if we can prove either that angles C & F are right angles, or that angles A & D are right angles, that would be enough to use HL congruence.
Hence, from the answer choices provided, proving that angle C and angle F are both right angles would be sufficient to prove the triangles are congruent via HL congruence.
Side note: Proving angles B and E would not be enough to use HL congruence, because the hypotenuse is always across from the right angle. So, if angle B were a right angle, it would mean that side AC was the hypotenuse (which hadn't yet been proven or stated to be congruent).
While not enough to prove triangle congruence via HL, if angle B and E were congruent at all (right angles or not), it would be enough to prove that the triangles were congruent by SAS (side-angle-side) because it would have proven that two sides and the included angle were congruent.
PLS HELP I DON’T UNDERSTAND
The question asks for the probability that a marble is NOT YELLOW
Total Marbles: orange+yellow+blue=7+3+2=12
We need to count all marbles except yellow:
orange+blue=7+2=9
Now to find the probability that is NOT YELLOW:
[tex]\frac{All Marbles Except Yellow}{Total Marbles}[/tex]= [tex]\frac{9}{12} = \frac{3}{4}[/tex]
Answer is 3/4
Hope it helps!
Help please !!
The graph of the invertible function f is shown on the grid below.
Answer:
4
Step-by-step explanation:
→ We go up the y axis to 6 and read of the x coordinate which is 4. This is because an inverse function does the the opposite i.e. if f ( x ) = y
f⁻¹ ( y ) = x.
(Look at picture, not this) 4. Use the following equation to perform the operations below: y = (²+5 ÷ (2+3)(2-2))-21/2₂2 4. Use the following equation to perform the operations below : y = ( ² + 5 ÷ ( 2 + 3 ) ( 2-2 ) ) - 21 / 2₂2
Thank you!
The solutions when y = 0 are x = -4.796 and x = 4.796
The graph of the functionThe function is given as:
[tex]y = (\frac{x + 5}{x + 1} \div \frac{(x + 3)(x - 2)}{(x -4)(x + 1)})- \frac{1}{x - 2}[/tex]
See attachment for the graph of the function
The vertical asymptoteWhen the function is simplified, we have:
(x +3)(x -2) at the denominator of one of the terms
Set this factor to 0
(x +3)(x -2) = 0
Expand
x + 3 = 0 and x -2 = 0
Solve for x
x = -3 and x = 2
Hence, the vertical asymptotes are x = -3 and x = 2
The feature at x = -1The feature at x = -1 is a hole and, not a vertical asymptote.
This is so because the absolute value of -1 is less than the absolute values of the vertical asymptotes at x = -3 and x = 2
The solution when y = 0From the attached graph, we have:
x = -4.796 and x = 4.796 when y = 0
Hence, the solutions when y = 0 are x = -4.796 and x = 4.796
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g Minimizing the sum of the squared deviations around the line is called: predictor regression. mean squared error technique. least squares estimation. double smoothing. mean absolute deviation.
Minimizing the sum of the squared deviations around the line is called Least square estimation.
It is given that the sum of squares is around the line.
Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.
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Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER?
Answer:
66 dollars
Step-by-step explanation:
15+6=22
15×2=30
15+22+30=66
Answer:
Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER is 66 dollars.
Step-by-step explanation:
→ Is know :
Tim's money = 15 dolars Paul's money = 15 dolars + 6 dollarsRick's money = 2 × 15 dolars→ Asked :
How much did they have ALTOGETHER ?
→ Solution :
[tex] \bf{x =Tim's \: \: money + Paul's \: \: money + Rick's \: \: money }[/tex]
[tex]\bf{x =15 + (15 + 6) + (2 \times 15) }[/tex]
[tex]\bf{x =15 + 21 + 30 }[/tex]
[tex]\bf{x =36 + 30 }[/tex]
[tex]\bf{x =66 \: \: dollars }[/tex]
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Solve for m. 10m = 1
m = 0
m = 1
m = 2
m = 3
Answer:
wouldn't it be 0.1
Step-by-step explanation:
Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively.
(a) Express the position vector of p and q.
i. In terms of p and q.
ii. In terms of i, j and k
(b) Hence state the coordinates of R.
(a) i. See comment...
(a) ii. We have
[tex]\vec p = 6\,\vec\imath - 3\,\vec\jmath + 9\,\vec k[/tex]
and
[tex]\vec q = 3\,\vec\imath - 6\,\vec\jmath - 3\,\vec k[/tex]
(b) We can parameterize the line segment from P to Q by the vector function
[tex]\vec r(t) = (1-t) \vec p + t \vec q = (6-3t) \, \vec\imath + (-3-3t) \,\vec\jmath + (9-6t) \,\vec k[/tex]
with [tex]0\le t\le1[/tex]. The point R is located 1/3 of the way along this line segment, i.e. at [tex]t=\frac13[/tex], so its position vector is
[tex]\vec r\left(\dfrac13\right) = 5\,\vec\imath -4\,\vec\jmath + 7\,\vec k[/tex]
and hence its coordinates are [tex]\boxed{(5,-4,7)}[/tex].
Find the sum of a third of (a+b) and a fifth of (a+b)
Answer:
Step-by-step explanation:
If geometry symbol represented as small triangle with three sides. abc geometry congruent symbol represented as two small horizontal parallel lines and a horizontal symbol s. geometry symbol represented as small triangle with three sides. dec, what is the value of x?
The value of x in the congruent triangles abc and dec is 1
How to determine the value x?The question implies that the triangles abc and dec are congruent triangles.
The congruent sides are:
ab = de
bc = ce = 4
ac = cd = 5
The congruent side ab = de implies that:
4x - 1 = x + 2
Collect like terms
4x - x = 2 + 1
Evaluate the like terms
3x = 3
Divide through by 3
x = 1
Hence, the value of x is 1
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Complete question
Two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is 4x - 1, side bc is 4, side ac is 5. in triangle cde, side cd is 5, side de is x + 2, side ce is 4. If Δabc ≅ Δdec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
It’s is already stated on the picture.
Answer:
radius = 5
Step-by-step explanation:
Since the line is a tangent, that means the PT and OP are perpendicular (they make a right angle) Sooo, the triangle is a right triangle. Use Pythagorean Theorem to calculate or Pythagorean Triples for a shortcut (5, 12, 13)
r^2 + 12^2 = 13^2
r^2 + 144 = 169
Subtract 144
r^2 = 25
Squareroot both sides.
sqrt(r^2) = sqrt25
r = 5
The radius is 5.
X
-3
-2
Intro
-1
0
1
2
3
f(x)
-15
0
3
0
-3
O
15
Predict which statements are true about the intervals of
the continuous function. Check all that apply.
Of(x) > 0 over the interval (-3).
Of(x) ≤0 over the interval [0, 2].
Of(x) <0 over the interval (-1, 1).
Of(x) > 0 over the interval (-2, 0).
f(x) ≥ 0 over the interval [2, ..).
Done
Answer: B, D, E
Step-by-step explanation:
Statement 1 cannot be true because f(1)<0.
Statement 2 might be true.
Statement 3 cannot be true because if f is continuous, then for some value between -1 and 0, f(x) is positive by the Intermediate Value Theorem.
Statement 4 might be true.
Statement 5 might be true
can you please solve 2x+29+3x - 4
Answer:
5x + 25
Step-by-step explanation:
2x+29+3x+4
Step 1: Arrange it:- 2x+3x+29-4
Step 2:- Add and Subtract the terms:- 5x + 25
HOPE IT HELPS!
Hey there!
EQUATION:
2x + 29 + 3x - 4
COMBINE the LIKE TERMS
(2x + 3x) + (29 - 4)
2x + 3x + 29 - 4
SIMPLIFY IT!
5x + 25
Therefore, your answer should be:
5x + 25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Can someone help me out with this geometry problems? And explain how u got the answers, it’s urgent
Answer:
Step-by-step explanation:
TODAY, Kyle has 11 pounds to lose to get to his goal weight. Tuesday he was 196 lbs. TODAY, he is down 3 lbs.
What is Kyle’s weight today?
What is Kyle’s goal weight?
How much water should be added to a 15 gallon solution of 35% hydrogen peroxide to create an 8% solution? how many gallons would there be of the 8% solution?
15 gallons of 35% peroxide solution contains 0.35 × 15 = 5.25 gallons of hydrogen peroxide. The rest of the volume is made up of 15 - 5.25 = 9.75 gallons of water.
If we add [tex]x[/tex] gallons of water to the solution, the amount of hyrdrogen peroxide in the solution stays the same, but the volume of water increases to [tex]9.75+x[/tex] gallons, and the total volume increases to [tex]15+x[/tex] gallons.
To get a concentration of 8% in this diluted solution, we add [tex]x[/tex] gallons of water such that
[tex]\dfrac{5.25}{15+x} = 0.08[/tex]
Solve for [tex]x[/tex].
[tex]5.25 = 0.08 (15 + x)[/tex]
[tex]5.25 = 1.2 + 0.08x[/tex]
[tex]0.08x = 4.05[/tex]
[tex]x = 50.625[/tex]
To get the desired concentration, one must add 50.625 gallons of water, and one will end up with a total volume of 65.625 gallons of solution.
On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4).
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary.
x =
y =
The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 is; (-2.6, 5.2)
How to find coordinate points?
The coordinate of the points are given as:
A(-4, 8)
B(2, -4)
Ratio of partition is given as; 3:10
Now, the point at the given ratio is calculated from the formula;
C = [(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]
Thus;
C = [(3*2 + 10*-4)/(3 + 10)], [(3*-4 + 10*8)/(3 + 2)]
C = (-34/13, 68/13)
C = (-2.6, 5.2)
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Answer:
-2.6, 5.2
Step-by-step explanation:
50 more points
sdadadada
Switch the variable x and y with each other. Then the correct option is B.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = 3x – 10
Then the inverse function of the f(x) will be
Put y in place of f(x).
x = 3y – 10
3y = x + 10
y = (x + 10) / 3
Switch the variable x and y with each other.
Then the correct option is B.
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What is the slope of the graphs and the equation?
Answer:
The slope formula is used to find the slope of a line that joins two points (x₁, y₁) and (x₂, y₂). Using this formula, the slope of the line is, m = (y₂ - y₁) / (x₂ - x₁). We can use the same formula to find the slope of a line from its graph also.
3
Writing Linear Equations Using Similar Triangles
y
2
Intro
(xy)
Use similar triangles to determine the equation of the
line with a slope of 2/3 that passes through the point (0,
3).
What is the ratio of the rise to the run in the smaller
triangle in the diagram? |
What is the ratio of the rise to the run in the larger
triangle in the diagram?
What is the equation of the line in slope-intercept form?
Done
The solutions are given below:
1. 3y- 9 = 2x
2. 2/3.
3. y/x
4. y = (2/3)x + 3
What is equation of line?The equation of a line with one given point (x1, y1) is (y - y1) = m(x - x1). Here m is the slope of the line.
The complete question is:
On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7.
Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).
What is the ratio of the rise to the run in the smaller triangle in the diagram?
What is the ratio of the rise to the run in the larger triangle in the diagram?
What is the equation of the line in slope-intercept form?
1. slope= 2/3
coordinates= (0, 3)
y-y1 = m(x-x1)
y-3 = 2/3(x-0)
y-3 = 2/3x
3y- 9 = 2x
2. The ratio of the rise to the run in the smaller triangle in the diagram
is y/x = 2/3
3. The ratio of the rise to the run in the larger triangle = y/x
4. The equation of the line in slope-intercept form is given by:
y = (2/3)x + 3
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VERBAL
1. Explain how to find the input variable in a word problem that uses a linear function.
Answer:
The independent variables in most cases is input variable. That is a value that does not depend on any other value and it can change independently.
Step-by-step explanation:
In the question, it is given that a problem uses an input variable.It is required to explain how to find the input variable in a word problem that uses a linear function.In order to find the input variable in a world problem, seek for the independent variable.That is a value that does not depend on any other value and it can change independently.Some other values change based on that value. In these types of functions, this value is mostly marked as x.Dalinda spins a spinner 60 times. the table shows her data.
spinner
results
color spins
red
10
blue
30
yellow
15
green
5
dalinda will spin one more time,
based on her data, what is the probability that the pointer will land on blue?
od. 110
o e
10 a 1
o b. 1 / 3
o c. 1 /
The answer is 1/2 .
What is probability ?The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes. The chance that a given event will occur. The number of ways of achieving success. the total number of possible outcomes.In given question ,
Dalinda spins a spinner = 60 times.
blue = 30
The probability that the pointer will land on blue = 30 / 60 ⇒ 1/2
Therefore, the answer is 1/2 .
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help me please!!! 50 points
I am unfortunately not too sure about this, I have not heard of a proportional equation before even after getting my degree, because an equation usually isn't proportional, only expressions are and there are usually 2 terms.
Here's my best attempt. The first equation isn't proportional since y is inversely proportional to the 7 in the denominator. The second is proportional, and the k constant is 10.
I cannot provide any further explanations.
Let me know if this was helpful!
Answer: Since y is inversely proportional to the 7 in the denominator, the first equation cannot be a proportional expression. The k constant is 10 and the second is proportional.
Step-by-step explanation:
25) lan bikes 18 mph for 15 miles. Which is true? a. lan rode exactly 1 hour b. lan rode more than 1 hour C. lan rode less than 1 hour
Answer:
C. Ian rode less than 1 hour
Step-by-step explanation:
It never hurts to think about what the problem statement is telling you. Ian rode at a speed that would take him 18 miles in 1 hour.
InterpretationClearly, Ian would pass the 15-mile mark in a 1-hour ride before an hour had elapsed. If he only rode 15 miles, he rode less than 1 hour.
The actual time Ian rode is given by the relation between speed, time, and distance.
time = distance/speed
time = (15 mi)/(18 mi/h) = (15/18) h = 5/6 h
Ian's riding time was 5/6 of an hour, which is less than 1 hour.
Help me please!
a = 3, b = 5, and c = 7. What is m&Bº to the nearest tenth?
Answer: m∡B°=38,2°.
Step-by-step explanation:
a=3, b=5, c=7 ∡B°=?
[tex]b^2=a^2+c^2-2*a*ccosB^0\\2*a*c*cosB^0=a^2+c^2-b^2\\cosB^0=\frac{a^2+c^2-b^2}{2*a*c} \\cosB^0=\frac{3^2+7^2-5^2}{2*3*7} \\cosB^0=\frac{9+49-25}{2*3*7} \\cosB^0=\frac{33}{42} \\cosB^0=\frac{11}{14}\\[/tex]
m∡B°=arccos[tex](\frac{11}{14})[/tex]
m∡B°≈38,2°.
Good luck!
Select the correct answer.
Consider the following equation.
4(-) + 5 = 3 + 4
Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point.
PLEASE HELP BEFORE TOMORROW MORNING!! I’ll give Brainiest answer!!
The solution to the graph given is 7/16.
How to illustrate the graph?It should be noted that a graph is used to show the relationship between the variables illustrated.
Here, the successive approximation is used to solve equations.
This is done by the comparison to the sequence of the known quantities.
Here, the equation given is 4(-)x + 5 = 3^x + 4. solution to the graph given is 7/16. This is based on the graph given.
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A (not necessarily convex) 11-sided polygon can have at most how many reflex interior angles?
The value for each interior angle in the polygon will be 147.27°.
How to calculate the interior angles?The total angles in the 11 sided polygon will be:
= (n - 2) × 180
= (11 - 2) × 180
= 9 × 180°
= 1620°
Each angle will be:
= 1620°/11
= 147.27°
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GEOMETRY)
What is the equation of a circle having radius 8 and center (2,-7)?
(Picture is below) Thank you!
Answer:
(x - 2)² + (y + 7)² = 64
(fourth option listed / option D)
Step-by-step explanation:
as you likely know, the equation of a circle (centered at origin) is x²+y²=r²
now, let's say we want to write this using the center (the origin), it could look like this:
(x - 0)² + (y - 0)² = r²
(the center is 0,0)
[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]
We can use this for any center, and we write our circle equation as:
(x - h)² + (y - k)² = r²
(h, k) is the center
So, let's apply the information we know
our (h, k) is (2, -7)
so let's fill that in:
(x - h)² + (y - k)² = r²
(x - 2)² + (y - -7)² = r² (simplify)
(x - 2)² + (y + 7)² = r²
now, we also know that our "r" (r is the radius) is 8, so let's fill that in too:
(x - 2)² + (y + 7)² = r²
(x - 2)² + (y + 7)² = 8² (simplify)
(x - 2)² + (y + 7)² = 64
So, we have found the equation of our circle to be:
(x - 2)² + (y + 7)² = 64
hope this helps! (and hope this makes sense) have a lovely day :)