Answer:
The correct answer option is 'orthocenter'.
Step-by-step explanation:
The point of concurrency of the altitudes of a triangle is called the 'orthocenter'.
Orthocenter is the point in a triangle where all of the three altitudes of the triangle intersect each other.
Explaining further, a line which is perpendicular to the opposite side and passes from a vertex of a triangle is called the altitude of the triangle.
Therefore, the correct option is D. orthocenter.
Match each inequality to the number line that represents its solution
Answer:
Part 1) shaded area at left of x=8 (close circle) ---> [tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Part 2) shaded area at left of x=-5 (close circle) ---> [tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Part 3) shaded area at left of x=-6 (close circle) ---> [tex]\frac{3x}{2}+105 \leq 96[/tex]
Part 4) shaded area at left of x=7 (close circle) ---> [tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
see the attached figure
Step-by-step explanation:
Part 1) we have
[tex]-\frac{x}{10}+\frac{1}{5} \geq-\frac{33}{55}[/tex]
Multiply by -10 both sides
[tex]x-2 \leq 6[/tex]
Adds 2 both sides
[tex]x \leq 6+2[/tex]
[tex]x \leq 8[/tex]
The solution is the interval -----> (-∞,8]
All real numbers less than or equal to 8
In a number line the solution is the shaded area at left of x=8 (close circle)
Part 2) we have
[tex]-\frac{50x}{3}-\frac{11}{6} \geq \frac{163}{2}[/tex]
Multiply by -6 both sides
[tex]100x+11 \leq -489[/tex]
Subtract 11 both sides
[tex]100x \leq -489-11[/tex]
[tex]100x \leq -500[/tex]
Divide by 100 both sides
[tex]x \leq -5[/tex]
The solution is the interval -----> (-∞,-5]
All real numbers less than or equal to -5
In a number line the solution is the shaded area at left of x=-5 (close circle)
Part 3) we have
[tex]\frac{3x}{2}+105 \leq 96[/tex]
Multiply by 2 both sides
[tex]3x+210 \leq 192[/tex]
Subtract 210 both sides
[tex]3x \leq 192-210[/tex]
[tex]3x \leq -18[/tex]
Divide by 3 both sides
[tex]x \leq -18/3[/tex]
[tex]x \leq -6[/tex]
The solution is the interval -----> (-∞,-6]
All real numbers less than or equal to -6
In a number line the solution is the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]-\frac{13x}{18}+\frac{5}{9} \geq -\frac{81}{18}[/tex]
Multiply by -18 both sides
[tex]13x-10 \leq 81[/tex]
Adds 10 both sides
[tex]13x \leq 91[/tex]
Divide by 13 both sides
[tex]x \leq 91/13[/tex]
[tex]x \leq 7[/tex]
The solution is the interval -----> (-∞,7]
All real numbers less than or equal to 7
In a number line the solution is the shaded area at left of x=7 (close circle)
What is the ordered pair of M’ after point M (5, 6) is rotated 90° counterclockwise?
ANSWER
(-6,5)
EXPLANATION
The mapping for 90° counterclockwise rotation has mapping
[tex](x,y)\to (-y,x)[/tex]
The coordinates of M are (5, 6)
To find the coordinates of M' we substitute the coordinates of M into the rule.
[tex]M(5, 6)\to M'(-6,5)[/tex]
Hence the ordered pair of M' after point M (5, 6) is rotated 90° counterclockwise is (-6,5)
What is the equation of the tangent line passing through the point (1, 3) of the graph of the function f(x) = x2 + x + 1?
ANSWER
[tex]y = 3x[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + x + 1[/tex]
To find the gradient function, we find the first derivative;
[tex]f'(x) = 2x+ 1[/tex]
To find the gradient at (1,3), we put x=1 into the gradient function to get;
[tex]f'(1) = 2(1)+ 1 = 3[/tex]
The equation of the tangent line is
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get,
[tex]y-3=3(x-1)[/tex]
This simplifies to
[tex]y = 3x - 3 + 3[/tex]
[tex]y = 3x[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The roots of an equation are x = -1 ± i. The equation is x2 + + 2 = 0.
Answer:
If the roots of an equation are x = -1 ± i, it means that the factorized form of that equation is: (x + 1 + i)(x+ 1 - i) = 0.
Using the distributive property, we have:
(x + 1 + i)(x+ 1 - i) = x^2 + x - ix + x + 1 - i + ix + i + 1
Combining like-terms and simplifying:
⇒ x^2 + x + x + 1 + 1 = x^2 + 2x + 2 = 0
Therefore, the stament is correct. If the roots of an equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.
Answer:
equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.
Step-by-step explanation:
its correct
. You deposit $10,000 in an account that pays 6.92% annual interest. Find the balance after 5 years if the interest is compounded with the given frequency.
Final answer:
To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, use the formula A = P(1 + r/n)^(nt). The balance after 5 years will be $13,933.16.
Explanation:
To find the balance after 5 years with an annual interest rate of 6.92% compounded annually, you can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal is $10,000, the annual interest rate is 6.92%, and n is 1 (compounded annually), and t is 5 years.
Calculate (1 + r/n)^(nt): (1 + 0.0692/1)^(1 * 5) = 1.0692^5 = 1.39331595
Calculate the final amount using the formula: A = 10,000 * 1.39331595 = $13,933.16
Therefore, the balance after 5 years will be $13,933.16.
How can you verify that the solution to a proportion is correct?
Final answer:
To verify a proportion solution, substitute the answer back into the original equation, check that the units are consistent, and ensure the answer's reasonableness in terms of magnitude, sign, and units.
Explanation:
To verify that a solution to a proportion is correct, one effective method is to perform a check by substituting the solution back into the original proportion equation. Here's how you can ensure the correctness of the solution step by step:
First, solve the proportion problem and record your answer.Next, substitute the solution for the unknown in the original proportion to see if the two ratios are equivalent.Ensure that the units make sense both in the proportions and when substituting the solution back in.Check to see if the answer is reasonable: Does it seem too large or too small? Does it have the correct sign? Are the units consistent with the problem?Which situation is most likely to have a constant rate of change?
O
A. Distance a school bus travels compared with the number of stops
O
B. Number of trees in a park compared with the area of the park
C. Length of a bead necklace compared with the number of identical
beads
D. Number of runs scored in a baseball game compared with the
number of innings
Final answer:
The situation with a constant rate of change is the length of a bead necklace compared with the number of identical beads, as it represents a linear relationship with a constant slope.
Explanation:
The situation that is most likely to have a constant rate of change is option C, which describes the length of a bead necklace compared with the number of identical beads.
In this scenario, each bead added to the necklace increases its length by a consistent amount. This defines a linear relationship, where the rate of change, also known as the slope in a linear equation, remains constant.
For example, if one bead adds one centimeter to the necklace, then ten beads will add ten centimeters, indicating that the rate of change is one centimeter per bead.
This can be depicted graphically as a straight line when you plot the number of beads against the length of the necklace.
Find the area of a trapezoid if the altitude is 6 inches and the median is 8 inches. (Hint: Recall that the median of a
trapezoid is equal to half the sum of the bases.)
24 sq units
48 sq. units
96 sq. units
Answer:
48 sq. units
Step-by-step explanation:
The area of a trapezoid is given by half sum of the bases multiplied by the height
[tex]=\frac{1}{2} (a+b)h[/tex]
where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid
But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae is covered by the median
[tex]Median=\frac{1}{2} (a+b)[/tex]
Hence area, A, of a trapezoid is simplified to product of median and amplitude
[tex]A=amplitude*median\\\\A=6*8=48sq.units[/tex]
Answer:
=48 sq. units.
Step-by-step explanation:
Area of a trapezoid =h× (a+b)/2
(a+b)/2 is the median ( half of the sum of the two parallel sides also called the bases.
Median=8 inches
Altitude is the distance between the two parallel sides= 6 inches
A=6 inches×8 inches
=48 sq. units.
What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?
Answer:
see explanation
Step-by-step explanation:
Let u = x² ( choice of variable is flexible ), then
4u² - 21u + 20 = 0 ← expressed as a quadratic
This can now be solved for u and converted back into terms of x
Answer:
refer the explanation
Step-by-step explanation:
this question can be written as
X^2=y
so,x^4=y^2
so it will be 4y^2-21y+20=0
Carly withdraws $18 from her bank account which number line represents this amount ?
Answer:
it would be D
Step-by-step explanation:
Answer:
The number line D)
Step-by-step explanation:
Carly withdraws $18 from her bank account.
We assume that Carly has $x in her account. She withdraws $18 from her bank account.
So we have to subtract $18 from $x amount.
Which is $x - 18.
So we are subtracting $18 from her account.
It should be represented by an integer -18.
Now we have to identify the which number line represents -18.
It is D)
-3 < n < 1
n is an integer
write down the possible values of n
The notation of the above inequality:
[tex]-3<n<1[/tex]
Can be written as an interval:
[tex]n\in(-3,1)[/tex]
Or group of points on a line that satisfy the linear inequality.
[tex]n\in\mathbb{G}=\{n; -3<n<1\wedge n\in\mathbb{Z}\}[/tex]
Or simply:
[tex]n\in\mathbb{G}=\{-2,-1,0\}[/tex]
Hope this helps.
r3t40
What is the value of Y? WILL GIVE BRAINLIEST
Answer
54 degrees
Step-by-step explanation:
Using angle sum property(angles in a triangle add up to 180),
y+y+72=180
2y+72=180
2y=180-72
2y=108
y=108/2
y=54 degrees
pls mark brainliest
hope it helped
Answer:
A 54
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
72+y+y = 180
Combine like terms
72 +2y = 180
Subtract 72 from each side
72-72 +2y = 180-72
2y = 108
Divide by 2 on each side
2y/2 = 108/2
y = 54
Which is the graph of f(x) = 3(2/3)?
Answer:
Last graph on the right.
Step-by-step explanation:
Try substituting some values for x and see which graph is valid.
when x = 0, y = f(0) = 3 [tex](2/3)^{0}[/tex] = 3 (1) = 3
When we compare this to the graphs, we immediately see that the first 2 are not correct because in those cases, when x=0, y = 6 (i.e not 3).
Next we try x = 1
when x = 1, y = f(1) = 3 [tex](2/3)^{1}[/tex] = 3 ([tex]\frac{2}{3}[/tex]) = 2
Comparing the graphs ones again, show that only the last graph has x=1 and y = 2.
Answer:
D
Step-by-step explanation:
PLEASE HELP.!! THANK YOUU. accurate answers appreciated:)
[tex]\bf \cfrac{1}{1-sin(x)}+\cfrac{1}{1+sin(x)}=\cfrac{2}{cos^2(x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the LCD of [1-sin(x)][1+sin(x)]}}{\cfrac{[1+sin(x)]1~~+~~[1-sin(x)]1}{\underset{\textit{difference of squares}}{[1-sin(x)][1+sin(x)]}}} \\\\\\ \cfrac{1+sin(x)+1-sin(x)}{1^2-sin^2(x)}\implies \cfrac{1+sin(x)+1-sin(x)}{1-sin^2(x)}[/tex]
recall that 1 - sin²(θ) = cos²(θ).
You manage inventory for Swim Chem, a large distributor of chemicals for indoor and outdoor pool companies. Your division sold 2.4 tone of chlorine on Monday, 4.4 on Tuesday, 1.8 on Wednesday, and 2.8 on Thursday. If last week's sales totaled 14.4 tons, how much chlorine sold on Friday?
Answer:
[tex]\boxed{\text{3.0 T}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}M + T + W + Th + F & = & \text{Total}\\2.4 + 4.4 + 1.8 + 2.8 + F & = & 14.4\\11.4 + F & = & 14.4\\F & = & 3.0\\\end{array}\\\text{Friday's sales of chlorine were }\boxed{\textbf{3.0 T}}[/tex]
Answer: There are 3 tons of chlorine sold on Friday.
Step-by-step explanation:
Since we have given that
Number of tone of chlorine on Monday = 2.4
Number of tone of chlorine on Tuesday = 4.4
Number of tone of chlorine on Wednesday = 1.8
Number of tone of chlorine on Thursday = 2.8
Total number of week's sales = 14.4 tons
So, we need to find the number of tone of chlorine on Friday.
According to question we get that
[tex]14.4=2.4+4.4+1.8+2.8+x\\\\14.4=11.4+x\\\\x=14.4-11.4\\\\x=3[/tex]
Hence, there are 3 tons of chlorine sold on Friday.
cant fully understand, help would be appreciated lol
I don’t know the answer
Answer:
AC ≈ 12.9 cm
Step-by-step explanation:
Using the ratio
sin40° = [tex]\frac{b}{20}[/tex]
Multiply both sides by 20
20 × sin40° = b, hence
AC = b = 20 × sin40° ≈ 12.9
Circle A has been dissected into 16 congruent sectors. The base of one sector is 1.95 units, and its height is 4.9 units. What is the approximate area of circle A?
a) 27.52 units^2
b) 48.92 units^2
c) 78.39 units^2
d) 76.44 units^2
Answer:
Option d) 76.44 units^2
Step-by-step explanation:
The approximate area of the circle is equal to the area of one sector, multiplied by 16
The area of one sector is approximate the area of one triangle
[tex]A=\frac{1}{2}(b)(h)[/tex]
we have
[tex]b=1.95\ units[/tex]
[tex]h=4.9\ units[/tex]
substitute
[tex]A=\frac{1}{2}(1.95)(4.9)=4.7775\ units^{2}[/tex]
Multiplied the area of one sector by 16
[tex]4.7775*16=76.44\ units^{2}[/tex]
Answer:
76.44 took test
Step-by-step explanation:
the point (4,0) lies on a circle with the center at the orgin. what is the area of the circle to the nearsest hundreth?
Answer:
50.27 units²
Step-by-step explanation:²
The standard equation of a circle with center at the origin is x² + y² = r², where r is the radius. Substituting 4 for x and 0 for y yields 4² + 0² = r², so we see immediately that r = 4 units.
The formula for the area of a circle is A = πr².
Here, with r = 4, the area is A = π(4 units)² = 16π units², or
50.27 units² to the nearest hundredth.
Please help with this question
Answer:
all pairs are congruent
1) Congruent by SAS (Side-Angle-Side)
2) Congruent by SAS (Side-Angle-Side)
3) Congruent by HL (Hypotenuse-leg)
Answer:
• Each pair of triangles is congruent
~You can tell that each pair is congruent for the following reasons: (1) The legs, or sides, of the triangles in both #1 & #3 are both the same number. (2) The tick marks in #2 are the same, meaning the side lengths are similar.
• Both triangles in each pair are right triangles.
• The triangle pairs in #1 & #3 are rotations, while the triangle pair for #2 is a translation.
I was unaware of any specific answers, so I hope this is helpful!!!
Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded?
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answer:
Option C is correct.
Step-by-step explanation:
Option C above the dashed line is correct option.
we will graph the inequality
6y - 3x > 9
6y > 9 +3x
y >9/6 +3x/6
y > 3/2 + x/2
The line is dashed because the values are greater and not equal.
The graph is shown in the figure attached.
Answer: Third option
Above the dashed line
Step-by-step explanation:
First we solve the inequality for the variable y.
[tex]6y - 3x > 9[/tex]
[tex]6y - 3x +3x > 9 +3x[/tex]
[tex]6y> 9 +3x[/tex]
[tex]y> \frac{9}{6} +\frac{3}{6}x[/tex]
[tex]y> \frac{3}{2} +\frac{1}{2}x[/tex]
Notice that the line that limits the region is given by the equation
[tex]y= \frac{3}{2} +\frac{1}{2}x[/tex]
The region is formed by all the points that are greater than the points that are on the line [tex]y= \frac{3}{2} +\frac{1}{2}x[/tex].
Therefore the region does not include the points that are on the line, but those that are above the line. Then the line is dashed.
The answer is the third option
A.) x+7/x-1
B.) x+1/x+7
C.) x-1/x+7
Answer:
C
Step-by-step explanation:
If there is an expression such as:
[tex]\frac{A*B}{A*C}[/tex]
we can cancel out A from top and bottom and that will leave us with [tex]\frac{B}{C}[/tex]
Note: Let A, B, C, be any algebraic expression
For the problem given, we can simply cut (x+1) from top and bottom by rules of algebra. So the remaining terms are:
[tex]\frac{(x-1)}{(x+7)}[/tex]
This is option C
Answer:
C)
Step-by-step explanation:
When you have a*b/c*a, a crosses out, simplifying to b/c:
(x+1)(x-1)/
(x+1)(x+7)
When "crossing out", you are really just simplifying it to 1/1:
1*(x-1)/
1*(x+7)
Which is the same as:
(x-1)/(x+7)
Therefore, C is the correct answer
2x^2(-5x^2-4)+4x^4 in simplist form, plz help
Answer:
-6x^4-8x^2 or -2x^2(3x^2+4)
Step-by-step explanation:
Given expression is:
[tex]2x^2(-5x^2-4)+4x^4[/tex]
In order to write the expression in simplest form we have to multiply the terms which needs to be multiplied.
So,
[tex]= -10x^4-8x^2+4x^4[/tex]
Combining alike terms
[tex]= -10x^4+4x^4-8x^2\\=-6x^4-8x^2\\[/tex]
Can also be written as:
[tex]= -2x^2(3x^2+4)[/tex]
Answer:
-2x^2(3x^2 + 4).
Step-by-step explanation:
2x^2(-5x^2 - 4) + 4x^4
Distribute the 2x^2 over the parentheses:
= -10x^4 - 8x^2 + 4x^4
= - 6x^4 - 8x^2
= -2x^2(3x^2 + 4).
In this figure angles p and w are examples of what
Answer:
D. alternate interior angles
Step-by-step explanation:
The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles
So p and w are alternate interior angles
Please help me Find a, b, and c
Answer:
It is A.
Step-by-step explanation:
To solve for b, use the 45-45-90 triangle theorem, in which each of the legs is x, so the legs would be 8. The hypotenuse would therefore be 8√2.
So without further solving the answer is A, since it's the only one with 8√2.
However, I will still solve for A and C. Using the 30-60-90 theorem, we have the sides as x, x√3, and 2x. The second longest side is b. Using this, we find a = 4√6 and c to be 4√2
What are the vertices of PQR?
Answer:
your answer is C
Step-by-step explanation:
vertices neither contain angle nor contain complement
Answer:
C. P, Q and R.
Step-by-step explanation:
In geometry to express verticles, we use only the capital letter for that point.
It's not A because that's the symbol to represent angles.
It's not B because of the right answer in into the options.
it's not D because having both capital letters with the lines above means the line between those points.
The correct answer is C.
Subtract.
(6x2 + 5) - (4x - 3)
Answer:
6x^2 -4x +8
Step-by-step explanation:
(6x^2 + 5) - (4x - 3)
Distribute the negative sign
(6x^2 + 5) - 4x + 3
Combine like terms
6x^2 -4x +5+3
6x^2 -4x +8
Sketch the graph of the given function. The state the functions domain and range
f(x)=-2{1/4}^x
Answer:
Domain: -∞ < x < ∞
Range: f(x) < 0
Step-by-step explanation:
[tex]f(x)=-2(\frac{1}{4})^x[/tex]
We need to sketch the graph and identify domain and range of the function f(x).
The graph is attached in the figure below.
Domain:
The domain of the function is all the values of x that gives the real values for f(x).
So, in our case all values of x gives real values for f(x). So domain is:
-∞ < x < ∞
Range:
The range of the function is the resulting f(x) values when we put all the values of x.
In our case the value of f(x) will always be less than zero because of the negative sign.
Range is:
f(x) < 0
Solve |x| < 12
A. {-12,12}
B.{x|-12
C. {x|x<-12 or x>12}
ANSWER
{x|x>-12 or x<12}
EXPLANATION
The given inequality is
[tex] |x| \: < \: 12[/tex]
This implies that
[tex] - x \: < \: 12 \: or \: x \: < \: 12[/tex]
Divide the first inequality by -1 and reverse the sign to get;
[tex] x \: > \: - 12 \: or \: x \: < \: 12[/tex]
The correct answer is
{x|x>-12 or x<12}
What is the area of a sector with a central angle of 5π6 radians and a radius of 5.6 ft? Use 3.14 for π and round your final answer to the nearest hundredth.
Answer:
41.03 square feet
Step-by-step explanation:
The area of a sector is given by the formula:
[tex]A=\frac{1}{2}r^2\theta[/tex]
Where A is the area, r is the radius and [tex]\theta[/tex] is the angle in radians.
Given the values, we plug into the formula and solve:
[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(5.6)^2(\frac{5\pi}{6})\\A=41.03[/tex]