Answer:
C. 10 units
Step-by-step explanation:
The half diagonals of a rhombus are the legs of a right triangle with the hypotenuse being the side of the rhombus.
EG and FH are the diagonals of the rhombus. The half-diagonals measure 8 and 6.
We can use the Pythagorean theorem to find the hypotenuse length with is the length of the side of the rhombus.
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c^2 = 100
c = 10
Answer: 10 units
The length of one side of the rhombus is 10 units.
What is Rhombus?A rhombus is a two dimensional shape which consists of four equal sides with opposite side being parallel and opposite angles being equal.
Given that,
EFGH is a rhombus.
Length of the two diagonals are also given.
EG = 16 and FH = 12
In a rhombus, the diagonals bisect each other at right angles.
Let the intersection point of the diagonals be O.
Consider ΔOFG.
Using Pythagoras Theorem,
(FG)² = (OG)² + (OF)²
OG = EG / 2 = 16 / 2 = 8
OF = FH / 2 = 12 / 2 = 6
(FG)² = 8² + 6²
= 100
FG = √100 = 10
Hence the length of one side of the rhombus is 10 units.
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A swim teacher sells lesson packages. The best deal has the highest ratio of lessons to total cost.
Swim Lesson Packages
Number of Lessons Total Cost
$10
$40
10 1 $80
15
$80
Which package is the best deal?
l lesson for $10
5 lessons for $40
10 lessons for $80
15 lessons for $80
Mark this and return
Save and Exit
Answer:
the best package is 15 lessons for $80
Answer:
Which package is the best deal? Option D
(D) 15 lessons for $80 100% Answer
Step-by-step explanation:
Find the value of Q in the following system so that the solution to the system is (2,3)
x-2y=-4
3x+5y=Q
Answer:
Q = 21Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-2y=-4&(1)\\3x+5y=Q&(2)\end{array}\right\\\\\text{From (2, 3), put x = 2 and y = 3 to (2):}\\\\Q=3(2)+5(3)=6+15=21[/tex]
(2x + 3).x (4x + 1)
Answer:
8x^2 +14x +3
Step-by-step explanation:
(2x + 3)* (4x + 1)
FOIL
first 2x *4x = 8x^2
outer 2x*1 = 2x
inner 3*4x =12x
last = 3*1 =3
Add them together
8x^2 +2x+12x +3 = 8x^2 +14x +3
Solve for x.
x(x+1)≤0
Write the solution using interval notation. Use the union symbol ∪ to express the solution as a union of disjoint intervals. Finite endpoints of all intervals should be integers. If there are no solutions, use the symbol ∅ for the empty set. Use the set notation {a} to represent an isolated solution a.
Answer:
x(x + 1) ≤ 0
-1 ≤ x ≤ 0
{x | x ≥ -1 and x ≤ 0}
Follow steps:
Solving the Inequality x(x+1)≤0
To solve x(x+1)≤0, we need to find values of x where the product is negative or zero. X can be split into the regions x < 0 and x > 0. As x approaches zero from either direction, x(x+1) approaches zero as well. The function is zero at the roots of the equation x(x+1) = 0, which are x = 0 and x = -1. These two roots divide the real line into three intervals: (-∞, -1), (-1, 0), and (0, ∞). Analyzing each interval:
For x in (-∞, -1), x < -1 and x+1 < 0, so the product x(x+1) is positive.
For x in (-1, 0), x is negative and x+1 is positive, so the product x(x+1) is negative.
For x in (0, ∞), both x and x+1 are positive, and thus, the product x(x+1) is positive.
The inequality is only satisfied in the interval where the product is negative or zero. Therefore, the solution is [{-1}, 0], which can be written in interval notation as (-1, 0]. This is a single continuous interval that includes the root x = 0 and excludes the root x = -1.
Finally, using interval notation, we express the solution to the inequality x(x+1)≤0 as (-1, 0].
Solve the following word problems using your knowledge
9 word problems using your knowledge of fractions. Be sure to express your answers
in simplest form.
Mike had 9 1/2 cups of Gatorade in a bottle. After he darom 2 3/4 cups of Gatorade, how much was left in the bottle?
can you please help me and I will get you brainliest.
Answer:
27/4 or 6 3/4
Step-by-step explanation:
( 19 x 4 ) - ( 11 x 2 )
------------------------------
2 x 4
=54/8
54/2
-------------
8/2
demand for a brand of clock radio is given by p+3q=390 , and the supply for these radios is given by p=7q=90 , where is the price and is the quantity demanded at price . Solve the system containing these two equations to find the price at which the quantity demanded equals the quantity supplied and the equilibrium quantity.
Answer:
p=$300 and q=30 clock radio
Step-by-step explanation:
we have
p ----> is the price
q ----> is the quantity
[tex]p+3q=390[/tex] ----> equation A
[tex]p-7q=90[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The intersection point is (300,30)
see the attached figure
therefore
The solution is
p=$300
q=30 clock radio
Which of the following pair(s) of circles have / as a common external tangent? Select all that apply.
A and B
A and C
B and C
Answer with explanation:
A tangent to a circle is a Line which touches a circle at a single point.
There can be Infinite number of tangents to a circle which are external only.
In the given figure:
⇒ There are three circles having Centers A, B and C.Circle having Center B lies inside the circle having center C.
⇒The three circles intersect at point T.
⇒The common tangent of these three circles passes through Point T.
⇒Circles having Center B and Center C , have a common external Tangent.
Option A,B and C:
→A and B
→A and C
→B and C
Tangent is the line that intersects the circle at a single point. Thus, Option A, B, and C all apply.
Three different circles are given in the question that is A, B, and C.
We have to determine the pair of circles that have a common external tangent.
Therefore, take circles A and B from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option A applies.
Now, take circles A and C from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option B applies.
Further, take the circles B and C from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option C applies.
Thus, Option A, B, and C all apply.
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Which expression is the factorization of x2 + 10x + 21?
You must remember that a polynomial is written like so...
ax^2 + bx + c
In this case...
a = 1
b = 10
c = 21
To factor you must find two numbers who both add up to b (10) AND multiply to c (21)
3 + 7 = 10
3 * 7 = 21
so...
(x + 3 )(x + 7)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: 12x + 21 or C. F(x) = (x - 2)(x + 2)
Step-by-step explanation:
x2 + 10x + 21
2x + 10x + 21
Rearrange to put the coefficient in front/move it in front of the term.
Ex. (× · 4 ⇒ 4×)
(×( 7 ) ⇒ 7×)
Identify and group like terms.
(2x + 10x) + 21
Group the coefficients together.
(2+ 10)x + 21
Combine 2 + 10 to get 12.
12x + 21
= 12x + 21
You're Welcome! :))
Can someone pls answer this?
255 square centimeters
Step-by-step explanation:First, break this into two shapes: a triangle and a rectangle.
The rectangle is 22 cm by 10 cm. [tex]22 * 10 = 220[/tex] square centimeters
The triangle's base is 10 cm ([tex]22-12=10[/tex]) and its height is 7 cm ([tex]17-10=7[/tex]). [tex]\frac{1}{2} * 10 * 7 = 5 * 7 = 35[/tex] square centimeters
Add the areas together. [tex]220 + 35 = 255[/tex] square centimeters
is x 2 = y a function?
Answer:
yes
Step-by-step explanation:
a
The answer is:
Yes, the given equation is also a function. (it's a quadratic function)
Why?We know a function exists when there is only one value of y (output) for each x (input).
We can easily know if an equation (relation) is also a function using the graphic method:
To know if a relation is a function, we need to graph it a draw a vertical line, if the line cut the graph in only one point, the relation is a function, otherwise, if the vertical line cuts the graph in two or more points, the relation is a not a function. Remember, the condition for a function is that there is only one output for each input.
Note: I have attached a picture for better understanding.
Have a nice day!
Calculate the approximate mean absolute deviation of the given data set.
5, 7, 8, 10, 11, 17, 19, 24
8
12.625
5.53
10.5
Answer:
12.625
mean=total sum value /total data set
The mean of given data set is: 12.625.
The correct option is (B)
What is mean?
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean = (Sum of all the observations/Total number of observations)
Given data: 5,7,8,10,11,17,19,24.
Mean=
sum of observation/ Total number of observation
=5+7+8+10+11+17+19+24/8
=101/8
=12.625.
Hence, the mean is 12.625.
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Which of the following is needed to construct the figure below?
A. 8 Acute triangles
B. 5 isosceles triangles
C. 6 Equilateral triangles
D. 10 obtuse triangles
Answer:
C. 6 equilateral triangles
6 Equilateral triangles needed to construct the hexagon option (C) 6 Equilateral triangles is correct.
What is hexagon?A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.
We have a given a hexagon in the figure.
As we know hexagon is a polygon made up from six sides also hexagon can be made using six equilateral triangles by joining them.
Thus, 6 Equilateral triangles needed to construct the hexagon option (C) 6 Equilateral triangles is correct.
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what two integers is √42 between? explain
[tex]\sqrt{36}=6[/tex] and [tex]\sqrt{49}=7[/tex], so it stands to reason that [tex]\sqrt{42}[/tex] lies somewhere between 6 and 7.
suppose y varies directly with x. if y=7 when x=2, find y when x=3
A. 8
B. 7/6
C. 21/2
D. 6/7
List the following numbers from least to greatest: -4, |-6|, 3, -2, |5
-4, -2, 3, |5|, |-6
|-6|, -4, -2, 3, |5
|-6|, 5, -4, 3, -2
-6|, |5|, 3, -2, -4
Answer:
-4,-4,-4,-4,-2,-2,-2,-2,3,3,3,3,3,|5|,|5|,|5|,5,|6||6||-6||-6|
Numbers' absolute values are outputted as non-negative numbers. The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|
What is modulus of a real number?Modulus of a real number, also called absolute value, is non-negative result of the input value.
This is defined as:
[tex]|x| = x ; \text{ (x is non-negative)}\\\\|x| = -x ; \text{ (x is negative)}[/tex](so that the outer negative makes the negative number positive).
Example:
[tex]|5| = 5\\|-5| = -(-5) = 5[/tex]
What is magnitude and sign?A number has both magnitude(its absolute value) and its sign(positive or negative).
If numbers are negative, the more their magnitude increases, the lesser they become.
If numbers are positive, the more their magnitude increases, the greater they become.
Thus, for -5, the magnitude is 5, and sign is –ve.
Also, positive numbers > 0 > negative numbers.
For given case, we get:
-4 = -4|-6| = 63 = 3-2 = -2|5| = 5Arranging, we get:
-4 < -2 < 3 < 5 < 6
or
-4 < -2 < 3 < |5| < |-6|
Thus,
The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|
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What number is missing from the number pattern? 1,2,5,10,__,26,37
Answer:
17 is the missing the number
Step-by-step explanation:
Pattern: +1, +3, +5, +7, etc.
Hector keep close tabs on his bank account. His account had a balance of -$22.80. The next day, he made a deposit of $56.60. His account balance changed to $.
What is the solution to the system of equations?
Answer:
[tex]\large\boxed{\left(7,\ \dfrac{13}{3}\right)}[/tex]
Step-by-step explanation:
You must use the algebraic method: substitution or elimination.
I will solve a given system of equations the substitution method.
[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{3}x+2&(1)\\\\y=\dfrac{4}{3}x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\\dfrac{4}{3}x-5=\dfrac{1}{3}x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}x-(3)(5)=3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=\dfrac{1}{3}\cdot7+2\\\\y=\dfrac{7}{3}+\dfrac{6}{3}\\\\y=\dfrac{13}{3}[/tex]
In the triangle below, what is the measure of Angle z
Answer:65
Step-by-step explanation:
The triangle is isosceles triangle and the base angles must be the same
The measure of angle z is 65°.
Given that, in ΔXYZ XZ=XY=7 cm.
We need to find the value of ∠Z.
What is the isosceles triangle?In an isosceles triangle with two equal sides. The angles opposite the equal sides are also equal.
Since XZ=XY=7 cm.
Here, ∠Y=∠Z=65°
Therefore, the measure of angle z is 65°.
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match the meaning of each of the following expressions
1: n+5
2: n-5
3: x+8
4: x-8
5: 8-x
6: 5-n
7: x+(5+7)
8: x+(8+2)
9: x+(8-2)
10: x+x
given that (5,4) is on the graph of f(x), found the corresponding point for the function f (x)+4
Answer:
The corresponding point is (5,8)
Step-by-step explanation:
In this problem we know that
The rule of the transformation is equal to
(x,f(x)) ------> (x,f(x)+4)
so
for the point (5,4)
x=5, f(x)=4
substitute
(5,4) ------> (5,4+4)
(5,4) ------> (5,8)
therefore
The corresponding point is (5,8)
The two-way table below describes the attendance at a movie theater at various times of the day.
Which statement best describes the relationship between the two variables?
There is an association because the relative frequencies by column are different.
There is an association because the relative frequencies by column are similar.
There is no association because the relative frequencies by column are different.
There is no association because the relative frequencies by column are similar.
Answer:
There is an association because the relative frequencies by column are different.
Step-by-step explanation:
For checking the association of a two-way table we have to calculate the relative frequency of the table. Here we see that there is an association between timing and day pf watching the movie. Also here relative frequencies of both columns are similar.
What value of b will cause the system to have an infinite number of solutions?
y = 6x – b
–3x + y = –3
Solving for b by simplifying both sides of the equation, then isolating the variable.
b = −y + 6x
----
Choosing three values for x and substitute in to find the corresponding y values.
(0,−3) , (1,0) , (2,3)
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Answer:
Step-by-step explanation:
y = 6x -b
and -3x +y =-3
on simplifying equation 2 ,we have y = 3x -3
System of equation has infinite number of solution if one equation can be obtained by multiplying by suitable non zero number
if we multiply equation by 2 we get y =6x -6
Since coefficient of x and y is same therefore comparing the value of x b with constant in another equation which is 6 .
therefore b =6
Which expression is equivalent to the expression below?
Answer:
A
Step-by-step explanation:
Given
[tex]\sqrt{-108}[/tex] - [tex]\sqrt{-3}[/tex]
= [tex]\sqrt{36(3)(-1)}[/tex] - [tex]\sqrt{3(-1)}[/tex]
= 6[tex]\sqrt{3}[/tex] i - [tex]\sqrt{3}[/tex] i
= 5[tex]\sqrt{3}[/tex] i
Answer:
Step-by-step explanation:
√(-108) - √(-3)
= √(-3*36) - √(-3)
= √[(-3)*36] - √(-3)
= √(-3)*(√36 - 1)
= √[(-1)*(3)]*(6-1)
= i*√(3)*(5)
= 5√3i
Muli spent 3/10 of thus salary on flood and 2/3 on rent. He was left with sh. 2100.what was his salary?
Step-by-step explanation:
Let the total amount of salary be X, then
3/10X + 2/3X + amount left= his salary(X)
(9X + 20X)/ 30 + 2100 = X
29X/30 - X = -2100
(29X - 30X)/30 = -2100
by cross multiplying
-X = -2100×39
-X = -81900
divide both side by -1
X = 81900.
therefore his salary = 81900
Answer:
Muli's salary = 62,000
Step-by-step explanation:
Let Muli's salary be x.
Money spent on food = 3/10 of x = 3x/10
Money spent on rent = 2/3 of x = 2x/3
Money left with him = 2100
(3x/10) + (2x/3) + 2100 = x
x - (3x/10) - (2x/3) = 2100 ( LCM = 30)
30x/30 - 9x/30 - 20x/30 = 2100
(30x - 9x - 20x ) / 30 = 2100
x/30 = 2100
x = 2100 * 30 = 62,000
20pts
Solve for x
(4(x-5))/8=9y
Answer:
x=18y+5
Step-by-step explanation:
Answer:
x = 5 + 18y
Step-by-step explanation:
Equation: [tex]\frac{4(x - 5)}{8}[/tex] = 9y
Multiply and distribute: 4x - 20 = 72y
Add: 4x = 20 + 72y
Divide: x = 5 + 18y
What is the simplified form of sqrt 10,000
Answer:
100
Step-by-step explanation:
10,000 is merely 100 x 100 = 100²
so √10,000 = √100² = 100
find the nature of the quadratic equation 2x^2+5x+8=0
[tex]
2x^2+5x+8=0 \\
x=\dfrac{-5+\vee-\sqrt{5^2-2\cdot2\cdot8}}{2\cdot2} \\
x=\dfrac{-5+\vee-\sqrt{25-64}}{4} \\
x=\dfrac{-5+\vee-\sqrt{-39}}{4}\Longrightarrow x\notin\mathbb{R} \\
x\notin\mathbb{R}\Longrightarrow x\in\mathbb{C}
[/tex]
So no real solutions for x. But two complex solutions for x.
[tex]
x_1=\boxed{\dfrac{-5-39i}{4}} \\ \\
x_2=\boxed{\dfrac{-5+39i}{4}}
[/tex]
Hope this helps.
r3t40
How do you do right Triangle
Answer:
right triangles should have one right angle (90 degrees) and it should liik like an L, and then draw a line connecting the gap (the hypotenuse)
Step-by-step explanation:
Answer:
make a 90 degree angle and connect the two points to finish the shape of the triangle.
Step-by-step explanation:
HINT: the corner of a piece of paper is a 90 degree angle
A length on a map is 7.5 inches. The
scale is 1 inch:5 miles. What is the
actual distance?
A 1.5 miles C 12.5 miles
B 2.5 miles D 37.5 miles
Answer:
Option D 37.5 miles
Step-by-step explanation:
we know that
The scale on a map is [tex]\frac{1}{5}\frac{in}{mi}[/tex]
so
using proportion
Find the actual distance for a length on a map of 7.5 in
Let
x ----> the actual distance
[tex]\frac{1}{5}\frac{in}{mi}=\frac{7.5}{x}\frac{in}{mi}\\ \\ x=7.5*5\\ \\x=37.5\ mi[/tex]