Answer:
missing side lengths are
leg 1 is 4√2
leg 2 is 4√2
hypotenuse is 8
Step-by-step explanation:
leg 1 is y
leg 2 is 4√2
45-45-90 right triangle means
legs are equal
the longest side is the hypotenuse which is
x
pythagorean theorem =
a² + b² = c²
a and b are the legs
c is hypotenuse
(4√2)² + (4√2)² = c²
4√2 = √16*2 = √32
(√32)² + (√32)² = c²
32 + 32 = c²
64 = c²
take the square root of both sides
√64 = √c²
8 = c
c = 8
Smallest to greatest 4/9, 4.9, 49%
Answer:
4/9, 49%, 4,9
Step-by-step explanation:
4/9=0,444444
49%=0,49
4,9=4,9
Can someone please help
Answer:
Option 1
Step-by-step explanation:
Angle bisector:
Angle bisector is a line that divides the angle into two equal angles.
⇒ ∠KLM = ∠MLN
Given the system of inequalities: 4x – 5y < 1 one-halfy – x < 3 which shows the given inequalities in slope-intercept form? y < four-fifthsx – one-fifth y < 2x 6 y > four-fifthsx – one-fifths y < 2x 6 y > negative four-fifthsx one-fifth y > 2x 6
The slope- intercept is y> (1-4x) / 5 and y< 2x + 6
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
4x – 5y < 1 and 1/2y – x < 3
Solving
4x – 5y < 1
-5y < 1- 4x
-y < (1-4x) / 5
y> (1-4x) / 5
Now, the second inequality,
1/2y – x < 3
1/2y< 3+x
y< 2x + 6
Learn more about this concept here:
https://brainly.com/question/13762480
#SPJ1
[tex]3x^{2} +8x- 10[/tex]
Answer:
07698+96965#5_(-&)!:86539'6";
The solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The given equation will be solved as:-
= 3x² + 8x - 10
Using the formula of factors:-
x = [tex]\dfrac{-b\pm\sqrt{b^-4ac}}{2a}[/tex]
x = [tex]\dfrac{-8\pm\sqrt{64-(-120)}}{2\times 3}[/tex]
x = [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
Therefore the solution to the given expression will be [tex]\dfrac{-8\pm\sqrt{180}}{6}[/tex].
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ1
A swimming pool is 50 metres long and 25 metres wide. How many lengths of the pool will a competitor in a 1500 metre race have to swim?
Reason:
I'm assuming that the swimmer travels along the 50 meter side
Divide 1500 over 50 to get 1500/50 = 30, which tells us that the swimmer must make 30 trips.
Write the quadratic equation whose roots are 3 and 1, and whose leading coefficient is 1
Answer:
x² - 4x + 3 = 0
Step-by-step explanation:
given roots x = a and x = b then the corresponding factors are
(x - a) and (x - b)
the equation is then the product of these factors , that is
(x - a)(x - b) = 0
given
roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then
(x - 3)(x - 1) = 0 ← expand factors using FOIL
x² - 4x + 3 = 0
The graph of a function f(x) is shown. What is the value of f(-2)?
Answer:
f(-2) = 0
Step-by-step explanation:
The value of the function for a particular x-value can be read from the graph.
GraphThe graph is a map showing the value of f(x) for each value of x for which the function is defined. The x-values are identified by the numbers on the horizontal x-axis. The corresponding function values are found by referencing the vertical y-axis.
Function valueTo find the function value f(x) for x=-2, we locate the vertical grid line marked with -2 at the x-axis. We then locate the point on the graph of the function where it crosses that vertical grid line. Tracking horizontally from that point to the vertical y-axis, we can read the function value from the vertical scale.
The attachment has a red arrow pointing to the intersection of the graph with the grid line x=-2. That point of intersection lies on the x-axis, where the y-value is 0. That means ...
f(-2) = 0
__
Additional comment
On this graph, the axis crossing point (x=0, y=0) is not labeled. It is halfway between x=-1 and x=1. Similarly, it is halfway between y=-1 and y=1. Based on this and on experience with similar graphs, you can assume that the axis crossing has coordinates (x, y) = (0, 0).
what is the measure of this angle
Answer:
135
Step-by-step explanation:
Depending on where you start, the protractor can read in different ways. Since the measure of this angle started from the left, you read the numbers at the top. If the measure would have started from the right, you read the numbers below.
A good rule of thumb is that if the angle appears to be greater than 90 degrees, or an obtuse angle, you would choose the only answer choice that is above 90 degrees.
Hope this helps!
Which of the following are solutions to the equation below?
Check all that apply.
4x²-12x+9 = 5
□ A. x = -√5 + ³/2
B. x= √√4-3
C. X= -√√4-3
D. x = √5 + 1/2
3
N|W
□ E. x= -√5 +3
2
□ F. X=
√√5+3
2
The solutions of the given equation are x= (√5+3)/2 & x= (-√5+3)/2
What is sridharacharya formula ?
If ax²+bx+c = 0 is a quadratic equation ,where a,b,c are real numbers, Then the solution is x = (-b±√(b²-4ac))/2a , where a≠0
Which are the solutions of the equation ?The given equation is, 4x²-12x+9 = 5
So, 4x²-12x+9 = 5
⇒ 4x²-12x+9-5 = 0
⇒ 4x²-12x+4 = 0
Comparing this equation with ax²+bx+c = 0 we get,
a = 4, b = -12, c = 4
Applying sridharacharya formula we get,
x = (-(-12)±√((-12)²-4×4×4))/(2×4)
= (12±√(144-64)/8
= (12±√80)/8
= (3±√5)/2
The values of x are (√5+3)/2 & (-√5+3)/2
Learn more about sridharacharya formula here :
https://brainly.com/question/13655213
#SPJ10
Does the chart below represent a proportional relationship? What is the rate of change?
x
y
1
4
2
7
3
10
4
13
Answer:
C will be your answer.
Please Mark as brainlist!
A seal went 15 feet below sea level to catch a fish. A sea lion dove 6 feet less than two times as deep as the seal to catch a larger fish. What expression represents the sea lion’s position in relation to sea level?
Answer:
The sea lion dives 24 feet.
Step-by-step explanation:
A seal (S) dives 15 feet.
A sea lion (SL) dives 6 feet less than 2 times the seal's dive. That can be expressed as:
SL = 2S -6
Since we know S = 15, we can say:
SL = 2*(15) - 6
SL = 24 feet
The sea lion dives 24 feet.
Se calcula que el 2013 habia 19,000 árboles en la ciudad. el año 2014.para prevenir caídas de árboles viejos, se corto el 2% y el 2015 se quemó en un incendio el 5% de lo que quedaba
A) En que porcentaje disminuyó el número de árboles de 2013 a 2015?
B) Cuantos árboles quedan en esta ciudad a fines del 2015?
Answer:
yyjyidsksjsjsosiddhdoehsudidhdhsjidjsjsjejsksksksjsjsjdd
What is the measurement of m? 24 6
The value of n is 12. and m is 6root5
We have given the diagram,
The measurement of m,
n = 12
According to the altitude theorem
What is the altitude theorem?
The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.
24/n = n/6
The Cross multiply
24 * 6 = n²
144 = n²
n² = 144
n = √144
n = 12
[tex]m^2=6^2+n^2[/tex]
[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]
[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]
Hence the value of n is 12.
To learn more about the measurement visit:
https://brainly.com/question/25716982
#SPJ1
Answer:
12
Step-by-step explanation:
Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
To solve the problem substitute the value of n as 5 in each expression and then simplify to check if it equals to 16 or not.
A.) (25/n) + 7
= (25/5) + 7
= 12
This is not the required expression.
B.) 30 - 3n
= 30 - 3(5)
= 15
This is not the required expression.
C.) 7+ (45/n)
= 7 + (45/5)
= 7 + 9
= 16
This is the required expression.
D.) n² - 114
= (5)³ - 114
= 125 - 114
= 11
This is not the required expression.
Hence, the correct option is C.
Learn more about Expression:
https://brainly.com/question/13947055
#SPJ1
ST
6
9
10
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
O 5 units up
O 5 units down
O 5 units right
O 5 units left
The answer to the question is 5 units up.
Please help me on this question!
Answer:
u = 10 ft
Step-by-step explanation:
cuboid volume = w × h × l
width * hight * length
560 = 7 × 8 × u
u = 10 ft
Answer:
u = 10 ft
Step-by-step explanation:
Volume of a rectangular prism = lwh
where:
l = lengthw = widthh = heightGiven:
Volume = 560 ft³width = 7 ftlength = 8 ftheight = uSubstitute the given values into the formula and solve for h:
⇒ 560 = 8 × 7 × u
⇒ 560 = 56u
⇒ 56u ÷ 56 = 560 ÷ 56
⇒ u = 10 ft
Therefore, the height of the prism is 10 ft.
What is the vertex of the graph of y = x^2+ 4x?
Answer:
(-2, -4)
Step-by-step explanation:
You can complete the square of the equation to get
y+(4/2)^2 = x^2+4x+(4/2)^2
y+4 = x^2 + 4x + 4
y+4 = (x+2)^2
y = (x+2)^2 - 4
This gives the form y = a(x-h)^2 + k where (h, k) is the vertex of the equation. You can also arrive at the same conclusion by making some observations of the equation. (x+2)^2 minimum value is going to be 0 since and negative values resulting from x+2 is going to become positive because of the square. So the minimum value is when x+2 is 0 or when x is equal to -2 and when it's at that minimum value of 0 it's going to have 4 subtracted from it which gives the vertex of (-2, -4)
Which of the following is equivalent to
(16 3/2)^1/2 ?
O 6
O 8
O 12
O 64
Step-by-step explanation:
[tex] = { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} } [/tex]
[tex] = {2}^{4 \times \frac{3}{2} \times \frac{1}{2} } [/tex]
[tex] = {2}^{ \frac{12}{4} } [/tex]
[tex] = {2}^{3} [/tex]
[tex] = 2 \times 2 \times 2[/tex]
[tex] = 8[/tex]
The answer is B.
simplify 2e + 3f + 7e + 5f
Which of the following are solutions to the equation below?
(2x+3)^2 = 10
Check all that apply.
Answer:
x = (√10 -3)/2 and (-√10 -3)/2
Step-by-step explanation:
(2x+3)^2 = 10
To solve the equation, take the square root of each side
sqrt((2x+3)^2) = ±√10
2x+3 = ±√10
Subtract 3 from each side
2x+3-3 = ±√10 -3
2x = ±√10 -3
Divide each side by 2
2x/2 = (±√10 -3)/2
x = (±√10 -3)/2
There are two solutions
x = (√10 -3)/2
and (-√10 -3)/2
Answer:
[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
Step-by-step explanation:
Given: (2x + 3)² = 10
In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.
Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.
Step 1: Square both sides of the equation.
[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]
Step 2: Separate into possible cases.
[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]
Step 3: Solve for x in both cases.
[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]
[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]
Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
Learn more about quadratic equations here:
brainly.com/question/27031173
Jesse is traveling up and down a stream in a kayak. He can paddle the kayak at an average rate of 5 miles/hour, and the round-trip is a total distance of 16 miles. When c is the speed of the current, this expression can be used to find the difference of the time it takes Jesse to travel upstream (against the current) and downstream (with the current).
Find the difference in simplest form.
The time it takes = 3 hours 12 minutes
What is rate?Rate is a ratio which compares two quantities of different units.
Analysis:
Speed = 5 miles/hour
distance covered = 16 miles
speed taken = distance covered/time taken
time taken = 16/ 5 = 3.2 hours = 3 hours 12 minutes
Learn more about Rate: brainly.com/question/24304697
#SPJ1
The area of this rectangle is 270 cm².
Work out the value of y.
(5r-8) cm
(3x + 6) cm
y cm
Not drawn accurately
Answer:
the area of rectangle is 270 cm and its length is 18 cm
the breath of the perimeter of given rectangle respectively
used concept
area of rectangle l into b where is is v is breadth of the rectangle perimeter of rectangle 2 into l + b where I and b stands for same as the
solution
let's the length of rectangle is equal to l is equal to 18 cm
breath of rectangle is is equal to b is equal to
area of rectangle is equal to 270 CM
now according to the question and l into b is equal to a
18 into b is equal to 1070
b is equal to 270 upon 18
b is equal to 15 CM
p no no perimeter of the rectangle is equal to 2 into l + b
2 multiply 18 + 15
2 X 33
is equal to 66 cm
therefore the breath and the perimeter of rectangle are 15 cm and 66 respectively
simplify (3+√5)(3+√2)
When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
Surd operationa√b × c√d = (a × c)√(b × d)
How to simplify (3 + √5)(3 + √2)(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
Learn more about surd:
https://brainly.com/question/24700530
#SPJ1
Question 1 of 5
Select the correct answer.
Which expression is equivalent to 6√z ÷ 3√8z, if z> 0?
36/2
O 3
33/z
3√22
Submit
The expression that is equivalent to the given expression is [tex]3\sqrt[6]{z}[/tex]
Simplifying an expressionFrom the question, we are to determine which of the expressions is equivalent to the given expression
The given expression is
[tex]6\sqrt{z} \div \sqrt[3]{8z}[/tex]
The expression can be simplified as
[tex]6\sqrt{z} \div \sqrt[3]{8z}[/tex]
[tex]\frac{6\sqrt{z}}{\sqrt[3]{8z}}[/tex]
[tex]= \frac{6 \times \sqrt{z}}{\sqrt[3]{8} \times \sqrt[3]{z}}[/tex]
[tex]= \frac{6 \times z^{\frac{1}{2} } }{2 \times z^{\frac{1}{3} }}[/tex]
[tex]= 3\times z^{\frac{1}{2} -\frac{1}{3}}[/tex]
[tex]= 3\times z^{\frac{1}{6}}[/tex]
[tex]= 3\times\sqrt[6]{z}[/tex]
[tex]= 3\sqrt[6]{z}[/tex]
Hence, the expression that is equivalent to the given expression is [tex]3\sqrt[6]{z}[/tex]
Learn more on Simplifying an expression here: https://brainly.com/question/10864685
#SPJ1
Please Help!!!!!
Write the equation of a parabola with focus (-1, 3) and directrix x = -5. Also include a sketch of the parabola. Show all your work.
Answer:
Equation of parabola is (x+1)²=20(y-3)
Step-by-step explanation:
And the graph above
(x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given, focus : (-1, 3)
directrix : x + 5 = 0 or x=-5
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
√(x+1)²+(y-3)²=|x+5|
squaring both sides,
(x+1)²+(y-3)²=(x+5)²
(x+1)²=20(y-3)
Hence, (x+1)²=20(y-3) is the equation of a parabola with focus (-1, 3) and directrix x = -5.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all three cards are the same for exactly $1$ attribute.
C. For the first card, there are three ways to choose the number of card.
For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.
Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.
D. The cards may have the same number, color, shapess, orshading.
However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.
If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.
what is Probability?
Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.
Learn more about Probability here
https://brainly.com/question/13604758
#SPJ10
Kevin earns $240,000 a year as a surgeon. He contributes $20,500 to
his pre-tax 401(k) retirement account and pays the government 28% of his
remaining salary per year. How much is his net pay?
Using proportions, it is found that his net pay is of $158,040.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
His first discount is for the retirement account, hence the taxable amount is:
T = 240000 - 20500 = $219,500.
He pays 28% of that in taxes, hence his net pay is of 100 - 28 = 72% of $219,500, hence:
N = 0.72 x 219500 = $158,040.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Given that h={A,E,I,O,U},which is the number of possible subsets of set h
There are 32 subsets of the set h.
We have given that h={A,E,I,O,U},
We should count the elements of the set, then put that number as the exponent of 2.
What is the subset?A set A is a subset of another set B if all elements of set A are elements of set B. In other words, set A is contained inside set B.
Remember that 2 should always be the base in finding the number of subsets: 2^5=32
Therefore there are 32 subsets of the set h.
Here set h is denoted by small h but the set is always denoted by capital letters.
To learn more about the subset visit:
https://brainly.com/question/2280091
#SPJ1
What is the y-intercept of the line shown?
-1
0
1
Answer:
-1
Step-by-step explanation:
The y-intercept is where the line crosses the y-axis.
Answer:
[tex]\huge\boxed{\sf y-intercept = -1}[/tex]
Step-by-step explanation:
Y-intercept is the point of the line of the equation where:x = 0the line of the equation passes through the y-axis.Here,
y-intercept = -1Since, this is the point where x = 0 and where the line passes through the y-axis.
[tex]\rule[225]{225}{2}[/tex]
If f(x) is a linear function, which statement must be true?
O f(x) has no constant term.
O f(x) has no x²-term.
Of(x) has no terms with a coefficient other than 1.
Of(x) has no x-term.
Answer:
has no x^2 term
Step-by-step explanation:
Has no x^2 term <====== that would make it an exponential function, not linear
