The triangle below is isosceles. Find the length of side x in simplest radical form with a rational denominator.
Answers
Solution given:
it is a right angled isosceles triangle
so
perpendicular [p]=base[b]=5
hypotenuse [h]=x
we have
by using Pythagoras law
p²+b²=h²
5²+5²=h²
50=h²
h=[tex]\sqrt{50}[/tex]
x=[tex]\bold{5\sqrt{2}}[/tex]
Related Questions
Which equation in slope-intercept form represents a line that is parallel to y=-4x-5 and passes through the points (0,0)?
Answers
Answer:
y = 0x
Step-by-step explanation:
y=-4x-b
0 = -4(0) + b
0 = 0 + b
0
What is the solution of ?
Answers
Answer:
x=12 is the answer
Step-by-step explanation:
[tex] \frac{5}{2} x - 7 = \frac{3}{4} x + 14[/tex]
[tex] \frac{5}{2} x - \frac{3}{4} x = 14 + 7[/tex]
[tex] \frac{10}{4} x - \frac{3}{4} x = 21[/tex]
[tex] \frac{7}{4} x = 21[/tex]
[tex]x = 21 \div \frac{7}{4} [/tex]
[tex]x = 21 \times \frac{4}{7} [/tex]
[tex]x = 3 \times 4[/tex]
[tex]x = 12[/tex]
La potencia que se obtiene de elevar a un mismo exponente un numero racional y su opuesto es la misma verdadero o falso?
Answers
Answer:
Falso.
Step-by-step explanation:
Sea [tex]d = \frac{a}{b}[/tex] un número racional, donde [tex]a, b \in \mathbb{R}[/tex] y [tex]b \neq 0[/tex], su opuesto es un número real [tex]c = -\left(\frac{a}{b} \right)[/tex]. En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:
(a) El exponente es cero.
(b) El exponente es un negativo impar.
(c) El exponente es un negativo par.
(d) El exponente es un positivo impar.
(e) El exponente es un positivo par.
(a) El exponente es cero:
Toda potencia elevada a la cero es igual a uno. En consecuencia, [tex]c = d = 1[/tex]. La proposición es verdadera.
(b) El exponente es un negativo impar:
Considérese las siguientes expresiones:
[tex]d' = d^{-n}[/tex] y [tex]c' = c^{-n}[/tex]
Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:
[tex]d' = \left(\frac{a}{b} \right)^{-n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}[/tex]
[tex]d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]y [tex]c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{b}{a} \right)\right]^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = - \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' \neq c'[/tex], la proposición es falsa.
(c) El exponente es un negativo par.
Si [tex]n[/tex] es par, entonces:
[tex]d' = \left(\frac{b}{a} \right)^{n}[/tex] y [tex]c' = \left(\frac{b}{a} \right)^{n}[/tex]
Puesto que [tex]d' = c'[/tex], la proposición es verdadera.
(d) El exponente es un positivo impar.
Considérese las siguientes expresiones:
[tex]d' = d^{n}[/tex] y [tex]c' = c^{n}[/tex]
[tex]d' = \left(\frac{a}{b}\right)^{n}[/tex] y [tex]c' = \left[-\left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}[/tex]
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es impar, entonces:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = - \left(\frac{a}{b} \right)^{n}[/tex]
(e) El exponente es un positivo par.
Considérese las siguientes expresiones:
[tex]d' = \left(\frac{a}{b} \right)^{n}[/tex] y [tex]c' = \left(\frac{a}{b} \right)^{n}[/tex]
Si [tex]n[/tex] es par, entonces [tex]d' = c'[/tex] y la proposición es verdadera.
Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.
pls help- the question kept cutting off before:
If cos(πr) = 2 cos(πr) and 0 < r < 3, what is one possible value of r?
Answers
Answer:
r can be 0.5
Step-by-step explanation:
Here, we want to get a possible value of r
From the question, the value of r is between 0 and 3
Mathematically, we know that in degrees pi is the same as 180 degrees
In a case where we have r = 1/2
we have it that;
cos(pi/2) = 2 cos (pi/2)
Since pi/2 is 90 and cos 90 is zero; then we have it that the two sides of the equation is the same and r can be 1/2
instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: SAS
Answers
Answer:
please I don't know can u please help me out
Answer:
The answer to your question where SAS is given
∠T ≈∠ W
A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38. The stock price beyond which 0.05 of the distribution falls is _________.
Answers
Answer:
$12.43
Step-by-step explanation:
Given :
Mean = $8.52
Standard deviation, = $2.38
Stock price which falls beyond 0.05 of the distribution is at the 95th percentile
The 95th percentile distribution has a Pvalue of 1.645 (standard normal table)
We obtain the value of x, with z = 1.645
Using the Zscore relation :
Zscore = (score - mean) / standard deviation
1.645 = (score - 8.52) / 2.38
Cross multiply :
1.645 * 2.38 = score - 8.52
3.9151 = score - 8.52
Score = 8.52 + 3.9151
Score = $12.4351
Stock price beyond 0.05 is $12.43
To maintain a balanced diet, ensure that your food contains minimal amounts of certain ingredients. Which ingredient is missing in the sentence below?
One’s diet should include small amounts of fat, , and sugar.
Answers
Step-by-step explanation:
i think minerals and vitamins since they are micro nutrients
2
Solve the equation log, (3t+9) - log, 21 =1
Answers
Answer:
67
Step-by-step explanation:
log(3t+9)-log21 = 1
Applying, the law of logarithm,
log(3t+9)/21 = 1
converting the log into index
(3t+9)/21 = 10
solving for t
3t+9 = 21×10
3t+9 = 210
3t = 210-9
3t = 201
t = 201/3
t = 67
if the sum is 4 and one of the integers is 1 what must the other integer be
Answers
Step-by-step explanation:
The answer to the question is 3
Answer:
3
Step-by-step explanation:
1 + X = 4
4 - 1 = X
3 = X
HELP! how do I find the degrees for this problem
Answers
Answer:
90°
Step-by-step explanation:
m∠x+m∠y+m∠z=180°
m∠x+m∠y+90=180
m∠x+m∠y=180-90=90°
A parabola opens upward. The parabola goes through the point (3,-1),
and the vertex is at (2,-2).
Find the value of A for the parabola. Show your work. Use Part 1 and 2 to write the equation of the parabola.
Answers
Answer:
a=1
Step-by-step explanation:
Hopefully this helps :)
The equation of the parabola is: y = (x - 2)² - 2. Finding the value of A
The vertex of the parabola is at (2,-2). Since the parabola opens upward, the equation of the parabola will be of the form:
y = A(x - 2)² - 2
We can plug the point (3,-1) into this equation to find the value of A.
-1 = A(3 - 2)² - 2
Simplifying the right side of the equation, we get:
-1 = A - 2
Adding 2 to both sides of the equation, we get:
1 = A
Therefore, the value of A is 1.
Writing the equation of the parabola
The equation of the parabola is:
y = (x - 2)² - 2
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Quadrilateral ABCD is reflected across the x-axis and then reflect across the y-axis to form quadrilateral A′B′C′D′. If the coordinates of vertex A are (-7, 3), what are the coordinates of vertex A′?
Answers
(7,3)
Hope this helps
How many marbles do you need to be able to arrange them into the shape of an equilateral triangle with 75 rows
Answers
Answer:
2850
Step-by-step explanation:
1+2+3+4+5+6+7...74+75
just add up all the numbers from 1 to 75
Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.
Answers
Answer:
there are 2 apples in the basket
there are 10 banana in the basket
Step-by-step explanation:
According to the Question,
We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.let x for apple And y for banana So, x+y=12---Equation 1
And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.Thus, 5x+7y=80 ----Equation 2
Now, (Equation 1) × 5 Subtract with (Equation 2) We get,
2y = 20 ⇒ y=10 (there are 10 banana in basket)
Put value of y=10 in Equation 2 we get5x+70=80 ⇔ x=2(there are 2 apples in basket)
A boat has a ladder that's ten feet long, and hangs off the side of the boat,
with its last two feet submerged in water. If the ocean tide rises five feet,
how much of the ladder will be underwater?
Answers
Answer:
2ft
Step-by-step explanation:
The tide doesn't effect the part of ladder that is underwater that is always 2ft
How much of the ladder that will be underwater is 7 ft.
Since the ladder is 10 ft long and its last two feet are submerged under water, this implies that 2 ft of the ladder are submerged under water.
When the tide rises by five feet, the part of the ladder that would be under water is 2 ft + 5ft = 7ft.
So, how much of the ladder that will be underwater is 7 ft.
Learn more about tide here:
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You're working as a floor rep in the local home improvement store. The store wants to increase its inventory. Last year, 40 lawn mowers cost $4,776. At the same cost, how much will 120 lawn mowers cost this year?
Answers
To set up this problem first you'll need to find out the price of one lawn mower.
Divide the amount if lawn mowers bought last year with the cost to get the cost of one lawn mower
Take the number you get and multiply that bu the amount of lawn mowers this year (120)
answer: $14,328
Question 1 (5 points)
Determine the value of x.
3
3V2
6
3V3
Answers
Answer:
Step-by-step explanation:
Nathan is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 38.15 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answers
Answer:
11.26 m
Step-by-step explanation:
The height of the tree is about 11.25 meters.
What are similar triangles?When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.
Let the height of the tree be x.
Note that the scenario makes two similar triangles.
Since the ratio of the side lengths of similar triangles is proportional, it follows:
(38.15 - 32.9)/1.55 = 38.15/x
5.25/1.55 = 38.15/x
3.39 = 38.15/x
x = 38.15/3.39
x = 11.25
Hence, the height of the tree is about 11.25 meters.
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Carla packed this box with one centimeter cubes what is the volume of the box plus is it cubic centimeters or just centimeters or is it square centimeters pls help you'll get brainlist
Answers
Cubic centimetres since they are cubes. Did you add any picture of the question? There seems to be none.
Does the point (1, 3) satisfy the equation y = 5x? yes no
Answers
Answer:
Nope
Step-by-step explanation:
we can graph y = 5x as y = 5 units up and one unit to the right
but for right now let me be specific on what i mean
Specifically:
y = 5x is a Slope-Intercept equation, the original Slope-Intercept equation would be y = mx + b but in this case, we don't have b so we're focusing now on y = 5x, but what are we suppose to do with 5x??? well 5x represents the slope of the line so to graph a slope, use rise over run = rise/run. so only 5 is being used so 5 = rise/run = 5/1.
------------------------------------------------------------------------------------
Answer: (1, 3) doesn't satisfy the equation
Answer:
No, it does not satisfy the equation
Step-by-step explanation:
Hi there!
We are given the equation y=5x and we want to know if the point (1,3) will satisfy the equation
If we substitute the values of a point into the equation, and the result is a true statement (ex. 2=2), then the point satisfies the equation
If we substitute the values of a point into the equation and the result is a false statement (ex. 0=7), then the point doesn't satisfy the equation
The reason for this is because when we plug the value of a point into an equation, we're seeing if the equation will pass through that given point.
So let's substitute 1 as x and 3 as y into y=5x
3=5(1)
multiply
3=5
The result is a false statement; therefore, the point doesn't satisfy y=5x
Hope this helps!
P÷✓2=✓t/r+q
express t in the terms of p and q
Answers
Given:
Consider the given equation is:
[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]
To find:
The value of t in terms of p, q and r.
Solution:
We have,
[tex]p\div \sqrt{2}=\sqrt{\dfrac{t}{r+q}}[/tex]
It can be written as:
[tex]\dfrac{p}{\sqrt{2}}=\sqrt{\dfrac{t}{r+q}}[/tex]
Taking square on both sides, we get
[tex]\dfrac{p^2}{2}=\dfrac{t}{r+q}[/tex]
Multiply both sides by (r+q).
[tex]\dfrac{p^2(r+q)}{2}=t[/tex]
Therefore, the required solution is [tex]t=\dfrac{p^2(r+q)}{2}[/tex].
Find the measure of Angle B
Answers
Answer:
45
Step-by-step explanation:
Both angles have the same value, therefore, you can set your formula up as
5x-105=2x+30
5x = 2x + 30 + 105
5x - 2x = 135
3x = 135
x = 135/3
x = 45
e) (x + 1)/(2x ^ 3 - 4x ^ 3) + (x - 1)/(2x ^ 3 + 4x ^ 2) = 1/(x ^ 2 - 4)
Answers
Answer:
X= − x ^3 + 2 x^2 − 3 x − 2 x ^3 ( x + 2 ) ( x − 2 ) = 0
Step-by-step explanation:
What are the coordinates of points E, F, and GS
A. E (2, 3), F (8,5), G (5,8)
B. E (3, 2), F (8,3), G (5,6)
C. E (3, 2), F (8,4), G (5,7)
D. E (3, 3), F (9, 4), G (6,7)
Answers
Answer:
its a i think
Step-by-step explanation:
Length of a rope is 5 metre. What does it mean?
Answers
Step-by-step explanation:
Length of a rope is 5 meter. it means the rope is 5 meter long..
hope it helps.stay safe healthy and happy...What is the slope of the line? What is the y-intercept of the line? y = 1
Answers
Answer:
m = 0
y intercept = 1
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = 1[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = 0 [/tex]
[tex]\implies y - intercept= 1[/tex]
Slope of the line is 0, since y=mx+c, if m = 0, then y = c, where the constant (c)=1
y intercept of the line is y = 1.
Answered by GAUTHMATH
Find the area of the triangle with vertices A(-3,2), B(1,-2), and c(1,3)
Answers
Answer:
[tex]A(-3,2)\: B(-1,-2)\: C(1,3)[/tex]
[tex]A=1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
[tex]=1/2[-3(-2-3)(+1(3-2)+1(2-(-2))][/tex]
[tex]=1/2(15+1+4)[/tex]
[tex]=1/2(20)[/tex]
[tex]=10[/tex]
[tex]ANSWER: 10 ~units^{2}[/tex]
------------------------------
hope it helps...
have a great day!!
The area of triangle with vertices A(-3,2), B(1,-2), and c(1,3) is 12 units^2.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The green line represents the height of the triangle = 4 units
The red line represents the base of the triangle = 6 units
Area of the triangle = 1/2 x 6 x 4 = 12 units^2
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the temperature of a city was 26 degrees celsius on Monday the temperature rise by 2 degrees celsius on everyday upto thrusday and fell by 5 degree Celsius on Friday what was the temperature of the city on Friday
Answers
Answer: 29 degrees Celsius
Step-by-step explanation:
On Monday, Tuesday, Wednesday, and Thursday, the temperature increased by 2 degrees for a total increase of 8 degrees. Then, on Friday, the temperature decreased by 5 degrees. Since 8 - 5 = 3, the total temperature change is +3 degrees, so the answer is 26 + 3 = 29 degrees
7r-15/s when r= 3 and s = 5.
Answers
Answer:
21-3=18
Hope This Helps!!!
Answer:
18
Step-by-step explanation:
7(3)= 21
15/5=3
21-3=18
∣1/12 − 5/6∣ − (2/5 + 1/10)
I WILL GIVE BRAINLYST
Answers
Answer:
forst mark me as a brainleast
