Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ?
Answers
Answer:
[tex]\bold{\sqrt{75}}[/tex]
Step-by-step explanation:
Given
A [tex]\triangle GHJ[/tex] in which
[tex]\angle GHJ = 90^\circ[/tex]
Hypotenuse = 10
Length of another side = 5
To find:
HJ = ?
Solution:
Kindly refer to the image attached in the answer area.
We know that there are only 3 sides in a triangle.
We are given hypotenuse is 10.
i.e. GJ = 10
To find HJ, Base = ?
So, we are given the side length of GH, perpendicular i.e. 5.
Kindly refer to attached image for further details.
Let us use Pythagorean theorem here.
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow GJ^{2} = GH^{2} + HJ^{2}\\\Rightarrow 10^2=5^2+HJ^2\\\Rightarrow HJ = \sqrt{100-25}\\\Rightarrow \bold{HJ = \sqrt{75}}[/tex]
Answer:
hJ = B 5 route 3
Step-by-step explanation:
got it right on edg 2020-2021
Related Questions
The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is pure fruit juice
Answers
Answer:
The pints of each of the two existing types of drinks are 22 and 88 respectively.
Step-by-step explanation:
We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.
Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.
So, according to the question;
The first condition states that we have to make 110 pints of a mixture of two types that is pure fruit juice, that means;x + y = 110
x = 110 - y ---------------- [equation 1]
The second condition states that the first type is 70% pure fruit juice, and the second type is 95% pure fruit juice, that means;[tex]0.70x+0.95y=0.90\times 110[/tex]
[tex]70x+95y=9900[/tex]
[tex]70(110-y)+95y=9900[/tex]
[tex]7700-70y+95y=9900[/tex]
[tex]25y=9900-7700[/tex]
[tex]y=\frac{2200}{25}[/tex]
y = 88
Now, putting the value of y in equation 1 we get;
x = 110 - y
x = 110 - 88 = 22
Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.
ABCD is a square. Length of one diagonal is 5cm.
a) What is the length of AB
b) Find the perimeter of ABCD
c) Find the area of
Answers
Answer:
Below
Step-by-step explanation:
Let D be the diagonal of this square.
D forms with AB and BC a right triangle where D is the hypotenus.
We will apply then the Pythagorian theorem
●The Pythagorian theorem
● D^2 = AB^2 + BC^2
ABCD is a square, so AB=BC
● D^2 = AB^2 + AB^2
● D^2 = 2AB^2
We khow that is D= 5 cm
● 25 = 2AB^2
● 25/2 = AB^2
● 5/√2 = AB
AB is 5√2 cm
■■■■■■■■■■■■■■■■■■■■■■■■■
The perimeter is:
● P = 4AB
● P = 4×(5/√2)
● P = 20/√2
● P = 10×2/√2
● P = 10√2 cm
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area is
● A = AB^2
● A = (5/√2)^2
● A = 25/2 cm^2
Answer:
Step-by-step explanation:
the sides of a square are equal ( AB=BC=CD=DA)
diagonal of the square creates two right angle triangle
to find the side of the triangle we apply the Pythagorean theorem:
a²+b²=c² ( let AB=a, and BC=b)
2a²=25 ( since AB=BC=a)
a²=25/2
a=(5√2)/2 cm
a=3.54 ( rounded to the nearest 10)
perimeter = 4a
P=4(5√2/2)
P=10√2 cm
Area=a²=(5√2/2)²=25/2=12.5 cm^2
If the first differences of a sequence are a constant -7 and the third term is 22, find the first 5 terms of the sequence.
Answers
Answer:
36, 29, 22, 15, 8
Step-by-step explanation:
Step 1: State known information
First difference is -7
Third term of the sequence is 22
Step 2: Find first 5 terms
You just need to add and subtract 7 to 22 and the answer 5 times
1. 36 +7
2. 29 +7
3. 22 <- We know 22 is the 3rd term
4. 15 -7
5. 8 -7
Therefore the first 5 terms of the sequence is 36, 29, 22, 15, 8
X + + x plus StartFraction x Over 7 EndFraction plus StartFraction 1 Over 11 EndFraction left-parenthesis x plus StartFraction x Over 7 EndFraction right-parenthesis equals 60.(x + ) = 60
Answers
Answer:
[tex]x = \frac{770}{16}[/tex]
Step-by-step explanation:
Given
[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]
Required
Solve for x
[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]
Start by solving the bracket [Take LCM]
[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{7x + x}{7}) = 60[/tex]
[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{8x}{7}) = 60[/tex]
Open the bracket
[tex]x + \frac{x}{7} + \frac{8x}{77} = 60[/tex]
Take LCM
[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]
[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]
[tex]\frac{96x}{77} = 60[/tex]
Multiply both sides by 77
[tex]77 * \frac{96x}{77} = 60 * 77[/tex]
[tex]96x = 60 * 77[/tex]
Divide both sides by 96
[tex]\frac{96x}{96} = \frac{60 * 77}{96}[/tex]
[tex]x = \frac{60 * 77}{96}[/tex]
Divide the numerator and denominator by 6
[tex]x = \frac{10 * 77}{16}[/tex]
[tex]x = \frac{770}{16}[/tex]
Answer:
48.125
Step-by-step explanation:
Read the table. 1/2 = 2 gallons 1 = 4 gallons 1 1/2 = 6 gallons. If this goes on. how much gallons is 6 1/2?
Answers
Answer:
24 1/2
Step-by-step explanation:
Every 1/2 is 2 gallons.
1/2 x 2 gallons = 4 gallons.
The whole number in 6 1/2 is 6.
1 x 6 = 6.
Now, we multiply 6 by 4 because each 1 = 4 gallons.
6 x 4 = 24.
There is still an 1/2 left in 6 1/2.
You add that.
Your answer is 24 1/2.
Hope this helps you!
The record high temperature in Alabama is 112f and the record low temperature is -27f. What is the difference between the highest and lowest temperature? A. 139 degrees B. 27 degrees C. 85 degrees D. 112 degrees
Answers
Answer:
(A) 139°
Step-by-step explanation:
What we are trying to find here is the distance between -27 and 112.
To do this, we have to think of it as a number line.
The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.
So the total distance is [tex]112+27=139[/tex]
Hope this helped!
What is the solution to this equation?
X-7 = 18
A. X = 25
B. x= 35
C. x = 11
D. X = 9
Answers
Answer:
A
Step-by-step explanation:
x - 7 = 18
Adding 7 to both sides (to get rid of the -7 on the left side) gives us:
x - 7 + 7 = 18 + 7
x = 25
Answer:
25 is the correct answer
Step-by-step explanation:
i got it right on the test
midpoint of the segment with endpoints A(-5, -2) and B(-7, 6).
Answers
(-6,2)
Inbox me on fb for more help with math same name as my brainly
Answer:
(-6,2)
Step-by-step explanation:
help this is hard Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below.
Answers
Answer:
x = [tex]-\frac{3}{b}[/tex]
x = -1
Step-by-step explanation:
The given equation is,
-2(bx - 5) = 16
Dividing by (-2) on both sides of the equation,
[tex]\frac{-2(bx-5)}{(-2)}=\frac{16}{(-2)}[/tex]
(bx - 5) = -8
By adding 5 on both the sides of the equation,
(bx - 5) + 5 = -8 + 5
bx = -3
Dividing by 'b' on both the sides of the equation,
[tex]\frac{bx}{b}=\frac{-3}{b}[/tex]
x = [tex]-\frac{3}{b}[/tex]
If b = 3,
x = [tex]-\frac{3}{3}[/tex]
x = -1
8. Laurenpacksanorderofblocksin 2 crates and 7 stacks. How many blocks does Lauren pack?
Answers
Answer:
14
Step-by-step explanation:
(multiply 2by7)
2×7
=14
How can you invest your money as a student or a teenager???
Answers
Answer:
Buy stuff and sell them at a higher price
Step-by-step explanation:
Answer:
get a job
Step-by-step explanation:
A comfy jacket is normally $200. It is on sale for 40% off. What is the sale price?
Answers
Answer:
120
Step-by-step explanation:
First find the discount
200 * 40%
200 * .40
80
Subtract the discount from the original price
200-80
120
The sale price is 120
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 120}}[/tex]
Step-by-step explanation:
Calculating the discount on the jacket.
[tex]200 \cdot 40\% \\ \\ 200 \cdot 0.4 \\ \\ 80[/tex]
The discount on the jacket is $80.
Let’s find the sale price of the jacket.
[tex]\sf sale \ price = original \ price - discount.[/tex]
[tex]200-80 \\ \\ 120[/tex]
The sale price of the jacket is $120.
In the problem below, AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9. Is F prime? A B + C D E F B and D are consecutive integers. C = 8.
Answers
Answer:
When both the conditions hold true, F is prime.
Step-by-step explanation:
AB, CD, and EF are two-digit numbers, where A, B, C, D, E and F represent distinct digits from 1 to 9.
AB
+ CD
--------
EF
1st condition, B and D are consecutive.
Adding B and D gives us F.
Possible values can be (F being the unit value after adding not considering the carry over):
B + D = F
1+2=3
2+3=5
3+4=7
4+5=9
5+6=1
6+7=3
7+8=5
8+9=7
Here F is not prime (because 9 is not prime).
Now, let us consider the 2nd condition as well.
i.e. C = 8
For the following
AB
+ CD
--------
EF
C is 8 then A must be 1 because any value other than 1 for A will make the sum of A and C greater than 9 and there will be a carry which is not the case here.
So, E = 8 + 1 = 9
Now, B and D are consecutive and can not be 1, 8 or 9.
So, possible values are:
B + D = F
2 + 3 = 5
3 + 4 = 7
Here F is prime.
So, when both the conditions hold true, F is prime.
Solve. Write your answer in the simplest form using integers, fractions, and natural logarithms. 9=ex
x=
Thanks!
Answers
Answer:
x = ln9
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] = nlogx , lne = 1
Given
[tex]e^{x}[/tex] = 9 ( take the ln of both sides )
ln[tex]e^{x}[/tex] = ln9, thus
xlne = ln9, that is
x = ln9
HELP ASAP I HAVE 48 MINUTES LEFT
The graph of y = |xl is transformed as shown in the graph below. Which equation represents the transformed
function?
y=|1/4x|
y=|2x|
y=|4x|
y=|1/2x|
Answers
Answer:
y = |1/4x|
Step-by-step explanation:
The slope is 1/4
An economist wishes to conduct a survey in two different cities in the same county to determine the difference in the proportions of residents who believe that economy is improving under president Trump. A 99% confidence interval is to be constructed for the difference between the proportions. If the sample sizes for both cities are to be equal, find the minimum sample size needed for each city so that the margin of error not to exceed 6%.
Answers
Answer:
The minimum sample size needed for each city = 922
Step-by-step explanation:
From the information given:
the objective is to find the minimum sample size needed for each city so that the margin of error not to exceed 6%.
If we take a look at the question very well:
we are only given the confidence interval of 99% and the margin of error of 6%
we were not informed or given the value or estimate of any proportions>
so we assume that:
[tex]p_1 =q_ 1= p_2 = q_2 = 0.5[/tex]
At confidence interval of 0.99 , the level of significance = 1 - 0.99 = 0.01
The critical value for [tex]z_{\alpha/2} = z_{0.01 /2}[/tex]
= [tex]z_{0.005}[/tex] = 2.576
The minimum sample size needed can be calculated by using the formula :
[tex]n = \dfrac{z^2_{\alpha/2}}{E^2}(p_1q_1+p_2q_2)[/tex]
[tex]n = \dfrac{2.576^2}{0.06^2}((0.5 \times 0.5)+(0.5 \times 0.5))[/tex]
[tex]n = \dfrac{6.635776}{0.0036}(0.25+0.25)[/tex]
[tex]n =1843.271 \times (0.5)[/tex]
n = 921.63
n [tex]\simeq[/tex] 922
∴ The minimum sample size needed for each city = 922
Question 4 (1 point)
(01.02)
Evaluate the following expression using the given values: (1 point)
Find x - 3y if x = 3 and y=-2.
A -9
B -3
C 3
D 9
Answers
Answer: 9
Step-by-step explanation:
plug in numbers to get 3+6
add them
boom
Answer:
D. 9
Step-by-step explanation:
Plug in 3 as x and -2 as y in the expression:
x - 3y
3 - 3(-2)
3 + 6
= 9
which expression is equivalent to 4n+ 28
A 28n + 4
B 4(n+28)
C 4( +7)
D 32
Answers
Answer:
It would be B
Step-by-step explanation:
what is the answer to |3x-4|=|3x-5|
Answers
Answer:
i think this is the answer
Answer:
the answer is [tex]\frac{3}{2}[/tex] or 1.5 or 1[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
In each expression below identify the coefficient constant and variable
Answers
Answer:
The expression is missing in the question.
The expression is 4x +450
The variable is x and the coefficient is 4
Step-by-step explanation:
In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.
The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.
Please help me with this Operation: (-17+4+1-6)÷(-3)×(-1)?
Answers
Answer:
-6
Step-by-step explanation:
(-17+4+1-6)=-18
-18/-3=6
6*-1=-6
Answer:
-6
Step-by-step explanation:
(-17+4+1-6)÷(-3)×(-1)
PEMDAS
Parentheses first
(-17+4+1-6)÷(-3)×(-1)
Add and subtract inside the left parentheses
(-18)÷(-3)×(-1)
Multiply and divide from left to right
6 * -1
-6
5h-2(11-h)=h-4
what’s the value of h
Answers
Answer:
The correct answer is h = 3.
Step-by-step explanation:
To solve this problem, we should first use the distributive property on the left side of the equation. This means that we can multiply each of the terms inside the parentheses by -2 (be careful that you distribute the negative as well). This is modeled below:
5h - 2(11 - h) = h - 4
5h - 22 + 2h = h - 4
Next, we can combine like terms on the left side of the equation.
7h - 22 = h - 4
Now, we can subtract h from both sides of the equation to move all of the variable terms to the left side of the equation.
6h - 22 = - 4
Next, we can add 22 to both sides of the equation to isolate the variable term on the left side of the equation.
6h = 18
Finally, we can divide both sides by 6 in order to get the variable completely isolated.
h = 3
Therefore, the correct answer is h = 3.
Hope this helps!
Carrie spent 1/4 of her allowance on a shirt, 1/3 of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Answers
Answer:
$24
Step-by-step explanation:
1/4x + 1/3x + 8 = 22
1/4x + 1/3x = 7/12x
7/12x + 8 = 22
22 - 8 = 14
7/12x = 14
14/ 7/12
x = 24
Find m∠PQR. A. 81 B. 90 C. 77 D. 72
Answers
Work Shown:
Angle PQR = (far arc - near arc)/2
Angle PQR = ( (major arc PR) - (minor arc PR) )/2
Angle PQR = ( (2x+252) - (2x+108) )/2
Angle PQR = 144/2
Angle PQR = 72
Notice how we didn't need to find the value of x at all.
Using one complete sentence give a mathmatical definition of zero
Answers
Answer:
Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.
Step-by-step explanation:
A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.
Find the measure of angle A. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answers
Answer:
x = 7.6°, so A = 18.8°
Step-by-step explanation:
What we need to know in order to utilize algebra is the total sum of all triangle's angle. It's 180°. So, we can write
25 + 17x - 1 + 3x - 4 = 180
20x + 28 = 180
20x = 152
x = 7.6°
Now what you need to do is substitute 7.6° into each expression 17x - 1 and 3x - 4.
In which number is the value of the 7 ten times the value of 7 in the number 1,273?
Answers
Answer:
1723
Step-by-step explanation:
10 x 70=700
Answer:
1723
Step-by-step explanation:
Solve each equation using the Zero Product Property and the Distributive Property (as necessary)
11. f(x)=3x(2x-6)
12. f(x)=3x(x+7)-2(x+7)
Answers
Answer:
11) x=1 or x=3.
12) x=2/3 or x=-7.
Step-by-step explanation:
So we have two equations:
[tex]f(x)=3x(2x-6)\\f(x)=3x(x+7)-2(x+7)[/tex]
And we want to solve them. To do so, make each of them equal 0 and then solve for x:
11)
[tex]f(x)=3x(2x-6)\\0=3x(2x-6)[/tex]
Using the Zero Product Property, either one or both of the factor must be zero for this to be true. Therefore, make each factor equal to zero and solve:
[tex]3x=0 \text{ or } 2x-6=0[/tex]
Divide the left by 3. On the right, add 6 and then divide by 2:
[tex]x=0\text{ or } 2x=6\\x=0 \text{ or } x=3[/tex]
Therefore, the solutions to the first equation is:
x=1 or x=3.
12)
[tex]f(x)=3x(x+7)-2(x+7)[/tex]
First, use the distributive property to group the terms together. The equation is equivalent to:
[tex]f(x)=(3x-2)(x+7)[/tex]
Now, set the function to zero and solve:
[tex]0=(3x-2)(x+7)[/tex]
[tex](3x-2)=0 \text{ or } x+7=0\\3x=2 \text{ or } x=-7\\x=2/3 \text{ or } x=-7.[/tex]
Therefore, the answer is:
x=2/3 or x=-7.
Answer:
[tex]\large \boxed{{\bold{11.} \ x=0, \ x=3}} \\ \\ \large \boxed{{\bold{12.} \ x=-7, \ x=2/3}}[/tex]
Step-by-step explanation:
We will set the outputs of the functions to 0 and solve for x.
0 = 3x(2x - 6)
Set factors equal to 0.
First possibility:
3x = 0
x = 0
Second possibility:
2x - 6 = 0
2x = 6
x = 3
0=3x(x+7)-2(x+7)
Take (x+7) as a common factor.
0 = (3x-2)(x+7)
Set factors equal to 0.
First possibility:
x + 7 = 0
x = -7
Second possibility:
3x - 2 = 0
3x = 2
x = 2/3
Pls help with questions
1. What is the volume of a cylinder that has a radius of 5 inches and height of 9 inches?
2. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, the width is 1.8 ft and the height is 2 ft?
Answers
Step-by-step explanation:
1. volume = πr²h
= π×(5²)×9
= π×225
= 225π
= 707.1 cubic inches
2. volume = lwh
= 5.2 × 1.8 × 2
= 18.72 square feets
Evaluate the expression when x = 5 and z= 7.
5z +x
Simplify your answer as much as possible.
Answers
Reason 5(7)+(5)=40
Answer:
12
Step-by-step explanation:
We are given the expression:
[tex]\frac{5z+x^2}{x}[/tex]
and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.
[tex]\frac{(5(7)+(5)^2)}{5}[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, evaluate the exponent.
(5)²= 5*5= 25
[tex]\frac{(5(7)+25)}{5}[/tex]
Next, multiply 5 and 7.
5*7=35
[tex]\frac{(35+25)}{5}[/tex]
Next, add 35 and 25.
25+25=60
[tex]\frac{60}{5}[/tex]
Finally, divide 60 by 5.
[tex]12[/tex]
The expression (5z+x²)/x when x=5 and z=7 is 12.