Answer:
49 unit²
Step-by-step explanation:
Right triangle with equal legs given, let the leg be x.
Hypotenuse of isosceles right triangle is
√x² + x² = x√2Area of triangle:
1/2ah= 1/2x²Since we have hypotenuse = 14 units:
x√2=14x= 14/√2Then area:
1/2x² = 1/2*(14/√2)² = 1/2*14²/2 = 7² = 49 unit²I need help on both answers. They’re different from my other problems so I’m kinda confused
The day before an exam, Jacob spent 2 1/5
hours studying in the morning and 3 3/4 hours
studying in the afternoon. How many hours
did Jacob spend studying that day?
Answer:
5 19/20 or 5.95
Step-by-step explanation:
You can add these numbers as decimal numbers or as mixed numbers.
Decimal
2.2 +3.75 = 5.95 . . . hours spent studying
Mixed Numbers
(2 1/5) +(3 3/4) = (2 4/20) +(3 15/20) = (2 +3) +(4/20 +15/20)
= 5 19/20 . . . hours spent studying
A shop sells DVDs and CDs.
DVDs are sold at one price.
CDs are sold at a different price.
2 DVDs and 1 CD cost £35
2 DVDs and 2 CDs cost £45
Martin has £50 Does he have enough to buy 1 DVD and 3 CDs?
Answer:
Step-by-step explanation:
Lets Price of a DVD is fixed i.e. 15
and One CD price is 5 (Not fixed)
In First situation
2 DVDs and 1 CD cost = 35 as given
2 x 15 + 5 = 35
Lets one CD price is 7.5
In Second situation
2 x 15 + 2 x 7.5 = 45
Its mean CD price may be between 5 to 7.5
In asked scenario, Martin has 50
1 DVD and 3 CDs?
1 x 15 + 3 x 7.5 = 37.5
37.5 is lesser than 50
Hence Martin has enough to buy 1 DVD and 3 CDs.
1. In a right triangle, the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=1, b=1; 2. In a right triangle, the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg, if: c=5, a=3;
Answer:
1. [tex]c = \sqrt{2}[/tex].
2. b = 4.
Step-by-step explanation:
To solve these two questions, keep the Pythagorean Theorem in mind: [tex]a^2 + b^2 = c^2[/tex]. Also remember that measurements cannot be negative, so we will disregard the negative answers.
1. a = 1, and b = 1. c = ?
[tex]1^2 + 1^2 = c^2[/tex]
[tex]1 + 1 = c^2\\[/tex]
[tex]c^2 = 1 + 1\\c^2 = 2\\\sqrt{c^2} = \sqrt{2}\\c = \sqrt{2}[/tex]
2. a = 3, c = 5. b = ?
[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\\sqrt{b^2} = \sqrt{16}\\b = 4[/tex]
Hope this helps!
What is 12.5% of 72
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf of \ refers \ to \ multiplication.[/tex]
[tex]12.5\% \times 72[/tex]
[tex]\frac{12.5}{100} \times 72[/tex]
[tex]\sf Multiply.[/tex]
[tex]\frac{900}{100} =9[/tex]
23. The measure of an angle is 46º. The measure of
the complement is
The measure of the
supplement is.
help if you can
Answer:
Complement = 44 degrees, supplement = 136 degrees
Step-by-step explanation:
Complement of an angle is the difference of the angle from 90 degrees.
Complement of 46 = 90-46 = 44 degrees.
Supplement of an angle is the difference of the angle from 180 degrees.
Supplement of 46 = 180-46 = 134 degrees.
Answer:
Complement = 44 degrees, supplement = 136 degrees
Step-by-step explanation:
A laundry basket contains 18 blue socks and 24 black socks. What is the probability of randomly picking 2 black socks, with replacement, from the basket?
Answer:
144/441
Step-by-step explanation:
There are 18+24=42 total socks
There are 24 black socks
So the probability is (24/42)*(24/42)=12/21 * 12/21 = 144/441
Answer:
189
Step-by-step explanation:
|3x–1|=8 please help!!!!!
Answer: -3
Add 1 to both sides
[tex]3x-1+1=8+1[/tex]
[tex]3x=9[/tex]
Divide both sides by 3
[tex]3x/3=9/3\\x=3[/tex]
Can i please have help thanks.
Answer:
[tex] q = 2(3r + 8) [/tex]
Step-by-step explanation:
There are two variables, q and r in the expression given. To make r the independent variable, it simply means, make q the subject of the formula, so that variable q would be dependent on variable r. As r changes, q changes also.
Thus,
[tex] q - 10 = 6(r + 1) [/tex]
Open the parenthesis
[tex] q - 10 = 6r + 6 [/tex]
Add 10 to both sides
[tex] q - 10 + 10 = 6r + 6 + 10 [/tex]
[tex] q = 6r + 16 [/tex]
[tex] q = 2(3r + 8) [/tex]
Bob says that he can find the area of the triangle below using the formula: A = [tex]\frac{1}{2}[/tex] * 8 *18 * sin (120°). Is he correct? Explain why or why not.
Answer:
No.
Step-by-step explanation:
No, Bob is not correct.
The formula he's using is the following:
[tex]A=\frac{1}{2} ab\sin(C)[/tex]
The important thing here is that the angle is between the two sides.
In the given triangle, 120 is not between 8 and 18. Therefore, using this formula will not be valid.
Either Bob needs to find the other side first or find the angle between 8 and 18.
20 squared (+5) divided by 100
The answer is 4.05
Step-by-step explanation:
20^2 is 20•20 which is 400 || +5=405 || /100=4.05
Please help! Explanation please!
Answer:
11 meters.
Step-by-step explanation:
The important thing to note here is that the backyard is a square. Since it's a square, all of its sides all equivalent in length. Thus, let's find the length of the sides. To do this, we use the area formula.
The formula for the area of a square is:
[tex]A=n^2[/tex]
Where n is a side. Since we know the area already, we can find n. Find n:
[tex]121=n^2\\n=11[/tex]
Since every side in a square are equivalent, all sides are 11 meters in length.
Therefore, each section of the fence should be 11 meters long.
Remember, a percent is a fractional part
of 100. In a bag of candy, 15 of the 50
pieces are red. What percentage of the
candy is red?
mex
B 50%.
C 3006
D 659
Answer:
Step-by-step explanation:
B
Answer:
The answer would be 30% (although I don't see that as an answer).
Step-by-step explanation:
This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.
15/50 = (15*2)/(50*2) = 30/100 = 30%
LCM of x<sup>2</sup>+5x+6 and x<sup>2</sup>-x-6 is ………………………
Answer:
[tex] (x^2 - 9)(x + 2) [/tex]
Step-by-step explanation:
Given:
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 - x - 6 [/tex]
Required:
LCM of the polynomials
SOLUTION:
Step 1: Factorise each polynomial
[tex] x^2 + 5x + 6 [/tex]
[tex] x^2 + 3x + 2x + 6 [/tex]
[tex] (x^2 + 3x) + (2x + 6) [/tex]
[tex] x(x + 3) + 2(x + 3) [/tex]
[tex] (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 [/tex]
[tex] x^2 - 3x +2x - 6 [/tex]
[tex] x(x - 3) + 2(x - 3) [/tex]
[tex] (x + 2)(x - 3) [/tex]
Step 2: find the product of each factor that is common in both polynomials.
We have the following,
[tex] x^2 + 5x + 6 = (x + 2)(x + 3) [/tex]
[tex] x^2 - x - 6 = (x + 2)(x - 3) [/tex]
The common factors would be: =>
[tex] (x + 2) [/tex] (this is common in both polynomials, so we would take just one of them as a factor.
[tex] (x + 3) [/tex] and,
[tex] (x - 3) [/tex]
Their product = [tex] (x - 3)(x + 3)(x +2) = (x^2 - 9)(x + 2) [/tex]
1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?
Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
[tex]v_1 = 60\ mph[/tex]
Sheyna drives back from the lake with average speed of 36 mph
[tex]v_2 = 36\ mph[/tex]
It took 2 hours less time to get there than it did to get back.
Let [tex]t_1[/tex] be the time taken to drive to lake.
Let [tex]t_2[/tex] be the time taken to drive back from lake.
[tex]t_2-t_1 = 2[/tex] hrs ..... (1)
To find:
Total time taken = ?
[tex]t_1+t_2 = ?[/tex]
Solution:
Let D be the distance to lake.
Formula for time is given as:
[tex]Time =\dfrac{Distance}{Speed }[/tex]
[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]
[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]
Putting in equation (1):
[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]
So,
[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]
[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]
So, the answer is:
[tex]t_1+t_2 = \bold{8\ hrs}[/tex]
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100 100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 8 88 finishers in the final round of the 2012 20122012 Olympics. The lower dot plot shows the times of the same 8 88 swimmers, but in the semifinal round. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.) Choose all answers that apply: Choose all answers that apply:
Answer:
The center of the semifinal round distribution is greater than the center of final round distribution.
The variability in the semifinal round distribution is less than variability in the final round distribution.
Step-by-step explanation:
The mean value of each distribution set is not calculates as the center of semifinal round distribution is greater than the final round distribution. MAD Mean Absolute Deviation is calculated from the dotted graph plot, the distribution of semifinal round is less spread out than the final round distribution.
Answer:
correct answer is None of the above i understood nothing the other person was trying to say...
Step-by-step explanation:
mark me brainliest please...
Please Answer THIS QUESTION ASAP ty!! First 2 answer right is BRAINLESS
Hi there! :)
Answer:
[tex]\huge\boxed{A = 119.44 cm^{2} }[/tex]
To find the area of the shaded region, we will need to find the areas of both the rectangle and the circle:
Rectangle: A = l × w
A = 11 × 12
A = 132 cm²
Circle: A = πr² (Let π = 3.14)
A = π(2)²
A = 4π
A ≈12.56 cm²
Subtract the area of the circle from the area of the rectangle:
132 - 12.56 = 119.44 cm².
1: The best statement for reason 6 of this proof is -∠A ≅ ∠C
-∠B ≅ ∠D
-∠B and ∠D are supplements
-∠B ≅ ∠B
2.The best reason for statements 3.5. and 7 in this proof is
- Alternate interior angles are congruent.
-Corresponding angles are congruent.
-Alternate exterior angles are congruent.
-Interior angles on the same sides of a transversal are supplements.
3. The best statement for reason 8 of this proof is
-∠B ≅ ∠B -∠A and ∠C are supplements.
-∠B ≅ ∠D
-∠A ≅ ∠C
Answer:
1) -∠B ≅ ∠D
2) -Interior angles on the same side of a transversal are supplementary
3) -∠A ≅ ∠C
Step-by-step explanation:
1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D
2) Given that ABCD is a parallelogram, therefore ∠A and ∠B, ∠A and ∠D and ∠B and ∠C are interior angles on the same side of a transversal and are therefore supplementary
3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.
. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
Dos secretarias deben escribir el mismo número de cartas. La primera escribe 2 cartas por hora y la otra, 5 cartas por hora. Si la primera ha empezado 6 horas antes que la segunda. ¿Cuántas horas
trabajó la primera?
Ayuden!!
Answer:
El número de horas que trabajó la primera secretaria es de 10 horas
Step-by-step explanation:
Los parámetros dados son;
El número de letras que la primera secretaria puede escribir por hora = 2 letras
El número de letras que el segundo secretario puede escribir por hora = 5 letras
Dado que la primera secretaria comenzó 6 horas antes que la segunda secretaria, tenemos;
Sea el tiempo en horas en que ambas secretarias habrán escrito el mismo número de letras = [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 2 × 6 = 5 × [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 12 = 5 × [tex]t_e[/tex]
12 = 5 × [tex]t_e[/tex] - 2 × [tex]t_e[/tex] = 3 × [tex]t_e[/tex]
12 = 3 × [tex]t_e[/tex]
3 × [tex]t_e[/tex] = 12
[tex]t_e[/tex] = 12/3 = 4 horas
El número de horas que trabajó la primera secretaria = Tiempo de inicio anticipado + Tiempo que le toma a la segunda secretaria que comenzó 6 horas más tarde y a la primera secretaria que había estado escribiendo durante 6 horas (inicio anticipado) escribir la misma cantidad de cartas
El número de horas que trabajó la primera secretaria = 6 + 4 = 10 horas.
Por lo tanto, el número de horas que trabajó la primera secretaria = 10 horas.
Annie left her house at 10:00AM walking at 2 mph. In exactly 1 hour, Davis left the same house and headed the same route in the same direction with his dog. The dog was constantly running between Davis and Annie until Davis caught up with Annie. Davis was walking at 3 mph and the dog was running at 6 mph. How many miles did the dog run by the time Davis caught up with Annie?
Answer:
the dog was running 3mph faster than david
Please help! Urgent! Will mark Brainliest!
Answer:
[tex]x = 15[/tex]
Step-by-step explanation:
Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.
The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:
[tex]3x + 3x + (6x + 45) + (6x+45) = 360[/tex]
Combine like terms so we can get a simpler equation:
[tex]6x + 12x + 90 = 360\\18x + 90 = 360[/tex]
Now let's solve for x!
[tex]18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15[/tex]
So [tex]x = 15[/tex].
Hope this helped!
Answer:
15
Step-by-step explanation:
3x + 6x + 45 = 180
9x = 135
x = 15
Basic math for 20 points + brainliest!
Answer:
Look at photo
Step-by-step explanation:
y is inversely proportional to x². When x=4, y=7.5 Find y when x=5 (i also forgot the symbol for directly and inversely proportional and i'm pretty sure there is one)
Answer:
y = 4.8
Step-by-step explanation:
Given that y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of proportion
To find k use the condition when x = 4, y = 7.5 , then
7.5 = [tex]\frac{k}{4^2}[/tex] = [tex]\frac{k}{16}[/tex] ( multiply both sides by 16 )
k = 16 × 7.5 = 120
y = [tex]\frac{120}{x^2}[/tex] ← equation of proportion
When x = 5 , then
y = [tex]\frac{120}{5^2}[/tex] = [tex]\frac{120}{25}[/tex] = 4.8
Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)
Step 1: What is Sam's rate as stated?
63,756 feet
63, 756 ft
70 min
70 minutes
Step 2: What factor is used to convert feet per minute into
miles per minute?
Step 3: what factor is used to convert miles per minute to miles per hour
Answer:
10.35 miles per hour
Sam's rate as stated is 63,756 feet per 70 minutes
Divide by 5,280 feet
Divide by 60 minutes
Step-by-step explanation:
1. Find how many feet Sam ran in one minute
63,756 ÷ 70 = 910.8 ft.
2. Find how many feet he ran in one hour
910.8 · 60 = 54,648 ft.
3. Convert the feet to miles
54,648 ÷ 5280 = 10.35
Step 2: There are 5280 feet in one mile. Therefore, you would divide by 5280 feet to convert feet per minute into miles per minute.
Step 3: There are 60 minutes in one hour. Therefore, you would divide by 60 minutes to convert miles per minute to miles per hour.
Answer:
1: 63,756 and 70 mins
2: 1 mile and 5,280 feet
3: 60 mins and 1 hour
4: 10.35
Fill in the blank with a number to make the expression a perfect square.
u^2+8u+?
Answer:
16
Step-by-step explanation:
Hello, do you remember that result?
For any a and b real numbers,
[tex](a+b)^2=a+2\cdot a \cdot b+b^2[/tex]
In this example, we have.
[tex]u^2+8u=u^2+2\cdot 4 \cdot u\\\\\text{ This is the beginning of ... } u^2+8u+4^2=u^2+8u+16\\\\\text{ So, we need to add 16 to make a perfect square}\\\\u^2+8u+\boxed{16}=u^2+2\cdot 4\cdot u +4^2=(u+4)^2[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Consider the plot created from the residuals of a line of best fit for a set of data.
Does the residual plot show that the line of best fit is appropriate for the data?
Yes, the points have no pattern.
No, the points are evenly distributed about the x-axis.
No, the points are in a linear pattern.
Yes, the points are in a curved pattern.
Answer:
No, the points are in a linear pattern.
Step-by-step explanation:
Residual plot is a graph that shows the residuals on the vertices. The y-axis has residual values and x-axis has independent variables. The horizontal axis shows the independent variables to determine the best fit for a set. The graph given is in a linear pattern. The random pattern shows that linear model is good fit.
Answer:
C: No, the points are in a linear pattern
Step-by-step explanation:
edg2021
I have been seeing this question with multiple different answers, and no one is sure about anything! All I can say for sure is that IT IS NOT A! So C makes the most sense. B is simply not true, and neither is D, its not curved or evenly distribute.
i will mark brainlist!!
Answer:
3/5 + 2 3/4 = 3 7/20
Step-by-step explanation:
2 = 8/4
2 3/4 = 2 + 3/4
then:
3/5 + 2 3/4 = 3/5 + 8/4 + 3/4
= 3/5 + (8+3)/4
= 3/5 + 11/4
3/5 = 12/20
11/4 = 55/20
then:
3/5 + 11/4 = 12/20 + 55/20 = 67/20
67/20 = 60/20 + 7/20 = 3 + 7/20
= 3 7/20
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
ху
1 | 20
3 | 10
5 | 0
7 | -10
A. Initial value: 20, rate of change: 10
B. Initial value: 30, rate of change: 10
C. Initial value: 25, rate of change: -5
D. Initial value: 20, rate of change: -10
Answer:
C, at 0/25, 1/20, 2/15, 3/10,...
Answer:
C
Step-by-step explanation:
Please solve (will make brainiest)
Answer:
1a) 1/64
1b) 1/169
1c) 1/9
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{ - n} = \frac{1}{ {a}^{n} } [/tex]
Question A,
[tex] {4}^{ - 3} = \frac{1}{ {4}^{3} } = \frac{1}{64} [/tex]
Question B,
[tex] {13}^{ - 2} = \frac{1}{ {13}^{2} } = \frac{1}{169} [/tex]
Question C,
[tex] {( - 3)}^{ - 2} = {( - \frac{1}{3}) }^{2} = \frac{1}{9} [/tex]
