Answer:
(10, - 1 )
Step-by-step explanation:
Given the 2 equations
x - 3y = 13 → (1)
x + 2y = 8 → (2)
Rearrange (1) making x the subject by adding 3y to both sides
x = 3y + 13 → (3)
Substitute x = 3y + 13 into (2)
3y + 13 + 2y = 8
5y + 13 = 8 ( subtract 13 from both sides )
5y = - 5 ( divide both sides by 5 )
y = - 1
Substitute y = - 1 into (3) for corresponding value of x
x = 3(- 1) + 13 = - 3 + 13 = 10
solution is (10, - 1 )
Work out the area of the shaded shape.
Answer:
65 m²
Step-by-step explanation:
Area 1 :-
A = 3m * 9m A = 27 m²Area 2 :-
A = (12-3-2) m * (9 - 5) m A = 7m * 4 mA = 28 m²Area 3 :-
Area = 2m * 5 m A = 10 m²Total Area :-
A = ( 27 + 28 + 10 ) m²A = 65 m²0.2(x + 20) – 3 > –7 – 6.2x
Answer:
x > - 1.25
Step-by-step explanation:
0.2(x + 20) – 3 > –7 – 6.2x
0.2x + 4 - 3 > - 7 - 6.2x
0.2x + 1 > - 7 - 6.2x
Collect like terms
0.2x + 6.2x > -7 - 1
6.4x > -8
x > - 8/6.4
x > - 1.25
Note:
The > didn't change because you didn't divide by a negative value
Inequality signs changes when divided by a negative value
Answer:
Step-by-step explanation:
-1.25
represent the following additions on a number line 3+5=8 3+(-5)
Answer:
8 &-2
Step-by-step explanation:
<-------------------------->
-2-1 0 1 2 3 4 5 6 7 8
________________
-2<8 and 8>-2
Which of the following is the parent function of all absolute value functions?
f(x) = 3x
f(x) = |x|
f(x) = 2|x|
f(x)=x²
What is the value of the constant in the equation that relates the height and
width of this rectangle?
Answer:
14 or 10.4
Step-by-step explanation:
I don’t really understand the question but here I go I’ll try;
The height is 4 and the width is 10, so I think it’s 14 or 10.4.
The Constant that relates the height and width is 5/2.
What is Constant of Proportionality?The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
Given:
we have the coordinates as (10, 4)
The coordinates shows that when the height of the rectangle is 4 unit then the width of the rectangle is 10.
Using Constant of Proportionality
y= k x
10 = k(4)
k = 10/ 4
k = 5/2
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Perimeter of a Garden
Answer:
Step 1: W = 7 - L
Step 2: Widths = 4, 3, 2, 1
Step-by-step explanation:
step1:
14 = 2L + 2W
14 - 2L = 2W
W = 7 - L
step2:
W = 7 - L
W = 7 - 3 = 4
W = 7 - 4 = 3
W = 7 - 5 = 2
W = 7 - 6 = 1
In ΔTUV, the measure of ∠V=90°, UT = 65, VU = 56, and TV = 33. What ratio represents the cosine of ∠T?
Answer: The ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]
Step-by-step explanation:
We are given:
UV = 56 units
VT = 33 units
UT = 65 units
∠V = 90°
Cosine of an angle is equal to the ratio of base and the hypotenuse of the triangle. ΔTUV is drawn in the image below.
[tex]\cos \theta=\frac{\text{base}}{\text{hypotenuse}}[/tex]
Base of the triangle is UV and the hypotenuse of the triangle is TU
Putting values in above equation, we get:
[tex]\cos \theta=\frac{UV}{TU}=\frac{56}{65}[/tex]
Hence, the ratio that represents the cosine of ∠T is [tex]\frac{56}{65}[/tex]
Please help me... I stink at math
Answer:
142 [tex]cm^3\\[/tex]
Step-by-step explanation:
You have to do [tex](7*5)+(5*3)+(7*3)+(7*3)+(5*7)+(3*5)[/tex].
This equals 142 [tex]cm^3\\[/tex].
Answer:
The answer is 142cm
Step-by-step explanation:
help I need help with my homework no link please BTW its 9th grade work I need help with number 1 a) I still need help with it
Answer:
you need to learn how to "prime factor" numbers....
primes are 2,3,5,7,11,13,17....
they go on forever. ALL whole numbers can be "broken down" into a bunch of primes multiplied together.
take the fractions (top and bottom) and start dividing them bu the smallest prime, and going up until all the numbers multiplied make the original number...
15 = 3 * 5
24= 2 * 12 = 2 * 2 * 6 = 2* 2* * 2 * 6
thus [tex]\frac{15}{24}[/tex] = [tex]\frac{3 * 5 }{2* 2* 2* 3}[/tex] now just cancel all the SAME numbers from to to bottom
"pair them up" .... in this case only one of the threes in the bottom "takes out" one of the threes in the top
result [tex]\frac{5}{2*2*2 } = \frac{5}{8}[/tex]
~~~~~~~~~~~~~~~~~~~~
[tex]\frac{21}{35}[/tex]
21= 3 * 7
35= 5* 7
[tex]\frac{3*7}{5*7} = \frac{3}{5}[/tex]
Step-by-step explanation:
Find the value of cos J rounded to the nearest hundredth, if necessary.
Answer:
cosJ ≈ 0.38
Step-by-step explanation:
This is a 5- 12- 13 right triangle
with HI = 12, HJ = 13, IJ = 5
cosJ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{IJ}{HJ}[/tex] = [tex]\frac{5}{13}[/tex] ≈ 0.38 ( to nearest hundredth )
The required value of Cos(J) for the given triangle is 0.38.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
In the given ΔHIJ the sides are given as,
JH = 13 and HI = 12.
Now, apply Pythagoras theorem to obtain,
IJ² + HI² = JH²
⇒ IJ² = 13² - 12²
⇒ IJ = 5
Use trigonometric ratio to obtain,
Cos(J) = IJ/HI = 5/13 = 0.38
Hence, the value of Cos(J) is obtained as 0.38.
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Consider the graph of f(x) = 5x + 1. Explain how to find the average rate of change between x = 0 and x = 4.
What is the average rate of change?
Answer:
5
Step-by-step explanation:
You divide the change in the output value by the change in the input value.
Input: 0 | 4
Output: 1 | 21
20/4= 5
Kato must write 60 percent of a 20- page report by tommorow. Kato wants to determine the number of pages that he needs to write by Tommorow. Katos work is shown below
Answer:
60% of 20 pages = .6 * 20 = 12 pages
Step-by-step explanation:
plz help ASAP with explanation
Answer:
19.5 cm
Step-by-step explanation:
the remaining height = 1200 /(12×8)
= 1200/96 = 12.5 cm
so, the height of the tank = 7+ 12.5 = 19.5 cm
[tex]\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm[/tex]
Find the value of x. Round to the nearest tenth.
Answer:
x = 7
Step-by-step explanation:
First we find out what we are using sin,cos, or tan then we plug in the numbers
Sin 26 x 16 = 7
What is the scale factor from abc to xyz?
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C
The scale factor will be equal to 1 / 5. the correct option is C.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,
Scale factor = Original size / dilated size
Scale factor = XY / AB
Scale factor = 9 / 45
Scale factor = 1 / 5
Therefore, the scale factor will be equal to 1 / 5. the correct option is C.
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(6x-5)/7-(2x-1)/3=2?
You borrow $25,000 to buy a boat. The simple interest rate is 4%. You pay the loan off after 10 years. What is the total amount you paid for the loan?
Answer:
$35000
Step-by-step explanation:
A = P(1+rt)
A = 25000*(1+4%*10)
A = 35000
BRAINLIEST PLEASEEEEEEEEEEE
A bag contains 6 apples and 4 oranges. If you select 5 pieces of fruit without
looking, how many ways can you get 5 apples?
Answer:
6 I think
Step-by-step explanation:
How do you work out the volume of a cube
Answer:
V=a cubed
Step-by-step explanation:
Find the length of side AB.
Give your answer to 1 decimal place.
12 cm
62°
A
B
Hey there!
To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.
1. Cosine Ratio
Currently, there are 6 Trigonometric Ratios. But we will be talking about Cosine Ratio instead since it is what we will be using in your question! Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. You know what adjacent and hypotenuse are right? If not then head to the next topic!2. Adjacent and Hypotenuse
Adjacent is basically the base of a triangle. It is basically drawn from right angle to any measure/angles. Hypotenuse is the longest side of a right triangle. It is also an opposite side of right angle.Hope you understand this topic! If not, feel free to ask!
3. Solve The Problem
Since our adjacent is length AB but we don't know its exact value. What we have to do is to determine AB as any variables which I will determine AB as "x". Next, we have the value of hypotenuse which is 12 cm. Then we also know the Cosine Ratio which is adjacent to hypotenuse.Therefore, the equation for the problem is:
[tex] \large{cos62 \degree = \frac{x}{12} }[/tex]
*cos is the short form of cosine*
At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.
When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.
When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:
[tex] \large{0.5 = \frac{x}{12} }[/tex]
Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.
[tex] \large{0.5 \times 10 = \frac{x}{12} \times 10} \\ \large{5 = \frac{10x}{12} }[/tex]
10x/12 can be simplified again.
[tex] \large{5 = \frac{5x}{6} }[/tex]
Then we isolate x-value by multiplying 6 the whole equation.
[tex] \large{5 \times 6 = \frac{5x}{6} \times 6} \\ \large{30 = 5x} \\ \large{x = 6}[/tex]
Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.
When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.
Hence, the equation and value above is just a rounded to the whole number from 5.63365875.
Because you want a one place decimal. Hence,
4. Final Answer
The length AB is 5.6 (rounded to nearest tenth)X,Y and Z from a business with capitals Rs 5000,Rs.4500 and Rs.6500 respectively,after 6 month,X doubles has capital and after next 3 months Y trebles his capital .If the profit at the end of the year amount to RS.8300,find the profit obtained by each X,Y and Z.
Answer:
Profit obtained by X = Rs. 2,976.64
Profit obtained by Y = Rs. 2,545.58
Profit obtained by Z = Rs. 2,777.78
Step-by-step explanation:
Total capital for the first 6 months = Rs 5000 + Rs.4500 + Rs.6500 = Rs. 16,000
Total capital for the next 3 months = Rs. 16,000+ Rs 5000 = Rs. 21,000
Total capital for the last 3 months of the year = Rs. 21,000 + (Rs 4500 * 2) = Rs. 30,000
Share of profit of each partner is the sum of all the ratios of his capital to total capital of the business at each point in time multiply by the ratio of the numbers of months covered by each capital to 12 months and then multiply by RS.8300.
Profit obtained by X = ((Rs 5000 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 10,000 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 10,000 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,976.64
Profit obtained by Y = ((Rs 4500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 4500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 13,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,545.58
Profit obtained by Z = ((Rs 6500 / 16,000) * (6 / 12) * Rs. 8300) + ((Rs 6500 / 21,000) * (3 / 12) * Rs. 8300) + ((Rs 6,500 / 30,000) * (3 / 12) * Rs. 8300) = Rs. 2,777.78
Confirmation of total profit shared = Rs. 2,976.64 + = Rs. 2,545.58 + Rs. 2,777.78 = Rs. 8,300
Sarah borrows £500 for 2 years at a rate of 15% to buy a
new laptop.
Calculate the simple interest she will pay on this loan.
Answer: 150 pounds
Step-by-step explanation:
if the measure of angle def is 65° what is the measure of arc de?
EF is tangent to the circle we'll assume; otherwise there's no progress.
Call the center C. ECD is isosceles, formed from two radii and the chord.
Angle CED is complementary to DEF
CED = 90 - 65 = 25 degrees
CDE is congruent, isosceles triangle and all that: CDE=25
That leaves DCE=180-25-25=130 degrees
That's the measure of arc DE as well:
Answer: 130 degrees, choice A
Answer:
130
Step-by-step explanation:
5. If 40 of 160 moviegoers who watched a certain movie said that they would like to see the movie again, what is the probability that any moviegoer who saw the said movie would like to see it again? A. 0.25
B. 0.50
C. 0.75
D. 0.85
Answer: A. 0.25
Step-by-step explanation:
You need to divide 40 by 160 to calculate the percentage.
Please hurry I will mark you brainliest
Answer:
D. -1/7
Step-by-step explanation:
Substitute and solve
Answer:
[tex]-\frac{1}{7}[/tex]
Step-by-step explanation:
When given the following expression,
[tex]\frac{a+c}{a^2-c^2}[/tex]
With the information that the values (a = -2) and (c = 5), one is asked to evaluate the expression. One's first instinct is probably to substitute the values into the expression and solve, however, a faster approach is to simplify the expression. The denominator is the difference of squares, thus one can rewrite it as the product of two linear expressions. Then one can simplify it by canceling out like terms in the denominator and the numerator. Finally, one can then substitute the values of the (a) and (c) into the simplified expression and solve.
[tex]\frac{a+c}{a^2-c^2}[/tex]
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
Cross out like terms in the numerator and denominator,
[tex]=\frac{a+c}{(a+c)(a-c)}[/tex]
[tex]=\frac{1}{a-c}[/tex]
Now substitute the values of (a) and (c) into the expression and simplify to evaluate,
[tex]=\frac{1}{a-c}[/tex]
[tex]=\frac{1}{(-2)-(5)}\\\\=\frac{1}{-2-5}\\\\=-\frac{1}{7}[/tex]
Find the value of the following
Answer:
110.01 (aprox)
Step-by-step explanation:
x + (1/x) = 5
x(x + (1/x)) = x(5)
x*x + x*1/x = 5x
x² + 1 = 5x
x² - 5x + 1 = 0
x = {-(-5)±√((-5²) -(4*1*1))} / (2*1)
x = {5±√(25-4)} / 2
x = {5±√21} / 2
x = {5±4.5826} / 2
x₁ = {5-4.5826} / 2 = 0.4174/2 = 0.2087
x₂ = {5+4.5826) / 2 = 9.5826/2 = 4.7913
Comprobación:
x₁
0.2087 + 1/0.2087 = 5
0.2087 + 4.7913 = 5
x₂
4.7913 + 1/4.7913 = 5
4.7913 + 0.2087 = 5
Respuesta:
x₁
(0.2087)³ + 1/(0.2087)³ = 0.0091 + 1/0.0091 = 0.0091 + 110.0101 = 110.019
x₂
(4.7913)³ + 1(4.7913)³ = 110 + 1/110 = 110 + 0.01 = 110.01
what is the mid point of AB?
Answer:
G
Step-by-step explanation:
I did this on edge and it was right
Answer:
O Point G
Step-by-step explanation:
A = -6
B = 8
To find the midpoint, calculate how much would it take for both points to have a value of zero.
-6 + ? = 0
-6 + 6 = 0
8 - ? = 0
8 - 8 = 0
so the midpoint will be about 7 (between 6 & 8)
Now which of the points best shows 7 units apart of AB
Answer: point G
Robert took 8 minutes to complete his 12 worksheets. What is his unit rate of completing worksheets
Answer: 40 seconds per worksheet
Step-by-step explanation:
From the information given in the question, we are informed that Robert took 8 minutes to complete his 12 worksheets.
Based on this, his unit rate of completing worksheets will be given as:
= 8 minutes / 12
= 480 seconds / 12
= 40 seconds per worksheet
Note 1 minute = 60 seconds
8 minutes = 8 × 60 = 480 seconds
Can someone help me with this
Answer:
a = 17
c = 9
Step-by-step explanation:
2a + 3c = 61
3a + 5c = 96
3a = 96 - 5c (solve for 'a'. Then you can substitute)
a = 32 - [tex]\frac{5}{3}[/tex] c
2(32 - [tex]\frac{5}{3}[/tex]c) + 3c = 61 (Substitute)
64 - [tex]\frac{10}{3}[/tex]c + 3c = 61 ([tex]\frac{10}{3}[/tex] = 3 [tex]\frac{1}{3}[/tex]. So subtracting, adding a negative, leaves [tex]\frac{-1}{3}[/tex])
-[tex]\frac{1}{3}[/tex] c= -3
c = 9
2a + 3(9) = 61
2a + 27 = 61
2a = 34
a = 17
seventy of myra’s classmates are traveling by the bus to a football game in another town. they hired 2 buses, but there were only 64 seats. the remaining 6 students had to travel in a separate van the equation 2b+6=70 represents the given scenario. what does b represent
Answer:
The b represents the people on each bus.
Step-by-step explanation:
Answer:
C.the number of students who rode on each bus.
Step-by-step explanation:
