Given:
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex].
To find:
The value of k.
Solution:
The gradient or slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The gradient of the line passing through A(2,3), B(k,7) is [tex]\dfrac{2}{3}[/tex]. So,
[tex]\dfrac{2}{3}=\dfrac{7-3}{k-2}[/tex]
[tex]\dfrac{2}{3}=\dfrac{4}{k-2}[/tex]
On cross multiplication, we get
[tex]2(k-2)=4(3)[/tex]
[tex]2k-4=12[/tex]
[tex]2k=12+4[/tex]
[tex]2k=16[/tex]
Divide both sides by 2.
[tex]k=\dfrac{16}{2}[/tex]
[tex]k=8[/tex]
Therefore, the value of k is 8.
Can someone please help me with this question
Answer:
The answer should be: B
I think it's B because there are 2 cups of water (2c) and 7 bottles of water (7w) which costs $16 so that would be 2c +7w=16. Also for the other one, it's 3 cups (3c) and 8 bottles of water (8W) and the cost is $19 so that would be
3c + 8w =19
Step-by-step explanation: Hope this helps and gl :))
Can someone help with this?
Answer:
(a) is 8 x 7 x 3 = 168
(b) is 8 x 7 = 56
(b2) is weird I don't know what it's asking
Answer:
FOR LETTER A
Volume of prism (expression) = Length x Width/Breadth x Height
Volume of prism (expression) = 8 units x 7 units x 3 units = 168 cubic units
FOR LETTER B
Area of the shaded base = 8 x 7 = 56 square units
Volume of prism = Area of the shaded base x Height
Volume of prism = 56 square units x 3 units = 168 cubic units
Step-by-step explanation:
To find the volume of rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.
Volume of rectangular prism = length × width × height
To get the area of the shaded base, when the base is in rectangular shape:
Definition: Area of rectangle is the region occupied by a rectangle within it's four sides or boundaries.
The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area. But in the case of a square, since all the sides are equal, therefore, the area of the square will be equal to the square of side-length.
Area of rectangle = Length × Breadth
A = l × b
Express sin O as a fraction in simplest form
Answer:
sin o = opposite/hypotenuse
sin o= 7/12
solve for
(6x + 9)/3 =
Hello!
(6x + 9)/3 =
= 3(2x + 3)/3 =
= 2x + 3
Good luck! :)
Helppppp and explain pls and thankyouu
Answer:
-13 is the answer I think so but wait for others also because my could be wrong
Evaluate function from their graph
Answer:
f(-5) = 7
Step-by-step explanation:
f(-5) means find the y value when x = -5
y = 7 when x = -5
Which equations are true?
Choose All Answers That Apply (10 Points)
Answer:
B
Step-by-step explanation:
Two negatives is a positive, and you want your outcome to be a positive x, therefore b is the correct answer.
Answer:
second one
A negative multiplied by a negative is a positive.
- (-x) is multiplication.
Use the graph below, find f(10).
6points!!!
Answer:
the answer is a
tell me if it’s rite or wrong I did the work as best as I could
f(10) is undefined.
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is the graph of a function?"It is the set of points on the coordinate plane which satisfies the given function."
For given question,
We need to find the value of a function at x = 10.
We can observe that, when x = 10, the function value 2 is denoted by an open circle.
This means the function do not have value 2 when x = 10
Therefore, f(10) is undefined.
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Angle A and angle B are supplementary. If the measure of angle B is one-third the measure of angle A, what is the measure of angle B?
E. 22.5°
F. 45°
G. 67.5°
H. 135°
Answer:
vertically opposite angles
Step-by-step explanation:
supplementaries angles
The measure of angle B is 45° since option F. is correct in the given question.
What do we mean by supplementary angles?Any two angles (say X & Y), are said to be supplementary when their summation (X + Y) is equal to 180°.
How to determine Angle B?Angle A and Angle B are supplementary, which implies A+B=180°.
Angle B is one-third angle A, which implies
[tex]B=\frac{1}{3} A[/tex]
or, 3B = A
Using the value of A in the previous equation, we get 3B + B = 180°.
4B = 180°
or, B = 45°.
Thus, the measure of angle B is 45°. The correct answer is option F.
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What degree of rotation about the origin will cause the triangle below to map
onto itself?
A.90
B.270
C.360
D.180
Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.
Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
[tex]2(11x)=10x^2[/tex] and
[tex]10x^2-22x=0[/tex] and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to [tex]\frac{22}{10}=2.2[/tex]
So x = 2.2 and y = 22.
Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. How many months will it take for the second phone to be less expensive than the first phone?
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is
.
The solution to the inequality is
.
Sal’s mother would have to keep the second cell phone plan for at least
months in order for it to be less expensive.
Answer:
It will take 13 months for the second phone to be less expensive than the first phone.
Step-by-step explanation:
Since Sal is trying to determine which cell phone and service plan to buy for his mother, and the first phone costs $ 100 and $ 55 per month for unlimited usage, while the second phone costs $ 150 and $ 51 per month for unlimited usage, to determine how many months will it take for the second phone to be less expensive than the first phone, the following calculation must be performed:
100 + (55 x 10) = 100 + 550 = 650
150 + (51 x 10) = 150 + 510 = 660
100 + (55 x 12) = 100 + 660 = 760
150 + (51 x 12) = 150 + 612 = 762
100 + (55 x 13) = 100 + 715 = 815
100 + (51 x 13) = 150 + 663 = 813
Therefore, it will take 13 months for the second phone to be less expensive than the first phone.
Answer:
1) 100 + 55x > 150 + 51x
2) x > 12.5
3) 13
Step-by-step explanation:
Got it right on Edge :D
sin^2x + sin2x +2cox^2x = 2
Answer:
Step-by-step explanation:
[tex]sin^2 \ x + sin ^2 \ x + 2cos^ 2\ x = 2\\\\2sin^2 \ x + 2 cos^2 \ x = 2\\\\2 ( sin^2 \ x + cos^2 \ x ) = 2 \\\\2 \times 1 = 2 \\\\2 = 2 \\\\LHS = RHS \\\\Hence \ proved.[/tex]
What does 8 represent in the decimal 478.92
A. Tenths
B. Hundreds
C. Dozen
D. Units
Answer:
Units
Step-by-step explanation:
From the value above 478.92
4 represents hundreds
7 represents tens
8 represents units
Hence the answer is units
Question 3: use the image and your knowledge of the isosceles triangle to find the value of x
Answer:
72 +72=144
180-144=36
the answer is 36°
The measure of the angle x is 36° obtained by the concept of an Isosceles triangle and interior angle sum.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know an isosceles triangle has two similar sides and angles opposite to the similar side and also measures the same.
So, By the interior angle sum concept,
72° + 72° + x = 180°.
x = 36°.
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What is the solution
Answer:
x = -72
Step-by-step explanation:
-72 + 8 = -64
The third square root of -64 is -4
How can an expression written in either radical form or rational exponent form be rewritten to fit the other form? Explain thoroughly and thank you for your time.
Answer:
Step-by-step explanation:
We'll start with going form exponential to radical, since it may be easier to follow. For example,
[tex]x^{\frac{4}{3}[/tex] can be written, in radical form, as
[tex]\sqrt[3]{x^4}[/tex]. What happens is that the denominator of the fraction serves as the index (the number that sits in the bend of the radical) and the numerator serves as the power on the variable (or number, if that's the case). Let's look at another one:
[tex]4^{\frac{2}{3}[/tex] becomes
[tex]\sqrt[3]{4^2}=\sqrt[3]{16}=\sqrt[3]{8*2}=2\sqrt[3]2}[/tex]
And you can go the other way with it. For example,
[tex]\sqrt[5]{x^4}[/tex] becomes
[tex]x^{\frac{4}{5}[/tex], etc. Get it?
Answer:
When you're given a problem in radical form, you may have an easier time if you You can rewrite every radical as an exponent by using the following property — the top ... For example, 643/2 is easier if you write it as (641/2)3 = 83 = 512 rather than (643)1/2, Rewrite the entire expression using rational exponents.
A circular sheet covers 425cm on the table,find the area of the sheet.
solve this question plz.
Answer:
sorry i cannot help you
Based on the table below, what is the relationship between cups and tablespoons?
Answer:
the answer is A
Step-by-step explanation:
For his long distance phone service, Justin pays a $3 monthly fee plus 11 cents per minute. Last month, Justin's long distance bill was $12.79. For hov minutes was Justin billed?
Answer:
89 minutes
Step-by-step explanation:
let he talked for x minutes.
$12.79=1279 cents
1279=300+11x
11x=1279-300=979
x=89
Select the correct answer. . Which value of x makes this equation true? -12x - 2(x + 9) = 5(x + 4) ОА. 13/19 OB. -1/3 OC. -2 OD. 5
Answer:
B -1/3
Step-by-step explanation:
The value of x that makes this equation true is x = -2
Which value of x makes this equation true?We have the equation:
-12x - 2(x + 9) = 5(x + 4)
To solve it, we need to isolate x on one side of the equation:
-12x - 2x - 18 = 5x + 20
-12x - 2x - 5x = 20 + 18
-19x = 38
x = 38/-19 = -2
The value of x that makes this equation true is x = -2
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find the compound interest on rs 800 for 2 years at 8% per annum interest being payable annually
Answer:
Rs 968
Step-by-step explanation:
Given :-
P = Rs 800 Rate = 8% Time = 2 yrs .To Find :-
Compound Interest .Solution :-
We know CI as ,
> CI = P ( 1 + R/100)ⁿ
> CI = Rs 800 ( 1 + 10/100)²
> CI = Rs 800 × 11/10 × 11/10
> CI = Rs 968 .
Find the value of y.
A.74 B.20 C.66 D.62
Answer:
It's letter D.
Step-by-step explanation:
3.14÷60×50= 2.61 but you have to opposite remember if the number is a little number you have to opposite and that is the answer 6.2 but do not joy like this . so the real answer is 62
Tele-Mart instituted a 5-for-1 split in April. After the split, Ashlee owned 1,860 shares. How many shares had she owned before the split?
Answer:
372 shares
Step-by-step explanation:
Let
x = shares owned before the split
Share after split : share before split = 5 : 1
Share after split : share before split = 1,860 : x
Equate both ratios
5 : 1 = 1,860 : x
5/1 = 1,860/x
Cross product
5 * x = 1 * 1,860
5x = 1,860
x = 1,860/5
x = 372
x = shares owned before the split = 372 shares
Vicki and Tamra are working on their math homework together. Vicki has worked p problems, and Tamra has worked 4 times as many problems as Vicki. The expression shows how many problems they have worked altogether.
Answer:
p + 4p
5p
Step-by-step explanation:
Problems Vicki solved = p
Tamra worked 4 times as many problems as Vicki = 4 x p = 4p
total problems solved by both of them =4p + p
= 5p
3(y+6)=30 solve equation
Answer:
3(y+6)=30
3y + 18 = 30
18 - 30 = 3y
12 = 3y
12/3 = y
4 = y
or
y = 4
I need who help .. who can be my lifesaver
Answer:
Q = G
Step-by-step explanation:
We are already given that angle P = angle H
We are also given that side QP = side GH
Remember if two sides are congruent then so are their opposite angles meaning that the opposite angle of GH ( which would be angle F ) would be congruent to the opposite angle of QP ( which would be angle R )
The remaining angles would be angle q and angle g so the additional information needed would be G = Q
Read the text and answer the following questions:
1. Kolman shop was once a very rich town
True
False
2. The UFO buildings are a popular tourist attraction in Taipei.
True
False
3. Fordlandia became a problem because there was nowhere for the factory workers to live.
True
False
4. The Ford family sold Fordlandia for $20 million.
True
False
Answer:
1. False
2. True
3. True
4. False
Step-by-step explanation:
[tex]{hope it helps}}[/tex]
Does the point (7, 2) satisfy the equation y = x - 5? yes no
Yes
Replace x in the equation with the x in the solution and see if t equals the y in the solution:
Y = 7-5 = 2
The answer is yes.
Help me with these 3 and explain too thank you :))
Answer:
1) 25
2) 2
3) f(g(1)) = 42
Step-by-step explanation:
1) Given that f(x) = 4x^2 + 9
If x = -2
f(-2) = 4(-2)^2 + 9
f(-2) = 4(4) + 9
f(-2) = 16 + 9
f(-2) = 25
2) Given that f(x) = 4x - 6
y = 4x - 6
Replace y with x
x = 4y - 6
MAke y the subject of the forfmula
4y = x+ 6
y = (x+6)/4
SInce x = 2
f^(-1)(2) = (2+6)/4
f^(-1)(2) = 8/4 = 2
3) If f(x) = 6x and g(x) = x+6
f(g(x)) = f(x+6)
f(x+6) = 6(x+6)
Since x = 1
f(g(1)) = 6(1+6)
f(g(1)) = 6(7)
f(g(1)) = 42
