Answer:
a) -2
b) y = -2x + 6
Step-by-step explanation:
Question (a)
Point A = (-1, -2)
Point B = (7, 2)
[tex]\sf gradient\:of\:AB=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{2-(-2)}{7-(-1)}=\dfrac{4}{8}=\dfrac12[/tex]
If lines are perpendicular to each other, the product of their gradients will be -1.
Let g be the gradient of the perpendicular line:
[tex]\implies \sf \dfrac12 \times g=-1[/tex]
[tex]\implies \sf g=-1 \div \dfrac12=-2[/tex]
Therefore, the gradient of the line perpendicular to AB is -2
---------------------------------------------------------------------------------------------
Question (b)
[tex]\sf midpoint\:of\:line = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\sf let\:point\:A=(x_1,y_1)=(-1,-2)[/tex]
[tex]\sf let\:point\:B=(x_2,y_2)=(7,2)[/tex]
[tex]\sf \implies midpoint\:of\:line\:AB = \left(\dfrac{-1+7}{2},\dfrac{-2+2}{2}\right)=(3,0)[/tex]
We now know the gradient and a point on the perpendicular line.
So we can use the point-slope form of a linear equation:
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=-2(x-3)[/tex]
[tex]\implies \sf y=-2x+6[/tex]
Find the surface area of this figure.
Answer: 297 in.^2
Step-by-step explanation:
Area of a triangle: b*h/2 ---> (9*12)/2=544 triangles--->4*54(area of triangle)= 216Area of square: b*h ----> 9*9 = 81Add area of all four triangles plus are of square-----> 216+81 = 297 in.^2
Order the steps to solve the equation
log(x^2-15)= log(2x) form 1 to 5
x^2-2x-15=0
Potential solutions are -3 and 5
x^2-15=2x
x-5=0 or x+3=0
(x-5)(x+3)=0
Answer:
Step-by-step explanation:
When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:
[tex]log_1_0(x^2-15)=log_1_0(2x)[/tex]
Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:
[tex]x^2-15=2x[/tex]
Subtract 2x on both sides to get:
[tex]x^2-2x-15=0[/tex]
Use the quadratic formula to solve for 'x' to get:
[tex]x=(-b+\sqrt{b^2-4ac} )/2a[/tex]
[tex]x=(-b-\sqrt{b^2-4ac} )/2a[/tex]
Beginning with the first solution:
[tex]x=(-(-2)+\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=2+\sqrt{4+60} )/2[/tex]
[tex]x=(2+\sqrt{64}) /2[/tex]
[tex]x=(2+8)/2[/tex]
[tex]x=5[/tex]
Second solution:
[tex]x=(-(-2)-\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]
[tex]x=(2-\sqrt{4+60} )/2[/tex]
[tex]x=(2-8)/2[/tex]
[tex]x=-6/2[/tex]
[tex]x=-3[/tex]
Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.
Karly borrowed $6,200 from her parents for 4 years at an annual simple interest rate of 2.8%. How much interest will she pay if she pays the entire loan at the end of the fourth year?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Answer:
$724.11
Step-by-step explanation:
This requires the use of the growth formula.
Growth Formula:
[tex]y = a*(1+r)^x[/tex]
y = total/answer
a = starting value
r = rate (1.25 = 25%)
x = the amount of time (years/months)
Equation:
[tex]y = 6200 * (1+0.028)^4[/tex]
Solving:
y = $6924.11
$6924.11 - $6200 = total interest
$724.11
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$6200\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (6200)(0.028)(4)\implies I=694.4[/tex]
y=x+2
y=-2x-1
solve by addition method
Answer:
x = -1, y = 1
Step-by-step explanation:
NEED HELP ASAPPP!!!!!!
Answer:
B
Step-by-step explanation:
Square both sides, and get s^2 = k3/p
next multiply both sides by p and get (s^2)(p)=k3
Therefore k3 equals s^2 times p
state the rule obeyed by the variables in each relation diagram below
Answer:
y = 2x + 1
Step-by-step explanation:
You can see a pattern in the group of x's that the numbers go up by 1 Also in the y-set that the numbers go up by 2. So this pattern is linear, that means the "rule" you are looking for does not have exponents or square roots or any very complicated stuff. You can use a guess and check method. Say to yourself how can I get a 7 out, when I put a 3 in? "times by2 and plus 1" works.
3 times 2, and plus1
gives you 7.
Test it on the other numbers.
-1 times2, and plus1
2(-1)+1 = -1
2(0)+1 = 1
2(1)+1 = 3
2(2)+1 = 5
It works for all the numbers.
You can calculate it also, using any two pairs of (x,y) from the data set. Put y-y on top of a fraction and x-x on the bottom. You will get the slope and that is the 2 in the "rule"
(3,7) and (2,5) for example. 7-5 so put 2 on top and 3-2 so put 1 on the bottom. 2/1 is just 2. From the point (0,1) we know the y-intercept is 1. This also gives the equation y=2x+1.
If you are just starting to learn this, probably just guess and check a rule. The rule has to work for all the points.
I need help pls guys
Answer:
11
Step-by-step explanation:
11 is ur answer to the question.
I hope it helped yoy
can someone please help me with this question
Answer: I think its D
Step-by-step explanation:
i need help 9th grade math
Answer:
-x + 1
Step-by-step explanation:
f(x) = 2x + 3
g(x) = 3x + 2
we want to find (f-g)(x)
(f-g)(x) is the same as saying f(x) - g(x)
f(x) - g(x) = (2x + 3) - (3x + 2)
==> remove parenthesis and apply negative sign
f(x) - g(x) = 2x + 3 - 3x - 2
==> combine like terms
f(x) - g(x) = -x + 1
Put values
2x+3-(3x+2)2x+3-3x-2-x+1
For the curve y=x^4+1, find the gradient of the secant between the point (1, 2) and
the point where x=1.01.
Answer:
4.06.
Step-by-step explanation:
Where x = 1.01, y = (1.01)^4 + 1 = 1.0406 + 1
= 2.0406
So the gradient between (1, 2) and (1.01, 2.0406)
= (2.0406 - 1)/(1.01 - 1)
= 4.06.
Find the area of the given triangle. Round your answer to the nearest tenth.
A right triangle with a base of 36. The angle of elevation is 25 degrees.
Group of answer choices
302.2 units squared
1 comma 389.6 units squared
766.6 units squared
Using relations in a right triangle, it is found that it's area is of 302.2 units squared.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, we have that the opposite side to the angle of 25º is of x, while the adjacent side is of 36, hence:
[tex]\tan{25^\circ} = \frac{x}{36}[/tex]
[tex]x = 36\tan{25^\circ}[/tex]
x = 16.79.
What is the area of a right triangle?It is given by half the multiplication of it's sides, hence:
A = 0.5 x 16.79 x 36 = 302.2 units squared.
More can be learned about relations in a right triangle at https://brainly.com/question/26396675
the number in this sequence increase by 40 each time. 30 70 110 115... the sequence is continued with the same rule. Which number in the sequence will be the closest to 300
Answer:
310
Step-by-step explanation:
150,190,230,270,310
hope this helps!
the product of a number and 6 decreased by 2
(don't solve,i just need it in a equation)
[tex]y = 6x - 2[/tex]
I believe this is correct
Order the set of numbers from least to greatest: square root 64, 8 and 1 over 7, 8.14 repeating 14, 15 over 2
A 15 over 2, square root 64, 8 1 over 7, 8.14 repeating 14
B 8 1 over 7, 8.14 repeating 14, square root 64, 15 over 2
C square root 64, 8 1 over 7, 8.14 repeating 14, 15 over 2
D 15 over 2, square root 64, 8.14 repeating 14, 8 1 over 7
Answer:
D
Step-by-step explanation:
15/2= 7.5
square root of 64= 8
8 1/7= 8.14285...
please help URGENT!! What is the area of the red shaded region?
Answer:
5
Step-by-step explanation:
54÷8 x 4 ÷2 means that your answer would be 12
You received your $1,200 stimulus check from the government due to the coronavirus. If you choose to invest this into an investment account that pays 5.25% compounded continuously (rather than spending it), how long will it take to double your money?
Answer: IRS has sent $6 billion in stimulus payments just in June. Here's how to track your money Your stimulus check could be on its way, along with child tax credit money and unemployment tax refunds.
Step-by-step explanation:
can i pleas have help with this
Answer:
133m²
Step-by-step explanation:
Super easy!
A = BxH
= 9.5x14
= 133
So hence, your answer is 133.
The area of this rhombus is 133m²
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Read the short selection and answer the questions from 11 to 16. Ann, Bill, Carl, and Dan work in the same office building. Dan works in the basement while Ann, Bill, and Carl share an office on level X. At any given moment of the day, they are all typing at their desks. Bill likes a window seat; Ann likes to be near the bathroom; and Carl prefers a seat next to the door. Their three cubicles do not line up.
__________________.
Answer:
can you add more context to the question it makes no sense with current given clues
Is this correct please give correct answer but no links
Answer:
I give answers I think their correct but as humans we make mistakes so there may be errors
Can someone convert 5cm to milimeter?
Answer:
50 milimeters
If y’all r smart, then answer this.
Please help..
Answer
just add everything but the answer is 130
help please this is hardddddddd
Answer:
#1: 4) D
#2: 1) 34.89 = 3 × C
#3: 4) 6y + 18
Step-by-step explanation:
#1
Using the distributive property:
3 × 5z = 15z
3 × -3 = -9
The correct expression is 15z - 9. Hence, D is the right option.
#2
You need to find the cost of each box.
3 × C = 34.89
34.89 ÷ 3 = 11.63
3 × 11.63 = 34.89
Hence, 1) is the right option.
#3
Using the distributive property:
6 × y = 6y
6 × 3 = 18
The expression is 6y + 18. Hence, 4) is the right option.
hope this helps!! p.s. i really need brainliest :)
Answer:
1. #4, D
2. #1, 34.89 = 3 x c
3. #4, 6y + 18
Step-by-step explanation:
1. Which pair of expression are equivalent (=)?
A.
10c + 20 = 5(5c + 4) <== distribute
10c + 20 = 25c + 20
This pair is not equivalent
B.
3(4e - 2) = 7e - 5 <== distribute
12e - 6 = 7e - 5
This pair is not equivalent
C.
4(4h + 6) = 16 + 24 <== distribute
16h + 24 = 16 + 24
This pair is not equivalent (look carefully, it's missing an h)
D.
15z - 9 = 3(5z - 3) <== distribute
15 - 9 = 15z - 3
This pair is equivalent
Therefore, the correct answer is D
2. Mr. James bought 3 boxes of pencils for $34.89. Each box of pencils costs the same. Which equaiton can be used to find the cost, c, of each box?
We know that 3 boxes of pecils cost $34.89, and c represents the cost of one box. If c represents the cost of one box and there are 3 boxes, it would be 3c or 3 x c.
Looking at the answer choices, #1 is the only option that represents that.
Therefore, the correct answer is 1) 34.89 = 3 x c
3. Aidan wrote an expression 6(y + 3). Which expression is equivalent to the one Aidan wrote?
6(y + 3) <== distribute
6y + 18
Therefore, the answer is 4) 6y + 18
Hope this helps!
help me ??????? please
Answer:
58%
Step-by-step explanation:
vertical angles are always the same
An event has probability of 3/4.
How would you best describe
the likehood of this event?
Answer:
more likely
Step-by-step explanation:
3/4 is 0.75 or 75%. I would describe it as likely.
elimination-
3/4 is not equal to 1 or 0.5 or 0. It is also not equal to 0.25
The total number of balls in a bag will be 4 in which 3 balls are red and 1 ball is blue.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The probability of the event is 3/4.
Let the total number of balls be 4 of two colors that are red and blue and the probability of red color be 3/4.
There will be a total of 4 balls in the bag, 3 of which will be red and 1 blue.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ7
What is the approximate side length of the square? 3. 0 units 3. 5 units 4. 2 units 4. 9 units.
Answer:
4.9 units
Step-by-step explanation:
No trolls or links or i will report
Answer:
92.4 ft²Step-by-step explanation:
Total surface area comprises one rectangular base and two pairs of diferent triangles.
Area of rectangle
A = lwArea of triangle
A = 1/2bhSubstitute and find
A = 7*4 + 2(1/2*4*6.3) + 2(1/2*7*5.6) = 92.4 ft²Area of base rectangle
7(4)28ft²Area of rest triangles
2(1/2BH)+2(1/2bh)BH+bh4(6.3)+7(5.6)64.56ft²Now
TSA
64.56+2892.56ft²The volume of a cylinder is 10.14 cudic centimeters. If a cone has the same height and radius as the cylinder, what is its volume?
Answer:
3.38 cm^3
Step-by-step explanation:
volume of cylinder = pi r^2 h
10.14 / pi = r^2 h
volume of a cone = 1/3 pi r^2 h
V = 1/3 pi (10.14/pi) = 3.38
(16.05 MC)
What two attributes have been used to sort these shapes?
Two groups of shapes, group A and B. Group A has three shapes. The first shape is a quadrilateral with two right angles and one pair of parallel lines, the second shape is a square, and the third shape is a rectangle. Group B has three shapes. The first shape is a quadrilateral that has two pairs of sides equal in length and no right angles, the second shape is a parallelogram with no right angles, and the third shape is a quadrilateral with two pairs of sides equal in length but no right angles and no parallel lines.
Shapes with perpendicular sides and shapes without perpendicular sides
Shapes with parallel sides and shapes without parallel sides
Shapes with equal sides and shapes with unequal sides
Shapes with equal angles and shapes with unequal angles
what is correct
Answer:
(a) Shapes with perpendicular sides and shapes without perpendicular sides
Step-by-step explanation:
This appears to be a reading comprehension problem, along with a requirement that you recognize squares and rectangles have right angles and pairs of parallel equal-length sides.
__
The group descriptions are very careful to say that the members of Group B have no right angles. Members of both groups have equal-length sides and parallel lines, so those are not distinguishing criteria.
The relevant attribute for sorting appears to be right angles/no right angles.
please help me? tysm!!!!!!!
Answer:
Round 55.99 to the nearest tenth is: 56.0
I NEED THIS ANSWER IN THE NEXT 10 MINUTES
Answer:
D
Step-by-step explanation:
Consecutive integers are integers with the progression n, n+1, n+2 (EXAMPLE)
Since w, x, y are consecutive integers, that means w, w+1, w+2; x = w+1, y = w+2
By referring to D,
w + x + y = w + w+1 + w+2
= 3w + 3
Hence, D is true.
Answer:
D
Step-by-step explanation:
A is wrong because if w is -1, x is 0, and y is 1, then wy is negative.
B is wrong because if w is -1, x is 0, and y is 1, then -1 + 1 = 0, which is x.
C is wrong because if w is -1, x is 0, and y is 1, then w³ + 3 = -1 + 3 = 2, which is greater than w + x + y which is 0.
D is correct because w + x + y is always equal to 3w + 3. For example, if w is 1, x is 2, and y is 3, then w + x + y = 6. 3w + 3 = 3(1) + 3 = 6.
E is wrong because if w is 1, x is 2, and y is 3, then wx is 2 and xy is 6, which means xy is greater than wx.
I hope this helps and please mark me as brainliest!