Answer:
We conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
Step-by-step explanation:
Given the line
y+2x=4
converting into the slope-intercept form y = mx+b where m is the slope
y = -2x+4
comparing with the slope-intercept form
Thus, the slope is: m = -2
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -2
The slope of the new line perpendicular to the given line = – 1/m
= -1/-2 = 1/2
Using the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 1/2 and the point (-3, 5)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-5=\frac{1}{2}\left(x-\left(-3\right)\right)[/tex]
[tex]y-5=\frac{1}{2}\left(x+3\right)[/tex]
Add 5 to both sides
[tex]y-5+5=\frac{1}{2}\left(x+3\right)+5[/tex]
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
Therefore, we conclude that an equation in slope-intercept form for the line that passes through (-3,5) and is perpendicular to the graph of y+2x=4 will be:
[tex]\:y=\frac{1}{2}x+\frac{13}{2}[/tex]
Find the value of x. 8,13,x
Answer:
x=18
Step-by-step explanation:
Key skills needed: Arithmetic Sequences, Addition
1) We have a sequence of 8,13,x
2) To find the number being added every time, we do 13-8. This is 5.
3) This means x would be 13+5
4) 13+5 is 18 so x is 18.
Hope you understood and have a nice day!! :D
ABC DEF
AB corresponds to DF.
True
False
it's false
I guess
have a nice day
Find the lowest common multiple (LCM) of the 90 and 150
Answer:
450
Step-by-step explanation:
790 × 150 = 13500
GCF = 30
13500/30 = 450
A line with a slope of 3 passes
through the points (2, -1) and (4, 5).
Which of the following is not an
equation of the line that passes
through those points?
B. y = 3x-11
A. y+1 = 3(x-2)
D. y-5 = 3(x-4)
C. y = 3x-7
Answer:
We conclude that only the equation y = 3x-11 is not an equation of the line that passes through the points.
Hence, option B is correct.
Step-by-step explanation:
Given the points
(2, -1)(4, 5)Finding the slope between (2, -1) and (4, 5)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(4,\:5\right)[/tex]
[tex]m=\frac{5-\left(-1\right)}{4-2}[/tex]
[tex]m=3[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 3 and the point (2, -1)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-2=3\left(x-\left(-1\right)\right)[/tex]
[tex]y-2=3\left(x+1\right)[/tex]
Add 2 to both sides
[tex]y-2+2=3\left(x+1\right)+2[/tex]
[tex]y=3x+5[/tex]
So, y = 3x+5 is one of the equation lines.
We can also check by substituting the values m = 3 and the point (4, 5)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
y - 5 = 3(x-4)
So, y - 5 = 3(x-4) is also one of the equation lines.
Now, let say take the point (4, 5) an substitute in y = 3x-11
y = 3x-11
put x = 4 and y = 5
5 = 3(4)-11
5 = 12-11
5 = 1
FALSE!
Hence, the equation y = 3x-11 does not pass through (4, 5). Thus, the equation y = 3x-11 is not an equation of the line that passes through the points.
Now, let say take the point (4, 5) an substitute in y+1 = 3(x-2)
y+1 = 3(x-2)
put x = 4 and y = 5
5+1 = 3(4-2)
6 = 3(2)
6 = 6
TRUE!
Now, let say take the point (2, -1) an substitute in y+1 = 3(x-2)
-1+1 = 3(2-2)
0 = 0
TRUE!
Thus, the equation y+1 = 3(x-2) is an equation of the line that passes through the points.
Now, let say take the point (2, -1) an substitute in y = 3x-7
y = 3x-7
put x = 2 and y = -1
-1 = 3(2) - 7
-1 = 6-7
-1 = -1
TRUE!
Now, let say take the point (4, 5) an substitute in y = 3x-7
y = 3x-7
put x = 4 and y = 5
5 = 3(4)-7
5 = 12-7
5 = 5
TRUE!
Thus, the equation y = 3x-7 is an equation of the line that passes through the points.
Conclusion:
We conclude that only the equation y = 3x-11 is not an equation of the line that passes through the points.
Hence, option B is correct.
Answer:b
Step-by-step explanation:
help me please. i need it
Answer: See explanation
Step-by-step explanation:
m∠A and m∠O are alternate interior angles so they're congruent.
m∠A = m∠O
m∠A = 65°
AM and SO are congruent sides
AM = SO
AM = 86
m∠S and m∠M are alternate interior angles so they're congruent.
m∠S = m∠M
m∠S = 60°
ON and NA are congruent sides.
ON = NA
ON = 75
m∡SNO, m∠S, and m∠O form a triangle so they should add up to 180°
m∡SNO + m∠S + m∠O = 180°
m∡SNO + 60 + 65 = 180
m∡SNO + 125 = 180
Subtract both sides by 125
m∡SNO = 55°
Hope that helped!
What expression is equivalent to 3z
Answer:
3 * z
Step-by-step explanation:
3 * z
if u multiply them, u get 3z
is that what u meant? or are there options to choose from, or did u forget to add something else?
If the diagonal of a television screen is 24 inches and the width is 16 inches,
what is the height of the screen? Leave the answer in simplified radical form
Please show you're work
Step-by-step explanation:
Let x be the height of the screen.
Using Pythagoras' Theorem,
we have x² + 16² = 24².
Therefore x² = 24² - 16² = 320,
x = √320 = 8√5 in.
The height of the screen is 8√5 inches.
Solve the equation.
x2 + 13x + 30 = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution(s) is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O B. There is no solution.
Given that,
An equation : [tex]x^2 + 13x + 30 = 0[/tex]
To find,
The value of x.
Solution,
We have, [tex]x^2 + 13x + 30 = 0[/tex]
We can solve it as follows :
[tex]x^2 + 10x +3x+ 30 = 0\\\\x(x+10)+3(x+10)=0\\\\(x+3)(x+10)=0\\\\(x+3)=0\ \text{and}\ (x+10)=0\\\\x=-3\ \text{and}\ x=-10[/tex]
So, the solution of the given equations are -3 and -10.
Help fast please
What types of angles are in each of these quadrilaterals?
acute and right angles
obtuse angles only
acute angles only
acute and obtuse angles
Answer:
Acute and Obtuse..I cant see any right
Step-by-step explanation:
Answer:
D) Acute and Obtuse angles
Step-by-step explanation:
The pink quadrilateral has obtuse angles and I believe it has 2 acute angles.
The orange one has 2 acute and 2 obtuse angles
And the green one has both acute and obtuse angles.
A recipe requires 1\4 of a cup of cranberries for 1 batch. How many beaches of scones can be made using 6 1/2 cups of cranberries?
Answer:
26
Step-by-step explanation:
1 batch is 1/4 cups of cranberries.
This means that we have to find the number of groups of 1/4 in 6 1/2 cups to find the number of batches.
(The decimal forms of these numbers are 6.5 and 0.25)
6.5/0.25=26
There are 26 batches
Y=60x+180
It's part of a question for my midterms
-3y - 12< -6
Help i need this for an assignment and i’m almost done this is the last question
Answer:
y>2
Step-by-step explanation:
-3y-12<-6
-3y<6
y>2
I hope this answer helped, and if it was correct, please mark this as brainliest! Thank you!
Answer:
y>-2
Step-by-step explanation:
-3y-12<-6 (move the constant to the right)
-3y<-6+12 (calculate)
-3y<6 (divide both sides)
solution: y>-2
hope this helps!
Part B: What are the values of x and y?
4
Answer:
can anyone help me with this problem plzzz
Step-by-step explanation:
Find equation of straight line passing through (2,3) and having slope 1/2
Answer:
y=1/2x+2
Step-by-step explanation:
2=x 3=y slope=1/2
y=mx+b
3=1/2(2)+b
3=1+b
3-1=b
2=b
The length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, working on it. It takes 16 children 6 hours to put the jigsaw puzzle together. How many children are needed to put the same jigsaw puzzle together in 4 hours?
Answer:
24 children
Step-by-step explanation:
If the length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, this is represented as;
[tex]y \alpha \frac{1}{x}\\y =\frac{k}{x}[/tex]
k is the constant of proportionality
If it takes 16 children 6 hours to put the jigsaw puzzle together, this means at x = 16, y = 6
Substitute:
6 = k/16
k = 6*16
k = 96
W are to find number of children needed to put the same jigsaw puzzle together in 4 hours, this is done by substituting k = 96 and y = 4 into the expression y = k/x
y = 96/4
y = 24
Hence it will take 24 children to put the same jigsaw puzzle together in 4 hours
A football team won 75% of 60 games in a season. How many games did they win?
Answer:45 games
Step-by-step explanation: 1+1 is 2 so yeah
Answer:
I think its 45 games
Step-by-step explanation:
75% times 60 = 45
*My school in middle school was rushed about math when we learned percent. Like the teachers were talking so fast, sorry if I'm wrong. <--- reason if I'm wrong.
2x+4y²-6y² -9+1-x+3x
Options 1,2,3 or 4?
Answer:
Option 2
Step-by-step explanation:
A house on the market was valued at $212,000. After several years, the value decreased by 7%. By how much did the house's value decrease in dollars? What
is the current value of the house?
Answer:
It decreased by $14,840 and the current value is $197,160
In a rectangle FGHI, diagonals FH and GI intersect at E
What is the length of FH?
Answer:
The length of [tex]\overline {FH}[/tex] is;
D. 38 units
Step-by-step explanation:
The given parameters are;
The type of the given quadrilateral FGHI = Rectangle
The diagonals of the quadrilateral = [tex]\overline {FH}[/tex] and [tex]\overline {GI}[/tex]
The length of IE = 3·x + 4
The length of EG = 5·x - 6
We have from segment addition postulate, [tex]\overline {GI}[/tex] = IE + EG
The properties of a rectangle includes;
1) Each diagonal bisects the other diagonal into two
Therefore, [tex]\overline {FH}[/tex] bisects [tex]\overline {GI}[/tex], into two equal parts, from which we have;
IE = EG
[tex]\overline {GI}[/tex] = IE + EG
3·x + 4 = 5·x - 6
4 + 6 = 5·x - 3·x = 2·x
10 = 2·x
∴ x = 10/2 = 5
From which we have;
IE = 3·x + 4 = 3 × 5 + 4 = 19 units
EG = 5·x - 6 = 5 × 5 - 6 = 19 units
[tex]\overline {GI}[/tex] = IE + EG = 19 + 19 = 38 units
[tex]\overline {GI}[/tex] = 38 units
2) The lengths of the two diagonals are equal. Therefore, the length of segment [tex]\overline {FH}[/tex] is equal to the length of segment [tex]\overline {GI}[/tex]
Mathematically, we have;
[tex]\overline {FH}[/tex] = [tex]\overline {GI}[/tex] = 38 units
∴ [tex]\overline {FH}[/tex] = 38 units.
Troy and Phillip both noticed that each time they represented a problem with a division sentence, they could write a related multiplication sentence. Their team decided
to see if they could represent each situation below in four ways: with words, diagrams, a multiplication number sentence, and a division number sentence.
Help them finish what they started by filling in the missing representations. Part (a) is already completed.
a. Question in Words: How many quarter-pies make three whole pies?
Symbols (2 sentences): 3 + 1 = 12 and 3 . 4 = 12
Diagram:00
Answer in Words: Twelve quarter-pies make three whole pies.
b. Question in Words: f is of how much money?
Symbols (2 sentences):
Diagram:
Answer in Words:
c. Question in Words: How many half-dollars make $30?
Answer:
yeah same its just nice to have the person's presence their
(1) In 2019, the energy company divided its profits in the ratio;
shareholders : bonuses : development = 5 : 2 : 6
In 2019, its profits were $390 million.
Calculate the amount the company gave to shareholders.
(2) The share price of the company in June 2019 was $285.25. This was an increase of 3.3% on the share price in May 2019.
Calculate the share price in May 2019.
9514 1404 393
Answer:
(1) $150 million
(2) $276.14
Step-by-step explanation:
(1) The ratio 5 : 2 : 6 to shareholders : bonuses : development tells us that the fraction of profits to shareholders is ...
5/(5+2+6) = 5/13
The dollar amount to shareholders is then ...
(5/13)($390 million) = $150 million
__
(2) We have ...
$285.25 = (1 +3.3%) × (May price)
May price = $285.25/1.033 = $276.14
Answer:
19
Step-by-step explanation:
solve for x what is the solution to the system of equations
Answer:
x=-6,12
Step-by-step explanation:
Answer:
3,-2
Step-by-step explanation:
Find the vertices of the following functions.
Y=4(x-2)(x-3)
Y=-4(x+2)^2 -5
Answer right and I will give u brainly and if u dont know dont answer
Answer:
Step-by-step explanation:
j+28.6=43
-28.6 -28.6
_________________
j=14.4
Hope this helps :>
what are the X and Y intercepts of f(x)=-√x
Answer:
The function intercepts the x and y axis in the same spot, namely (0,0)
I NEED HELPPPPPP!!!! :DDDD WILL MARK BRAINLIEST TO THE BEST ANSWER!!!! PLEASE SHOW ALL SOLUTIONS!!!! In triangle ABC, the exterior angle at A measures (3x + 10)°, the exterior angle B measures (5x)°, and the exterior angle C measures (2x + 4)°. Determine the measure of the interior angle at A. THANK YOU AND GOD BLESS....!!!!
9514 1404 393
Answer:
∠A = 66.2°
Step-by-step explanation:
The sum of exterior angles of any polygon is 360°, so you have ...
(3x +10)° +(5x)° +(2x +4)° = 360°
10x +14 = 360 . . . . . . . . . . . . . . .collect terms, divide by °
x + 1.4 = 36 . . . . . . . . . divide by 10
x = 34.6
The interior angle at A is the supplement of the exterior angle there:
∠A = 180° -(3x +10)° = 180° -(3(34.6) +10)°
∠A = 66.2°
-8b + 4(1 + 5b) = -6b - 14
Answer:
b = -1
Step-by-step explanation:
-8b + 4 + 20b = -6b - 14
12b + 4 = -6b - 14
18b + 4 = -14
18b = -18
b = -1
You are swinging a bucket in a circle at a velocity of 7.8 ft/s. The radius of the circle you are making is 1.25 ft. The acceleration is equal to one over the radius multiplied by the velocity squared.
a. What is the acceleration of the bucket?
b. What is the velocity if the acceleration is 25 ft/sec2?
Given that,
velocity, v = 7.8 ft/s
Radius, r = 1.25 ft
To find,
a. What is the acceleration of the bucket?
b. What is the velocity if the acceleration is 25 ft/sec²?
Solution,
(a) The centripetal acceleration is given by :
[tex]a=\dfrac{v^2}{r}[/tex]
Put v = 7.8 ft/s and r = 1.25 ft
[tex]a=\dfrac{(7.8)^2}{1.25}\\\\=48.672\ ft/s^2[/tex]
(b) Put a = 25 ft/s² to find velocity.
[tex]v=\sqrt{ar} \\\\v=\sqrt{25\times 1.25} \\\\v=5.59\ ft/s[/tex]
Hence, this is the required solution.
20+3xy-3xy+y²+10-y²
Options 1,2,3 or 4?
Answer:
It is option 4.
Step-by-step explanation:
Key skills needed to solve this problem: Combining like terms and simplifying
1) We have to combine like terms and simplify to the maximum
We first start with 3xy and - 3xy. These cancel out as they add up to make 0. Next. there is y^2 and -y^2. These also cancel out. The only 2 terms left are 20 and 10 which add up to make 30.Therefore, it is option 4.
Hope you understood! Have a nice day!! :D
Danielle picks 744 apples at an apple orchard. She divides the apples equally into 40 baskets.
Part A
When dividing 744 ÷ 40, the first digit of the quotient will be in what place?
Hundreds
Tens
Ones
Thousands
Part B
How many apples will be in each basket? Enter your answer in the box.
apples=??
Part C
How many apples will be left? Enter your answer in the box.
apples=??
Answer:
Answer:
Tens
PART B: 18
PART C: 24
Step-by-step explanation: