There is a point $A$ with positive coordinates such that the sum of the coordinates of $A$ is $14$. If the $x$-coordinate of $A$ is $a$, then point $P$ is at $(3a, a^2+13a-11)$. If the slope of a line passing through $A$ and $P$ is $7$, find $a$.
Answer:
The x-coordinate of A is:
a = 6.1
Step-by-step explanation:
For point A:
x-coordinate = a
x-coordinate + y-coordinate = 14
y-coordinate = 14 - x-coordinate
y-coordinate = 14 - a
So point A can be written as (a, 14-a)
Let (a,14) be (x₁,y₁)
Point P can be written as (3a, a²+13a-11)
Let P be (x₂,y₂)
Slope of a line passing through 2 point is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m=7
Substitute all values
[tex]7=\frac{(a^2+13a-11)-(14-a)}{3a-a}\\7=\frac{a^2+13a-a-11-14}{3a-a}\\7=\frac{a^2+12a-25}{2a}\\14a=a^2+12a-25\\a^2-2a-25=0\\a=6.1,a=-4.1[/tex]
As A has only positive coordinates
a = 6.1
On a winter morning, the temperature In Pittsburgh Is -13°F and the temperature in Cleveland Is-10°F. On the same morning, the temperature in Chicago is higher than the temperature in Pittsburgh. Which statement explains what the temperature in Chicago could be?
Answer:
-12°F o -11°F.
Step-by-step explanation:
We have two statements, which are the following:
- the temperature In Pittsburgh Is -13 ° F
- the temperature in Cleveland Is-10 ° F
Then they tell us, "the temperature in Chicago is higher than the temperature in Pittsburgh"
Which means that the statement that helps us is the first, which is the one that tells us about Pittsburgh, now, a higher number since it is a higher temperature, we know that when a number is negative, the higher the number is , actually the number is less, therefore the temperature should be at least -12 ° F or -11 ° F. That is, anyone with sense between the city's temperature ranges greater than -13.
sarra spent $45 at las hadas and left a 15% tip. how much was the bill
Answer:
$51.75
Step-by-step explanation:
15% of 45 or .15*45 will equal $6.75. Then you add that onto the $45 and you'll get your anwser, $51.75.
SM=3x−4, and RN=9x−20. Find the value of x
Answer:
Option (A).
Step-by-step explanation:
Given question is incomplete; find the complete question with the attachment.
In the triangle NRL,
Points P, S and M are the midpoints of the sides NR, RL and LN respectively.
Sides SM = (3x - 4), NR = (9x - 20)
By the theorem of midpoints in a triangle,
SM = [tex]\frac{1}{2}\text{NR}[/tex]
(3x - 4) = [tex]\frac{1}{2}(9x-20)[/tex]
6x - 8 = 9x - 20
9x - 6x = 20 - 8
3x = 12
x = 4
Therefore, Option (A) will be the answer.
The value of x is equal t 4
Data;
midpoint = SM = 3x - 4Length of line = 9x - 20Midpoint of a LineThe midpoint of a line is half the distance of the line.
Since the length of the line is RN and midpoint of the line is SM.
[tex]SM = \frac{1}{2} RN[/tex]
Let's substitute the values into the equation
[tex]SM = \frac{1}{2} NR\\3x - 4 = \frac{1}{2}(9x- 20)\\ 3x - 4 = \frac{1}{2} (9x - 20)\\2(3x - 4) = 9x - 20\\6x - 8 = 9x - 20\\9x-6x = 20 - 8 \\3x = 12\\\frac{3x}{3} = \frac{12}{3} \\x = 4[/tex]
The value of x is equal t 4
Learn more on midpoint here;
https://brainly.com/question/26749964
on a recent test matthew got 18 out of 40 problems correct at the same rate how many problems would matthew get correct if there were 60 problems
Answer:
27
Step-by-step explanation:
18/40 = 27/60
Answer:
27 :)
Step-by-step explanation:
Write sin 49° in terms of cosine.
Answer:
cos 41°
Step-by-step explanation:
[tex] \sin 49 \degree = \cos(90 \degree - 49 \degree) = \cos41 \degree \\ \\ \huge {\boxed{\red{ \bold{ \therefore \: \sin 49 \degree }}= \purple{ \bold{\cos 41 \degree}}}}[/tex]
The trigonometry expression sin 49° is written in the form of cosine will be cos 41°.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The trigonometry expression is given below.
⇒ sin 49°
We know that sin (90 - A) = cos A. Then the expression is also written as,
⇒ sin 49°
⇒ sin (90° - 41°)
⇒ cos 41°
The trigonometry expression sin 49° is written in the form of cosine will be cos 41°.
More about the trigonometry link is given below.
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1.) What is the surface area of the figure below?
Answer:
Step-by-step explanation:
length (l) = 3 ft
Width (w) = 3 ft
Height (w) = 6 ft
Surface area = 2*( lw + wh + hl)
= 2* (3*3 + 3*6 + 6*3)
= 2*(9 + 18 + 18)
= 2 * 45
= 90 square ft
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(6x)?
Answer: C. It is the graph of f(x) shrunk horizontally by a factor of 6.
Step-by-step explanation:
When we multiply a function’s input by a positive constant, we get a function whose graph is stretched or compressed horizontally in relation to the graph of the original function. If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function.
Find the value of x.
Answer:
x≈47.4
Step-by-step explanation:
Use sine, since the triangle is a right triangle and doesn't have any special properties.
sin28=x/101
101*sin28=x
solving this, you get that x≈47.4.
Please help I don’t get how to do it.
Answer:
Step-by-step explanation:
a) -2g
putting the value of g
-2[tex](\frac{3}{-1} )[/tex]
opening the brackets by multiplying
=[tex](\frac{-6}{1})[/tex]=-2g
b)f+3g
=[tex]\frac{-2}{4}+\frac{9}{-3}[/tex]
taking LCM AS 12
=[tex]\frac{-2*3}{4*3} +\frac{9*4}{-3*4}[/tex]
=-6/12-36/12
=-42/12
=-7/2
c)2f-4g
=[tex]2(\frac{-2}{4})-4(\frac{3}{-1} )[/tex]
=[tex]\frac{-4}{4}-\frac{12}{-1}[/tex]
=-1+12
=11
Please Help!!
Quadrilateral HIJK is similar to quadrilateral STUV. What's the scale factor from HIJK to STUV?
A)
3
B)
2∕3
C)
1∕2
D)
1∕3
Answer:
D
Step-by-step explanation:
18(Side of HIJK)/6(Corresponding side of STUV) = 1/3
Find the length of the radius for this circle.
(x - 3)² + (y - 5)² = 8
8
4
2√2
After Mia gave 1/4 of her milk to Dante, Dante had twice the amount of milk as Mia. What was the ratio of the amount of milk Mia had to the amount of milk Dante had at first?
Answer:
4:5
Step-by-step explanation:
You start with the equation:
2(3/4m)=D+1/4m
Simplify it to solve:
5/4m=D
The ratio of the amount of milk Mia had to the amount of milk Dante had at first = 4 : 5
What is ratio?"It is the comparison of two quantities of the same kind."
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical statements."
For given question,
Let 'x' be the initial amount of milk Mia had and 'y' be the initial amount of milk Dante had.
After Mia gave 1/4 of her milk to Dante, Dante had twice the amount of milk as Mia.
We write above statement inn equation form as,
[tex]2(\frac{3}{4} x)=(y+\frac{1}{4} x)[/tex]
We simplify above equation to find the ratio of the amount of milk Mia had to the amount of milk Dante had at first.
[tex]\Rightarrow 2(\frac{3}{4} x)=(y+\frac{1}{4} x)\\\\\Rightarrow \frac{6}{4}x- \frac{1}{4} x=y\\\\\Rightarrow \frac{5}{4}x=y\\\\ \Rightarrow \frac{x}{y} =\frac{4}{5}\\\\ \Rightarrow x:y=4:5[/tex]
Therefore, the ratio of the amount of milk Mia had to the amount of milk Dante had at first = 4 : 5
Learn more about the ratio here:
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PlS HELP ASP HURRY BEST ANSWER GETS TO PICK BRAINLESST OR FOLLOW!!!
Answer:
Step-by-step explanation:
1. 6 L = 6000 mL
2. 54000 mL = 54 L
3. 11000 mL = 11 L
4. 13 L = 13000 mL
5. 23500 mL = 23.5 L
6. 0.201 L = 201 mL
Answer:
1. = 6000 ML 2.= 13000 ML 3.= 54 L 4.= 23.5 L 5.= 11 L 6.= 201 ML
Step-by-step explanation:
too find answer for ML divide it by 1000
and for L multiply it by 1000
How does the graph of y= Vx+2 compare to the graph of the parent square root function?
The graph is a horizontal shift of the parent function 2 units right.
The graph is a horizontal shift of the parent function 2 units left.
The graph is a vertical shift of the parent function 2 units up.
The graph is a vertical shift of the parent function 2 units down.
Answer:
a) The graph is a horizontal shift of the parent function 2 units right.
Step-by-step explanation:
Explanation:-
Type of transformation Change to co-ordinate point
Vertical translation up 'd' units (x,y) →(x ,y+d)
Vertical translation down 'd' units (x,y) →(x ,y- d)
Horizontal translation left 'c' units (x,y) →(x-c ,y)
Horizontal translation right 'c' units (x,y) →(x+c ,y)
Reflection over X-axis (x,y) →(x ,-y)
Reflection over y-axis (x,y) →(-x ,y)
Given graph f(x) = √x
The graph is a Horizontal shift of the parent function '2' units right
Therefore the transformation of the graph [tex]y = \sqrt{x+2}[/tex]
Identify the type of sample this is:
To determine the types of music their customers like, all the people attending a concert of a country music singer were surveyed
A) voluntary response sample
B) strateified random sample
C) convenience sample
D) simple random sample
4x + 7y <14
Into slope intercept form
Slope
Y-intercept
Answer: y < [tex]\frac{4}{7}[/tex]x + 2
Slope: [tex]\frac{4}{7}[/tex]
Y-intercept: 2
If y(x) - 3(x+5) +-, what is f(a + 2)?
A. 3(a + 2) + + 2
4
B. 3(/(a)+5) +
(a) + 2
C. 3(a + 7) +
2{ 3[9 + 4(7 -5) - 4]} can you guys help me
The answer is 78
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex] = 78[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
list the sided of the triangle in order from shortest to longest
please answer asap!!
options in picture!
Answer:
Step-by-step explanation:
The side opposite to the biggest angle be longest side.
110 + 28 + ∠H= 180 { sum of all angles of triangle }
138 + ∠H = 180
∠H= 180 -138
∠H = 42°
Shortest side is opposite to 28° =====> FH
Next shortest side is opposite to 42° =========> GF
The longest side is opposite to 110° =======> GH
The answer is:
FH , GF , GH
Answer:
FH , GF , GH
Step-by-step explanation:
What is the value of x in the equation 2(x-4) = 4(2x + 1)?
1.
-2
2.
2
3.
Nime
2.
1
4.
2
Answer:
The value of x is -2.
Step-by-step explanation:
First, you have to eliminate the brackets by expanding :
[tex]2(x - 4) = 4(2x + 1)[/tex]
[tex]2x - 8 = 8x + 4[/tex]
Next, you have to move all the like-terms to one side :
[tex]2x - 8 - 8x = 4[/tex]
[tex] - 6x = 4 + 8[/tex]
[tex] - 6x = 12[/tex]
[tex]x = 12 \div ( - 6)[/tex]
[tex]x = - 2[/tex]
Answer:
[tex]x = - 2[/tex]
Step-by-step explanation:
[tex]2(x - 4) = 4(2x + 1) \\ 2x - 8 = 8x + 4 \\ 2x - 8x = 8 + 4 \\ - 6x = 12 \\ \frac{ - 6x}{ - 6} = \frac{12}{ - 6} \\ x = - 2[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find the slope of the line that contains the points named.
R(0, 4), S(5, 0)
-4/5
4/5
-5/4
Answer:
Step-by-step explanation:
4/5
ON MONDAY SARAH HAD HOMEWORK IN 7/10 OF HER CLASSES, TUESDAY 3/5, WEDNESDAY 9/11, AND THURSDAY 1/2.
WHICH DAY DID SHE HAVE THE MOST HOMEWORK ?
Answer:
Wednesday
Step-by-step explanation:
This System is called ratios. Let’s take Thursday for example. She has homework for one out of two of her classes. Wednesday she had nine homework’s for eleven of her homeworks
Side A B is parallel to Side D E in the map below.
Triangle A B C. Side A B is 15 feet and side B C is 9 feet. Triangle C D E. Side C D is 6 feet and side D E is x feet.
Which proportion solves for the distance between D and E?
StartFraction 9 Over 6 EndFraction = StartFraction x Over 15 EndFraction
StartFraction 6 Over x EndFraction = StartFraction 15 Over 9 EndFraction
StartFraction 9 Over 6 EndFraction = StartFraction 15 Over x EndFraction
StartFraction 6 Over 15 EndFraction = StartFraction 9 Over x EndFraction
Answer:
I think its C
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
4 times 1/3 in fraction
Answer:
4/3 or 1 and 1/3
Step-by-step explanation:
4 * 1/3. You would do 4*1 over 3, which gives you 4/3.
Use the Pythagorean theorem to find the unknown side of the right
triangle
Answer:
26
Step-by-step explanation:
→ Utilise Pythagoras theorem
a² + b² = c²
→ Substitute in the values
10² + 24² = c²
→ Simplify
100 + 576 = c²
→ Simplify further
676 = c²
→ Square root both sides to isolate c
26 = c
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for p.
Answer:
Cylinder B
Step-by-step explanation:
V = [tex]\pi r^{2} h[/tex]
Cylinder A : π × 3² × 5 = 141.37
Cylinder B: π × 5² × 3 =235.62
GIVING OUT BRAINLIEST
If c is a constant such that x^2+100x+c is equal to the square of a binomial, then what is c?
Answer:
c = 2500
Step-by-step explanation:
[tex]x^2+100x + c\\x^2+2\times 50\times x + (50)^2\\=x^2+2\times 50\times x + 2500\\=x^2+100 x + 2500\\equating \: it \: with\: \\x^2+100x + c\\we\; find:\\c = 2500[/tex]
Answer:
c = 2500
Step-by-step explanation:
x² + 100x + c where c = ?
100 x : 100x / 2x = 50
(50)² = 2500
HOPE ITS HELPFUL!!
70 times 10 by the power of 2
Answer:
I'm not sure which you mean, so I'll give the answer to both:
[tex]70 X 10^2 = 7000\\(70x10)^2 = 490000[/tex]
Please Help Me. Work must be shown for this problem. Solve for x. Round answers to the nearest hundredth (2 decimal places).
Answer:
About 188.71 feet
Step-by-step explanation:
The cosine of an angle is equivalent to the adjacent side divided by the length of the hypotenuse. Therefore:
[tex]\cos 58=\dfrac{100}{x} \\\\x=\dfrac{100}{\cos 58}\approx 188.71[/tex]
Hope this helps!
Answer:
x = 188.71
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent/ hypotenuse
cos 58 = 100/x
Multiply by x
x cos 58 = 100
Divide by cos 58
x = 100/cos 58
x =188.7079915
To the nearest hundredth
x = 188.71
