Answer:
[tex]\large\boxed{y=3x-11}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=3x-4\to m_1=3\\\\\text{Therefore}\ m_2=3.\\\\\text{We have the equation:}\ y=3x+b.\\\\\text{Put the coorsdinates of the point (2, -5) to the equation of the line}\\\\-5=3(2)+b\\-5=6+b\qquad\text{subtract 6 from both sides}\\-11=b\to b=-11[/tex]
Nat bought 3 colas for $1.25 each, 2 hot-dogs for $2.50 each, and a hamburger for $6.50. He paid with $20 bill. How much money does Nat have left?
Answer:
$4.75 is how much money is left over
Step-by-step explanation:
3* 1.25= 3.75
2* 2.50= 5.00
1* 6.50+ 6.50
5.00+3.75+6.50= 15.25
20- 15.25= 4.75
Final answer:
Nat spent a total of $15.25 on colas, hot dogs, and a hamburger. After paying with a $20 bill, he has $4.75 left.
Explanation:
To calculate how much money Nat has left after his purchases, we will add up the cost of the items he bought and subtract that total from the $20 bill he used for payment.
Cost of 3 colas: 3 × $1.25 each = $3.75
Cost of 2 hot-dogs: 2 × $2.50 each = $5.00
Cost of 1 hamburger: $6.50
Now we'll sum these amounts to find the total spending:
Total spending = $3.75 + $5.00 + $6.50 = $15.25
Next, we subtract the total spending from the $20 bill:
Change = $20.00 - $15.25 = $4.75
Therefore, Nat has $4.75 left after his purchase.
Given the function f(x)=-5x^2-x+20 find f(3)
Answer:
-28
Step-by-step explanation:
-5(3)^2 - 3 + 20
-5*9 - 3 + 20
-45 -3+ 20
-48+ 20
-28
Hope it helps!
Alex and his father took a taxi cab that charges $2.60 per mile plus $1.50 for each passenger, and they paid a total of $18.60. Alex wrote the equation 18.60=2.60b+3 for this situation and found b=6. Which statement is true about the solution b=6?
Answer:
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi
Step-by-step explanation:
Given
18.60=2.60b+3
Here 18.60 is the total amount paid, 2.60 is the rate per mile and 3 is the charges for two passengers.
The solution b=6 tells us that Alex and his father traveled 6 miles on the taxi i.e. b represents miles ..
the answer is: the solution b = 6 gives the number of miles the taxi traveled.
i just did the workbook :)
The length of a rectangle is three times its width, and its area is 9 cm2
. Find the
dimensions of the rectangle.
Answer:
3√3 cm. = l
√3 cm. = w
Step-by-step explanation:
l = 3w
9 = 3w[w] ↷
9 = 3w² [Divide by 3]
3 = w² [Take the square root]
√3 = w [plug this back into the top equation to get a length of 3√3 cm.]
I am joyous to assist you anytime.
55. If 3x = 4y, the value of (x + y)^2 : (x - y)^2 is:
Answer:
[tex]\large\boxed{(x+y)^2:(x-y)^2=49}[/tex]
Step-by-step explanation:
[tex]3x=4y\qquad\text{subtract}\ 3y\ \text{from both sides}\\\\3x-3y=y\qquad\text{distributive}\\\\3(x-y)=y\qquad\text{divide both sides by 3}\\\\x-y=\dfrac{y}{3}\qquad(*)\\------------------\\3x=4y\qquad\text{add}\ 3y\ \text{to both sides}\\\\3x+3y=7y\qquad\text{distributive}\\\\3(x+y)=7y\qquad\text{divide both sides by 3}\\\\x+y=\dfrac{7y}{3}\qquad(**)\\------------------[/tex]
[tex](x+y)^2:(x-y)^2=\dfrac{(x+y)^2}{(x-y)^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x+y}{x-y}\right)^2\qquad\text{substitute}\ (*)\ \text{and}\ (**)\\\\=\left(\dfrac{\frac{7y}{3}}{\frac{y}{3}}\right)^2=\left(\dfrac{7y}{3}\cdot\dfrac{3}{y}\right)^2\qquad\text{cancel}\ 3\ \text{and}\ y\\\\=(7)^2=49[/tex]
using the rate of Rs. 124.40 per using US dollar, find the US dollar for Rs. 158610.
Answer:
1275 USD
Step-by-step explanation:
124.40 Rs -----> 1 USD
158610 Rs -----> x USD
124.40x=158610
×=158610/124.40
x=1275 USD
HELP!!!! PLEASE need help now its an emergency.
Answer:
121,6
Step-by-step explanation:
Since the only difference between the triangles are the letters and a few missing numbers, just replace the letters to get your answer. A and D are the same B and E are the same and C and F are the same. So the measurement of angle A is 121 degrees and the length of AB is 6
Subtract. 5x^2-5x+1-(2x^2+9x-6)
The answer is:
[tex]3x^{2} -14x+7[/tex]
Why?To solve the problem we need to add/subtract like terms. We need to remember that like terms are the terms that share the same variable and the same exponent.
For example, we have:
[tex]x^{2} +2x+3x=x^{2} +(2x+3x)=x^{2}+5x[/tex]
We have that we were able to add just the terms that were sharing the same variable and exponenr (x for this case).
So, we are given the expression:
[tex]5x^2-5x+1-(2x^2+9x-6)=5x^{2}-2x^{2}-5x-9x+1-(-6)\\\\(5x^{2}-2x^{2})+(-5x-9x)+(1-(-6))=3x^{2}-14x+7[/tex]
Hence, the answer is:
[tex]3x^{2} -14x+7[/tex]
Have a nice day!
Select the correct answer from each drop-down menu. The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides. The heights of the pyramids are the same. The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.
Step-by-step explanation:
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
H - height of pyramids
Pyramid A:
[tex]B=(10)(2)=200\ m^2[/tex]
[tex]V_A=\dfrac{1}{3}(200)H=\dfrac{200}{3}H\ m^3[/tex]
Pyramid B:
[tex]B=10^2=100\ m^2[/tex]
[tex]V_B=\dfraC{1}{3}(100)H=\dfrac{100}{3}H\ m^3[/tex]
[tex]V_A>V_B\\\\V_A=2V_B[/tex]
The volume of the pyramid A is twice as large as the volume of the pyramid B.
The new height of pyramid B: 2H
The new volume:
[tex]V_{B'}=\dfrac{1}{3}(100)(2H)=\dfrac{200}{3}H\ m^3[/tex]
The volume of the pyramid A is equal to the volume of the pyramid B.
To compare the volumes of the two pyramids, we first need to calculate the volume of each pyramid using the formula for the volume of a pyramid:
\[ V = \frac{1}{3}Bh \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.
First, let's calculate the volume of pyramid A:
\[ \text{Area of base of pyramid A} = \text{length} \times \text{width} = 10 \, \text{meters} \times 20 \, \text{meters} = 200 \, \text{square meters} \]
Now, let's call the height of pyramid A (and originally pyramid B) \( h \). Then, the volume of pyramid A is:
\[ V_{\text{A}} = \frac{1}{3} \times 200 \, \text{m}^2 \times h = \frac{200h}{3} \, \text{cubic meters} \]
Next, let's calculate the volume of pyramid B with its original height \( h \):
\[ \text{Area of base of pyramid B} = \text{side} \times \text{side} = 10 \, \text{meters} \times 10 \, \text{meters} = 100 \, \text{square meters} \]
So the original volume of pyramid B is:
\[ V_{\text{B}} = \frac{1}{3} \times 100 \, \text{m}^2 \times h = \frac{100h}{3} \, \text{cubic meters} \]
Now we can compare the volumes of pyramid A and the original volume of pyramid B:
\[ \frac{V_{\text{A}}}{V_{\text{B}}} = \frac{\frac{200h}{3}}{\frac{100h}{3}} = \frac{200}{100} = 2 \]
So, pyramid A has twice the volume of pyramid B.
Now, if the height of pyramid B increases to twice that of pyramid A, its new height is \( 2h \). Therefore, the new volume of pyramid B is:
\[ V_{\text{B new}} = \frac{1}{3} \times 100 \, \text{m}^2 \times 2h = \frac{200h}{3} \, \text{cubic meters} \]
Comparing this new volume of pyramid B to the volume of pyramid A:
\[ \frac{V_{\text{B new}}}{V_{\text{A}}} = \frac{\frac{200h}{3}}{\frac{200h}{3}} = 1 \]
So, the new volume of pyramid B is equal to the volume of pyramid A.
In summary, the volume of pyramid A is twice the volume of pyramid B when their heights are the same. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is equal to the volume of pyramid A.
how do I solve this: 9b less than 40
Answer:
b < 4.44
Step-by-step explanation:
This is an inequality.
The sign for 'less than' is '< '
Write 9b less than 40 in inequality form.
9b < 40 (Take 9 on the other side of the inequality and divide it by 40)
b < 40/9
b < 4.44
!!
1.
1400
Simplify: -
Show your work.
Answer:
1400
Step-by-step explanation:
Nothing can be done further. If I saw the rest of the question, I would be capable of assisting you.
I am joyous to assist you.
What is the ratio of 102 steps walked in 1 minute?
Answer:
102 steps/1minute
In seconds it would be 102/60 which can be reduced to 17/10, or 1.7
A = B/2 = C/5 a:b:c=?
Answer:
[tex]\large\boxed{A:B:C=\dfrac{1}{10A}}[/tex]
Step-by-step explanation:
[tex]A=\dfrac{B}{2}=\dfrac{C}{5}\\\\A=\dfrac{B}{2}\qquad\text{multiply both sides by 2}\\\\2A=B\to\boxed{B=2A}\\\\A=\dfrac{C}{5}\qquad\text{multiply both sides by 5}\\\\5A=C\to C=5A\\\\A:B:C=A:2A:5A=1:2:5A=\dfrac{1}{2}:5A=\dfrac{1}{2}\cdot\dfrac{1}{5A}=\dfrac{1}{10A}[/tex]
$1334 is deposited into a savings account at 8% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $1,000,000?
Answer:
84 years
Step-by-step explanation:
The future value of an investment is given by ...
FV = P(1 +r/n)^(nt)
where P is the principal amount, r is the annual rate, and n is the number of times per year interest is compounded. Filling in the given values and solving for t, we get ...
1000000 = 1334(1 +.08/4)^(4t)
749.6252 ≈ 1.02^(4t) . . . . divide by 1334 and simplify
log(749.6252) ≈ 4t·log(1.02) . . . . take logarithms
t ≈ log(749.6252)/(4·log(1.02)) ≈ 83.57
It will take about 84 years for the account balance to reach $1,000,000.
Rodney is given two linear equations: x – y = 11 and 2x + y = 19. What value of x should he get as a solution for this system of linear equations
Answer:
x = 10
Step-by-step explanation:
Given the 2 equations
x - y = 11 → (1)
2x + y = 19 → (2)
Adding the 2 equations term by term eliminates the term in y, that is
(x + 2x) + (- y + y) = (11 + 19), simplifying gives
3x = 30 ( divide both sides by 3 )
x = 10
Answer:
x = 10
Step-by-step explanation:
We know that Rodney is given the following two linear equations and we are to find the value of x at which he would get a solution for this system of linear equations:
[tex] x - y = 1 1 [/tex] - (1)
[tex] 2 x + y = 1 9 [/tex] - (2)
From (1):
[tex]x=11+y[/tex]
Substituting this value of x in (2):
[tex]2(11+y)+y=19[/tex]
[tex]22+2y+y=19[/tex]
[tex]3y=19-22[/tex]
[tex]y=-\frac{3}{3}[/tex]
[tex]y=-1[/tex]
Substituting this value of y in (1) to find x:
[tex]x=11+(-1)[/tex]
x = 10
If ELF is congruent to GJH, EF=12 and LF=7.8 find IJ. Round answer to the hundredths place. A. 4.78 B 5.62 C 4.98 D 5.07
EF = 12
KF = 6
LF = 7.8
LK = sqrt(7.8^2-6^2) = 4.98
IJ = LK
Answer with explanation:
→ΔELF ≅ Δ GHJ-------[Given]
→EF=GH----------[CPCT]
→GJ=FL-------[CPCT]
Let , O be the center of the circle.
→ EK=KF--------[Perpendicular from the center to the chord bisects the chord.]
→GI=IH------[Reason same as Above]
→→EK=GI, KF=HI
→→OJ=OL
→OK=KI
→OJ-OK=OL-KI
→LK=IJ
⇒→Δ LKF ≅ Δ JIG-------[SAS]
Now, In Δ LKF, By Pythagorean Theorem
→(LF)²=(LK)²+(KF)²
→(7.8)²=(LK)²+(6)²
→60.84-36=(LK)²
→24.84=(LK)²
LK=4.98
→→LK=IJ=4.98
Option C:→4.98
Is 24/40= 4/8 true proportion?
Answer:
No, that is not the true proportion.
Step-by-step explanation:
40 divided by 8 is 5. 5 multiplied by 4 is 20. Therefore, the true proportion would be 20/40 = 4/8.
Follow the steps and finish the solution.
7(x-3) = 28
Distributive property
7x-21 = 28
Addition property of equality
7x = 49
Division property of equality
X
=
What is the value of x?
07
O 42
O 56
Mark this and return
Save and Exit
Save and Exit
Next
Next
Submit
Answer:
x=7
Step-by-step explanation:
7(x-3) = 28
Distributive property
7x-21 = 28
Addition property of equality
7x = 49
Division property of equality
7x/7 = 49/7
x = 7
The value of x is 7 ..
Answer:
7
Step-by-step explanation:
Solve the system of equations and choose the correct answer from the list of options. (4 points)
x − y = 7
y = 3x + 12
2 over 19 comma 2 over 33
negative 2 over 19 comma negative 33 over 2
negative 19 over 2 comma negative 33 over 2
19 over 2 comma 33 over 2
Answer:
x=-19/2 y=-33/2
Step-by-step explanation:
x − y = 7
y = 3x + 12
Substituting the second equation into the first
x − (3x+12) = 7
Distribute the minus sign
x-3x-12 = 7
Combine like terms
-2x-12 =7
Add 12 to each sid
-2x-12+12 =7+12
-2x=19
Divide each side by -2
-2x/-2 = 19/-2
x = -19/2
Now we need to find y
y = 3x+12
y = 3(-19/2) +12
y = -57/2 +24/2
y = -33/2
Answer:
(-19/2, -33/2)
Step-by-step explanation:
A toy plush weighed one- sixth of a pound. A flimsy box can hold 4 pounds. How many toy plushes could the box hold?
Answer:
24 plushies
Step-by-step explanation:
1 pound = 6 toy plushies
6(4)=24
simplify the following fraction (9/16/1/4)-1/5
Answer: [tex]\frac{41}{20}[/tex]
Step-by-step explanation:
The first step is to make the division of the fractions [tex]\frac{9}{16}[/tex] and
[tex]\frac{1}{4}[/tex]. To do this, you can flip the fraction [tex]\frac{1}{4}[/tex] over and multiply the numerators and the denominators of the fractions. Then:
[tex](\frac{\frac{9}{16}}{\frac{1}{4}})-\frac{1}{5}=(\frac{9}{16}*4)-\frac{1}{5}=\frac{36}{16}-\frac{1}{5}[/tex]
Reduce the fraction [tex]\frac{36}{16}[/tex]:
[tex]=\frac{9}{4}-\frac{1}{5}[/tex]
Now you can make the subtraction: in this case the Least Common Denominator (LCD) will be the multiplication of the denominators. Divide each denominator by the LCD and multiply this quotient by the corresponding numerator and then subtract the products. Therefore you get:
[tex]=\frac{45-4}{20}=\frac{41}{20}[/tex]
PLZ HELP, WILL GIVE BRAINLIEST
What is the value of x?
A.
73°
B.
45°
C.
35°
D.
25°
Answer:
x = 35
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 base angles from 180 for angle at vertex
vertex = 180° - (73 + 51)° = 180° - 124° = 56°
The vertex angle is composed of x and 21, so
x + 21 = 56 ( subtract 21 from both sides )
x = 35
helppppppppppppppppppppping
Answer:
B
Step-by-step explanation:
First we simplify the equation:
3y − 2x = k (5x − 4) + 6
3y − 2x = 5k x − 4k + 6
3y = (5k + 2) x − 4k + 6
y = (5k + 2)/3 x + (6 − 4k)/3
The line has a positive slope and negative y-intercept. So:
(5k + 2)/3 > 0
(6 − 4k)/3 < 0
Solving for k in each:
k > -2/5
k > 3/2
k must be greater than -2/5 and 3/2. Since 3/2 is already greater than -2/5, then k must be greater than 3/2.
If k > 3/2, then it's also true that k > 0. So the answer is B.
The apother is 4 m and a side is 5.8 m. What is the area
of the pentagon? Round to the nearest whole number.
Answer:
58 m^2.
Step-by-step explanation:
The area of one of the 5 triangles is:
1/2 * 5.8 * 4 = 11.6 m^2
So the area of the pentagon
= 5 + 11.6
= 58 m^2
Answer:
The area is 58 meters squared.
Step-by-step explanation:
Since the pentagon is conveniently split into 5 separate but equal triangles, we only need to find the area of 1 triangle to find the rest. The area of triangles, as I'm sure you know, is 1/2bh. Using this equation, we get (1/2)x4x5.8. This equals 11.6. This is the area of one of the triangles. There are 5 triangles, so we multiply the area of 1 triangle by 5. 11.6x5= 58 meters squared. Hope this helped. :)
Two lines and a transversal form corresponding angles that are congruent. Describe the two lines
Answer:
parallel
Step-by-step explanation:
If you have two lines and a transversal that form corresponding angles that are congruent. Then the alternate interior angles are congruent and the same-side interior (some people call these consecutive angles) are supplementary.
This has to deal with Parallel Lines Theorem or the Converse of Parallel Lines Theorem.
The lines would be parallel.
Two lines will be parallel.
What is corresponding angle?When two lines are cut by a transversal then the angles formed relatively same position in their respective line at the intersection transversal and two lines are called corresponding angles.
What is converse of corresponding angles theorem?
Converse of corresponding angles theorem states that When two lines are cut by a transversal and the formed corresponding angles are congruent then the two lines will be parallel.
Here given that two lines and transversal are forming corresponding angles which are congruent. So by converse of corresponding angles theorem, the two lines will be parallel to each other.
Therefore two lines will be parallel.
Learn more about corresponding angle
here: https://brainly.com/question/2496440
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what is the solution to x=√3x+10?
Answer:
x=5
Step-by-step explanation:
Given
[tex]x=\sqrt{3x+10}[/tex]
Squaring on both sides
[tex]x^2=(\sqrt{3x+10})^2 \\x^2=3x+10\\x^2-3x-10 = 0\\x^2-5x+2x-10 = 0\\x(x-5)+2(x-5) = 0\\(x-5)(x+2)=0\\x=5\\and\\x=-2[/tex]
Since putting -2 gives us:
[tex]-2=\sqrt{3(-2)+10} \\-2=\sqrt{-6+10}\\-2=\sqrt{4}\\-2\neq 2[/tex]
2 is an extraneous solution.
Therefore, the solution to x=√3x+10 is x=5 ..
Help please and fast
Answer:
b. 7/16
Step-by-step explanation:
We can see in the figure that the total dimension parallel to C is 15/16.
The other half dimension with c is 1/2
We will get the dimension C by subtracting 1/2 from 15/16
So,
C = 15/16 - 1/2
= (15-8)/16
=7/16
So the dimension C is 7/16.
Hence option b is correct ..
f(x) = -x^3 + 3x^2 + x - 3 Using the end behavior of f(x), determine the graph of the function
Answer:
Here, the given function,
[tex]f(x) = -x^3 + 3x^2 + x - 3[/tex]
Since, the leading coefficient is negative, and degree is odd,
Thus, the end behaviour of the function is,
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow \infty[/tex]
Therefore, the graph rises to the left and falls to the right.
Now, when f(x) = 0
[tex]-x^3+3x^2+x-3=0[/tex]
[tex]\implies -(x-3)(x-1)(x+1)=0[/tex]
[tex]\implies x=3, 1, -1[/tex]
That is, graph intercepts the x-axis at (3, 0), (1, 0) and (-1, 0).
When x = 0,
[tex]f(x) = - 3[/tex]
That is, graph intersects the y-axis at ( 0, -3),
Also, for 0 > x > -1 , f(x) is decreasing,
For 2.55 > x > 0, f(x) is increasing,
For 3 > x > 2.55, f(x) is decreasing,
Hence, by the above explanation we can plot the graph of the function ( shown below )
Answer:w
Step-by-step explanation: it should be w i got it on plato
m2 - 36 = 0
Several solutions please
Answer:
m = ±6
Step-by-step explanation:
m^2 -36 =0
Add 36 to each side
m^2-36 +36 = 0+36
m^2 = 36
Take the square root of each side
sqrt(m^2) = ±sqrt(36)
m = ±6
Answer:+6 or -6
Step-by-step explanation:m^2 - 6^2
it becomes difference of two squares,
(m+6) (m-6)=0
m-6=0,m=6
m+6=0,m=-6
Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 8 millimeters long, and each passing week it grew 2 additional millimeters.
Graph the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks).
Please help me to understand how to graph this problem.
A function that models the situation is f(x) = 2x + 8.
A graph of the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks) is shown in the picture below.
In Mathematics, the slope-intercept form of the equation of a straight line refers to the general equation of a linear function and it is represented by this mathematical equation;
y = mx + b
where:
m represents the slope.x and y are the points.b represents the y-intercept or initial value.Since Rip van Winkle's beard was 8 millimeters long when he fell asleep, and each passing week it grew 2 additional millimeters, we can logically deduce the following parameters;
slope, m = 2.
initial value or y-intercept, b = 8.
In this context, an equation for the function that relates the length of his beard (in millimeters) to time (in weeks) can be written as follows;
y = mx + b
f(x) = 2x + 8