Answer:
7
Step-by-step explanation:
Substitute x = 2 into the equation and evaluate
y = 5(2) - 3 = 10 - 3 = 7
Answer:
[tex]{ \tt{y = 5x - 3}} \\ y = (5 \times 2) - 3 \\ y = 7[/tex]
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
The two INTEGERS are :-
-3 and +4
-3 * (+4) gives us -12
-3 + (+4) gives us 1
hope it helps
have a nice day
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3.
Evaluate the expression 2
2^5 = 32
Hope this helps! :)
Answer:
32
Step-by-step explanation:
[tex]2^{5}[/tex]
= 2 × 2 × 2 × 2 × 2
= 4 × 4 × 2
= 16 × 2
= 32
which equation represents a line parallel to the y-axis?
Answer:
B. x=4
Step-by-step explanation:
I hope this helps!
Which number line shows the solution to −4 − (−1)?
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Answer:
number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow
Olivia bought 525 Euros at an exchange rate of $1.76/Euro. How many Canadian dollars did she pay for the Euros she bought?
the total amount of money for the price of one euro is equal to 1.76 [tex]\displaystyle\bf 525\cdot1.76=\underbrace{0,44\cdot 4}_{1.76}\cdot 525=2100\cdot0,44=21\cdot 44=924$\\\\Answer:She can exchange \underline{924\$ }for 525 euros[/tex]
why is the sum of two negative numbers not a positive number
please dont make the whole answer a example:)
Answer:
because when two negatives are together they can't add
Step-by-step explanation:
because when two negatives are together they can't add no matter if there's an addition sign
6) Qual número deve ser acrescentado a expressão x² - 12x, para que se obtenha um trinômio quadrado perfeito? * 6 5 12 10
Respuesta:
36
Explicación paso a paso:
Para completar el cuadrado tendremos que sumar la mitad del cuadrado del coeficiente de x a la expresión;
Coeficiente de x = -12
Mitad del coeficiente = (-12/2) = -6
Tomando el cuadrado del resultado = (-6) ^ 2 = 36
Por lo tanto, el número que se debe sumar para obtener un cuadrado perfecto es 36.
If a polynomial function f(x) has roots -9 and 7-i, what must be a factor of f(x)
(x-(7+i))
(x-(-7-i))
(x+(7+i))
(x+(7-i))
Answer:
f(x) = [x-(7-2i)][x-(7+2i)]
= [(x-7)+2i][(x-7)-2i]
= (x-7)2 - (2i)2
= x2 - 14x + 49 - 4i2 = x2 - 14x + 49 +4
= x2 - 14x + 53
Answer:
[tex](x-(7-i))[/tex]
Step-by-step explanation:
For a polynomial with roots [tex]a[/tex] and [tex]b[/tex], the polynomial [tex]f(x)[/tex] can be written in factored form [tex](x-a)(x-b)[/tex]. That way, when you plug in any of the roots, [tex]f(x)[/tex] returns zero.
Since the polynomial has at least two roots-9 and 7-i, two of its factors must then be:
[tex](x-(-9)\implies (x+9)\\(x-(7-i))\impli[/tex]
Therefore, the desired answer is [tex]\boxed{(x-(7-i))}[/tex]
The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise money for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.
Answer: [tex]6\sqrt{5}[/tex] miles
This is the same as writing 6*sqrt(5) miles
==========================================================
Work Shown:
P = park
C = city hall
Point P is at the location (10,11)
Point C is at the location (7,5)
Apply the distance formula to find the length of segment PC
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\[/tex]
The exact distance between the park (P) and city hall (C) is [tex]3\sqrt{5}[/tex] miles.
This doubles to [tex]2*3\sqrt{5} = 6\sqrt{5}[/tex] miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.
Extra info:
[tex]6\sqrt{5} \approx 13.41641[/tex] so the runner travels a total distance of roughly 13.4 miles.
PLEASE HURRY
perform the following series of rigid transformations on ∆abc
translate triangle abc by moving it 5 units to the right and 2 units up
Draw the line y=-x and reflect Triangle A’B’C’ across the line
Rotate A’’B’’C’’ counterclockwise about the fact origin by 270 degress
Answer:
Step-by-step explanation:
Coordinates of the vertices of ΔABC,
A(-6, -1), B(-3, -3), C(-1, -2)
Step - 1
Rule for the translation of a point (x, y) by 'h' units right and 'k' units upwards,
A(x, y) → A(x + h, y + k)
If ΔABC is translated by 5 units right and 2 units up, image points will be,
A(-6, -1) → H(-6 + 5, -1 + 2)
→ H(-1, 1)
B(-3, -3) → J(-3 + 5, -3 + 2)
→ J(2, -1)
C(-1, -2) → K(-1 + 5, -2 + 2)
→ K(4, 0)
Step - 2
If the image triangle HJK is reflected across a line [tex]y=-x[/tex], rule for the reflection will be,
H(x, y) → A'(-y, -x)
By this rule,
H(-1, 1) → A'(-1, 1)
J(2, -1) → B'(1, -2)
K(4, 0) → C'(0, -4)
Step - 3
Rule for the rotation of a point 270° counterclockwise about the origin,
A'(x, y) → A"(y, -x)
By this rule, image points of ΔA'B'C' will be,
A'(-1, 1) → A"(1, 1)
B'(1, -2) → B"(-2, -1)
C'(0, -4) → C"(-4, 0)
Now we can graph the image triangle A"B"C".
Answer:
(∠ABC) 108 (for all)
(∠ACB) 27 (for all)
(∠CAB) 45 (for all)
Step-by-step explanation:
Question
Example
Step by Step
A
You can represent the measures of an angle and its complement as xºand (90-x)º.
Similarly, you can represent the measures of an angle and its supplement as x and
(180 - x )°. Use these expressions to find the measures of the angles described.
The measure of an angle increased by 68° is equal to the measure of its complement.
The measure of the angle is
and the measure of its complement is
Answer:
The measure of the angle is 11 and its complement is 79 degrees
Step-by-step explanation:
Mathematically, when two angles are complementary, the sum of the angles equal 90 degrees
so now, if the first angle is x , the second angle which is increased by 68 degrees will be x + 68
So now if we add these two, the value we will get is 90 degrees
Mathematically, we have this as;
x + x + 68 = 90
2x + 68 = 90
2x = 90-68
2x = 22
x = 22/2
x = 11
the measure of the angle is 11 and its complement will be 11 + 68 = 79
Luego de su cumpleaños, Benjamín ha decidido donar la tercera parte del dinero que recibió de regalo de sus familiares a una fundación. Considerando las variables cantidad de dinero recibido por Benjamín y cantidad de dinero que donará Benjamín. a. ¿Cuál es la variable dependiente en esta situación.
Answer:
The dependent variable is the amount of money he received for birthday.
Step-by-step explanation:
After his birthday, Benjamin has decided to donate a third of the money he received as a gift from his relatives to a foundation. Considering the variables amount of money received by Benjamin and amount of money that Benjamin will donate. to. What is the dependent variable in this situation.
Here, the money he received for the birthday is x.
So, he donated x/3.
The variable is the money which he gets, so the dependent variable is amount of money he received for the birthday.
PLEASE SOMEONE HELP I need help ASAP!!!
Answer:
using the pythagoras theorem
Step-by-step explanation:
[tex] \sqrt{4 {}^{2} - ( \sqrt{7}) {}^{2} } = 3[/tex]
The daily listening audience of an AM radio station is five times as large as that of its FM sister station. If 144,000 people listen to these two radio stations, how many listeners does the FM station have?
Answer:
The number of FM listereners are 24000.
Step-by-step explanation:
Let the listeners of FM are p and thus the istereners of AM are 5p.
According to the question,
p + 5 p = 144000
6 p = 144000
p = 24000
The number of FM listereners are 24000.
Can someone help with both questions 19 & 20
Answer:
19.
h=0, the result is 1000×2⁰ = 1000
this is the population of bacteria the excitement started with at the very beginning.
h=-3, the result is 1000×2-³ = 1000/(2³) = 1000/8 = 125
this is a calculation 3 hours backwards from the very start of the experiment, saying that if we started the experiment 3 hours earlier, this would have had to be the starting population of the bacteria so we would arrive at the same amount of population at any given time (value of h).
20.
D 25x⁶
Step-by-step explanation:
for 19 there is not more explanation. it is all ashtray in the answer.
for 20 we see that we are dealing with a square, so ask 4 sides have the same length.
one side is 5x³.
the area of a square is simply side².
so, here (5x³)² = 25x⁶
At a point 25 ft. from the base of a totem pole, the angle of elevation of the top of the pole is 50.1 °. How tall is the totem pole to the nearest foot?
Answer:
height ≈ 30 ft
Step-by-step explanation:
The situation is modelled by a right triangle.
let h be the height of the totem pole, then
tan50.1° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{25}[/tex] ( multiply both sides by 25 )
25 × tan50.1° = h , then
h ≈ 30 ft ( to the nearest foot )
A nunber when divided by 12 gives remainder 7 if the same number is divided by 6 the remainder must be ?
Answer:
1
Step-by-step explanation:
Let the number be n.
We are given:
n/12=q1+(7/12) where q1 is the quotient
n/6=q2+(?/6) where q2 is the quotient and ? is the remainder value we are trying to find.
? must be a integer between 0 and 5, inclusive. A remainder cannot be bigger than or equal to the divisor.
Let's rewrite the first equations
Multiply equation 1 on both sides by 2:
n/6=2q1+7/6
Remainder cannot be 7.
Rewrite again.
6 goes into 7 1 time with remainder 1.
n/6=2q1+(1+1/6)
n/6=(2q1+1)+1/6
So q2=2q1+1 and the remainder is 1 when dividing n by 6.
For fun. What is a number n with such conditions on it?
So what number has remainder 7 when divided by 12 and a remainder 1 when divided by 6.
n=12q1+7
n=6q2+1
If q1=1, we find a number right away that works.
19/12=1+7/12
19/6=3+1/6
Simplify. Your answer should contain only positive exponents.
fraction numerator 2 b squared over denominator 2 b end fraction 2b^2/2b
A. fraction numerator 3 over denominator 4 b end fraction 3/4b
B. 3 b squared 3b^2
C. b
D. 3b
Answer:
D.6b C.v B.8squared 7b<9
cross out 3 digits in the number 51489704 so that the number remaining is divisible by 45
Answer:
1,152
Step-by-step explanation:
So here, we shall be removing random numbers
For ease, since the number is divisible by 45: it is advisable to end the selected number with zero
So we have it that;
we are crossing the first 4, 9 and 7
So, we are left with;
51,840
dividing this by 45 will give 1,152
(iii) If a, b, c are rational numbers, then
a x (b-c) #ax b-ax c. true or false
Answer:
false
Step-by-step explanation:
answer:ab-ac=ab-ac
There are 24 students in a class. Three new students join the class. Work out the percentage change in the number of students in the class.
Answer:
12.5% increase
Step-by-step explanation:
To find the percentage increase ( students joined)
Take the new number minus the original amount
There are 27 students in the class after 3 joined
27 - 24 = 3
Divide by the original amount
3/24 = 1/8 = .125 = 12.5%
Answer:
12.5%
Step-by-step explanation:
Intial number = 27
Final number = 24 + 3 = 27
Percentage change :-
% change = 3/24 × 100 % change = 100/8 % Change = 25/2 % change = 12.5 %One national survey found that 86 percent of those who were unhappily married, but who stayed with the marriage, were when reinterviewed five years later:
Comolete question is;
One national survey found that 86 percent of those who were unhappily married but who stayed with the marriage were, when re-interviewed five years later,
A) preparing to divorce
B) resigned to the situation
C) mostly "very" or "quite" happy
D) mostly "very" happy
Answer:
C) mostly "very" or "quite" happy
Step-by-step explanation:
From social psychology, we know that;
Sometimes people could be happy about something but later on as things progress they become satisfied and are happy about that same thing or person.
The same is the case here with marriage and more importantly in this research.
It says they were unhappily married but they stayed in the marriage and were interviewed 5 years after that. Thus, for them to stay that long even after being unhappy, it means that they began to become a bit happy along the line.
Thus, they would gradually become happy or mostly happy.
What number, divided by 3/7 , will result in a value of 2 1/3?
answer asap --------------
Answer:
h(n) = - 5.3 [tex](-11)^{n-1}[/tex]
Step-by-step explanation:
This is a geometric sequence with explicit formula
h(n) = h(1) [tex](r)^{n-1}[/tex]
where h(1) is the first term and r the common ratio
Here h(1) = - 5.3 and r = - 11 , then
h(n) = - 5.3 [tex](-11)^{n-1}[/tex]
Can someone please help with this problem
Answer:
f(x)=-3(x+2)^2-2
Step-by-step explanation: the the FX graph the -3 in my equation represents the decrease(for being negative) in the graph, the positive 2 represents the x axis if that number is positive the negative 3 is going to change the x axis then will end up being negative which is why the x starts off in negative 2, the last number represents the y axis if the y axis is negative 2 the y will start off at -2
In the description of the following experiment, determine the experimental factor. A research team is testing a paste form of a drug to alleviate inflammation. Participants are grouped into Team A and Team B. Team A receives the paste form of the drug. Team B receives a similar paste with no active ingredients.
Answer:
The experimental factor is the drug to alleviate inflammation paste form
Step-by-step explanation:
An experimental factor is an independent variable that is being controlled by the experimenter which are the input values which the experimenter sets specifically
In the given experiment, two teams, Team A and Team B are administered different treatments (inputs)
Team A is administered the paste form of the drug being experimented
Team B is administered a similar paste with no active ingredient
Therefore, the experimental factor is the drug being administered in paste form
How long is JK?
Choose 1 answer:
A: 3
B: 2 square root 3
C: 3 square root 3
D: 6
E: 9
Answer:
C) 3 times the sq root of 3
Step-by-step explanation:
In a right angle triangle, the COS is definned as the ajacent side over the hypotenuse. So
COS 60 = JK/JL
COS 60 = JK/(6*sq root 3)
.5 = JK/(6*3**1/2)
JK = .5 *(6*3**1/2)
JK = 3*3**1/2
If the volume of a given cube is 729 cubic inches, what is the surface area of the
cube?
486 sq.inches
230 sq.inches
120 sq.inches
222 sq.inches
Answer:
SA = 486
Step-by-step explanation:
Its a cube. s = side length
V = [tex]s^{3}[/tex]
729 = [tex]s^{3}[/tex]
take cube root of each side : [tex]\sqrt[3]{729}[/tex] = 9
so, s = 9
Surface Area of a cube
SA = 6[tex]s^{2}[/tex]
SA = 6([tex]9^{2}[/tex])
SA = 6(81)
SA = 486
The surface area of the cube is 486 square inches. The correct option is A.
To find the surface area of a cube, we need to use the formula:
Surface Area = 6 x (side length)²
Given that the volume of the cube is 729 cubic inches, we can determine the side length of the cube using the formula for volume:
Volume = (side length)³
729 = (side length)³
Taking the cube root of both sides:
side length = ∛(729) = 9 inches
Now, we can substitute the side length into the surface area formula:
Surface Area = 6 x (9 inches)² = 6 x 81 = 486 square inches
Therefore, the surface area of the cube is 486 square inches.
To know more about the surface area of a cube follow
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x = 4y + 3, 2x + y = -3
System of Equations
Answer:
x = -1, y = -1
Step-by-step explanation:
x = 4y + 3
2x + y = -3
We have the value of x in terms of y, so we substitute that in 2x + y = -3:
2(4y+3)+y = -3
8y+6+y = -3
9y = -9
y = -1
Now we substitute the value of y in x = 4y + 3:
x = 4(-1)+3
x = -1
Answer:
y = -1 & x = -1
Step-by-step explanation:
x = 4y + 3 .... ( 1)
2x + y = -3 ........(2)
substitute the 4y + 3 as x in the second equation
2( 4y + 3) + y = -3
simplify and solve for y
8y + 24 + y = -3
9 y + 24 = -3
9y = -3 -24
9y = -27
y = -27 / 9
y = -1
Now, substitute the value of y -1 in first equation
x = 4y + 3
solve for x
x = 4 ( - 1 ) + 3
x = -4 + 3
x = -1
If / is a midsegment of /, find x.
A.
2
B.
3
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
Answer:
It is d
Step-by-step explanation: