Answer:
Intersects; intersection point: (-2,3)
Step-by-step explanation:
Substitute -1.5x for y into y=0.5x+4:
-1.5x = 0.5x +4
-1.5x - 4 = 0.5x
-4 = 2x
x = -2
Plug in -2 for x into y=-1.5x
y = -1.5(-2)
y = 3
Organize the x and y values into an ordered pair:
(-2,3)
Answer:
y=0.5x+4 intersects y=-1.5x.
The intersection point is (-2,3)
Step-by-step explanation:
First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.
So we have the equation:
[tex]y=-1.5x[/tex]
Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5
The equation given to us is:
[tex]y=0.5x+4[/tex]
As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.
To find the x-value of their intersection, simply set the equations equal to each other and solve for x.
[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]
Now, plug -4 into either of the equations:
[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]
Therefore, the point of intersection is (2,3).
△ABCis reflected to form △A′B′C′. The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). Which reflection results in the transformation of △ABC to △A′B′C′? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x
Answer:
reflection across y = x
Step-by-step explanation:
Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.
If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)
If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)
If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)
If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)
The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form △A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged
Answer:
reflection across y = x
Step-by-step explanation:
A blue print for a house has a scale of 1:10. A wall in the blueprint is 8in. What is the length of the actual wall?
6.67. inches
80 feet
969 feet
6.67 feet
Answer:
80 feet
Step-by-step explanation:
1 inch represents 10 feet
Then 8 inches represent = 8 × 10
= 80 feet
Please help me with this
verifying, by putting [tex] \theta=60^{\circ}[/tex]
LHS≠RHS
hence the question is FALSE
Samantha’s college runs on a trimester schedule so she receives a bill 3 times a year for tuition. Each trimester costs $1,450, and Samantha must complete 2 years of college to receive her degree. The average cost for books each trimester is $350. Approximately what will be the total cost for Samantha to get her degree?
Answer:
10800
Step-by-step explanation:
1 trimesters cost = 1450 + 350 $
2 year -> 6 trimester
1800$ x 6 = 10800 $
write 1,245 in word form
Answer:
One thousand two hundred and forty five.
Hope this helps! （づ￣3￣）づ╭❤～
Step-by-step explanation:
Solve. 100+[12×{20−(10÷5)}]
Answer:
316
Step-by-step explanation:
Evaluate f (x) = 2 x torx =-5.
Answer:
-10.
Step-by-step explanation:
f(x) = 2x, x = -5.
f(-5) = 2(-5)
= 2 * (-1) * 5
= 10 * (-1)
= -10.
Hope this helps!
Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4
Answer:
Step-by-step explanation:
[tex]9^{-4}[/tex]
=[tex]\frac{1}{9^{4} }[/tex] ∴ [tex]x^{-n} = \frac{1}{x^{n} }[/tex]
=[tex]\frac{1}{9*9*9*9}[/tex]
=[tex]\frac{1}{6561}[/tex]
5. Eight adults and six children travel in a cable car.
Estimate the total mass of the people in the cable car.
Answer: 1880 pounds
Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs
A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 years, how much interest will the company pay?
Answer:
about 11.03 million
Step-by-step explanation:
Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):
Substitute the values given:
I = 70,000,000(1 + 5/100)^3 - 70,000,000
Use a calculator to solve and you will get ~11.03 million.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
The interest the company paid is $11 million.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $70 million
r = 5%
t = 3 years
n = 1
A = 70 ( 1 + 0.05)³
A = 70 ( 1.05)³
A = 70 x 1.05 x 1.05 x 1.05
A = $81 million
The amount of interest.
= A - P
= 81 - 70
= $11 million
Thus,.
The interest the company paid is $11 million.
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Use the first four terms of the binomial theorem to approximate 2.2^7
A. 248.96
B. 248.4688
C. 23.424
D. 249.4357888
please explain the steps to how you got your answer thank you!!
Answer:
248.96.
Step-by-step explanation:
We write it as:
(2 + 0.2)^7 = 2^7 + 7*2^6*0.2 + 7C2*2^5*(0.2)^2 + 7C3*2^4(*(0.2)^3
= 128 + 89.6 + 26.88 + 4.48
= 248.96.
Simplify the expression (x)^3(x^3y)^2
A) x^9y^2
B) -x^6y^2
C) x^5y^2
D) -x^9y^2
Answer:
A)
Step-by-step explanation:
[tex](a^{m})^{n} = a^{mn}\\\\x^{3}*(x^{3}*y^{2})^{2}=x^{3}*(x^{3})^{2}*(y)^{2}\\\\\\=x^{3}*x^{3*2}*y^{2}\\\\\\=x^{3}*x^{6}*y{2}\\\\\\=x^{3+6}*y^{2}\\=x^{9}y^{2}[/tex]
Find the area of the following rectilinear figure.
Answer:
Area : 14+10+40=64 square unit
Step-by-step explanation:
the area of the top rectangle with sides 2 and 7
A=2*7=14 square unit
the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5
Area=5*2=10 square unit
the bottom rectangle : sides 10 and 4
Area=10*4=40
add the areas : 14+10+40=64 square unit
Make the biggest possible number using the digits below only once 3 , 1 , 3 answer
Answer:
331 the biggest possible number
Please answer this question now
Answer:
Surface area of a cone = 461.58 In²
Step-by-step explanation:
Surface area of a cone = πrl + or
Surface area of a cone = πr(r+l)
Where r = radius
Radius= diameter/2
Radius=14/2
Radius= 7 inch
And l slant height= 14 inch
Surface area of a cone = πr(r+l)
Surface area of a cone = π*7(7+14)
Surface area of a cone = 7π(21)
Surface area of a cone = 147π
Surface area of a cone = 461.58 In²
...................................................
Answer:
11.21157846 =x
Step-by-step explanation:
We know log b (a) = c can be written as b^c =a
log 3 (x) = 2.2
3^2.2 = x
11.21157846 =x
Answer:
[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]
Step-by-step explanation:
[tex]\large \sf log_3 (x)=2.2[/tex]
Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:
[tex]\large \sf log_b(y)=x[/tex]
[tex]\large{\sf y=b^x}[/tex]
Apply the relationship.
[tex]\large \sf log_3 (x)=2.2[/tex]
[tex]\large \sf x=3^{2.2}[/tex]
[tex]\large \sf x=11.21157845...[/tex]
[tex]\large \sf x \approx 11.21[/tex]
How would you write 7 is subtracted from the cube of a number
Answer:
n³ - 7
Step-by-step explanation:
n³ - 7
The required expression for the 7 subtracted from the cube of a number is x³- 7.
Given that,
A string of statements is given,
Here, we have to transform the statement, 7 is subtracted from the cube of a number into a mathematical inscription.
Arithmetic, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is an expression?A mathmetical expression is formulated structure of a statement using variables.
Let the number be x,
Now 7 subtracted from the cube of number x
= x³ - 7
Thus, the required expression for the 7 subtracted from the cube of a number is x³- 7.
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Waldnice!
8. I have a maximum/minimum thermometer in my greenhouse. It records the highest and
lowest temperatures reached since the time I reset it. I reset it on Sunday when the
temperature was 4°C. Overnight the temperature fell by 5°C. Then during Monday it rose by
6°C. before falling by 10°C during the night. On Tuesday it rose by 4°C and fell by 2°C
overnight.
What were the maximum and minimum temperatures recorded when I looked at the
thermometer on Wednesday morning?
Answer:
The maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C
Step-by-step explanation:
The given parameters are;
A maximum and minimum thermometer is used which records maximum and minimum values as follows;
Initial temperature on Sunday at the time of resetting the thermometer = 4°C
Temperature drop overnight = 5°C, new low = 4 - 5 = -1°C,
Temperature rise on Monday = 6°C. New high = -1 + 6 = 5°C
Temperature drop on Monday night = 10°C. New low = 5 - 10 = -5°C
Temperature rise on Tuesday = 4°C = New high = 4 + - 5 = -1°C
Temperature drop on Tuesday night = 2°C. New low = -1 - 2 = -3°C
Therefore, the maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C.
find the perimeter of a square of length of 5cm
Answer:
20cm
Step-by-step explanation:
If each side of the square = 5 cm, 5 cm times 4 sides = 20 cm.
Answer:
P=20cm
Step-by-step explanation:
To find the perimeter of a square, you just add all the four sides.
Because it says the sides are 5cm, and squares always have the same length, you just:
5+5+5+6=20cm
So, the perimeter of this square is 20cm.
Hope this helps, and have a nice day:)
Find the distance between the two points (-4,4) and (1,0)
Answer:
The answer is
[tex] \sqrt{41} \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
( x1 , y1) and ( x2 , y2) are the points
So the distance between (-4,4) and (1,0) is
[tex] \sqrt{( { - 4 - 1})^{2} + ( {4 - 0})^{2} } [/tex][tex] = \sqrt{ ({ - 5})^{2} + {4}^{2} } [/tex][tex] = \sqrt{25 + 16} [/tex]We have the final answer as
[tex] \sqrt{41} \: \: \: units[/tex]Hope this helps you
Which equation represents a population of 300 animals that decreases at an annual rate of 23%? A. p=300(1.23)t B. p=300(1.77)t C. p=300(0.77)t D. p=300(0.23)t
For a given initial quantity A, a decrease of x% can be written as:
A - A*(x%/100%) = A*(1 - x%/100%)
With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:
P(t) = 300*(0.77)^t
Now let's see how we found that.
In this case, we know that:
The initial number of animals is 300.
They decrease at an anual rate of 23%.
This means that after the first year, the population will be:
P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)
After another year, the population decreases again, so we get:
P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2
Here we already can see the pattern, the population in the year t, we will get:
P(t) = 300*(0.77)^t
Then we can see that the correct option is C.
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Find the exact value of cos A in simplest radical form.
Answer:
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Step-by-step explanation:
Since we are finding cos A we have
[tex] \cos(A) = \frac{AC}{AB} [/tex]From the question
AC = √96
AB = 14
Substitute the values into the above formula
That's
[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]We have the final answer as
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Hope this helps you
SP=2x+3, and LN=5x−14. Find SP. A. 20 B. 86 C. 43 D. 50
Answer:
C
Step-by-step explanation:
A segment joining the midpoints of two sides of a triangle is half the length of the third side.
SP is a midline segment, thus
SP = [tex]\frac{1}{2}[/tex] LN , that is
2x + 3 = [tex]\frac{1}{2}[/tex] (5x - 14) ← multiply both sides by 2
4x + 6 = 5x - 14 ( subtract 4x from both sides )
6 = x - 14 ( add 14 to both sides )
20 = x
Thus
SP = 2x + 3 = 2(20) + 3 = 40 + 3 = 43 → C
1 - Os coeficientes numéricos de uma equação do 2º grau (ax² + bx + c = 0), são números reais representados pelas letras “a, b e c”. Para que uma equação do 2º grau possa existir, é necessário que o coeficiente “a” seja DIFERENTE de: * 1 ponto a) -2 b) -1 c) 0 d) 1 2) Usando o método de Tentativa e Erro, visto na aula, qual das alternativas abaixo representa uma raiz da equação: x²-5x+6=0 * 1 ponto a) x = 0 b) x = 1 c) x = 2 c) x = -2
Answer:
1) La opción correcta es;
c) 0
2) La opción correcta es;
c) x = 2
Step-by-step explanation:
1) La forma general de una ecuación cuadrática se puede escribir en la forma;
a · x² + b · x + c = 0
Dónde;
a, y b son los coeficientes de x², x y c es el término constante
Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0
De lo que tenemos;
(0) × x² + b · x + c = 0, lo que da;
(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado
Por tanto, la opción correcta es c) 0
2)
La ecuación dada se presenta como sigue;
f (x) = x² - 5 · x + 6 = 0
Usando el método de prueba y error, tenemos;
Cuando x = 0
f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución
Cuando x = 1
f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución
Cuando x = 2
f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución
Cuando x = -2
f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución
Por tanto, la opción correcta es c) x = 2
Identify the relation that is not a function. weight of an apple to the apple's cost time of day to the temperature at that time weight of a person to a person's height phone number to a person's name
Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.
The diagram shows 2 straight line , PQ and QR
Find the equation of QR
Help me to explain :)
Answer:
Step-by-step explanation:
We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:
3h + 4(3) = 6 and
3h + 12 = 6 and
3h = -6 so
h = -2
The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:
[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]
So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:
y - 8 = 1(x - 3) and
y - 8 = x - 3 and
y - x = 5 or
-x + y = 5. If your teacher does not want you to lead with a negative:
x - y = -5 would be your equation in standard form.
PLEASE HELP ME I GIVE 5 STARS !
Answer:
It's the 2nd option 2*2*3*3*5
Step-by-step explanation:
Answer:
b.
Step-by-step explanation:
you find a square root that goes into 180. i did 4 times 45. when you break apart 4 you get two times two. when you break apart 45 to get another square root, you get 9 times 5. when you break down 9 you get 3 and 3. so it is 2 times 2 times 3 times 3 times 5
Patrick deposited $6,875 into a savings account 17 years ago. The account has an interest rate of 4.9% and the balance is currently $15,734.11. How often does the interest compound
Answer:
Quaterly
Step-by-step explanation:
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + z2 + z – 24.
The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
How to find product of expressions(4z² + 7z – 8) and (–z + 3)
= -4z³+ 12z² - 7z² + 21z + 8z - 24
collect like terms= -4z³ + 5z² + 29z - 24
Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
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Evaluate 5(14 - 2³) +8 ÷ 2.? Plz help me, will mark you as brainliest A. 26 B. 34 C. 44 D. 56
Answer:
[tex]\large \boxed{\sf B. \ 34}[/tex]
Step-by-step explanation:
[tex]5(14 - 2^3 ) +8 \div 2[/tex]
[tex]\sf Solve \ brackets.[/tex]
[tex]2^3 =8[/tex]
[tex]5(14 - 8 ) +8 \div 2[/tex]
[tex]14-8=6[/tex]
[tex]5(6 ) +8 \div 2[/tex]
[tex]\sf Multiply \ and \ divide.[/tex]
[tex]5(6)=30[/tex]
[tex]8 \div 2 = 4[/tex]
[tex]30 +4[/tex]
[tex]\sf Add.[/tex]
[tex]34[/tex]
Answer: 34
Step-by-step explanation: It's very easy to make mistakes in order of operations problems if you try to do too much of the problem in your head.
It really is worth the extra time it takes to write out every step.
P E M D A S
Parenthses
Exponents
Multiplication/Division
Addition/Subtraction
In this problem, simplify (14 - 2³) first
because it's located inside the parenthses.
2³ is 8 so our second step reads 5(14 - 8) + 8 ÷ 2.
14 - 8 is 6 so we have 5(6) + 8 ÷ 2.
Now multiplication and division are based on order of appearance.
Since multiplication comes first, we do it first.
5(6) is 30 so we have 30 + 8 ÷ 2.
Now we can do the division.
8 ÷ 2 is 4 and we have 30 + 4 which is 34.
