Answer:
(x - 10)(x - 5)
Step-by-step explanation:
Well to factor X^2-15x+50
we need to find 2 numbers that multiply to get 50 and add to get -15.
-5 * -10 = 50
-5 + -10
x*x = x^2
Factored (x - 10)(x - 5)
Hope this helps :)
Answer:
(x - 10)(x - 5)
Step-by-step explanation:
Step 1- Find 2 numbers that multiply to be 50.
10 × 5
-10 × -5
25 × 2
-25 × -2
All these multiply to get 50.
But the numbers must also add up to be -15.
Step 2- Find the 2 numbers that also add up to be -15.
10 + 5 = 15
-10 + -5 = -15
25 + 2 = 27
-25 + -2 = -27
The correct equation would be - 10 + -5
The 2 number you would use when you factor would be -10 and -5
Step 3- Write the equation
You can write the equation as (x - 10)(x - 5)
Or you can also write it as (x - 5)(x - 10)
Write the following phrase as an expression. "the product of 6 and n" Please helpMEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
6n=
Step-by-step explanation:
I hope this helps you
The expression is 6n.
What is an Expression ?An expression is a mathematical statement that has variables , constants and mathematical operators.
The phrase 6 and n in expression form is
6n
Therefore, the expression is 6n.
To know more about Expression
https://brainly.com/question/2060304
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Please help me someone
Answer: Surface area is 169π
Step-by-step explanation:
[tex]A=\pi \cdot \:d^2[/tex]
[tex]A=\pi d^2[/tex]
[tex]A=\pi 13^2[/tex]
[tex]A=169\pi[/tex]
The cost of tea varies directly with the mass. Liz bought 4.5kg of tea for $10.35. What is the cost of 12kg of tea?
Answer:
$ 27.6.
Step-by-step explanation:
Let the cost of tea be C.
Let the mass of tea be M
From the question given, we were told that the cost of tea varies directly with the mass. This can be expressed as:
C & M
C = KM
K is called constant of proportionality.
C is the cost of the tea.
M is the mass of tea.
Next, we shall determine the constant of proportionality, K.
Cost (C) = $ 10.35
Mass (M) = 4.5 kg
Constant (K) =..?
C = KM
10.35 = K × 4.5
Divide both side by 4.5
K = 10.35/4.5
K = 2.3
Finally, we shall determine the cost of 12kg of tea as follow:
Mass (M) = 12 kg
Constant (K) = 2.3
Cost (C) =..?
C = KM
C = 2.3 × 12
C = $ 27.6
Therefore, the cost of 12 Kg of tea is $ 27.6
Answer:
$27.6
Step-by-step explanation:
10.35 divided by 4.5 = 2.3
$2.3 for 1 kg
2.3 times 12= 27.6
the sum of the first 16th term of an A.P is 240 and the sum of the next 4 term is 220 find the next term of the A.P
Answer:
65
Step-by-step explanation:
The sum of the first 16 terms of an arithmetic progression (A.P) is 240
The sum of the next 4 terms is 220
The sum of n terms in an A.P is given by;
[tex]s_{n}[/tex] = n/2(2a + (n - 1)d)
240 = 8(2a + 15d) ... (i)
460 = 10(2a + 19d) .... (ii)
Simplifying this gives;
2a + 15d = 30 ... (i)
2a + 19d = 46 ... (ii)
Subtracting (i) from (ii) we get;
4d = 16
d (common difference) = 4
and a (first term) = (30 - 60)/ 2 = -15
The sequence upto 21 terms is here:
-15, -11, -7, -3, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 51, 55, 59, 61, 65
So the next term (21^st term) is 65.
Answer: a₂₁ = 65
Step-by-step explanation:
The Sum of an Arithmetic Progression is the sum of the first term plus the sum of the last term divided by 2 and multiplied by the number of terms.
[tex]a_1\ \text{is the first term}\\a_n=a_1+d(n-1)\quad \text{is the value of the nth term}\\\\[/tex]
Let's find the 16th term (n = 16)
[tex]a_{16}=a_1+d(16-1)\\\\.\quad =a_1+15d[/tex]
Now let's find the sum of the first 16 terms. This will be Equation 1:
[tex]S_{16}=\dfrac{(a_1)+(a_1+15d)}{2}\times 16=240\\\\\\.\qquad 8(2a_1+15d)=240\\\\\\.\qquad 2a_1+15d=30\qquad \leftarrow \text{Equation 1}[/tex]
************************************************************************************
Repeat what we did above for the next 4 terms (n = 17 to n = 20). This will be Equation 2:
[tex]a_{17}=a_1+d(17-1)\\\\.\quad =a_1+16d\\\\\\a_{20}=a_1+d(20-1)\\\\.\quad =a_1+19d[/tex]
[tex]S_{17-20}=\dfrac{(a_1+16d)+(a_1+19d)}{2}\times 4=220\\\\\\.\qquad 2(2a_1+35d)=220\\\\\\.\qquad 2a_1+35d=110\qquad \leftarrow \text{Equation 2}[/tex]
*********************************************************************************************
Now we have a system of equations. Solve using the Elimination Method:
2a₁ + 15d = 30 → -1(2a₁ + 15d = 30) → -2a₁ - 15d = -30
2a₁ + 35d = 110 → 1(2a₁ + 35d = 110) → 2a₁ + 35d = 110
20d = 80
d = 4
Input d = 4 into one the equations to solve for a₁:
Equation 1: 2a₁ + 15d = 30
2a₁ + 15(4) = 30
2a₁ + 60 = 30
2a₁ = -30
a₁ = -15
Given a₁ = -15 and d = 4, we can find the next term (n = 21)
[tex]a_n=a_1+d(n-1)\\\\a_{21}=-15+4(21-1)\\\\.\quad =-15+4(20)\\\\.\quad = -15+80\\\\.\quad = 65[/tex]
How to do this question plz answer me step by step plzz plz
Answer:
112
Step-by-step explanation:
Define the variables:
x = number of French students sent by the school
Write the equation:
x / 21 = 1 / 3
Solve:
x = 7
The school sent 7 French students and 21 German students, for a total of 28 students.
The other 3 schools also sent 28 students. So the total number of students sent is:
4 × 28 = 112
Answer:
Step-by-step explanation:
French students=F
[tex]\frac{F}{21} =\frac{1}{3} \\F=\frac{1}{3} \times 21 =7\\Total~ students~ of ~one~ school=21+7=28\\Total~language~students=28 \times 4=112[/tex]
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
I really need help plzz. This is due it 20 mins and I would REALLY appreciate someone if they help. I will mark u as brainiest. I've been needing help since the morning :(
Answer:
Page 1:
I chose Cartoon 3
=> It can be difficult to save money because we don't actually know where all of our money goes. In this cartoon, the lady has bought something of which she had no idea but she bought that just because it was on sale. It is of no use to her and she even doesn't know how to use it. She didn't same money (as it was on sale), she rather wasted the money on buying a think she doesn't even know how to use.
I found this cartoon persuasive as the cartoonist tried its best to persuade the watcher. The cartoon would look more persuasive if the cartoonist added more colors to it. So, it would look more attractive.
Page 2:
I feel really depressed about the situation but thanks to God I've that $1000. I think I would e able to spend 30 days with those $1000 by restricting my expenditures. Then I'll have a happy 30 days. Also, I can find a new job during these 30 days too.
In a fiftness class, there was a warm up of 14 press-ups. Anyone unable to do 14 or more recives a punishment. Jessica can do 10 press-ups without ever failing, however, the chances of her successfully doing each subsequent press-up halves. Whats the probality of her receiving a punishment? A. 1 in 8 B. 1 in 1024 C. 15 in 16 D. 1023 in 1024
Answer:
The correct option is;
C. 15 in 16
Step-by-step explanation:
The given information are;
The number of press-ups required = 14 press-ups
The number of press-ups Jessica is sure to do = 10 press-ups
The chance of Jessica doing subsequent press-ups after 10 halves each time
The consequence of not completing the 14 press-ups = Punishment
The probability that Jessica does goes on to do 11 press-ups = 1/2
The probability that Jessica does goes on to do 12 press-ups = 1/2×1/2
The probability that Jessica does goes on to do 13 press-ups = 1/2×1/2×1/2
The probability that Jessica does goes on to do (completes) 14 press-ups = 1/2×1/2×1/2×1/2 = 1/16
Therefore;
Since the probability that Jessica does not receive a punishment because she completed the 14 push-ups is 1/16, we have;
The probability that Jessica does not complete the 14 press-ups and receives a punishment = 1 - 1/16 = 15/16 which is 15 times out of 16 or 15 in 16.
Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds?
Answer: 20.8 cm
Step-by-step explanation:
Notice that the corners of the squares form a line.
Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.
At 0 seconds the side length is 1 --> (0, 1)
At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)
First, find the slope between the coordinates using [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)
[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]
Next, use the Point-Slope formula to find the equation of the line:
[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]
Lastly, find the side length (y) when x = 1.5
y = 2.8(1.5)x + 1
= 4.2 + 1
= 5.2
Perimeter of a square = 4 times the side length
P = 4(5.2)
= 20.8
THE LANDSCAPER IS PLANTING A TREE THAT IS NOW 55 CM TALL. THE TREE WILL GROW 4 CM PER MONTH FOR X MONTHS. THE TREE WILL GROW TO BE AT MOST Y CM TALL. WRITE AN INEQUALITY SHOWING THIS RELATIONSHIP.
Answer: 55cm + X*4cm < Y.
Step-by-step explanation:
The initial height of the tree is 55cm
The tree will grow 4cm per month, for X months.
then the height of the tree is the initial height, plus X times 4cm
H = 55cm + X*4cm
If Y is the maximum height that this tree can grow, then we can write the inequality as:
H < Y.
55cm + X*4cm < Y.
WILL GIVE BRAINLIEST Find the value of x, rounded to the nearest degree. 26° 25° 28° 62°
Answer:
X rounded to the nearest degree can me calculated based on parallel lines or if there is a straight line bisected by a line, 180 degress is a staright line. There is not enough info nor a picture to give a direct answer.
Answer:
its D
Step-by-step explanation:
Solve the following system using substitution.
Answer/Step-by-step explanation:
3. By substitution method, let's substitute [tex] \frac{2}{3}x- 4 [/tex] for y in the first equation.
Thus,
[tex] \frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1 [/tex]
Solve for x
[tex] \frac{x}{3} + \frac{4x}{3} - 4 = 1 [/tex]
Add 4 to both sides
[tex] \frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4 [/tex]
[tex] \frac{x}{3} + \frac{4x}{3} = 5 [/tex]
[tex] \frac{x + 4x}{3} = 5 [/tex]
[tex] \frac{5x}{3} = 5 [/tex]
Multiply both sides by 3
[tex] \frac{5x}{3}*3 = 5*3 [/tex]
[tex] 5x = 15 [/tex]
Divide both sides by 5
[tex] x = 3 [/tex]
Now, substitute 3 for x in the equation.
[tex] y = \frac{2}{3}x- 4 [/tex]
[tex] y = \frac{2}{3}(3) - 4 [/tex]
[tex] y = 2 - 4 [/tex]
[tex] y = -2 [/tex]
The solution of the equation is x = 3, y = -2
4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.
[tex] 3x - 2y = 11 [/tex]
[tex]-3x - y = 4[/tex]
[tex] -3y = 15 [/tex] => [tex] (-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15) [/tex]
Divide both sides by -3 to solve for y
[tex] \frac{-3y}{-3} = \frac{15}{-3} [/tex]
[tex] y = -5 [/tex]
Substitute -5 for y in the first equation to find x
[tex] 3x - 2(-5) = 11 [/tex]
[tex] 3x + 10 = 11 [/tex]
Subtract 10 from both sides
[tex] 3x + 10 - 10 = 11 - 10 [/tex]
[tex] 3x = 1[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{1}{3} [/tex]
[tex] x = \frac{1}{3} [/tex]
The solution is [tex] x = \frac{1}{3}, y = -5 [/tex]
what is a measure ∠x
Answer:
x = 138
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
x = B+ C
x = 68+ 70
x =138
Answer:
138 degrees
Step-by-step explanation:
A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.
So 180-138 is 42 degrees, which would be the last angle within the triangle.
Since a line is also 180 degrees, its 180-42, which makes x 138 degrees
Help help help help help
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answer: Pam earns $41,667 in one year.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Pam's salary (x) multiplied by the percentage represented by expenses (18%) in decimal form (divided by 100) must be equal to $7500.
Mathematically speaking:
x (18/100) = 7500
Solving for x:
x (0.18) = 7500
x = 7500/0.18
x = 41,667
Pam earns $41,667 in one year.
Feel free to ask for more if needed or if you did not understand something.
The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction
Answer: 1:5
Step-by-step explanation:
Given: The cost of every mirror is proportional to the cube of the mirror's radius.
i.e. [tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}[/tex]
Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.
Then,
[tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}[/tex]
The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:
[tex]\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}[/tex]
Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .
Find the legs of a 30° -60°-90° triangle whose hypotenuse is:
10 in.
PLEASE ANSWER ASAP IM really STRUGGLING!!
You use Pythagoras' Theorem and the theorem of 30-60-90 triangle
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answer:
1521 pi in^3
radius x radius x height x pi = volume
13 x 13 x 9 = 1521
We do not multiply by pi because it is already included
Hope this helps
Step-by-step explanation:
Determine whether the function shown in the graph is even or odd. The graph starts at the top left, continues down through the x axis at negative two to a minimum around y equals negative five, goes up to a maximum on the x axis at y equals negative one, goes back down to a minimum around y equals negative five, and goes back up through the x axis at two.
Answer:
Might be D
Step-by-step explanation:
took the test and that was the other one i was thinking
Answer: D: The function is odd because it is symmetric with respect to the origin.
Step-by-step explanation:
Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of n?
40nt in
43n in
O
100nt in
108n in
Hey there! I'm happy to help!
I assume that n is supposed to be π. To find the volume of a cone, you multiply the base by the height and then divide by three.
First, we find the area of the base, which is a circle. To find the area of a circle, you square the radius and multiply by π.
5²=25
And we multiply by π.
25π
Now we multiply by the height.
25π×13=325π
We divide by three.
325π/3≈108π
Therefore, the answer is 108π in.
Have a wonderful day! :D
Help please!!!!!thxxxx
Answer:
144
Step-by-step explanation:
An angle of a regular pentagon is of 180(5-2)/5=108°
and that all the sides are equal so angle MNL=108/3=36
then MNK=180-MNL=180-36=144
I don't know if you understand this but it's hard to work without more points :)
If the m1 = 40, what is the m 3
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps UWhich represents the solution(s) of the system of equations, y + 4 = x2 and y – x = 2? Determine the solution set by graphing.
(–2, 0)
(–2, 0) and (2, 0)
(–2, 0) and (3, 5)
no solutions
Answer:
c
Step-by-step explanation:
c
Answer:
the answer is C ;D
Step-by-step explanation:
Please answer this in two minutes
Answer:
20/29
Step-by-step explanation:
SOH CAH TOA
so its opposite/hyp...
20/29
is the answer
6 root 5 plus 6 root 5
Answer:
12√5
Step-by-step explanation:
6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.
Answer:
12 [tex]\sqrt{5}[/tex]
Step-by-step explanation:
When you add the surds which are the same type, (both are root 5), just add the integers before them together.
HELPPP!! Calculate the side lengths a and b to two decimal places. (there is a picture included)
Answer:
Option (D)
Step-by-step explanation:
In the given triangle ABC,
Sum of all interior angles = 180°
m∠A + m∠B + m∠C = 180°
72° + 85° + m∠C = 180°
m∠C = 180 - 157
m∠C = 23°
By applying Sine rule in the triangle,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{\text{SinC}}{c}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=\frac{\text{Sin23}}{6.2}[/tex]
[tex]\frac{\text{Sin72}}{a}=\frac{\text{Sin85}}{b}=0.06302[/tex]
[tex]\frac{\text{Sin72}}{a}=0.06302[/tex]
a = [tex]\frac{\text{Sin72}}{0.06302}[/tex] = 15.09
[tex]\frac{\text{Sin85}}{b}=0.06302[/tex]
b = [tex]\frac{\text{Sin85}}{0.06302}[/tex]
b = 15.81
Therefore, option (D) will be the answer.
Mr.lopez wrote the equation 32g+8g-10g=150
Answer:
g=5
Step-by-step explanation:
32g+8g-10g=150
30g=150
g=5
Please answer this question now
Answer:
[tex] Area = 538.5 m^2 [/tex]
Step-by-step Explanation:
Given:
∆XVW
m < X = 50°
m < W = 63°
XV = w = 37 m
Required:
Area of ∆XVW
Solution:
Find side length XW using Law of Sines
[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]
W = 63°
w = XV = 37 m
V = 180 - (50+63) = 67°
v = XW = ?
[tex] \frac{v}{sin(67)} = \frac{37}{sin(63)} [/tex]
Cross multiply
[tex] v*sin(63) = 37*sin(67) [/tex]
Divide both sides by sin(63) to make v the subject of formula
[tex] \frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = \frac{37*sin(67)}{sin(63)} [/tex]
[tex] v = 38 [/tex] (approximated to nearest whole number)
[tex] XW = v = 38 m [/tex]
Find the area of ∆XVW
[tex] area = \frac{1}{2}*v*w*sin(X) [/tex]
[tex] = \frac{1}{2}*38*37*sin(50) [/tex]
[tex] = \frac{38*37*sin(50)}{2} [/tex]
[tex] Area = 538.5 m^2 [/tex] (to nearest tenth).
what is
5/14 mulitypled by 4 in simplest form
Answer:1 3/7
Step-by-step explanation:When you multiply the nominator and 4you get 20.So it would 20/14 but if you find the simplest form of fraction you would get 1 3/7
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of miles and a standard deviation of miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Complete question is;
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answer:
The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.
Step-by-step explanation:
Let X = Life expectancy of the automobile tire
For the normal distribution, we are given;
μ = 34000
σ = 2700
Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.
Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:
P(X ≤ y) = 0.1
Using the z formula, we have;
P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1
Thus;
P(Z ≤ ([y - μ]/σ) = 0.1
From z-distribution table the Z-score at 0.1 is approximately -1.2816
This is P(Z ≤ -1.2816)
Thus;
[y - μ]/σ = -1.2816
(y - 34000)/2500 = -1.2816
y - 34000 = -1.2816 × 2500
y - 34000 = -3204
y = 34000 – 3204
y = 30796
So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.