Answer:
Its A) 23
Step-by-step explanation:
Its right, trust me
The possible value of the third side of the triangle is 23.
What is the range of the third side when two sides of a triangle are known?The range of third side c when two sides a and b of a triangle are known is given by the inequality:
[tex]a-b < c < a+b[/tex]
It is given that:
a =15
b = 9
So, by the triangle inequality
[tex]15-9 < c < 15+9[/tex]
6 <c <24
The third side will take the value between 6 and 24.
so, the possible value of the third side of the triangle i.e. c is 23.
Therefore, the possible value of the third side of the triangle is 23.
To get more about triangles visit:
https://brainly.com/question/309896
A geometric sequence is defined by the general term tn = 75(5n), where n ∈N and n ≥ 1. What is the recursive formula of the sequence?
Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}t_1=375\\t_{n}=5t_{n-1}\end{array}\right}[/tex]
Step-by-step explanation:
[tex]t_n=75(5^n)\\\\t_{n+1}=75(5^{n+1})\\\\\text{The common ratio:}\ r=\dfrac{t_{n+1}}{t_n}\\\\\text{Substitute:}\\\\r=\dfrac{75(5^{n+1})}{75(5^n)}\qquad\text{cancel 75 and use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\r=5^{n+1-n}=5^1=5\\\\\text{Calculate}\ t_1.\ \text{Put}\ n=1\ \text{to}\ t_n:\\\\t_1=75(5^1)=75(5)=375\\\\\text{The recursive formula of a geometric sequence:}\\\\t_1\\t_n=(t_{n-1})(r)[/tex]
Answer:
t1=375, tn = 5tn-1, where n EN and >1
Step-by-step explanation:
USA test prep said so
The slope intercept form of the equation of a line that passes through point (-2, -13) is y = 5x - 3. What is the point slope form of the equation for this line?
A. y - 13 = 5(x - 2)
B. y + 13 = 5(x + 2)
C. y - 2 = 5(x - 13)
D. y + 2 = 5(x + 13)
Answer:
B. y+13=5(x+2)
Step-by-step explanation:
I personally do y=_+_(x-_) when solving these equations
Plug in -2 the x coordinate for (x- (-2) to be (x+3)
Plug in -13 for the y intercept.
5 from 5x is the slope.
Thus y=-13+5(x+3)
Then just move 13 to the other side
Divide. Write your answer in simplest form.
5/6 ÷ 8
Answer:
5/48
Step-by-step explanation:
Answer:
5/48
Step-by-step explanation:
Evaluate the determinant by using diaganals
Answer:
C. 26
Step-by-step explanation:
The question is on finding determinant of 3×3 matrix
General formulae is given by
if we have matrix (a b c)
(d e f)
(g h i ) then the determinant will be given by
a× D( e f) - b × D (d f) + c× D ( d e)
(h i) (g i) (g h)
where D is the determinant
Evaluate
(a b c) (-4 3 3)
(d e f) = (3 0 2) = -4 ×D(0 2) - 3×D (3 2) + 3×D (3 0)
(g h i ) (3 1 1) (1 1) (3 1) (3 1)
= -4 × {(I×0)-(1×2)} -3 {(3×1)-(3×2)} + 3 { (1×3)-(3×0)}
= -4 ×{-2} - 3×{-3} +3× {3}
=8+9+9= 26
Find the following bases.
a. 8% of ? = 20
b. 75% of ? = 30
c. 20% of ? = 45
d. 150% of ? = 36
It is pretty easy.
[tex]20 = x \times 0.08 \\ x = 20 \div 0.08 = 250[/tex]
[tex]30 = x \times 0.75 \\ x = 30 \div 0.75 = 40[/tex]
[tex]45 = x \times 0.20 \\ x = 45 \div 0.20 = 225[/tex]
[tex]36 = x \times 1.50 \\ x = 36 \div 1.5 = 24[/tex]
Answer:
a. 250
b. 40
c. 225
d. 24
Step-by-step explanation:
pls HURRY 12 Points!!!
what is the area of this trapezoid?
A:96 in²
B:132 in²
C:168 in²
D:1344 in²
Answer:
(B) 132 in²
Step-by-step explanation:
Top Length = 3 + 8 + 3 = 14 in
Bottom Length = 8 in
Area of the trapezoid
= 1/2 (14 + 8) x 12
= 1/2 (22) (12)
= 132 in²
Answer:
B
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where h is the perpendicular height and a, b the parallel bases.
here h = 12, a = AB = 8 and b = DC = 3+ 8 + 3 = 14
A = [tex]\frac{1}{2}[/tex] × 12 × (8 + 14) = 6 × 22 = 132 in² → B
11.
ALGEBRA Zakama Hussein earned $77.00 in simple interest in 18 months ( 1.5 years) at an annual interest rate of 7%. How much money did she invest?
$1466.67
$1650.00
$85.22
$733.33
Answer:
$733.33
Step-by-step explanation:
The question is on finding the principal value
Formulae for simple interest
S.I= P×R/100×T where P is the invested amount of money, R is interest rate and T is time in years
Given that;
Simple interest=$77 , R=7% and T=1.5 years then
S.I= P×R/100×T...................substituting the values given
77=P×7/100 × 1.5
77=P×0.105
77/0.105 =P
$733.33=P
chris bought 4 4/5 pounds of raisins. he shared the raisins equally between himself and five friends. how many raisins did each person get? i already know the answer but i just need to show the work. please answer quickly!!
first off let's convert the mixed fraction to improper fraction, and then do the division, since it was divided among all 6, he and 5 friends.
[tex]\bf \stackrel{mixed}{4\frac{4}{5}}\implies \cfrac{4\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{24}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{24}{5}\div 6\implies \cfrac{24}{5}\div \cfrac{6}{1}\implies \cfrac{24}{5}\cdot \cfrac{1}{6}\implies \cfrac{24}{6}\cdot \cfrac{1}{5}\implies \cfrac{4}{1}\cdot \cfrac{1}{5}\implies \cfrac{4}{5}[/tex]
Answer:
0.8 or 4/5
Step-by-step explanation:
4/5=.8 4.8/6=.8
Grade 4
96. Shelly uses a scoop to fill a container with
flour. The scoop holds cup of flour.
If Shelly uses 12 scoops of flour to fill the
container, how many cups of flour does she
use?
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Suppose you roll a regular 6-faced die. What is the probability of rolling: a 6?, a 2?, and a 4?
3/6 because there are 6 sides and there are 3 numbers that you want to roll. They are even numbers so if you want to roll half of the numbers but not the other half well you have 3/6
8x+10-2x=4(x-5) solve for x
Answer:
[tex]x=-15[/tex]
Step-by-step explanation:
[tex]8x+10-2x=4(x-5) \\ \\ 6x+10=4x-20 \\ \\ 2x=-30 \\ \\ x=-15[/tex]
x = -15
First, distribute the 4 to the x - 5 to get 8x + 10 - 2x = 4x - 20.
Now, subtract 4x and 10 from each side to get 4x - 2x = -30
Simplify the subtraction to get 2x = -30.
Divide both sides by 2 to get a final answer of x = -15.
A man walks 10 miles in x hours. How far does he walk in one hour?
Which expression represents this?
10+x miles
10x miles
10/x miles
Answer: It can't be 10 + x, it can't be 10x, so it will be 10/x
please mark as brainliest
Step-by-step explanation:
Answer:
[tex]\frac{10}{x} \ miles[/tex]
Step-by-step explanation:
Givens
A man walks 10 miles in x hours.So, how far does he walk in one hour?
Basically, the question is asking the constant rate of change of the person's position. In other words, it's asking about the man's velocity: how many miles per hour.
The expression that represents this situation is
[tex]\frac{10}{x} \ miles[/tex]
Because, the problem refers to the ratio of change, which is the quotient between the distance traveled and the time that took to travel that distance.
What is the quadratic function f(x)=x^2+6x-2 In vertex form?
A:f(x)=(x-3)^2+7
B:f(x)=(x+3)^2+7
C:f(x)=(x-3)^2-11
D:f(x)=(x+3)^2-11
Answer: Option D
[tex]f(x)=(x+3)^2 -k[/tex]
Step-by-step explanation:
For a quadratic function of the form
[tex]ax ^ 2 + bx + c[/tex]
The x coordinate of the vertice is:
[tex]x =-\frac{b}{2a}[/tex]
In this case the function is:
[tex]f(x)=x^2+6x-2\\\\[/tex]
So
[tex]a=1\\b=6\\c=-2[/tex]
The x coordinate of the vertice is:
[tex]x=-\frac{6}{2*1}\\\\x=-3[/tex]
The y coordinate of the vertice is:
[tex]f(-3) = (-3)^2 +6(-3) -2\\\\f(-3)=-11[/tex]
The vertice is: (-3, -11)
The form e vertice for a quadratic equation is:
[tex]f(x)=(x-h)^2 +k[/tex]
Where
the x coordinate of the vertice is h and the y coordinate of the vertice is k.
Then h=-3 and k =-11
Finally the equation [tex]f(x)=x^2+6x-2\\\\[/tex] in vertex form is:
[tex]f(x)=(x+3)^2 -k[/tex]
Answer:
The correct answer option is D. f(x) = (x + 3)² - 11.
Step-by-step explanation:
We know that the standard form of a quadratic function is given by:
y = ax² + bx + c
The vertex form of a parabola is given by
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
h = -b / 2a and k = f(h)
In the given equation f(x) = x² + 6x - 2
a = 1, b = 6 and c = -2
Finding h:
h = -6 / (2 × 1)
h = -6/2
h = -3
Finding k:
k = 1(-3)² + 6(-3) + 3
k = 9 - 18 - 2
k = -11
Therefore, the given quadratic function in vertex form: f(x) = (x + 3)² - 11
What is the vertex of the function f(x) = x2 + 12x?
0 (6-36)
(6.0)
(6.0)
(6 -36)
Mark this and retum
Save and Exit
SUR
Answer:
(-6, -36)
Step-by-step explanation:
The vertex [tex](h,k)[/tex] of a function of the form [tex]f(x)=ax^2+bx+c[/tex] is given by the formula:
[tex]h=\frac{-b}{2a}[/tex]
[tex]k=f(h)[/tex] in other words, we find h and then evaluate function at h to find k.
We know from our function that [tex]a=1[/tex], [tex]b=12[/tex].
Replacing values
[tex]h=\frac{-12}{2(1)}[/tex]
[tex]h=-\frac{12}{2}[/tex]
[tex]h=-6[/tex]
Now we can evaluate our function at -6 to find k:
[tex]k=f(h)=f(-6)[/tex]
[tex]k=(-6)^2+12(-6)[/tex]
[tex]k=36-72[/tex]
[tex]k=-36[/tex]
We can conclude that the vertex (h, k) of our function is (-6, -36)
Answer:
(-6,-36)
Step-by-step explanation:
The given function is
[tex]f(x)=x^2+12x[/tex]
We complete the square to write this function in the vertex form.
Add and subtract the square of half the coefficient of x.
[tex]f(x)=x^2+12x+6^2-6^2[/tex]
[tex]f(x)=x^2+12x+36-36[/tex]
The first three terms is now a perfect square trionomial
[tex]f(x)=(x+6)^2-36[/tex]
Or
[tex]f(x)=(x--6)^2-36[/tex]
The function is now in the form:
[tex]f(x)=a(x-h)^2+k[/tex]
where h=-6 and k=-36
The vertex is therefore (h,k)=(-6,-36)
Which of the following is equal to the rational expression when x does not equal -3 x^2-9/x+3
Answer:
x - 3
Step-by-step explanation:
Given
[tex]\frac{x^2-9}{x+3}[/tex]
Note that x² - 9 is a difference of squares and factors as
x² - 9 = (x + 3)(x - 3), thus
[tex]\frac{(x+3)(x-3)}{x+3}[/tex]
Cancel the x+ 3 factor on the numerator/ denominator leaving
x - 3 ← in simplified form
The simplified form of the given rational expression x²-9/x+3, provided x is not equal to -3, is x-3.
Explanation:The given rational expression is x²-9/x+3. To simplify this expression, we can recognize that the numerator (x^2-9) is a difference of squares. In fact, we can rewrite the expression as (x+3)(x-3)/(x+3). As long as x doesn't equal -3 (to prevent division by zero), we can simplify the expression by canceling out the common factor of 'x+3' in both the numerator and denominator. Therefore, the simplified form of the rational expression is x-3 when x does not equal -3.
Learn more about Simplifying Rational Expressions here:https://brainly.com/question/14595765
#SPJ3
A radius is _____ the diameter.
The answer is 1/2.
2r = d.
Hope this helps!
A Radius Of The Circle Is Always Half The Diameter. This Means That The Radius Is Half Way Across A Circle.
Laverne already knew 2 appetizer recipes before starting culinary school, and she will learn 3 new
appetizer recipes during each week of school.
After 2 weeks of culinary school, how many total
appetizer recipes will Laverne know?
Answer:
the answer is 8
Step-by-step explanation:
You would do use the equation (3×2)+2=8
Hope this helps :)
Answer:
8 appetizer recipes.
Step-by-step explanation:
Given,
The number of appetizer recipes Laverne already knew = 2,
Also, she learns 3 new appetizer recipes during each week of school.
So, the additional number of recipes she learn in 2 weeks = 2 × 3 = 6,
Hence, the total appetizer recipes she would know = The recipes she already knew + the additional number recipe she learnt in 2 weeks
= 2 + 6
= 8
What is the range of possible sizes for side x?
Answer:
all real numbers
Step-by-step explanation:
Explain the rule for multiplying two negative integers. Use a number line or algebra tiles to illustrate three examples. Make a sketch of your work.
Multiplying two negative numbers would always give you a positive product
Example 1) -2 * -1 = 2
Example 2) -5 * -4 = 20
Example 3) -10 * -3 = 30
What is the slope of a line with the given coordinates (6,-4) and (-3,-7)
Answer:
m= 1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
-4-(-7) / 6-(-3)
3/ 9
1/3
What would be the answer to this?
Answer:
D
Step-by-step explanation:
Distribute the negative 1 in the second group.
[tex]5k^4*-1=-5k^4 \\ 5k^3*-1=-5k^3 \\ -k*-1=k[/tex]
Now add by combining like terms.
[tex]3k^4-5k^4=-2k^4 \\ -2k^3-5k^3=-7k^3 \\ k+k=2k[/tex]
[tex]-2k^4-7k^3+2k[/tex]
DEFG is an isosceles trapezoid find the measure of E
Answer:
The last option (62 degrees)
Step-by-step explanation:
Angle F is the same measure as angle E, just like angle D is the same measure as G.
The measure of angle ∠E will be 62°. Then the correct option is D.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
DEFG is an isosceles trapezoid.
Then the angle ∠E and ∠F will be congruent.
∠E = ∠F
∠E = 62°
Then the correct option is D.
More about the trapezium link is given below.
https://brainly.com/question/22607187
#SPJ2
What is the equation (4, 5) m=-1/4 solved in point slope form?
Answer:
y - 5 = -1/4(x - 4)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = -1/4 and the point (4, 5). Substitute:
[tex]y-5=-\dfrac{1}{4}(x-4)[/tex]
How do I solve this?
Answer:
[tex]\large\boxed{x=\log_\frac{5}{3}5}[/tex]
Step-by-step explanation:
[tex]3^x=5^{x-1}\qquad\text{use}\ a^{n-m}=\dfrac{a^n}{a^m}\\\\3^x=\dfrac{5^x}{5^1}\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=\dfrac{5^x}{3^x}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\5=\left(\dfrac{5}{3}\right)^x\qquad\text{logarithm both sides}\ \log_\frac{5}{3}\\\\\log_\frac{5}{3}5=\log_\frac{5}{3}\left(\dfrac{5}{3}\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_\frac{5}{3}5=x\log_\frac{5}{3}\dfrac{5}{3}\qquad\text{use}\ \log_aa=1\\\\\log_\frac{5}{3}5=x[/tex]
The normal price of a jacket is £54 in a sale, the price is reduced by 30% what is the sale price
Answer:
£37.80
Step-by-step explanation:
To find the sale price of a jacket during a 30% off sale, first subtract 0.30 from 1.00, obtaining 0.70, and then multiply the regular price (£54) by 0.70:
0.70(£54) = £37.80
The sale price of the jacket after a 30% discount is applied to the original price of £54 is £37.80.
Explanation:The student's question is about calculating the sale price of a jacket after a discount of 30% is applied to the normal price of £54. This is a typical percentage problem that can be solved using the following steps:
Calculate the discount amount by multiplying the original price by the discount rate.Subtract the discount amount from the original price to find the sale price.To calculate the discount amount: 30% of £54 = 0.30 × £54 = £16.20.
Then, subtract the discount amount from the original price: £54 - £16.20 = £37.80.
Therefore, the sale price of the jacket is £37.80.
The product of two numbers is −72. One of the factors is −9, what is the other factor?
Answer:
8.
Step-by-step explanation:
-9 x x = -72.x = 8.In all of the steps to solve this specific question, x is a variable to represent the other factor, that we are trying to find out the answer to, and our equation that we need to set up for this problem, is -9 times x equals -72, because -9 multiplied by the other factor that we are trying to solve for, which is x in this case, should equal -72. So then, to completely finish simplifying this equation, we need to divide -9 from both sides, so we can get our variable x, that we are trying to get the answer for, by itself. Then finally, you get x equal to 8, as our final, simplified answer. These are all of the steps to completely get the correct answer to your question.
Hope this helps!!!
Kyle.
Jason will use a 3 1/3 gallon pitcher to fill an empty 3/4 gallon water jug. How much water will he need in order to completely fill the water jug?
Answer:
Option B) Between 2 & 3 full pitchers
Step-by-step explanation:
Note In this problem the volume of the pitcher is 1/3 gallon instead of 3 1/3 gallon
The options of the questions are
A) Between 1 & 2 full pitchers
B) Between 2 & 3 full pitchers
C) About 1/2 of a full pitcher
D) About 1/4 of a full pitcher
so
we know that
To find the number of water pitchers Jason will need to fill the water jug, we will divide the amount of water needed to fill the jug by amount of water in the pitcher
[tex](3/4)/(1/3)=9/4\ water\ pitchers[/tex]
Convert to mixed number
[tex]9/4\ water\ pitchers=(8/4)+(1/4)=2(1/4)\ water\ pitchers[/tex]
therefore
Is Between 2 & 3 full pitchers
Despite having a 3 1/3 gallon pitcher, Jason will only need 3/4 gallon of water to fill his 3/4 gallon jug. The size of the pitcher doesn't matter, only the size of the jug.
Explanation:Considering that Jason is seeking to fill a 3/4 gallon water jug with a 3 1/3 gallon pitcher, it is evident that the entire capacity of the pitcher will not be required. To determine precisely the volume of water required, we examine the jug's capacity. Given that the jug has a maximum volume of 3/4 gallon, that is the exact volume of water Jason will require to fill it. Regardless of the pitcher's volume, it's the jug's capacity, which is 3/4 gallon, that establishes the quantity of water needed. Consequently, 3/4 gallon is the volume of water he needs to fill the jug.
Learn more about Volume Measurement here:https://brainly.com/question/1814591
#SPJ3
A phone number contains 7 digits. How many different numbers can be made using the digits 0–9 if the first digit is not 0 and all of the digits can be repeated?
The Options are:
A. 10 × 96
B. 9 × 107
C. 9 × 106
D. 107
Answer:
[tex]9 \cdot 10^6[/tex]
Step-by-step explanation:
A phone number contains 7 digits. How many different numbers can be made using the digits 0–9 if the first digit is not 0 and all of the digits can be repeated
In 7 digit phone number, the first number cannot be 0
So only 1 to 9 are used to get the first digit. 9 numbers can be used
other digits can use number from 0 to 9. 10 number can be used
So possible numbers can be made is
[tex]9 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10 \ times \ 10[/tex]
[tex]9 \cdot 10^6[/tex]
The correct option is C.[tex]\ 9 \times 10^6[/tex]
To solve the problem of finding how many different [tex]7[/tex]-digit phone numbers can be made using the digits [tex]0–9[/tex], with the first digit not being 0 and digits allowed to repeat, we can follow these steps:
1. First Digit Choices
The first digit has 9 possible choices ([tex]1[/tex] through [tex]9[/tex]) since it cannot be 0.
2. Remaining Digits Choices
Each of the remaining [tex]6[/tex] digits can be any of the [tex]10[/tex] digits ([tex]0[/tex] through [tex]9[/tex]).
So, the total number of different [tex]7[/tex]-digit phone numbers can be calculated by multiplying the number of choices for each digit:
[tex]\[9 \text{ choices for the first digit} \times 10 \text{ choices for each of the remaining 6 digits}\][/tex]
This can be represented mathematically as:
[tex]\[9 \times 10^6\][/tex]
Calculating [tex]\(10^6\)[/tex]
[tex]\[10^6 = 1,000,000\][/tex]
So,
[tex]\[9 \times 1,000,000 = 9,000,000\][/tex]
Someone help me out please
Answer:
Do you need work shown?
Step-by-step explanation:
(I don't know where to comment here)
OPTIONS OVER HERE AND FOR A BETTER VIEW OF THE QUESTION LOOK AT THE PICTURE THANK YOU AND PLEASE HELP!!!
Select the correct answer from each drop-down menu.
QUESTION
FOR THIS EXPRESSION, A = ((( 15 OR 4 OR 7 ))) . B = (( 7 OR 4 OR 15 ))) , C = ((( 4 OR 15 OR 7)))
Answer:
a = 15
b = 7
c = 4
Step-by-step explanation:
Given in the question an expression [tex]\sqrt[4]{15}^{7}[/tex]
This expression can be written as [tex]15^{\frac{7}{4} }[/tex]
As we know that roots are most often written using a radical sign, like this, [tex]\sqrt[n]{x}[/tex] But there is another way to represent the taking of a root.
You can use rational exponents instead of a radical. A rational exponent is an exponent that is a fraction. For example, [tex]\sqrt[n]{x}[/tex] can be written as [tex]x^{\frac{1}{n} }[/tex]
Secondly two powers having same base can be multiply
[tex]x^{n}(^{m})=x^{nm}[/tex]