Answer:
-15
Step-by-step explanation:
In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.
Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.
Thus, we have;
2a(b-3) + 5b + _
Now, putting -15 will give us the same expression in the first bracket and this gives us the following;
2a(b-3) + 5b-15
2a(b-3) + 5(b-3)
So we can have ; (2a+5)(b-3)
Hence the constant used is -15
Kate travels for 1 1/3hour to visit a friend
who lives 4 1/2 miles away. Martin travels 4 1/4
miles to visit his friend, and it takes him 1 1/5
hours. Who travels more miles per hour?
Answer:
Martin
Step-by-step explanation:
Calculate their speeds with the formula s = d/t (speed = distance/time)
Calculate Kate's speed:
s = d/t
s = 4.5/1.33
s = 3.375 mph
Calculate Martin's speed:
s = d/t
s = 4.25/1.2
s = 3.541 mph
So, Martin travels more miles per hour
Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Answer:
6.11km/hr
Step-by-step explanation:
Let the speed that Kelli swims be represented by Y
Speed of the river = 5km/hr
Distance = Speed × Time
Kelli swam upstream for some distance in one hour
Swimming upstream takes a negative sign, hence:
1 hour ×( Y - 5) = Distance
Distance = Y - 5
She then swam downstream the same river for the same distance in only 6 minutes
Downstream takes a positive sign
Converting 6 minutes to hour =
60 minutes = 1 hour
6 minutes =
Cross Multiply
6/60 = 1/10 hour
Hence, Distance =
1/10 × (Y + 5)
= Y/10 + 1/2
Equating both equations we have:
Y - 5 = Y/10 + 1/2
Collect like terms
Y - Y/10 = 5 + 1/2
9Y/10 = 5 1/2
9Y/ 10 = 11/2
Cross Multiply
9Y × 2 = 10 × 11
18Y = 110
Y = 110/18
Y = 6.1111111111 km/hr
Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.
PT.1 Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Choose the most logical value for the variable to represent.
Let x = Kelli's swimming speed in still water
PT.2 Which expression represents the distance Kelli traveled upstream?
1(x – 5)
PT.3 Which expression represents the distance Kelli traveled downstream?
0.1(x + 5)
PT.4 Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about 6.11 km/hour.
Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation?
0.75x+0.8(x + 10) = 101
Answer:
0.75x+0.8(x+10)=101
Step-by-step explanation:
Jared attempted x shots and made 75% of them, or 0.75x. Zach attempted 10 more shots than Jared did, which is represented as x + 10. He made 80% of them, or 0.8(x + 10). Together, they made 101 shots. So, add the two expressions and set the sum equal to 101:
0.75x + 0.8(x + 10) = 101.
I need help please i will do brainliest
A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price
Answer:
162.5 Cedis
Step-by-step explanation:
Cost Price= 125
Profit % = 30%
Selling price=?
Selling price= Cost price+ profit
Profit = ?
[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]
[tex]30 \% = \frac{x}{125} \times 100[/tex]
[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]
[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]
Profit = 37.5 gh Cedis
Selling price= 125+37.5
Selling price= 162.5 gh Cedis
The selling price of a bag is 162.5Cedis.
It is required to find the selling price.
What is profit?The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.
Given that :
Let the profit be x.
Cost Price= 125
Profit % = 30%
profit%=profit/cp*100
30=profit/125*100
3750=100x
x=37.5
profit=37.5
Selling price= Cost price+ profit
Selling price=125+37.5
Selling price=162.5ghcedis
So, the selling price of a bag is 162.5Cedis.
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how many words can be formed by using the W,X,Y,Z if repetitions is not allowed?
- 30
- 24
- 18
- 12
Answer:
24
Step-by-step explanation:
What you have here is a permutation, seeing as each element can only be used once.
We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter
However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.
Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.
Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.
Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter
The way to calculate how many permutations we have without repetition is using factorials
N!
Where N is the number of elements you have.
In this case, it would be 4!
4! is 4 * 3 * 2 * 1
Which equals 24
If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on
Evaluate the problem
Answer:
.6
Step-by-step explanation:
First find < ABC
Since this is a right triangle, we can use trig functions
tan < ABC = opp / adj
tan < ABC = 2/4
Take the inverse tan of each side
tan ^-1 tan < ABC = tan ^-1 2/4
< ABC = 26.56505118
Multiply by 2
53.13010235
Take the cos
cos (53.13010235)
.6
Help now for brainliest,5stars and thanks.Find the values of x in the range 0≤x≤180° for which 15sin^2 x+11cox-17=0
Answer:
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
Step-by-step explanation:
Given equation is:
[tex]15sin^2 x+11cosx-17=0[/tex]
To find:
Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].
Solution:
First of all, let us recall one identity of square of sine and square of cosine.
Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.
[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]
So
Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.
[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]
So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]
[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]
Find the value of y.
148°
y
x
y = [?]°
Answer:
y=90 degree
Step-by-step explanation:
bcz this triangle is drawn in the semi-circle and the greatest angle of triangle in a semi-circle is always right angle.
Evaluate the expression below for x =4 and y = 5.
x2 + 3(x + y)
When x = 4 and y = 5, x2 + 3(x + y)= |
(Type an integer or a decimal.)
Answer:
positive 35
Step-by-step explanation:
x2 + 3(x + y) given
4(2) + 3(4+5) problem
4(2) + 3(9)
8 + 27= 35
PLS HELP!! Consider the exponential functions f, g, and h, defined as shown. Determine which function or functions have each key feature. Drag the tiles to the correct boxes. Not all tiles will be used.
Answer:
1) increases on all interval of x = only g(x)
2) approaches an integer as x approaches -∞ = only f(x)
3) y-intercept at (0, 4) = only g(x)
4) x-intercept at (1, 0) = f(x) and h(x)
Step-by-step explanation:
1) The functions that increases on all interval of x are;
f(x) = -2(3)ˣ + 6 decreases on all interval of x
The function g(x) which is 4 × 4ˣ increases on all interval of x
The function h(x) is observed to be decreasing as x increases, therefore, the only function that increases on all interval of x = g(x)
2) The function that approaches an integer as x approaches -∞ = -2(3)ˣ + 6
-2(3)ˣ + 6 approaches 6 as x approaches -∞ which is only f(x)
3) The functions that have a y-intercept at (0, 4) is only g(x)
4) The function that have a x-intercept at (1, 0) are f(x) and h(x).
Answer:
A) f(x) and g(x)
B) only g(x)
C) All three functions
D) f(x) and h(x)
Step-by-step explanation:
In my uploaded image on the test I have gotten C) wrong but if you graph all three functions, you can see that all three functions have the same style of -∞
end behavior so I think that would be the most logical answer.
In comparing two distributions, which attribute would you not compare?
A. Shape
B. Center
C. Marginal frequency
D. Spread
Answer:
The correct option is;
C. Marginal frequency
Step-by-step explanation:
The objective of comparison of two distributions is to check the significant difference from each other
The general measures used to compare the difference between distributions are the measures of centers such as the mean, the measures of spread such as the standard deviation and the shape of the compared distribution curves
Marginal frequencies are the values found in the total row and total column portion of a two way frequency distribution table
The marginal frequency is used to calculate the marginal relative frequency
The values of the marginal frequency, which is a sum, does not characterize the details of a distribution to a large extent.
Answer:
C. Marginal frequency
Step-by-step explanation:
Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express coordinates as fractions, using the slash mark (/) for the fraction bar. (-12, -3) (3, -8)
Answer:
[tex]=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]
Step-by-step explanation:
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\\\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-12,\:-3\right),\:\left(x_2,\:y_2\right)=\left(3,\:-8\right)\\\\=\left(\frac{3-12}{2},\:\frac{-8-3}{2}\right)\\\\=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]
The sales tax for an item was $15.60 and it cost $390 before tax. Find the sales tax rate. Write your answer as a percentage.
Answer:
15.60 times 100 divided by 390=4%
Step-by-step explanation:
The required sales tax rate percentage is 4%.
The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.
the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
= 15
It shows that 10 percent of 150 is 15.
sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost * 100
= 15.60/390 * 100
= 0.04 * 100
= 4 %
Thus, the required sales tax rate percentage is 4%.
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Someone pls help . Thank you sm☄️ .
1) 3 is the Coefficient.
2) 10 is the constant.
3) 10.8 is the ans.
This diagram is a straightedge and compass construction. A is the center of one circle,
and B is the center of the other. Explain how we know triangle ABC is equilateral.
ABC is a equilateral triangle .
Proof :-
Let's assume both circles as C1 and C2 [ as shown in the figure ]
AB is the radius of circle C1 AB is the radius of Circle C2AC is the radius of circle C1.
BC is the radius of circle C2 .
AB and AC both are radius of circle C1 so both are equal ie AB = AC .
AB and BC both are radius of circle C 2 so both are equal ie AB = BC .
Hence we conclude that .
AB = BC = AC.
So the triangle is equilateral triangle.
Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are about to eat it, an unexpected guest arrives and Nandini has to now re-divide the halwa into five equal portions. By what percentage has each family member's share reduced due to this? A. 5% B. 10% C. 20% D. 25%
Answer:
5%
Step-by-step explanation:
Total 'halwa' made = 1
Divided into four equal portion = 1/4
Arrival of an unexpected guest = 1/5
By what percentage has each family member's share been reduced:
Change in the sharing proportion:
Previous share ratio - new sharing ratio
(1/4 - 1/5) = (5 - 4) / 20 = 1/20
That means total reduction in the sharing = 1/ 20
Since each member comes contributed equally:
Reduction in each family member's share ;
(1 / 20) ÷ 4
(1 / 20) * 1/4 = 1/ 80
Percentage reduction:
(Reduction / original share) * 100%
[(1/80) ÷ (1/4)] * 100
(1/80 * 4/1) * 100%
(1/20) * 100%
= 5%
Reduction in each family members share = 5%
(x-yi)(3+5i) is the conjugate of 6+24i
Answer:
x=-3
y=3
(-3-3i)(3+5i)
Step-by-step explanation:
[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]
and we have that must equal
6-24i
3x+5y=6
5x-3y=-24 and if we work it we found out that the solutions are
x=-3 and
y=3
What type of triangles has no equal sides and one right angle?
Answer:
Scalene Right Triangle
Step-by-step explanation:
A possible type of triangle that has no equal sides and one right angle is a right triangle.
Right triangles have just one angle that is equal to 90°, and they can be either isosceles or scalene triangles.
Hope this helped!
explain how the phrase oh heck another hour of algebra can help a student recall the trigonometric ratios
Answer:
its a mnemonic
Oh Heck Another Hour Of Algebra
(O = opposite side, H = hypotenuse ) = sine
(A = adjacent side, H = hypotenuse ) = cosine
(O = opposite side, A = adjacent ) = tangent
What is the solution to this system of equations?
5x + 2y = 29
x + 4y= 13
Answer:
x = 4.5
y = 3.25
Step-by-step explanation:
Use elimination
5x + 2y = 29
x + 4y = 13 (-5)
4y(-5) = 13(-5)
2y = 29
-20y = -65
y = 3.25
Sub it back into the equation
5x + 6.50 = 29
5x = 22.5
x = 4.5
The teacher wants to make a fruit punch for the class party. She needs 30 quarts of juice. If there are 15 kids bringing in juice, how many pints should each person bring?
Answer:
4 pints
Step-by-step explanation:
30 quarts ÷ 15 kids = 2 quarts per kid
there are 2 pints in a quart so..
2 quarts per kid x 2 pints per quarter = 4 pints
Solve for X in the diagram below
PLS HELP BRAINLIST AND A THANK YOU WILL BE REWARDED :)
The 3 angles need to equal 180
The middle angle is given as 100.
180 -100 = 80
There is an x on each side so you have 2x
2x = 80
X = 80/2
X = 40 degrees
[tex] \frac{5 + n}{4} = - 1[/tex]
What is n?
Answer:
n= -9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
5 + n
==== = -1
4
Multiply both sides by 4
5 + n = - 1 * 4
5 + n = - 4
Subtract 5 from both sides
5-5 + n = - 4 - 5
n = - 9
Congratulations on being able to use latex.
I REALLY NEED HELLP with these 3 questions PLLZZZZ!!!!
Answer:
Below
Step-by-step explanation:
6)
The sum that we have is 85 +99
We want to express it as the product of a whole number thar is greater than 1 and a sum of two whole numbers.
Notice that: 85 = 84+1
● 85 + 99 = 84 + 1 + 99 = 84 + 100
84 and 100 are even numbers so we can factor using 2.
● 84 + 100 = 2(42 +50)
2 is greater than one and 42+50 is the sum of two whole numbers so all the conditions are satisfied.
■■■■■■■■■■■■■■■■■■■■■■■■■■
7)
Dasha go on business trips every 9 months while Charlie go every 6 months.
They came back at the same time.
So Charlie has to wait 6 months before going and Dasha nine months.
Dasha will be alone home for 3 months so she doesn't need to hire someone.
Here is what happens:
● Both Dasha and Charlie are home.
● After 6 months Charlie go and Dasha is at home
● after 3 months Dasha goes also and Charlie is home
● after 3 months charlie go and Dasha is home
● after 3 months both are home.
● aftet 3 months they both go
So the period is:
● 6+3+3+3+3 = 18
So after 18 months they should hire someone.
The picture below makes the understanding easier. ( x is Charlie and y is Dasha)
■■■■■■■■■■■■■■■■■■■■■■■■■■
8)
Pime factorisation
● 96÷2= 48
● 48÷2= 24
● 24 ÷ 2 = 12
● 12 ÷ 2 = 6
● 6÷2 = 3
● 3÷3 = 1
=> 96 = 2 × 2 ×2×2×2 ×3 =2^5 ×3
● 80÷ 2 = 40
● 40 ÷ 2 = 20
● 20÷2 = 10
● 10÷2 = 5
● 5÷5 = 1
=> 80 = 2×2×2×2×5 = 2^4 × 5
So the GCF is 2^4 wich is 16
He can make 16 party
● 80÷16 = 5
There will be 5 boxes of raisin in each one
● 96÷16 = 6
There will be 6 pencils in each party
A lawn-mowing company is trying to grow its business. It had 18 clients when they started its business and wants to increase by 4 new clients each week. Use an arithmetic sequence to write a function to represent this real-world situation and determine the range of the function for the first four weeks of data.
Answer: y=18+4x
Step-by-step explanation: Let y stand for the number of customers the business has in total, and x stand for the number of weeks that have passed. If the business increases by 4 clients per week as described by the scenario, then the range will go as followed: 18, 22, 26, 30...
Simplify. Can you explain it also?
[tex] \frac{9 {c}^{3} {de}^{2} }{12 {c}^{2}d {e}^{3} }[/tex]
Answer:
The answer is
[tex] \frac{3c}{4e}[/tex]Step-by-step explanation:
[tex] \frac{9 {c}^{3}d {e}^{2} }{12 {c}^{2} d {e}^{3} } [/tex]To solve the fraction reduce the fraction with d
That's we have
[tex] \frac{9 {c}^{3} {e}^{2} }{12 {c}^{2} {e}^{3} } [/tex]Next simplify the expression using the rules of indices to simplify the letters in the fraction
For c
Since they are dividing we subtract the exponents
We have
[tex] {c}^{3} \div {c}^{2} = {c}^{3 - 2} = c^{1} = c[/tex]For e
[tex]e^{2} \div {e}^{3} = e^{2 - 3} = {e}^{ - 1} = \frac{1}{e} [/tex]Substituting them into the expression we have
[tex] \frac{9c}{12e} [/tex]Reduce the fraction by 3
We have the final answer as
[tex] \frac{3c}{4e} [/tex]Hope this helps you
is this right? someone please check?
Answer:
The answer looks correct.
Step-by-step explanation:
All the other option doesn't match the above question's statement.
The last answer is the correct (in my opinion)
Answer:
Absolutely Correct
Step-by-step explanation:
Based on the definition of midpoint;
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
meaning the distance from the midpoint to one end is the same as the distance to the other end
Follow the process of completing the square to solve x2 = -4x + 3
Answer:
x1 = 0.64575
x2 = -4.64574
Step-by-step explanation:
Step 1: We want to rearrange the equation so all the variables are on one side
0 = -x² - 4x + 3
Step 2: We take out -1 in the first 2 terms so a = 1
0 = -(x² + 4x) + 3
Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets
b = 4
4/2 = 2
2² = 4
0 = -(x² + 4x + 4 - 4) + 3
Step 4: Move the -4 out remembering to apply the -
= -(x² + 4x + 4) + 4 + 3
Step 5: We notice is inside the brackets is a perfect square
0 = -(x + 2)² + 7
Therefore the vertex form of the equation is
y = -(x + 2)² + 7
Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x
0 = -(x + 2)² + 7
-7 = -(x + 2)²
7 = (x + 2)²
[tex] \sqrt{7 } = x + 2 [/tex]
[tex]x = \sqrt{7} - 2[/tex]
1st Solution:
x = +2.64575 - 2
x = 0.64575
2nd Solution:
x = -2.64575 - 2
x = -4.64574
SOS...Complete the following proof. 25 POINTS!!!
Answer:
See below
Step-by-step explanation:
Given:
AC ≅ CE
To Prove:
ΔABC ≅ ΔEDC
Proof:
Statements | Reasons
ΔABC ⇔ ΔEDC |
AC ≅ CE | Given
∠ACB ≅ ∠ECD | Vertical Angles are congruent
∠BAE ≅ ∠DAE | Alternate Interior Angles are Congruent
ΔABC ≅ ΔEDC | S. A . A Postulate
[Hence Proved]
