Answers
Answer:
The coordinates of the point of intersection is (2, 7)
Step-by-step explanation:
From the graph, we have the two intersecting straight lines each described as follows;
The first straight line graph from the left, we have;
y-intercept = (0, 5), x-intercept = (-5, 0) therefore, the slope, m = (0 - 5)/(-5 - 0) = 1
The equation of the graph is slope-intercept form is y - 5 = 1×(x - 0)
Which gives;
y = x + 5.........................(1)
The second lie graph has y-intercept = (0, 9), x-intercept = (9, 0) therefore, the slope, m = (0 - 9)/(9 - 0) = -1
The equation of the graph in slope-intercept form is y - 9 = -1×(x - 0)
Which gives;
y = -x + 9.......................(2)
To find the point of intersection, we equate equation (1) to equation (2), which are the y-value function of x, we have;
x + 5 = -x + 9
x + x = 9 - 5
2·x = 4
x = 4/2 = 2
x = 2
From either equation (1) or equation (2), we can find the value of y as follows;
y = -x + 9, where x = 2 gives;
y = -2 + 9 = 9 - 2 = 7
y = 7
The coordinates of the point of intersection is (2, 7).
Related Questions
Someone pls HELP MEEEE i’m giving the rest of my points away . i have like 20 mins to turn this in
Answers
Answer:
1) 27.89
2) 20
Step-by-step explanation:
#1)
9.5x + 75 --> 340
340 - 75 --> 265
265 / 9.5 = 27.89
#2)
120 / 6 =
20 minutes
The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00?
Answers
Answer:
239 ft².
Step-by-step explanation:
Let P represent the price for tiling.
Let S represent the size of the room.
From the question,
Price (P) varies directly as the size (S) i.e
P & S
P = KS
Where K is the constant of proportionality.
Next, we shall determine the value of K as follow
Price (P) = $ 4224
Size (S) = 264 ft²
Constant of proportionality (K) =?
P = KS
4224 = K × 264
Divide both side by 264
K = 4224/264
K = 16
Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.
This is illustrated below:
Price (P) = $ 3824
Constant of proportionality (K) = 16
Size (S) =?
P = KS
3824 = 16 × S
Divide both side by 16
S = 3824/16
S = 239 ft²
Therefore, the size of the kitchen is 239 ft².
this math question is about logarithm
Answers
Answer:
(k+2h)/(k+h)
Step-by-step explanation:
log 6 12 = (log a 12)/(log a 6) ( Log base change property)
log a 12 = log a (3*4) = log a 3 + 2*log a 2 = k+2h
log a 6 = log a (2*3) = log a 3 + log a 2 = k+h
log 6 12 = (k+2h)/(k+h)
what equation accurately represent this statement three less than 4 times a number is less than 12
Answers
Answer: 4t - 3 < 12
Step-by-step explanation:
What is the hundredth term in the sequence 15, 22, 29, 36, 43…?
A. 50
B. 78
C. 700
D. 708
Answers
Answer:
708
Step-by-step explanation:
We are adding 7 each time
15+7 = 22
22+7 = 29
29+7 = 36
So the common difference is 7
The first term is 15
The formula is
an = a1+d(n-1) where n is the term number
an = 15+7(n-1)
We want to find the 100th term
a100 = 15+7(100-1)
a100 = 15+7(99)
= 15+693
= 708
find the value of x
Answers
angle at center is twice angle at circumference
so therefore the lengths of WU and WV are proportional along with WC and WT.
WU / WV = WC / WT
4 / 2 = 11 / x
2 = 11 / x
x = 11 / 2 or 5.5 u
2^3*2^4=2^x
Solve for X PLZ HELP
Answers
Answer:
7
Step-by-step explanation:
if the bases of the exponents are the same then we can add the powers. so 2^3 * 2^4 = 2^7 = 128.
Answer:
7
Step-by-step explanation:
2^3⋅2^4= 2^7
2^7=2^x
since it had the same base you wouldn't need to worry about it you can just focus on the exponent.
7=x
swap it over
x=7
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
Answers
Answer:
Quaterly
Step-by-step explanation:
Think of a value for a and a value for x so that the triangles are still similar.
Answers
Answer:
x=6
a=9
Step-by-step explanation:
Because 21 is 1.5 times 14, and 15 is 1.5 times 10, a has to be 1.5 times x. Also, x must be more than 4 in order for it to make a triangle. To make it simple, I'd use either 6 or 8. Just for ease, I'll use 6.
x=6
a=6*1.5=9
Identify whether each phrase is an expression, equation, or inequality.
Term
Phrase
Expression
3 - 53 =y
Inequality
7-5 <2.9
2 + 0
Equation
24"
t
Answers
Answer:
The identities of the terms are;
3 - 53 = y is an equation
7.5 < 2.9 is an inequality
2 + 0 is an expression
t is a term
24" is a term
Step-by-step explanation:
An equation is an expression with the equal to sign
3 - 53 = y is an equation
An inequality is a mathematical expression that contains an inequality sign
7.5 < 2.9 is an inequality
A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷
t and 24" are terms.
please help!!
Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
Answers
Answer:
C
Step-by-step explanation:
A line parallel to a side of the triangle and it intersects the other two sides, then it divides those sides proportionally, that is
[tex]\frac{a}{b}[/tex] = [tex]\frac{d}{c}[/tex] → C
Someone plz round 6.675 to the nearest hundredth
Answers
Answer:
6.68
Step-by-step explanation:
To round 6.675 to the nearest hundredth consider the thousandths’ value of 6.675, which is 5. Therefore, the hundredths value of 6.675 increases by 1 to 8.
6.675 rounded to the nearest hundredth = 6.68
Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the full tank in 6 hours. If the three pipes A, B, and Care opened at the same time, find how long it will take for the tank to be full. *
Answers
Answer:
30/11 (hours)
Step-by-step explanation:
Pipe A can fill the tank until it is full in 3 hours.
=> In 1 hour, pipe A can fill 1/3 of tank
Pipe B can fill the tank until it is full in 5 hours.
=> In 1 hour, pipe A can fill 1/5 of tank
Pipe C can empty the full tank in 6 hours.
=> In 1 hour, pipe A can empty 1/6 of tank
Assume that we open 3 pipes A, B, and C at the same time.
Then, in 1 hour, the amount of water in tank is:
A = 1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)
=> The time to fill up the tank is:
T = 1/A = 1/(11/30) = 30/11 (hours)
Answer:
30/11
Step-by-step explanation:
Imagine the tank can hold x litre of water
So,A can fill x/3 litre water per hour
And B can fill x/5 litre water per hour
And C can reduce x/6 litre of water per hour which is filled by A and B.
So the gross calculation per hour is:
(x/3+x/5)-x/6
=11x/30
Now suppose it tooks 'a' hour to fill the tank.
So, a(11x/30)=x
⇨ a= (30/11x)x
⇨a=30/11
HELP ME PLEASE!!!! ITS DUE TODAY
Answers
Answer:
A: (draw figure 3 and on the right end add two more tiles on the top and bottom stack of tiles)
B: Figure 10 will have 20 tiles because each figure is increasing by 2 tiles.
Step-by-step explanation:
The figures are increasing by 2 so we can multiply 2 by 10 to get the number of tiles on the 10th figure.
Determine the intercepts of the line.
-6x + 3y = -7
z-intercept:
y-intercept:
Answers
Answer:
(7/6, 0) and (0,-7/3)
Step-by-step explanation:
I think you mean x-intercept and y-intercept not z-intercept and y-intercept. The first step is to convert the equation to slope intercept form:
-6x+3y=-7
3y=6x-7
y=6/3x-7/3
y=2x-7/3
Now, to find the x-intercept we find the value of x when y is 0.
0=2x-7/3
7/3=2x
7/6=x so the x-intercept is (7/6,0)
Now, to find the y-intercept we find the value of y when x is 0.
y=2(0)-7/3
y=0-7/3
y=-7/3 so the y-intercept is (0,-7/3)
How to do this question plz answer me step by step plzz plz
Answers
Answer:
New depth of the milk will be 4 cm.
Step-by-step explanation:
If the carton (shaded side) is standing vertically, milk in the box will acquire the dimensions of the box.
Length of the cuboid formed by the the milk = 8 cm
Width = 5 cm
Height = 12 cm
Volume of the cuboid formed by the milk in the carton = Length × width × height
V = 8 × 5 × 12
= 480 cm³
If the carton is turned so that the carton stands on the shaded face,
Volume of the milk remains unchanged but the dimensions of the cuboid formed by the milk inside the carton will get changed.
Length = 15 cm
Width = 8 cm
Height = h cm
Then volume of the cuboid = Length × width × height
V = 15 × 8 × h
480 = 120h
h = [tex]\frac{480}{120}[/tex]
h = 4 cm
Therefore, new depth of the milk will be 4 cm.
Will Mark Brainlest Help Please ,,,,
Answers
Step-by-step explanation:
from the second:
A=[3 -1]. -2B
[-5 0]
input this into 1
2([3 -1]) -(2B) -B =[1 3]
([-5 0]). [0 5]
[6 -2] -4B-B=[1 3]
[-10 0]. [0 5]
-5B=[1 3] -[3 -1]
[0 5]. [-5 0]
-5B= [1-3 3+1]
[0+5 5+0]
B= [-2/5 4/5]
[1 1]
A=[(19/5) (3/5)]
[-3. 2]
using the formula I derived
that's how I got A
Need help pls will give you a good rating.
Answers
Answer:
x+4
.....................
Answer
[tex] \boxed{x + 4}[/tex]
Option C is the correct option
Step by step explanation
Let's find the expression which represents the length of the box:
[tex] \mathsf{length \times width \times height \: of \: prism \: = \: volume \: of \: prism}[/tex]
[tex] \mathsf{lengh \times \: (x - 1) \times (x + 8) = {x}^{3} + 11 {x}^{2} + 20x - 32}[/tex]
[tex] \mathsf{length = \frac{ {x}^{3} + 11 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]
Write 11x² as a sum
[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} + 20x - 32 }{(x - 1)(x + 8)} }[/tex]
Write 20x as a sum
[tex] \mathsf{ = \frac{ {x}^{3} - {x}^{2} + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)}}[/tex]
Factor out x² from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12 {x}^{2} - 12x + 32x - 32 }{(x - 1)(x + 8)} }[/tex]
Factor out 12 from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32x - 32 }{(x - 1)(x + 8)} }[/tex]
Factor out 32 from the expression
[tex] \mathsf{ = \frac{ {x}^{2}(x - 1) + 12x(x - 1) + 32(x - 1) }{(x - 1)(x + 8)} }[/tex]
Factor out x+1 from the expression
[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 12x + 32) }{(x - 1)(x + 8)} } [/tex]
Factor out 12x as a sum
[tex] \mathsf{ = \frac{(x - 1)( {x}^{2} + 8x + 4x + 32) }{(x - 1)(x + 8)} }[/tex]
Reduce the fraction with x-1
[tex] \mathsf{ = \frac{ {x}^{2} + 8x + 4x + 32 }{(x + 8)} }[/tex]
Factor out x from the expression
[tex] \mathsf{ = \frac{x(x + 8) + 4x + 32}{(x + 8)} }[/tex]
Factor out 4 from the expression
[tex] \mathsf{ = \frac{x(x + 8) + 4(x + 8)}{x + 8} }[/tex]
Factor out x+8 from the expression
[tex] \mathsf{ = \frac{(x + 8)(x + 4)}{x + 8} } [/tex]
Reduce the fraction with x+8
[tex] \mathsf{ = x + 4}[/tex]
hence, x+4 is the expression that represents the length of a box.
Hope I helped!
Best regards!
In right triangle ΔABC (m∠C = 90°), point P is the intersection of the angle bisectors of the acute angles. The distance from P to the hypotenuse is equal to 2 in. Find the perimeter of △ABC if AB = 12 in. PLEASE HELP ILL AWARD MORE BRAINLY POINTS
Answers
Answer:
28 inches
Step-by-step explanation:
The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.
In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.
The perimeter of the triangle is ...
P = DA +DB +FA +EB +CF +CE
Using the above relations, this can be written as ...
P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)
We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...
P = 2(12 in) + 2(2 in) = 28 in
The perimeter of triangle ABC is 28 inches.
A bank is offering 5.5% simple interest on a savings account. If you deposit $15000, how much interest will you earn in six year?
What is this question asking for?
What Kinda Interest?
Answers
Answer:
a. $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
Step-by-step explanation:
a. We want to calculate the amount of interest to be earned in six years
To calculate this, we use the formula for simple interest.
Mathematically;
Simple interest I = PRT/100
Where P is the principal which is the amount deposited = $15,000
R is the rate which is 5.5%
T is the time which is 6 years
Substituting these values in the simple interest formula, we have
I = (15,000 * 5.5 * 6)/100 = $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
If QR = 3x; LM - 8x -17; and ST = 31 calculate LM.
Answers
Answer:
5
Step-by-step explanation:
The midsegment of a trapezoid is equal to one half the sum of the bases.
1. Set up the equation using the midsegment formula: 1/2 (QR + ST)
1/2 (3x + 31) = 8x - 17
2. Solve
1.5x + 15.5 = 8x - 17
32.5 = 6.5x
x = 5
Answer:
[tex]\huge \boxed{23}[/tex]
Step-by-step explanation:
QR < LM < ST
LM is the middle segment, it is in between the length of QR and ST.
LM is also the average or mean of QR and ST.
(QR+ST)/2 = LM
(3x+31)/2 = 8x-17
Multiply both sides by 2.
(2)(3x+31)/2 = (2)8x-17
3x + 31 = 16x - 34
Subtract 16x and 31 from both sides.
3x + 31 - 16x - 31 = 16x - 34 - 16x - 31
-13x = -65
Divide both sides by -13.
(-13x)/-13 = -65/-13
x = 5
Substitute x = 5 for LM.
8(5) - 17
40 - 17
= 23
what is the lcm of 7÷25 and 3÷25
Answers
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
write -7.08 as a mixed number or fraction in a simplest from
Answers
Answer:
7 2/5
Step-by-step explanation:
7.08 to improper fraction:
708/100
= 7 2/25
the cube root of 2 to the seventh power
Answers
Answer:
4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal
Step-by-step explanation:
Simplify the following:
(2^(1/3))^7
Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.
Multiply exponents. (2^(1/3))^7 = 2^(7/3):
2^(7/3)
Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.
2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):
2^(6/3) 2^(1/3)
Hint: | Divide 6 by 3.
6/3 = (3×2)/3 = 2:
2^2 2^(1/3)
Hint: | Evaluate 2^2.
2^2 = 4:
Answer: 4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal
In 1 through 3, what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
Answers
Answer:
7000 (7 thousand)
700 (7 hundred)
20 (2 tens)
2 (2 units)
Step-by-step explanation:
what is the relationship between the values of the given digits?
1. The 7s in 7,700
2. The 2's in 522
From the knowledge of place values;
7,700 could be broken down thus :
7000 + 700 + 0 + 0
The first 7 depicts thousands as it has 3 trailing digits (7000)
The second 7 depicts hundred as it has 2 trailing digits (700)
522 could be broken down thus :
500 + 20 + 2
From 522
The first '2' has one trailing digit = tens
The ending / last digit ia always = Unit value
19. If CD _|_ EF, M<ECH = x + 5 and m<HCD = 3x - 7 find each missing value.
G# F
a) x =
b) m<ECH=
c) m<HCD=
d) m<GCF =
e) m<ECG=
f) m<GCD =
Answers
[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]
Given:
[tex]m \angle ECH = x + 5\\m \angle HCD = 3x - 7[/tex]
Note the following:
Since CD is perpendicular to EF, therefore:
[tex]m \angle ECD = 90^{\circ}\\m \angle FCD = 90^{\circ}[/tex]
Thus:
a. Find x
[tex]m \angle ECH + m \angle HCD = m \angle ECD[/tex]
Substitute
[tex](x + 5) + (3x - 7) = 90[/tex]
Add like terms
[tex]x + 5 +3x - 7 = 90\\4x -2 = 90\\4x = 90 + 2\\4x = 92[/tex]
Divide both sides by 4
[tex]x = 23[/tex]
b. Find [tex]m \angle ECH[/tex]
[tex]m \angle ECH = x + 5[/tex]
Plug in the value of x
[tex]m \angle ECH = 23+ 5\\m \angle ECH =28^{\circ}[/tex]
c. Find [tex]m \angle HCD[/tex]
[tex]m \angle HCD = 3x - 7\\m \angle HCD = 3(23) - 7\\m \angle HCD = 62^{\circ}[/tex]
d. Find [tex]m \angle GCF[/tex]
[tex]m \angle GCF = m \angle ECH[/tex] (vertical angles are congruent)
Substitute
[tex]m \angle GCF = 28^{\circ}[/tex]
e. Find [tex]m \angle ECG[/tex]
[tex]m \angle ECG = 180 - m \angle GCF[/tex] (angles on a straight line)
Substitute
[tex]m \angle ECG = 180 - 28\\m \angle ECG = 152^{\circ}[/tex]
f. Find [tex]m \angle GCD[/tex]
[tex]m \angle GCD = m\angle FCD + m \angle GCF[/tex]
Substitute
[tex]m \angle GCD = 90 + 28\\m \angle GCD = 118^{\circ}[/tex]
Therefore:
[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]
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https://brainly.com/question/18292462
Use the distributive property to rewrite the given expression without parentheses.
7(x+2)
7(x+2) =
Answers
Answer:
7x+14
Step-by-step explanation:
The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.
In this case it will be 7×x and 7×2
7(x+2)=7x+14
pls answer i will mark brainliest
Answers
Answer:
Part one:
In terms of price;
[tex]2x + \frac{5}{2} y = 19 \\ \\ 4x + 5y = 38 - - - (equation \: \: 1)[/tex]
In terms of people, each person will get one snack:
[tex]x + y = 8 - - - (equation \: \: 2)[/tex]
Part two:
[tex]in \: equation \: 2 : \\ x = 8 - y \\ substitute \: for \: x \: in \: 1 : \\ 4(8 - y) + 5y = 38 \\ 32 - 4y + 5y = 38 \\ y = 6 \\ \\ therefore : x = 2[/tex]
Sam bought 2 bags of chips
What is the formula to find the area of the sector?
Answers
Answer:
There are 3 ways
Step-by-step explanation:
The formula for a sector's area is:
1. A = (sector angle / 360 ) * (pi *r2)
2. A = (sector angle / (2*pi)) * (pi * r2)
3. A = (fraction of the circle) * (pi * r2)
A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (
Answers
Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST