Given:
The product of two consecutive numbers is 72.
To find:
The two numbers by using the quadratic equation.
Solution:
Let the two consecutive numbers are x and (x+1).
The product of two consecutive numbers is 72.
[tex]x(x+1)=72[/tex]
[tex]x^2+x-72=0[/tex]
Splitting the middle term, we get
[tex]x^2+9x-8x-72=0[/tex]
[tex]x(x+9)-8(x+9)=0[/tex]
[tex](x+9)(x-8)=0[/tex]
Using zero product property, we get
[tex]x+9=0[/tex] and [tex]x-8=0[/tex]
[tex]x=-9[/tex] and [tex]x=8[/tex]
If [tex]x=-9[/tex], then
[tex]x+1=-9+1[/tex]
[tex]x+1=-8[/tex]
If [tex]x=8[/tex], then
[tex]x+1=8+1[/tex]
[tex]x+1=9[/tex]
Therefore, the two consecutive numbers are either 8,9 or -9,-8.
When y = 5; 3y - 21=
the area of a figure is 36cm2. Give 3 shapes of figure. where possible give 3 possible sets of dimensions for each possible shape. answer in less than one minute pls)
Answer:
121
Step-by-step explanation:
can someone help me how to do this problem >_<
how do I found X with this triangle?
Answer: 14
tip: search up oster Miller triangle calculator
You have $45 n your bank account
You start a lawn mowng busness
making $12 per own
How many lawns wl you have to
mow before you have more than
$1179
An item is regularly priced at $ 70. It is on sale for 40% off the regular price. How much in dollars) is discounted from the
regular price?
Answer:
42
Step-by-step explanation:
70 minus 40 percent equals 42
Almost 36% of the students at a middle school are seventh graders. What percent of students are in the seventh grade?
Answer:
Almost 36%
Step-by-step explanation:
According to the diagram below, which similarity statements are true?
Check all that apply.
P
S
R
A. APQR - APRS
B. APQR ~ APSQ
O C. APQR ~ AQSR
D. APQS ~ AQRS
The required triangle PQS and triangle QRS are similar triangles. Option D is correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
According to the diagram,
It can be inferred that triangle PQS and triangle QRS are similar to each other. The term "similar" implies that these two triangles have the same shape but can be different in size. Specifically, the corresponding angles of these triangles are equal, and the corresponding sides are in proportion.
Consider triangle, PQS, and triangle QRS
Angle S is the common angle in both the triangles
And angle Q is similar to angle R
So both the triangle are similar by AA similarity postulate
Therefore, option D is correct.
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14. A system of equations is shown below. For what value of a will this system have no solutions? Justify your answer.
y = 4x-9
y = ax+6
Answer:
a = 4
Step-by-step explanation:
a = 4
If a = 4, then both lines have the same slope and different y-intercepts. That makes both lines parallel. Since the lines never intersect, there is no solution.
Answer:
x can not equal zero, as it would cause division by zero.
Step-by-step explanation:
First, let's make one equation out of them and see what we get. Because both of them have y on the left, we can say that the two right sides are equal, giving us:
4x - 9 = ax + 6
If we solve for a, we get:
ax + 6 = 4x - 9
ax = 4x - 15
a = 4 - 15 / x
With that arrangement we can see clearly that x can not be equal to zero, as it would give us division by zero.
5. Solve the triangle. A = 54°, b = 11, c = 8
O a = 11.5, C = 45.8°, B = 80.2°
O a = 9.0, C = 40.6°, B = 86.4°
O No triangles possible
O a = 9.0, C = 45.8°, B = 80.2°
Answer:
no triangles possible
Step-by-step explanation:
I hope this helps
How many solutions does the following equation have?
13(y + 3) = 13y +39
Choose 1 answer:
No solutions
Exactly one solution
Infinitely many solutions
Answer:
Infinitely many solutions
Step-by-step explanation:
This equation has an infinite number of solutions, so it will be categorized as an identity.
A group of friends are at a baseball game and are purchasing souvenirs. Olivia purchased 1 t-shirt and 5 baseball caps, spending a total of $165. Her Marco purchased 1 t-shirt and 4 baseball caps, which cost him a total of $137. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?
Answer:
baseball cap = $28
t-shirt = $25
Step-by-step explanation:
Olivia: t +5b = 165
Marco: t + 4b = 137
isolate t in Olivia's equation
t = 165 - 5b
plug t into Marco's equation
165 - 5b + 4b = 137
165 - b = 137
b = 28
plug b into either equation
t + 4b = 137
t + 4(28) = 137
t + 112 = 137
t = 25
Graph the function.
h(x) = -4(x – 3)(x - 1)
Khan sucks
Answer:
The graph is a translation 3 left and 1 up from the function f(x) = x3.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Vertex: (2,4)
Focus: (2, 63/16)
Axis of Symmetry: x=2
how many ounces are equivalent to 6 pounds?
Answer:
96
Step-by-step explanation:
1 pound is 16 ounces
6 pounds=x ounces
So we use the X to signal it's presence
1x16 is 16,
That means 16 ounces
6xP=Q
6x16 will give us our answer
Because it will tell us how many pounds there are since ounces is multiplied to get ounces.
6x16=96
P=16
Q=96
96 is our answer.
I hope this helps!!!!
If you need help, don't hesitate to ask!
I'm here until 2:30
May I please have brainliest?
Find the missing length. Round to the nearest tenth
Answer:
x ≈ 30.9 (Choice D)
Step-by-step explanation:
We can use cosine for solving this question:
cos (61°) = 15 / x
x = 15 / cos (61°)
x = 30.93998011
x ≈ 30.9 (Choice D)
a trapezoid is a parallelogram always sometimes never
Answer:
never
Step-by-step explanation:
trapezoids only have one set of parallel lines. a parallelogram has to have two or more
Number 13 and 14 don’t matter but help ‼️
Hermes earns $6 an hour for babysitting. He wants to earn at least $168 for a new video game system. Determine the number of hours he must babysit to earn enough money for the video game system. Then interpret the solution.
Answer:
28 hours
Step-by-step explanation:
6x28=168
To earn atleast $168, Hermes should do babysit for atleast 28 hours.
What is inequality?Inequality is just like an equation showing relationship between two or more variables but this is expressed in greater than ,less than form.
It defines a range of value of the relationship.
How to form inequality?We have been given that Hermes earns $6 per hour for babysitting and he wants to earn atleast $168 for a new video game. We have to calculate the minimum number of hours that he should do babysit in order to earn $168.
We know that total revenue will be number of hours* payment of 1 hour.
let the number of hours that he does babysit is x.
The inequality will be :
6x>168
x>168/6
x>28
Hence to earn atleast $168 he should work for atleast 28 hours.
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if b = -3, what is the value of b³?
Answer:
-27
Step-by-step explanation:
b³=(-3)³
b³=(-3×-3×-3)
b³=-27
What is the volume of the rectangular pyramid below?
Classify Two-Dimensional Figures
Answer:
The bottom left ( square )
Step-by-step explanation:
top left : parallelogram
top right : irregular shape, i'm not sure on it's name
bottom left : square, which in special cases can be a rectangle.
bottom right : Trapezium which comes under the category of a parallelogram
The third figure in the given diagram is a rectangle.
What is a rectangle?A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree.
From the given figure we can see that the third figure is having four sides in which two opposite sides are parallel and equal all the four sides are perpendicular to each other making an angle of 90 degrees.
Therefore the third figure in the given diagram is a rectangle.
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find the vertex. y=10x^2+3
Answer:
(h,k)
(0,3)
Step-by-step explanation:
What is the slope of a line perpendicular to the line of the equation in the above ? Please help answer !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!!!
Answer:
- 4Step-by-step explanation:
Slopes of perpendicular lines are negative-reciprocals.If m is the slope of one line, the slope of the perpendicular line is -1/m.Let's find the slope of the given line:
x - 4y = -12Rewrite this in the slope-intercept form: y = mx + b
x - 4y = -124y = x + 12y = 1/4x + 3The slope is 1/4
The perpendicular line has slope
- 1/(1/4) = - 4y2 + x3 + 7 for y = 2, x = 1 algebraic example ano po solve dito medyo nakakalito po
Answer:
Substitute y and x
(2)2 + (1)3+7
then multiply 2 * 2
4+ (1)3+7
then multiply 1* 3
4+ 3+7
add those numbers
14 ang iyong sagot, tandaan kapag nakikita ang panaklong tulad ng nakikita mo dito nangangahulugang dumami
Solve the inequality and write the solution in set-builder notation.
t-3>-8
I have no idea what set builder is, so I'll just solve it if that's okay.
t-3>-8
First, to cancel out -3, you need to add it to both sides.
t-3>-8
+3 +3
t>-5
---
hope it helps
Jackson record the elevations relative to sea level that two fish are swimming.The first was at 6 feet, and second was at 11 feet What are the opposite elevations and what do they represent
the answer is
-6 and -11 which are the opposites
Can someone please answer this (please don’t send a tinyurl link)
The value of Kensington's car decreases in value according to the exponential decay
function V
Pe-0.12t , where Vis the current value of the vehicle, t is the
number of years Kensington has owned the car and P is the purchase price of the car,
$20,000. To the nearest dollar, what will be the value of Kensington's car in 8 years?
PLZZ HELPP
Find the volume.
Answer:
330yd^3
Step-by-step explanation:
multiply all of them
Answer:
330 yd^3
Step-by-step explanation:
V=w*h*l
V=5*6*11
V=330 yd^3
Anyone help me on this plzzzz :((
Answer:
Answer should be 47
Step-by-step explanation:
Answer:
47
Step-by-step explanation:
180-133(because of straight angle )