Answer:
a = -1 and 6
Step-by-step explanation:
[tex] \frac{a(a - 5)}{6} = 1[/tex]
[tex]a(a - 5) = 6[/tex]
[tex] {a}^{2} - 5a = 6[/tex]
[tex] {a}^{2} - 5a - 6 = 0[/tex]
[tex](a + 1)( a- 6)[/tex]
a = -1 and a = 6
5 schools sent some students to a conference.
One of the schools sent both boys and girls.
This school sent 16 boys.
The ratio of the number of boys it sent to the number of girls it sent was 1 : 2
The other 4 schools sent only girls.
Each of the 5 schools sent the same number of students.
Work out the total number of students sent to the conference by these 5 schools.
The total number of students who went to the conference was 240 students
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The total number of schools = 5 schools
Let the schools be A , B , C , D , E
One of the schools sent boys and girls
The number of boys A = 16 boys
The ratio of boys to girls is = 1 : 2
So , the number of girls = 2 x number of boys
The number of girls A = 2 x 16
= 32 girls
Now , the equation will be
The number of students sent to conference by school A = 16 + 32
The number of students sent to conference by school A = 48 students
Now , the equation will be
All the schools sent the same number of students
So , The total number of students = Total number of students in A x 5
The total number of students = 48 x 5
= 240 students
Therefore , the total number of students is 240 students
Hence , The total number of students who went to the conference was 240 students
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What is the height of a cone with a radius of 4 inches and of volume 8 cubic inches? Round your answer to the nearest tenths place
HELP!!!!! (30 points) and brown list if you answer all these questions
Answer:
.09 meters: 90 mm
Convert 27 feet: 324 inches
Step-by-step explanation:
90 milimeters.
324 inches.
PLEASE HELP I DON'T UNDERSTAND! A florist is making regular bouquets and mini bouquets. The florist has 118 roses and 226 peonies to use in the bouquets. Each regular bouquet has 5 roses and 11 peonies. Each mini bouquet has 3 roses and 5 peonies. Reply to this post by doing the following: 1. Write an equation that shows the total number of roses to be used in both kinds of bouquets. 2. Write an equation that shows the total number of peonies to be used in both kinds of bouquets. 3. Find how many of each bouquet can the florist make.
Answer:
The florist can make 11 regular bouquets and 21 mini bouquets
Step-by-step explanation:
The number of roses the florist has = 118 roses
The number of peonies the florist has = 226 peonies
The number of roses in each regular bouquet = 5 roses
The number of peonies in each regular bouquet = 11 peonies
The number of roses in each mini bouquet = 3 roses
The number of peonies in each mini bouquet = 5 peonies
1. The equation that gives the total number of roses to be used in both kinds of bouquet is given as follows;
Let r represent the number of regular bouquet the florist can make and let m represent the number of mini bouquet the florist can make, we have;
5·r + 3·m = 118...(1)
2. Similarly, we have;
11·r + 5·m = 226...(2)
Making m the subject of the formula of both equations, and equating both values of m to find a common solution, we have;
m = (118 - 5·r)/3
m = (226 - 11·r)/5
(118 - 5·r)/3 = (226 - 11·r)/5
5 × (118 - 5·r) = 3 × (226 - 11·r)
590 - 25·r = 678 - 33·r
33·r - 25·r = 678 - 590 = 88
8·r = 88
r = 88/8 = 11
r = 11
The number of regular bouquet the florist can make = r = 11
m = (118 - 5·r)/3 = (118 - 5×11)/3 = 21
m = 21
The number of mini bouquet the florist can make = m = 21
The number of regular bouquet the florist can make = 11 bouquets
The number of mini bouquet the florist can make = 21 bouquets.
The solutions to the equation f(x) = g(x) are -2 and 1. If f and g are graphed on the same coordinate plane, which statement must be true?
A.the functions will intersect at x = -2 and x=1
B. The functions will intersect at y = -2 and y = 1
C. Both functions will have y-intercepts at -2 and 1
D. Both functions will have x- intercepts at -2 and 1
Answer:
c
they will both have to intersect since you have a negative and positive number. Hope it helps.
Step-by-step explanation:
The functions will intersect at y = -2 and y = 1. Option B is correct.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The solutions to the equation f(x) = g(x) are -2 and 1.
Solution of the equation state the definition that, when two functions intersect each other, is the solution of the functions. So as mentioned both functions as f(x) = g(x) gives y = -2 and y = 1, implying that The functions will intersect at y = -2 and y = 1.
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Gloria uses 2/5 hours of butter to make eats 1/3 of a pound of jelly. how much jelly can she make with 1 ounce of butter
if the radius of a circle is 44 cm what is the diameter
Answer:
88
Step-by-step explanation:
multiply 44 times 2 which gives you 88 as the diameter.
Hope this helps!!
Graph the linear equation using slope-intercept form. Y=-5/3x+4
Answer:
Graph is in the picture below
Step-by-step explanation:
HELPPPP ASAPP WITH EXPLANATION IW WILL GIVE BRAINLIEST THANK YOUUUU!!!!
The Rodriguez family went to dinner at Pasta Palace. Mr. Rodriguez ordered a
meal for $16.25; Mrs. Rodriguez ordered a meal for $19.50; the three children
ordered individual pizzas for $6.99 each. The tax rate is 8.75% and the family
wants to leave an 18% tip applied after the tax. How do they leave in all
including tax and tip?
Answer:
$72.79
Step-by-step explanation:
16.25+19.5+(6.99*3)=56.72
56.72* 1.0875=61.683
61.683 * 1.18= 72.78594
rounded, you get $72.79
1 + (-1) + (-3) + 0 + 0 + 6 =
Answer: 3.
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
To find 1.56 X 2.7, multiply
decimal point in the product to show
Then place the
decimal places.
Answer:
You would get 4.2 when you finish rounding.
Step-by-step explanation:
Answer:
4.2 I got that so if you round it youre gonna get 44.2 is between 4 and 5, but it is closer to 4. The answer is that 4.2 rounds to 4.
Step-by-step explanation:
Which expression is equivalent to 30°?
Answer:
A
Step-by-step explanation:
Edge 2020
Answer:
Can confirm it's A
Explanation:
Edg2020
Give the coordinates for the reflection of Rectangle MNOP with vertices M(-2, 6), N(2,8), O(5,2), and P(1, 0) across the line y = -x.
Answer:
M' = (-6,2)
N '= (-8,-2)
O' = (-2,-5)
P' = (0,-1)
Step-by-step explanation:
y=-x equals to (-y,-x)
Answer:
both are negative the answer is B
Step-by-step explanation:
Complete the sentence
Answer: function notation
Step-by-step explanation:
What is the y-intercept of the equation 8x – 3y = 24?
Answer:
-8
Step-by-step explanation:
Create this equation into a y=mx+b form
8x-3y=24
-8x -8x -8 to solve for -3y
-3y=-8x+24
---- --- --- divide by -3 to leave y by itself
-3 -3 -3
y= 8
--- x-8
3
y intercept is -8
Answer: −8
Step-by-step explanation:
Subtract 8x from both sides of the equation.
−3y=24−8x
Divide each term by −3 and simplify.
y=8x/3−8
Reorder terms.
y=8/3x−8
Y-INTERCEPT = -8
Josiah did a survey of his 24 classmates to find out how many have at least one pet at home. •the number of classmates that did not have pets can be represented by p
•the number of classmates that did have pets is three times the numbers that did not have pets. What is p the number of classmates that did not have pets? A.18 B.8 C.12 D.6
The length of a rectangle is 6 inches longer than the width. The perimeter is 28 inches. What is the length of the rectangle?
Answer:
rectangle and the perimeter of the rectangle is 28 inches.
explain
p= 2 * length + 2 * width.
Hence, we can set up an equation as following.
2 y + 2x = 28.
i need helpppp plzzz!!!!
Answer:
23°
Step-by-step explanation:
You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=2x+4. There is a tree in your yard at the point (−4, 11). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.
Answer:
Distance is 6.7units to the nearest tenth.
Explanation:
To solve this problem, we the distance formula. And this is given as:
[tex]D = \frac{|a x + b y + c|}{\sqrt{a^2 + b^2}}[/tex]
We were given the equation:
y = 2 x + 4
This can also be rewritten as:
y – 2 x – 4 = 0.
Therefore, a = -2, b = 1 and c = -4
Also, we were given the points:
(x, y) = (–4, 11)
Making use of the above formula for distance, we have:
[tex]D = \frac{|-2\times -4 + 1\times 11 + -4|}{\sqrt{-2^2 + -4^2}}[/tex]
[tex]D = \frac{15}{\sqrt{5}}[/tex]
D = 6.7units (to the nearest tenth)
the first two terms of an exponential sequence are 18 and 6. what are the next 4 terms of this sequence?
Answer:
g
Step-by-step explanation:
4/9 - (-2/9) plzzzz help
Answer:
18 is it
Step-by-step explanation:
Solve for x. -x + 4 = 32 x = -28 x = 36 x = 28 x = -36
Answer:x=-28
Step-by-step explanation:
-x+4=32
Subtract 4 from each side
-x=28
Multiply each side by (-1)
x=-28
Answer: -28
Step-by-step explanation:
Simplify the expression:Two-thirds divided by (negative 4) minus (one-sixth minus StartFraction 8 over 6 EndFraction)
1
StartFraction 29 over 24 EndFraction
StartFraction negative 24 over 17 EndFraction
StartFraction 23 over 24 EndFraction
Answer:
the answer is 1
Step-by-step explanation:
i just answered that question and i got it right
Answer:
1
Step-by-step explanation:
When this polynomial is divided by (m + 1), the remainder is 0. What is the value of the polynomial's constant term?
-2m^3 + m^2 - m + (blank)
Answer:
The value of the polynomial's constant term is -4
Step-by-step explanation:
Given polynomial;
= -2m³ + m² - m + c
where;
c is the constant term
factor of the polynomial = m+1
then, f(m+1) = 0
m = -1
Substitute the value of m in the given polynomial and solve for the constant term "c";
-2m³ + m² - m + c = 0
-2(-1)³ + (-1)² - (-1) + c = 0
2 + 1 + 1 + c = 0
4 + c = 0
c = -4
Therefore, the value of the polynomial's constant term is -4
A woman is out driving her car. She stops at a store for a while. Then she gets into the car again and drives back home. Which graph represents the function modeling the amount of gas used by the car in terms of time?
Here, I made a graph through MS Paint.
Donna is on the swim team. Each week she swims a total of 8000 meters. How many kilometers does she swim each week? Be sure to include the correct unit in your answer.
Answer:
Donna swims 8 km each week.
Step-by-step explanation:
To be able to find the answer, you have to consider that 1 km is equal to 1000 meters and with this, you can use rule of three to find the kilometers in 8000 meters:
1 km → 1000 meters
x ← 8000 meters
x=(1*8000)/1000=8 km
According to this, the answer is that Donna swims 8 km each week.
You plan to reach the top of a 30 foot tall building using a ladder if the ladder forms a 70 degree angle with the ground find how long must the ladder be to reach the top of the building
Answer:
Step-by-step explanation:
The set up is a right angles triangle where;
Height of the building = 30feet (opposite)
Angle of elevation = 70 degrees
Length of the ladder (hypotenuse) = x
Using SOH trig identity;
sin theta = opp/hyp
sin 70 = 30/x
x = 30/sin 70
x = 30/0.9397
x = 31.93feet
Hence the ladder must be 31.93 feet long to reach the top of the building
To prepare for a bake-off, Korina used 610 grams of flour each day for 4 weeks. How many kilograms did Korina use in those 4 weeks?
1 g = 0.001 kg
If b/a equals 4, what does a/b equal
Answer: 1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
Assuming b/a is 4/1, getting a/b will just be getting the reciprocal or 1/4
Mr.Martin states that in order for the solution to the equation 3x + q = 6 to be positive, the value of q must be less than 6. Select a value of q that is less than 6 and show that the solution to the equation 3x + q = 6 is positive. Select a value of q that is not less than 6 and show that the solution to the equation 3x + q = 6 is not positive
Answer:
Mr. Martin's statement is correct.
Step-by-step explanation:
First we select a value of q that is less than 6:
q = 3
Then we write the equation:
3x + 3 = 6And solve for x:
3x = 6 - 43x = 3x = 3/3x = 1The solution is positive because x > 0.
--
Then we select a value of q that is not less than 6:
q = 9
Then we write the equation:
3x + 9 = 6And solve for x:
3x = 6 - 93x = -3x = -3/3x = -1The solution is negative because x > 0.