[tex]\displaystyle\bf 4x^2+3=-7x\\4x^2+7x+3=0 \\\\D=49-48=1 \\x_1=\frac{-7+1}{8} =-\frac{3}{4} \\x_2=\frac{-7-1}{8} =-1\\\\Answer: \boxed{ x_1=-\frac{3}{4} \quad ; \quad x_2=-1}[/tex]
Find the x-intercepts of the parabola with
vertex (1,20) and y-intercept (0,16).
Answer:
Step-by-step explanation:
Since we are finding the x-intercepts, that implies that this is a parabola that opens either up or down as opposed to right or left. It would benefit us to know the equation of the parabola so we could factor it to find the roots (which are also known as the x-intercepts).
Here's what we know:
h = 1, k = 20, x = 0, and y = 20. Filling in the vertex form of a parabola is already halfway to factored, so we'll use that format as opposed to the standard form, which is
[tex]y=ax^2+bx+c[/tex]. The vertex form is
[tex]y=a(x-h)^2+k[/tex] and filling in our values from above:
[tex]16=a(0-1)^2+20[/tex] and
[tex]16=a(1)+20[/tex] and
-4 = a. So the equation for the parabola is
[tex]y=-4(x-1)^2+20[/tex]. Now set it equal to 0 and factor.
[tex]-20=-4(x-1)^2[/tex] and divide both sides by -4 to get:
[tex]5=(x-1)^2[/tex] and take the square root of both sides to get
±[tex]\sqrt{5}=x-1[/tex] and then add 1 to both sides to get the x-intercepts (or roots or solutions or zeros...they're all the same).
x = 1 ±√5 and you're done!
How many pieces ,each of length 3 ¾ m can be cut from a rope of length 30m?
Answer:
8
Step-by-step explanation:
Divide 30 by 3.75 to get 8.
Hope that this helps!
Megan uses cup of almonds to make 4 cups of trail mix. Using this
same proportion, how many cups of almonds would Megan need to make
9 cups of trail mix?
Which is the graph of inequality 2 - (x + 3) < 4 - 2x?
Answer:
x<5
Step-by-step explanation:
In 2019, Tessa earned $32000. (a) She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018. [2] (b) In 2020, Tessa's earnings increased by 7%. Work out her earnings in 2020.
Answer:
$7,680
$34,240
Step-by-step explanation:
Amount Tessa earns in 2019 = $32000
a. She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018.
Percent of tax = 24%
Amount of tax paid = 24% of $32,000
= 24/100 * 32,000
= 0.24 * 32,000
= $7,680
Amount of tax paid = $7,680
b. Tessa's earnings increased by 7%. Work out her earnings in 2020.
Percentage increase in earnings = 7%
Amount of increase in earnings = 7% of $32,000
= 7/100 * 32,000
= 0.07 * 32,000
= $2,240
Amount of increase in earnings = $2,240
Total earnings in 2020 = Amount Tessa earns in 2019 + Amount of increase in earnings
= $32,000 + $2,240
= $34,240
Total earnings in 2020 = $34,240
Kathie buys a bottle of fruit juice for $2.50 and a few loaves of bread for $1.20 each.
a. If she spent $8.50, how many loaves of bread did she buy?
b. If she can spend AT MOST $20, how many loaves of bread can she buy?
Answer:
a. 5 loaves, b. 14 loaves
Step-by-step explanation:
a.8.50=2.50+1.20x
6.00=1.20x
5=x
5 loaves
b.20=2.50+1.20x
17.50=1.20x
14.6=x
14 loaves
Anil bought 6 exercise books at Rs 40 each and an eraser for Rs 10, He gave a Rs 500 note to the shopkeeper for the payment. How much change did the shopkeeper return him?
Help pls!!!!!!!!!!!!!!
Answer:
160 for each
Step-by-step explanation:
A normal distribution means that mean = median = mode. Furthermore, in a normal distribution, 68% of values are within 1 standard deviation of the mean, 95% of values are within 2 standard deviations, and 99.7% are within 3 standard deviation.
The mean is 150 and the standard deviation is 15. 165 and 135 1 standard deviation away from the mean, so 68% of values are between 135 and 165. This means that 32% of values are not between those values. A normal distributuion is symmetric, so 16% of values are greater than 1 standard distribution and 16% are less. Therefore, 16% of values (160) are less than 135 and 16% of values (160) are greater than 165
Ellus
Find the range of the data.
The ages of people eating
chocolate ice cream at a park.
12, 2, 8, 5, 3, 2,5
Range: [? ]
Enter the number that belongs in the green box.
Answer:
range = 10
Step-by-step explanation:
The range is the difference between the largest and smallest values in the data set.
largest value = 12
smallest value = 2
range = 12 - 2 = 10
Find the value of x when : 2^30/8^9=2^x
The line means divide
please i need step by stem explanation I already know answer
Answer:
x = -3
Step-by-step explanation:
Okay, the first thing to do is get that 8 away from the fraction. How can we do it? When you have 2³ you have 8, is the same thing, so let's do it:
2³⁰/(2³)⁹ = 2^x
When you have a number with the shape (a^x)^y, you can write it as a^(x•y), so:
(2³)⁹ = 2^3•9 = 2²⁷
Now we have:
2³⁰/2²⁷ = 2^x
When you have a division like this: (a^x)/(a^y), you can write it as a^(x-y), so:
2^(30-27) = 2^x
2^-3 = 2^x
Now you know that x = -3
If you are using a compound microscope with an ocular lens with a magnification of 10x and an objective lens of 25x, what is the total magnification of the sample?
Answer:
250×
Step-by-step explanation:
The ocular lens of the compound microscope is 10×
The objective lens of the compound microscope is 25×
Therefore the total magnification can be calculated as follows
= 10×25
= 250
Hence the total magnification of the compound microscope is 250×
In which part of the graph is the height of the water increasing?
Answer:
A. 3
Step-by-step explanation:
Section 1: decrease
Section 2: level, no increase, no decrease
In section 3, the slope is positive. The graph goes up to the right. The level of water increases in section 3.
Section 4: decrease
Section 5: decrease
Answer: A. 3
Answer:
A. 3
Step-by-step explanation:
Three hikers equally shared One-half gallon of water. Explain how you would use an area model to find the amount of water each hiker drank.
Answer:
1/6 gallon of water
Step-by-step explanation:
Number of hikers = 3
Quantity of water shared = 1/2 gallon of water
If the water was shared equally among the hikers, then,
Amount of water each hiker drank = Quantity of water shared ÷ Number of hikers
= 1/2 ÷ 3
Multiply 1/6 by the reciprocal of 3
The reciprocal of 3 = 1/3
1/2 ÷ 3
= 1/2 × 1/3
= (1 * 1) / (2 * 3)
= 1/6
Amount of water each hiker drank = 1/6 gallon of water
Answer:
Sample Response: Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1
6
of a gallon.
Step-by-step explanation:
UwU
PLEASEEEE ANSWER THIS IM BEING TIMED AND SHOW YOUR WORK ILL GIVE TOU BRAINLIST IF YOU DO!!!!
Pleaseee Helpp. If the radius is 21 m and area of sector of the circle are 27.72 m2, calculate the angle at the centre of the circle.
Given:
Radius of a circle = 21 m
Area of a sector of the circle = 27.72 m²
To find:
The angle at the center of the circle.
Solution:
The area of a second is:
[tex]A=\pi r^2\times \dfrac{\theta}{360^\circ}[/tex]
Where, r is the radius of the circle and [tex]\theta[/tex] is the central angle.
Putting [tex]\pi=\dfrac{22}{7},\ r=21,\ A=27.72[/tex] in the above formula, we get
[tex]27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}[/tex]
[tex]27.72=1386\times \dfrac{\theta}{360^\circ}[/tex]
[tex]27.72=3.85^\circ \times \theta[/tex]
[tex]\dfrac{27.72}{3.85^\circ }=\theta[/tex]
[tex]7.2^\circ=\theta[/tex]
Therefore, the central angle of the sector is [tex]7.2^\circ[/tex].
The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, and why?
Answer:
BStep-by-step explanation:
not sure if i am right but go off process of elimination
A is a not it to get slope you need to do Y=Mx+b because the slope should be 1.3 and if you get the deciml form of 3 over 9 it would be 0.75
and if you do same process on all of then you will see it is B
20,085 rounded to the nearest hundreds place is?
Answer:
20,100
Step-by-step explanation:
hundreds place is the third from the right
Answer:
20,100
Step-by-step explanation:
085 represents 0 hundreds, 8 tens and 5 ones.
That place keeper 0 is rounded up to a 1 because the following '8' is greater than 5.
Thus, the desired rounded off number is 20,100.
The sum of two consecutive numbers is one less than three times the smaller integer. Find the two integers.
Answer:
2 and 3
Step-by-step explanation:
Let us start by representing the first consecutive number with x. In a similar sense, the next consecutive number would be x+1. According to the given question, we can write the following equation:
[tex]x+x+1=3x-1[/tex]
Solving for the equation by isolating the term containing x, we have:
[tex]2x+1=3x-1\\2x+2=3x\\\fbox{x=2}[/tex]
Since we have designated x as the first consecutive integer, the other integer we are looking for is x+1, or [tex]\fbox{3}[/tex] .
I hope this helps! Let me know if you have any questionss :)
Please help asap! will give brainliest
Answer:
we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm
During a school event, Noah is selling pizza at the food stand for $1.25 per slice. How many slices of pizza would Noah need to sell to earn $120? Explain your reasoning.
Answer:
96
Step-by-step explanation:
120/1.25=96
Noah needs to sell 96 slices of pizza to earn $120.
Find the mean, median, and mode of the following set of data:
54, 48, 37, 55, 51, 54, 42, 52, 53
pls help me
Answer:
Mean: 52.8
Median:52
Mode:54
Step-by-step explanation:
Mean: 54+48+37+55+51+54+42+52+53=476
476/9=52.8
Median: 37,42,48,51,52,53,54,54,55. The middle one is 52.
Mode: Most common one = 54
Hope this helps! Have a nice day!
Find the missing angle
Answer:
x = 72.09555249
Step-by-step explanation:
Since this is a right angle, we can use trig functions
tan x = opp / adj
tan x = 65/21
Taking the inverse tan of each side
tan ^-1 ( tan x) = tan ^-1 ( 65/21)
x = 72.09555249
Can 17, 9, and 11 be the side lengths of a triangle?
Answer:
No it cant
Step-by-step explanation:
You have to use the Pythagoras theorem which is a^2 + b^2 = c^2. So 9^2 + 11^2= 202. Then 17 is the hypotenuse so 17^2= 289. They are not equal so they are not.
PLEASE HELP! BRAINLIEST! AND EXTRA POINTS
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars
Answer:
The discount is $0.8d.
Step-by-step explanation:
Given that,
The original cost of Tamara's purchase is d dollars.
Tamara uses a coupon to save 20% off her purchase at the bookstore.
Discount = 20%
Discount is applied to the original cost.
Discount = d-(20/100)d
Discount = 0.8 d
Hence, the discount is $0.8d.
If 34+5= 36
56 +2 = 39
27 +6 = 45
47 +5 = 48
28 +1 = 33
then 41 + 5=
please help
Answer:
I'm guessing 46 if its actually adding
Jane and Tannic split the cost of buying a video game. The game costs$25, and the sales is 6% markup. How much do they each pay?
Answer:
$13.25
Step-by-step explanation:
Given data
Cost of game = $25
Markup= 6%
Let us find the total cost of the game
First, the markup cost
=6/100*25
=0.06*25
=$1.5
Now the total cost is
=25+1.5
=$26.5
So, each is expected to pay
=26.5/2
=$13.25
y< 3x + 12
y> 5x + 7
Answer:y< 3x + 12
y> 5x + 7
Step-by-step explanation:
Martha has x pence and Peter has twice the amount as Martha and 8 more. Together they have 200 pence. How much do Martha and Peter have?
WILL GIVE BRAINLIEST
Step-by-step explanation:
x+2x+8 =200
3x=200-8
3x=192
x = 64
Martha has 64 pence
Peter jas 136 pence
The equation represents a hyperbola centered at the origin with a focus of (0,-10).
What is the value of b?
4
6
10
12
Answer:
Second option - 6
Explanation:
Trust! (And the image)
I really ope this helped! :)
p
[tex]97x + 58y - 66y + 44x[/tex]
[tex]\longrightarrow{\blue{ 141x - 8y }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]97x + 58y - 66y + 44x[/tex]
Let us rewrite the expression so that the like terms are next to each other.
[tex] = 97x + 44x+ 58y - 66y[/tex]
Combine the coefficients.
[tex] = (97 + 44)x + (58 - 66)y[/tex]
[tex] = 141x - 8y[/tex]
[tex]\sf\pink{Happy\:learning! }[/tex]