The numbers that add to -5 and multiply to -4 are -5.7015 and 0.7015.
There are two numbers. The addition of the two numbers is -5. The multiplication of the two numbers is -4. We need to find the two numbers. Let the first number and the second number be represented by the variables x and y, respectively. Then, we can write the two following equations.
x + y = -5
x*y = -4
We will substitute the value of y from the first equation into the second equation.
x*(-5 - x) = -4
x*(x + 5) = 4
x² + 5x - 4 = 0
Now, we will use the quadratic formula.
x = [-5 ± √(5² - 4(1)(-4))]/2(1)
x = [-5 ± √(25 + 16)]/2
x = [-5 ± √41]/2
x = [-5 ± 6.403]/2
The values of x are -5.7015 and 0.7015. The corresponding values of y are 0.7015 and -5.705.
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The length of a rectangle is the sum of the width and 2. The area of the rectangle is 63 units. What is the width, in units, of the rectangle?
Answer:
WITDTH=7
Step-by-step explanation:
width = w
length = w + 2.
w(w + 2) = 63 (area)
quadratic equation in w:
w2 + 2w = 63
w2 + 2w - 63 = 0
FACTOR:
(w + 9)(w - 7) = 0
9-7=2
9x(-7) = -63
Two possible solutions:
w + 9 = 0 (solution w = -9) or
w - 7 = 0 (solution w = 7)
The width must be positive, the answer is 7 units.
length = w+2
length = 9
PLEASE HELP!!!!!!! A warehouse store sells 5.5-ounce cans of tuna in packages of 5. A package of 5 cans costs $10.45. The store also sells 4.5-ounce cans of the same tuna in packages of 8. A package of 8 cans costs $12.96. The store sells 3.5-ounce cans in packages of 4 cans for $4.76. Which package is the best buy? find the one with the smallest unit rate!!!
Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
A discount store sells 5.5 - ounce jars of fish in bundles of 5. A bundle of 5 jars costs $10.45. Then the unit rate is given as,
⇒ ($10.45 x 5) / (5.5 x 5 x 5)
⇒ $0.38 per ounce
The store likewise sells 4.5-ounce jars of similar fish in bundles of 8. A bundle of 8 jars costs $12.96. Then the unit rate is given as,
⇒ ($12.96 x 8) / (4.5 x 8 x 8)
⇒ $0.36 per ounce
The store sells 3.5 - ounce jars in bundles of 4 jars for $4.76. Then the unit rate is given as,
⇒ ($4.76) / (3.5 x 4)
⇒ $0.34 per ounce
Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.
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x3+3x2−10x+24
Factorice el polinomio
The expression x³ + 3x² - 10x + 24 cannot be factorized
How to factorize the polynomial?From the question, the polynomial is given as
x3+3x2−10x+24
Rewrite the polynomial properly
So, we have the following representation
x³ + 3x² - 10x + 24
Next, we represent the above expression on a graph
From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -5.569
This implies that the expression cannot be factored
So, we cannot further rewrite the given expression
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196 prime factorization pls help
Question 4 (10 points)
(02. 07 MC)
The figure shows triangle ABC and line segment PQ, which is parallel to BC:
Triangle ABC has a point P on side AB and point Q on side AC. The line PQ is parallel to the line BC.
Part A: Is triangle ABC similar to triangle APQ? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle APQ corresponds to line segment BC? Explain your answer. (3 points)
Part C: Which angle on triangle APQ corresponds to angle B? Explain your answer. (2 points)
Part a: ΔABC≈ΔAPQ
Part b: The line segment PQ corresponds to the line segment BC.
Part c: Angle P in APQ triangle angle equates to angle B.
Define the term similarity rule of triangles?If two triangles have a similar ratio of adjacent angles and an equal proportion of corresponding sides, they are comparable. When two or more objects share the same shape but differ in size, they are referred to as comparable figures.Part a: line segment PQ parallel to BC; PQ||BC
Thus, ∠ABC =∠APQ AND, ∠ACB=∠AQP
So, by (AA similarity rule)
ΔABC≈ΔAPQ
Part b: The line segment APQ on the triangle corresponds to the line segment BC:
By CPST, line segment PQ on triangle APQ equates to line segment BC (corresponding parts of similar triangle).
Part c: APQ triangle angle equates to angle B:
Angle P on triangle APQ equals angle B via CPST (corresponding parts of similar triangle).
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Pls Help BrainliestBegging u PlsPLS!!!!!!!!!!!!
How many positive three-digit integers have at least one digit that is a 5 or a 7?
Answer:
452 integers------------------------
Three-digit integer in the form of abc.
Possible numbers for each digit
a - 1 to 9, nine options,b and c - 0 to 9, ten optionsLet a = 5 or 7, then for a we have 2, for b and c 10 options:
5bc or 7bc2*10*10 = 200Let b = 5 or 7, then for a we have 9 - 2 = 7, for b 2 and for c 10 options
a5c or a7c7*2*10 = 140Let c = 5 or 7, then for a we have 9 - 2 = 7, for b 10 - 2 = 8 and for c 2 options
ab5 or ab77*8*2 = 112Total options200 + 140 + 112 = 452What is the slope of the line represented by the equation y = x-3?
03
-3
Answer:
slope of the line = 1
Step-by-step explanation:
i hope i helped
an experiment involves selecting a random sample of 256 middle managers for study. one item of interest is their annual incomes. the sample mean is computed to be $35,420.00. if the population standard deviation is $1,650.00, what is the standard error of the mean?
Answer:
Step-by-step explanation:
mu = 35,420 sigma = 2,050 n = 256 s...
I need help with these problems in Geometry (Similar Triangles)
Looking at the triangles, the values of x in the figures are
14. x = 1715. x = 3What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
figure in 14)
The solution for x
8 / (x + 5) = (x - 9) / 21
21 * 8 = (x + 5)(x - 9)
168 = x^2 - 4x - 45
x^2 - 4x - 213
x = 16.73 or -12.73
using the positive value
x = 17
figure in 15)
The solution for x
(x + 3) / 15 = 4 / (3x + 1)
cross multiplying
(x + 3)(3x + 1) = 15 * 4
3x^2 + 10x + 3 = 60
3x^2 + 10x - 57 = 0
x = 3 OR -6.333
taking the positive value
x = 3
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-8-(b-3)=13-4b i need an answer but not a fraction or decimal
Answer:b=2/3 if u don't need an answer that is not a fraction or decimal u can write 17. as a whole number.
Step-by-step explanation:
A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.
Check answer below in the image.
What are the solutions of 8x2 = 6 + 22x? Check all of the boxes that apply.
x = -3
x = 3
x = 6
The solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
Given expression is,
8x² = 6 + 22x
Rewrite this expression as,
8x² - 6 - 22x = 0
8x² - 22x - 6 = 0
Now, we get the form quadratic equation i.e, ax² + bx + c = 0
Solve the equation and find roots
8x² - 22x - 6 = 0
2(4x² - 11x - 3) = 0
4x² - 11x - 3 = 0
4x² - 12x + x - 3 = 0
Take common terms out,
4x(x - 3) + 1(x - 3) = 0
we get the brackets same that means we're on right way,
(4x + 1) (x - 3) = 0
split the values into two,
4x + 1 = 0 and x - 3 = 0
4x = -1 x = 3
x = -1/4
Therefore, the solution of quadratic equation 8x² = 6 + 22x is x = 3 and x = -1/4
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15 POINTS HELP!
A liquid used to unclog sinks has a pH value of 14. This liquid is _____.
neutral
an acid
a base
Answer:
A base
Step-by-step explanation:
its not an acid bc a ph level of 14 means is has a strong base.
- 6 000 frs for 3 years at 4% p.a.
- 2 000 frs for 2 years 3 months at 3% p.a.
Principal for 6000 frs for 3 years at 4% p.a. and 2000 frs for 2 years 3 months at 3% is 461.5 and 148.1.
Amount A = P(1+rt)
6000 = p(1+4*3)
6000 = p13
p = 6000/13
p = 461.5
Amount A = P(1+9/2*3)
2000 = P*27/2
P = 2000*2/27
P = 148.1
Therefore Principal for 6000 frs for 3 years at 4% p.a. and 2000 frs for 2 years 3 months at 3% is 461.5 and 148.1.
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Given the linear function f(x) = -4x+8, what is the value of x if f(x) = 24?
Answer:
[tex]f(x) = - 4x + 8 = 24 \\ \\ = > - 4x + 8 = 24 \\ \\ => - 4x = 24 - 8 = 16 \\ = > - 4x = 16 \\ = > x = \frac{ - 16}{4} = - 4 \\ \\ [/tex]Step-by-step explanation:
Sᴏ ᴛʜᴇ value of x= -4
x = -4
Step-by-step explanation:
Solution:-
[tex]{ \blue{ \sf{f(x) = - 4x + 8}}}[/tex]
In order to find the value of x, put 24 in the place of f(x) (given) then,
[tex]{ \blue{ \sf{24 = - 4x + 8}}}[/tex]
[tex]{ \blue{ \sf{24 - 8 = - 4x}}}[/tex]
[tex]{ \blue{ \sf{16 = - 4x}}}[/tex]
We should find the value of x. So divide bith the sides by -4. then,
[tex]{ \blue{ \sf{ - \frac{16}{4} = \frac{ - 4}{ - 4} x}}}[/tex]
[tex]{ \bold{ \boxed{ \red{ \sf{ -4 = x}}}}} \: (or) \: { \bold{ \boxed{ \red{ \sf{x = - 4}}}}}[/tex]
A floral shop earns an average yearly revenue of $195,280. Which compound inequality correctly shows the amount of money, m, the floral shop needs each month to pay for rent if the monthly budget for rent is between 10% and 15%? $375.54 sm≤ $563.31 $751.08 sm≤ $1,126.62 $1,627.33 sm ≤ $2,441.00 $1,502.15 sm s $2,523.23
The monthly budget for rent is $1,627.33 ≤ m ≤ $2,441.00
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let m represent the monthly rent of the shop.
The average yearly revenue is $195,280. Hence:
Monthly revenue = $195,280 / 12 = $16273.33
If the monthly budget for rent is 10%, hence:
m = 10% of $16273.33 = 0.1 * $16273.33 = $1627.33
If the monthly budget for rent is 15%, hence:
m = 15% of $16273.33 = 0.15 * $16273.33 = $2441.00
$1,627.33 ≤ m ≤ $2,441.00
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One-third of a number decreased by six equals eight. What is the number?
Answer:
42
Step-by-step explanation:
6+8=14x3=42
42/3=14-6=8
In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?
Step-by-step explanation:
In a candy box, there are 3 times as many candies with nuts as candies without nuts. There are 12 candies in the box. How many candies with nuts are in the box?
let:
without nuts = x
with nuts = 3x
so:
x + 3x = 12
4x = 12
x = 3, so there are 3 candies without nuts.
Because there are three times more candies with nuts than without:
3 * 3 = 9 candies with nuts
Answer:
9 candies with nuts
Step-by-step explanation:
Suppose the number of candies is x
there three times as many candies with nuts as candies without nuts, so 3x
there are 12 candies in total
3x+x=12
4x=12
x=3
3x=9
2(x + 3) = x-4
What is the answer?
Answer:
x=-10
Step-by-step explanation:
2(x+3) = 2x+6
2x+6=x-4
2x+6-6=x-4-6
2x=x-10
2x-x=x-10-x
x=-10
Using the figure below, which table correctly lists the steps and reasons used to find the measure of angle d?
Answer:
140
Step-by-step explanation:
140
Triangle DEF with coordinates D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH. If G has
coordinates (9, 3), what are the coordinates for H?
The coordinates for H are (9,2)
What are the coordinates?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Here, we have
D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH.
coordinates are (x,y) = (x+6,y+2)
F's coordinate is (3,0)
using the coordinates we get (9,2)
Hence, the coordinates of H are (9,2)
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Undergraduates
Graduates
Total
University Data
Receiving
Financial Aid
4222
1879
6101
Not Receiving Total
Financial Aid
3898
731
4629
8120
2610
10730
If you know that a student receives financial aid,
what is the probability that the student is a
graduate student?
Write your answer as a percent, rounded to the nearest
whole number [?]%
Answer: 31%
Step-by-step explanation:
Out of the students that receive financial aid, 1879 out of the 6101 total students are graduates.
So, the probability is [tex]\frac{1879}{6101} \approx 31\%[/tex]
The half-life of a radioactive kind of americium is 7,380 years. How much will be left after
22,140 years, if you start with 188,320 grams of it?
grams
CARPENTRY A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood. The rectangle must be
sawed along the dashed line in the figure.
The measure of angle1 in the given rectangular figure is 64° .
In the question ,
it is given that ,
the one of the angle is 116° .
From the figure below ,
we can see that
the dashed line is a transversal to AB and CD ,
the angles on the line AB form a linear pair ,
So , angle2 + 116° = 180°
angle2 = 180° - 116°
angle2 = 64°
Since the side panel of the podium is cut from rectangular piece
the figure is representing two parallel lines , cut by the transversal .
By the property of transversal that alternate interior angles are equal in measure ,
angle 1 = angle 2
hence , angle 1 = 64° .
Therefore , The measure of angle1 in the given rectangular figure is 64° .
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-
Find the equation of a line parallel to x - 4y = 36 that passes through the point
(-4,-5).
The equation of a line parallel to x - 4y = 36 is x - 4y = 16.
If the two lines are parallel then their slope must be equal. Two parallels lines have different intercepts but same slope. The slope intercept form of a line is y = mx + c. Where m is the slope and c is the intercept.
Now, writing the given equation in slope-intercept form,
x - 4y = 36
4y = x - 36
[tex]y=\frac{1}{4}x-9[/tex]
By comparing it with slope-intercept form, we get
[tex]m=\frac{1}{4}[/tex]
c = -9
Now, Finding the equation of line passing through (-4,-5) with slope as [tex]\frac{1}{4}[/tex],
[tex]m=\frac{y-y_1}{x-x_1} \\\\\frac{1}{4}=\frac{y-(-5)}{x-(-4)}\\\\ \frac{1}{4}=\frac{y+5}{x+4}\\x+4=4y+20\\x-4y=16[/tex]
The equation of parallel line is x - 4y = 16.
Hence, the equation of a line parallel to x - 4y = 36 is x - 4y = 16.
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Can you please help me in this question.
Answer:
Don't know if i did it right but i think it is:
a=14
b=6
c=5
a shelf in the metro department store contains 80 colored ink cartridges for a popular ink-jet printer. seven of the cartridges are defective. (a) if a customer selects 2 cartridges at random from the shelf, what is the probability that both are defective? (round your answer to five decimal places.)
The probability that both are defective when a customer selects 2 cartridges at random from the shelf will be 0.00766.
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
The probability of choosing defective cartridge=7/80
So, the probability of choosing 2 defective cartridge=(7/80)²
=0.00765625
=0.00766
When a customer randomly chooses two cartridges from the shelf, the likelihood that both are flawed is 0.00766.
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Helen draws a random circle.
She then measures
its diameter and circumference.
She gets a
circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm
correct to 2 significant figures.
Helen wants to find the value of rt using the formula
T= G
Calculate the upper bound for Helen's value of TC.
Give your answer correct to 3 decimal places.
If Helen wants to find the value. the upper bound for Helen's value of TC is 3.123 and lower bound is 3.092.
How to find upper and lower bound?Upper bound
405 = 405.999
130 =130.99
Lower bound
405 = 405.001
130 =130.01
Now let find the upper and lower bound
Upper bound = 405.999/130.01
Upper bound =3.123
Lower bound = 405.001 /130.99
Lower bound = 3.092
Therefore the upper bound is 3.123.
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HELPPPPPPPPPP
A) 2
B) 3
C) 4
D)5
Answer:
it's b extra words. extra words. extra words. extra words
Step-by-step explanation:
I took the test
30 POINTS AND BRAINIEST PLEASE HELP ASAP!!!!
Part A: Given the function g(x) = |x − 5|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 3, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answer:
Part A The vertex domain and range of the function g(x) = \x-7\ is (7,0),(-∞,∞) and [0,∞)
Part B The function f(x) =lxl is vertically shifted by 2 units to get the function h (x) = lxl { 2. The y - coordinate of the vertex is shifted by 2