Answer:
A
Step-by-step explanation:
We have the system of equations:
-3x + 4y = -22
2x + 7y = 5
Let's solve this using elimination, so multiply the first equation by 2 and the second equation by 3:
2 * (-3x + 4y = -22) ⇒ -6x + 8y = -44
3 * (2x + 7y = 5) ⇒ 6x + 21y = 15
Our equations are now:
-6x + 8y = -44
6x + 21y = 15
Add these two together to eliminate the x term:
-6x + 8y = -44
+ 6x + 21y = 15
______________
0x + 29y = -29
y = -29/29 = -1
Plug this back into one of the equations to find x:
-3x + 4y = -22
-3x + 4 * (-1) = -22
-3x - 4 = -22
-3x = -18
x = -18/(-3) = 6
The answer is (6, -1) or A.
Answer:
A. (6,-1)
Step-by-step explanation:
-3x + 4y = -22
2x + 7y = 5
x = (5 - 7y)/2
-3[(5 - 7y)/2] + 4y = -22
-15/2 + 21y/2 + 4y = -22
29y/2 = -29/2
y = -1
x = (5 - 7(-1))/2
x = 12/2
x = 6
a baseball league finds the speeds of pitches are normally distributed, with a mean of 89 mph and a standard deviation of 2.4 mph. One pitch is thrown at a speed of 85.2 mph. What is the z-score of this pitch? Round your answer to two decimal places.
Answer:
-1.58
Step-by-step explanation:
We have that the mean (m) is equal to 89 and the standard deviation (sd) 2.4
They ask us for P (x <85.2)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd)
We have all these values, replacing we have:
z = (85.2 - 89) / (2.4)
z = -1.58
Geri built a pencil box in the shape of a right rectangular prism. The amount of space inside of the box is 176 cubic inches
What is the height of Geri's pencil box?
2 inches
4 inches
8 inches
9 inches
Answer:2 inches
Step-by-step explanation:
8*11=88
176/88=2
Check answer: 2*8*11
Answer:
A) 2 inches
I took the test, picture for proof
Step-by-step explanation:
Taylor tried to solve an equation step by step.
7(y + 4.5) = 32.5
7y + 4.5 = 32.5 step 1
7y = 28 step 2
y=4 step 3
Find Taylor's mistake.
Choose 1 answer:
A: step 1
B: step 2
C: step 3
D: Taylor did not make a mistake.
Answer: step 1
Step-by-step explanation:
Bethany used the steps below in an attempt to solve for angle B in triangle ABC.
4.1 cm
2.7 cm
4.5 cm
[Not drawn to scale]
4.12 - 4.52+2.72 -2(4.5)(2.7)cos B
4.1=4.5+2.7-24.3cos B
-3.1--24 3cOSB
0.1276= COS B
Final answer:
To solve for angle B in triangle ABC, you can use the Law of Cosines. Rearrange the equation to isolate the cosine of angle B and then take the inverse cosine to find the value of angle B. The value of angle B is approximately 99.99 degrees.
Explanation:
To solve for angle B in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.
In this case, you are given the lengths of sides AB, BC, and AC as 4.1 cm, 2.7 cm, and 4.5 cm respectively. You are also given the equation 4.1 = 4.5 + 2.7 - 24.3cos B. To solve for angle B, you can rearrange the equation to isolate the cosine of angle B and then take the inverse cosine to find the value of angle B.
Let's go step-by-step:
Start with the equation 4.1 = 4.5 + 2.7 - 24.3cos B
Subtract 4.5 and 2.7 from both sides: 4.1 - 4.5 - 2.7 = -3.1 - 24.3cos B
Combine like terms: -3.1 - 24.3cos B = -7.1
Add 7.1 to both sides: -3.1 - 24.3cos B + 7.1 = -7.1 + 7.1
Simplify: -3.1 + 7.1 - 24.3cos B = 0
Subtract -3.1 + 7.1 from both sides: -3.1 + 7.1 - 3.1 + 7.1 - 24.3cos B = -3.1 + 7.1
Simplify: -24.3cos B = 4.0
Divide both sides by -24.3 to isolate cos B: (-24.3cos B) / -24.3 = 4.0 / -24.3
Simplify: cos B = -0.1645
Take the inverse cosine of -0.1645 to find the value of angle B: B = cos-1(-0.1645)
Using a calculator, you can find that angle B is approximately 99.99 degrees.
Combine the like terms to create an equivalent expression:
- 4y - 4+ (-3)
Answer:
4y - 7
Step-by-step explanation:
Like terms are terms that have the same variable part. Variable part means the part of a term that is one or more variables and the exponents of the variables.
For example, in 2x^2 + 4xy + 5x^2 + 2y + 5 - 3y, the terms 2x^2 and 5x^2 have x^2 as their variable part. They are like terms. Likewise, 2y and -3y have y as their variable part. They are like terms. 2x^2 and 5x^2 can be combined into 7x^2. 2y and -3y can be combined into -y. The terms 4xy and 5 are not like terms and cannot be combined. By combining like terms in 2x^2 + 4xy + 5x^2 + 2y + 5 - 3y, you end up with 7x^2 + 4xy - y + 5.
Now we deal with your problem.
-4y - 4 + (-3)
The term -4y has a y as a variable. There is no other term with a y in it, so the term -4y cannot be combined.
The terms -4 and -3 have no variables. These two terms are like terms and can be combined.
-4y - 4 + (-3) =
-4y - 7
Which equation and solution can be used to solve this problem? Twenty-two less than a number is twenty-four. q + 22 = 24: Subtract 22 from both sides. The answer is 2. 24 + q = 22: Subtract 22 from both sides. The answer is 2. q minus 24 = 22: Add 24 to both sides. The answer is 46. q minus 22 = 24: Add 22 to both sides. The answer is 46.
Answer:
D. q minus 22 = 24: Add 22 to both sides. The answer is 46.
Step-by-step explanation:
From the list of options, one would notice that the number is represented with letter q.
So, we'll analyse the question base on the assumption that the number is represented with letter q.
The statement "Twenty-two less than a number is twenty-four".
First, this statement can be splitted into two.
"Twenty-two less than a number" and "is twenty-four."
Taking them one after the other.
"Twenty-two less than a number" as it is means; q - 22
Then we have "is twenty-four."
is represents =
twenty-four = 24
This gives "= 24"
Bringing the two expressions together;
q - 22 = 24
To get the value of q; simply add 22 to both sides
q - 22 + 22 = 24 + 22
q = 46
Hence, option D is correct.
Answer:
ITS D
Step-by-step explanation:
What is the image point of ( 1 , 2 )after a translation right 5 units and up 3 units?
Answer:
Step-by-step explanation: 6,5
Answer:
6, 5
Step-by-step explanation:
1+5=6 It moves to the right so it's addition
2+3=5 It moves up so it's addition
Una empresa desea contratar 3 nuevos
empleados, pero hay 8 candidatos, 6 de los
cuales son hombres y 2 son mujeres. Si la
seleccion es al azar:
a) 2De cuántas maneras diferentes se pueden
elegir los nuevos empleados?
b) De cuántas maneras distintas se puede
elegir a un solo candidato hombre?
c) De cuántas maneras distintas se puede
elegir por lo menos a un candidato horribre?
Rptas a)56 b)6 c)56
Answer:
A company wants to select 3 new employees.
We have 8 candidates, 6 males, and 2 females.
1) What is the number of combinations in which the new employees can be selected?
We have 3 positions.
For the first position, we have 8 options.
For the second position, we have 7 options, because we already selected one.
For the third position, we have 6 options, because we already selected two.
The number of different combinations is (8*7*6)/(3*2*1) = 56
The division by 3*2*1 is because if we no divide by this, we are counting multiple times the same combination of employees, but they are contracted in different orders.
2) How many ways you can select only one male?
In this case, we have 3 positions, two of those positions must be for the 2 women, so in the other position, we can select only one male.
We have 6 different males for that position, so we have only 6 combinations in this case.
3) In how many ways we can select at least one male?
Previously found that we have 56 combinations in total.
We only have 2 women and 3 positions, so in all of these combinations, we have at least one male. So there are 56 combinations with at least one male.
The number of combinations in which these 3 new employees can be selected is equal to 56.
Given the following data:
Number of candidates = 8 candidates.Number of males = 6 males.Number of females = 2 females.Number of employees = 3 new employees.How to find the number of combinations?Since the company needs 3 employees, it simply means there are 3 vacant positions. Thus, the number of combinations in which these 3 new employees can be selected is given by:
_nC_r = \frac{n!}{r!(n-r)!}
Combination(n, k) = n!/(r!(n - r)!)
Combination(8, 3) = 8!/(3!(8 - 3)!)
Combination(8, 3) = 8!/(3!(5)!)
Combination = (8 × 7 × 6)/(3 × 2 × 1)
Combination = 336/6
Combination = 56.
How many ways can a single male be selected?Two (2) of the 3 vacant positions must be taken by 2 women, so we can only select one male. Thus, the number of ways is given by:
Number of ways = 6 × 1
Number of ways = 6.
In how many different ways can at least one male candidate be chosen?Choosing 1 male = 6 ways
Choosing 2 males = two males from 6 males and 1 male from two females.
Comb(6, 2) × 2 = 6!/(2!(6 - 2)!) × 2
Comb(6, 2) × 2 = 6!/(2!(4)!) × 2
Comb(6, 2) × 2 = 15 × 2
Comb(6, 2) × 2 = 30 males.
Choosing 3 males = three males from 6 males;
Comb(6, 3) = 6!/(3!(6 - 3)!)
Comb(6, 3) = 6!/(3!(3)!)
Comb(6, 3) = 20 males.
Total combination = 6 + 30 + 20
Total combination = 56.
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A student said the volume of a cylinder with a 7-inch diameter is two times the volume of a cylinder with
the same height and a 3.5-inch radius. What is the error?
Answer:
When you find the volume of the cylinder you square instead which isn't equal to multiplying so the answer will be more then doubled.
Step-by-step explanation:
Answer:
The volume of the first is not 2 * volume of the second. They both have the same volume.
Step-by-step explanation:
The 2 cylinders described are identical. The diameter = 2 times the radius, so the radius of the first cylinder = 1/2 * 7 = 3.5 in, which is the same as the radius of the second one. Also the heights are the same so the volumes are the same too.
Find the length of the unknown side round your answer to the nearest 10th
Answer:
A. 20
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
Plug in the numbers
[tex]15^{2} + b^{2} = 25^{2}[/tex]
Simplify the equation
225 + b = 625
Subtract both sides by 225
625 - 225 = 400
Your equation should look like
b = 400
Because you squared it, now you have to get it back to the formula you started with first. To do this, just find the square root.
The square root of 400 is 20
[tex]15^{2}+ 20^{2} =25^{2}[/tex]
What is the volume of the composite figure ?
Answer:
Volume Area 1 - Long Rectangle = 8 x 4 x 2 =64
Volume smaller Rectange = 2 x 2 x 3 = 12
Total Volume = 64 + 12 = 76 cubic inches
Step-by-step explanation:
Answer:
68
Step-by-step explanation:
Whitney walks from her house to school, a distance of 1 mi. It takes her 14 min. How long will it take Whitney to walk home from school if, on her way, she walks at a rate of 1 mi/7 min?
Answer:
7 minutes
Step-by-step explanation:
If Whitney walks 1 mile at a rate of 1 mile every 7 minutes, then it would take her 7 minutes to walk home from school.
what is (f • g)(x)
f(x) = x^4 — 9
g(x) = x^3 + 9
Answer:
x^12 + 9x^4 - 9x^3 - 18
Step-by-step explanation:
When there is a circled in black dot in the middle of f and g, then it means to multiply. Using the distributive property and the FOIL method, the answer should be x^12 + 9x^4 - 9x^3 - 18.
how many gallons of a 15% sugar solution must be mixed with 5 gallons of a 40% sugar solution to make a 30% sugar solution
To find the number of gallons of a 15% sugar solution needed to mix with a 40% sugar solution to make a 30% sugar solution, set up an equation.
Explanation:In order to solve this problem, we can set up an equation based on the given information.
Let's say we need to mix 'x' gallons of the 15% sugar solution with the 5 gallons of the 40% sugar solution to get a 30% sugar solution.
The equation would be: 0.15x + 0.40(5) = 0.30(x + 5).
Solving this equation will give us the value of 'x', which represents the gallons of the 15% sugar solution needed.
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In ΔEFG, the measure of ∠G=90°, the measure of ∠E=40°, and EF = 75 feet. Find the length of GE to the nearest tenth of a foot.
Answer:
57.453 ft
Step-by-step explanation:
Glad to help ! :)
Answer:
the answer is 57.5
A granola recipe calls for 3/4 of a cup of peanuts and 2/3 of cup raisins. How many cups of raisins should be used for every one cup of peanuts? A. 1/2 B.8/9 C. 1 1/4 D. 2 cups please help! This is kinda urgent ;w;
Answer:
8/9
Step-by-step explanation:
It has to be bigger than 2/3 which is equivalent to 6/9.It cannot be a half which is too less.1 or above is too much.B. is just right.
I need help please it gives a hint I don’t get it
Answer:
Lower quartile: 72
Upper quartile: 84
Step-by-step explanation:
Follow the instructions in the hint to solve the problem.
First, divide the data set into halves:
70, 70, 72, 75, 79
80, 80, 84, 89, 95
Now, find the median of the two sets. The median of set #1 is 72, as that is the number in the middle of the data.
The median of set #2 is 84 for the same reason.
Upper and lower quartiles are just different words for upper and lower medians. The upper quartile is the higher number, and the lower quartile is the lower number.
What is the measure of θ in radians?
Enter an exact expression.
In the diagram, θ is a central angle.
Answer:
pi
Step-by-step explanation:
Theta is 1/2 of a circle
A circle is 360 degrees or 2pi radians
Take 1/2 of that for a semi circle
180 degrees or pi radians
Answer:
pi
Step-by-step explanation:
Arc length = r × theta
8pi = 8 × theta
theta = 8pi/8
= pi radians
Find The surface area of the prism enter your answer in the box someone please help!
Answer:
[tex]252 \: {m}^{2} [/tex]
Step-by-step explanation:
Two Squares area:
[tex]2 \times (6 \times 3) = 36 \: {m}^{2} [/tex]
1 Square perimeter:
[tex]2 \times (6 + 3) = 18 \: m[/tex]
Lateral area:
[tex](18 \times 12) = 216 \: {m}^{2} [/tex]
Total area:
[tex](216 + 36) \: = 252 \: {m}^{2} [/tex]
The surface area of the prism is 252 m².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given is rectangular prism with dimensions, 12m × 6m × 3m, we need to find its surface area,
The surface area of a rectangular prism with dimensions, L × W × H, is given by = 2(LH+LW+WH)
Therefore,
SA = 2(12×3+12×6+6×3)
= 2(36+72+18)
= 2 × 126
= 252 m²
Hence, the surface area of the prism is 252 m².
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The length of a rectangular prism is 5 more than twice the width w. The volume of the prism is 2w^3+13w^2+20w. What is a simplified expression for the height of the prism?
Answer:
w + 4
Hope the picture helps
Five metal cubes with sides of 7 cm are melted and then casted into a spherical ball.
Find the radius of the sphere that is formed. Round your answer to the nearest
hundredth.
To find the radius of the sphere formed by melting five metal cubes with 7 cm sides, calculate the combined volume of the cubes and equate it to the volume of the sphere; then solve for the radius, which is approximately 7.24 cm.
To find the radius of the sphere formed by melting five metal cubes, we need to equate the total volume of the cubes to the volume of the sphere. The volume of a cube with a side length of 7 cm is found by the formula V = s³, where s is the side length of the cube. For one cube, this is V = 7 cm x 7 cm x 7 cm = 343 cm³. Since there are five cubes, the total volume is 5 x 343 cm³ = 1715 cm³.
The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere. We must solve for r when the volume is 1715 cm³. Setting the volumes equal gives 4/3 * π * r³ = 1715 cm³. Solving for r yields:
r³ = (1715 cm³) / (4/3 * π)
r = (1715 cm³) / (4.14159)^√(1/3)
r ≈ 7.24 cm
Therefore, the radius of the sphere is approximately 7.24 cm.
What shape will the vertical cross-section of a cylinder be?
Is 5.39 a repeating decimal
Answer:
No.
Step-by-step explanation:
Unless you see a bar over one or more of the numbers (specifically 9 or 39), then it is not a repeating decimal, but rather a terminated decimal.
If there is a bar over the number, it means that specific set of numbers are repeated. Another way to tell if it is repeated is if there are dots at the end.
~
Match the terms to their definition.
parallel lines
function
independent variable
1. a mathematical sentence whose verb is 'equal' E)
a relation in which each first coordinate is paired with exactly
one second coordinate
3. an equation that is true for all values of the variable
the variable representing the first elements of the ordered
pairs in a function; the inputs
an open sentence whose graph is a line; the general form for
such an equation is Ax + By + C = 0
6. an equation containing more than one variable
identity
equation
literal equation
7. lines that never intersect
linear equation
Need the answer ASAP!!
Answer:
parellel lines = 7
function = 3
independent variable = 6
Pls help with this
Answer:
under 7 is 35 and the next box is 9 on top and 45 on the bottom
Step-by-step explanation:
you have to multipy the books Jillian read by how many times 3 can go into 15, which is 5 times. You can also divide 15 by 3 to find out if its multiplied by 5.
Divide.
1/7 ÷ 6
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:
1/42
Step-by-step explanation:
You can use a calculator and input the equation.
Answer:
1/42
Step-by-step explanation:
1/7 divided by 6= 1/7 multiplied by 1/6. We get 1/6th because we have to flip 6/1 around, 1/6 times 1/7 =1/42
Solve the logarithmic equation for x.
2 log x = log 2 + log(3x - 4)
x= [
(smaller value)
X
=
(larger value)
Answer:
x = 2 or x = 4
Step-by-step explanation:
Solve: 2 log x = log 2 + log(3x - 4)
log (x^2) = log 2 + log (3x - 4)
log (x^2) = log [2*(3x - 4)]
x^2 = 2*(3x - 4)
x^2 = 6x - 8
x^2 - 6x + 8 = 0
factor:
(x - 2 )(x - 4) = 0
x = 2 or x = 4
debbie is making bows that use 1/6 yards of ribbion each, if debbie has 2 yards of ribbion, how many bows can she make? write a division equation and multipcation equation to show this
Debbie can make 12 bows from 2 yards of ribbon, as shown by the division equation (2 ÷ 1/6 = 12) and confirmed by the multiplication equation (12 × 1/6 = 2).
Explanation:The student is asking about division and multiplication of fractions in the context of making bows from a length of ribbon. To determine how many bows Debbie can make with 2 yards of ribbon, when each bow requires 1/6 yard, we formulate a division equation and a multiplication equation.
The division equation is:
Number of bows = Total yards of ribbon ÷ Yards of ribbon per bow
Number of bows = 2 yards ÷ 1/6 yard
The multiplication equation is the inverse of the division equation, which helps us to check our work:
X bows × 1/6 yard per bow = 2 yards (X represents the number of bows)
By solving the division equation:
Number of bows = 2 yards × (6/1 bows)
Number of bows = 12 bows
So, Debbie can make 12 bows from 2 yards of ribbon. The multiplication equation confirms this since 12 bows × 1/6 yard equals 2 yards.
in the diagram below chords AB and CD intersects at E. If mAC=72 and mAEC=58. how many degrees are in mDB?
Answer:
44°
Step-by-step explanation:
∠ DEB and ∠ AEC are vertical and congruent
Thus ∠ DEB = 58°
The measure of the chord- chord angle DEB is half the sum of the measures of the arcs intersected by the angle and its vertical angle, that is
[tex]\frac{1}{2}[/tex] (DB + AC ) = 58° ( multiply both sides by 2 )
DB + AC = 116°, that is
DB + 72° = 116° ( subtract 72° from both sides )
DB = 44°
Answer:
Hey, and also, The Answer to Your question is 44 Degrees.
Step-by-step explanation:
∠ DEB and ∠ AEC are vertical and congruent
Thus ∠ DEB = 58°
The measure of the chord- chord angle DEB is half the sum of the measures of the arcs intersected by the angle and its vertical angle, that is
(DB + AC ) = 58° ( multiply both sides by 2 )
DB + AC = 116°, that is
DB + 72° = 116° ( subtract 72° from both sides )
DB = 44°...... Stay safe Guys.
I have 3 digits. If I round to the nearest hundred, I am 200. Multiply my ones digit by 2 and you get my tens digit. Both my ones and tens digits are even.
Answer:
the answer is 393
Step-by-step explanation:
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