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3 years ago

Question 4 (1 point)

Mathematics

1 answer:

igomit [66]3 years ago

4 0

Answer:

x = 15

Step-by-step explanation:

We want to solve for x in 3*(2x + 5) = 3x + 4x

First simplify.

3*(2x + 5) = 7x

Next, distribute the 3.

3*2x + 3*5 = 7x

6x + 15 = 7x

15 = 7x - 6x

15 = x

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3 years ago

One afternoon in January, the temperature outside was -4*F. By midnight, the temperature had dropped by 10*F. what was the tempe

loris [4]

The temperature at midnight would be -14*F. Subtract 10 from -4 and you get -14*F

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2 years ago

√₂

snow_lady [41]

Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

<u>Simple Interest Formula</u>

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

$\implies \sf P_2=5000$

Substitute the found value of P₂ into Equation 1 and solve for P₁:

$\implies \sf P_1+5000=7000$

$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

brainly.com/question/27743947

brainly.com/question/28350785

5 0

1 year ago

0.09×0.7 <br>help me please

dem82 [27]

0.09x0.7= 0.063

That its the answer

7 0

3 years ago

The height h of a projectile is a function of the time t it is in the air. the height in feet for t seconds is given by the func

alexgriva [62]

Domain means the values of independent variable(input) which will give defined output to the function.

Given:

The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function

$h(t)=-16t^2 + 96t$

Solution:

To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.

$To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)$

$Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution$

Conclusion:

The domain of the function is the time in between 0 to 6 seconds

$0 \leq t \leq 6$

The height will be positive in the above interval.

7 0

3 years ago

Read 2 more answers